Liquefaction Modelling using the PM4Sand Constitutive ...

Liquefaction Modelling usingthe PM4Sand Constitutive

Model in PLAXIS 2D

by

P.V. Tolozato obtain the degree of Master of Science

at the Delft University of Technology

Student number: 4623762Graduation Date: November 27th, 2018

Graduation Committee: Dr. ir. R. B. J. Brinkgreve, TU Delft, Geo-Engineering & Plaxis BV, chairmanProf. dr. M. A. Hicks, TU Delft, Geo-EngineeringDr. ing. M. Z. Voorendt, TU Delft, Hydraulic EngineeringIr. E. Bouzoni, Witteveen+Bos

Contents

Preface vii

Abstract ix

1 Description of the Project 11.1 Problem Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.3 Research Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.4 Research Approach. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2 Theoretical Framework 52.1 Earthquakes-induced Liquefaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.1.1 Seismic waves. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62.1.2 Earthquake Size. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62.1.3 Definition of Liquefaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.2 Simplified Stress-Based Triggering Assessment . . . . . . . . . . . . . . . . . . . . . . 72.2.1 Cyclic Stress Ratio, CSR. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.2.2 Cyclic Resistance Ratio, CRR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.2.3 Factors that affect Soil Liquefaction Resistance . . . . . . . . . . . . . . . . . . 10

2.3 Undrained Cyclic Response of Sands . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.3.1 Cyclic Laboratory Tests. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.3.2 Modulus Reduction Curve and Soil Damping . . . . . . . . . . . . . . . . . . . 16

2.4 Liquefaction Modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172.4.1 Type of Constitutive Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172.4.2 Soil Constitutive Models for Liquefaction . . . . . . . . . . . . . . . . . . . . . 18

2.5 PM4Sand Soil Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192.5.1 Critical State Soil Mechanics Framework . . . . . . . . . . . . . . . . . . . . . . 192.5.2 Bounding, Dilatancy, Critical and Yield Surfaces . . . . . . . . . . . . . . . . . . 202.5.3 Fabric Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222.5.4 Main model parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

2.6 Failure mechanism of anchored quay walls . . . . . . . . . . . . . . . . . . . . . . . . 242.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

3 Verification of PM4Sand Model at Soil Element Level 273.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273.2 Data analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283.3 Determination of Input Model Parameters . . . . . . . . . . . . . . . . . . . . . . . . . 303.4 Starting point: Assessment of CRR curves . . . . . . . . . . . . . . . . . . . . . . . . . 31

3.4.1 Cyclic DSS test in PLAXIS 2D. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313.4.2 Cyclic strength curves (CRR vs Nc) . . . . . . . . . . . . . . . . . . . . . . . . . 32

3.5 Parametric assessment of primary model parameters. . . . . . . . . . . . . . . . . . . 353.5.1 Assessment of the apparent relative density, DR . . . . . . . . . . . . . . . . . . 353.5.2 Assessment of the Shear modulus coefficient, G0 . . . . . . . . . . . . . . . . . 39

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iv Contents

3.6 Parametric assessment of secondary model parameters . . . . . . . . . . . . . . . . . 43

3.6.1 Bounding surface parameter, nb . . . . . . . . . . . . . . . . . . . . . . . . . . 43

3.6.2 Critical state line parameter, R. . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

3.6.3 Assessment of final set of parameters. . . . . . . . . . . . . . . . . . . . . . . . 48

3.7 Initial state condition effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

3.7.1 Effect of confining stress, Kσ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

3.7.2 Effect of initial static shear stress, Kα . . . . . . . . . . . . . . . . . . . . . . . . 52

3.7.3 Effect of lateral earth pressure coefficient at rest, K0 . . . . . . . . . . . . . . . . 53

3.8 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

4 Validation of the PM4Sand Model for Design Purposes 594.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

4.2 Case Study: Akita Port and Nihonkai-Chubu Earthquake (1983) . . . . . . . . . . . . . 60

4.3 Modelling in PLAXIS 2D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

4.3.1 Input ground motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

4.3.2 Interpretation of soil stratigraphy . . . . . . . . . . . . . . . . . . . . . . . . . . 65

4.3.3 Soil Liquefaction Potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

4.3.4 Parameter Selection - Hardening Soil Small Model . . . . . . . . . . . . . . . . 67

4.3.5 Calibration of the PM4Sand for upper layers . . . . . . . . . . . . . . . . . . . . 69

4.3.6 Structural elements of the quay wall . . . . . . . . . . . . . . . . . . . . . . . . 70

4.3.7 Geometry and Mesh Generation . . . . . . . . . . . . . . . . . . . . . . . . . . 71

4.3.8 Static Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

4.4 Dynamic Analysis of the Quay Wall Structures . . . . . . . . . . . . . . . . . . . . . . . 76

4.5 Analysis of the Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

4.5.1 Generation of Excess Pore Pressures . . . . . . . . . . . . . . . . . . . . . . . . 77

4.5.2 Displacements at the top of the sheet-pile wall . . . . . . . . . . . . . . . . . . 80

4.5.3 Post-Liquefaction Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

4.5.4 Comments related to modelling process . . . . . . . . . . . . . . . . . . . . . . 82

4.6 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

5 Final Remarks and Recommendations 85

Appendix 87

A Cyclic Resistance Ratio from CPT 89

B PM4Sand Model Formulation 93B.1 Critical State Soil Mechanics Framework . . . . . . . . . . . . . . . . . . . . . . . . . . 93

B.2 Bounding, Dilatancy, Critical and Yield Surfaces. . . . . . . . . . . . . . . . . . . . . . 94

B.3 Fabric Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

B.4 Elastic Part of the Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96

B.5 Plastic Part of the Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

C Site Investigation at Akita Port 103C.1 Standard Penetration Test and Grain-size Distribution . . . . . . . . . . . . . . . . . . 103

C.2 Shear-wave velocity profile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

C.3 Soil liquefaction resistance from Cyclic Triaxial tests . . . . . . . . . . . . . . . . . . . 106

C.4 Filtering and correction input ground motion . . . . . . . . . . . . . . . . . . . . . . . 107

Contents v

D Soil Liquefaction Potential 109D.1 Ohama No.1 Wharf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

D.1.1 Cyclic Stress Ratio, CSR. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110D.1.2 Cyclic Resistance Ratio, CRR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

D.2 Ohama No.2 Wharf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113D.2.1 Cyclic Stress Ratio, CSR. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113D.2.2 Cyclic Resistance Ratio, CRR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114

D.3 Factor of Safety for Soil Liquefaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116

Bibliography 117

Preface

I would like to take this opportunity to thank the different actors who have participated in this in-tense and enriching academic and professional process of my life.

First of all, I would like to thank the committee members for having accepted to be part of thisproject and for having allowed me to carry out this interesting research. To Ronald Brinkgreve forhaving shown the best willingness to clarify all kinds of technical and complex doubts that werearising throughout the project. To Michael Hicks for his valuable suggestions on how to strengthenthe conclusions of my study. To Mark Vordent for having always had the greatest willingness to dis-cuss the project from a point of view related to the development of it and for sharing his knowledgeon hydraulic structures. And within this group, I especially want to thank Elena Bouzoni, my super-visor, for her constant motivation, being a great support for me in all phases of this project, to whomI undoubtedly owe much of what I have done and learned in this professional stage of my life.

I would also like to thank the people and colleagues at the Witteveen+Bos office in Rotterdam,who were always very kind to me and were available to discuss any topic related to my project. Ireally enjoyed the activities we spent together, as well as our lunchtime walks.

A separate paragraph to mention that the realization of this project is due to the valuable col-laboration of Willem van Elsacker and Antonia Makra, who kindly shared important information tobe able to develop the different evaluations of the model during the project.

With a big hug I want to thank the great people I met during my stay in Holland, many of themtoday are great friends who have reached out on many occasions. Among them, I would like tomention my classmates, friends from Jaagpad, the great International Gang, the Digga’s group, myhousemates and, of course, my brave Chilean friends who left for faraway lands in pursuit of theirdreams, within them, ’Los Impostores’.. lo mas grande.

I cannot not thank my old friends, from Chile and mainly from Coyhaique, since distance hasnever been an impediment to continue cultivating our bonds and until today they have been a fun-damental support in my life and I know that they will continue to be.

Finally, I want to thank my parents and siblings infinitely, for their love and unconditional sup-port, soon we will meet again at the table, with some good laughs and many stories to tell.

Patricio TolozaDelft, November 2018

vii

Abstract

The phenomenon of earthquake-induced soil liquefaction has been a major issue among geotech-nical engineers mainly due to the dramatic consequences this could have on civil structures. Basi-cally, earthquakes propagate shear waves generating excess pore pressures and thus weakening theeffective shear resistance of granular soils to their minimum until they liquefy behaving like a vis-cous fluid. This occurs because the soil experiences undrained behaviour against these rapid cyclicloads. In practice, the cyclic shear resistance of the soil against earthquakes is assessed by means ofempirical correlations from in-situ penetration tests and cyclic laboratory tests. However, the lique-faction phenomena analysis is still a topic under research in which soil constitutive models play animportant role.

The PM4Sand is an advanced soil constitutive model that has been developed to simulate soilliquefaction behaviour of granular soils by defining mainly three model parameters being an easycalibration model and therefore very attractive for the industry. The current project aims, firstly, toverify the PM4Sand model response at soil element level and secondly, to validate its use for quaywall structures design using the finite element methods software, PLAXIS 2D.

During the first phase of the project, a comparison between the PM4Sand model response anddocumented cyclic DSS tests documented by Sriskandakumar (2004) is performed. In this, a para-metric assessment identifies the influence of the model parameters on the model response, allow-ing also to evaluate the original calibration methodology proposed by Boulanger and Ziotopoulou(2017). Consequently, initial state conditions are evaluated. It was observed that a proper calibra-tion of the PM4Sand model provides satisfactory response both in terms of stress paths and gener-ation of excess pore pressure, even though the model tends to overestimate the cyclic resistance ofthe soil at higher cyclic stress levels and to underestimate this at lower levels with respect to a target‘CRR vs Nc’ relation. Moreover, static shear stress effect is not well captured by the model but this isstill under discussion as this effect is not fully understood yet.

In the next phase, modelling of the case study is developed based on research carried out byIai and Kameoka (1993). The PM4Sand model is calibrated based on the representative SPT testsat the site to then be implemented on the upper liquefiable soil layers. The dynamic analysis ofthe collapsed quay wall was applied using different approaches: dynamic analysis with and withconsolidation effect, and using free-field and tied-degree of freedom lateral boundaries. The resultsshowed that the PM4Sand model is able to properly simulate the onset of liquefaction even thoughthe displacements obtained were much lower than those documented.

Finally, an initial evaluation of the post liquefaction effect of the model was performed thatcould be considered as a starting point for future research.

ix

1Description of the Project

1.1. Problem AnalysisEarthquakes around the world and throughout history have had a significant impact on the sur-rounding places where these events have been triggered. Shear waves are generated and propa-gated through different layered soils until they reach the surface, which could case soil liquefactionendangering the stability and resistance of multiple civil structures and also putting into risk peo-ple’s lives.

Loose sands are well known to be prone to liquefy. When they are subjected to vibrations theytend to compact decreasing their volume. In presence of water, drainage is unable to occur so thetendency to decrease in volume results in excess of pore water pressure. If excess pore pressurereaches the same magnitude as the effective overburden pressure, the effective vertical stress be-comes zero making the soil to lose its strength completely and liquefaction occurs. Basically, soilliquefaction can be defined as the transformation of a granular material from a solid to a liquefiedstate as a consequence of increased pore-water pressure and reduced effective stress (Marcuson,1978).

In general and currently in the geotechnical engineering practice, soil liquefaction resistanceanalysis is determined by semi-empirical approaches and also by cyclic soil laboratory tests thatprovide cyclic resistance curves (CRR) for the soil profile or either for a specific soil type. Soil in-situtests are used to characterize the soil profile by means of test indices and this way estimate their liq-uefaction resistance. However, these procedures are not meant to analysis behaviour experiencedby soils based on stress-strain, stress-path and generation of excess pore pressure responses. Fromthis, soil laboratory tests can be used to study soil behaviour allowing also to assess cyclic lique-faction resistance at specific state, stress and boundary conditions, being cyclic Triaxial and DirectSimple Shear tests the most popular.

The development of constitutive soil models has allowed the evaluation of soil behaviour from atheoretical point of view through physical and mathematical formulations as they are meant to sim-ulate in an approximated way what soil experiences under different loading and stress conditions.Thus, different types of constitutive models have been generated for different types of soil relatedto different problems within geotechnical engineering. Consequently, soil liquefaction behaviourof loose sands shows a progressive strength and stiffness reduction what lead to continuous con-tractive deformation as the excess pore pressure increases. Soil stiffness is influenced by stress andstrain levels and also by the initial state that is mainly defined by soil density. Soil strength is influ-enced mainly by age and soil density, undrained behaviour and consolidation ratio. From this, soilmodels for liquefaction should consider the generation of excess pore pressure in undrained con-ditions, degradation of stiffness and strength of the soil and irreversible plastic deformation at least

1

2 1. Description of the Project

during the process of liquefaction triggering. Among soil liquefaction models developed until now,the most promising ones are the plasticity-based that incorporate the effective stress and criticalstate concepts, though recently developed hypo-plastic modelshave shown remarkable predictivecapability (Tasiopoulou and Gerolymos, 2015).

Some models for liquefaction, such as UBC3D-PLM (Galavi and Petalas, 2013) and Ta-Ger (Tasio-poulou and Gerolymos, 2015) models are briefly presented in this project. Unfortunately, in spiteof the great advance of these soil constitutive models, their responses still present certain limita-tions as they cannot reproduce all features and characteristics of the soil throughout different stressand state conditions. So for this reason, so far soil models for liquefaction should be used wisely toevaluate specific problems.

From this, the project will explore liquefaction phenomenona through the use of an advancedsoil constitutive model called PM4Sand implemented in the finite element method software, PLAXIS2D. PM4Sand, ’plasticity model for sands’, has been developed by Boulanger and Ziotopoulou (2017),from University of California at Davis, USA, with the purpose of simulating the behaviour of sandsagainst monotonic and cyclic loads, in drained and undrained conditions. Being a very promisingand efficient tool for earthquake engineering applications, PM4Sand model is a plasticity soil modelfor non-linear seismic deformation analysis that basically aims to estimate stress-strain behavioursand predict liquefaction-induced ground deformations during earthquakes. This soil model fol-lows the basic framework of the stress-ratio controlled, critical state compatible, bounding surfaceplasticity model for sand initially presented by Manzari and Dafalias (1997) and later extended byDafalias and Manzari (2004). Modifications to the Dafalias-Manzari model were developed and im-plemented to improve its ability to approximate engineering design relationships that are used toestimate the stress-strain behaviours that are important to predicting liquefaction-induced grounddeformations during earthquakes (Boulanger and Ziotopoulou, 2017). One of the big advantages ofthe model is its calibration as it can be defined by few model parameters.

The first edition of the model dates from 2010, the second from 2012 and the third and last from2017, all of them have been implemented in the finite difference software, FLAC. The current versionof the model that is used in this project, has been implemented in the finite element methods soft-ware, PLAXIS 2D, version 2018. PLAXIS 2D, is a well recognized tool for analysis of deformation ingeotechnical engineering field which is used for engineering projects all over the world developedby the privately owned company in the Netherlands, Plaxis b.v. The implementation of PM4Sandsoil model in PLAXIS 2D has been already compared with soil model performance implemented inFLAC presenting very similar responses.

1.2. ObjectiveThe objective of this project is to evaluate the PM4Sand soil model response at soil element leveland its performance for design purposes in a large-scaled engineering project modelled in PLAXIS2D, by means of two main assessments:

1. To verify if the model is capable of reproducing approximately the liquefaction resistancecurves, the stress-strain relationship, the stress-path and the generation of excess pore pres-sures, obtained from the cyclic direct simple shear tests applied to sands from the Fraser River.

2. To validate, through finite element modelling of a quay wall structure collapsing due to anearthquake, if the model is able to simulate the onset of liquefaction in the liquefiable soillayers and reproduce approximately the observed displacements.

1.3. Research QuestionsThe following research questions guide the realization and development of this project to meet theobjectives, through the analysis of the soil model by means of the aforementioned assessments.

1.4. Research Approach 3

Verification of the PM4Sand soil model at soil element level:

1. In the original document of the PM4Sand soil model (Boulanger and Ziotopoulou, 2017) thecalibration of the soil model is performed by only modifying the contraction rate parameter,hpo. By following this procedure, is the PM4Sand able to match the empirical liquefactionstrength curves and capture the soil behaviour from various laboratory cyclic DSS tests? If not,could the expected liquefaction strength curves and the stress paths be obtained by modifyingand/or calibrating other parameter(s)?

2. What is the influence of the input parameters on the PM4Sand model response?

3. Does the PM4Sand model approximately reproduce the results observed from the laboratorycyclic DSS test applied on the sands from Fraser River at different initial state and stress con-ditions?

4. What are the limitations of the PM4Sand soil model observed in the verification phase of themodel at soil element level?

Validation of the PM4Sand soil model for design purposes:

1. It is stated that the quay wall collapsed due to soil liquefaction of the backfill layer. From this,is the PM4Sand model able to capture the onset of liquefaction in the liquefiable soil layers?

2. Once the dynamic analysis of the quay wall structure in the finite element software has beenperformed, are the deformations obtained similar to those observed and registered in the casestudy? What would be the reason for these similarities and/or differences?

3. The dynamic analysis of the quay wall structure is performed using different mesh bound-aries and also two dynamic calculations, one considers consolidation and the other does not.What would be the most suitable dynamic analysis approach to be performed for this type ofengineering projects? What are the advantages and disadvantages observed?

4. Are larger displacements obtained by applying the post-liquefaction effect by means of thePM4Sand model?

1.4. Research ApproachThe project structure starts addressing the literature review in Chapter 2, which consists in research-ing, studying and organizing the necessary and useful theoretical framework to perform this study.Topics presented are mainly related to: earthquake-induced liquefaction phenomenon; analysis ofsoil liquefaction resistance from soil in-situ tests and cyclic laboratory tests; an introduction to liq-uefaction modelling and soil constitutive models; presentation of the PM4Sand soil model and itsmodel parameters; and an introduction to dynamic analysis of sheet-pile wall structures.

The verification phase of the PM4Sand model at soil element level is presented in Chapter 3 andit is carried out based on the cyclic DSS tests applied on sands from Fraser River (Sriskandakumar,2004). First, a data analysis is performed to check the information provided and how this can beused to determine the primary soil model parameters: apparent relative density (DR), shear modu-lus coefficient (G0) and the contraction rate parameter (hpo). The cyclic strength curves reproducedby the PM4Sand model are compared with those obtained from cyclic DSS tests. A parametric as-sessment is performed to analyse the influence of the model parameters on the model response.Finally, the effect of static shear stress, confining stress levels and lateral earth pressure coefficientat rest are assessed.

4 1. Description of the Project

The validation phase of the PM4Sand model for design purposes is presented in Chapter 4. Inthis, wharves Ohama No.1 and No.2 from the well-documented Akita Port case study are modelledin PLAXIS 2D to assess in this way the onset of liquefacion and displacements using the PM4Sandmodel in the liquefiable soil layers. While the Ohama No.1 Warf did not presented any damagecaused by the earthquake, the Ohama No.2 Wharf collapsed due to soil liquefaction. From this,soil site investigation allows to determine and calibrate the soil model parameters for the soil lay-ers. During the elaboration of the case study in PLAXIS 2D, different aspects of the modelling pro-cess must be considered, among them: mesh generation, boundary conditions, construction stages,soil-structure interaction and the dynamic analysis.

Finally,in Chapter 5 the final conclusions about the PM4Sand model performance, features andlimitations, and recommendations with respect to its use on geotechnical engineering projectsmodelled in the finite element methods software are presented, emphasizing to give answer andargumentation to the objectives and research questions stated for this project.

2Theoretical Framework

2.1. Earthquakes-induced LiquefactionEarthquakes are movements of the Earth’s crust mainly caused by energy release from the constantactivity of geological faults and friction of tectonic plates. They can also be caused by volcanic pro-cesses or even by human intervention in smaller magnitudes. The propagation of this energy makesthe subsoil to shake inducing changes in shear stresses at different depths of the soil mass, whatcould cause significant deformations in the soil at surface level leading to important damage oncivil structures. The following figure shows an historical record of earthquakes, where the largesthave been unleashed mainly on the coasts of the continents adjacent to the Pacific Ocean.

Figure 2.1: Map of earthquakes 1900-2017 (Data source: Search Earthquake Archives, USGS)

From the point of view of geotechnical engineering, earthquakes provide learning opportunitiesto further investigate about liquefaction phenomenona on soil that have suffered its consequences,how is its triggering process and how soil behaves under liquefaction state. Basically, cyclic hori-zontal movement on the rock base enforces the sand layers above it to accelerate and decelerate

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6 2. Theoretical Framework

similarly generating shear-waves that act as cyclic shear stresses on the soil that can decrease theeffective shear strength of the soil due to generation of excess pore pressures, which occur becauseof poor drainage conditions. These drainage conditions are considered poor or undrained due tothe quick action of cyclic loads on the soil, thus the water between the grains does not have enoughtime to flow. This leads to no variation of the volume despite the fact soil tends to decrease in vol-ume, and the pore-water pressure increases until water pressure exceeds contact stresses betweensoil grains.

An important soil condition to take into account for this phenomenon, is its relative density.Dense granular soils will tend to dilate while loose granular soils will tend to contract under shearloading. During cyclic loading a gradual loss of strength and stiffness has been widely observed, un-til soil loses all resistance to shear becoming a viscous fluid. This process can be identified as lique-faction triggering, in which there is a progressive accumulation of shear strains reaching significantirreversible deformations as the generation of excess pore pressures decrease the soil effective shearstrength to its minimum.

2.1.1. Seismic wavesFor most relatively simple geotechnical seismic analyses, the measure of the cyclic ground motion isrepresented by the maximum horizontal acceleration at the ground surface amax, also known as thepeak horizontal ground acceleration (PGA). Since it is not possible to predict earthquakes, the valueof the peak ground acceleration must be based on prior earthquakes and fault studies (Boulangerand Idriss, 2008). Seismic waves are composed by compressional (primary) and shear (secondary)waves, called ’P-waves’ and ’S-waves’ respectively. Compressional waves moves in the propagationdirection while S-waves oscillate perpendicularly to the wave propagation and they are defined asfollows:

Vp =√

Eoed

ρ(2.1)

Vs =√

G

ρ(2.2)

According to soil heterogeneity, these waves experience changes that are mostly because of ma-terial and radiation damping of soils. According to radiation damping, specific energy can decreasedue to geometric spreading. Consequently, the amplitude of the stress waves decreases with dis-tance even though the total energy remains constant. Furthermore, material damping affects prop-agated stress waves as a portion of the elastic energy of these is lost due to heat generation.

2.1.2. Earthquake SizeThe impact of an earthquake can be defined according to its magnitude or intensity, which are dif-ferent terms. The magnitude measures the energy that is released at the source of the earthquakewhile the intensity measures the strength of shaking produced by the earthquake at a certain loca-tion. For the purposes of this study, no further study will be made on topics related to earthquakeengineering in this chapter. However, in Chapter 4 of this project, the process of filtering and cor-recting an acceleration-time record of an earthquake is developed and presented in order to imple-ment this signal in the model created in PLAXIS 2D, and thus evaluate the dynamic analysis of thestructure of the case study. For more information regarding the history of earthquake engineering, itis recommended to study the following material presented in the bibliography: Day (2002), Kramer(1996) and PIANC (2001).

2.2. Simplified Stress-Based Triggering Assessment 7

2.1.3. Definition of LiquefactionAccording to Eurocode 8 (2004), soil liquefaction is "a decrease in the shear strength and/or stiff-ness caused by the increase in the pore water pressures in saturated cohesionless material duringearthquake ground motion, such as to give rise to significant permanent deformations or even to acondition of near-zero effective stress in the soil". In addition, liquefaction can be defined in twodifferent ways presented below:

1. Flow (static) liquefaction: it occurs when the static shear stress is greater than the shear strengthof the soil in its liquefied state producing one of the most dramatic effects known as flow failures.Once triggered the large deformations produced by flow liquefaction are actually driven by staticshear stresses. Cyclic stresses may bring the soil to an unstable state which its strength drops suf-ficiently to allow the static stresses to produce the flow failure. Flow liquefaction failures are char-acterized by the sudden nature of their origin, the speed with which they develop and the largedistance over which the liquefied materials often move (Kramer, 1996).

2. Cyclic (softening) mobility: in contrast to flow liquefaction, cyclic mobility occurs when the staticshear stress is less than he shear strength of the liquefied soil. Deformations produced by cyclic mo-bility failures develop incrementally during earthquake shaking, and are driven by both cyclic andstatic shear stresses. Among these deformations, it can be identified lateral spreading on very gentlysloping ground or level-ground liquefaction, what can produce large, chaotic movement known asground oscillation during earthquake shaking but produces little permanent lateral soil movement(Kramer, 1996).

Soil liquefaction could lead to the following effects:

• Ground surface settlement.

• Bearing capacity failure of foundations.

• Lateral movement of slopes.

• Permanent displacements in the soil.

• Changes in the original site conditions (post-liquefaction including loss of strength and stiff-ness).

2.2. Simplified Stress-Based Triggering AssessmentIn this section the simplified Stress-Based Triggering assessment is presented which defines the soilliquefaction potential. This method proposed by Seed and Idriss (1971) is one of the most com-monly used in practice. By means of the factor of safety FS, the ratio between the seismic loadingto trigger liquefaction (liquefaction resistance) and the seismic loading expected for the earthquake(seismic demand) is determined. The liquefaction resistance and the seismic demand are definedas cyclic stress ratios, defined as the ratio of the cyclic shear stress τcyc to the initial vertical effectivestress σ’

vo. The seismic demand is the earthquake-induced cyclic stress ratio CSR and the liquefac-tion resistance is the cyclic resistance ratio CRR. The factor of safety is as follows:

F S = C RR

C SR(2.3)

In addition, Juang et al. (2006) and Ku et al. (2012) related the soil liquefaction potential, repre-sented by the factor of safety already mentioned, to the probability of liquefaction PL. according tothe following expression:


PL = 1

1+ (F S/0.9)6.3 (2.4)

The seismic demand and the liquefaction resistance are determined according to the followingsubsections. In this case, the liquefaction resistance is defined according to the Standard Penetra-tion Test as this is the procedure used to calibrate the PM4Sand soil model for the case study inChapter 4.

2.2.1. Cyclic Stress Ratio, CSRThe earthquake-induced cyclic stress ratio CSR, represents the cyclic shear stress at a given depthdue to earthquake shaking and it can be defined based on historic recorded earthquakes by meansof their peak ground acceleration (PGA) as it is expressed in Equation 2.5. The following expressionto determine the CSR assumes a one-dimensional dynamic response of the soil deposit (Seed andIdriss, 1971), as it is shown in the following figure.

Figure 2.2: Conditions assumed for the derivation of the CSR earthquake equation (Day, 2002).

C SR = τav

σ′vo

= 0.65 ·[

amax

g

](σvo

σ′vo

)rd (2.5)

In the formula presented above, amax/g is the peak horizontal acceleration at the ground surfaceas a fraction of gravity, σv0 and σ′

v0 are the total and effective initial vertical stresses at depth z, andrd is the shear stress reduction coefficient that accounts for the dynamic response of the soil profile.The 0.65 factor was introduced to reduce the CSR from the peak value of the earthquake-inducedshear stress, which occurs only once during the earthquake, to a more representative value thatoccurs multiple times during strong shaking (Kavazanjian, 2016). The value of rd is equal to 1.0 at theground surface and decreases with depth below the surface to account for the non-rigid responseof the soil column subjected to the vertically propagating shear wave. The figure 2.3 presents the rd

curves for different earthquakes magnitudes which are obtained based on the following equationsexpressions proposed by Idriss (1999) (Idriss and Boulanger, 2014):

rd = exp[α (z)+β (z) ·M

](2.6)

α (z) =−1.012−1.126 · sin( z

11.73+5.133

)(2.7)


β (z) = 0.106+0.118 · sin( z

11.28+5.142

)(2.8)

Figure 2.3: Stress reduction coefficient rd versus Depth curves.

2.2.2. Cyclic Resistance Ratio, CRRHistorical soil test information has been compiled to relate the soils that have presented liquefac-tion with the corresponding resistance indices extracted from the soil field tests. From this, semi-empirical correlations representing liquefaction strength curves have been defined from differentsoil in-situ tests, such as SPT, CPT or Shear-wave velocity measurements. In general, these strengthcurves have been normalized for a earthquake magnitude equal to 7.5 and for a overburden pressureequal to 1 [atm]. In this section, the liquefaction resistance determined based on SPT is presented.Liquefaction resistance determined by cone penetration test is presented in the Appendix, ChapterA.

The liquefaction resistance is defined by means of the soil test index (N1)60, which is the SPTblow count normalized to an overburden pressure of approximately 100 [kPa] and a hammer energyratio or hammer efficiency of 60%. The CRR curve for fines content <5% is the basic penetrationcriterion for the simplified procedure and it is called "SPT clean-sand base curve", whose expressionhas been proposed by Rauch (1998) (Idriss and You, 2001) as follows:

C RR7.5 = 1

34− (N1)60+ (N1)60

135+ 50

[10 · (N1)60+45]2 − 1

200(2.9)

This aforementioned liquefaction resistance expression is valid for (N1)60 < 30 and for gentlyslopes whose inclination is less than 6%. For (N1)60 ≥ 30, clean granular soils are too dense to liquefyand are classed as non-liquefiable soils. The (N1)60-parameter is defined according to the followingcorrection factors:

(N1)60 = (N )60 CN =CE CR CB CS NSPT CN (2.10)

where, CE is the correction factor equal to the measured value of the delivered energy as a per-centage of the theoretical free-fall hammer energy, i.e. ERm / 0.6 Eff; CR is the correction factor toaccount for different rod lengths; CB is the correction factor for the borehole diameter; and CS is thecorrection factor that depends on the sampler. These correction factors can be determined based


on the values presented in the Figure 2.4. Finally, CN is the correction factor due to overburden ef-fects and it can be defined based on the relative density according to Idriss and Boulanger (2004b)as follows:

CN =( p A

σ′vo

)m

(2.11)

m = 0.784−0.521 ·DR (2.12)

mSPT = 0.784−0.0768√

(N1)60 (2.13)

mC PT = 1.338−0.249(qc1n)0.264 (2.14)

Figure 2.4: Correction factors for SPT (Youd and Idriss, 2001)

2.2.3. Factors that affect Soil Liquefaction ResistanceThere are different conditions that may affect the liquefaction resistance of soils. These are mainlyreferred to different earthquake magnitudes, fine content, the effect of static shear stress and theeffect of confining stress levels, as it can be seen in the following expression:

F S = C RR7.5

C SR·MSF ·Kσ ·Kα (2.15)

Below the correction factors considered in this project and which are generally used to deter-mine the resistance of soils to liquefaction are presented.

Magnitude Scaling Factor, MSF

The Magnitude Scaling Factor, MSF, has been introduced to convert the liquefaction resistancecurve for an earthquake magnitude equal to 7.5, CRR7.5, to an equivalent CRR for a design earth-quake, taking into account duration effects on the triggering of liquefaction. Originally, the MSFwas introduced by Seed and Idriss (1982), and then many researchers have proposed expressionsfor this effect. Equation 2.16 has been suggested as a result of a revaluation of the data done by


Idriss, while the Equation 2.17 was also developed by Idriss (1999) and used by Idriss and Boulanger(2008).

MSF = 174

M 2.56 (2.16)

MSF = 6.9 ·exp

(−M

4

)−0.058 ≤ 1.8 (2.17)

Figure 2.5: Magnitude scaling factor MSF curves (Idriss and Boulanger, 2014).

Overburden Correction Factor, Kσ

The confining stress is defined as the overburden pressure or stress imposed on a soil layer by theweight of overlying material. Previous research has shown that the cyclic resistance ratio (CRR) of asand for a given relative density decreases with increasing confining stress (Seed and Harder, 1990;Sriskandakumar, 2004). This effect can be taken into account by means of the correction factor, Kσ,as follows:

Kσ = C RRσ6=1

C RRσ=1(2.18)

where CRRσ6=1 is the cyclic resistance ratio of a soil sample with an initial confining stress differentthan 1 [atm], and CRRσ=1 is the cyclic resistance ratio of a soil sample with an initial confining stressof 1 [atm]. Also defined as overburden correction factor, Kσ was developed by Boulanger (2003)based on liquefaction resistance for a clean reconstituted sand in laboratory can be related to thestate parameter index, ξR . The following expressions assume that Kσ can be expressed in terms ofqc1N and (N1)60 according to Idriss and Boulanger (2008) as follows:

Kσ = 1−Cσ ln

(σ′

vc

p A

)≤ 1.1 (2.19)

Cσ = 1

18.9−2.55√

(N1)60

(2.20)


Cσ = 1

37.3−8.27(qc1n)0.264 (2.21)

with (N1)60 and qc1n limited to maximum values fo 37 and 211, respectively in the expressionsabove, so Cσ ≤ 0.3.

Figure 2.6: Overburden correction factor Kσ relationship (Idriss and Boulanger, 2014).

Effect of static shear stress, Kα

Investigations have indicated that the presence of initial static stress has an important influenceon the cyclic resistance of sands which can increase or decrease the cyclic resistance according tothe initial relative density. While loose contractive sands experience a reduction in cyclic resistancewith initial static shear stress, dense dilative sands experience an increase. Cyclic resistance to liq-uefaction would increase if the deformation mechanism is of ’cyclic mobility’ type, and vice versa(Sriskandakumar, 2004).

In order to consider the initial static shear effect on cyclic resistance of sand, Seed and Harder(1990) proposed the following empirical correction factor:

Kα = C RRα6=0

C RRα=0(2.22)

where CRRα6=0 represents the liquefaction resistance without initial sustained static shear stress(i.e. gently slope grounds, inclination less than 6%) and CRRα=0 the liquefaction resistance for thecase with initial sustained static shear stress.

Two failure modes are identified for loose sand sheared under cyclic loading conditions withinitial static shear: flow deformation and residual deformation failure. The flow liquefaction oc-curs accompanied by a sharp increase both in pore pressure and axial strain (Yang and Pan, 2017).According to Idriss and Boulanger (2003) static shear stress effect considers the relative density in-fluence, so the correction factor, Kα, can be expressed as follows:

2.3. Undrained Cyclic Response of Sands 13

Kα = a +b ·exp

(−ξR

c

)(2.23)

a = 1267+636α2−634 ·exp(α)−632 ·exp(−α) (2.24)

b = exp(−1.11+12.3α2+1.31 · ln(α+0.0001)

)(2.25)

c = 0.138+0.126α+2.52α3 (2.26)

where α represents the ratio between the static shear stress τst ati c and the effective verticalstress of the soil σ

′v0. However, there is still no consensus on recommended Kσ factors for use in

engineering practice as even though these factors were developed with guidance from soil mechan-ics principles and were compared with experimental data for three different sands, this was only alimited amount of data (Kavazanjian, 2016).

Figure 2.7: Correction factor for effect of static shear stresses (Harder and Boulanger, 1997)

2.3. Undrained Cyclic Response of SandsThe undrained cyclic response of sands is directly linked to what soils would experience underearthquake shaking, whose behaviour mainly depends on the soil density level being granular loosesoils the most important to be evaluated as they are prone to liquefy.

For loose-medium sands, liquefaction triggering involves continuous contractive deformationwhich is limited by a transformation phase right before the critical state. When this phase is reachedthe contractive response of the soils change to dilative. During this process, a loss of stiffness leadsto a progressive development of shear strains. In addition, multiple loading cycles leads to densifi-cation of the soil as there is a collapse of the grains structure during undrained shearing.

Observations made on laboratory tests show increase in pore water pressure per cycle is usu-ally relatively strong in the beginning, which corresponds to relatively large contraction during firstcycles. It is also large at the end due to the relatively large pore pressure and consequent large rel-ative effective shear stress amplitude causing a significant increase in shear strain amplitude and areduction in the apparent shear stiffness (De Groot et al., 2006).


The characteristics mentioned above have been observed by means of cyclic laboratory tests.Among the most popular ones there are the cyclic triaxial test and cyclic direct simple shear test,both briefly presented in the following section. Moreover, in Chapter 3 undrained cyclic responseof loose sands is analysed more in detail while comparing the PM4Sand model response with reallaboratory data.

2.3.1. Cyclic Laboratory TestsSoil liquefaction resistance at soil element level can be approached by a laboratory-based assess-ment in which a representative CSR is applied to an specimen and obtaining the number of cyclesloading to liquefaction under this stress ratio to Neq . Cyclic loading is usually applied by a shearforce or shear displacement on a horizontal plane to either the top or the bottom of the specimenassuming that a complementary shear stress develops on vertical planes along the sides of the spec-imen.

Despite the fact non-uniform cyclic loading tests can be performed, there is no generally ac-cepted procedure for performing and interpreting the results of such laboratory tests. Differentcase occurs with uniform cyclic loading tests that are commonly performed to obtain cyclic strengthcurves.

Among the most common laboratory tests applied in practice to analyse the cyclic response ofsoil samples, there are the triaxial and the direct simple shear tests. Triaxial tests are widely usedbecause of its relative simplicity in use and its more common availability in research facilities com-pared to other testing apparatuses, however DSS tests provide a better representation of both thein-situ initial K0 stress and strain state in level ground and the earthquake-induced stresses dueto vertically propagating shear waves. Cyclic DSS tests use cylindrical specimens with a height-to-diameter ratio typically equal to 0.5.

The cyclic resistance of the soil for liquefaction is generally defined by the cyclic strength ratioCSR at which a soil sample will reach liquefaction, in this case, at 15 number of uniform cycles. TheCSR is defined as the ratio between the applied amplitude of a cyclic shear stress τc yc over the initial

effective vertical stress σ′vc , as follows:

C SR = τc yc

σ′vc

(2.27)

Figure 2.8: Cyclic strength curves from CDSS test (Sriskandakumar, 2004)

2.3. Undrained Cyclic Response of Sands 15

Figure above presents some aforementioned cyclic strength curves obtained by the study carriedout by Sriskandakumar (2004), that consisted of cyclic DSS tests applied on sand samples from theFraser River, same soil testing data used in Chapter 3.

Moreover, cyclic laboratory tests can be used to extrapolate correlations obtained from in-situsoil tests and also they are very useful for developing constitutive relationships for pore pressuredevelopment prior to liquefaction and for the post-liquefaction behaviour of soils as they couldprovide an understanding of strength loss mechanisms.

Relation between the earthquake magnitude and the number uniform cycles of loading can beseen in Figure 2.9, in which 15 uniform number of cycles would represent an earthquake magnitudeequal to 7.5.

Figure 2.9: Relation between earthquake magnitude and the number of uniform cyles of loading to causedliquefaction (Seed and Idriss, 1982)

It has been assumed that even tough a selected strain level is not necessarily an appropriatemeasure of liquefaction, this could work as an ’index’ of comparison for certain discussion purposesconsidering this way that liquefaction is triggered when the single-amplitude horizontal shear strainγ reaches a value of 3.75% in a DSS sample. This strain level is assumed to be equivalent to a 2.5%single-amplitude axial strain in a triaxial sample, which also is a definition for liquefaction previ-ously suggested by the National Research Council of United States (NRC, 1985) (Sriskandakumar,2004).

It is important to mention that sand are highly susceptible to disturbance using conventionaltube sampling methods. Sand can drain during sampling procedure loosing most of its effectivestress becoming easily disturbed by the vibrations and strains from the moment the sample is takenfrom the borehole outside and taken to the laboratory (Boulanger and Idriss, 2004).

Figure 2.10: Representation of cyclic DSS test during one cycle.


As it was already mentioned, level-ground free-field response induced by earthquake shakinginvolves a simple shear mode of deformation which is reproduced more rigorously in a DSS test.The conversion of triaxial test data to simple shear mode of deformation, as encountered in level-ground free-field conditions, has traditionally been formulated in terms of the cyclic stress ratio CSRusing the following expression:

C SR =[τ

σ′v

]f i eld

= (1+2K0)

3·[ ∣∣q∣∣

2σ′c

]T X

(2.28)

and it can be reformulated as,

C RRDSS =(

1+2(K0)DSS

3

)C RRT X (2.29)

Figure 2.11: Triaxial and idealized simple shear cyclic loading conditions (Cappellaro, et al., 2017)

The relationship for the liquefaction resistances between triaxial and simple shear conditions isconsidered to be a complex function that depends on factors such as tested soil, amplitude of im-posed cyclic stresses, soil fabric, among others that are not captured by the equation 2.28 (Tatsuokaet al., 1986; Cappellaro et al., 2017). It has to be taken into account that stresses imposed on a triaxialtest specimen are very different from the stresses induced by earthquakes. From this, direct simpleshear tests overcome the aforementioned shortcoming of triaxial testing.

2.3.2. Modulus Reduction Curve and Soil DampingModulus reduction curve relates the reduction of the soil stiffness, as measured by the shear mod-ulus to the amplitude of shear strain, representing strain-dependent stiffness of the soil. Incrementin the cyclic shear strain will result decrease of the shear modulus.

On the other hand, cyclic loading (unloading and reloading) leads to an hysteretic loop in thestress-strain curve, what represents dissipation of energy in a load cycle and in dynamics analysisthis leads to damping. This depends on the shear strain amplitude in the load cycle, so the largerthe cyclic shear strain, the larger damping level.

The damping ratio (ξ) is usually defined according to the following expression:

ξ= 1

4π· ∆w

W(2.30)

where 4w is the dissipated energy per unit volume in one hysteresis loop and W, the energy storedin an elastic material having the same shear modulus as the visco-elastic material.

2.4. Liquefaction Modelling 17

Figure 2.12: Representation of the shear modulus reduction curve related to different geotechnical problems(left) (PLAXIS, 2018a) and hysteretic damping loop (right).

2.4. Liquefaction Modelling2.4.1. Type of Constitutive ModelsA soil constitutive model aims to relate stress-strain behaviour of soils observed mainly in laboratorytests based on a numerical formulation. Each soil model has advantages and limitations related totheir use and applicability. The following is a list of different type of constitutive models that can beused for several engineering purposes, which have been previously explained by Beaty and Perlea(2011). The first two categories can be applied for non-liquefiable soil layers while the next threecan be used for liquefiable soil layers.

• Linear elastic models.Being the simplest type of models, they formulate a constant proportional relationship be-tween stress and strain increments. These type of models do not consider yielding and can-not be used to directly model permanent plastic shear strains. Although considered to over-simplify soil behaviour, they can be used to model rocks where shear failure or significantnon-linearity are unlikely.

• Elastic perfectly-plastic models.Plasticity-based with fixed yield or failure surface in which stress increments that attempt toexceed the strength envelope result in the generation of plastic strains. These type of modelsare useful where material yielding is possible. However, effects due to pore water generation,pore water migration or cyclic degradation will not be significant. The well-known Mohr-Coulomb soil model is part of these type of models.

• Total stress modelsThere models simulate softening of liquefiable elements at the time of triggering. More so-phisticated models use cycle counters based on laboratory data and theoretical formulationto predict the evolution of liquefaction on an element. Pore pressures are not directly pre-dicted in a true total stress model. Strengths in saturated elements are specified as undrainedvalues with friction angle zero.

• Loosely-coupled effective stress modelsThe element response of an effective stress model is a function of the evolving effective stressstate. These models are mainly used for soils subject to changes in effective stress due tocyclic loading. However, they have an independent pore water pressure generator, so they


do not directly predict volumetric strains that lead to pore water pressure changes. In thiscase, estimation of pore water pressure is made by prediction of cycle of shear stress (or shearstrain).

• Fully-coupled effective stress modelsThese models are used to predict tendency to dilate or contract in response of each load incre-ment. The resulting volumetric strains are resisted by the stiff pore fluid in saturated elements,resulting in generation or reduction of pore water pressure depending on whether the strainis contractive or dilative. The fully-coupled models allow to predict soil behaviour observedin laboratory specimens, being the most suitable models for liquefiable soils that are affectedby changes in pore water pressure due to cyclic loading or pore water pressure migration.

Finally, the type of constitutive model selected is based on the anticipated material behaviourand the objective of the analysis. All constitutive models can be wisely used according to the antic-ipated material behaviour and the problem to be analysed. The feasibility of all models is stronglyrelated to their strengths and limitations.

2.4.2. Soil Constitutive Models for LiquefactionIn general, formulation of a constitutive model should adequately address the key features of the an-ticipated soil behaviour which may include relationships between shear stiffness and strain, stress-level dependency, generation of excess pore pressure and strain softening. In the case of soil modelsfor liquefaction, stress-strain and pore pressure generation in monotonic and cyclic laboratory testsshould be reasonably modelled. Furthermore, they should capture the behaviour represented bythe empirical relationships for liquefaction triggering and post-liquefaction behaviour.

Soil material behaves non-linearly and often shows anisotropic and time dependent behaviourwhen it is subjected to stresses. Generally, soil behaviour is different in primary loading, unloadingand reloading. It exhibits non-linear behaviour well below failure condition with stress dependentstiffness. Soil undergoes plastic deformation and is inconsistent in dilatancy. Moreover, soil alsoexperiences small strain stiffness at very low strains and upon stress reversal (Daftari, 2015).

Among some soil models for liquefaction, it can be mentioned the Finn Constitutive Model andthe UBC3D-PLM Model. The first one calculates generation of excess pore pressure by calculatingirrecoverable volumetric strains during dynamic analysis and the void ratio is considered to be con-stant and it can be calculated as a function of volumetric strain. More information about this modelcan be found in research made by Nabili et al, (2008).

On the other hand, UBC3D-PLM Model has been widely evaluated during the last years. Thismodel is an effective stress model that has been developed based on the UBCSand Model. TheUBC3D-PLM model controls pore water pressure generation by means of two yield surfaces in hard-ening process. The model is able to model excess pore pressure in monotonic and cyclic loadingconditions. In addition, the effect of densification is modelled by increasing the plastic shear mod-ulus with the number of cycles (UBCSand).

Features of the UBC3D-PLM model are presented below:

• Yield surface is allowed to evolve or harden in response of loading history allowing to predicthysteretic behaviour as plastic behaviour may occur at loading increments below the strengthenvelope.

• Hardening of the yield surface is based on a hyperbolic relationship between plastic shearstrain and the stress ratio.

• The flow rule is based on stress ratio, where stress states below the constant volume frictionangle are contractive and stress states above are dilative.

2.5. PM4Sand Soil Model 19

Limitations and disadvantages of the UBC3D-PLM model as follows:

• There is no compaction hardening.

• Cyclic loading and liquefaction behaviour are not always realistic.

• There is an over-estimation of damping in dynamic calculations

• In order to calibrate the model, a high number of parameters have to be define and/or cali-brated, what leads to the need of more field and laboratory testing.

2.5. PM4Sand Soil ModelThe current sand plasticity model follows the basis framework of the stress-ratio controlled, criticalstate compatible, boundingsurface plasticity model for sands that has been elaborated by Dafaliasand Manzari (2004). In the current version of the model, a fabric-dilatancy tensor has been added totake into account the effects of fabric changes during loading and which is used to model observedchanges in grains structure of the sand during plastic dilation due to contractive response uponreversal of loading direction.

The soil model is developed based on effective stresses taking into account the generation ofexcess pore pressure due to cyclic loading under undrained conditions. The model is formulated intwo dimensions while a third out-of-plane direction is considered with an elastic evolution, so it isout of scope for this project.

The PM4Sand model takes into account elastic and plastic strains increments which are com-posed by volumetric and deviatoric terms. The elastic strains increments are generated accordingto acting stress levels and are restricted by the shear modulus G and the bulk modulus K of the soilmaterial, while the plastic strains increment are produced by the loading index L and restricted bythe dilatancy D and the distance between the stress levels in comparison to the position of the yieldsurface, by means of the normal tensor n. From this, the excess pore pressure generation occurs un-der undrained conditions and it is calculated through the volumetric strain increments decreasingthe effective stresses of the soil.

In this section the PM4Sand model is briefly presented. A more detailed explanation of themodel can be found in the Appendix, Chapter B, in the original document prepared by Boulangerand Ziotopoulou (2015) and in the consequent document elaborated by PLAXIS (Brinkgreve, Vilharand Zampich, 2018).

2.5.1. Critical State Soil Mechanics FrameworkSoil critical state refers to the state in which the soil continues to deform at constant stress and con-stant void ratio (Schoefield and Wroth, 1968). This concept is related to the steady state in which thedeformation for any mass of particles continuously evolves to a constant volume, normal principalstresses and velocity.

The PM4Sand model follows critical state soil mechanics frameworks proposed by Bolton (1986)by means of the relative state parameter index ξR which has been adapted in terms of the differencebetween the current apparent relative density DR and the relative density at the critical state DR,cs,as follows:

ξR = DR,cs −DR (2.31)

DR,cs = R

Q − ln(100 p

p A

) (2.32)


Figure 2.13: Definition of the relative state parameter index and effects of varying Q and R.

In Figure 2.13, in the left side it can be seen the critical state line with parameters Q and R equalto 10 and 1.5 respectively, while in the right side how the critical state line variates with modifyingthese values. Parameter Q indicates the normalized level of mean effective stress p’ where the criticalstate line starts to significantly bend due to significant particle crushing (Parra, 2016). Setting thecoefficient R equal to 1.5 provides better approximation to typical results observed in direct simpleshear loading (Boulanger & Ziotopoulou, 2015). Once the critical state line is reached because ofshearing, the soil material will flow as a frictional fluid.

2.5.2. Bounding, Dilatancy, Critical and Yield SurfacesThe model uses bounding, dilatancy and critical surfaces according to Dafalias and Manzari (2004).The current version of the model has been simplified by removing the Lode angle dependence sofriction angles are the same for compression or extension loading. Bounding and dilatancy ratiosare related to the critical stress ratio M by the following formulas:

M b = M ·exp(−nb ξR

)(2.33)

M d = M ·exp(nd ξR

)(2.34)

M = 2sin(ϕcv ) (2.35)

where the model parameters nb and nd define the computation of Mb and Md with respect to M.The bounding stress ratio controls the relationship between the peak friction angle and the relativestate. During shearing, bounding and dilatancy surfaces will approach the critical surface at thesame time the relative state parameter index approaches the critical state line (ξR tends to zero).

The bounding surface cannot be surpassed, instead for any given stress state ’q/p’ there is al-ways and ’image’ stress state lying on the failure surface so the distance between the actual and the’image’ stress states can be measured (Tasiopoulou and Gerolymos, 2015). The bounding surfaceframework aims to simulate plastic deformations within the yield surface.

Dilatancy surface defines the location where transformation from contractive to dilative be-haviour occurs, also known as transformation phase state PT. Under undrained cyclic loading, change


in effective stress is associated with shear-induced volumetric dilative or contractive tendency ofsoil (Wang and Xie, 2014).

The yield surface is formulated as a small cone in the stress space with the following expression:

f =√

(r −α) : (r −α)−√

1

2pm = 0 (2.36)

where,

r =(

rxx rx y

rx y ry y

)=

( σxx −pp

σx y

pσx y

pσy y −p

p

)(2.37)

p = (1+K0)

2·σy y (2.38)

Tensor r is the deviatoric stress ratio tensor and p the mean effective stress (σyy is also consideredas effective stress). The back-stress ratio tensor α determines the position of the yield surface in thedeviatoric stress ratio space and m defines the radius of the cone (m = 0.01), hence the size of theyield surface. From the equation (2.36), the yield function is defined by the distance between thedeviatoric stress levels and the position of the yield surface (by means of r-α). Then, bounding anddilatancy surfaces are defined in terms of the image back-stress ratios, αb and αd , as follows:

αb =√

1

2

[M b −m

]n (2.39)

αd =√

1

2

[M d −m

]n (2.40)

where n is the deviatoric unit normal to the yield surface defined as

n = r −α√12 m

(2.41)

The following figure shows a scheme of bounding, dilatancy, yield and critical surfaces.

Figure 2.14: Yield, critical, dilatancy and bounding lines in q-p space (left) and yield, dilatancy and boundingsurfaces in the ry y -rx y stress-ratio plane (right) (Boulanger and Ziotopoulou, 2015)


2.5.3. Fabric EffectsSoil fabric corresponds to the structure and arrangement of the grains showing inherent anisotropy.Because of cyclic shearing there is a rearrangement and/or destruction of the soil fabric. From this,fabric effects are carried out by means of the fabric-dilatancy tensor z which evolves according to dz.The fabric-dilatancy tensor considers prior straining of the model and it has been implemented tomodel effects of changes in sand fabric during plastic dilation generated as a contractive responseupon reversal of loading direction.

The evolution of z is according to the following expression:

d z =− cz

1+⟨

zcum2 zmax

−1⟩

⟨−d εpl

v

⟩D

(zmax n + z) (2.42)

where cz controls the rate of the evolution and zmax is its maximum limit. The fabric-dilatancytensor evolves with plastic deviatoric strains that occur only during dilation, so it is restricted toonly occur when (

αd −α)

: n < 0 (2.43)

The cumulative value of absolute changes of the fabric tensor z is defined as follows:

d zcum = |d z| (2.44)

The rate of evolution of the fabric-dilatancy tensor decreases with increasing values of zcum whatmakes to progressively accumulate shear strains during undrained cyclic loading avoiding this wayto lock-up into a repeating stress-strain loop.

In addition, additional memory of fabric formation history, represented by the initial fabric ten-sor zin, is included in the model to improve the ability of the model to take into account effects due tosustained static shear stresses and differences in fabric effects for various drained versus undrainedloading conditions.

Shear strains evolve according to an elastic and to a plastic part, whose both explanations canbe seen in the Appendix, Chaper B.

2.5.4. Main model parametersIn order to implement this soil model in PLAXIS, PM4Sand has been defined as ’user-defined’ modelin which only three primary parameters are meant to define the model behaviour while the rest ofthe parameters are considered as default values, so initially there would be no need to modify them.Below the primary and secondary parameters of the model are presented, in which it is specifiedhow these can be determined from laboratory tests and/or by means of proposed correlations.

Primary input parameters:

1. Apparent Relative Density, DR.Having significant influence on all phases of the model formulation, this primary variable controlsthe dilatancy and stress-strain relation responses of the model.

The initial relative density defines whether the soil material will experience contractive or dila-tive behaviour and also how close the soil material is to the transformation phase, represented bythe dilatancy surface.

Regarding the stress-strain response, the initial relative density has an impact on the elasticshear modulus G by means of the stress ratio effects (see equation B.22). This input is defined asa fraction, not as a percentage. In case the soil material were tested in a laboratory, the relativedensity can be determined from maximum and minimum void ratios (emax and emin) as follows:


DR = emax−e

emax−emin(2.45)

However, if there were no information from laboratory testing, the initial relative density canalso be estimated based on CPT or SPT penetration resistances, such as the following relationshipsused by Idriss and Boulanger (2008):

DR =√

(N1)60

Cd(2.46)

with Cd = 46, and

DR = 0.465

( qc1N

Cd q

)0.264

−1.063 (2.47)

with Cdq = 0.9

It is important to mention that the relative density parameter can be defined as an "apparentrelative density" and it could be modified for calibration purposes.

2. Shear Modulus Coefficient, G0.The shear modulus coefficient controls the shear modulus G at small strains Gmax and it is mainly af-fected by environmental factors such as cementation and ageing (Boulanger & Ziotopoulou, 2015).G0-value restrains the elastic deviatoric and volumetric increments and should be chosen to matchestimated or measured shear-wave velocities according to Gmax = ρ V2

s . Also, G0 can be estimatedbased on the modified correlation between SPT-value (N1)60 and Vs1. The value of G0 can thus becomputed as,

G0 = Gp A

√p A

p(2.48)

or,

G0 = 167√

(N1)60+2.5 (2.49)

or,

G0 = 167 ·√

46 ·D2R +2.5 (2.50)

3. Contraction Rate Parameter, hpo

Primary variable that adjusts plastic volumetric strains during contraction. During model calibra-tion, this variable can be adjusted to obtain a target cyclic resistance ratio (liquefaction resistance)with respect to cyclic laboratory tests or penetration resistances from in-situ soil tests. This can beperformed by using the soil test facility ’cyclic DSS test’ in PLAXIS 2D.

Secondary input parameters:

Refinements in these parameters for a practical problem may not be necessary, as the calibra-tion of the other parameters will have a stronger effect on monotonic or cyclic strengths. However,any modification applied on these parameters can be assessed in order to check their influence onthe model responses.


1. Atmospheric pressure, pA.Default value is 101.3 [kPa].

2. Maximum and minimum void ratios, emax and emin.The maximum and minimum void ratios affect the computation of density, and affect how volumet-ric strains translate into changes in relative state. Default values are 0.8 and 0.5, respectively.

3. Bounding surface parameter, nb.The bounding surface parameter controls the rate of the bounding surface approach the criticalstate surface. It has a default value equal to 0.50 and it controls dilatancy and thus also the peakeffective friction angle. For loose of critical states (DR < DR,cs, ξR > 0) nb is divided by 4.

4. Dilatancy surface parameter nd.Having default value equal to 0.10, this parameter controls the stress-ratio at which contractiontransitions to dilation, which is often referred to the phase transformation. A value of 0.10 producesa phase transformation angle slightly smaller than ϕcv, which is consistent with experimental data.For loose of critical states (DR < DR,cs, ξR > 0), nd is multiplied by 4. Both parameters nb and nd aredefined different for loose of critical states to avoid underestimation of the peak friction angle.

5. Constant volume friction angle,ϕ′cv.

Default value is 33 degrees.

6. Poisson’s ratio, ν.Default value is 0.30.

7. Critical state line parameters Q and R.Default values are 10 and 1.5 respectively.

2.6. Failure mechanism of anchored quay walls

For the purposes of this project, the failure mechanisms for quay wall structures are presented inorder to analyze the failure mechanism observed once the dynamic analysis of the port structuremodelled in the finite element method software has been performed.

Typical failure models during earthquakes depend on structural and geotechnical conditions(PIANC, 2001). The following figures present different failure mechanisms related to quay wallstructures due to earthquakes. The first two indicated with letter (a) are related to unacceptabledeformation or failure at anchor, while the second two indicated with letter (b) are related to failureat sheet-pile wall and tie-rod, and the last one indicated with letter (c) presents failure at the passivewedge.

2.7. Summary 25

Figure 2.15: Deformation/failure modes of sheet pile quay wall (PIANC, 2001)

2.7. SummaryIn this chapter the literature review is presented, which mainly focus on definition of liquefactionphenomena and how this can be avoided by analysing soil liquefaction potential. Semi-empiricalprocedures are performed based on in-situ tests while laboratory tests allow to study the soil be-haviour more in detail according to the specific test conditions. A step forward in the scale of howthis analysis has evolved over time are the constitutive soil models, which from a physical and math-ematical formulation mainly seek to emulate the behaviour of soils from their initial stress and stateconditions, the type of load and specific restrictions.

The most important part of this chapter related to the objective of this project is to identify howthe PM4Sand soil model could be defined and/or calibrated based on the available soil information,as this can be composed by in-situ field tests or cyclic laboratory tests.

3Verification of PM4Sand Model at Soil

Element Level

3.1. Introduction

PM4Sand soil constitutive model has been developed to capture liquefaction triggering of sandsthrough the undrained cyclic response of the model by mainly determining three primary modelparameters: the apparent relative density DR, the shear modulus coefficient G0 and the contrac-tion rate parameter hpo, even though the user has access to modify more parameters if necessary(secondary model parameters). The soil model response varies with applying different cyclic stresslevels and test conditions so it has to be analysed and compared with what has been observed inpractice. For this purpose, the PM4Sand soil model implemented in the finite element methodssoftware PLAXIS 2D, is assessed at soil element level to check whether the soil model can generatesimilar responses in comparison to those observed in real laboratory tests. For this purpose, cyclicDSS tests performed on sands from the Fraser River, in Canada, are used. According to the cyclicstrength curves the PM4Sand model is first calibrated, so then the responses obtained are evaluated.After this, a parametric assessment is performed allowing to identify the influence of the differentmodel parameters on the model response. Finally, the effect of initial state conditions analysedbased on three typical site conditions: confining stresses, static shear stresses and the lateral earthpressure coefficient.

The following figure presents the verification phase procedure applied for this study:

27

28 3. Verification of PM4Sand Model at Soil Element Level

Figure 3.1: Flow chart for verification phase of PM4Sand.

The whole verification process is explained in more detail in the following sections.

3.2. Data analysis

The well-documented Fraser River sand from British Columbia, Canada, has been selected for ver-ification of the PM4Sand model. Loose and dense Fraser River sand samples were tested by cyclicDSS tests at different cyclic stress levels providing the cyclic strength curves (cyclic resistance ratio,CRR, vs number of cycles for liquefaction, Nc) which present a clear trend in a logarithmic scaleplot. Furthermore, stress-strain curves and effective stress paths at different cyclic stress levels areprovided.

The Fraser River sand has an average particle size D50 = 0.26 [mm], D10 = 0.17 [mm] and uni-formity coefficient cu = 1.6. The maximum and minimum void ratios are 0.94 and 0.62 respectively.In addition, Fraser River sand is composed by 40% quartz, quartzite, and chert, 11% feldspar, and45% unstable rock fragments and the sand grains are generally angular to sub-rounded in shape(Sriskandakumar, 2004). The following figure shows its grain size distribution whose curve is withinthe range for liquefiable soils, according to Hishihara (1985) (see Figure 3.3).

3.2. Data analysis 29

Figure 3.2: Grain size distribution of Fraser River sand (Sriskandakumar, 2004).

Figure 3.3: Grain size distribution of Fraser River sand (Sriskandakumar, 2004).

Cyclic DSS tests were applied on loose and dense sands whose samples were reconstituted by theair-pluviation method, which basically is a specimen preparation technique that is used to replicategranular structure through raining of sand in air. Loose and dense sand samples were prepared tohave relative densities equal to 40% and 80% respectively.

The loose sand was tested by means of four samples at low shear stress amplitudes (CSR = τcyc

/ σ′vc) between 0.081 and 0.15 while three dense sand samples were tested with higher shear stress

amplitudes, between 0.25 and 0.35. Loose sand tested with initial sustained static shear stress pre-sented weaker cyclic strength response whereas different case was observed for dense sand, wherethe measured cyclic strength curve was stronger as it is shown in Figure 3.4.

The exponential relationships between the cyclic resistance ratio and the number of cycles forliquefaction (CRR = a N−b

c ) based on trend lines applied for loose and dense samples with and with-out initial static shear stress, are specified in Figure 3.4.


Table 3.1: Loose and dense sand samples tested by CDSS (Sriskandakumar, 2004).

DR 40% 80%α 0,0 0,1 0,0 0,1

CSR Nc CSR Nc CSR Nc CSR Nc

0,081 17,5 0,066 15,5 0,25 46,0 0,35 330,10 6,5 0,081 3,5 0,30 20,0 0,4 18,50,12 2,5 0,10 1 0,35 8,0 0,45 8,50,15 1,0

Figure 3.4: Cyclic strength curves, Fraser River sand.

From the results presented above, it is important to mention that the loose sand sample testedwith static shear stress, with CSR = 0.1 and Nc = 0.5, it is thought to present a not trustful result be-cause defined as a number of cycles for liquefaction equal to 0.5 is difficult to understand.

3.3. Determination of Input Model ParametersOne of the main advantages of PM4Sand is the possibility of calibrating the model by only definingthree primary soil model parameters: DR, G0 and hpo, which are determined from the available soildata, while the secondary model parameters could be defined from the default values.

The relative density is specified from laboratory tests while there is no information related to dy-namic soil properties, so in this case the shear modulus coefficient can be estimated by correlation(See Equation 2.50). Regarding the contraction rate parameter, this can be defined/calibrated basedon the pore pressure ratio (ru ≈ 1) or based on a specific shear strain, in this case when γ = 3.75%.

In this current calibration of PM4Sand, only the loose sand material (DR = 40%) is going to bestudied as it is prone to liquefy. Determination of the primary soil model parameters is as follows:

• Apparent Relative Density, DR

The relative density parameter can be defined as the relative density measured in the labo-

3.4. Starting point: Assessment of CRR curves 31

ratory (DR = 40%) or, in case there were no information from laboratory, correlations can beapplied from in-situ penetration tests, as presented in section 2.5.4.

• Shear modulus coefficient, G0

This parameter is directly related to the elastic shear modulus at small-strains (G) (see equa-tion B.21). First approach to define this parameter is from shear-wave velocity measurements(Vs) according to Equation 2.48, otherwise correlations from in-situ penetration tests can beapplied (see equations 2.49 and 2.50) as in this case:

G0 = 167 ·√

46 ·D2R +2.5 = 524.4 where DR = 0.4

• Contraction rate parameter, hpo

In this case, the contraction rate parameter is calibrated according to the liquefaction condi-tion specified in laboratory tests, shear strain γ = 3.75%, for one single sample tested with aspecified cyclic stress level (CSR = 0.081). However, hpo could also be calibrated according tothe pore pressure ratio, when this values is close to one (ru ≈ 1), which represents the lique-faction onset and shear strains exceed the elastic shear strain threshold. Further explanationcan be seen in section 3.4.

Once the parameters of the model have been defined from the soil information that is available,the model is calibrated and then its response is evaluated.

3.4. Starting point: Assessment of CRR curvesIn this phase, an initial set of parameters is defined and then assessed by comparing the cyclicstrength curves (CRR vs Nc) that the soil model generates with those obtained from cyclic labo-ratory tests applied on the Fraser River sand samples, without and with application of static shearstress. For this purpose, the soil test facility provided by PLAXIS 2D is used.

3.4.1. Cyclic DSS test in PLAXIS 2DThe soil test facility in PLAXIS 2D allows to simulate different laboratory tests at soil element level.Among these, cyclic direct simple shear (CDSS) test is the one used to assess the PM4Sand model.According to cyclic laboratory tests, cyclic triaxial tests should not be applied as the PM4Sand modelhas been formulated in two dimensions. To analyse liquefaction phenomena at soil element level,the test has to be performed with undrained conditions. Furthermore, the lateral earth pressurecoefficient at rest for anisotropic conditions is defined as K0 = 1-sin(ϕcv) ∼ 0.46 (ϕcv = 33◦), while forisotropic conditions, K0 = 1.0. The initial input configuration is as follows:

• Initial vertical stress, |σ’yy| = 100 [kPa].

• Initial static stress, σxy [kPa] = 10 [kPa]. Only used for the case with sustained static shearstress.(α = τst / σ’

vc = σxy / σ’vc = 0.1).

• Stress-controlled test: shear stress amplitude, ∆σxy. This value defines the cyclic stress ratio.(CSR = τcyc / σ’

vc = ∆σxy / σ’vc).

• Number of cycles. It is the number of applied cycles in the test.


3.4.2. Cyclic strength curves (CRR vs Nc)The first set of parameters consists of relative density parameter DR = 0.40 (40%), shear modulus co-efficient G0 = 524.4, which has been defined by correlation proposed by Boulanger and Ziotopoulou(2017) (see equation 2.50) and contraction rate parameter hpo = 0.238, which has been calibratedaccording to the loose sand sample tested with cyclic stress ratio CSR = 0.081, measuring 17.5 cyclesto reach shear strain equal to 3.75%, without sustained static shear stress (α = 0) (see Table 3.1). Thecontraction rate parameter should be calibrated based on any sample tested if PM4Sand model isable to reproduce liquefaction condition at different cyclic stress ratio levels using one single set ofparameters. This leads to the first verification of the model.

Figure 3.5: CRR curve without sustained static shear stress using first set of parameters.

Figure 3.6: CRR curve with sustained static shear stress using first set of parameters.

3.4. Starting point: Assessment of CRR curves 33

Figures above present cyclic resistance ratio curves (CRR vs Nc) generated using PM4Sand modelfor the case without and with initial static shear stress, as well as the stress-strain curve, stress pathand generation of excess pore water pressure by means of the pore pressure ratio, ru, using the afore-mentioned set of parameters. As presented, PM4Sand model generates steeper ’CRR vs Nc’ curvesthan the referential one obtained from laboratory for the case without initial static shear stress. Thismeans that even though the model can be calibrated to satisfy a specific liquefaction condition (γliq

= 3.75%), PM4Sand is not able to reproduce the same liquefaction condition at different cyclic stresslevels, overestimating the cyclic shear resistance at higher cyclic stress levels and underestimatingthe cyclic shear resistance at lower cyclic stress levels. According to Boulanger and Ziotopoulou(2017), the expression used for the dilatancy D (See equation B.34) would define the slope of therelationship between CRR and the number of uniform loading cycles.

Furthermore, with initial static shear stress (α = 0.1) the PM4Sand model presented a strongerresponse than the one from laboratory (curve displayed more to the right) what differs from whathas been observed in practice. Generally, loose sands present weaker ’CRR vs Nc’ curves with initialstatic shear stresses unlike the dense sands, as shown in Figure 3.4.

Up to this point, based on the set of parameters selected and in comparison with the laboratorytest results from Fraser River sand, the PM4Sand model is not able to reproduce well approximatedcyclic strength curves at different cyclic stress levels and also is not able to generate reasonable re-sponse when applying initial static shear stress. The following figure aims to present the comparisonbetween the undrained cyclic response obtained from the laboratory tests and the one generated byusing PM4Sand with the aforementioned set of parameters. It is worth to mention that laboratorydata has been provided by Makra (2013).

Figure 3.7: Stress-strain relationship, PM4Sand model response versus cyclic laboratory data.


Figure 3.8: Stress path, PM4Sand model response versus cyclic laboratory data.

Figure 3.9: Generation of excess pore pressures, PM4Sand model response versus cyclic laboratory data.

The PM4Sand model has been run with 18 cycles, whose responses are presented in the figureabove. From the results, the pore pressure ratio ru is close to 1.0 with 16 cycles while the shear strainis equal to 3.75% with 17.5 cycles. Between the cycle 15 and 16, the shear strains exceed the elas-tic shear strain threshold and it starts a progressive increment at the same time that ru increasesfrom around 70% to a constant range between higher than 85% and less than 100% approximately(this difference is related to the cyclic stress ratio applied on the test). This behaviour represents’cyclic mobility’ definition, where the mean pore pressure does not change during the final load cy-cles but shear strains continue evolving. Some experiences show that the increase in pore pressuresper cycle is usually strong at the beginning due to relatively large contraction during the first cycles

3.5. Parametric assessment of primary model parameters 35

and it is also large at the end due to the relatively large pore pressure and consequent large rela-tive effective shear stress amplitude, 4τ/σ

′vc, what also causes a significant increase in shear strain

amplitude and a reduction in the (apparent) shear stiffness (De Groot et al., 2006).

During dilation, strain hardening is identified, which is regulated by the plastic modulus Kp

as this regulates the evolution of the back-stress ratio, dα. In addition during dilation, the fabric-dilatancy tensor z evolves decreasing this way the strain-hardening level.

Consequently and related to the generation of excess pore pressures, the stress path from thereal laboratory test presents the effect of the large contraction at the beginning of the test whereasPM4Sand response presents a more restrained decrease of the effective vertical stress. During thefollowing cycles, densification of the soil is observed where much less rearrangement of grains oc-curs in compared to the first loading cycle. Significant plastic deformation occurs with each cycle ifthe peak shear stress is close to the failure line (De Groot et al., 2006), at that point a considerabledegradation of the stiffness and the strength can be identified.

From the results presented above, the soil model provides similar behaviours with respect to theshear-strain relationship, the stress-path and the generation of excess pore pressures. A more ap-proximated shear-strain response would be obtained by the PM4Sand model if the hpo-parameterwere calibrated at pore pressure ratio ru ≈ 1, which is when shear strains overpass the shear-strainthreshold. From this point, larger shear strains evolve. The stress-path generated by the PM4Sandmodel presents a more restrained decrease of the effective vertical stress during the first cycle whatleads to a slower generation of excess pore pressures, and it does not present increment of the effec-tive vertical stress during unloading at any moment, which differs from the laboratory results.

Up to this point, it is necessary to check if it possible to decrease the slope of the ’CRR vs Nc’curves using different set of parameters, and also to check if ’CRR vs Nc’ curves with initial staticshear stress generated by the PM4Sand model can be better approximated to the referential curve.Regarding the stress-strain relation, the stress-path and the generation of excess pore pressure gen-erated by PM4Sand, they present reasonable consistent behaviours even though some differenceswith respect to the original behaviours are observed. From this, a parametric assessment is goingto be performed to analyse the influence of the main soil model parameters on the soil model re-sponses and by doing this, verifying if it is possible to generate better approximated ’CRR vs Nc’curves. Moreover, the influence of these parameters can be also analysed based on the stress-strainrelation, the stress-path and the generation of excess pore pressures.

3.5. Parametric assessment of primary model parameters

3.5.1. Assessment of the apparent relative density, DR

Four new set of parameters have been defined in order to assess the influence of the apparent rela-tive density on the ’CRR vs Nc’ curves. Two of them present variation of the relative density param-eter without recalibration of hpo while the other two have been recalibrated to satisfy the previousliquefaction condition: shear strain for liquefactionγ = 3.75% applying cyclic stress ratio CSR = 0.081with 17.5 cycles without initial static shear stress (α = 0). For all cases the shear modulus coefficientis kept constant (G0 = 524.4).

Table 3.2: Set of parameters to assess the influence of the apparent relative density, DR

Parameter I II III IV VDR 0,4 0,3 0,3 0,5 0,5G0 524,4 524,4 524,4 524,4 524,4hpo 0,238 0,238 0,68 0,238 0,07


Figure 3.10: ’CRR vs Nc’ curves for different apparent relative density DR, without initial static shear stress.

Figure 3.11: ’CRR vs Nc’ curves for different apparent relative density DR, with initial static shear stress.

From the results presented above, modifying the DR-parameter without recalibration of hpo

moves the ’CRR vs Nc’. The ’CRR vs Nc’ curve for looser material (DR = 0.3) goes more to the left(weaker cyclic shear resistance, yellow line) while denser material (DR = 0.5) moves the ’CRR vs Nc’more to the right (stronger cyclic shear resistance, dark red line). With recalibration of hpo and de-creasing the DR-value, the ’CRR vs Nc’ curve gets a flatter slope (green line) while increasing theDR-value, the slope is even more steeper (purple line) than the original one.

The responses observed above are because the apparent relative density defines initial bound-ing and dilatancy surfaces of the model by means of the relative state parameter index (ξR). Thelooser the soil material, the faster the bounding surface reaches the critical surface at the samecyclic loading conditions, in which plastic deformation evolves with no variation of the mean effec-tive stress and at that point significant excess pore pressure has been already generated leading to


lower effective shear strength left.

On the other hand, for the case with sustained static shear stress, none of the defined sets ofparameters presented well approximated ’CRR vs Nc’ curves in comparison to those obtained fromlaboratory.

The following figures present the stress-strain relation and the stress-path curve using two setsof parameters, both of them with recalibration of hpo to identify the evolution during shearing untilthe target shear strain and the critical state line are reached. The generation of excess pore pressuresis presented for all sets of parameters. Results obtained without recalibration of the contraction rateparameter are avoided as its clear that with DR = 30%, liquefaction is reached with lower number ofcycles and with DR = 50%, the sample will not reach liquefaction.

Figure 3.12: Stress-strain relation, DR = 30%, with recalibration of hpo = 0.68.

Figure 3.13: Stress-path , DR = 30%, with recalibration of hpo = 0.68.


Figure 3.14: Stress-strain relation, DR = 50%, with recalibration of hpo = 0.07.

Figure 3.15: Stress-path, DR = 50%, with recalibration of hpo = 0.07.

In the figure above, the contraction rate parameter hpo was recalibrated using the same liquefac-tion condition as before, for combinations with DR equal to 30% and 50% (combinations III and V).From this, recalibration of the model using lower DR-value led to a higher hpo-value and more cycleswere involved inside the shear strain threshold, while the opposite occurs when using a higher DR-value with a lower hpo-value. In the latter case, the critical state line is reached with a lower numberof cycles. The number of cycles inside the shear strain threshold are related with the number ofcycles during densification phase of the material. Finally, using lower DR-value PM4Sand presentsa more approximated stress-strain relationship, as it is shown in Figure 3.12.


Figure 3.16: Generation of excess pore pressure at different apparent relative density DR.

The figure above allows to see that when the pore pressure ratio is close to one, the critical stateline in the stress path has been reached. Furthermore, the apparent relative density has a signif-icant influence on the evolution of the excess pore water pressure. Without recalibration of hpo

looser sands generates excess pore pressure faster as it will also reach critical state earlier. Using alower relative density parameter will define a lower value for the bulk modulus K through the elasticshear modulus G and its stress ratio effects (See equation B.21), that finally restricts the incrementof volumetric elastic strains, hence the generation of excess pore pressure. From this, pore pressurebuild up is faster (lower number of cycles for liquefaction) in looser sands.

3.5.2. Assessment of the Shear modulus coefficient, G0

Four new set of parameters have been defined in order to assess the influence of the shear moduluscoefficient G0 on the ’CRR vs Nc’ curves without applying initial sustained static shear stress. In thisphase, DR-parameter is kept constant while G0 is assessed with an arbitrarily lower and higher value.The lower value has been set with half of the value used in the first combination (G0 = 524.4/2 =262.2) while a higher value has been set as the first G0-value multiplied by 1.5 (G0 = 786.6). Similarlyto the evaluation previously conducted, two sets of parameters have been defined, one withoutrecalibrating hpo and other with recalibration on hpo to reach liquefaction according to previouscondition: shear strain γliq = 3.75% reached with cyclic stress ratio CSR = 0.081 and 17.5 cycles,without initial static shear stress.

Table 3.3: Set of parameters to assess shear modulus coefficient G0, loose sand.

Parameter I II III IV VDR 0,4 0,4 0,4 0,4 0,4G0 524,4 262,2 262,2 786,6 786,6hpo 0,238 0,238 0,269 0,238 0,208


Figure 3.17: CRR curves for different shear modulus coefficient G0, without initial static shear stress.

Figure 3.18: CRR curves for different shear modulus coefficient G0, with initial static shear stress.

From the results presented above and unlike the results observed in the previous assessmentof the DR-parameter, using different G0-values, with or without recalibration of hpo, does not makebig differences between the generated ’CRR vs Nc’ curves for both cases, without and with initialsustained static shear stress. In addition, when the contraction rate parameter was recalibrated,there was no significant change in its own value, which ranged from 0.208 to 0.269.

The following figures present the stress-strain relationships and the stress-path curves using setof parameters without recalibrated hpo, and the generation of excess pore pressures for all set ofparameters.


Figure 3.19: Stress-strain relation, G0 = 262.2, without recalibration of hpo.

Figure 3.20: Stress-path, G0 = 262.2, without recalibration of hpo.

Figure 3.21: Stress-strain relation, G0 = 786.6, without recalibration of hpo.


Figure 3.22: Stress-path, G0 = 786.6, without recalibration of hpo.

With respect to stress-strain and stress-path curves, it can be seen that G0 has an influence onthe shear strains increment. However, G0 has no influence on the stress-path, as both are almostthe same with totally different G0-values. From this, it is known that the shear modulus coefficienthas direct influence on the elastic shear modulus G, but also it can be seen that it has a influence onthe model at larger shear strains.

Figure 3.23: Increment of pore pressure ratio at different shear modulus coefficient G0.

The figure above shows that the shear modulus coefficient has no effect on the generation ofexcess pore pressures, opposite case with respect to the apparent relative density parameter and thecontraction rate parameter. The generation of excess pore pressures occurs because in undrainedconditions, a change of pore volume cannot occur due to high compressibility of the water betweenpores. The compressibility of the water is directly related to the bulk modulus of the soil grains, soany variation of G0 will not have influence on the generation of excess pore water pressures, as itcan been in Figure 3.23.

3.6. Parametric assessment of secondary model parameters 43

3.6. Parametric assessment of secondary model parameters

During the parametric assessment of the PM4Sand model, different secondary soil model parame-ters were tested to analyse their impact on the model response and check whether more flatter ’CRRvs Nc’ slopes can be generated. Among the secondary model parameters tested, the following hada significant influence on the CRR curves: the bounding surface parameter nb and the critical stateline parameter R. The following sections present the results of the parametric assessment.

3.6.1. Bounding surface parameter, nb

The bounding surface parameter nb it is used to define the initial bounding surface of the modeland also it defines the rate of increment with which the bounding surface approaches the criticalsurface, as it is presented in Section 2.5.4. In addition, this parameter regulates the dilatancy tensorwhich defines the volumetric plastic strains increment. From this and in a similar way as in theprevious assessments, four new set of parameters has been defined, two of them with a lower nb-value and the other two with a higher nb-value. In both cases, the contraction rate parameter hasbeen kept constant and also recalibrated as it can be seen in the following table:

Table 3.4: Set of parameters to assess bounding surface parameter nb.

Parameter I II III IV VDR 0,4 0,4 0,4 0,4 0,4G0 524,4 524,4 524,4 524,4 524,4hpo 0,238 0,238 0,22 0,238 0,225nb 0,5 0,2 0,2 0,7 0,7R 1,5 1,5 1,5 1,5 1,5

Figure 3.24: CRR curves using different bounding surface parameter nb, without initial static shear stress.


Figure 3.25: CRR curves using different bounding surface parameter nb, with initial static shear stress.

From the results presented above, using a lower nb-parameter generates gentler ’CRR vs Nc’curves. However, when applying initial static shear stress (α = 0.1) there is no effect on the generated’CRR vs Nc’ curves and using all the different sets of parameters, once again all responses clearlydiffered from the referential curve.

Figure 3.26: Stress-strain relation, nb = 0.2, with recalibration of hpo = 0.22.


Figure 3.27: Stress-path, nb = 0.2, with recalibration of hpo = 0.22.

The set of parameters with better and more approximated response in comparison to those ob-tained from laboratory, was the one with nb = 0.2, which also presented very similar stress-straincurve than those from laboratory. The generation of excess pore pressure with respect to the analy-sis of this model parameter is presented in the following assessment.

3.6.2. Critical state line parameter, R

In the critical state line proposed by Bolton (1986), there are two coefficients that were defined toset the position and curvature of the curve based on tests and experiments, R and Q. During theparametric assessment, while variation of the parameter Q did not present significant impact on’CRR vs Nc’ curves, the parameter R did present impact on the ’CRR vs Nc’ curves as it can be seenin the following figures. Similar to the previous assessments, the parameter R was tested by meansof four new set of parameters, with a lower and a higher R-value and with and without recalibrationof hpo.

Table 3.5: Set of parameters to assess critical state line parameter R.

Parameter I II III IV VDR 0,4 0,4 0,4 0,4 0,4G0 524,4 524,4 524,4 524,4 524,4hpo 0,238 0,238 0,1 0,238 0,52nb 0,5 0,5 0,5 0,5 0,5R 1,5 1 1 2 2


Figure 3.28: CRR curves using different critical state line parameter R, without initial static shear stress.

Figure 3.29: CRR curves using different critical state line parameter R, with initial static shear stress.

From the results presented above, the influence of the parameter R on the ’CRR vs Nc’ curves issimilar than the influence of the apparent relative density DR as the ’CRR vs Nc’ curve is moved inboth cases. Applying higher R-value moves the ’CRR vs Nc’ curves more to the left (weaker cyclicshear resistance), while with recalibration of hpo a flatter ’CRR vs Nc’ curve is generated. However, itcan be seen that once again it was not possible to reproduce approximated ’CRR vs Nc’ curves whenapplying initial static shear stress.

The critical state line parameter R has a direct influence on the relative state parameter ξR. In-creasing R-value leads to a reduction of the ξR-value, making the model to reach the critical stateearlier (see Figure B.1).

The following figure presents the stress-strain relation and the stress-path produced by the PM4Sandmodel using a higher critical state line parameter R with recalibration of hpo to satisfy the previousliquefaction condition: shear strain γ = 3.75% with CSR = 0.081 and 17.5 cycles, without applyinginitial sustained static shear stress.


Figure 3.30: Stress-strain relation, R = 2, with recalibration of hpo = 0.52.

Figure 3.31: Stress-path, R = 2, with recalibration of hpo = 0.52.

As a higher R-value leads to a smaller ξR-value and a higher recalibrated hpo-value has to bedefined to satisfy the aforementioned liquefaction condition, whose stress-strain relation and thestress-path are presented in the figure above. Even though the parameter R has a similar influencethan the apparent relative density on the model response, the parameter R plays a key role by onlycomputing the state parameter index ξR while DR plays important role in mostly all phases accord-ing to the model formulation. The following figure shows the generation of excess pore pressuresusing set of parameters with lower nb-value and higher R-value, as doing this provided flatter ’CRRvs Nc’ curves.


Figure 3.32: Development of pore pressure ratio using lower bounding surface parameter nb and highercritical state line parameter R.

In the figure above, the influence of the critical state line parameter R and the bounding surfaceparameter nb can be seen based on set of parameters without recalibration of hpo. From this, in-creasing the R-value results of a steeper/faster generation of excess pore pressures (dark red line)while decreasing nb delays it (yellow line). Even though the bounding surface parameter has a sim-ilar role than the critical state line parameter R according to the relative state parameter ξR, nb isalso involved in more phases of the model, such as the evolution of the plastic modulus Kp and thedilatancy D.

3.6.3. Assessment of final set of parameters.

The following sets of parameters have been selected because they presented a better response whencomparing the liquefaction resistance curves (CRR vs Nc) with those from the laboratory. Conse-quently, the responses from these set of parameters are compared to this way conclude what wouldbe the best combination, and they are presented in Table 3.6. The last two sets of parameters aredefined as a combination in which the nb-parameter is decreased and the R-parameter is increased.

Table 3.6: Final sets of parameters.

Parameter I II III IV V VIDR 0,4 0,3 0,4 0,4 0,4 30G0 524,4 524,4 524,4 524,4 524,4 524,4hpo 0,238 0,68 0,22 0,52 0,451 1,29nb 0,5 0,5 0,2 0,5 0,2 0,2R 1,5 1,5 1,5 2 2 2


Figure 3.33: ’CRR vs Nc’ curves using final set of parameters

Figure 3.34: ’CRR vs Nc’ curves using final set of parameters

From the ’CRR vs Nc’ curves generated and presented in the figure above, the two sets of param-eters that showed a better liquefaction strength curves more similar than those from the laboratorywere when the nb-parameter is defined with a lower value (combination II, green line) and whenboth the DR-parameter and the nb-parameter were defined with lower values (combination VI, pur-ple line). In these two combinations, the role of the bounding surface parameter nb stands out.However, it is worth to mention that in none of the cases it was possible to reproduce approximated’CRR vs Nc’ curves when static shear stress is applied.

The following figure presents generation of excess pore pressures using all final set of parame-ters.


Figure 3.35: Generation of excess pore pressures using final set of parameters.

From the results presented above, although all the combinations applied presented similar re-sponses between them, it is considered that the best response is the one whose pore pressure ratiois close to one with around 17.5 cycles, what also leads to a better stress-strain response. From this,once again decreasing the bounding surface parameter nb results of better responses of the model(green and purple lines).

3.7. Initial state condition effects

The seismic deformation analysis of a civil engineering structure may need to account for strataor zones of sand ranging from very loose to dense states, under a wide range of confining stresses,initial static shear stresses, drainage conditions, and loading conditions. The engineering effort issignificantly reduced if the constitutive model utilized can reasonably approximate the predictedstress-strain behaviours under all these different conditions (Boulanger and Ziotopoulou, 2017).

3.7.1. Effect of confining stress, Kσ

As confining stresses increase, it has been observed in practice that the cyclic shear resistance of thesoil decreases. This response is well captured by the PM4Sand model as it can be appreciated in thefigure below, in which a defined soil type was tested at different confining stress levels.

3.7. Initial state condition effects 51

Figure 3.36: Correction factor for confining stress, Kσ

The following figure aims to compare the effect of confining stresses by means of curves pro-posed by Idriss and Boulanger (2003), while the correction factor for confining stresses determinedby the PM4Sand model is defined according to the following formula:

Kσ = C RRσ6=1[atm]

C RRσ=1[atm](3.1)

Figure 3.37: Correction factor for confining stress, Kσ

All combinations presented similar responses in comparison to the empirical relation proposedby Idriss and Boulanger. For confining stresses below 1 [atm], which can be related to soils close tothe surface, the PM4Sand model overestimates the effect of confining stresses resulting in strongercyclic shear resistances. The opposite occurs at higher confining stresses where PM4Sand generallypresents an underestimation of this effect. According to Parra (2016), the PM4Sand model has been


formulated to produce greater dependence of cyclic resistance ratio on consolidation stress than isobserved in experimental data.

3.7.2. Effect of initial static shear stress, Kα

The effect of the initial static shear stress on the response of the PM4Sand model is evaluated bycomparison with empirical relations proposed by Idriss & Boulanger (2008) (see equation 2.23). Inthe following figure, the aforementioned relations for sands with relative densities 30% and 40%are presented and also the PM4Sand response using different sets of parameters while consideringinitial static shear stress. These curves are generated based on 15 cycles to reach shear strain γ =3.75%. The correction factor Kα obtained by the PM4Sand model is determined according to thefollowing formula:

Kα = C RRα6=0

C RRα=0(3.2)

where CRRα 6=0 corresponds to the cyclic resistance ratio considering static shear stress andCRRα=0 is the cyclic strength ratio without static shear stress. Furthermore, the correction factorKα for Fraser River sand samples was defined according to exponential relationships from the ’CRRvs Nc’ curves with and without initial static shear stress at 15 cycles (see figure 3.4). Withα = 0.1, thecorrection factor Kα as follows:

Kα = C RRα6=0, Nc=15

C RRα=0, Nc=15= 0.0927 ·15−0.12

0.1484 ·15−0.213 = 0.067

0.083= 0.804

Figure 3.38: Correction factor for sustained static shear stress, Kα

First of all, as it was previously mentioned none of the set of parameters used for the case whenapplying initial static shear stress (α = 0.1) presented well approximated ’CRR vs Nc’ curves with re-spect to those from laboratory, even though they all presented slight tendency to reproduced weaker

3.7. Initial state condition effects 53

cyclic shear resistances. In addition, it can be seen that Fraser River sand samples presented evenlower correction factor than the curves proposed by Idriss & Boulanger. As the factorα increases, thePM4Sand model responses with a similar decrease of the correction factor. This response has beenalready reported by Boulanger and Ziotopoulou (2017) as it can be seen in the Figure 3.39. However,it is important to mention that this correction factor is still under discussion due to the wide rangeof Kα-values proposed so more research should be carried out to get deeper insight about this effect.

Figure 3.39: PM4Sand model response at different confining stresses and static shear stresses (Boulangerand Ziotopoulou, 2017)

In the presence of initial sustained shear stress, no complete liquefaction is reached if the av-erage relative shear stress is sufficiently large and the relative shear stress amplitude is sufficientlysmall, unless the sand is very loose. Instead equilibrium with constant average pore pressure isreached after sufficient cycles. The equilibrium point in the stress path is laying at the intersectionof the average shear stress and the phase transformation line. This equilibrium refers to the meanpore pressure keeps constant during the final cycles while shear strains continue, what is called’cyclic mobility’ (De Groot, et al. 2006).

3.7.3. Effect of lateral earth pressure coefficient at rest, K0

The lateral earth pressure coefficient (K0) is the ratio between the horizontal stress and the verticalstress of the soil at rest. Usually it is defined according to Jaky’s formula as follows:

K0 = 1− sin(ϕ

)(3.3)

The following figure presents the PM4Sand model response at different lateral earth pressure co-efficient at rest, K0, which defines the relation between the horizontal and vertical principal stresses,according to the following expression:

K0 =σhor i zont al

σver t i cal


Figure 3.40: Model response at different initial earth lateral earth pressure coefficients

From the results presented in the figure above, the PM4Sand model presents a reasonable re-sponse as increasing the K0-value leads to higher cyclic shear resistance. This response can be anal-ysed and compared with the empirical relation proposed by Ishihara (1977), which states that theanisotropic cyclic resistance of the soil is directly proportional to the the isotropic cyclic resistanceand the lateral earth pressure coefficient at rest, according to the following expression:

C RRK0 6=1 = 1+2K0

3·C RRK0=1

In the following figure, the final set of parameters are evaluated in order to compare the relationproposed by Ishihara (1977) with the relation obtained from PM4Sand. The theoretical curve (blackline) was generated by calculating CRRK0=1 with 15 cycles using first set of parameters (DR = 0.4, G0 =524.4 and hpo = 0.238). The following CRRK0 6=1 were obtained by using the relation presented above.Curves generated by final set of parameters defined were obtained by calculating CRRK0 6=1 one byone at different K0-value. Results are presented in the following figure.

3.8. Summary and Conclusions 55

Figure 3.41: Relation between cyclic resistance ratio and lateral earth pressure coefficients

Lower and higher values for K0 were defined as 0.29 and 3.39 respectively, as they would repre-sent the active and passive lateral earth pressure coefficients (consideringϕ = 33◦), according to thefollowing formulas:

Ka ≈ 1− sin(ϕ)

1+ sin(ϕ)(3.4)

Kp ≈ 1+ sin(ϕ)

1− sin(ϕ)(3.5)

All combinations for PM4Sand presented almost the same response, but with certain deviationin comparison to the previous theoretical relation. With K0-value higher than one, PM4Sand pre-sented lower anisotropic cyclic shear resistance while with lower K0-value, higher shear resistancewas observed.

3.8. Summary and Conclusions1. In the original document of the PM4Sand soil model (Boulanger and Ziotopoulou, 2017) thecalibration of the soil model is performed by only modifying the contraction rate parameter, hpo.By following this procedure, is the PM4Sand able to match the empirical liquefaction strengthcurves and capture the soil behaviour from various laboratory cyclic DSS tests? If not, could theexpected liquefaction strength curves and the stress paths be obtained by modifying and/or cali-brating other parameter(s)?

By following the calibration methodology proposed by Boulanger and Ziotopoulou (2017), thePM4Sand model produces steeper liquefaction strength curves in comparison to those obtainedfrom the laboratory tests applied on the Fraser River sand samples. Once the model is calibratedwith respect to a specific cyclic shear stress level, the model overestimates the liquefaction resis-tance at higher cyclic shear stress levels and underestimates at lower levels. This response has beenalready observed by Parra (2016), who states the PM4Sand model over-predicted the steepness ofthe CRR curves, also the dependence of the CRR on overburden stress and the rate of strain hard-ening in monotonic undrained loading. Furthermore, it was stated the PM4Sand produces cyclicstrength curves whose slopes are consistent with typical CRR curves for silica sands in the litera-ture, but may not match the slopes for specific sands whose effect increases with increasing relative


density and it is reduced with increasing confinement stress levels (Boulanger and Ziotopoulou,2017).

As the referential liquefaction resistance curve was not accurately reproduced, a parametric as-sessment was performed to analyse the influence of the model parameters on the model responsesand also to verify if flatter CRR curves could be generated. Results showed decreasing the nb-parameter or increasing the critical state line R-parameter, the responses of the model presentedless steep ’CRR vs Nc’ slopes, and therefore better approximation even though this would affectother responses, what was also observed by Parra (2016) when the nb-parameter is decreased.

2. What is the influence of the input parameters on the PM4Sand model response?

The parametric assessment was applied on the three primary parameters (DR, G0 and hpo) andon two secondary parameters (nb and R). The DR-parameter controls the dilatancy and the stress-strain relationship. Reducing the DR-parameter, the soil model responses with flatter ’CRR vs Nc’curves if the hpo-parameter is recalibrated. A looser sand presents a weaker liquefaction strengthbehaviour as the relative state parameter ξR will reach the critical state earlier.

The shear modulus coefficient G0 affects the shear strains increment not having impact on theliquefaction strength curves as it does not affect the generation of excess pore pressures produced bythe PM4Sand model. This is because in PLAXIS 2D, the compressibility of the water between poresis directly related to the compressibility of the soil grains. The compressibility of the soil grains isdefined by the bulk modulus K by means of the shear modulus G (See equation B.24). Generally, theshear modulus coefficient defines the elastic shear modulus at small strains, however, it has beenobserved that modifying G0 has a clear influence on the shear strains increment after liquefactionis triggered, even though this parameter is associated to small-strains range.

The contraction rate parameter hpo defines and regulates the dilatancy D during contraction,limiting the plastic volumetric strains increment and allowing to calibrate the soil model for a spe-cific liquefaction condition. Increasing the hpo-parameter limits the dilative response of the modelproducing less plastic volumetric strains increment, making the soil material stronger against cyclicloads in undrained conditions.

The bounding surface parameter nb, defines the rate at which the relative state parameter ξR ap-proaches the critical state condition. When the nb-parameter is decreased the liquefaction strengthcurves produced by the PM4Sand model present flatter slopes hence they result in a better approx-imation in comparison to those from real laboratory tests. Decreasing the nb-parameter would re-duce the overestimation and underestimation of the soil material at different cyclic stress levels.

Finally, the critical state line parameter R mainly defines the position of the critical state line(See Figure 2.13). Increasing the R-parameter reduces the distance between the current state (ini-tial relative density) and the relative density at critical state. Doing this results in flatter ’CRR vs Nc’slopes.

3. Does the PM4Sand model approximately reproduce the results observed from the laboratorycyclic DSS test applied on the Fraser River sands at different initial state and stress conditions?

When considering the initial static shear stress effect, the response of the model was comparedwith an estimated Kα-value from the laboratory test results and also compared with empirical cor-relations proposed by Idriss and Boulanger (2003). As the static shear stress increases the PM4Sandmodel responses with a decrease of the corrector factor, which is in agreement with what has beenobserved on loose sands. However, the magnitude of this correction factor differs from the labora-tory results and also from the empirical correlations. The static shear stress effects are still underdiscussion because a wide range of Kα-values have been proposed, indicating a lack of convergence


and a need for continued research (Youd and Idriss, 2001).Regarding confining stress level effects, the PM4Sand model presented good results in compar-

ison with the empirical correlations proposed by Boulanger (2003), specially when the boundingsurface parameter nb is decreased. The soil model slightly overestimates the confining stress effectsfor confining stresses below 1 [atm] and slightly underestimate this effect at higher confining stresslevels. The PM4Sand model recreates the dependence of the CRR on vertical effective stresses (Kσ)and horizontal static shear stresses (Kα) that are consistent with the Idriss and Boulanger (2008) andBoulanger (2003) relationships (see Figure 3.39), respectively, but again these may not match with aspecific sand.

Finally, regarding the effect of lateral earth pressure coefficient at rest, the PM4Sand model re-sponse is in agreement with was proposed by Ishihara (1977). When the soil is subjected to a pas-sive behaviour (K0>1) it presents higher liquefaction resistance, and the opposite occurs when it issubjected to an active behaviour. This represents an improvement in comparison to the UBCSandmodel, which independently from the initial K0-value, the model always tends to an isotropic stressstate, leading to larger resistance against liquefaction for K0 6= 1.0 (Van Elsacker, 2016).

4. What are the limitations of the PM4Sand model identified in this phase?

From the results and responses obtained in this phase, the following limitations can be men-tioned. First of all, as the model is formulated in two dimensions it should not be used for 3D-problems. For engineering problems whose response are also subjected to a third out-of-plane di-rection and a correction is applied to modify the 3D-problem to a 2D-problem, the model couldoverestimate the loading and displacements induced by liquefaction-lateral spreading (Gutierrezand Ledezma, 2017).

Second, the model shows a limited ability to modify the slope of the generated liquefactionstrength curves. When calibrating the model to reproduce CRR curves obtained from laboratorytests, PM4Sand generates steeper CRR curves what leads to overestimate the cyclic strength of thesoil at higher cyclic stress levels and underestimate this at lower levels. By modifying the testedmodel parameters it was observed that CRR curves can be moved to obtain weaker or strongerundrained cyclic resistance. Despite the fact that decreasing the bounding surface parameter nb

results in less steeper CRR curves, these were not flat enough to accurately reproduce the referentialCRR curves.

Third, the model did not reproduce weaker liquefaction resistance for the loose sand when ap-plying initial sustained static shear stress. Generally, it has been observed that loose sands haveweaker cyclic strength behaviour with sustained static shear stress, but the response was almostthe same as when not applying static shear stress. However, as this effect has not yet been fullyunderstood, further study of this phenomenon is still needed to determine the causes that may beinvolved.

Fourth, as the model is formulated in 2D, their parameters can only be calibrated through thecyclic DSS test option in PLAXIS 2D, which simulates a specific condition in the field, direct simpleshear. In reality and according to the different engineering problems, different initial state condi-tions can be involved apart from direct simple shear, such as extension and compression. So, thishas to be taken into account when using the PM4Sand model for geotechnical engineering prob-lems.

4Validation of the PM4Sand Model for

Design Purposes

4.1. IntroductionThe current chapter consists of analysing the PM4Sand model performance by making use of thisin a large-scaled case study modelled in PLAXIS 2D, where there has been failure and/or collapsedue to soil liquefaction caused by the action of a high intensity earthquake. Thus, the soil layersclose to the surface that liquefied because of this event are defined with the PM4Sand model gettinginsight on the onset of liquefaction allowing also to compare the documented displacements withthe obtained by the finite element software.

The case study used for this purpose is the well-documented Akita Port in Japan, which expe-rienced serious damage by the Nihonkai-Chubu Earthquake (1983) whose magnitude was 7.7 (Iaiand Kameoka, 1993). The consequences were reported based on two quay walls located in the sameport, in which one quay wall suffered considerable damage while the other did not. These two quaywalls slightly differ with respect to their structural configuration but they presented different resis-tance of the upper soil layers based on the SPT tests performed at the sites.

In the previous chapter, the PM4Sand soil model response was analysed at soil element level us-ing simulated controlled laboratory tests. In contrast to the previous phase, when applying the soilmodel in a case study the ground state and stress conditions could vary considerably from one pointto another. From this it is very important to verify if the soil model is able to reproduce properly soilbehaviour through all different initial state and stress conditions.

The modelling of the quay walls is carried out from the acceleration-time record, soil site investi-gation and the characteristics of the structures that compose the quay walls. The acceleration-timerecord is applied as a dynamic load on the engineering bedrock which is propagated through thesoil layers to the surface. The frequency domain of this input signal allows to determine frequen-cies that dominate the design, the dynamic properties of soils and also the mesh generation of themodel. The soil site investigation consists of representative standard penetration tests, grain-sizedistributions and a shear-wave velocity profile that lead to determine the soil stratigraphy, to esti-mate its properties and parameters for the soil models applied as well as to calibrate the PM4Sandsoil model for the liquefiable soil layers.

The dynamic analysis consists of simulating the earthquake mentioned for both port structuresand thus analysing the onset of liquefaction as well as comparing the displacements obtained withthose observed in the field. The dynamic analysis consists of different assessments in order to com-pare the response of the models mainly with respect to three points: dynamic analysis with andwithout consolidation, modeling with free-field boundary conditions and with tied-degree of free-dom, and response of the model when decreasing the bounding surface parameter.

59

60 4. Validation of the PM4Sand Model for Design Purposes

The flow chart for this chapter is presented below:

Figure 4.1: Flow chart, validation of the PM4Sand Model for designing quay walls in PLAXIS 2D

Finally, assessment of the post-liquefaction effect using the PM4Sand model is performed.

The following sections present the modelling procedure of the quay walls in the finite elementprogram in greater detail based on the aforementioned available information and the decisions andassumptions considered by the engineer generating the modelling.

4.2. Case Study: Akita Port and Nihonkai-Chubu Earthquake (1983)In May of 1983, the Nihonkai-Chubu Earthquake of magnitude Mw 7.7 hit the northern part of Japan,claiming the lives of at least 100 people and causing serious damage to one specific quay wall at AkitaPort located about 100 km from the epicenter. What makes this case study interesting is that closeto the damaged retaining structure (Ohama No.2 Wharf), it was one wharf (Ohama No.1 Wharf)that did not suffer any damage in comparison to the aforementioned one. From this, although bothquay walls were basically located in the same port and therefore located at a similar distance fromthe epicenter of the earthquake, the construction method of one of the two structures led to itscollapse.

The location of the Akita Port in Japan, the epicenter of the telluric event and the location of thequay wall structures are shown in the figure below:

4.2. Case Study: Akita Port and Nihonkai-Chubu Earthquake (1983) 61

Figure 4.2: Fault of the 1983 Nihonkai-Chubu Earthquake and liquefaction at Akita Port (Iai and Kameoka,1993)

Quay Wall Structures Ohama No.1 and No.2

The two port structures are presented in the Figure 4.3. They have the same seabed depth (-10[m]) and also they were constructed with the same type of sheet piles, type ’FSP-VIL’ manufacturedin Japan, even though they were installed until different depths, -15 [m] and -20.5 [m] respectively.Sheet-pile walls are connected to anchor piles by a high tensile strength steel tie rod which is con-sidered to have the same properties in the both cases but with different lengths, 18 [m] in the wharfOhama No.1 and 20 [m] in the Ohama No.2 Wharf. However, the anchor piles differ in both casesas in the Ohama No.1 Wharf, there is single row of steel anchor piles separated every 2 [m] whilein the Ohama No.2 Wharf, two rows of steel pipe piles are connected at their tops by a concreteelement. However, it is assumed the biggest difference between these two quay walls is the con-struction method, as the quay wall that collapsed was built through backfilling method being thebackfill soil layer that liquefied.

In addition, the deformations in the sheet-pile wall and in the anchors at five different crosssections of the Ohama No.2 wharf are presented. From this, deformations were registered accordingto horizontal and vertical displacements at the top of the sheet-pile as well as displacements at thetop and inclination of the anchors. At the both ends of the structure, displacements were morerestricted than the cross sections in the middle. In the middle there are two sections (A and B).Section A has a greater horizontal displacement at the top of the sheet pile wall in the cross section


’d’ of about 2 [m] and a vertical displacement of almost 0.5 [m]. Section B has a maximum horizontaldisplacement at the top of the sheet-pile wall of about 0.5 [m] and a vertical displacement of almost1.5 [m].

Below, a scheme of the typical cross sections of both port structures and the deformations of theOhama No.2 Wharf are presented:

Figure 4.3: Cross sections of the quay walls at wharves Ohama No.1 (left) andOhama No.2 (right) (Iai and Kameoka, 1993)

Figure 4.4: Deformation along the face line at Ohama No. 2 Wharf,a) cross sections, b) distribution along the face line (Iai and Kameoka, 1993)

4.2. Case Study: Akita Port and Nihonkai-Chubu Earthquake (1983) 63

Acceleration Strong Motion

About 2.5 km south east of the wharves (see Figure 4.2) a strong motion accelerograph in thestation recorded the earthquake motion of the Nihonkai-Chubu Earthquake. The following figureshows the maximum acceleration components of the input ground motion recorded, in which themaximum horizontal acceleration component corresponds to 0.235g, East-direction.

Figure 4.5: Recorded earthquake motion at Akita Port (Iai and Kameoka, 1993)

The ’GAL’ is a unit of acceleration that is defined as 1 [cm/s2]. The soil deposit at the accelero-graph site did not liquefy during the earthquake so the earthquake motion recovered from the ac-celerograph was not affected by soil liquefaction. It is important to mention that the input signalmust be corrected and filtered if necessary, a process which is presented in Section 4.3.1.

Soil site investigation

Soil site investigation of the case study is presented in the Appendix C.

First of all, to generate the models of the two port structures in the finite element program, therepresentative local stratigraphy for these two structures must be defined. Thus, standard penetra-tion tests (SPT) are interpreted to define the thicknesses and depths of the different soil layers aswell as their properties. The grain size distribution allows to determine the content of fines at cer-tain depths and finally, the shear-wave velocity profile allows to estimate the elastic shear modulus.The following chapter presents in detail the use of this information and therefore, the stratigraphyat both port structures. However, it should be noted that the decisions and assumptions made forthis phase are according to the engineer who generates the models, and may vary according to thecriteria of interpretation of the site investigation. In addition, the exactly location of these penetra-tion tests are unknown. In the Section C.1 of the Appendix, the SPT’s, grain-size distribution and theshear-wave velocity measurements are presented.


4.3. Modelling in PLAXIS 2D4.3.1. Input ground motionThe acceleration-time history used for this analysis has been provided from previous thesis projectcarried out by Van Elsäcker (2016) which corresponds to the signal presented in Figure 4.5. However,the signal had to be previously evaluated in order to decide whether can be applied in the model asit is. From this a signal processing is applied which consists of the following steps:

1. The acceleration signal could be cut to take into account only the relevant strong motion du-ration. In this case, the acceleration signal has a duration equal to 50 [seconds] and it is notgoing to be cut.

2. The acceleration-time record is generally composed by different principal directions, in whichthe strongest one is defined by the peak ground acceleration (PGA) and/or the earthquakeintensity (i.e. by means of the Arias energy).

3. Apply filtering and baseline correction to the predominant acceleration-time signal. Oncethe accele-ration-time signal is displayed, it is recommended to check final velocity valuesand displacements. As the final acceleration-time is zero, the velocity at the end of the signalshould also be zero. When the velocity at the end of the signal is not zero, this could be becausenoise or disturbance of the wave propagation. As this was the case, a bandpass Butterworthfilter was applied whose lower frequency was set as 0.35 [Hz] and the upper one was set as 20[Hz]. The Butterworth filter is a type of signal processing filter designed to have a frequencyresponse as flat as possible in the passband. The filtering procedure mainly depends on thefrequency content.

4. It is well-known that any correction or filtering process applied on the original signal wouldcause changes, specially related to the PGA. For this reason, the new signal was scaled to thedesired PGA.

5. The acceleration-time signal that is going to be applied on the model corresponds to the sig-nal at the bedrock level. In case this signal is captured at the surface level, a de-convolutionprocess should be carried out as this

would take into account how the signal varies due to the dynamic properties from all soil lay-ers. In this case, as the acceleration-time signal corresponds to the signal at the (engineering)bedrock level, there is no need to apply a de-convolution.

6. Once the signal has been corrected, this is applied in the finite element model at the engineer-ing bedrock as a dynamic displacement which generates incoming waves that propagates tothe surface. In addition, the Fourier Transform is applied on this signal to obtain the fre-quency domain and this way identify the fundamental frequencies to limit low and high fre-quencies that can be avoided for this analysis and also to define Rayleigh damping coefficientsfor the soil layers and structures (See Section 4.3.7).

In PLAXIS, the acceleration time record is defined by multipliers that specify the signal scale. Inthe following figure, the accelerations record filtered, corrected and scaled to 0.235g correspondingto the Nihonkai-Chubu Earthquake is presented.

4.3. Modelling in PLAXIS 2D 65

Figure 4.6: Filtered and corrected recorded earthquake motion at Akita Port using software SeismoSignal,scaled at 0235g.

Figure 4.7: Input motion signal in the frequency domain.

When applying the Fourier transform to the acceleration signal, the result presents the predom-inant frequencies of the signal which allows to determine between which ranges the signal shouldbe filtered. As it ca be seen from the figure above, the maximum Fourier amplitude is at frequency5.74 [Hz], which is used to determine the Rayleigh damping coefficients and are presented in theSection 4.3.7.

4.3.2. Interpretation of soil stratigraphyThe SPT’s performed at the two wharves would provide the necessary information to estimate thesoil stratigraphy, which is characterized by the thickness of the soil layers and also by the soil re-sistance properties estimated by means of the SPT N-values (See Appendix C.1). In the followingtables, the description of the soil layers for both wharves is presented. The resistance index deter-mined from the SPT test allows to estimate the relative density of the soil layers according to theEquation 2.46. From the relative density parameter, it is possible to estimate the internal frictionangle and the unit weight according to the correlations proposed by Brinkgreve et. al (2010), asfollows:

ϕ′ = 28+12.5 · DR

100

[◦] (4.1)

γunsat = 15+4 · DR

100

[kN/

m3

](4.2)


γsat = 19+1.6 · DR

100

[kN/

m3

](4.3)

Table 4.1: Interpretation soil stratigraphy Ohama No.1 Wharf

Layer ztop zbottom Description Density (N1)60 DR ϕ’ γunsat γsat c[m] [m] [%] [°] [kN/m3] [kN/m3] [kPa]

1 0 -7 Clean sand Medium dense 30 70 37 18 20 02 -7 -8,5 Very silty sand Medium dense 25 65 36 19 21 03 -8,5 -13 Slighty silty sand Medium dense 25 70 37 19 21 04 -13 -20,5 Slighty silty sand Very dense 35 80 38 19 21 05 -20,5 -21,6 Very sandy clay Very stiff 17 - 27 18 20 56 -21,6 -30 Slighty silty sand Medium dense 25 70 37 19 21 0

Table 4.2: Interpretation soil stratigraphy Ohama No.2 Wharf

Layer ztop zbottom Description Density (N1)60 DR ϕ’ γunsat γsat c[m] [m] [%] [°] [kN/m3] [kN/m3] [kPa]

1 0 -12 Clean backfill sand Loose 8 40 33 17 19 02 -12 -14,5 Slightly silty sand Loose 12 50 34 19 21 03 -14,5 -20 Slightly silty sand Dense 30 75 37 19 21 04 -20 -22,5 Very sandy clay Very stiff 29 - 27 18 20 55 -22,5 -25,5 Slightly silty sand Medium dense 22 70 37 19 21 06 -25,5 -30 Slightly silty sand Dense 30 75 37 19 21 0

When comparing the SPT results from the two wharves, it can be seen the SPT-values for the up-per soil layers in the Ohama No.1 are higher than those at the Ohama No.2. In the next subsectionthe influence of these results are analysed by means of the soil liquefaction potential assessment.

Coefficients of Permeability

According to the grain-size distribution, the coefficient of permeability for all soil layers are pre-sented below:

Table 4.3: Coefficients of permeability based on grain-size distribution, Ohama No.2 Wharf.

Grain size distribution

Layer Soil material < 2µm 2 - 50µm 50µm - 2mmPermeability coefficient,

k [m/s]1 Loose sand 0 0 100 1,16E-062 Loose sand 0 0 100 1,16E-063 Dense sand 10 15 75 3,04E-064 Very stiff clay 10 26 64 3,41E-105 Medium dense sand 20 52 28 1,94E-076 Dense sand 20 52 28 1,94E-07

4.3.3. Soil Liquefaction PotentialAs a first assessment, soil liquefaction potential is determined at both quay wall structures based onthe SPT results. According to the results presented in the Appendix D the quay wall that collapsed,Ohama No.2 Wharf, did not have enough liquefaction resistance at its upper soil layers unlike thequay wall that did not presented any damage, Ohama No.1 Wharf. The perform this analysis, the


cyclic stress ratio CSR is determined according to the semi-empirical procedure proposed by Seedand Idriss (1971) (Equation 2.5) and the cyclic resistance ratio CRR is determined based on the SPTresults (Equation 2.9) considering correction factors due to the earthquake magnitude, fine con-tent and confining stress levels. By applying this assessment, it is possible to compare the resultsobtained for the two quay wall structures modelled in PLAXIS 2D and verify this way the onset ofliquefaction.

The results of the soil liquefaction potential analysis for the first 15 meters depth for the twoquay wall structures is presented below.

Table 4.4: Results of the Soil Liquefaction Potential Analysis.

Ohama No.1 Wharf Ohama No.2 Wharf

Soil LayerDepth

[m]CSR CRR FS Soil Layer

Depth[m]

CSR CRR FS

1. Clean sand 1 0,19 0,51 2,6 1. Backfill sand 1 0,18 0,09 0,52 0,24 0,51 2,1 2 0,23 0,09 0,43 0,26 0,51 1,9 3 0,25 0,10 0,44 0,27 0,51 1,9 4 0,27 0,11 0,45 0,28 0,51 1,8 5 0,27 0,12 0,46 0,28 0,51 1,8 6 0,27 0,13 0,57 0,28 0,39 1,4 7 0,28 0,13 0,5

2. Very silty sand 8 0,28 0,48 1,7 8 0,28 0,12 0,4

2. Slightly silty sand 9 0,27 0,47 1,7 9 0,27 0,13 0,510 0,27 0,46 1,7 10 0,27 0,16 0,611 0,26 0,45 1,7 11 0,27 0,13 0,5

12 0,26 0,38 1,5 3. Slightly silty sand 12 0,27 0,13 0,513 0,26 0,43 1,7 13 0,26 0,16 0,6

3. Slightly silty sand 14 0,25 0,41 1,6 14 0,26 0,44 1,7

15 0,25 0,39 1,6 4. Slightly silty sand 15 0,25 0,43 1,7...

...

4.3.4. Parameter Selection - Hardening Soil Small ModelTh Hardening Soil Small model is used in all soil layers during the static analysis. During the dy-namic analysis, it is used for the not liquefiable soil layers as the liquefiable soil layers are definedusing the PM4Sand model. Below are the expressions used to define the parameters of the Hard-ening Soil Small model, which depend mainly on the relative density of the soil. The followingexpressions were proposed by Brinkgreve et al. (2010) as first estimation to define the soil modelparameters.

• Secant stiffness from triaxial test at reference pressure, Eref50

E r e f50 ≈ DR ·60 [MPa] (4.4)

• Tangent stiffness from oedometer test at reference pressure, Erefoed

E r e f50 = E r e f

oed ≈ DR ·60 [MPa] (4.5)


• Unloading/reloading stiffness, Erefur

Er e fur ≈ 2 ·E r e f

oed (4.6)

• Reference shear stiffness at small strains, Gref0

Gr e f0 = 60+68 · DR

100[MPa] (4.7)

• Shear strain at which G has reduced to 72.2%, γ0.7

γ0.7 =(2− DR

100

)·10−4 [−] (4.8)

• Rate of stress-level dependency in stiffness behaviour, m

m = 0.7− DR

320[−] (4.9)

• Horizontal over vertical stress ratio in primary 1D compression, Krefnc

K0,nc = 1− sin(ϕ′) [−] (4.10)

• Failure ratio, Rf

R f = 1− DR

800[−] (4.11)

The following tables show the soil model parameters using Hardening Soil Small model in thesoil layers of the two models in PLAXIS 2D:

Table 4.5: Parameter selection Hardening Soil Small model, Ohama No.1 Wharf

Layer Depth DR E50,ref Eoed,ref Eur,ref m K0,nc Rf G0,ref γ0,7

[m] [%] [kPa] [kPa] [kPa] [-] [-] [-] [kPa] [-]1 4,25 70 42000 42000 84000 0,481 0,402 0,91 107600 0,000132 7,8 65 39000 39000 78000 0,497 0,410 0,92 104200 0,0001353 10,5 70 42000 42000 84000 0,481 0,402 0,91 107600 0,000134 17 80 48000 48000 96000 0,450 0,384 0,90 114400 0,000125 21 - 20000 20000 40000 0,550 0,546 0,92 75000 0,0001656 24,5 70 42000 42000 84000 0,481 0,402 0,91 107600 0,00013

Table 4.6: Parameter selection Hardening Soil Small model, Ohama No.2 Wharf

Layer Depth DR E50,ref Eoed,ref Eur,ref m K0,nc Rf G0,ref γ0,7

[m] [%] [kPa] [kPa] [kPa] [-] [-] [-] [kPa] [-]1 5,5 40 24000 24000 48000 0,575 0,455 0,950 87200 0,000162 12,2 50 30000 30000 60000 0,544 0,437 0,938 94000 0,000153 16 75 45000 45000 90000 0,466 0,393 0,906 111000 0,000134 20 - 20000 20000 40000 0,550 0,546 0,920 75000 0,000175 23 70 42000 42000 84000 0,481 0,402 0,913 107600 0,000136 26 75 45000 45000 90000 0,466 0,393 0,906 111000 0,00013


4.3.5. Calibration of the PM4Sand for upper layersThe PM4Sand soil model is applied on the upper soil layers that are supposed to be prone to liquefy.In the case of the Ohama No. 1 Wharf, even though the two upper soil layer are dense enough to beconsidered not liquefiable layers, there are defined with PM4Sand model for the dynamic analysisto get some insight about the model response. The following explains how the primary parametersof the PM4Sand model are determined.

Apparent Relative Density, DR

The apparent relative density DR is defined according to SPT (N1)60-values, which are the same asthose used to determine model parameters using the Hardening Soil Small model.

Shear Modulus Coefficient, G0

The shear modulus coefficient G0 can be determined by different approaches. The first one canbe carried out by applying the correlation proposed by Boulanger & Ziotopoulou (2017) (See Equa-tion 2.50). A second option is to determine the G0 from the shear modulus at very small strains G0

defined for the Hardening Soil Small model, as follows:

G0,HS =Gr e f0 ·

(σ′

3 sin(ϕ

)pr e f sin

(ϕ

))m

(4.12)

so,

G0,P M4Sand = G0,HS

p A

√p A

p ′ (4.13)

However, it is important to mention that even though the G0-parameter has the same meaningin the Hardening Soil Small model and in the PM4Sand model, both models would provide totallydifferent responses as they have different formulation. And the third approach to define this param-eter is according to the shear-wave velocity profile provided from the case study, as follows:

G0,P M4Sand =(ρ ·Vs

2)

p A

√p A

p ′ (4.14)

The following table shows the values obtained for the G0-parameter according to the differentcriteria previously explained.

Table 4.7: Shear modulus coefficient G0 defined from different approaches.


Shear Modulus Coefficient G0 [-] Shear Modulus Coefficient G0 [-]

DR [%] CorrelationB&Z (2017)

From HSsmodel

From SW-V DR [%] CorrelationB&Z (2017)

From HSsmodel

From SW-V

70 836 842 599 40 524 619 53065 782 798 980 50 625 712 802

From the results obtained, it can be seen that there is some similarity between the first two cri-teria since both are determined from the relative density of the soil, unlike the third criterion whichdepends entirely on the shear-wave velocity profile (See Section C.1 in the Appendix). Finally, it hasbeen decided to use the third option since it is considered to be the most reliable information todefine the shear modulus for the surface soil layers.


Contraction Rate Parameter, hpo

The last primary parameter that has to be defined and calibrated is the contraction rate parameter,hpo. For this purpose, different correction factors to standardised the cyclic resistance of the soil,based on the SPT measurements, have to be identified and calculated. First, the normalized (N1)60-value equivalent to 60% hammer efficiency has to be determined based on correction factors (SeeSection C.1 in the Appendix). Consequently, the representative fine content percent for each soillayer based on the grain-size distribution allows to determine the (N1)60-value for clean sands. Inaddition, it has to be considered the correction factors due to the magnitude of the earthquake(MSF) and the confining stress effects, by means of the factor Kσ. In this case, the static shear stresseffects is not considered. In the following table the cyclic resistance ratios CRR to calibrate the hpo-parameter for the upper layers (two for each wharf) are presented.

Table 4.8: Cyclic resistance ratio CRR from SPT to calibrate hpo-parameter

Ohama No.1 WharfDR [%] (N1)60 FC [%] (N1)60,cs CRR7,5 MSF Kσ CRRM ,σ

70 22,5 0 22,5 0,242 0,94 1,10 0,24965 19,4 21 24,9 0,287 0,94 1,04 0,280

Ohama No.2 WharfDR [%] (N1)60 FC [%] (N1)60,cs CRR7,5 MSF Kσ CRRM ,σ

40 7,4 0 7,4 0,100 0,94 1,06 0,10050 11,5 17 15,2 0,158 0,94 0,99 0,146

In addition, different sets of parameters used to define the liquefiable soils with the PM4Sandmodel are presented in the following table, in a similar way to what was done in the previous chapterof this project. This was due to the fact that the displacements obtained when applying a first cali-bration of the model, were much smaller than those reported in the case study, so it was proceededto reduce for different scenarios, the nb-parameter and also the G0-parameter.

Table 4.9: Set of parameters using PM4Sand model on the upper soil layers

Wharf Calibration DR [%] G0 [-] nb [-] hpo [-]

Ohama No.1 1.170 599 0,5 0,8565 980 0,5 2,7

Ohama No.22.1

40 530 0,5 0,5850 802 0,5 1,00

2.240 180 0,2 0,4950 270 0,2 0,85

4.3.6. Structural elements of the quay wallThe structural properties defined for the two quay wall models are mainly according from the previ-ous thesis project carried by Van Elsacker (2016), in which these two quay walls were also modelledbut instead of evaluating the performance of the PM4Sand model, the UBCSand model was eval-uated for designing purposes. In addition, the structural properties of the sheet-pile wall and thesteel tie-rod were the same for the two quay walls while the properties related to the anchor pileswere different.

Sheet-pile wall


Table 4.10: Steel sheet-pile wall properties.

Sheet-pile wall propertiesUnit weight γ 7,5 t/m3

Section area A 306 cm2/mElastic modulus W 3820 cm3/mSecond moment of inertia I 86000 cm4/mProfile width w 500 mmProfile height h 225 mm

Young modulus E 2,10E+08 kN/m2

Flexural rigidity EI 1,81E+05 kN m2/mNormal stiffness EA 6,43E+06 kN/m

Anchor piles

The different configuration of the anchor piles for the two wharves makes changes on the struc-tural properties of these elements, which are modelled as plate elements in PLAXIS 2D.

Table 4.11: Steel anchor piles properties.

Anchor piles propertiesOhama No.1 Ohama No.2

Pile diameter D 750 550 mmPile thickness t 10 12 mmSection area A 23250 150100 mm2/mElastic modulus W 4,24E+06 1,98E+07 mm3/mSecond moment of inertia I 1,59E+09 5,43E+09 mm4/m

Steel Class S355 S355Young modulus E 2,10E+08 2,10E+08 kN/m2

Flexural rigidity EI 3,34E+05 1,14E+06 kN/m2

Normal stiffness EA 4,88E+06 4,26E+06 kN/m

Steel tie-rod

Table 4.12: High strength steel tie rod properties.

High strength steel tie rod propertiesOhama No.1 Ohama No.2

Young modulus E 2,10E+08 2,10E+08 kN/m2

Section area A 1,19E-03 1,19E-03 m2

Length L 20 18 mNormal stiffness EA 2,50E+05 2,50E+05 kN

4.3.7. Geometry and Mesh GenerationThe dimensions of the model depend on the size of the port structure to be modelled, where themost important thing is that the dimensions of the model are large enough not to affect the resultscaused by the boundary conditions, but at the same time determined in an optimal way so as not


to oversize the model as this would consume more calculation time than necessary. Furthermore, ithas been assumed the bedrock level is at depth -30m.

Mesh Generation and Time Step

The maximum element size 4lmax is defined according to Lysmer and Kuhlmeyer (1969), toguarantee a proper propagation of the shear wave in the finite element method. On the other hand,a too small element size would lead to longer computation time so the engineer who is modellingshould define an average element size as optimal as possible.

∆l max ≤vs,l ayer

5 · fmax(4.15)

where vs,layer is the shear wave velocity of the specific soil layer and fmax is the maximum fre-quency component of the input signal considered for the analysis, in this case fmax = 12 [Hz]. Thelatter can be determined by from the Fourier Transform applied on the acceleration-time historyrecord (See Figure 4.7). The critical time step has to be limited according to the following expressionto prevent that waves travel through more than one element within one dynamic time step:

∆t ≤ ∆l min

vs,l ayer(4.16)

Table 4.13: Average element size and critical step time, Ohama No.1 Wharf

Layer Soil typeVs1

[m/s]fmax

[Hz]Max element

size [m]Average element

size [m]Criticaltime [s]

1 Medium dense sand 160 12 1,67 1,35 0,0082 Medium dense sand 202 12 3,36 1,50 0,0073 Medium dense sand 186 12 3,11 1,50 0,0084 Very dense sand 251 12 4,18 1,50 0,0065 Very stiff clay 173 12 2,88 1,50 0,0096 Medium dense sand 165 12 2,75 2,00 0,012

Table 4.14: Average element size and critical step time, Ohama No.2 Wharf

Layer Soil typeVs1

[m/s]fmax

[Hz]Max element

size [m]Average element

size [m]Criticaltime [s]

1 Loose sand 150 12 1,56 1,50 0,0102 Loose sand 183 12 1,91 1,50 0,0083 Dense sand 170 12 1,77 1,10 0,0064 Very stiff clay 244 12 2,54 1,25 0,0055 Medium dense sand 170 12 1,78 1,50 0,0096 Dense sand 165 12 1,72 1,50 0,009

Rayleigh Damping

Calculation type used in this phase is ’Dynamic with consolidation’ in which drainage is con-trolled by permeability of soil material. The basic equation for the dynamic behaviour is as follows:

Mu +C u +K u = F (4.17)


Matrix C represents the material damping of the materials which is caused by friction or irre-versible deformations (plastic or viscosity). In finite element formulations, C is often formulatedas a function of the mass and stiffness matrices (Rayleigh damping) (Zienkiewicz & Taylor, 1991;Hugues, 1987), according to the following formula:

C =αR M +βR K (4.18)

When the contribution of the mass M is dominant more of the low frequencies are damped (i.e.αR approximately 10 times higher than βR ). when the Rayleigh coefficient αR is clearly higher thanβR, (i.e. αR = 10−2 and βR) = 10−3. In the opposite, high-frequencies will be damped if the differencewas inverted.

To determine the Rayleigh damping coefficients for the soil layers, two target frequencies haveto be defined according to Hudson et al. (1994):

f1 =vs,av

4H(4.19)

f2 ≈f f und

f1(4.20)

The fundamental frequency of the signal ffund is the frequency with the maximum Fourier am-plitude from the Fourier Transform applied on the corrected acceleration time-history signal. Thiswas obtained from the 1D column site response analysis in PLAXIS applying the acceleration signalat the bottom of the model, hence at the bedrock level. In this case, ffund = 5.74 [Hz] (See Figure 4.7).

ωi = 2π fi (4.21)

αR = 2ξω1ω2

ω1+ω2(4.22)

βR = 2ξ

ω1+ω2(4.23)

whereωi is the mode natural circular frequency, ξ the assumed material damping ratio for all thestructures’s vibrations modes necessary to ensure reasonable values for all modal damping ratiosprominent in structural response.

The following tables present the calculation related to the targte frequencies 1 for the two quaywall structures and the respective Rayleigh damping coefficients:

Table 4.15: Shear-wave velocities per soil layer, Ohama No.1 Wharf

Layer Depth [m] Soil type γ [kN/m3] σ’v [kPa] Vs [m/s] Vs1 [m/s] Vs1 · zi

1 4,25 Medium dense sand 19 44 130 160 6802 7,8 Medium dense sand 20 80 190 202 7163 10,5 Medium dense sand 21 109 190 186 5034 17 Very dense sand 21 181 290 251 16315 21 Very stiff clay 20 221 210 173 6916 25 Medium dense sand 21 265 210 165 661


Table 4.16: Shear-wave velocities per soil layer, Ohama No.2 Wharf

Layer Depth [m] Soil type γ [kN/m3] σ’v [kPa] Vs [m/s] Vs1 [m/s] Vs1 · zi

1 5,5 Loose sand 19 57 130 150 8252 12,2 Loose sand 19 118 190 183 12273 16 Dense sand 21 159 190 170 6454 20 Very stiff clay 21 203 290 244 9755 23 Medium dense sand 20 233 210 170 5116 26 Dense sand 21 266 210 165 495

Table 4.17: Target frequency 1 for the two wharves

Description Ohama No.1 Wharf Ohama No.2 WharfGlobal soil thickness H [m] 33 33Average shear wave velocity vs,av [m/s] 195,2 179,9Target frequency 1 f1 [Hz] 1,48 1,36

Table 4.18: Rayleigh damping coefficients.

DescriptionOhama No. 1

WharfOhama No. 2

WharfQuay WallStructures

Target damping ξ [%] 1,25 1,25 3Frequency target 1 f1 [Hz] 1,48 1,36 0,5Frequency target 2 f2 [Hz] 3 5 10Rayleigh damping coefficients αR 0,1556 0,1682 0,1795

βR 8,88E-04 6,25E-04 9,09E-04

Figure 4.8: Damping ratio defined for soils and structures at the two wharves.

The Rayleigh damping coefficients are defined based on the formulas already presented above.The target frequencies in combination with the target damping define frequencies that are goingto be over damped, hence, they are mainly absorbed by the soil layers. In contrast, frequencies


between this selected ranged are received with smaller damping values allowing these frequenciesto be taken into account in the dynamic analysis.

Frequencies greater than frequency target f2 are over damped. Using a lower frequency target f2

makes a higher range of frequencies to be over damped. On the contrary, when using a higher f2-value, higher frequencies are taken into account having bigger influence on the analysis as they arenot over damped like in the previous case. From what can be observed, higher horizontal deforma-tions are obtained when increasing the frequency range between target frequencies f1 and f2, whatis in line with the amplification of the acceleration signal which is also higher as the wave travels tothe surface.

Dynamic Boundary conditions

The lateral vertical boundaries in the models should be sufficiently far away from the region ofinterest, to avoid distortions in the computed results due to possible reflections even though viscousboundaries are applied for this. In practice, it is recommended to put the boundaries far away fromthe area or engineering structure that is analysed.

In this project all models have been developed applying two kind of boundaries, free-field andtied-degree of freedom boundaries, which are explained as follows:

• Free-field boundary conditionsA free-field element consists of a one-dimensional element coupled to the main grid by vis-cous dashpots and they have exactly the same material behaviour as the attached soil elementin the main domain does. These are used when the dynamic source is applied as a boundarycondition, such an earthquake motion. To avoid reflection of waves at the boundaries, viscousboundaries absorb the increment of stress caused by dynamic loads. In addition, they can beused to absorb waves reflected from internal structures, from boundary between two layersor from internal sources. These are used for problems where the dynamic source is inside themesh (PLAXIS, 2008b).

• Tied degrees of freedomIntroduced by Zienkiewicz et al (1988), nodes on the same elevation on the lateral sides ofthe finite element mesh are tied together whose condition works perfectly when performing1D wave propagation but it is unable to absorb the waves reflected from structures and/orexcavations within the model. To apply this to a finite element method model the number ofnodes at both lateral boundaries should be the same, so generally a mirror is applied on theoriginal design model.

• Complaint base boundary is modelled by applying an interface at the bottom of the model,which also work with viscous dampers.

4.3.8. Static AnalysisThe function of the static analysis previous the dynamic analysis performed considered the earth-quake, is to take into account the initial stresses prior the dynamic shaking. A better representationof the construction process would lead to a the better representation of the initial stresses and statesin the soil layers. However, this process is only an estimation and the dynamic analysis is the im-portant stage to consider since it is the PM4Sand soil model that must be evaluated. During theconstruction stages (static analysis) all soil layers are defined by the Hardening Soil Small model.


4.4. Dynamic Analysis of the Quay Wall StructuresThe dynamic analysis is performed in two different ways: without and with consolidation, being thelatter recently implemented in the last version of PLAXIS 2D (2018). In addition, the case study wasmodelled using two different lateral boundary conditions: free-field and tied-degree of freedom.

When applying dynamic analysis without consolidation, as it has been carried out in PLAXISbefore its latest version, drained soil clusters at the lateral boundaries have to be applied to pre-vent complete loss of support at the boundaries. However, it is possible now to perform dynamicanalysis with consolidation avoiding the use of these lateral drained soil clusters and defining thecoefficient of permeability for each soil layer that regulates drainage flow rate, hence excess porepressure dissipation.

Below the schemes corresponding to the quay walls modelled in PLAXIS 2D are presented:

Figure 4.9: Ohama No.2 Wharf model using free-field boundary conditions,dynamic analysis with consolidation

Figure 4.10: Lateral drained soil clusters, Ohama No.2 Wharf model, dynamic analysis without consolidation

Figure 4.11: Ohama No.1 Wharf model using free-field boundary conditions,dynamic analysis with consolidation

Figure 4.12: Ohama No.2 Wharf model using tied-degree of freedom boundary conditions,dynamic analysis with consolidation

4.5. Analysis of the Results 77

4.5. Analysis of the ResultsThis section presents the results obtained from the different models applied for the two quay walls.The dynamic analysis was performed with and without considering consolidation. Model were gen-erated with two different lateral boundaries: free-field and tied-degree of freedom. Finally, a newcalibration of the PM4Sand model was also applied.

4.5.1. Generation of Excess Pore Pressures

Dynamic analysis with consolidation, Ohama No.2 Wharf with free-field boundaries

After 4 seconds an excess pore pressure increase begins to be observed on the surface behindthe quay wall structure (from the anchor pile to the right) and at the seabed the level just next tothe sheet-pile wall leading to a decrease in the effective vertical stresses. In the following 3 seconds,an increase in excess pore pressures propagates from the surface downwards and also it starts todevelop in the soil next to the sheet-pile wall. At the end of the first 10 seconds, excess pore pressuresbegin to develop between the sheet-pile wall and the anchor piles and the vertical effective stressin the backfill behind the anchor piles it has decreased more than half of its initial strength. Localzones corresponding to the seabed level next to the sheet-pile wall and the top of the anchor pilespresent higher excess pore pressures (ru ∼ 1). In the following 6 seconds (from 10 to 16 seconds),most of the backfill sand behind the anchor piles have reached liquefaction condition (ru =1). Afterthis, a rapid increase of excess pore pressure is observed in the backfill sand located between thetwo vertical structures. From 20 seconds, the onset of liquefaction is also reached in the soil layerbelow the backfill sand close to the interface between these. From 30 seconds, most of the wholebackfill soil has liquefied and this condition remains constant until the end of the earthquake (at50 seconds). The following figures present the increment of excess pore pressure highlighting thesignificant increase from 15 seconds onwards.

Figure 4.13: Pore pressure ratio at 5s and 10s, Ohama No.2 Wharf, dynamic analysis with consolidation




Figure 4.16: Pore pressure ratio at 25s, Ohama No.2 Wharf, dynamic analysis with consolidation

Apart from the generation of excess pore pressures analysis, the model shows that the failuremechanism is totally related to soil liquefaction generated in the upper backfill soil layer and ispropagated next to the interface between this soil layer and the one below.

Dynamic analysis without consolidation, Ohama No.2 Wharf with free-field boundaries

In a similar way in comparison to the dynamic analysis with consolidation, in the first 5 seconds,the generation of excess pore pressures starts to happen in the backfill sand close to the surface andspecially at the top of the anchor piles. However, this phenomenon is not observed yet in the soilmaterial close to the sheet-pile wall. In this dynamic analysis, the generation of excess pore pres-sures occurs in a more localized way as there is no drainage, thus local initial state and stress condi-tions define soil liquefaction response which in this case is less uniformly spread out in comparisonwith applying dynamic analysis with consolidation.


Figure 4.17: Pore pressure ratio at 17s, Ohama No.2 Wharf, dynamic analysis without consolidation

Dynamic analysis with consolidation, Ohama No.2 Wharf with tied-degree of freedom bound-aries

When applying tied-degree of freedom lateral boundaries the results were very similar thanthose obtained in the model with free-field lateral boundaries. Small variation was observed ac-cording to the generation of excess pore pressures in the backfill soil layer whose reason could besue to differences in the numerical calculation. However, as both presented very similar results, andalso according to the displacements obtained (see Subsection 4.5.2) this assessment was useful tovalidate the generation and performance of both models for the same quay wall structure.

Applying tied-degree of freedom lateral boundaries leads to higher computation time in com-parison to applying the free-field boundaries. In this case, larger displacements were obtained inthe mirror-quay wall (right side) because of the direction of the dynamic displacement applied onthe bottom boundary, but the comparison was made according to the same quay walls.

Figure 4.18: Pore pressure ratio at 30s, Ohama No.2 Wharf, dynamic analysis without consolidation usingtied-degree of freedom boundary condition


Dynamic analysis with consolidation, Ohama No.1 Wharf, free-field boundaries

The generation of excess pore pressures in the upper ’liquefiable’ soil layers were not enough toliquefy, as it can be seen in Figure 4.19, which is in agreement with what happened in reality as thisquay wall did not collapsed.

Figure 4.19: Pore pressure ratio at the end of the earthquake, Ohama No.1 Wharf, dynamic analysis withconsolidation

4.5.2. Displacements at the top of the sheet-pile wallThe following figure presents the development of the horizontal displacements obtained at the topof the sheet-pile wall, for the two quay wall structures, applying different boundary conditions andalso with different calibration of the PM4Sand model for the upper liquefiable soil layers.

Figure 4.20: Deformations of the quay wall structure, Ohama No.2 Wharf

Five different cases were modelled in order to analyse their performances and results mainly fo-cused on the onset of liquefaction and maximum displacements in the sheet-pile wall. From this, itwas observed that the minimum horizontal displacement was obtained when modelling the OhamaNo.1 Wharf as expected, which is the quay wall structure that dis not collapsed. After this, applying


dynamic analysis without consolidation provided a lower deformation trend even though it pre-sented higher deformation amplitudes. The Ohama No.2 Wharf models, using the two differentlateral boundaries, showed very similar deformation trend even though the displacement develop-ment differs in these two approaches. Finally, a different calibration of the PM4Sand model for theupper layers of the Ohama No.2 Wharf model was performed by decreasing both the nb and G0 pa-rameters, what led to higher displacements as expected according to the assessment performed inthe previous phase of this project.

Figure 4.21: Displacements at the top of the sheet-pile wall

While the higher horizontal displacements occurred at the upper zone of the liquefiable soillayer, the highest vertical deformations were captured right next to the vertical structures. As thestructures begin to deform, a release of tensions between the structure and the adjacent soil is gen-erated, thus decreasing the initial horizontal resistance which brings with it a greater vertical defor-mation of the soil mass.

4.5.3. Post-Liquefaction Effect

A final assessment consists of evaluating the post-liquefaction effect in the liquefiable soil layers inorder to compare how this effect would influence the final results. The PM4Sand model gives thepossibility to activate this effect for the moment the soil material has reached liquefaction condi-tion. In order to apply this, the input signal should be split, the first part represents the liquefactiontriggering until liquefaction condition is reached, so then the post-liquefaction effect is activated onthe soil layers previously defined with th PM4Sand model and the input signal can continue goingon.

To carry out this evaluation, three calculations are presented in the following figure. The firstone consists of applying the full signal on the model, in the second calculation the signal is cut at 20seconds and in the third calculation the signal is cut at 30 seconds.


Figure 4.22: Assessment of post-liquefaction effect by splitting the input signal

From the results obtained and presented above, it can be seen that at the moment the signal issplit, the trend of the displacements deviates. This response is stronger when the signal is dividedearlier (at 20 seconds) and occurs regardless of whether or not the post-liquefaction effect is acti-vated in the liquefied soil layer. What should happen in this case, first, by dividing the signal at 20and 30 seconds without modifying the model by applying the post liquefaction effect, the evolutionof the displacements should be the identical. Second, when applying the post liquefaction effectthe displacements should be greater due to the softening behaviour experienced by the soil.

4.5.4. Comments related to modelling process

• It was observed that most of the soil material defined with PM4Sand model reaches plasticfailure points, even though liquefaction condition was not reached.

• When performing the dynamic analysis without consolidation, for instance defining drainedlateral soil clusters, it is recommended to define them with Hardening Soil Small model in-stead of PM4Sand model to avoid big global error that could abort calculation.

• It was observed during dynamic analysis with consolidation, a huge amplification of the ac-celerations close to the structural elements. From this, it is advised to deactivate the interfacesof the structural elements in flow, so then this effect is considerably reduced leading to betterresults.

4.6. Summary and Conclusions1. It is stated that the quay wall collapsed due to soil liquefaction of the backfill layer. From this,is the PM4Sand model able to capture the onset of liquefaction in the liquefiable soil layers?

The two wharves Ohama No.1 and No.2 were modelled in PLAXIS 2D. The structure that didnot collapse in reality, did not present onset of liquefaction in its upper soil layers. Different caseoccurred when modelling the structure that collapsed, which presented onset of liquefaction in


almost the whole backfill layer. The onset of liquefaction is assessed by means of the pore pressuresratio ru . As expected, the relative density defined for the upper layers plays a key role as loose sandsare more prone to liquefy.

In addition, this result allows to identify a failure plane according to interface between the soilthat liquefied and the one that did not liquefy. In the case of the quay wall that collapsed, this failureplane visibly develops between the two upper soil layers.

2. Once the dynamic analysis of the quay wall structure in the finite element software has been per-formed, are the deformations obtained similar to those observed and registered in the case study?What would be the reason for these similarities and/or differences?

The dynamic analysis performed in the quay wall structure that collapsed, was developed throughdifferent models that differed mainly from the boundary conditions and the type of dynamic calcu-lation applied. Although different horizontal deformations developments at the top of the sheet-pilewall and at the top of the anchor piles were observed during application of the earthquake, finallyin all cases the maximum displacements obtained were much smaller than those registered in thefield.

Explanation of this can be due to different reasons. First, this could be because the sheet-pilewall did not generate the crack observed in the field in the quay wall model, so implementing ahinge in the zone where the crack occurred could considerably increase the displacements obtainedand also would have an influence on the failure mechanism of the whole structure. Second, aspreviously mentioned the PM4Sand model overestimates the cyclic resistance of the soil materialat higher cyclic shear stress levels and underestimates at lower levels. From this, it could be anoverestimation of the cyclic resistance of the backfill layer resulting in lower deformations.

From the analysis performed in the previous chapter, nb and G0 parameters were decreasedpresenting larger displacements, as it was expected. In general, models have been created based onrepresentative estimation of the soil and structural properties for a whole quay wall structures.

3. The dynamic analysis of the quay wall structure is performed using different mesh boundariesand also two dynamic calculations, one considers consolidation and the other does not. Whatwould be the most suitable dynamic analysis approach to be performed for this type of engineer-ing projects? What are the advantages and disadvantages observed?

First of all, all of them can be applied to perform a dynamic analysis. However, the possibility toperform a dynamic analysis with consolidation presents a more realistic generation of excess porepressure through the whole model, providing better results. According to the lateral boundaries, itis good enough to apply free-field boundaries as by doing this the model would take less time forthe calculation in comparison to applying tied-degree of freedom boundaries. However, the lattercould help to validate the first model by comparing similarities between obtained results.

4. Are larger displacements obtained by applying the post-liquefaction effect by means of thePM4Sand model?

Through the evaluation of the post liquefaction effect, two main things were observed: by divid-ing the earthquake signal, the trend of the displacement evolution is modified independently if thepost liquefaction effect is activated, and second, by activating the post liquefaction effect, greaterdeformations in the structure were not obtained, as would have been expected. Based on these re-sults, it is recommended to carry out further studies in this field in order to understand in greaterdepth the reason for the observed responses.

5Final Remarks and Recommendations

The PM4Sand soil model is able to successfully capture the onset of liquefaction and it can providevery similar liquefaction behaviour curves based on shear-strain relation, stress-path and genera-tion of excess pore pressures in comparison to real cyclic DSS tests once the model is calibrated ac-cording to a target cyclic shear stress level. However, it was observed the PM4Sand model responseswith steeper liquefaction resistance curves what leads to an overestimation of the cyclic resistanceof the soil at higher shear stress levels and to an underestimation of it at lower levels. From this, it issuggested to decreased the nb-parameter to reduce this effect (i.e. nb = 0.2).

In addition, an alternative calibration methodology based on the primary model parameters isproposed and could be applied as follows: Once the relative density parameter is defined by labo-ratory studies or by correlations with field tests, the contraction rate parameter can be calibratedwith respect to the pore pressure ratio being equal to the unity (ru = 1.0) instead of using a targetshear strain for liquefaction γl i q (i.e. γl i q = 3.75%). Then, shear modulus coefficient could be de-fined to obtain a target shear strain level at certain number of cycles. Doing this will ends up in abetter capturing of the generation of excess pore pressures in combination with better curves forthe shear-strain relation. However, this is still under discussion as the meaning of G0 is related tothe elastic shear modulus at small-strains.

The analysis of initial state conditions allows to project a better use of the PM4Sand model forgeotechnical engineering designs modelled in a finite element method software. From this, it is rec-ommended to define multiple layers instead of only one whole liquefiable layer in order to reducethe overestimation and underestimation of the cyclic resistance of the soil at different shear stresslevels as also the model properly captures liquefaction behaviour at different confining stresses.Moreover, it is important to previously identify the stress-path in the problem to decide whether thePM4Sand model should be calibrated based on the initial state conditions.

According to the use of the PM4Sand model for design purposes, it is concluded that the modelshould be used only for practical problems as it successfully captures the onset of liquefaction onliquefiable soil layers, but results related to structure displacements can considerably differ. In thiscase, for quay wall structures the model should not be used to determine displacements. For othergeotechnical engineering projects, such as design of embankments without structures, it would beinteresting to compare if displacements obtained in this case are more similar than those registeredwhere there is no influence of the structural properties and their configuration.

Finally, the post-liquefaction effect should be studied much more in detail as in this case onlya starting assessment has been performed. Getting better insight of this effect would give the pos-sibility to check whether larger displacements can be obtained in geotechnical problems but also,this could provide a better representation of the soil after reaching liquefaction condition.

85

Appendix

87

ACyclic Resistance Ratio from CPT

Cone penetration tests give the possibility to mainly assess two things: to determine the cyclic resis-tance ratio (CRR) at certain cone resistance measured (qc1N) by means of correlations proposed byBoulanger & Idriss (2014), and also to identify and classify soil layers by means of the soil behaviourtype (SBTn) approach proposed by Robertson (2010) Robertson and Cabal (2015).

According to Robertson and Wride (1998), the clean-sand base curve that specify the cyclic re-sistance ratio (CRR) for an earthquake magnitude equal to 7.5 is defined as follows:

Figure A.1: Cyclic resistance ratio (CRR7.5) from CPT normalised clean sand equivalent cone resistance(qc1N,cs) Robertson and Cabal (2015)

If (qc1N )cs < 50 C RR7.5 = 0.833 ·[

(qc1N )cs

1000

]+0.05 (A.1)

If 50 ≤ (qc1N )cs C RR7.5 = 93 ·[

(qc1N )cs

1000

]3

+0.08 (A.2)

where (qc1N)cs (in some literature Qtn,cs) is the clean-sand cone penetration resistance normal-ized to approximately 100 kPa, which is defined as:

89

90 A. Cyclic Resistance Ratio from CPT

(qc1N )cs = Kc ·qc1N (A.3)

where Kc is a correction factor that is a function of behaviour characteristics of the soil, ex-plained and determined by means of the behaviour type index (Ic) in the following paragraphs.

The aforementioned index Ic is determined by CPT measurements and it is used to classify thesoil a-ccording to soil behaviour type. This way, CPT test measures the cone resistance (qc) and thesleeve friction (fs) which determine the normalized friction ratio (Fr). Then, the normalized frictionratio (Fr) and the normalized cone resistance (qc1N) are used to determine the behaviour type index(Ic), as follows:

Ic =[(

3.47− log(qc1N ))2+(

1.22+ log(Fr ))2

]0.5(A.4)

qc1N =( qc −σvc

pa2

)( pa

σvc

)n

(A.5)

Fr =(

fs

qc −σvc

)·100% (A.6)

n = 0.381 · (Ic )+0.05 · (σ′vo /Pa

)−0.15; n ≤ 1.0 (A.7)

where σvo and σ′vo are the total and the effective overburden stresses respectively, Pa is a refer-

ence pre-ssure in the units as σ′vo, Pa2 is a reference pressure in the same units as qc and σvo, and

n-value is a variable stress exponent dependent on SBTn Ic and effective overburden stress.

The relation between Kc and Ic is given as it follows:

Kc = 1.0 if Ic ≤ 1.64 (A.8)

Kc = 5.581 · I 3c −0.403 · I 4

c −21.63 · I 2c +33.75 · Ic −17.88 if Ic > 1.64 (A.9)

Finally, the state parameter index (ψ) is determined by the clean-sand cone penetration resis-tance qc1N,cs and the soil type is defined by means of the Soil Behaviour Type chart proposed andupdated by Robertson (2010) by the following formula:

ψ= 0.56−0.33 · log(qc1N ,cs

)(A.10)

The Soil Behaviour Type chart is presented in the following figure, as well as description of everyzone according to the behaviour type index Ic.

91

Figure A.2: Normalized CPT Soil Behavior Type (SBTn) chart, Qt - F Robertson and Cabal (2015)

Figure A.3: Normalized CPT Soil Behavior Type (SBTn) chart, Qt - F Robertson and Cabal (2015)

Finally, cone penetration tests are used to determine the relative density parameter of the soilDR and the shear modulus coefficient G0 by applying the following correlations:

DR = 0.465 ·( qc1N

Cd q

)0.264

−1.063 with Cd q = 0.9 (A.11)

The (N1)60-value is the standard penetration resistance measured by SPT test, and this can becalculated by relative density parameter as follows:

(N1)60 =Cd · (DR )2 with Cd = 46 (A.12)

92 A. Cyclic Resistance Ratio from CPT

Figure A.4: Zones of potential liquefaction/softening based on CPT Robertson and Cabal (2015)

Normalised CPT Soil Behaviour Type (SBTn) chart, Qt - F using general large strain ’soil be-haviour’ descriptors:

CD: Coarse-grained Dilative soil - predominately drained CPTCC: Coarse-grained Contractive soil - predominately drained CPTFD: Fine-grained Dilative soil - predominately undrained CPTFC: Fine-grained Contractive soil - predominately undrained CPT

BPM4Sand Model Formulation

B.1. Critical State Soil Mechanics FrameworkCritical state of the soil refers to the state in which the soil continues to deform at constant stressand constant void ratio (Schoefield and Wroth, 1968). This concept is related to the steady state inwhich the deformation for any mass of particles continuously evolves to a constant volume, normalstress shear stress and velocity.

The PM4Sand model follows critical state soil mechanics frameworks proposed by Bolton (1986)by means of the relative state parameter index ξR which has been adapted in terms of the differencebetween the current apparent relative density DR and relative density at the critical state DR,cs, asfollows:

ξR = DR,cs −DR (B.1)

DR,cs = R

Q − ln(100 p

p A

) (B.2)

Figure B.1: Definition of the relative state parameter index and effects of varying Q and R.

93

94 B. PM4Sand Model Formulation

In Figure B.1, in the left side it can be seen the critical state line with parameters Q and R equalto 10 and 1.5 respectively, while in the right side how the critical state line variates with modifyingthese values. Parameter Q indicates the normalized level of mean effective stress p’ where the criticalstate line starts to significantly bend due to significant particle crushing (Parra, 2016). Setting thecoefficient R equal to 1.5 provides better approximation to typical results observed in direct simpleshear loading (Boulanger & Ziotopoulou, 2015). Once the critical state line is reached because ofshearing, the soil material will flow as a frictional fluid.

B.2. Bounding, Dilatancy, Critical and Yield SurfacesThe model uses bounding, dilatancy and critical surfaces according to Dafalias and Manzari (2004).The current version of the model has been simplified by removing the Lode angle dependence sofriction angles are the same for compression or extension loading. Bounding and dilatancy ratiosare related to the critical stress ratio (M) by the following formulas:

M b = M ·exp(−nb ξR

)(B.3)

M d = M ·exp(nd ξR

)(B.4)

M = 2sin(ϕcv ) (B.5)

where the model parameters nb and nd define the computation of Mb and Md with respect to M.The bounding stress ratio controls the relationship between peak friction angle and relative state.During shearing bounding and dilatancy surfaces Mb and Md will approach critical surface M at thesame time the relative state parameter index approaches the critical state line (ξR tends to zero).

The bounding surface cannot be surpassed, instead for any given stress state (q/p) there is al-ways and ’image’ stress state lying on the failure surface so the distance between the actual and the’image’ stress states can be measured (Tasiopoulou and Gerolymos, 2015). The bounding surfaceframework aims to simulate plastic deformations within the yield surface.

Dilatancy surface defines the location where transformation from contractive to dilative be-haviour occurs what represents the transformation phase state (PT). Under undrained cyclic load-ing, change in effective stress is associated with shear-induced volumetric dilative or contractivetendency of soil (Wang and Xie, 2014).

The yield surface is formulated as a small cone in the stress space with the following expression:

f =√

(r −α) : (r −α)−√

1

2pm = 0 (B.6)

where,

r =(

rxx rx y

rx y ry y

)=

( σxx −pp

σx y

pσx y

pσy y −p

p

)(B.7)

p = (1+K0)

2·σy y (B.8)

Tensor r is the deviatoric stress ratio tensor and p the mean effective stress (σyy also consideredas effective stress). The back-stress ratio tensor α determines the position of the yield surface in thedeviatoric stress ratio space and m defines the radius of the cone (m = 0.01), hence the size of theyield surface. From the equation (2.36), the yield function is defined by the distance between thedeviatoric stress levels (by means of r) and the position of the yield surface (by means of α). Then,

B.3. Fabric Effects 95

bounding and dilatancy surfaces are defined in terms of the image back-stress ratios, αb and αd , asfollows:

αb =√

1

2

[M b −m

]n (B.9)

αd =√

1

2

[M d −m

]n (B.10)

where n is the deviatoric unit normal to the yield surface defined as

n = r −α√12 m

(B.11)

Figure B.2: Yield, critical, dilatancy and bounding lines in q-p space (left) andyield, dilatancy and bounding surfaces in the ry y -rx y stress-ratio plane (right) (Boulanger and Ziotopoulou,

2015)

B.3. Fabric EffectsSoil fabric corresponds to the structure and arrangement of the grains showing inherent anisotropy.Because of cyclic shearing there is a rearrangement and/or destruction of the soil fabric. From this,fabric effects are carried out by means of the fabric-dilatancy tensor z which evolves according to dz.The fabric-dilatancy tensor considers prior straining of the model and it has been implemented tomodel effects of changes in sand fabric during plastic dilation generated as a contractive responseupon reversal of loading direction.

The evolution of z is according to the following expression:

d z =− cz

1+⟨

zcum2 zmax

−1⟩

⟨−d εpl

v

⟩D

(zmax n + z) (B.12)

where cz controls the rate of the evolution and zmax is its maximum limit. The fabric-dilatancytensor evolves with plastic deviatoric strains that occur only during dilation, so it is restricted toonly occur when (

αd −α)

: n < 0 (B.13)

The cumulative value of absolute changes of the fabric tensor z is defined as follows:


d zcum = |d z| (B.14)

The rate of evolution of the fabric-dilatancy tensor decreases with increasing values of zcum whatmakes to progressively accumulate shear strains during undrained cyclic loading avoiding this wayto lock-up into a repeating stress-strain loop.

In addition, additional memory of fabric formation history, represented by the initial fabric ten-sor zin, is included in the model to improve the ability of the model to take into account effects due tosustained static shear stresses and differences in fabric effects for various drained versus undrainedloading conditions.

Stress Reversal and Initial Back-stress Ratio Tensors

The model proposed by Dafalias and Manzari (2004) keeps track of the initial back-stress ra-tio tensor αin which allows to compute the plastic modulus Kp. From this, a reversal in loading isidentified whenever

(α−αi n) : n < 0 (B.15)

The initial back-stress ratio tensor updates at the reversal in loading direction with every cyclebecoming the current back-stress ratio for the subsequent loading. In order to overcome over stiff-ness at small load reversal, the initial back-stress ratio is subdivided into three initial stress ratios:the apparent αapp

in , true αtruein and the previous initial stress ratio αp

in. Further detail about trackingthe stress reversals can be found in Boulanger & Ziotopoulou (2015).

B.4. Elastic Part of the ModelAs it was already mentioned in the introductory part, the soil model is formulated based on evo-lution of elastic and plastic strains increments, which are composed by volumetric and deviatoricterms. From this, the deviatoric and volumetric strains increments are defined as follows:

de = deel +depl (B.16)

d εv = d εvel +d εv

pl (B.17)

where the elastic volumetric and deviatoric terms are defined as follows:

deel = d s

2G(B.18)

d εvel = d p

K(B.19)

The elastic deviatoric strain increment occurs based on the increment of the deviatoric stresstensor s and its is restricted by the elastic shear modulus G. The deviatoric stress tensor s is definedas follows:

s =σ−pI =(

sxx sx y

sx y sy y

)=

(σxx −p σx y

σx y σy y −p

);

(r = s

p

)(B.20)

The elastic shear modulus is dependent on the mean effective stress, stress ratio effects and afabric component according to the following expression:

B.5. Plastic Part of the Model 97

G =G0 p A

√p

p ACSR

(1+ zcum

zmax

1+ zcumzmax

CGD

)(B.21)

where stress ratio effects are represented by the factor CSR as follows:

CSR = 1−CSR,0

(M

M b

)mSR

(B.22)

G0 called shear modulus coefficient, controls shear modulus at small strains and it is mainlyaffected by environmental factors, while CSR,0 and mSR impose the stress ratio effects according toYu & Richard Jr. (1984). CSR,0 is defined as 0.5 and mSR as 4, which keeps the effect of stress ratio onelastic modulus small at small stress ratios, but lets the effect increase to a 60% reduction when thestress ratio is on the bounding surface (Boulanger and Ziotopoulou, 2015).

Degradation of the elastic shear modulus is represented by the fabric term and the cumulativeplastic deviatoric strain term zcum as increasing plastic shear strains makes a progressive destruc-tion of the soil structure. The parameter zmax is computed at the beginning according to the initialrelative state index ξR0:

zmax = 0.7exp(−6.1ξR0

)≤ 20 (B.23)

CGD is a factor that controls the shear modulus degradation at very large values of zcum, and it isset internally with a value of 2.0.

On the other hand, the elastic bulk modulus K is defined by means of the elastic shear modulusG and the Poisson’s ratio ν (default value ν = 0.3), as follows:

K = 2(1+ν)

3(1−2ν)G (B.24)

The fabric component in the formulation of the elastic shear modulus (see equation B.21) con-sidered as a degradation factor, it also has influence on the elastic bulk modulus K improving themodel’s ability to track the stress-strain response of liquefying sand. The elastic bulk modulus de-creases as zcum increases, reducing this way the rate of strain-hardening after phase transformationat larger shear strain levels and improves the ability to approximate the hysteretic stress-strain re-sponse of a soil as it liquefies (Boulanger and Ziotopoulou, 2015).

B.5. Plastic Part of the ModelThe increment of plastic deviatoric and volumetric strains are according to the loading index (L),the deviatoric unit normal to the yield surface n and the dilatancy D, as follows:

depl = ⟨L⟩n (B.25)

d εvpl = ⟨L⟩D (B.26)

The loading index L derived by Dafalias and Manzari (2004) is defined as follows:

L = 2Gn : de −n : r K d εv

Kp +2G −K Dn : r(B.27)

where ’<>’ are MacCauley brackets that set negative values to zero. Furthermore, the stress in-crement is calculated by means of the following formula:

dσ= 2Gde +K d εv I −⟨L⟩ (2Gn +K D I ) (B.28)


Hardening-Softening Rule and the Plastic Modulus

The evolution of the back-stress ratio tensor α that corresponds to the yield surface axis, de-pends on the loading index, the distance between the current back-stress ratio α and the boundingback-stress ratio αb, and the hardening coefficient h as follows:

dα= ⟨L⟩ 2

3h

(αb −α

)(B.29)

where h is directly related to the plastic modulus Kp through the following formula:

h = 3

2· Kp

p · (αb −α): n

(B.30)

The plastic modulus Kp defined for this model depends on stress reversal, initial back-stressratio tensors and fabric effects and is calculated based on the following expression:

Kp =G ho

√(αb −α)

: n[exp

((α−αapp

i n

): n

)−1]+Cγ1

Cr ev · Ckα

1+CKp

(zpeak

zmax

)⟨(αb −α)

: n⟩√

1−Czpk2

(B.31)

where,

Cr ev =(α−αapp

i n

): n(

α−αtr uei n

): n

for(α−αapp

i n

): n ≤ 0

Cr ev = 1 otherwise (B.32)

The initial back-stress ratio αin is chosen between an apparent back-stress ratio αappin and a true

back-stress ratio tensor αtruein through the implementation of Crev coefficient to avoid over-stiffness

on the stress-strain response. The plastic modulus is larger when αin = αtruein , and it becomes softer

when αin = αappin . Furthermore, the parameter ho is used to adjust the ratio between plastic and

elastic moduli, and it is internally set according to the initial relative density parameter DR0, by thefollowing formula:

ho = (0.25+DR0)

2≥ 0.3 (B.33)

Cγ1 is a constant defined to avoid division by zero, and it is set as h0/200. It can be seen that Kp isproportional to G and to the distance between the back-stress ratio α and the bounding back-stressratio αb and inversely proportional to the distance between the back-stress ratio and the initialback-stress ratio αapp

i n .

The last term in the equation B.31 referred to fabric effects and it reduces the plastic modulusand hysteretic damping with increasing plastic shear strains improving this way the stress-path inundrained cyclic loading. The term Ckα controls the effects of sustained static shear stresses. It isimportant to mention that zpeak is equal to zero unless the soil has been loaded strongly enough topass outside the dilatancy surface.


Plastic volumetric strains - Contraction

Calculation of the dilatancy D is according whether the soil experiences contraction or dilation.The plastic volumetric contraction occurs when (αd −α):n > 0, dilatancy D is positive and it is cal-culated as follows:

D = Adc [(α−αi n) : n +Ci n]2

(αd −α)

: n(αd −α)

: n +CD(B.34)

where an upper limit is defined to prevent numerical issues.

D ≤ 1.5 · Ad0

(αd −α)

: n(αd −α)

: n +CD(B.35)

where,

Adc = Ado (1+⟨z : n⟩)hp Cd z

(B.36)

The dilatancy is proportional to the constant Ad0 and the distance of the back-stress ratio α tothe dilatancy back-stress ratioαd . The constant Ad0 is related to the dilatancy relationship proposedby Bolton (1986) who showed that the difference between peak and constant volume friction anglescould be approximated according to the following formula:

ϕpk −ϕcv =−0.8ψ (B.37)

where ϕpk is the peak friction angle of shearing resistance, ϕcv the angle of shearing resistanceat constant volume and ψ the dilatancy angle. From this,

Ad0 =1

0.4

arcsin(

M b

2

)−arcsin

( M2

)M b −M d

(B.38)

The function hp controls the dilatancy and it depends on the contraction rate parameter hp0 andthe current relative state parameter index ξR as follows:

hp = hp0 exp(−0.7+7

(0.5−ξR

)2)

for ξR ≤ 0.5

hp = hp0 exp(−0.7) for ξR > 0.5 (B.39)

The contraction rate parameter hp0 allows to calibrate the model for a specific cyclic stress ratioand number of cycles. Cin depends on the fabric and it is used to enhance the contraction rate at thestart of an unloading cycle. Constant CD is internally set as 0.16. The term Cdz improves modellingof the cyclic strength of denser sands. Further explanation about model formulation at this stagecan be found in Boulanger and Ziotopoulou (2015).

Plastic volumetric strains - Dilation

Plastic volumetric dilation occurs only when (αd−α):n < 0, so dilatancy D < 0. A rotated dilatancysurface with slope MdR has been added which evolves with the history of the fabric tensor z to fa-cilitate earlier dilation at low stress ratios under certain loading paths (Boulanger and Ziotopoulou,2015). The rotated surface is defined as follows:


M dR = M d

Cr ot1(B.40)

αdR = 1p2·(M dR −m

)n (B.41)

From this, D is computed by two different expressions. The first one corresponds to the rotateddilatancy surface while the second one corresponds to the non-rotated dilatancy surface.

Dr ot = Ad⟨−z : n⟩p

2 zmax·(αd −α)

: n

CDR(B.42)

Dnon−r ot = Ad ·(−

⟨−

(αd −α

): n

⟩)(B.43)

where Ad is defined by the following expression:

Ad = Ado (Czi n2)(z2

cumzmax

)(1− ⟨−z:n⟩p

2 zpeak

)3

(Cε)2(Cpzp

)(Cp min

)(Czi n1)+1

(B.44)

The terms in the denominator of the equation B.44 have the following roles: the first term facil-itates the progressive growth of strains under symmetric loading; the second term facilitates strain-hardening when the plastic shear strain reaches the prior peak value; the third term Cε is a calibra-tion constant that modifies the rate of plastic shear strain accumulation; the fourth term Cpzp causesthe effects of fabric on dilation to be diminished whenever the current value of p is near to pzp en-abling the model to provide reasonable predictions of responses to large number of loading cycles;Cpmin provides a minimum amount of shear resistance for a soil after it has temporarily reached anexcess pore pressure ratio of 100%; Czin1 facilitates strain-hardening when stress reversals are notcausing fabric changes. Lastly, Czin2 causes the dilatancy to be decreased by up to factor of 3 underconditions of large strains and full stress reversals, which improves the prediction of cyclic strainaccumulation during undrained cyclic loading (Boulanger and Ziotopoulou, 2015).

Factor CDR depends on the initial relative density parameter of the soil. Finally the dilatancy Dis defined according to following condition:

if Dnon−r ot < Dr ot ⇒ D = Dnon−r ot

else D = Dnon−r ot + (Dr ot −Dnon−r ot ) ·⟨

M b −M cur⟩⟨

M b −M cur +0.01⟩ (B.45)


Figure B.3: Dilatancy D calculation based on the stress state with respect to MdR, Md and Mb surfaces duringhalf-cycle of loading, from contraction to dilation (Boulanger and Ziotopoulou, 2015)

Finally, the distance between α and αd defines the amount of dilatancy or contractancy experi-enced by the soil.

CSite Investigation at Akita Port

C.1. Standard Penetration Test and Grain-size Distribution

Ohama No.1 Wharf:

Figure C.1: Standard penetration test and grain-size distribution for Ohama No. 1 Wharf.

Table C.1: Normalized SPT N-value after correction to an equivalent 60% hammer efficiency, Ohama No.1Wharf.

Soil layerDepth

[m]SPT

N-valueCE CB CR CS (N)60

γ

[kN/m3]σv

[kPa]pw

[kPa]σ’

v

[kPa]m[-]

CN (N1)60

1. Clean sand 4,3 18 1,33 1 1 1 21 19 81 37 44 0,43 1,43 302. Very silty sand 7,8 18 1,33 1 1 1 23 20 152 72 80 0,42 1,11 253. Slightly silty sand 10,5 20 1,33 1 1 1 25 21 208 99 109 0,40 0,97 254. Slightly silty sand 17 32 1,33 1 1 1 41 21 345 164 181 0,29 0,84 355. Very sandy clay 21 18 1,33 1 1 1 23 20 425 204 221 0,41 0,73 176. Slightly silty sand 24,5 26 1,33 1 1 1 35 21 498 239 259 0,33 0,73 25

103

104 C. Site Investigation at Akita Port

Ohama No.2 Wharf:

Figure C.2: Standard penetration test and grain-size distribution for Ohama No. 2 Wharf.

Table C.2: Normalized SPT N-value after correction to an equivalent 60% hammer efficiency, Ohama No.2Wharf.

Soil layerDepth

[m]SPT


γ

[kN/m3]σv

[kPa]pw

[kPa]σ’

v

[kPa]m[-]

CN (N1)60

1. Backfill sand 5,5 7 1,33 1 1 1 8 19 105 47 57 0,57 1,39 112. Slightly silty sand 12,2 7 1,33 1 1 1 8 19 232 114 118 0,56 0,92 83. Slightly silty sand 16 36 1,33 1 1 1 46 21 312 152 159 0,26 0,89 414. Very sandy clay 20 20 1,33 1 1 1 26 21 396 192 203 0,39 0,76 205. Slightly silty sand 23 16 1,33 1 1 1 21 20 456 222 233 0,43 0,70 156, Slightly silty sand 26 36 1,33 1 1 1 46 21 519 252 266 0,26 0,78 36

C.2. Shear-wave velocity profile 105

C.2. Shear-wave velocity profile

Figure C.3: Shear-wave velocity measurements for both wharves (Iai and Kameoka, 1993)

Table C.3: Calculation Shear Modulus Coefficient G0, Ohama No.1 Wharf.

Depth[m]

γ

[kN/m3]σv

[kPa]pw

[kPa]σ’

v

[kPa]Vs

[m/s]ρ

[ton/m3]Gmax

[kPa]ϕ

′

[°]K0,nc

[-]p’

[kPa]G0

[-]1 19 19 4 15 130 1,94 32732 36,8 0,402 10,5 6462 19 38 14 24 130 1,94 32732 36,8 0,402 16,8 6463 19 57 24 33 130 1,94 32732 36,8 0,402 23,1 6464 19 76 34 42 130 1,94 32732 36,8 0,402 29,4 5995 19 95 44 51 130 1,94 32732 36,8 0,402 35,7 5446 19 114 54 60 130 1,94 32732 36,8 0,402 42,1 5027 19 133 64 69 190 1,94 69918 36,8 0,402 48,4 9998 20 153 74 79 190 2,04 73598 36,1 0,410 55,7 9809 20 173 84 89 190 2,04 73598 36,1 0,410 62,8 923

10 21 194 94 100 190 2,14 77278 36,8 0,402 70,1 91711 21 215 104 111 190 2,14 77278 36,8 0,402 77,8 87112 21 236 114 122 190 2,14 77278 36,8 0,402 85,5 83013 21 257 124 133 190 2,14 77278 38,0 0,384 92,1 80014 21 278 134 144 190 2,14 77278 38,0 0,384 99,7 76915 21 299 144 155 190 2,14 77278 38,0 0,384 107,3 741

106 C. Site Investigation at Akita Port

Table C.4: Calculation Shear Modulus Coefficient G0, Ohama No.2 Wharf.

Depth[m]

γ

[kN/m3]σv

[kPa]pw

[kPa]σ’

v

[kPa]Vs

[m/s]ρ

[ton/m3]Gmax

[kPa]ϕ

′

[°]K0,nc

[-]p’

[kPa]G0

[-]1 19 19 3,3 15,7 130 1,94 32732 33,0 0,455 11,4 6462 19 38 13,3 24,7 130 1,94 32732 33,0 0,455 18,0 6463 19 57 23,3 33,7 130 1,94 32732 33,0 0,455 24,5 6464 19 76 33,3 42,7 130 1,94 32732 33,0 0,455 31,1 5835 19 95 43,3 51,7 130 1,94 32732 33,0 0,455 37,6 5306 19 114 53,3 60,7 130 1,94 32732 33,0 0,455 44,2 4897 19 133 63,3 69,7 190 1,94 69918 33,0 0,455 50,7 9758 19 152 73,3 78,7 190 1,94 69918 33,0 0,455 57,3 9189 19 171 83,3 87,7 190 1,94 69918 33,0 0,455 63,8 870

10 19 190 93,3 96,7 190 1,94 69918 33,0 0,455 70,4 82811 19 209 103,3 105,7 190 1,94 69918 33,0 0,455 76,9 79212 20 229 113,3 115,7 190 2,04 73598 34,3 0,437 83,1 80213 20 249 123,3 125,7 190 2,04 73598 34,3 0,437 90,3 76914 21 270 133,3 136,7 190 2,14 77278 37,4 0,393 95,2 78715 21 291 143,3 147,7 190 2,14 77278 37,4 0,393 102,9 757

C.3. Soil liquefaction resistance from Cyclic Triaxial tests

Figure C.4: Liquefaction resistance of sands, a) Ohama sand and b) Gaiko sand (Iai and Kameoka, 1993)

C.4. Filtering and correction input ground motion 107

C.4. Filtering and correction input ground motion

Filtering and correction of the acceleration-time history record, Nihonkai-Chubu Earthquake

Figure C.5: Uncorrected (grey line) and corrected (blue line) recorded earthquake motion at Akita Port usingsoftware SeismoSignal.

DSoil Liquefaction Potential

109

110 D. Soil Liquefaction Potential

D.1. Ohama No.1 WharfD.1.1. Cyclic Stress Ratio, CSR

Table D.1: Calculation CSR, Ohama No.1 Wharf.

Ohama No.1 Wharf

Soil LayerDepth

[m]γ

[kN/m3]σv

[kPa]pw

[kPa]σv’

[kPa]α(z) β(z) rd CSR

1. Clean sand 1 19 19 4 15 -0,027 0,003 1,00 0,192 19 38 14 24 -0,077 0,009 0,99 0,243 19 57 24 33 -0,134 0,015 0,98 0,264 19 76 34 42 -0,197 0,022 0,98 0,275 19 95 44 51 -0,266 0,030 0,97 0,286 19 114 54 60 -0,341 0,038 0,96 0,287 19 133 64 69 -0,420 0,047 0,95 0,28

2. Very silty sand 8 20 153 74 79 -0,504 0,057 0,93 0,283. Slightly silty sand 9 21 174 84 90 -0,591 0,066 0,92 0,27

10 21 195 94 101 -0,682 0,076 0,91 0,2711 21 216 104 112 -0,775 0,087 0,90 0,2612 21 237 114 123 -0,869 0,097 0,88 0,2613 21 258 124 134 -0,965 0,107 0,87 0,26

4. Slightly silty sand 14 21 279 134 145 -1,061 0,118 0,86 0,2515 21 300 144 156 -1,156 0,128 0,84 0,2516 21 321 154 167 -1,251 0,138 0,83 0,2417 21 342 164 178 -1,344 0,148 0,82 0,2418 21 363 174 189 -1,434 0,158 0,80 0,2419 21 384 184 200 -1,522 0,167 0,79 0,2320 21 405 194 211 -1,605 0,176 0,78 0,23

5. Very sandy clay 21 20 425 204 221 -1,685 0,184 0,76 0,226. Slightly silty sand 22 21 446 214 232 -1,759 0,191 0,75 0,22

23 21 467 224 243 -1,828 0,198 0,74 0,2224 21 488 234 254 -1,891 0,204 0,73 0,2125 21 509 244 265 -1,948 0,210 0,72 0,2126 21 530 254 276 -1,998 0,214 0,71 0,2127 21 551 264 287 -2,041 0,218 0,70 0,2028 21 572 274 298 -2,076 0,221 0,69 0,2029 21 593 284 309 -2,103 0,223 0,68 0,2030 21 614 294 320 -2,123 0,224 0,67 0,20

D.1. Ohama No.1 Wharf 111

D.1.2. Cyclic Resistance Ratio, CRR

Table D.2: Calculation (N1)60-value, Ohama No.1 Wharf.

Ohama No.1 Wharf

Soil LayerDepth

[m]SPT


m[-]

CN (N1)60

1. Clean sand 1 18 1,33 1 1 1 24 0,41 1,70 412 18 1,33 1 1 1 24 0,41 1,70 413 16 1,33 1 1 1 21 0,43 1,62 344 18 1,33 1 1 1 24 0,41 1,43 345 20 1,33 1 1 1 27 0,39 1,30 356 21 1,33 1 1 1 28 0,38 1,22 347 18 1,33 1 1 1 24 0,41 1,17 28

2. Very silty sand 8 19 1,33 1 1 1 25 0,40 1,10 283. Slightly silty sand 9 21 1,33 1 1 1 28 0,38 1,05 29

10 22 1,33 1 1 1 29 0,37 1,00 2911 23 1,33 1 1 1 31 0,36 0,96 3012 22 1,33 1 1 1 29 0,37 0,93 2713 25 1,33 1 1 1 33 0,34 0,91 30

4. Slightly silty sand 14 32 1,33 1 1 1 43 0,28 0,90 3815 34 1,33 1 1 1 45 0,27 0,89 4016 33 1,33 1 1 1 44 0,28 0,87 3817 41 1,33 1 1 1 55 0,22 0,88 4818 42 1,33 1 1 1 56 0,21 0,88 4919 42 1,33 1 1 1 56 0,21 0,87 4820 40 1,33 1 1 1 53 0,22 0,85 45

5. Very sandy clay 21 18 1,33 1 1 1 24 0,41 0,73 176. Slightly silty sand 22 20 1,33 1 1 1 27 0,39 0,73 19

23 22 1,33 1 1 1 29 0,37 0,72 2124 20 1,33 1 1 1 27 0,39 0,70 1925 20 1,33 1 1 1 27 0,39 0,69 1826 25 1,33 1 1 1 33 0,34 0,71 2427 25 1,33 1 1 1 33 0,34 0,70 2328 25 1,33 1 1 1 33 0,34 0,69 2329 25 1,33 1 1 1 33 0,34 0,68 2330 25 1,33 1 1 1 33 0,34 0,68 22



Ohama No.1 Wharf

Soil LayerDepth

[m](N1)60

FC[%]

α β (N1)60,cs CRR7,5 MSF Cσ Kσ CRR

1. Clean sand 1 41 0 0,00 1,00 30 0,48 0,95 0,38 1,10 0,512 41 0 0,00 1,00 30 0,48 0,95 0,38 1,10 0,513 34 0 0,00 1,00 30 0,48 0,95 0,25 1,10 0,514 34 0 0,00 1,00 30 0,48 0,95 0,25 1,10 0,515 35 0 0,00 1,00 30 0,48 0,95 0,26 1,10 0,516 34 0 0,00 1,00 30 0,48 0,95 0,25 1,10 0,517 28 0 0,00 1,00 28 0,38 0,95 0,18 1,07 0,39

2. Very silty sand 8 28 21 3,78 1,09 30 0,48 0,95 0,18 1,05 0,483. Slightly silty sand 9 29 10 0,87 1,02 30 0,48 0,95 0,20 1,02 0,47

10 29 10 0,87 1,02 30 0,48 0,95 0,20 1,00 0,4611 30 10 0,87 1,02 30 0,48 0,95 0,20 0,98 0,4512 27 10 0,87 1,02 29 0,41 0,95 0,18 0,97 0,3813 30 10 0,87 1,02 30 0,48 0,95 0,20 0,94 0,43

4. Slightly silty sand 14 38 10 0,87 1,02 30 0,48 0,95 0,32 0,88 0,4115 40 10 0,87 1,02 30 0,48 0,95 0,37 0,84 0,3916 38 10 0,87 1,02 30 0,48 0,95 0,32 0,84 0,3917 48 10 0,87 1,02 30 0,48 0,95 0,84 0,52 0,2418 49 10 0,87 1,02 30 0,48 0,95 0,95 0,41 0,1919 48 10 0,87 1,02 30 0,48 0,95 0,87 0,41 0,1920 45 10 0,87 1,02 30 0,48 0,95 0,57 0,58 0,27

5. Very sandy clay 21 17 10 0,87 1,02 19 0,19 0,95 0,12 0,91 0,166. Slightly silty sand 22 19 10 0,87 1,02 21 0,21 0,95 0,13 0,89 0,18

23 21 10 0,87 1,02 23 0,24 0,95 0,14 0,88 0,2024 19 10 0,87 1,02 20 0,20 0,95 0,13 0,88 0,1725 18 10 0,87 1,02 20 0,20 0,95 0,13 0,88 0,1726 24 10 0,87 1,02 25 0,29 0,95 0,15 0,85 0,2327 23 10 0,87 1,02 25 0,28 0,95 0,15 0,84 0,2328 23 10 0,87 1,02 24 0,28 0,95 0,15 0,84 0,2229 23 10 0,87 1,02 24 0,27 0,95 0,15 0,83 0,2130 22 10 0,87 1,02 24 0,26 0,95 0,15 0,83 0,21


D.2. Ohama No.2 WharfD.2.1. Cyclic Stress Ratio, CSR

Table D.4: Calculation CSR, Ohama No.2 Wharf.

Ohama No.2 Wharf

Soil LayerDepth

[m]γ

[kN/m3]σv

[kPa]pw

[kPa]σv’

[kPa]α(z) β(z) rd CSR

1. Clean backfill sand 1 19 19 3,3 15,7 -0,027 0,003 1,00 0,182 19 38 13,3 24,7 -0,077 0,009 0,99 0,233 19 57 23,3 33,7 -0,134 0,015 0,98 0,254 19 76 33,3 42,7 -0,197 0,022 0,98 0,275 19 95 43,3 51,7 -0,266 0,030 0,97 0,276 19 114 53,3 60,7 -0,341 0,038 0,96 0,277 19 133 63,3 69,7 -0,420 0,047 0,95 0,288 19 152 73,3 78,7 -0,504 0,057 0,93 0,289 19 171 83,3 87,7 -0,591 0,066 0,92 0,27

10 19 190 93,3 96,7 -0,682 0,076 0,91 0,2711 19 209 103,3 105,7 -0,775 0,087 0,90 0,27

2. Slightly silty sand 12 20 229 113,3 115,7 -0,869 0,097 0,88 0,2713 20 249 123,3 125,7 -0,965 0,107 0,87 0,2614 21 270 133,3 136,7 -1,061 0,118 0,86 0,26

3. Slightly silty sand 15 21 291 143,3 147,7 -1,156 0,128 0,84 0,2516 21 312 153,3 158,7 -1,251 0,138 0,83 0,2517 21 333 163,3 169,7 -1,344 0,148 0,82 0,2418 21 354 173,3 180,7 -1,434 0,158 0,80 0,2419 21 375 183,3 191,7 -1,522 0,167 0,79 0,24

4. Very sandy clay 20 20 395 193,3 201,7 -1,605 0,176 0,78 0,2321 20 415 203,3 211,7 -1,685 0,184 0,76 0,23

5. Slightly silty sand 22 20 435 213,3 221,7 -1,759 0,191 0,75 0,2323 20 455 223,3 231,7 -1,828 0,198 0,74 0,2224 20 475 233,3 241,7 -1,891 0,204 0,73 0,22

6. Slightly silty sand 25 21 496 243,3 252,7 -1,948 0,210 0,72 0,2226 21 517 253,3 263,7 -1,998 0,214 0,71 0,2127 21 538 263,3 274,7 -2,041 0,218 0,70 0,2128 21 559 273,3 285,7 -2,076 0,221 0,69 0,2129 21 580 283,3 296,7 -2,103 0,223 0,68 0,2030 21 601 293,3 307,7 -2,123 0,224 0,67 0,20


D.2.2. Cyclic Resistance Ratio, CRR


Ohama No.2 Wharf

Soil LayerDepth

[m]SPT


m[-]

CN (N1)60

1. Clean backfill sand 1 2 1,33 1 1 1 3 0,66 1,70 52 2 1,33 1 1 1 3 0,66 1,70 53 3 1,33 1 1 1 4 0,63 1,70 74 4 1,33 1 1 1 5 0,61 1,69 95 5 1,33 1 1 1 7 0,59 1,48 106 7 1,33 1 1 1 9 0,55 1,33 127 7 1,33 1 1 1 9 0,55 1,23 118 7 1,33 1 1 1 9 0,55 1,15 119 9 1,33 1 1 1 12 0,52 1,08 13

10 12 1,33 1 1 1 16 0,48 1,02 1611 10 1,33 1 1 1 13 0,50 0,98 13

2. Slightly silty sand 12 7 1,33 1 1 1 9 0,55 0,93 913 11 1,33 1 1 1 15 0,49 0,90 1314 20 1,33 1 1 1 27 0,39 0,89 24

3. Slightly silty sand 15 25 1,33 1 1 1 33 0,34 0,88 2916 33 1,33 1 1 1 44 0,28 0,88 3917 40 1,33 1 1 1 53 0,22 0,89 4718 49 1,33 1 1 1 65 0,16 0,91 5919 27 1,33 1 1 1 36 0,32 0,81 29

4. Very sandy clay 20 15 1,33 1 1 1 20 0,44 0,74 1521 20 1,33 1 1 1 27 0,39 0,75 20

5. Slightly silty sand 22 15 1,33 1 1 1 20 0,44 0,71 1423 13 1,33 1 1 1 17 0,46 0,68 1224 17 1,33 1 1 1 23 0,42 0,69 16

6 .Slightly silty sand 25 40 1,33 1 1 1 53 0,22 0,81 4326 30 1,33 1 1 1 40 0,30 0,75 3027 27 1,33 1 1 1 36 0,32 0,72 2628 27 1,33 1 1 1 36 0,32 0,71 2629 27 1,33 1 1 1 36 0,32 0,71 2530 27 1,33 1 1 1 36 0,32 0,70 25



Ohama No.2 Wharf

Soil LayerDepth

[m](N1)60

FC[%]

α β (N1)60,cs CRR7,5 MSF Cσ Kσ CRR

1. Clean backfill sand 1 5 0 0,00 1,00 5 0,08 0,95 0,07 1,10 0,092 5 0 0,00 1,00 5 0,08 0,95 0,07 1,10 0,093 7 0 0,00 1,00 7 0,10 0,95 0,08 1,09 0,104 9 0 0,00 1,00 9 0,11 0,95 0,09 1,08 0,115 10 0 0,00 1,00 10 0,12 0,95 0,09 1,06 0,126 12 0 0,00 1,00 12 0,13 0,95 0,10 1,05 0,137 11 0 0,00 1,00 11 0,13 0,95 0,10 1,04 0,138 11 0 0,00 1,00 11 0,12 0,95 0,09 1,02 0,129 13 0 0,00 1,00 13 0,14 0,95 0,10 1,01 0,13

10 16 0 0,00 1,00 16 0,17 0,95 0,12 1,01 0,1611 13 0 0,00 1,00 13 0,14 0,95 0,10 1,00 0,13

2. Slightly silty sand 12 9 17 3,01 1,06 12 0,13 0,95 0,09 0,99 0,1313 13 17 3,01 1,06 17 0,17 0,95 0,10 0,98 0,1614 24 42 5,00 1,20 30 0,48 0,95 0,15 0,95 0,44

3. Slightly silty sand 15 29 42 5,00 1,20 30 0,48 0,95 0,20 0,93 0,4316 39 42 5,00 1,20 30 0,48 0,95 0,33 0,85 0,3917 47 42 5,00 1,20 30 0,48 0,95 0,74 0,62 0,2818 59 42 5,00 1,20 30 0,48 0,95 -1,37 1,10 0,5119 29 42 5,00 1,20 30 0,48 0,95 0,20 0,88 0,40

4. Very sandy clay 20 15 80 5,00 1,20 23 0,24 0,95 0,11 0,92 0,2121 20 80 5,00 1,20 29 0,43 0,95 0,13 0,90 0,37

5. Slightly silty sand 22 14 80 5,00 1,20 22 0,23 0,95 0,11 0,92 0,2023 12 80 5,00 1,20 19 0,20 0,95 0,10 0,92 0,1724 16 80 5,00 1,20 24 0,27 0,95 0,11 0,90 0,23

6. Slightly silty sand 25 43 80 5,00 1,20 30 0,48 0,95 0,47 0,57 0,2626 30 80 5,00 1,20 30 0,48 0,95 0,20 0,81 0,3727 26 80 5,00 1,20 30 0,48 0,95 0,17 0,83 0,3828 26 80 5,00 1,20 30 0,48 0,95 0,17 0,83 0,3829 25 80 5,00 1,20 30 0,48 0,95 0,17 0,82 0,3830 25 80 5,00 1,20 30 0,48 0,95 0,16 0,82 0,38


D.3. Factor of Safety for Soil Liquefaction

Table D.7: Results of the Soil Liquefaction Potential Analysis.


Soil LayerDepth

[m]CSR CRR FS Soil Layer

Depth[m]

CSR CRR FS

1. Clean sand 1 0,19 0,51 2,6 1. Backfill sand 1 0,18 0,09 0,52 0,24 0,51 2,1 2 0,23 0,09 0,43 0,26 0,51 1,9 3 0,25 0,10 0,44 0,27 0,51 1,9 4 0,27 0,11 0,45 0,28 0,51 1,8 5 0,27 0,12 0,46 0,28 0,51 1,8 6 0,27 0,13 0,57 0,28 0,39 1,4 7 0,28 0,13 0,5

2. Very silty sand 8 0,28 0,48 1,7 8 0,28 0,12 0,4

3. Slightly silty sand 9 0,27 0,47 1,7 9 0,27 0,13 0,510 0,27 0,46 1,7 10 0,27 0,16 0,611 0,26 0,45 1,7 11 0,27 0,13 0,5

12 0,26 0,38 1,5 2. Slightly silty sand 12 0,27 0,13 0,513 0,26 0,43 1,7 13 0,26 0,16 0,6

4. Slightly silty sand 14 0,25 0,41 1,6 14 0,26 0,44 1,7

15 0,25 0,39 1,6 3. Slightly silty sand 15 0,25 0,43 1,716 0,24 0,39 1,6 16 0,25 0,39 1,617 0,24 0,24 1,0 17 0,24 0,28 1,218 0,24 0,19 0,8 18 0,24 0,51 2,119 0,23 0,19 0,8 19 0,24 0,40 1,7

20 0,23 0,27 1,2 4. Very sandy clay 20 0,23 0,21 0,9

5. Very sandy clay 21 0,22 0,16 0,7 21 0,23 0,37 1,6

6. Slightly silty sand 22 0,22 0,18 0,8 5. Slightly silty sand 22 0,23 0,20 0,923 0,22 0,20 0,9 23 0,22 0,17 0,824 0,21 0,17 0,8 24 0,22 0,23 1,0

25 0,21 0,17 0,8 6. Slightly silty sand 25 0,22 0,26 1,226 0,21 0,23 1,1 26 0,21 0,37 1,827 0,20 0,23 1,1 27 0,21 0,38 1,828 0,20 0,22 1,1 28 0,21 0,38 1,929 0,20 0,21 1,1 29 0,20 0,38 1,930 0,20 0,21 1,1 30 0,20 0,38 1,9

Bibliography

Andrus, R. and Stokoe, K. (2000). Liquefaction Resistance of Soils from Shear-Wave Velocity. Journalof Geotechnical and Geoenvironmental Engineering.

Arboleda-Monsalve, L. and Nguyen, H. (2016). Simulation of Liquefaction-Induced Damage of thePort of Long Beach using The UBC3D-PLM Model. Department of Civil and Construction Engi-neering Management, California State University, Long Beach, CA 90840.

Beaty, M. and Perlea, V. (2011). 21st Century Dam Design – Advanced and Adaptations. 31st AnnualUSSD Conference San Diego, California.

Been, K. and Jefferies, M. (1985). A state parameter for sands. Geotechnique 35, No. 2, 99-112.

Besseling, F. (2012). Soil-structure interaction modelling in performance-based seismic jetty design.

Bolton, M. D. (1986). The strength and dilatancy of sands. Cambridge University Engineering De-partment.

Boulanger, R. and Idriss, I. (2008). Soil Liquefaction During Earthquakes. Earthquake EngineeringReasearch Institute.

Boulanger, R. and Idriss, I. (2014). CPT and SPT based Liquefaction Triggering Procedures. Depart-ment of Civil and Environmental Engineering, College of Engineering, University of California atDavis.

Boulanger, R. and Ziotopoulou, K. (2017). PM4Sand (Version 3.1): A Sand Plasticity Model for Earth-quake Engineering Applications. Department of Civil and Environmental Engineering College ofEngineering University of California at Davis.

Brinkgreve, R., Engin, E., and Engin, H. (2010). Validation of empirical formulas to derive modelparameters for sands. Technical report, TU Delft, PLAXIS.

Brinkgreve, R., Vilhar, G., and Zampich, L. (2018). PLAXIS The PM4Sand model 2018. PLaxis bv.

Byrne, P. (1991). A Cyclic Shear-Volume Coupling and Pore Pressure Model for Sand Proceeding. 2ndInternational Conference on Recent Advances in Geotechnical Earthquake Engineering and SoilDynamics, St. Missouri, Paper No. 1.24.

Cappellaro, C., Cubrinovski, M., Chiaro, G., Stringer, M., Bray, J., and Riemer, M. (2017). Undrainedcyclic direct simple shear testing of Christchurch sandy soils. Proc. 20th NZGS Geotechnical Sym-posium. Eds. GJ Alexander and CY Chin, Napier.

Coombs, W., Crouch, R., and Augarde, C. (2009). Influence of Lode Angle Dependency on the CriticalState for Rotational Plasticity. X International Conference on Computational Plasticity.

Dabeet, A., Wijewickreme, D., and Byrne, P. (2012). Simulation of Cyclic Direct Simple Shear LoadingResponse of Soils Using Discrete Element Modeling. University of British Columbia, Vancouver,Canada.

117

118 Bibliography

Daftari, A. (2015). New Approach in Prediction of Soil Liquefaction. Faculty of Geosciences, Geo-Engineering and Mining of the Technische Universitat Bergakademie Freiberg.

Day, R. W. (2002). Geotechnical Earthquake Engineering Handbook. McGraw-Hill.

De Groot, M., Bolton, M., Foray, P., Meijers, P., Palmer, A., Sandven, R., Sawicki, A., and Teh, T. (2006).Physics of Liquefaction Phenomena around Marine Structures. Journal of Waterway, Port, Coastal,and Ocean Engineering. ASCE.

Dobry, R. and Abdoun, T. (2011). An Investigation into Why Liquefaction Charts Work: A NecessaryStep Toward Integrating The States of Art and Practice. Department of Civil and EnvironmentalEngineering, Rensselaer Polytechnic Institute, Troy, NY, USA.

Galavi, V. and Petalas, A. (2013). Plaxis Liquefaction Model: UBC3D-PLM. PLAXIS B. V.

Harder, L. and Boulanger, R. (1997). Application of Kσ and Kα correction factors. NCEER Work-shop on Evaluation of Liquefaction Resistance of Soils, Buffalo, National Center for EngineeringResearch, 129-148.

Hashash, Y., Groholski, D., and Phillips, C. (2010). Recent Advances in Non-Linear Site Response Anal-ysis. 5th International Conference on Recent Advances in Geotechnicl Earthquake Engineeringand Soil Dynamics and Symposium in Honor of Professor I.M. Idriss, San Diego, California.

Hudson, M., Idriss, I., and Beirkae, M. (1994). QUAD4M User’s manual.

Iai, S. and Kameoka, T. (1993). Finite Element Analysis of Earthquake Induced Damage to AnchoredSheet Pile Quay Walls. Soil and Foundations, Vol. 33, No. 1, 71-91. Japanese Society of Soil Me-chanics and Foundation Engineering.

Idriss, I. and Boulanger, R. (2003). Relating Kα and Kσ to SPT blow count and to CPT tip resistancefor use in evaluating liquefaction potential. Technical report, Proceedings of the 2003 Dam SafetyConference, ASDSO.

Idriss, I. and Boulanger, R. (2004a). Evaluation of Potential for Liquefaction or Cyclic Failure of Siltsand Clays. Department of Civil and Environmental Engineering, College of Engineering, Univer-sity of California at Davis.

Idriss, I. and Boulanger, R. (2004b). Semi-empirical Procedures for Evaluating Liquefaction PotentialDuring Earthquakes. Department of Civil and Environmental Engineering, University of Califor-nia, Davis, CA 95616-5924.

Ishihara, K. (1985). Stability of Natural Deposits during Earthquakes. Proc. 11th Int. Conf. on SoilMechanics and Foundation Engineering, Vol. 1, A. A. Balkema, Rotterdam, The Netherlands.

Ishihara, K., Iwamoto, S., Yasuda, S., and Takatsu, H. (1977). Liquefaction of anisotropically consoli-dated sand. Technical report, Japanese Society of Soil Mechanics and Foundation Engineering.

Jamiolkowski, M. (2003). Evaluation of Relative Density and Shear Strength of Sands from CPT andDMT. Soil Behaviour and Soft Ground Construction, ASCE, GSP No. 119, 201-238.

Jefferies, M. (1993). Nor-Sand: a simple critical state model for sand. Geotechnique 43, No. 1, pp.91-103.

Kavazanjian, E. (2016). State of the Art and Practice in the Assessment of Earthquake-Induced SoilLiquefaction and its Consequences. National Academy of Sciences, Washington, DC.

Bibliography 119

Kokusho, T. (2016). Major Advances in Liquefaction Research by Laboratory Tests compared with InSitu Behaviour. Soil Dynamics and Earthquake Engineering 91, 3-22.

Kramer, S. (1996). Geotechnical Earthquake Engineering. Upper Saddle River, N.J.: Prentice Hall.

Krzysztof, S. and Felix, D. (2007). Constitutive Models for Predicting Liquefaction of Soils. 18emeCongrès Français de Mécanique, Grenoble.

Lysmer, J. and Kuhlmeyer, R. (1969). Finite Dynamic Model for Infinite Media. Journal of Engineeringand Mechanical Division, 859-877.

Makra, A. (2013). Evaluation of the UBC3D-PLM Constitutive Model for Prediction of EarthquakeInduced Liquefaction on Embankment Dams. Master Graduation Thesis, TU Delft.

Marcuson, W., Hynes, M., and Franklin, A. G. (1991). Response to P. Byrne’s "discussion of ’evalua-tion and use of residual strength in seismic safety analysis of embankments’". Technical report,Earthquake Spectra: Vol. 7, No. 1.

Martin, G. (1975). Fundamentals of Liquefaction Under Cyclic Loading. J. Geotech., Div. ASCE, 101:5,423-438.

Nabili, S., Jafarian, Y., and Baziar, M. (2008). Seismic Pore Water Pressure Generation Models: Nu-merical Evaluation and Comparison. The 14th World Conference on Earthquake Engineering,Beijing, China.

Nagase, H., Shimizu, K., Hiro-oka, A., Maeda, H., and Ishihara, H. (2004). Effects of Overconsolidationon Liquefaction Strength Characteristics of Sand Samples under K0-Stress Condition. 13th WorldConference on Earthquake Engineering, Vancouver, B. C., Canada, Paper No. 1637.

Obrzud, R. and Truty, A. (2018). The Hardening Soil Model - A Practical Guidebook. Z Soil PC 100701Report, Switzerland.

Parra, A. M. (2016). Ottawa F-65 Sand Characterization. Department of Civil and EnvironmentalEngineering, University of California at Davis.

PIANC (2001). Seismic Design Guidelines for Port Structures. Working Group No. 34 of the MaritimeNavigation Commission, International Navigation Association.

PLAXIS (2018a). PLAXIS 2D Reference Manual 2018. PLAXIS.

PLAXIS (2018b). PLAXIS 2D Scientific Manual 2018. PLAXIS.

Randolph, M. and Gourvenec, S. (2011). Offshore Geotechnical Engineering. Centre for OffshoreFoundation Systems, University of Western Australia.

Robertson, P. and Cabal, K. (2015). Guide to Cone Penetration Testing for Geotechnical Engineering,6th Edition. Gregg Drilling and Testing, INC.

Schofield, A. and Wroth, P. (1968). Critical State Soil Mechanics. Lectures in Engineering at Cam-bridge University.

Seed, H. and Idriss, I. (1970). A Simplified Procedure for Evaluating Soil Liquefaction Potential. Col-lege of Engineering, University of California, Berkeley, California.

Sesov, V., Edip, K., and Cvetanovska, J. (2012). Evaluation of the Liquefaction Potential by In-situ Testsand Laboratory Experiments in Complex Geological Conditions. University Ss. Cyril and Method-ius, Institute of Earthquake Engineering and Engineering Seismology-Skopje, Macedonia.

120 Bibliography

Sriskandakumar, S. (2004). Cyclic loading response of Fraser River Sand for validation of numer-ical models simulating centrifuge tests. Department of Civil Engineering, University of BritishColumbia, Canada.

Tasiopoulou, P. and Gerolymos, N. (2015). Constitutive modelling of sand: Formulation of a newplasticity approach. Soil Dynamics and Earthquake Engineeging, pp. 205-221.

Van Elsacker, W. (2016). Evaluation of Seismic Induced Liquefaction and Related Effects on DynamicBehaviour on Anchored Quay Walls using UBC3D-PLM Constitutive Model. MSc. Thesis, TU Delft.

Vilhar, G., Laera, A., Foria, F., Gupta, A., and Brinkgreve, R. B. J. Implementation, Validation andApplication of PM4Sand Model in PLAXIS.

Wang, G. and Xie, Y. (2014). Modified Bounding Surface Hypoplasticity Model for Sands under CyclicLoading. Journal of Engineering Mechanics, ASCE, 140:91-101.

Yang, Z. and Pan, K. (2017). Flow deformation and cyclic resistance of saturated loose sand consider-ing initial static shear effect. Soil Dynamics and Earthquake Engineering 92, 68-78.

Youd, T. and Idriss, I. (2001). Liquefaction Resistance of Soils: Summary Report from the 1996 NCEERand 1998 NCEER/NSF Workshops on Evaluation of Liquefaction Resistance of Soils. Journal ofGeotechnical and Geoenvironmental Engineering, pp. 297-313.

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