Research Paper Sensitivity Analysis of Soft Clay ...

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Research Paper

Sensitivity Analysis of Soft Clay Parameters on an Existing Quay Wall at the East Port in Port Said, EgyptEhab R. Tolba1, Sherif Abd Ellah2, Elsayed M. Galal3, Ezzat Ahmed Sallam4, and Mohammad Ahmad Kamal5*

Abstract: This paper presents a soil interaction sensitivity analysis using a three-dimensional finite ele-ment analysis of existing quay wall diaphragm at the east port in Port Said in northeast Egypt. The main objective of this analysis was to study the influence of soft clay layer parameters on the results of FEM analyses on an existing quay wall. At first, background information on the soil strata used in this study is introduced. Then, a full description of the existing diaphragm quay wall located at the east port is provid-ed. A parametric study was carried out for three different soil profiles using strain-hardening constitutive model (HSM) parameters and clay layer thickness, and the results are presented and discussed. The rec-ommended constitutive soil parameters of the marine clay determined using the HSM for the optimization analysis of the quay walls in that location are also presented.

Keywords: Port Said clay, quay wall, Plaxis 3D, strain-hardening soil model, soft clay

Introduction The soil engineering properties depend on a combination of different soil interacting factors that include compositional and environmental factors. The compositional factors can be evaluated using disturbed samples, while the environmental factors need undisturbed samples or in-situ measurements (Mitchell, 1993). For a proper design, it is necessary to carry out comprehensive geotechnical characterization for differ-ent soil materials. This characterization includes data about the subsoil physical and mechanical properties, and its be-havior under different loading conditions.

The behavior of cohesive soils is generally more complicated than cohesionless materials due to their rela-tive strengths and high compressibility in addition to their time-dependent strength and deformations. These aspects are more pronounced in soft to medium stiff clays, where their properties have a significant effect on man-made structures

and earthworks including quay walls structures systems. Marine clays are encountered in many places in the world, such as Leda Clay in eastern Canada (Bozozuk, 1963; Garga and Khan, 1992), Norwegian clay (Lunne et al., 2005), and Bangkok clay (Likitlersuang et al., 2013). Many previous re-searchers have extensively studied the properties of marine clays, which depend on its mineral and chemical composi-tions that differ according to the site source of the materi-al. Therefore, the study of clay properties is sensitive to its source location.

The east area of Port Said is geologically located within the eastern Nile River Delta where it crosses over and into vast thick soft marine clay and sand deposits. The hub port of East Port-Said has been considered one of the strategic devel-opments in Egypt. This harbor was planned to be constructed in successive phases. The first phase included the construc-tion of a 1200 m long quay wall located about 1.3 km east of the Suez Canal bypass and about 1 km from the shoreline of the Mediterranean Sea. The existing quay wall was designed using deep rectangular barrettes and T-panel diaphragm walls (Hamza et al., 2002).

Subsurface ConditionsIn general, soft soils can be characterized by high moisture content, high initial void ratio, high clay content, high plas-ticity, low permeability, and low unit weight. Soft clays are found in Egypt at the north of the Nile River Delta and extend from western Alexandria to eastern Port Said. El-Dash (1984) analyzed the in-situ and laboratory tests conducted for differ-ent case studies in Egypt at Damietta, Abu-Qir (Alexandria), Bahr-El-Baqar, and Port Said. The study indicated that the soil formation consisted of marine clay deposits that had a thickness of 8 m at Abu-Qir, 30 m at Damietta, 5 m at Bahr-

1 Professor of Port and Coastal Engineering, Faculty of Engineering, Port-Said University, Port-Fouad City, 42526, Egypt

2 Associate Professor of Port and Coastal Engineering, Faculty of Engineering, Port-Said University, Port-Fouad City, 42526, Egypt

3 Associate Professor of Port and Coastal Engineering, Faculty of Engineering, Port-Said University, Port-Fouad City, 42526, Egypt

4 Associate Professor of Civil Engineering, Faculty of Engineering, Port-Said University, Port-Fouad City, 42526, Egypt

5 Marine Engineer, TOA corporation, Port-Said, Port-Fouad, El Geish Street, Building 15, 42523, Egypt

* Corresponding author, email: [email protected]

© 2020 Deep Foundations Institute, Print ISSN: 1937-5247 Online ISSN: 1937-5255Published by Deep Foundations InstituteReceived 02 June 2020; received in revised form 17 August 2020; accepted 1 September 2020https://doi.org/10.37308/DFIJnl.20200602.219

vol14no1tolba219.indd 1 06/10/20 2:16 PM

2 | DF I JOURNAL | VOL . 14 | ISSUE 1 © Deep Foundations Institute

Tolba, Ellah, Galal, Sallam, Kamal | Sensitivity Analysis of Soft Clay Parameters on an Existing Quay Wall at the East Port in Port Said, Egypt

Figure 1. Locations map showing the executed boreholes at East Port-Said

Figure 2. Stress strain curve showing various modulus definitions

El-Baqar, and 40 m at Port-Said. Three previous field in-vestigations (Figure 1) were carried out to estimate the soil properties of the eastern Port Said area, and the results of those investigations were used in the present research. Seven boreholes were performed to a depth of 80 m at the north region, while ten and six boreholes were performed to depths of about 63 m and 55 m at the middle and south regions, re-spectively. Soil stiffness is determined by its modulus value,

Table 1. Typical elasticity modulus (ES) values for different soil types, Burt G. Look (2007)

Type of Soil Strength of soil Elastic modulus, E (MPa)

Fine sand Loose 5–10

Medium 10–25

Dense 25–50

Silt Soft <10

Stiff 10–20

Hard >20

Clay Very soft <3

Soft 2–7

Firm 5–12

Stiff 10–25

Very stiff 20–50

Hard 40–80

which is the ratio of stress versus strain at a particular point or area under consideration (Figure 2). Typical modulus of elasticity values for various soils are presented in Table 1. In general, every field investigation results in different parame-ters, depending on the site specific physical and geotechnical properties.

Hamza and Hamed (2000) and Hight et al. (2001) report-ed on the geotechnical site investigations that were performed for different major projects at East Port Said. The site char-acterization was carried out by the Norwegian Geotechnical Institute (NGI), which presented the engineering properties of a thick deposit of highly plastic clay that extended from


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about 20 m to 60 m below ground level. The undrained shear strength of the soft clay varies linearly with depth: cu=20 + 1.24 z [kPa] for a depth range of z = -11.0 m to -56.0 m. The shear modulus also varies linearly with depth: G = 5.6 + 0.14 z (MPa) for the same depth range. The relation between the shear modulus, G, and the elastic modulus, E, is given as E = 2G (1+ ν), where ν is the Poisson’s ratio. Five (5) main lith-ological layers have been defined with the elastic and plastic parameters as presented in Table 2 according to Hamza and Hamed, (2000). For the numerical analysis process, the thick soft clay layer was divided into two (2) sublayers to simulate the various stiffness values per depth. All soil layer levels are referenced to the Lowest Astronomical Tide of East Port Said (LAT). The sea water level was considered at elevation zero.

Additional in-situ and laboratory tests were conducted in 2017 for the characterization of Port-Said clay by the soil mechanics team at the Suez Canal Authority Research Center (SCARC). The investigation covered the industrial zone area, about 42 sq. km, at the southeast portion of the port. The field-testing program consisted of drilling six boreholes to depths ranging from 42 to 63 m. Triaxial testing was per-formed on the soil samples, which resulted in the following Mohr-Coulomb total and effective shear strength parameters:

c =17 kPa and φ = 12° and c' = 0 kPa and φ' = 22°, respec-tively. Figure 3 shows the deviator stress variation with the axial strain for ten samples tested at each depth. The applied confining pressures ranged from 72 to 375 kPa.

Figure 4 shows the variations in undrained stiffness mod-ulus, Eu50, and the constrained modulus, Eoed, with depth for the clay deposit. The upper and lower boundaries of the clay were defined between El. -5.50 m and El. -47.5 m, referenced to the Lowest Astronomical Tide (LAT) of East Port Said. Based on the results of consolidation tests, the unloading-re-loading stiffness modulus, Eur, can be taken as seven times the value of the undrained modulus (7×Eu50) for cohesive soil (El-Nahhas et al., 2017), whereas cohesionless soils are usu-ally characterized by Eur/E50 of 2 to 3 (Yong and Oh, 2016). The expressions used to compute E50 and Eur are shown in Equations 1 and 2:

E Ec

cref

ref

m

50 503cos sin

cos sin (1)

E Ec

cur urref

ref

mcos sincos sin

3 (2)

Table 2. Port Said east port geotechnical parameters (Hamza and Hamed, 2000)

Layer Levelstart

Level Finish

Layer Thick

[m]

Unit weightγ

[KN/m3]

Ko[-]

Cu[kPa]

ϕ°[deg]

G

[MPa]E

[MPa]ν

[-]

Clay +2.50 -2.50 5.0 17 0.60 0 24 01 2.4 0.2

Sand -2.50 -11.0 8.5 18.5 0.50 0 35 12 30.0 0.25

Soft to medium Clay -11.0 -26.0 15.0 15.5 0.60 20 24 16.5 16.580.2

-26.0 -56.0 30.0 15.0 0.70 38 20 22.5 22.79

hard clay -56.0 -90.0 34.0 17.5 1.0 150 20 25 74.00.2

Dense sand -90.0 -120 Inf 20 1.0 0 35 60 144.0

Figure 3. Deviator stress against axial strain for undrained triaxial tests on Port-Said clay (after El-Nahhas et al., 2017)




Table 3. Soil parameters for Port Said east port industrial region El-Nahhas et al. (2017)

Layer Type Level Start[m LAT]

Level Finish[m LAT]

Layer Thick

[m]

Unit weightγ

[KN/m3]Ko

ϕ°(deg)

Eu50ref

(MPa)m Rint

Fill and Sand Drained +2.5 -5.5 8.0 17 0.52 29 20 0.5 0.67

Very soft to firm clay Undrained

-5.5 -17.5 12.0

16

0.59

22

3.20

0.81

1.00

-17.5 -27.5 10.0 0.64 4.80 1.00

-27.5 -37.5 10.0 0.68 6.40 0.85

-37.5 -47.5 10.0 0.72 8.00 0.85

Dense Sand Drained -47.5 -52.5 52.5 18 0.43 35 30.0 0.5 0.67

Figure 4. Variations of Eu50 and Eoed with depth for Port-Said clay (after El-Nahhas et al., 2017)

where, c, φ = cohesion and friction angle according to the Mohr-Coulomb model

m = power for stress-level dependency of stiffness Eref

50 = secant stiffness in standard drained triaxial test

Erefur = unloading/reloading stiffness at engineering

strains ρref = reference stress for stiffness (default

ρref = 100 stress units)

Table 3 summarizes the soil parameters according to El-Nahhas et al. (2017). The southern region of east Port-Said soil consisted of the following layers:

• Fill and sand layer which consists of fill with brown to yellow very loose coarse to fine silty sand with shell traces

in the depth range 0.0 to 1.75 m. Then a grey loose fine to medium silty sand in the depth range of 1.75 to 8.0 m.

• Port-Said grey very soft to firm fat clay in the range of 8.0 to 50.0 m.

• Grey dense fine to medium sand in the range of 50.0 to 55.0 m.

For the numerical analysis process, the thick soft clay layer was divided into four (4) sublayers to simulate the various stiffness values per depth.

In August 2018, a different site investigation program was conducted in the north region of East Port Said by GEO GROUP EGYPT Company, where seven boreholes were performed down to El. -80.00 m LAT. The main lithological layers are:

• Layer (1): Fill composed of silt, clay, sand, rock fragments• Layer (2): Clayey SILT some sand traces of broken shells,

greenish gray• Layer (3): Silty SAND Fine, loose to medium dense, trac-

es of broken shells, dark gray.• Layer (4): Clayey Sandy SILT, Traces of broken shells,

dark gray.• Layer (5): Soft to medium stiff silty clay• Layer (6): Very dense sand• Layer (7): Very stiff to hard clay

Table 4 summarizes the soil layers and their properties ac-cording to GEO GROUP EGYPT Company for the north re-gion of East Port Said. For the numerical analysis process, the thick soft clay layer was divided into three (3) sublayers to simulate the various stiffness values per depth.

Figure 5 presents a general subsurface profile for the soils at this site based on the prior parameters presented in tables 2, 3 and 4. The cross-section is distributed into three profiles to reflect the three different areas that were investi-gated, as shown in Figure 1. Profiles A, B and C belong to site locations (a), (b) and (c) respectively in Figure 1. The clayey sandy silt layer was present in profile B but was not observed in profiles A and C. It is also clear that a thick very soft to medium stiff clay layer is present from El. -5.50 m LAT to El. -56.00 m LAT. Taking into consideration that deepest exist-ing quay wall structure system extends to El. -60.00 m LAT. The undrained stiffness modulus EU at top of the layer varies




Table 4. General properties for East Port Said Soil according to GEO GROUP (2018)

Layer Type Level start[m LAT]

Level Finish[m LAT]

Layer Thick[m]

Unit weight[KN/m3]

Cu[kPa]

ϕ°[deg]

Eun[MPa]

Layer (1) Fill +2.5 -0.10 2.60 17 … 29 …

Layer (2) Clayey silt -0.10 -5.55 5.45 14.7 0 28-30 3.6

Layer (3) Silty sand -5.55 -17.50 11.95 16 5 30-32 11.9

Layer (4) Clayey sandy silt -17.5 -20.90 3.40 17 8.75 23 5.25

Layer (5) Very Soft to medium clay

-20.90 -32.65 11.75 17 13.30

23

2.78

-32.65 -44.70 12.05 17 28.75 6

-44.70 -59.50 14.80 17.5 47.30 9.6

Layer (6) Dense silty sand -59.50 -65.55 6.05 18 0 38-42 55

Layer (7) V. Stiff to hard clay -65.55 -66.95 1.40 18 155-210 25 31-42

Layer (6) Dense silty sand -66.95 -70.10 3.15 18 0 38-42 55

Layer (7) V. Stiff to hard clay -70.10 -77.50 7.40 18 155-210 25 31-42

Figure 5. Interpreted geotechnical profile for east of Port Said soil

from 1.83 MPa to 13.44 MPa while at bottom varies from 9.0 MPa to 28.56 MPa. On the other hand, the drained shear strength cu at top of the layer varies from 6.00 kPa to 20.00 kPa and increases down to bottom of clay layer from 58.0 kPa to 75.80 kPa. A value for Poisson ratio of 0.3 was selected for the soils. The comparative study for the different parameters of the soft clay layer along the different soil profiles focused on evaluating the axial forces, moments, shear forces, and deformations of the existing front quay diaphragm wall.

Sensitivity AnalysisSoil sensitivity analyses of different types of retaining struc-ture systems have been performed by various researchers us-ing the finite element technique to understand the influence of the soil parameters. Chogueur et al. (2018) investigated the influence of soil stiffness on the performance of a diaphragm wall: secant stiffness, Eref

50 , from triaxial testing and reloading stiffness, Eref

ur , considering Erefoed = Eref

50 It was reported that the

value of Erefur = 3Eref

50, and provided good coherence with the experimental data. The relationships of Eref

ur = 2Eref50 and Eref

ur = 4Eref

50 underestimated and slightly over-estimate the calculated results, respectively. Brinkgreve (2012) recommended using Eref

ur = 3Eref50, which has been used to describe the behavior of

soil-wall interaction. Wong et al. (1997) presented data ob-tained from a tunneling construction site for the second phase of the Central Expressway (CET) in Singapore. Analytical analyses were performed to evaluate the influence of the soft clay layers on the deformations of the retaining wall system. It was concluded that the wall movements are less about 0.005H and 0.003H when the thickness of soft-soil layers was less than 0.9H and 0.6H overlying stiff soils, respectively, where H is the depth of excavation in front of the wall (Figure 6).

Port Said quay wall structural system consisted of front and back concrete diaphragm walls. Both walls are connect-ed by a group of transverse main beams with four concrete barrettes, which extended down to El. -60.0 m LAT. Each




Figure 6. Influence of soft layer thickness on the maximum lateral deflection for five different walls types (after Wong et al., 1997)

Figure 8. Existing quay wall section plan (after Hamza et al., 2002)

Figure 7. Section elevation in the existing quay wall of the East Port Said Port

barrette was 3 m long by 1 m thick, where the spacing be-tween the barrette’s framing system is about 7.0 m along the harbor. The main beam was 800 mm wide and 3 m deep. The deck structure for this quay wall system is located at El. +2.5 m LAT. The front and back diaphragm walls extend down to

El. -32.0 m LAT and El. -8.0 m LAT, respectively (Hamza and Hamed, 2000). The quay wall system has longitudinal seaside front beam and land side back beam with a depth of 3.5 m and 3 m, respectively, and a width of 3 m. The beams are located at the end of the slab deck. Elevation and plan views indicating the different elements of the quay wall sys-tem are presented in Figures 7 and 8, respectively.

The properties of the different structural beam systems and of the diaphragm concrete walls are listed in Tables 5 and 6, respectively. The diaphragm walls were modelled as linear elastic materials with plates. The strain hardening soil (HS) constitutive model is an advanced model for simulating the behavior of different types of soil, both soft soils and stiff soils (Schanz, 1999). The interaction between the different soil layers/profiles and the existing quay wall structural ele-ments was simulated using Plaxis 3D (2013) and using lay-ered nonlinear elasto-plastic hardening constitutive soil mod-el for drained and undrained conditions. For all soil layers, Poisson’s ratio was set as 0.2 unloading-reloading.

Table 5. Properties of the different beams (after Hamza and Hamed, 2000)

Property Main Beam

Seaside Beam

Land Side

Beam

Slab Beam

Area (A), [m2] 2.4 10.5 9.0 1.00

Unit Weight [KN/m3] 25.00

Young’s Modulus (E), [kPa] 2 x 107

Moment of Inertia (I22), [m4] 0.128 10.719 6.75 0.083

Moment of Inertia (I33), [m4] 1.8 7.875 6.75 0.083

Poisson’s Ratio (ν), [-] 0.15

Table 6. Basic properties of diaphragm walls

Diaphragm Walls Section Plaxis 3D plate properties

Depth [m] 1.00

γsteel [kN/m3] 25

E [kPa] 20E6

Poisson’s Ratio (υ) [-] 0.2

G [kPa] 8.33




Comparison analysis of East Port Said soil parametersThree different models were developed according to each of the soil profiles (A, B, and C), and the soil parameters were defined separately for each layer per the respective soil pro-file. Parametric study with six cases (Table 7) were modeled to assess how well the HS model predicted soil behavior. For each case, the values Eu and cu are assigned as the medium value at the middle between the maximum and minimum val-ues of clay layer shown in Figure 5 where the stiffness values increase linearly with depth which range from about 40 % to 160 % of the mentioned median values in Table 7.

The numerical 3D model was developed for only three panels of the quay wall system, as the barrettes’ frame sys-tem is completely repetitive every 7 m. Hence, the typical model was developed with plan dimensions of 150 m by 21 m and a total depth of 122.5 m, as shown in Figure 9. The finite element mesh was modeled using tetrahedral el-ements with 10 nodes (Figure 10) and was generated after defining the model’s material properties. In addition to the soil elements, special types of elements were used to model structural behavior. For beams, 3-node line elements were used, which are compatible with the 3-node edges of a soil element where 6-node plate elements were used to simu-late the behavior of plates. Moreover, 12-node interface ele-ments were used to simulate soil-structure interaction (SSI) behavior. The total number of elements utilized in the 3D models are 16257, 23814, and 19444 elements for profiles A, B, and C, respectively. To show the connection between the front diaphragm wall and back wall with the barrette frames, the soil mass was partially hidden from the model, and the configuration of 3D finite element mesh perspective is shown in Figure 11.

Applied loads on Port-Said quay wallWith reference to the original design of the existing quay wall system, different loads values were assigned to the model (Table 8) according to Hamza and Hamed (2000). The loads acting over the deck included a vertical surcharge of 60 kPa. Two vertical line loads of 800 kN/m were also applied by the Gantry Cranes at the lines representing the front and back beams. The mooring operations on the quay wall were rep-resented by a horizontal force of 2,000 kN every 21 m of the quay wall. Therefore, a line load of 95 kN/m was applied to the 21 m wide numerical model along the line representing the front beam. The loads acting behind the deck included a vertical surcharge load of 20 kPa for a 30 m wide road direct-ly behind the deck and a vertical surcharge load of 60 kPa until the right boundary. Figure 12 shows a general view of the quay wall structure under the working loads.

The actual construction sequences described by Hamza et al. (2002) were followed in this case study (Table 9). The construction phases included the initial stresses, construction of the substructure system, and subsequent dredging. The loads were applied into the three main components as: (1) loads acting over the deck, (2) loads acting over the beams, and (3) loads acting behind the deck (i.e., behind the back wall: road and the storage yard area).

In the initial stresses phase, the initial pore water pressure and the effective vertical and horizontal stresses were calculat-ed. The horizontal effective stresses (σ'h) were taken equal to the vertical effective stresses (σ'v) multiplied by the coefficient of the at-rest earth pressure (Ko) for each soil layer. The results from the six modeled case studies were compared for each model with the different soil profiles. Figure 13 illustrates the total displacement |u| of the quay wall substructure for phase 10, where the maximum displacement |U| of the quay wall system was equal to about 141 mm. The maximum horizontal displacement Ux of the quay wall was about 139 mm, where the maximum vertical displacement Uz was about 30 mm.

Figures 14 to 17 present sample behavior of the front quay diaphragm wall using the soil properties from profile B for each of the six cases. Figure 14 depicts the variations of the horizontal movements over the existing front wall depth for the last construction phase based on the quay wall structural elements parameters and soil HS Model. It is clear that the maximum horizontal displacement decreases from 130 mm to 60 mm by about 50% when the soil stiffness became almost doubled. Figures 15, 16 and 17 show the variations of the axial

Figure 9. Horizontal mesh plan of the existing quay wall structure model (150 m x 21 m)

Table 7. Parametric study cases for east Port Said soft clay

Study Case Eu [MPa] cu [kPa]

Case 1 6.00 30

Case 2 9.00 32

Case 3 11.50 34

Case 4 14.00 36

Case 5 17.00 38

Case 6 20.00 40




Table 8. Types and values of design loads.

Type of load Value

Berthing loads 2000 kN or 95 KN/m

Crane load Vertical crane load = 800 kN/m Horizontal crane load = 80 kN/m

Surcharge loads Deck of the quay wall = 60 kN/sq. m Road behind quay = 20 kN/sq. m Stacking area behind the road = 60 kN/sq. m

Figure 10. Nodes and stress points distribution in the 10-node tetrahe-drons

Figure 11. Generated 3-D mesh (Profile B)

Figure 12. General view of the quay wall structure under the working loads

Table 9. Description of the construction phases

Phase Description

0 Initial phase calculation based on the defined pressure coefficient (Ko) value for each soil layer

1 Construction of diaphragm walls

2 Construction of beams

3 Construction of deck Slab

4 Excavation under deck up to El. -5.50 m LAT

5 Excavation in front of deck up to El. -5.50 m LAT

6 Dredging in front of deck up to El. -18.0 m LAT

7 Construction of the back road and yard

8 Application of the deck load of 60 kN/sq. m

9 Application of crane and fender loads (800 kN/m + 95 kN/m)

10 Application of loads on the back road and yard (20 kN/sq. m + 60 kN/sq. m)

force, shear force and bending moment results acting on bar-rettes for the different six cases under working loads. In gen-eral, when the soil stiffness increases, the internal forces con-siderably reduced. The settlement values behind the back wall along the road and yard distance are also shown in Figure 18. It can be said that the settlement maximum reduction reached 20 % if soil parameters increased from case 1 to case 6.

The results obtained from each profile were compared for the six cases to evaluate the sensitivity of the clay param-eters on the quay wall model outputs. Figures 19 to 24 pres-ent the results of best-fit regression analysis for the three soil profiles under consideration. The x-axis refers to the soft soil




Figure 13. East Port Said existing quay wall horizontal displacement - Phase 10 (Profile B-Case 1)

Figure 14. Horizontal movements for all cases over combi wall depth - Profile B

Figure 15. Normal Force for front barrette over depth - Profile B

Figure 16. Shear force for front Barrette over depth - Profile B




Figure 17. Bending moment for front Barrette over depth - Profile B

Figure 18. Settlement a long distance behind the back-diaphragm wall - Profile B

stiffness ratio (Eu/cu), while the y-axis refers to the maximum estimated output resulting from Plaxis 3D 2013 as drawn from the six cases. The resulting coefficient of correlation R2 for each of the considered soil profiles is given in these figures. The coefficient of correlation, R2, is a measure that determines the degree to which soil stiffness and quay wall behavior are associated. It gives a statistical correlation be-tween the measured soil stiffness and the numerical analysis results of the distribution of the displacement and internal forces over the front diaphragm barrette. Higher value means a better model, with a value of unity indicating a perfect sta-tistical correlation, and a value of zero indicating that there is no correlation. In general, the values of the stiffness ratio (Eu/cu) for the current studied cases varied from 200 to 500.

Figure 19. Effect of soil stiffness on quay wall horizontal deflection

Figure 20. Effect of soil stiffness on quay wall vertical deflection

Figure 21. Effect of soil stiffness on surface ground settlement subject to vertical loads

Table 10 summarizes the results of regression analysis for all the soil profiles. It is clear that the correlation coefficient R2 for all soil profiles have high degree of relationship with the output results, which shows the sensitivity of soft clay lay-er in all east Port Said soil profiles on the numerical analysis results. The average correlation of the estimated results ob-tained from profile C interaction with the existing quay wall is


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Figure 22. Effect of soil stiffness on axial force for quay wall front barrette

Figure 23. Effect of soil stiffness on bending moment for quay wall front barrette

Figure 24. Effect of soil stiffness on shear force for quay wall front barrette

As clear from Figure 19, the maximum horizontal dis-placement Ux at the top of the quay wall ranges from 35.9 mm to 131.7 mm for all cases analysis. it can be observed that the horizontal displacement decreases with increasing the soil elasticity modulus and shear resistance. The increase in the soil stiffness ratio from 200 to 500 significantly decreases the quay wall horizontal displacement. In general, the hori-zontal displacement results derived from profile B interaction are more conservative if compared to those of profiles A and C. The quay wall maximum horizontal displacement results for soil profiles A and B are close to each other at the min-imum stiffness ratio however, profile B average results are about 35% higher than profile C. This indicates that influence of Profile B soft clay is more significant on the horizontal displacement results if compared to those of profiles A and C.

The results obtained for the maximum vertical displace-ment on top of the quay wall are presented in Figure 20. It is also clear that both profile A and B are close to each other for every individual set of results; except for profile C. The average vertical displacement results derived from profile C is about three times higher than that of profiles A and B. This can be interpreted due to the disappearance of the hard clay layer underneath the quay wall barrette system which is re-placed by the dense silty sand layer.

On the other hand, the behavior of soil profiles B and C are almost equally for the settlement results behind the quay wall system along the road and back yard as shown in Fig-ure 21. Results from both soil profiles B and C are about 64 % higher than those of soil profile A. Figure 25 illustrates the deformed mesh for both models that contains soil profile A and soil profile C. It can be observed that the deformation starts from surface layer and extended down to the top level of (dense silty sand) layer which measures 65 mm in aver-age for soil profile C however, soil deformation stops at the top level of (very stiff to hard clay) layer for soil profile A. This confirms the serious effect of the (very stiff to hard clay) layer for dispersion of the deformation due to vertical loads.

Figures 22 shows the maximum values of normal force for front barrettes at the different soil cases which are in range of 11460 KN to 14550 KN. It is clear that the value of normal force decreases in a linear relationship when stiffness of soft layer increases for all soil profiles. It can be said that

about 13 % lower than profile A and B results. Consequently, it can be said that the effectiveness of soft clay in profile C for Port Said Quay wall numerical analysis results, has fewer influences if compared to those of profiles A and B.

Table 10. Regression analyses results

OutputR2

Profile A Profile B Profile C

Horizontal displacement Ux 0.905 0.955 0.847

Vertical displacement Uz 0.954 0.981 0.911

Settlement S 0.903 0.961 0.840

Axial force 0.956 0.999 0.842

Bending moment 0.910 0.920 0.860

Shear force 0.976 0.848 0.575

Average R2 value 0.934 0.944 0.812




Figure 26. East Port Said Port normalized soil model

Figure 25. Model deformed mesh for profiles A, and C




Table 11. Summary of existing quay wall analysis results for all case histories

Case StudiesAverage

Case 01 Case 02 Case 03 Case 04 Case 05 Case 06

Maximum horizontal displacement UX [mm]

Profile A 129.703 92.341 74.014 62.302 54.301 48.489 76.858

Profile B 131.739 96.255 79.148 69.156 62.403 58.447 82.858

Profile C 109.988 73.495 58.811 48.792 41.589 35.875 61.425

Maximum vertical displacement Uz [mm]

Profile A 20.389 17.491 15.985 14.896 13.988 13.104 15.976

Profile B 29.219 24.502 21.951 20.295 18.975 18.051 22.165

Profile C 65.586 60.486 58.122 56.246 54.749 53.276 58.078

Maximum settlement behind the quay wall S [mm]

Profile A 101.501 84.809 76.674 71.602 68.110 65.458 78.026

Profile B 150.658 134.325 126.786 121.771 118.325 116.279 128.024

Profile C 149.998 133.598 126.885 122.902 119.658 117.211 128.375

Maximum normal forces for front barrette N [1000 x kN]

Profile A 14.556 13.302 12.781 12.369 11.998 11.552 12.759

Profile B 14.925 14.182 13.597 13.101 12.667 12.440 13.485

Profile C 13.201 12.298 11.998 11.798 11.610 11.461 12.061

Maximum bending moment for front barrette M [1000 x kN.m]

Profile A 7.191 6.293 5.852 5.561 5.349 5.228 5.912

Profile B 6.555 6.402 6.335 6.296 6.274 6.273 6.356

Profile C 6.276 5.486 4.871 4.587 4.389 4.267 4.979

Maximum shear forces for front barrette Q [1000 x kN]

Profile A 1.892 1.465 1.211 1.009 0.857 0.668 1.183

Profile B 1.287 0.875 0.720 0.651 0.651 0.639 0.804

Profile C 0.981 0.674 0.593 0.591 0.572 0.584 0.666

Table 12. Summary of average of analysis results for all case histories

Numerical analysis outputAverage Results Evaluation

Profile A Profile B Profile C Worst Max %

Horizontal displacement Ux [mm] 76.858 82.858 61.425 82.858 35

Vertical displacement Uz [mm] 15.978 22.166 58.078 58.078 263

Settlement S [mm] 78.026 128.024 128.375 128.375 65

Axial force N [1000 x kN] 12.760 13.485 12.061 13.485 12

Bending moment [1000 x kN-m] 5.912 6.356 4.979 6.356 28

Shear force [1000 x kN] 1.184 0.804 0.666 1.184 78

the behavior of both profiles A and B are almost equal at the minimum soil stiffness however, the corresponding value for profile C is about 11% lower. Behaviors of soil profiles A and C become closer to each other with increasing the soft soil stiffness value while profile B result value is about 8% higher at maximum soil stiffness. On average, the normal force re-

sults derivate from profile B is about 11% higher than those of profile A and profile C.

In Figure 23, the E50/cu ratios are plotted as a function of bending moment for quay wall front barrette. Results show that the bending moment values decreases linearly with in-creasing the soil stiffness ratios for profiles A and C. It may




be inferred that soft soil stiffness for profile B would have a negligible influence on the bending moment response along the front barrette diaphragm walls.

The calculated shear forces for quay wall front barrette at the eighteen cases are ranged from 580 KN to 1889 KN as shown in Figure 24. The values obtained from soil profile A are the highest if compared to results of profile B and profile C. For small soil stiffness ratio, the maximum shear force re-sulting from profile A is about 60 % higher than that of profile B and about two times as large as the results of profile C. the values became much closer to each other with the increment of soil stiffness values which match about 600 KN. It can be also strongly saying that the soil stiffness influence on shear forces dissipates for those ratios higher than 300 at both pro-files B and C while shows an exponentially decreasing rate for profile A.

Summary and ConclusionsSo far, six case studies for three different soil profiles at east Port Said with total eighteen cases are analyzed. The main soil characteristics of those profiles are summarized in Figure 5. Then the general description of east Port Said ex-isting quay wall is given followed by the properties of the structure elements. Comparisons among the average output values derivate from the six case studies for each soil profile are listed in Table 11. In addition to the average numerical analysis results, Table 12 gives the evaluation of the worst results for all cases associated with the percentage difference to the best values. The study of the results given shows that:

a. All soil profiles under consideration for east Port Said Port have a thick deposit of soft clay which extended from about 20 m to 60 m below ground level. The stiffness va-riety of that layer is obviously a meaningful parameter af-fecting the east port Said model output result,

b. The results show the ratio of E50/cu concentrated in the range of 200 to 500 are in good correlation with the nu-merical analysis results of front diaphragm barrette,

c. In all the analyzed cases, the values of quay wall structural internal forces do clearly reduce with increasing the soft soil stiffness values,

d. Calculated vertical displacement of the present quay wall analysis derivate with the soil profile C, are mostly the worst if compared to the results of other models. The same can be said for the calculated soil settlement results,

e. When a hard clay layer is located under the soft clay lay-ers, the shear forces acting on the barrette wall penetrating that hard layer are increased with about 80%. However, it decreases the settlement with about 65%,

f. When the soft clay layer exists between two silty sand lay-ers at East Port Said Port, lateral deformation, axial forces, and the bending moments acting on the barrette diaphragm wall increased considerably.

Finally, sensitivity analyses were carried out in this research to reach the critical soil model from the collected data at the

available locations along the east Port-said harbor based on the soil profile and the existing quay wall design properties. It can be said that predictions of the numerical results, for the existing quay wall at east Port Said derivate from profile C were mostly more conservative if compared to those of Pro-files A and B. Consequently, Figure 26 shows the constitutive soil model for the optimization analyses with the hardening soil parameters based on Profile C. This model is presented to be able to control the future analysis for East Port Said Area. Obviously, we are aware that the recommended soil model requires additional verification by performing further research considering other sensitive soil parameters and more diverse sites at east Port Said Port.

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