Presentation IQPC Africa

Seismic Design Aspects of Underground Structures

Asrat Worku (Dr-Ing) Gibb International, Nairobi Kenya (Formerly, Associate Professor at Addis Ababa University, Addis Ababa, Ethiopia)

Outline 1. Types of UG Structures Addressed 2. Earthquake Effects on UG Structures 3. Performance of UG Structures to Earthquakes 4. Seismic Design Procedures 5. Seismic Hazard Analysis 6. Seismic Design Load Criteria 7. Ground Motion Parameters 8. Response of UG Structures to Ground Shaking 9. Large Ground Deformations 10. Conclusions

1. Types of UG Structures The presentation focuses on tunnels

Cut-and-cover tunnels Bored tunnels Immersed tunnels

Most issues are applicable to other UG structures including Cut-and-cover structures Portal Structures Deep Chambers Waste Repositories (e.g.: nuclear)

2. Earthquake Effects on UG Structures

Two major effects 1. Ground Shaking (major concern)

Due to seismic waves 2. Ground Failure

Liquefaction Slope instability Fault Displacement


Severity in both Effects depends on Structure geometry Depth to structure Soil properties Structural properties Ground motion characteristics


On-ground structures Inertia of the structure and resonance are

important

UG structures Inertia of structure (gross11kN/m3) is less than the

inertia of surrounding soil - mostly disregarded


Misguided conception exists due to the small structural inertia

However, seismic design of UG structures is governed by Free-field ground motion, and SSI

(see figures)


(Kawashima 2006)

Significant inertia effect


(Kawashima 2006)

Insignificant inertia effect

Similar frequency content

3. Observed Performance of UG Structures to EQ Documented case histories of EQ damages to UG

structures exist (ASCE, JSCE, Researchers)

In western US UG structures built as early as 1927 Measured free-field PGA: 0.1g - 0.25g Observed damages to date are insignificant

(including during Loma Prieta and Northridge) However, experts warn: maximum anticipated

seismic events not reached Hashash et al, 2001

3. Observed Performance of UG Structures to EQ Daikai Subway Station, Japan, exhibited

severest damages so far: Existing Conditions

Cut-and-fill, box-type construction Central columns at 3.5m interval Box: 17m wide by 7.17m high Columns: 0.4m by 1.0m in section and 3.82m high 4.8m overburden No seismic consideration in its design (1962)

Kawashima 2000, 2006

3. Observed Performance of UG Structures to EQ Daikai Subway Station: Extent of Damage

Severe damage occurred during 1995 Kobe EQ 35 center columns damaged (See figure) Roof slab collapsed Road on the surface settled by 2.5m Columns with light shear r. bars failed Columns with additional zigzag r. bars survived Transverse walls provided at change of station width

were damaged saving the columns

Hashash et al, 2000; Kawashima, 2000, 2006

3. Observed Performance of UG Structures to EQ Center column failure Mechanism of failure

Kawashima 2000, 2006

3. Observed Performance of UG Structures in General Less damage than in surface structures

Damages decrease with depth

Cut-and-cover tunnels are more vulnerable than deep bored tunnels

Structures in rocks are safer than in soils

Stabilization of surrounding soil is more

effective than increasing liner thickness

Hashash et al, 2001

3. Observed Performance of UG Structures to EQ - General

Damage may be related to PGA and PGV

Strong-motion duration is very important to fatigue and excessive deformation

Slope stability is important in portal structures

Damages to lined tunnels are less than in pipelines

Hashash et al, 2001

4. Seismic Design Procedure

Step 1: Defining the Seismic Environment

Step 2: Evaluation of Ground Response to Shaking

Step 3: Assessment of Structural Behavior

4. Seismic Design Procedure

Step 1: Defining the Seismic Environment Conducting Seismic Hazard Analysis (SHA)

Establishing Design Criteria

Establishing Design Ground Motion Parameters

4. Seismic Design Load Procedure

Step 2: Evaluation of Ground Response

It involves evaluating Ground Shaking: the main focus here

Ground Failure

4. Seismic Design Load Procedure

Step 3: Assessment of Structural Behavior

Establishing Seismic Design Loading Criteria

Determination of Response of UG Structures to Ground Deformation

Any Special considerations

Hashash et al, 2001

5. Seismic Hazard Analysis

Characterizes potential for strong ground motions for a given region by studying Extent of active faulting, Potential for fault motion, and Recurrence rate

Two approaches available Deterministic seismic hazard analysis (DSHA) probabilistic seismic hazard analysis (PSHA)

5.1. DSHA Aims at a particular seismic scenario to

summarize hazard at a site and involves 1. Identification of EQ sources: geometry, potential

(M) 2. Source-to-site distance of each 3. Identification of controlling EQ in terms of a

ground motion parameter: attenuation Relations are employed for this purpose

4. Definition of seismic hazard in terms of PGA, PGV, PGD, RS and TH of the design EQ

5.2 PSHA Accounts for uncertainties in the size, location,

and recurrence rate of EQs probabilistically 1. Identification of EQ sources with probability

distribution of location for each 2. Characterization of seismicity/temporal

distribution 3. Determination of ground motion by all sizes of EQs

with uncertainties considered 4. Combination of uncertainties to establish the

probability that a given ground motion parameter will be exceeded for a given time period

5.2 PSHA Seismic Hazard Maps (GSHAP)

PGA up to 0.24g in Africa

The EARS has possibly the highest hazard

SA may experience up to 0.16g

PGA for 475-years return period

5.2 PSHA Seismic Hazard Maps

PGA up to 0.24g In EARS region

Many vulnerable populous cities and towns in EARS region

Capital cities with high hazard: Asmara, Djibouti, Addis Ababa, Juba, Kampala, Bujumbura

5.2 PSHA Seismic Hazard Maps (GSHAP)

According to SABS 2010, SA may experience up to 0.1g from EQ And up to 0.2g from mining activities

SABS Standards Division, 2010

5.2 PSHA Generally, site-specific seismic hazard studies are

recommended for major structures in a specific area

A lot has yet to be done in Africa regarding seismic hazard assessment, especially in EARS region

The lack of awareness among policy makers even engineers is quite alarming

In contrast to its relatively low seismic hazard, SA can be cited as a good example in updating seismic codes (e.g. SABS 2010)

6. Seismic Design Load Criteria

Dual Criteria: 1. MDE: aims at life safety (corresponds to ULS)

In PSHA, 3 5% probability of exceedance in the

life span of the facility (usually 50 years)

Worst combination of DL, LL, EQ to be considered


Dual Criteria: 2. ODE: minimizes economic risk (corresponds to

SLS) Occurrence: at least once in design life In PSHA, 40 50% probability of exceedance Facility should be operational during and after

event with little or no damage Thus, response must remain elastic


Load Combinations: 1. MDE

Cut-and-cover tunnels

U=DL+LL+E1+E2+EQ

Bored tunnels U=DL+LL+EX+H+EQ


Load Combinations: 2. ODE Cut-and-cover tunnels

U=1.05DL+1.3LL+1.05(E1+E2)+1.3EQ

Bored tunnels U=1.05DL+1.3LL+1.5EX+H+1.3EQ

7. Design Ground Motion Parameters

Maximum/effective A, V and D are employed to define MDE or ODE

Damage to UG structures are better correlated to particle v and u than to a

Most attenuation relations available for A, but also for V and D

In the absence of site-specific data, available relations may be used to estimate PGV and PGD from PGA (see Tables)

7. Design Ground Motion Parameters (Power et al. 1996)

Mw Ratio: PGV(cm/s)/PGA(g)

Source-to-site distance (km)

0-20 20-50 50-100

Rock (vs>750m/s)

6.5 66 76 86

7.5 97 109 97

Stiff soil (200-750m/s)

6.5 94 102 109

7.5 140 127 155

Soft soil (

7. Design Ground Motion Parameters (Power et al. 1996)

Mw Ratio: PGD(cm)/PGA(g)

Source-to-site distance (km)

0-20 20-50 50-100

Rock (vs>750m/s)

6.5 18 27 30

7.5 43 56 69

Stiff soil (200-750m/s)

6.5 35 41 48

7.5 89 99 112

Soft soil (

8. Response of UG Structures

Modes of Response (see Figures)

1. Compression-extension

2. Longitudinal bending

3. Ovaling (for circular shapes)

4. Racking (for rectangular)

8. Response of Ground Shaking

Hashash et al 2001

8. Response of UG Structures

MAIN Focus: Response to ground shaking A number of approaches available

1. Free-field deformation Approach 2. SSI Approach 3. Seismic Deformation Method (for soft ground) 4. Numerical Approaches

8.1 Free-Field Deformation (FFD) Approach FFD describes strains due to elastic plane

waves in the absence of structures It imposes the free-field deformation on the UG

structure Does not account for SSI Provides first-order estimate of structural

response Closed-form relations available FFD is effective tool for small soil deformations

(low-seismic areas, stiff soils)

8.1 Free-Field Deformation (FFD) Approach Axial and Bending FFD is based on Newmarks (1968) idealization of

elastic waves (see sketch)

St. John and Zahrah (1987) used this to calculate axial and curvature strains analytically due to the three wave types shown schematically (see sketch)

All solutions are available in closed form: longitudinal, normal and shear strains and curvature due to P-, S- and Rayleigh waves

8.1 Free-Field Deformation (FFD) Approach Axial and Bending

Power et al 1996

8.1 Free-Field Deformation (FFD) Approach Axial and Bending Tunnel modeled as an elastic beam, combined

free-field axial and curvature deformations are obtained as

For P-waves:

For S-waves:

For Rayleigh waves (compression component):

8.1 Free-Field Deformation (FFD) Approach - Axial and Bending

With increasing r, the curvature contribution increases

However, this component is generally small

Note: the apparent wave velocities, VP and VS, fall in

the range of 4-8km/s and 2-4km/s, respectively These are close to wave velocities in deep rock

than in the shallow soil

8.1 Free-Field Deformation (FFD) Approach Ovaling Deformation

Ovaling

refers to the distortion of circular tunnels (see Figure)

is caused by waves inducing transverse strains

Is predominantly due to vertically propagating shear waves

8.1 Free-Field Deformation (FFD) Approach Ovaling Deformation Non-perforated ground Perforated ground

Wang 1993


In non-perforated ground (see Figure):

In perforated ground (see Figure):

This is an upper bound


The perforated ground scenario

gives 2 to 3 times larger distortion than the non-perforated case

gives an upper bound distortion criterion

Provides a good estimate for thin linings


The non-perforated ground scenario gives better estimate for lining stiffness

comparable with the medium

For stiffer linings, distortion can even be less than in the non-perforated case

8.1 Free-Field Deformation (FFD) Approach Racking Deformation

Racking

refers to the distortion of rectangular tunnels (see Figure)

Associated deformations can be computed from shear strains available in closed form

Alternatively, numerical site response analysis can be used

8.1 Free-Field Deformation (FFD) Approach Racking Deformation

8.2 Soil-Structure-Interaction (SSI) Approach

Accounts for soil-structure interaction

Tunnels are modeled as beams on elastic foundation (see Figure)

SSI is accounted for quasi-statically through use of linear springs

No dynamic inertia interaction is considered

The internal forces are as shown (see Figure)

8.2 Soil-Structure-Interaction (SSI) Approach - Model

(After Kawashima 2000)

8.2 Soil-Structure-Interaction (SSI) Approach: Internal Forces Sectional forces Circumferential forces

Hashash et al . 2001

8.2 Soil-Structure-Interaction (SSI) Approach - Axial and Bending

The maximum axial strain (due to a 45-degrees incident shear wave):

A= free-field displacement response amplitude of idealized sinusoidal shear wave; Q= frictional force; L=Wave length; Ka= longitudinal spring stif



The maximum bending strain due to a zero-degree incident shear wave:

The maximum shear force:

Kt= transversal spring stiffness; Ic=mom. of inertia



The spring coefficients:

The wave length:

Where, for an assumed uniform soft soil layer over rock:



The ground displacement amplitude for a sinusoidal wave:

For free-field axial strains

For free-field bending strains


A conservative estimate of the total axial strain is given by

Finally, the structure is designed to sustain these strains

8.2 Soil-Structure-Interaction (SSI) Approach - Ovaling

The ovaling response of a tunnel is a function of the compressibility and flexibility ratios, C and F defined as:

C: a measure of extensional stiffness F: a measure of flexural stiffness


Assuming full slip conditions (for soft soils and severe shaking):

The diametric strain:

Maximum thrust: (see Figure) The maximum b. moment:

Where (See Plots)

K1= Lining response coefficient

8.2 Soil-Structure-Interaction (SSI) Approach Forces due to ovaling


For most tunnels, the interface condition is between the full-slip and no-slip cases

The full-slip case may cause significant underestimation of Tmax


The no-slip condition can give maximum thrust as given by

Where the lining response coefficient is given by:


Variation of K2, and thus of Tmax, against C and F for =0.35 is as plotted (see graph)


The normalized lining deflection:

(see Plots)


Observations from the plots: For F1 (softer lining in stiffer soil): The lining deforms more than the free field

For F: lining deflection equals that of the perforated ground

8.2 Soil-Structure-Interaction (SSI) Approach - Racking Box-type structures are less efficient to transmit

static loads Thus,

the walls and slabs are thicker and the structure stiffer SSI is more important than in circular tunnels

Besides, ground deformations may be larger due to Site amplification at shallow depth Decreased soil stiffness due to lower overburden

pressure Different nature of backfill

8.2 Soil-Structure-Interaction (SSI) Approach - Racking

The increased rigidity for statics reduces structural strains

Hence, design based on free-field strains is too conservative

Closed-form solutions are not available due to variable geometric characteristics

The stiffness of the soil in simple shear relative to the structure is the most important factor

(Wang 1993)


It can be easily shown that the soil-to-structure flexibility ratio is given by (see Figure) Where W is the width and S1 is the unit racking

stiffness of the structure given by (see Figure)

(Hashash et al 2001)


(Hashash et al 2001)

8.2 Soil-Structure-Interaction (SSI) Approach - Racking For simple structures the racking stiffness can be

determined from ordinary frame analysis

Thus, F for a one-barrel frame with moments of inertia, IR=IS and IW, for the slabs and walls is

F can similarly be obtained for other common forms


FE studies showed the following F0: structure is rigid; do not rack regardless of

ground distortion F1: Structure racking is larger than soil F: Nearly Zero stiffness of structure; same

deformation as the perforated ground

8.2 Seismic Deformation Method

Emerged out of a 5-year research in Japan (1972-1977) for UG structures in soft ground

The modeling accounts for SSI Consists of idealizing the UG structure as

Beam on elastic foundation (for axial and bending deformations) (see Figure)

Spring-mass modeling 2D FE model for in-plane ovaling/racking

(After Kawashima 2006)

8.2 Seismic Deformation Method Beam on elastic foundation

(Kawashima 2006)


The governing DE neglecting inertia Axial deformation:

Bending deformation:

The idealized ground deformation (see sketch):


(Kawashima 2006)


The wave length based on Guide Specifications: Where

VS and VSB: shear wave velocities of soil (average) and

rock; L1 and L2 are corresponding wave lengths

TS: fundamental natural period


The ground surface displacement amplitude: SV: design velocity response spectrum at bedrock

level The surface strains are determined by

differentiating the surface deformation, the amplitudes being


The ratio of the strain amplitudes:

For a uniform soil over rock, it can be easily shown that

Thus, for a uniform soil:

The strain ratio varies in the range of


The deformation of the structure is determined by solving the DEs

The internal forces for design easily follow from the constitutive laws

8.2 Seismic Deformation Method Spring-mass system

(Kawashima 2006)

Soil mass is included

3D analysis is possible

8.2 Seismic Deformation Method In-plane 2D FE model

(Kawashima 2006)

Suitable for ovaling/ racking

Analysis is in 2D

9. Large Ground Deformations Large ground deformations during EQ are

associated with Liquefaction Fault displacement Slope Instability

Since UG structures are commonly long, They may generally cross soil formations susceptible

to liquefaction Crossing active faults may not be avoidable Certain structures like portals ca be susceptible to

slope instability Hence, considerations for these issues are equally

important as for the ground shaking

10. Conclusions Knowledge is not as well established as in on-

ground structures

Measured data and studies are fewer

A few state-of-the-art reviews are available

Seismic loadings on UG structures are not as insignificant as commonly perceived

FFD and SSI are very important considerations

In contrast, structure inertia plays a minor role

10. Conclusions

The FFD Approach is sufficient for anticipated small ground deformations (case in point: Africa?)

The SSI approach and SDM are also easy to use

For the continent: FFD, SSI and SDM approaches are recommendable Complicated numerical modeling do not appear to be

necessary, at least currently

10. Conclusions

Considerations for large ground deformations are equally important

Adaptation of design guides is not difficult and is recommendable

Regular follow-up of the global state-of-the-art is helpful for improvement

Thank You

Seismic Design Aspects of Underground StructuresOutline1. Types of UG Structures2. Earthquake Effects on UG Structures2. Earthquake Effects on UG Structures2. Earthquake Effects on UG Structures2. Earthquake Effects on UG Structures2. Earthquake Effects on UG Structures2. Earthquake Effects on UG Structures3. Observed Performance of UG Structures to EQ3. Observed Performance of UG Structures to EQ 3. Observed Performance of UG Structures to EQ3. Observed Performance of UG Structures to EQ3. Observed Performance of UG Structures in General3. Observed Performance of UG Structures to EQ - General4. Seismic Design Procedure4. Seismic Design Procedure4. Seismic Design Load Procedure4. Seismic Design Load Procedure5. Seismic Hazard Analysis5.1. DSHA5.2 PSHA5.2 PSHA Seismic Hazard Maps (GSHAP)5.2 PSHA Seismic Hazard Maps5.2 PSHA Seismic Hazard Maps (GSHAP)5.2 PSHA6. Seismic Design Load Criteria6. Seismic Design Load Criteria6. Seismic Design Load Criteria6. Seismic Design Load Criteria7. Design Ground Motion Parameters7. Design Ground Motion Parameters(Power et al. 1996)7. Design Ground Motion Parameters(Power et al. 1996)8. Response of UG Structures8. Response of Ground Shaking8. Response of Ground Shaking8. Response of Ground Shaking8. Response of UG Structures8.1 Free-Field Deformation (FFD) Approach8.1 Free-Field Deformation (FFD) Approach Axial and Bending8.1 Free-Field Deformation (FFD) Approach Axial and Bending8.1 Free-Field Deformation (FFD) Approach Axial and Bending8.1 Free-Field Deformation (FFD) Approach Axial and Bending8.1 Free-Field Deformation (FFD) Approach - Axial and Bending8.1 Free-Field Deformation (FFD) Approach Ovaling Deformation8.1 Free-Field Deformation (FFD) Approach Ovaling Deformation8.1 Free-Field Deformation (FFD) Approach Ovaling Deformation8.1 Free-Field Deformation (FFD) Approach Ovaling Deformation8.1 Free-Field Deformation (FFD) Approach Ovaling Deformation8.1 Free-Field Deformation (FFD) Approach Racking Deformation8.1 Free-Field Deformation (FFD) Approach Racking Deformation8.2 Soil-Structure-Interaction (SSI) Approach8.2 Soil-Structure-Interaction (SSI) Approach - Model8.2 Soil-Structure-Interaction (SSI) Approach: Internal Forces8.2 Soil-Structure-Interaction (SSI) Approach - Axial and Bending8.2 Soil-Structure-Interaction (SSI) Approach - Axial and Bending8.2 Soil-Structure-Interaction (SSI) Approach - Axial and Bending8.2 Soil-Structure-Interaction (SSI) Approach - Axial and Bending8.2 Soil-Structure-Interaction (SSI) Approach - Axial and Bending8.2 Soil-Structure-Interaction (SSI) Approach - Ovaling8.2 Soil-Structure-Interaction (SSI) Approach - Ovaling8.2 Soil-Structure-Interaction (SSI) Approach Forces due to ovaling8.2 Soil-Structure-Interaction (SSI) Approach Forces due to ovaling8.2 Soil-Structure-Interaction (SSI) Approach - Ovaling8.2 Soil-Structure-Interaction (SSI) Approach - Ovaling8.2 Soil-Structure-Interaction (SSI) Approach - Ovaling8.2 Soil-Structure-Interaction (SSI) Approach - Ovaling8.2 Soil-Structure-Interaction (SSI) Approach - Ovaling8.2 Soil-Structure-Interaction (SSI) Approach - Ovaling8.2 Soil-Structure-Interaction (SSI) Approach - Ovaling8.2 Soil-Structure-Interaction (SSI) Approach - Racking8.2 Soil-Structure-Interaction (SSI) Approach - Racking8.2 Soil-Structure-Interaction (SSI) Approach - Racking8.2 Soil-Structure-Interaction (SSI) Approach - Racking8.2 Soil-Structure-Interaction (SSI) Approach - Racking8.2 Soil-Structure-Interaction (SSI) Approach - Racking8.2 Seismic Deformation Method8.2 Seismic Deformation Method Beam on elastic foundation8.2 Seismic Deformation Method Beam on elastic foundation8.2 Seismic Deformation Method Beam on elastic foundation8.2 Seismic Deformation Method Beam on elastic foundation8.2 Seismic Deformation Method Beam on elastic foundation8.2 Seismic Deformation Method Beam on elastic foundation8.2 Seismic Deformation Method Beam on elastic foundation8.2 Seismic Deformation Method Spring-mass system8.2 Seismic Deformation Method In-plane 2D FE model9. Large Ground Deformations10. Conclusions10. Conclusions10. ConclusionsThank You

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