Earthquake Design of Retaining StructuresMaster thesis

Antonela-Flavia Achimp

Supervisor: Varvara Zania, Technical University of Denmark

External supervisors: Andrija Krivokapic, Rambøll

Carsten Lyse, Cowi

22/10/2015Earthquake Design of Retaining Structures2 Dansk Geoteknisk Forening, Aarhus

Contents

Introduction

• Problem Statement

• Motivation of the Study

• Investigation Strategy

Literature

• Pseudostatic Analysis

• Dynamic Analysis

• Westergaard Solution

• Eurocode EN 1998-5

Numerical Modelling

• Westergaard Solution

• L-Shaped Retaining Wall

Case Study

• Pseudostatic Analysis

• Dynamic Analysis

Conclusions and Further Research

22/10/2015Earthquake Design of Retaining Structures3 Dansk Geoteknisk Forening, Aarhus

Problem Statement

Introduction-Problem Statement

Water Backfill + WaterWall

Static forces Dynamic forces

22/10/2015Earthquake Design of Retaining Structures4 Dansk Geoteknisk Forening, Aarhus

Motivation of the Study

Introduction-Motivation of the Study

• Pseudostatic

• Full-Dynamic

When taking a decision:-resources: seismic hazard analysis, time, software, personnel

One parameter to

give the inertia force

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Earthquake Analyses

Literature- Earthquake analyses

• Mononobe-Okabe Theory

• Richard-Elms Theory

• Full-Dynamic Analysis

-performed with use of Finite Element Software

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Westergaard Solution (1931)-Water Pressures on Dams during Earthquake-

Literature- Westergaard solution

• Two causes for added stresses during earthquake:

-accelerations of the mass of the dam-changes of water pressures

• Rigid vertical wall

• Horizontal acceleration

• No shear stresses

22/10/2015Earthquake Design of Retaining Structures7 Dansk Geoteknisk Forening, Aarhus

Eurocode EN 1998-5

Literature- Eurocode EN 1998-5

• Hydrodynamic pressure on the outer face of the wall (Westergaard)

• Hydrodynamic pressure: water on both faces of the wall

2 x

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Numerical Modelling

Numerical Modelling- Introduction

• Westergaard Solution-Numerical investigation in Abaqus of Westergaard solution using two different approaches: water as an acoustic medium; water as a continuum.

• L-Shaped Retaining Wall-Check of the failure surface using pseudostatic analysis in Plaxis

2D AE

CAE

22/10/2015Earthquake Design of Retaining Structures9 Dansk Geoteknisk Forening, Aarhus

Westergaard Solution

Numerical Modelling- Westergaard solution

20.5 m

4 m

64.5 m

4 m

Acoustic elements Acoustic elements

Infinite elements Infinite elements

- Type of elements- Resonance

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Westergaard Solution

Numerical Modelling- Westergaard solution

• Results

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L-Shaped Retaining Wall

Numerical Modelling- L-Shaped Retaining Wall

• Soil: M-C material

• Concrete: L-E material

• PGA=0.25g

3.7

m0.4

m

2 m

Total horizontal displacements

22/10/2015Earthquake Design of Retaining Structures12 Dansk Geoteknisk Forening, Aarhus

L-Shaped Retaining Wall

Numerical Modelling- L-Shaped Retaining Wall

Total deviatoric strains

(a) Braja Das, Principles of Foundation Engineering, 2011

(b) Niels Krebs Ovesen, Lærebog i Geoteknik,, 2007

22/10/2015Earthquake Design of Retaining Structures13 Dansk Geoteknisk Forening, Aarhus

Port of Beirut- New Quay Wall

Case Study- Introduction

8.5 m

Quay wall cross section (courtesy of Rambøll)

17 m

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Geometry of the Model and Geotechnical Conditions

Case Study- Introduction

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Pseudostatic Analysis

Case Study- Pseudostatic Analysis

• PGA= 0.25g

- Boundary conditions: standard fixities

- M-C Model for soil

- Static Young’s Modulus (average from the given range)

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Pseudostatic Analysis

Case Study- Pseudostatic Analysis

• Results

Horizontal displacement Deviatoric strain

22/10/2015Earthquake Design of Retaining Structures17 Dansk Geoteknisk Forening, Aarhus

Dynamic Analysis

Case Study- Dynamic Analysis

- Boundary conditions: free field ; viscous

- Hardening soil model with small strain stiffness for fill material; - Linear- Elastic soil model for bedrock

- Dynamic Young’s Modulus (3-4 times the static one)

22/10/2015Earthquake Design of Retaining Structures18 Dansk Geoteknisk Forening, Aarhus

Dynamic Analysis

Case Study- Dynamic Analysis

• Hardening Soil model with small strain stiffness

- Stress dependent stiffness

- Strain dependent stiffness

m=0

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Dynamic Analysis

Case Study- Dynamic Analysis

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Dynamic Analysis

Case Study- Dynamic Analysis

• Results- Horizontal Displacements

Maximum horizontal displacement [mm]

TH1 TH2 TH3

A 20 11 10

B 4.5 5 1

TH 1

TH 2

TH 3

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Dynamic Analysis

Case Study- Dynamic Analysis

• Results- T-H along the wall

Peak ground acceleration [g]

TH1 TH2 TH3

A 1.9 0.73 1.1

B 2.5 0.9 0.61

TH 1

TH 2

TH 3

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Conclusion and Further Research

Case Study- Dynamic Analysis

• Further research

• Analysis of the quay wall

-interface between the concrete blocks – relative movements-parametric study performed -displacement-based methods

Maximum horizontal displacement [mm]

EC8 Pseudostatic Dynamic

90 60 20

Analysis time [h]

Pseudostatic Dynamic

1 8-43

Thank you for your attention!