Click to edit Master title styleIntegral Bridges and the

Modeling of Soil-Structure

Interaction

Julian Moses, Principal Engineer, LUSAS

Introduction

2

Introduction

3

Introduction

4

About soil-structure interaction

5

About soil-structure interaction

6

Active Movement

0.0250.025

Passive Movement

Wall movement / Height H

1.0

2.0

4.0

8.0

0.5

0.25

K

H

H

Kp

K0

Ka

Seasonal changes

7

Seasonal changes

8

Ko

Soil

Pressure

Ka

Pressures increase

every year for

100-200 cycles

Wall displacement

1st summer

2nd summer

3rd summer

For design, consider

maximum and

minimum pressures

Analysis methods

1. Limiting equilibrium approach

2. Soil-structure interaction (continuum)

3. Soil-structure interaction (springs)

9

1 – Limiting equilibrium

10

Full height integral

abutment on pad footingFull height integral

abutment on pilesBank pad

1 – Limiting equilibrium

11

1 – Limiting equilibrium

12

Full height integral

abutment on pad footingFull height integral

abutment on pilesBank pad

(Es in MPa)

1 – Limiting equilibrium

14

Structural idealisation

• Shell elements

– Shear, bending, twisting and in-plane forces

Twisting MXY

Twisting MXY

Bending MX

Bending MX

15

XY

Z

XY

Z

XY

Z

Structural idealisation

16

3D beam elements

(girders)

Shell elements

(slab)

Straight girders,

Precast etc

X

Y

Z

Structural idealisation

17

3D beam elements

(flanges & stiffeners)

3D beam elements

(bracing)

Shell elements

(slab)

Shell elements

(web)

Skew or curved etc

X

Y

Z

Structural idealisation

18

Grid models

“The conventional 2D-grid models used in current practice

• Substantially underestimate the girder torsional

stiffnesses in I-girder bridges

• Substantially misrepresent the cross-frame responses

• Do not address the calculation of girder flange lateral

bending in skewed I-girder bridges” Section 2.9

19

Grid models

20

“...difficulties arise when in-plane effects are

considered... the real problem is the occurrence of

local in-plane distortions of the grillage members...

which are clearly inconsistent with the behaviour of the

bridge deck.” Section 7.5

1 – Limiting equilibrium

21

Shell elements

(slabs)

K* approach not adequate

22

Full height integral abutment

on single row of piles

Bank pad on single

row of piles

Discrete

piles

Embedded wall

integral abutment

Wall

2 – SSI with soil continuum

23

Material Key

Concrete

Limestone

Sands

Tilgate

Weald clay

Plane strain

elements

2D Beam elements

Check extents

2 – SSI with soil continuum

Mesh checks

1. Width & depth of soil block

2. Element shapes and aspect ratios

3. Mesh refinement

4. Element formulation – quadratic better

24

Avoid angles <30°1:1 ideal

1:3 max (areas of interest)

1:10 max (remote)

Need automatic re-meshing

2 – SSI with soil continuum

25

Material Key

Concrete

Limestone

Sands

Tilgate

Weald clay

Check shape

& refinement

Plane strain

elements

Check extents

2D Beam elements

2 – SSI with soil continuum

26

10

m

10m

Mohr Coulomb yield surface

3

2

1

1

2

3

2 – SSI with soil continuum

27

2 – SSI with soil continuum

30

Material Key

Concrete

Limestone

Sands

Tilgate

Weald clay

Check shape

& refinement

Plane strain

elements

Check extents

Mohr-Coulomb

material

2D Beam elements

2 – SSI with soil continuum

• Cohesive soils

– Strain ratcheting may be ignored

• Granular soils

– Use modified elastic modulus

– Based on K* equations

– Determine effective height, H, iteratively

31

2 – SSI with soil continuum

32

Material Key

Concrete

Limestone

Sands

Tilgate

Weald clay

Mohr-Coulomb

material

Modified elastic

modulus*Check shape

& refinement

Plane strain

elements

Check extents

2D Beam elements

2 – SSI with soil continuum

• Interface between soil and structure

– Joint elements

– Contact slidelines

– Elasto-plastic interface materials

• Back of wall friction angle, δ

– Maximum δ=φ’

– Smooth δ=0

– Suggested δ=φ'/2

33

2 – SSI with soil continuum

34

Material Key

Concrete

Limestone

Sands

Tilgate

Weald clay

Mohr-Coulomb

material

Modified elastic

modulus*Check shape

& refinement

Plane strain

elements

Check extents

Frictional interface

δ=φ'/2 2D Beam elements

K* approach not adequate

35

Full height integral abutment

on single row of piles

Bank pad on single

row of piles

Discrete

piles

Embedded wall

integral abutment

Wall

Continuum Soil modeled with nonlinear springs

3 – SSI with soil springs

36

Deck

(shells/ 3D beams)

End screens

(shells/ 3D beams)Piles

(3D beams)

Ka and K*

pressures

Soil springs /

nonlinear

joints

Discrete

piles

3 – SSI with soil springs

37

3 – SSI with soil springs

Deck

shells & 3D beams

End screens

shells & 3D beams

Piles

3D beamsSoil springs

38

3 – SSI with soil springs

39

κ = 0 for cohesive soil under moderate loads

κ = 0.5 for medium cohesive soil and non-cohesive soil above water table

κ = 1.0 for non-cohesive soil below the groundwater level or under greater loads

κ = 1.5-2.0 for loose non-cohesive soil under very high loads

κ

κ

κ

κ

3 – SSI with soil springs

40

Stiffer,

stronger

Softer,

weaker

Discrete

piles

3 – SSI with soil springs

41

Lateral pressure

kh

Horizontal deflection

'a

'p

Active Movement

Passive Movement

'0

3 – SSI with soil springs

42

Software requirements

• Structural elements (beams, shells)

• Geotechnical elements (joints, springs,

continuum)

• Automatic remeshing

• Nonlinear materials (e.g. Mohr Coulomb)

• Easy way to vary properties with depth

43

Summary

44

Soil continuum

Soil Springs UK Guidance: PD6694-1