Click to edit Master title styleIntegral Bridges and the
Modeling of Soil-Structure
Interaction
Julian Moses, Principal Engineer, LUSAS
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
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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)
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1 – Limiting equilibrium
10
Full height integral
abutment on pad footingFull height integral
abutment on pilesBank pad
1 – Limiting equilibrium
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Full height integral
abutment on pad footingFull height integral
abutment on pilesBank pad
(Es in MPa)
Structural idealisation
• Shell elements
– Shear, bending, twisting and in-plane forces
Twisting MXY
Twisting MXY
Bending MX
Bending MX
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XY
Z
XY
Z
XY
Z
Structural idealisation
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3D beam elements
(girders)
Shell elements
(slab)
Straight girders,
Precast etc
X
Y
Z
Structural idealisation
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3D beam elements
(flanges & stiffeners)
3D beam elements
(bracing)
Shell elements
(slab)
Shell elements
(web)
Skew or curved etc
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
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Grid models
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“...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
K* approach not adequate
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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
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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
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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
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Material Key
Concrete
Limestone
Sands
Tilgate
Weald clay
Check shape
& refinement
Plane strain
elements
Check extents
2D Beam elements
2 – SSI with soil continuum
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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
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2 – SSI with soil continuum
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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
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2 – SSI with soil continuum
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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
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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
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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
Deck
shells & 3D beams
End screens
shells & 3D beams
Piles
3D beamsSoil springs
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3 – SSI with soil springs
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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
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Lateral pressure
kh
Horizontal deflection
'a
'p
Active Movement
Passive Movement
'0
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
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