Soil Structure Interaction

Soil-structure interaction

c©ZACE Services Ltd

August 2011

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Examples of soil-structure interaction

Sheet-pile walls

Prestressed anchors

Diapraghm walls

Nailing

Foundation rafts with piles

Building-foundation

In all the above problems strong displacement/pressurediscontinuity may appear → soil-structure interfaces play animportant role

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Sheet-pile wall: example

N Preface N N 2D problems

1.4 HOW TO RUN SHEET-PILE WALL PROBLEM

• Data file: tutorials/sheet-pile-wall.INP

• Description

Generation of a complex geotechnical model of installation of an anchored sheet pile wall,followed then by an excavation is the goal of this tutorial. The geometry of the modelwill evolve in time and some model components like wall, anchors or excavated soil layerswill appear or disappear according to the assumed scenario. The geometry of the model isshown in the figure below.

Clay

Excavation zone-1

Excavation zone-2

6 m3

3

8 m

6m12 m 18 m

3

Medium sandAnchors

Sheet pile wall

5

23

Sequence of all steps is shown in the following table.

Initial state (t = 0) Installation of sheet pile wall (t = 1)

Excavation zone-1

Installation of first anchor (t = 2) Excavation of 1 sand layer (t = 3)

Excavation zone-1 Excavation zone-1

Installation of second anchor (t = 4) Excavation of 2 sand layer (t = 5)

June 16, 2007Z Soilr-3D-2PHASE v.7

QuickHelp DataPrep Theory BenchmarksTU–37

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Sheet-pile wall: Modeling issues

2D/3D model?

Ultimate limit state analysis (ULS) (M-C model is enough)

Serviceability limit state (SLS) is (or not) main concern ? (ifyes then M-C model is too poor and HS small strain modelshall be used)

Each construction step must be reproduced (if SLS is majorconcern and to avoid numerical problems witch convergence)

Contact interfaces must be present

Sheet-pile wall can be modeled using beam/shell elements orspecial continuum elements (Continuum for structures)(only elastic behavior is possible)

Fixed anchor zones can be activated possibly with adhesiveinterface

Prestress can be controlled in time

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Sheet-pile wall: Constitutive aspects

G - current secant shear modulus

Go - shear modulus for very small strains

Atkinson 1991

If serviceability limit state is our major concern then weshould use more sophisticated model for soils (HS with smallstrain)

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Sheet-pile wall: 2D/3D model ?Linear / nonlinear beams in plane strain

2D domain:

Plane strain continuum shell Plane strain discrete ribb system

Beam elements

Interval between beams a = 1 Interval between beams a = L

L

User data: A, Iz ( data per beam )Program computes automatically A’=A/a I’=Iz/a(A’, I’ – values per unit length ) Results are given per beam (!)

Linear / nonlinear beams in plane strain

2D domain:


Beam elements


L


(a)

2D domain:

Beam elements

(b)Here 2D (a) or axisymmetric (b) model is good enough

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Sheet-pile wall: 2D/3D model ?


2D domain:


Beam elements


L



2D domain:


Beam elements


L


L

1 Here 2D model may not be good enough.....2 Results in beams and in anchors (same definition for L) will be

output per beam/anchor (!)8 / 60

Sheet-pile wall: Construction steps


1.4 HOW TO RUN SHEET-PILE WALL PROBLEM

• Data file: tutorials/sheet-pile-wall.INP

• Description

Generation of a complex geotechnical model of installation of an anchored sheet pile wall,followed then by an excavation is the goal of this tutorial. The geometry of the modelwill evolve in time and some model components like wall, anchors or excavated soil layerswill appear or disappear according to the assumed scenario. The geometry of the model isshown in the figure below.

Clay

Excavation zone-1

Excavation zone-2

6 m3

3

8 m

6m12 m 18 m

3

Medium sandAnchors

Sheet pile wall

5

23

Sequence of all steps is shown in the following table.

Initial state (t = 0) Installation of sheet pile wall (t = 1)

Excavation zone-1

Installation of first anchor (t = 2) Excavation of 1 sand layer (t = 3)

Excavation zone-1 Excavation zone-1

Installation of second anchor (t = 4) Excavation of 2 sand layer (t = 5)



Use existence/unloading functions associated with elements(continuum, beam, etc..) plus time dependent drivers (driven

load/consolidation)9 / 60

Sheet-pile wall: Drivers

Accessible from menu: Control/Analysis & Drivers


• Project preselection

In the dialog box for project preselection (it appears automatically for option File/New

in main Z Soil menu) set } Plane strain to ON and select Deformation item fromthe Problem type list. The predefined system of units for both data preparation andvisualization of results can be verified in menu Control/Units.

• Drivers

The whole computational process will consist of three drivers i.e. the Initial state

which will yield the initial stress distribution (including user defined coefficient of in situlateral pressure Ko = 0.8 in clay layer), Time dependent/Driven load to analyze allconstruction and excavation steps and at the end Stability (using c− tan(φ) reductionalgorithm) will be carried to assess the global safety factor. The complete set of drivers isgiven in the following figure.

To learn on how to set up the drivers list watch the video Set drivers



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Sheet-pile wall: Existence functions

Accessible from menu: Assembly/Existence functions


• Existence function

Introduction of contact elements leads to discontinues mesh connectivity along the in-terface. For that reason before the sheet-pile wall is installed, full compatibility of thedisplacement field must be preserved in the interface. This effect can easily be achievedduring generation of interface elements, where contact is defined in dual mode (full conti-nuity first and then real interface behavior). Both modes are controlled by the two existencefunctions (in our case continuity is controlled by the existence function number 7 while realcontact behavior by function number 6). It is strongly recommended to apply a distinctlabel to each existence function.

To edit existence functions use menu Assembly/Existence function.

To learn on how to enter existence functions watch the video Edit existence functions.

• Generation of the model

The computational model is built in the following steps and some of them are documentedin form of video films.

1 Create a new project2 Edit materials videos/tut2d-6/tut2d-6-materials.avi3 Edit existence functions videos/tut2d-6/tut2d-6-exf.avi4 Edit construction lines videos/tut2d-6/tut2d-6-constr-

lines.avi5 Draw macro-model videos/tut2d-6/tut2d-6-macro-

model.avi6 Create beam/anchor/continuum sub-

domainsvideos/tut2d-6/tut2d-6-macro-model-1.avi

7 Add interface and generate mesh videos/tut2d-6/tut2d-6-macro-model-2.avi

8 Set drivers videos/tut2d-6/tut2d-6-drivers.avi9 Run computation10 Visualize results videos/tut2d-6/tut2d-6-results.avi



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Sheet-pile wall: Contact interfaces

singular point

1 Contact interface is defined on edges of continuum subdomains only; contactelements are created automatically once the virtual and then the real mesh iscreated

2 Selected edges must be shared by the two subdomains3 The interface can be created along continuum-continuum, continuum-beam,

continuum-membrane and continuum-truss interfaces4 Nonstandard situations like connection of the bottom point of the sheet-pile

wall with soil ( by default beam is separated from the continuum at this point)must be handled at the FE model level

5 To connect/disconnect separated nodes at singular points use methodInterface/Update/Link singular nodes/Interface/Update/Delete link

6 Any mesh refinement in the adjacent continuum or structure automaticallyenforces mesh refinement in the contact interface

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Contact interface: Setting continuity/real contact mode

Contact interface may behave in a different manner in certaintime periods

Possible contact modes:1 Full continuity of all degrees of freedom (DOF)

(displacements, pressures, temperatures etc..) on bothsegments of the interface element

2 Full continuity of all DOF except pressure field3 True contact behavior; in this case decision on how to

handle non-kinematic DOF (pressure, temperature, humidity)in the interface can be set at the material level (switching

ON/OFF and editing groups of parameters: � Flow ,

� Heat and � Humidity ).

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A

B

Remarks

1 The three aforementioned contact type behaviors can be selected fromcombo-box (A)

2 For contact type: Continuity... only the existence function is meaningful

3 For contact type: Contact existence function, material number and unloadingfunction are all meaningful

4 The existence function, unloading function and material ID can be set in theedit fields or selected from lists of predefined ones

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Contact interface: mesh discontinuity

1 Here at the interface 3 nodal points are created to modelstrong discontinuoes motion of the neighbouring domains

2 In the initial state we want all these nodes to be compatible

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A

B

Remarks

1 The � Continuity for all inactive periods check-box set to ON will enforce

automatic generation of contact elements with full continuity attribute in allinactive periods of true contact behavior

2 The � Automatic generation of continuity prior to first contact apparition

option enforces automatic generation of contact elements with full continuityattribute only in the first inactive period for true contact behavior

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Contact interface: Flow through...

Fully permeable contact with compatible pressures on both faces

z’ x’

z’ x’

Permeable contact k′x = kx h k

′z = kz /h (h is a thin layer thickness)

z’ x’

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Contact interface: Effective vs total stress

For permeable interfaces effective stress mode is enforced

For impermeable interfaces effective/total stress mode can beselected NB. Effective stress mode makes sense only when at leastto one side of the interface a permeable continuum is adjacent

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Contact interface: General remarks

singular point

Interface elements are treated as any other elements

If we do not deactivate the interface during excavation theprogram will do it automatically

If we do not assume an unloading function (0 index) then theinterface will inherit it from the excavated adjacent continuum

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Contact interface: Setting existence/unloading functions

singular point

Interface elements are treated as any other elements

If we do not deactivate the interface during excavation theprogram will do it automatically

If we do not assume an unloading function (0 index) then theinterface will inherit it from the excavated adjacent continuum

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Contact interface: Setting material data

Instead of generating several contact zones one may set onlyone contact material activating automatic inheritage ofstrength properties from adjacent continuum

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Contact interface: Controling overpenetration

Penalty approachkn

P P

P P

overlap

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Contact interface: Controling overpenetration

1 The overpenetration can be checked in the postprocessing(Element info for interface element)

2 If excessive overpenetration appears one may try to increasethe kn multiplier (this must be made with care) or to activateAugmented Lagrangian option through menuControl/Contact algorithm

3 In case of convergence problems due to contact try todecrease slowly the kn multiplier

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Contact interface: Augmented Lagrangian approach

P P

t=0 t=1 t=1after augmentation

Contact force/stress is computed as N = No + kn gn

(No is an estimate of a Lagrange multplier)

(a) Force P generates overpeneration gn =P

kn(b) Force in the interface will be equal to N = P(c) Update Lagrange multiplier No = N = P(d) Compute force in the interfaceN = No + kn gn = P + P = 2P while N should be equal toN = P hence gn = 0

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Contact interface: Augmented Lagrangian approach

Accessible from menu: Control/Contact algorithm

This algorithm in nonlinear applications must be used withcare

Excessive overpenetration leads to underestimation ofinternal forces in contacting bodies

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Modeling elastic structures with aid of continuumelements

Standard continuum finite elements representing structureslike beams/shells yield very poor results unless very fine meshis used

To remedy the problem a family of robust continuum elementswas implemented to enhance bending/shear behavior

These elements are generated exactly in the same manner asstandard continuum but at the material level Continuum forstructures instead of Continuum must be selected

Elastic model is the only one allowed by Continuum forstructures formulation

Minimum 2 elements per thickness must be generated torecover properly bending moment

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Modeling elastic structures with aid of continuum ele...

Example of cantilever beam (recovering of sectional forces)

q=1 kN/m2

4m

Standard Q4 elements

Enhanced elements

Mz=7.33 kNm/m

Mz=7.95 kNm/m

NB. New stress recovery technique is used for postprocessinghence only results from the central point are stored

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Prestressed anchors: General remarks

anchoranchor fixedzone

Anchor consists of two parts: active and fixed part

Stiffness of both parts is assumed to be the same

The active part joins the anchor head and fixed part

Adhesive interface can be generated between soil and fixedpart

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Prestressed anchors: prestressing

Prestress marker

Link marker

The anchor endpoint may be attached to the backgroundcontinuum at any pointPrestress can be controled via existence function and loadtime function

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Prestressed anchors: fixed zone

anchor

Anchorfixed zone

The fixed part may can be created but exlusively in thedirection indicated by the local X axis of the truss elementThe split value should be compatible with the meshdensity of the background continuumGeneration of fixed anchor zone interface is optional

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Prestressed anchors: fixed zone interface

d

Same option option applies to nails31 / 60

Diapraghm walls: Modeling issues

2D/3D model?

Serviceability limit state (SLS) is the main concern → smallstrain stiffness must be considered

Each construction step must be reproduced (if SLS is majorconcern and to avoid numerical problems witch convergence)

Contact interfaces must be present

Diapraghm wall can be modeled using beam/shell elements orspecial continuum elements (Continuum for structures)(only elastic behavior is possible)

Fixed anchor zones can be activated possibly with adhesiveinterface

Prestress in anchors can be controlled in time

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Diapraghm walls: 2D/3D model ?

photo from Master thesis by A. Burmer, Poland

In the Milano method when floors are partially made the 3D isrecommendedIn the 3D one may analyze full model including foundationraft, piles, floorsIn the 3D one may optimize the structure including groundsupports

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Diapraghm walls: 2D/3D model ?

photo from Master thesis by A. Burmer, Poland

In the Milano method when floors are partially made the 3D isrecommendedIn the 3D one may analyze full model including foundationraft, piles, floorsIn the 3D one may optimize the structure including groundsupports

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Diapraghm walls: Constitutive aspects

G - current secant shear modulus

Go - shear modulus for very small strains

Atkinson 1991

Here we are in the range of small strains in major part of thecomputational domain

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Diapraghm walls: example of excavation in Berlin sand

(after Schweiger...)

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Diapraghm walls: excavation in Berlin, sand FE model

(after Schweiger...)

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Diapraghm walls: excavation in Berlin, results

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-5

0-600 -400 -200 0 200 400

M [kNm/m]

Y [m

[] HSHS-smallMC

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-25

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-10

-5

0-0.04 -0.03 -0.02 -0.01 0

Ux [m]

Y [m

] HS-smallHSMCMeasurement

-100

-90

-80

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-40

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-10

00 0.01 0.02 0.03 0.04

Uy [m]

Y [m

] HSHS-smallMC

-0.02

-0.015

-0.01

-0.005

0

0.005

0.010 20 40 60 80 100 120 140

X [m]

UY

[m] HS

HS-smallMC

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Nailing: general remarks

15o

L=30 ft

40ft

40ft

120 ft 120 ft

Excavated layers

12345678

Contrary to some simple limit equilibrium methods finiteelement model requires a multi-step excavation and nailinstallation procedure to eliminate spurious forces in nails andpotential numerical divergence problemsNails can be attached to the facing wall at any point notnecesarilly at the node (important mainly in 3D)Nail core is modeled as beam element

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Nailing: general remarks

Nail core=beam

Nail injection zone

d

Nail interface

Nail consists of two material zones: core + interface

Stiffness of the injection zone is neglected

Adhesive interface can be generated between soil and injectionzone

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Nailing: automatic excavation front for soil layers

12

3 4

1 Run method Macro model/Subdomain/Update/Defineexcavation front to set up existence functions forsubsequent layers to be excavated

2 In the dialog box for the excavation front activate flag

Existence function [ ] , set the label subsoil layers, select

first defined existence function (No 1) that will be applied tofirst row of excavated elements from the top, activate option} Edge 1-4 that indicates the direction of excavation frontpropagation and set value 1 to the edit field

For every .... layers of elements... [ ]

3 The above setting will enforce application of existencefunction No 1 to the first top row of elements in the realmesh, No 2 to the second one etc...

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Nailing: automatic construction front for facing layers

1

2

1 Run method Macro model/Subdomain/Update/Defineexcavation front to set up existence functions forsubsequent facing layers that are to be constructed

2 The above setting will enforce application of existencefunction No 11 to the first top row of facing elements(beams) in the real mesh, No 12 to the second one etc...

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Nailing: generating nails

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Nailing: generating nails

Nail interface is optional (if not created then full displacementcompatibility is enforced)

Mesh density for the nail (defined as split parameter) shouldcorrespond to the one in the background continuum

The material data for the interface is the same as for fixedanchor zones (see next slide)

During stability analysis both soil and soil-nail interfacestrength parameters are reduced (unless it is redefined at thematerial level)

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Nailing: setting material properties

d

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Foundation rafts: Problem to be solved

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Foundation rafts: discretization problem

If we have lot of piles it is almost impossible to

1 Create 3D compatible FE mesh for plate-piles-interfaces system2 Compute the problem on a PC platform3 Each redesign of piles generates new complex 3D mesh

Conclusion: we need absolutely a simplified treatment

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Foundation raft: real FE vs simplified FE model

plate-pile connection Shell Q4

beam elements

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Foundation rafts: Z Soil implementation

Piles are modeled with aid of beam elements

Beams are embedded in continuum without any restrictionput on FE meshes

Beam nodes can be connected to other elements likeshells/beams/membranes/continuum not necessarily atelement vertices

Beam nodes can be connected to other elements via selectedset of degrees of freedom

The sliding interface between beam and continuum is createdautomatically

The additional interface between bottom of the pile andsubsoil can be optionally added

Nodal forces can be applied at any point on the raft

Penalty approach is not accepted (except for the frictionalcontact)

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Nodal link option

1 2

3

4

A

Constraint equation(s): uA =∑4

i=1 Ni ui

Hence: stiffness, force vector from node A of a beam elementis dispatched on shell degree of freedom

DOF’s of node A are dependent on other DOF’s

Attention: constraints cannot be nested (!)

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Nodal link: example of beam-beam connection

Link node to theselected element

Deformation

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Nodal link: example of beam-shell connection

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Foundation rafts: pile frictional interface

τ=σn tan φ+c

ft=0, fc< fcult

How to estimate σn ?

NB. We can leave φ = 0 and make contact purely adhesive like incodes for pile design

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Foundation rafts: σn estimation in pile interfaces

xL

yL

zLR

R = SQRT (A/π)

ΔLiPi

σn =

∫L min (σni , 0)dl∫

L dl

σni is computed by effective stress transformation from thecontinuum elements in which interface and beam is embedded

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Foundation rafts: generating piles

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Foundation rafts: generating piles

1 Split parameter controls mesh density in pile macro-element;it is recommended to avoid too big differences in meshdensities between continuum and piles; such modeling maylead to axial force oscillations in the pile for high strengthparameters of subsoil

2 To avoid instabilities due to rigid rotation of the pile along itsaxis the rotation along local pile axis is fixed internally by thepreprocessor

3 Mesh refinement near the zone of the pile foot isrecommended to avoid underestimation of settlements

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Foundation rafts: real life example

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Building-subsoil interaction: Examples

Example 1

At the material level in groupMain

Next slide

Frame structure(static/pushover/dynamic analysis

Remark: Each member is discretized by one element (notnecessarily for reinforced concrete because of differentamount and position of the reinforcement)

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Building-subsoil interaction: Examples

Example 2

At the material level in groupMain

Next slide

Frame structure resting on subsoil

Remark: Each member is discretized by one element (notnecessarily for reinforced concrete because of differentamount and position of the reinforcement)

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Flexibility vs displacement based beam formulation

1.331.330.667

1.251.250.75

Mz for 1 „flexibility based” beam

Mz for 4 „displ. based” beam

q=1.0 kN/m

Gauss pointsNodal points

Note that result for Flexibility based beam (one per member)is exact !

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Soil Structure Interaction

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