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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/pressure discontinuity problems soil-structure interfaces play an Preface 2D may appear important role

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HOW TO RUN SHEET-PILE WALL PROBLEM

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

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· Description

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

12 m 18 m 6m

Excavation zone-1

2 3

6m

3

Anchors

Excavation zone-2

3

Medium sand Sheet pile wall Clay

8m

5

Sequence of all steps is shown in the following table.

3

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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 ? (if yes then M-C model is too poor and HS small strain model shall be used) Each construction step must be reproduced (if SLS is major concern and to avoid numerical problems witch convergence) Contact interfaces must be present Sheet-pile wall can be modeled using beam/shell elements or special continuum elements (Continuum for structures) (only elastic behavior is possible) Fixed anchor zones can be activated possibly with adhesive interface 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 we should use more sophisticated model for soils (HS with small strain)

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Linear / nonlinear beams in plane strain

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

2D domain:

L

Plane strain continuum shell between beams a = 1 discrete ribb system beams a = L Plane strain Interval between Interval

Beam elements

L

Interval between

User data: A, Iz ( data per beam ) (a) Program = 1 Interval between beams a = L beams a computes automatically A'=A/a I'=Iz/a (A', I' ­ values per unit length ) Results are given per beam (!)

2D domain:

2D domain:

Beam elements

Beam elements

User data: A, Iz ( data per beam ) Linear / nonlinear beams in plane strain (b) Program computes automatically A'=A/a I'=Iz/a (A', I' ­ values per unit length )strain continuum model is beamstrain discrete ribb system Results are shell Here 2D (a) or axisymmetric (b) given per good (!) Plane Plane enough

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near beams in plane strain Plane strain discrete ribb system Interval between

L beams a = 1 Interval between beams a = L

ell

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

2D domain:

L Interval

Beam elements

a=1

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

main:

L

ements

am ) 1 Here cally A'=A/a I'=Iz/a 2D model may not be good enough..... 2 Results in beams ) Results are given per beam (!)and in anchors (same definition for L) will be output per beam/anchor (!)

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the Problem type list. The predefined system of units for both data preparation and Clay visualization of results can be verified in menu Control/Units.

Sheet-pile wall: Construction steps

Sequence of all steps is shown in the following table.

5

Initial state (t = 0)

8

Installation of sheet pile wall (t = 1)

Excavation zone-1

Installation of first anchor (t = 2)

Excavation zone-1

Excavation of 1 sand layer (t = 3)

Excavation zone-1

Installation of second anchor (t = 4)

Excavation of 2 sand layer (t = 5)

· Drivers

Use June 16, 2007 existence/unloading functions associated with elements (continuum, beam, etc..) QuickHelp DataPrep Theory drivers (driven plus time dependent Benchmarks Z Soil -3D-2PHASE v.7 TU­37 load/consolidation)

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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 situ lateral pressure Ko = 0.8 in clay layer), Time dependent/Driven load to analyze all Sheet-pile wall: Drivers construction and excavation steps and at the end Stability (using c - tan() reduction algorithm)Accessible fromto assessControl/Analysis & Drivers complete set of drivers is will be carried menu: the global safety factor. The given in the following figure.

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

Set drivers

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Preface

Sheet-pile wall: Existence functions

2D problems

· Existence function menu: Assembly/Existence functions Accessible from

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Introduction of contact elements leads to discontinues mesh connectivity along the interface. For that reason before the sheet-pile wall is installed, full compatibility of the Sheet-pile be preserved in the interface. displacement field must wall: Contact interfacesThis effect can easily be achieved during generation of interface elements, where contact is defined in dual mode (full continuity first and then real interface behavior). Both modes are controlled by the two existence functions (in our case continuity is controlled by the existence function number 7 while real contact behavior by function number 6). It is strongly recommended to apply a distinct label to each existence function. To edit existence functions use menu Assembly/Existence function. To learn on how to enter existence functions watch the video singular point .

1

Edit existence functions

· Generation Contact interface is defined on edges of continuum subdomains only; contact of the model elements are created automatically once the virtual and then the real mesh is

created The computational model is built in the following steps and some of them are documented 2 Selected edges must be shared by the two subdomains in form of video films. 3 The interface can be created along continuum-continuum, continuum-beam, 1 Create a new project and continuum-truss interfaces continuum-membrane 4 Nonstandard situations like connection of the bottom point of the sheet-pile 2 Edit materials videos/tut2d-6/tut2d-6-materials.avi wall with soil ( by default beam is separated from the continuum at this point) 3 Edit must be handled at the FE model level videos/tut2d-6/tut2d-6-exf.avi existence functions 5 construction lines Edit To connect/disconnect separated nodes at singular points use method videos/tut2d-6/tut2d-6-constr4 Interface/Update/Link singular nodes/Interface/Update/Delete link lines.avi 6 Any mesh refinement in the adjacent continuum or structure automatically 5 Drawenforces mesh refinement in the contact interface macro-model videos/tut2d-6/tut2d-6-macro12 / 60 model.avi

Contact interface: Setting continuity/real contact mode

Contact interface may behave in a different manner in certain time periods Possible contact modes:

1

2 3

Full continuity of all degrees of freedom (DOF) (displacements, pressures, temperatures etc..) on both segments of the interface element Full continuity of all DOF except pressure field 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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Contact interface: Setting continuity/real contact mode

A

B

Remarks

1

The three aforementioned contact type behaviors can be selected from combo-box (A) For contact type: Continuity... only the existence function is meaningful For contact type: Contact existence function, material number and unloading function are all meaningful The existence function, unloading function and material ID can be set in the edit fields or selected from lists of predefined ones

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2 3

4

Contact interface: mesh discontinuity

1

Here at the interface 3 nodal points are created to model strong discontinuoes motion of the neighbouring domains In the initial state we want all these nodes to be compatible

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2

Contact interface: Setting continuity/real contact mode

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 all inactive periods of true contact behavior The Automatic generation of continuity prior to first contact apparition option enforces automatic generation of contact elements with full continuity attribute only in the first inactive period for true contact behavior

2

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z'

Contact interface: Flow through...

Fully permeable contact with compatible pressures on both faces

z'

x'

x'

Permeable contact kx = kx h kz = kz /h (h is a thin layer thickness)

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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 be selected NB. Effective stress mode makes sense only when at least to 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 the program will do it automatically If we do not assume an unloading function (0 index) then the interface 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 the program will do it automatically If we do not assume an unloading function (0 index) then the interface 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 only one contact material activating automatic inheritage of strength properties from adjacent continuum

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Contact interface: Controling overpenetration

Penalty approach

kn

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) If excessive overpenetration appears one may try to increase the kn multiplier (this must be made with care) or to activate Augmented Lagrangian option through menu Control/Contact algorithm In case of convergence problems due to contact try to decrease slowly the kn multiplier

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2

3

Contact interface: Augmented Lagrangian approach

P P

t=0

t=1

t=1 after augmentation

Contact force/stress is computed as N = No + kn gn (No is an estimate of a Lagrange multplier) P (a) Force P generates overpeneration gn = kn (b) Force in the interface will be equal to N = P (c) Update Lagrange multiplier No = N = P (d) Compute force in the interface N = No + kn gn = P + P = 2P while N should be equal to N = 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 with care Excessive overpenetration leads to underestimation of internal forces in contacting bodies

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Modeling elastic structures with aid of continuum elements

Standard continuum finite elements representing structures like beams/shells yield very poor results unless very fine mesh is used To remedy the problem a family of robust continuum elements was implemented to enhance bending/shear behavior These elements are generated exactly in the same manner as standard continuum but at the material level Continuum for structures instead of Continuum must be selected Elastic model is the only one allowed by Continuum for structures formulation Minimum 2 elements per thickness must be generated to recover 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

Mz=7.33 kNm/m

Standard Q4 elements

Mz=7.95 kNm/m

Enhanced elements

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

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Prestressed anchors: General remarks

anchor anchor fixed zone

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 fixed part

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Prestressed anchors: prestressing

Prestress marker

Link marker

The anchor endpoint may be attached to the background continuum at any point Prestress can be controled via existence function and load time function

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Prestressed anchors: fixed zone

anchor

Anchor fixed zone

The fixed part may can be created but exlusively in the direction indicated by the local X axis of the truss element The split value should be compatible with the mesh density of the background continuum Generation of fixed anchor zone interface is optional

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Prestressed anchors: fixed zone interface

d

Same option option applies to nails

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Diapraghm walls: Modeling issues

2D/3D model? Serviceability limit state (SLS) is the main concern small strain stiffness must be considered Each construction step must be reproduced (if SLS is major concern and to avoid numerical problems witch convergence) Contact interfaces must be present Diapraghm wall can be modeled using beam/shell elements or special continuum elements (Continuum for structures) (only elastic behavior is possible) Fixed anchor zones can be activated possibly with adhesive interface 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 is recommended In the 3D one may analyze full model including foundation raft, piles, floors In the 3D one may optimize the structure including ground supports

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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 is recommended In the 3D one may analyze full model including foundation raft, piles, floors In the 3D one may optimize the structure including ground supports

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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 the computational 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

-600 -400 -200 0 200 400 0 -5 -10 Y [m[]

Y [m] -0.04 -0.03 -0.02 -0.01 0 0 -5 -10

-15 -20 -25 -30 -35 M [kNm/m]

HS HS-small MC

-15 -20 -25 -30 -35 Ux [m]

0 20 40 60 80 100 120

HS-small HS MC Measurement

140

0 0 -10 -20 -30 -40

Y [m]

0.01

0.02

0.03

0.04

0.01

0.005

0

-50 -60 -70 -80 -90 -100

Uy [m]

HS HS-small MC

-0.005

HS HS-small MC

UY [m]

-0.01

-0.015

-0.02 X [m]

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Nailing: general remarks

120 ft

1 2 3 4 5 6 7 8

120 ft

15o

40ft

Excavated layers

L=30

ft

Contrary to some simple limit equilibrium methods finite element model requires a multi-step excavation and nail installation procedure to eliminate spurious forces in nails and potential numerical divergence problems Nails can be attached to the facing wall at any point not necesarilly at the node (important mainly in 3D) Nail core is modeled as beam element

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Nailing: general remarks

d

40ft

Nail core=beam

Nail injection zone 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 injection zone

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Nailing: automatic excavation front for soil layers

2 1

3

4

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Run method Macro model/Subdomain/Update/Define Nailing: automatic construction front for facing layers excavation front to set up existence functions for subsequent layers to be excavated 2 In the dialog box for the excavation front activate flag 1

1

Existence function [

] , set the label subsoil layers, select

2

first defined existence function (No 1) that will be applied to first row of excavated elements from the top, activate option Edge 1-4 that indicates the direction of excavation front propagation and set value 1 to the edit field For every .... layers of elements... [

3

]

1

2

The above setting will enforce application of existence function No 1 to the first top row of elements in the real mesh, No 2 to the second one etc... Run method Macro model/Subdomain/Update/Define excavation front to set up existence functions for subsequent facing layers that are to be constructed The above setting will enforce application of existence function 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 displacement compatibility is enforced) Mesh density for the nail (defined as split parameter) should correspond to the one in the background continuum The material data for the interface is the same as for fixed anchor zones (see next slide) During stability analysis both soil and soil-nail interface strength parameters are reduced (unless it is redefined at the material 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 2 3

Create 3D compatible FE mesh for plate-piles-interfaces system Compute the problem on a PC platform 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 restriction put on FE meshes Beam nodes can be connected to other elements like shells/beams/membranes/continuum not necessarily at element vertices Beam nodes can be connected to other elements via selected set of degrees of freedom The sliding interface between beam and continuum is created automatically The additional interface between bottom of the pile and subsoil can be optionally added Nodal forces can be applied at any point on the raft Penalty approach is not accepted (except for the frictional contact)

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Nodal link option

4 3 A

1

2

Constraint equation(s): uA =

4 i=1

Ni ui

Hence: stiffness, force vector from node A of a beam element is 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 the selected element

Deformation

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Nodal link: example of beam-shell connection

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Foundation rafts: pile frictional interface

=n tan +c

ft=0, fc< fcult

How to estimate n ?

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

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Foundation rafts: n estimation in pile interfaces

xL

R = SQRT (A/)

Li

yL

Pi

R

zL

n =

L min (n i , 0)dl L dl

ni is computed by effective stress transformation from the continuum 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 mesh densities between continuum and piles; such modeling may lead to axial force oscillations in the pile for high strength parameters of subsoil To avoid instabilities due to rigid rotation of the pile along its axis the rotation along local pile axis is fixed internally by the preprocessor Mesh refinement near the zone of the pile foot is recommended to avoid underestimation of settlements

2

3

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Foundation rafts: real life example

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Building-subsoil interaction: Examples

Example 1

At the material level in group Main

Frame structure (static/pushover/dynamic analysis

Next slide

Remark: Each member is discretized by one element (not necessarily for reinforced concrete because of different amount and position of the reinforcement)

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Building-subsoil interaction: Examples

Example 2

At the material level in group Main

Frame structure resting on subsoil

Next slide

Remark: Each member is discretized by one element (not necessarily for reinforced concrete because of different amount and position of the reinforcement)

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Flexibility vs displacement based beam formulation

q=1.0 kN/m

Mz for 1 ,,flexibility based" beam 1.33 0.667 1.33

Mz for 4 ,,displ. based" beam 1.25 0.75

Gauss points Nodal points

1.25

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

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Information

Soil-structure interaction

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