soil structure interaction
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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/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
4 / 60
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:
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 (!)
(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 ?
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:
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 (!)
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
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
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
N Preface N N 2D problems
• 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
June 16, 2007Z Soilr-3D-2PHASE v.7
QuickHelp DataPrep Theory BenchmarksTU–38
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Sheet-pile wall: Existence functions
Accessible from menu: Assembly/Existence functions
N Preface N N 2D problems
• 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
June 16, 2007Z Soilr-3D-2PHASE v.7
QuickHelp DataPrep Theory BenchmarksTU–40
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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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Contact interface: Setting continuity/real contact mode
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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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 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
-35
-30
-25
-20
-15
-10
-5
0-600 -400 -200 0 200 400
M [kNm/m]
Y [m
[] HSHS-smallMC
-35
-30
-25
-20
-15
-10
-5
0-0.04 -0.03 -0.02 -0.01 0
Ux [m]
Y [m
] HS-smallHSMCMeasurement
-100
-90
-80
-70
-60
-50
-40
-30
-20
-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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