MODELLING OF EXCAVATIONS USING PLAXIS · PLAXIS FINITE ELEMENT CODE FOR SOIL AND ROCK ANALYSES...

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MODELLING OF EXCAVATIONSUSING PLAXIS

William CheangPlaxisAsia

PLAXIS FINITE ELEMENT CODE FOR SOIL AND ROCK ANALYSES Plaxis Vietnam 2008

PLAXIS FINITE ELEMENT CODES1. 2-D Analysis + Modules

• Plaxis Professional 8.x• PlaxFlow 1 x• PlaxFlow 1.x• Dynamics

2. 3-D Analysis• 3D Foundation (Full control of X-Z space)• 3D Tunnel (Full control of X-Y space)

3 Other programs supporting Plaxis

PLAXIS FINITE ELEMENT CODE FOR SOIL AND ROCK ANALYSES Plaxis Vietnam 2008 2

3. Other programs supporting Plaxis1. Delft Geosystems (M-Series Codes + M-Geometry

Input.) [see Http://www.delftgeosystems.nl]

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Modelling of Excavations: Introduction to methods, tools and procedure.

A. Modelling of Excavations in PlaxisB. Model SpaceC. Continuum, Structural & Membrane ElementsD. Loads and Porewater Pressure BoundariesE. Constitutive ModelsF. Demonstration


A. Modelling of Excavations in Plaxis

The geometry is the representation of the physical problemproblem

• Consists of points, lines and clusters• Definition of soil layers, structural elements and loads


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B.Model Space-Part 1• Plaxis Professional Version 8.x (2D

code)• Plane Strain• Plane Strain• Axi-symmetry


B.Model Space-Part 2• 3D Foundation (X-Z space)


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B.Model Space-Part 3• 3D Tunnel (X-Y space)

yy

xz


C. Elements in Plaxis

• ContinuumS l• Structural

• Interfaces• Membrane (Geogrid)


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C1.Continuum Elements

Mesh6 d d 15 d d t i l l t• 6-noded or 15-noded triangular elements

• Displacements calculate in nodes• Stresses calculated in Gaussian integration points


C2.Structural elements in Plaxis

• Plates and shells • Anchors• Anchors• Geogrids (geotextiles)• Interfaces


strut anchored wall cofferdamgeotextile wall ground anchor

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Plates and shells

• 3 or 5 noded line elements• 3 degrees of freedom per node• Elastic or elastoplastic behaviour• To model walls, floors, tunnels


Input parameters for plates

• Flexural rigidity (b=1 m)

N l iff12

3 bhEEI ⋅⋅=

• Normal stiffness (b=1 m)

• Element thicknessbhEEA ⋅⋅=

EAEIhd 12==

h


b

h hb

b = 1 m in plane strainb = 1 meter in axisymmetry

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Plate weights

• Compensate for overlap:

• For soil weight use:γunsat above phreatic levelγsat below phreatic level

realsoilconcrete dw ⋅−= )( γγ


Fixed-end anchors

• To model supports, anchors and strutsEl t l ti i l t• Elasto-plastic spring element

• One end fixed to point in the geometry,other end is fully fixed for displacement

• Positioning at any angle• Pre-stressing option


strut

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Node-to-node anchors

• To model anchors, columns and rodsEl t l ti i l t• Elasto-plastic spring element

• Connects two geometry points in the geometry

• Pre-stressing option


anchored wall cofferdam

Anchor material properties

Normal stiffness, EA (for one anchor) [kN]Spacing, Ls (distance between anchors) [m]Maximum anchor force for compression

and tension, |Fmax,comp| and |Fmax,tens| [kN]


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Pre-stressing of anchors

• Defined in Staged construction phaseB h i ( h ) i ( )• Both tension (grout anchor) or compression (strut) possible


C3. Membrane Elements (Geogrids)

• 3 or 5 noded line element• Linear elastic behaviourLinear elastic behaviour• No flexural rigidity (EI), only normal stiffness (EA)• Only allows for tension, not for compression• Soil/Geogrid interaction may be modelled using interfaces


geotextile wall ground anchor

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C4.Interfaces

• Try to omit stress oscillations at corners of stiff structuresstructures

Inflexible corner points, causing bad

stress results


Flexible corner points with improved stress

results

C4.Interfaces

• Soil-structure interactionW ll f i ti• Wall friction

• Slip and gapping between soil and structure• Soil material properties

• Taken from soil using reduction factor RinterCinter = Rinter * Csoiltan(φ)inter = Rinter * tan(φ)soil


(φ)inter inter (φ)soil

• Individual material set for interface

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C4.Interfaces

Suggestions for Rinter:• Interaction sand/steel = R ≈ 0 6 0 7• Interaction sand/steel = Rinter ≈ 0.6 – 0.7• Interaction clay/steel = Rinter ≈ 0.5• Interaction sand/concrete = Rinter ≈ 1.0 – 0.8• Interaction clay/concrete = Rinter ≈ 1.0 – 0.7• Interaction soil/geogrid = Rinter≈ 1.0

(interface may not be required)• Interaction soil/geotextile = Rinter≈ 0.9 – 0.5 (foil, textile)


inter

C5.Combining Elementsg

• Example 1: Ground anchors• Example 2: Thick walls (‘Sandwich’ method)


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Example 1: Ground anchors

• Combination of node-to-node anchor and geogrid• Node to node anchor represents anchor rod (no interaction• Node-to-node anchor represents anchor rod (no interaction

with surrounding soil)• Geogrid represents grout body (full interaction with grid• No interface around grout body; interface would create

unrealistic failure surface


Combined Elements:Ground anchors

axial forces in geotextile element

real distribution of axial forces in ground anchorInput geometry


Generated mesh

Axial forces in ground anchors

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Anchor material properties

Normal stiffness, EA (for one anchor) [kN]Spacing, Ls (distance between anchors) [m]Maximum anchor force for compression

and tension, |Fmax,comp| and |Fmax,tens| [kN]


Pre-stressing of anchors

• Defined in Staged construction phaseB h i ( h ) i ( )• Both tension (grout anchor) or compression (strut) possible


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Example 2: Thick WallsE1=real


Scaled-down E2=fictitious(Try E2= 0.01 to 0.1 E1, to avoid double value)

Aim: Expedite data extraction like displacements, bending moments, axial & shear forces(but be careful!. Disp.=Correct. But F,S, M (Scale back to the correct value because E2=0.01 to 0.1 of E1)

D B d i Fi it L d d PWPD. Boundaries: Fixity, Loads and PWP


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D1.Input boundary conditions

Default fixities


D2.Input loads

Point force A & B


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D3.Porewater Generation

• Wet excavationI bl ( t ) ti fl• Impermeable (concrete) excavation floor

• Dry excavation• Undisturbed water table outside excavation• Drawdown outside excavation


D4.Options

• General phreatic levelApplies to all clusters that have not been separately defined.

L li d / Cl h i l l

A. Steady-state condition (Default)

• Localised / Cluster phreatic levelApplies to one specific cluster.

• Localised / Cluster dryMakes a specific cluster dry.

• InterpolateInterpolate pore pressures between clusters above and below.

• User-defined pore pressureS if t l l d i t i di ti


Specify pressure pref at level yref and increase pinc per meter in y-direction.

B. Transient-state condition (Plaxis + Plaxflow Integration)• Same input procedure

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D5.Wet excavation

• Excavate without changing water conditions (in stages or at once)stages or at once)

• Pore pressures outside excavated area remain unchanged


D6.Dry excavationUndisturbed water table outside excavation• For every excavation phase do

• Excavate soil• Set excavated area dry• Define area just below excavation floor as interpolate between

lines or clusters

Suitable for short-term excavations in lowbili il


permeability soils

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D6.Dry excavationUndisturbed water table outside excavation

dry

interpolate

GPL


D6.Dry excavationDisturbed water table outside excavation - DrawdownFor every excavation phase do

• Excavate soil• Define boundary conditions (heads)• Perform groundwater flow analysis.

Suitable for long-term excavations or excavations inhigh permeability soils

Simplified alternative:


Simplified alternative:• Draw GPL according to expected groundwater level and generate pore

pressures based on GPL.

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D6.Dry excavationDrawdown outside excavation


Groundwater flow calculation gives steady-state solution,so for time is infinite!

E.Constitutive Soil Models

• Linear ElasticM h C l b (MCM)• Mohr-Coulomb (MCM)

• Hardening Soil Model (HSM)• Soft-Soil Creep (SSCM)• Soft-Soil (SSM)• Hardening Soil + Small Strain Overlay (HSsmallM)


g y ( )• Jointed Rock Model

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Excavation Modelling: Workflowg


Model: PointsPoints

• Start and end of lines. • Positioning of anchors• Point forces• Point forces, • Point fixities

• Local refinements of the finite element mesh.

Model: LinesLines

fi h h i l b d i f h


• Define the physical boundaries of the geometry• Define discontinuities in the geometry:

• Sheet pile walls, distributed loads• Separations of distinct soil layers or construction stages.

• A line can have several functions or properties

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General modelling aspects

ClustersA t ti ll t d l d• Automatically generated enclosed areas

• Homogeneous soil properties.


Input

C i d l• Composing a geometry model• Creating and assigning data sets• Generating a finite element mesh• Generating initial conditions


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Example:


Composing a geometry model

• Graphical input of geometry contour, soil- layers, t ti t l t id i t f hconstruction stages, plates, geogrids, interfaces, anchors

• Designer for circular or non-circular tunnels

• Input of loads and boundary conditions


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• Geometry lines (between soil layers, etc.)

• Plates (Walls, Plates & Shells)

• Hinges (free rotation between beams)

• Geogrids

I t f l t ( il t t i t ti )


• Interface elements (soil-structure interaction)

• Anchors (node-to-node, fixed end)

Creating and assigning material data sets

• Enter model parameters as data sets in a material data base

• Assigning data sets to geometry components by means of ‘drag and drop’


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Generating a finite element mesh

• Fully automatic mesh generation based on geometry model

• Global and local refinement options


Generating initial conditions

• Generating initial pore pressures by means of phreatic line or groundwater flow calculation

• Flip switch - gives: Initial stresses and geometry mode


• Setting initial geometry configuration• Generating initial stresses (K0 procedure)

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Defining calculation phases

• Plastic calculation, Consolidation, Phi/c reduction and Dynamic analysis.Dynamic analysis.

• Updated mesh.• Loading input: Multipliers or Staged Construction.• Changing water conditions• Multiple calculation phases can be pre-defined and executed

at once.


Stress paths

Construction phases:• I 1st excavation

σK

K=1v0Kactive

III III

Point APoint A

I 1 excavation• II Pre-stressing anchor•III Final excavation


passivePoint B K

σh

Point B

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Calculation program


Output program


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View results

• Graphical and tabulated output of displacements, stresses and structural forcesstresses and structural forces

• Output in cross sections• Multiple output windows can be opened

simultaneously (comparison of results)


Demonstration : Anchored Sheet-pile Wall

• See demonstration


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Thank You!


MODELLING OF EXCAVATIONS USING PLAXIS · PLAXIS FINITE ELEMENT CODE FOR SOIL AND ROCK ANALYSES...

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