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
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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
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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
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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
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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
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C2.Structural elements in Plaxis
• Plates and shells • Anchors• Anchors• Geogrids (geotextiles)• Interfaces
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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
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Input parameters for plates
• Flexural rigidity (b=1 m)
N l iff12
3 bhEEI ⋅⋅=
• Normal stiffness (b=1 m)
• Element thicknessbhEEA ⋅⋅=
EAEIhd 12==
h
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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
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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
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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
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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
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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
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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
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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
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(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)
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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
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Combined Elements:Ground anchors
axial forces in geotextile element
real distribution of axial forces in ground anchorInput geometry
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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]
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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
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Example 2: Thick WallsE1=real
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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
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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
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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
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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
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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
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permeability soils
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D6.Dry excavationUndisturbed water table outside excavation
dry
interpolate
GPL
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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:
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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
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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)
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g y ( )• Jointed Rock Model
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Excavation Modelling: Workflowg
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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
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• 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.
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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:
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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 )
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• 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
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Generating initial conditions
• Generating initial pore pressures by means of phreatic line or groundwater flow calculation
• Flip switch - gives: Initial stresses and geometry mode
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• 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.
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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
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passivePoint B K
σh
Point B
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Calculation program
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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)
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Demonstration : Anchored Sheet-pile Wall
• See demonstration
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