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PLAXIS Standard Course Universti Teknologi Malaysia, Johor
May 14-16,2007
Presented by GOUW Tjie-Liong
[email protected] 1
PLAXISFINITE ELEMENT CODE FOR SOIL AND ROCK ANALYSES
Non-linear Computations
in PLAXIS
presented by:
GOUW Tjie-Liong, Ir., M.Eng, ChFCSenior Geotechnical ConsultantEmail: [email protected]
Source of Lecture Notes:
Paul Bonnier
PLAXIS BV
PLAXISFINITE ELEMENT CODE FOR SOIL AND ROCK ANALYSES
Contents
• Calculation
• Local level
• Global level
• Load advancement
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PLAXIS Standard Course Universti Teknologi Malaysia, Johor
May 14-16,2007
Presented by GOUW Tjie-Liong
[email protected] 2
PLAXISFINITE ELEMENT CODE FOR SOIL AND ROCK ANALYSES
Calculation
• Initial situation
• Geometry
(mesh, loads, boundary conditions)
• Material parameters
• Initial stresses and pore pressures
PLAXISFINITE ELEMENT CODE FOR SOIL AND ROCK ANALYSES
Calculation
• Calculation phases
• Calculation types
• Plastic• Consolidation
• Phi-c reduction (safety analysis)
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PLAXIS Standard Course Universti Teknologi Malaysia, Johor
May 14-16,2007
Presented by GOUW Tjie-Liong
[email protected] 3
PLAXISFINITE ELEMENT CODE FOR SOIL AND ROCK ANALYSES
Calculation
• Calculation phases
• Loading input
• Staged construction
• Switch on/off parts of geometry
(soil, structural elements)
• Switch on/off loads (change input values)
• Change pore pressures
• Total Multipliers (L.A. Ultimate level)
• Incremental Multipliers (L.A. no. of steps)
PLAXISFINITE ELEMENT CODE FOR SOIL AND ROCK ANALYSES
Calculation
Displacements Loads
Strains Stresses
Model(s)Parameters
Phase
• Find equilibrium in
final situation
• Subdivide in load
steps
Load step
• Find equilibrium for
load increment
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PLAXIS Standard Course Universti Teknologi Malaysia, Johor
May 14-16,2007
Presented by GOUW Tjie-Liong
[email protected] 4
PLAXISFINITE ELEMENT CODE FOR SOIL AND ROCK ANALYSES
Calculation
Loads and Multipliers
• Applied load = Load multiplier x Input load
• Standard setting: Input load = 1 stress unit
• Actual load is specified before each
calculation
• Staged construction : Input load
• Total incr. Multipliers : Load multipliers
PLAXISFINITE ELEMENT CODE FOR SOIL AND ROCK ANALYSES
Calculation
load increment
load
Total load
dis lacement or settlement
u
A
q
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PLAXIS Standard Course Universti Teknologi Malaysia, Johor
May 14-16,2007
Presented by GOUW Tjie-Liong
[email protected] 5
PLAXISFINITE ELEMENT CODE FOR SOIL AND ROCK ANALYSES
Calculation
Most calculations: Staged Construction
• Total load in last calculation step
Some calculations: Total multipliers
• Total load in last calculation step
• SMdisp, SMloadA, SMloadB, SMweight
Very few calculations: Incremental multipliers
• Additional load in one calculation step
• Mdisp, MloadA, MloadB, Mweight, Msf
PLAXISFINITE ELEMENT CODE FOR SOIL AND ROCK ANALYSES
u
A
q
Phase
q
∆u
Load-displacement curve for point A
∆q
1
Elasticstiffness
Ste s
Calculation
Global system of equations P u K = PuK ∆∆ = PuK δδ =or or
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PLAXIS Standard Course Universti Teknologi Malaysia, Johor
May 14-16,2007
Presented by GOUW Tjie-Liong
[email protected] 6
PLAXISFINITE ELEMENT CODE FOR SOIL AND ROCK ANALYSES
PK u 1
δδ −=
uuu δ∆∆ +=
uB∆ε∆ =
)(D pe0c
ε∆ε∆σσ −+=
∫ = dVBP
ct
in σ
inex PP ≈
2)PP(K u inex1 →−= −
δ
Calculation
Basic algorithm per step
• additional displacements 1:
• total increments 2:
• strain increment 3:
• determine stresses 4:
• internal reaction 5:• equilibrium ?? 6:
• No: next iteration 7:
PLAXISFINITE ELEMENT CODE FOR SOIL AND ROCK ANALYSES
Calculation
• Output
• Per step/phase:
• displacements, stresses, forces• Load-displacement curves
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PLAXIS Standard Course Universti Teknologi Malaysia, Johor
May 14-16,2007
Presented by GOUW Tjie-Liong
[email protected] 7
PLAXISFINITE ELEMENT CODE FOR SOIL AND ROCK ANALYSES
Local level
6-node triangle 15-node triangle
x x
xstress point (σ, ε)
node (ux, uy)
x-axis
y-axis x x
xx
xx xx
x
xx
x
6-node elements 15-node elements
Plane strain
Working load
Failure loads
Phi-c reduction
Axi-symmetry
PLAXISFINITE ELEMENT CODE FOR SOIL AND ROCK ANALYSES
Local level
f=0
c
σ3 σ1
φ
τ
σ
c
σ3 σ1
φ
τ
σ
Mohr Coulomb Mohr Coulomb
τ
ε
f=0
f<0
f<0
Mohr Coulomb
Elastic pointf<0
p
0ε =&
Plastic pointf=0
p0ε ≠&
τ
ε
f<0 Advanced models
Advanced plastic model
f=0
f=0
f=0
• Elastic and plastic stress point for Mohr-Coulomb
model
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PLAXIS Standard Course Universti Teknologi Malaysia, Johor
May 14-16,2007
Presented by GOUW Tjie-Liong
[email protected] 8
PLAXISFINITE ELEMENT CODE FOR SOIL AND ROCK ANALYSES
Local level
Cap (Advanced models only)-σ1
Normal plastic pointf<0
-σ3 Apex point
-σ 1
f<0
-σ 3
Tension point
• Apex stress point and tension stress point
PLAXISFINITE ELEMENT CODE FOR SOIL AND ROCK ANALYSES
eq
c
||||
||||c
eqc
Error Local σ
σσ −=
Local level
Local error Constitutive stress σc:
Stress that follows from the
constitute model (Mohr- Coulomb)
Equilibrium stress σeq:
Stress that is in equilibrium with the
external load
Inaccurate point: Local error > Tolerated error
Standard setting: To lerated error = 0.01
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PLAXIS Standard Course Universti Teknologi Malaysia, Johor
May 14-16,2007
Presented by GOUW Tjie-Liong
[email protected] 9
PLAXISFINITE ELEMENT CODE FOR SOIL AND ROCK ANALYSES
Global level
uuo
q0+∆q
q0
∆ue
∆up
• Initial stress method or Elastic stiffness
method
PLAXISFINITE ELEMENT CODE FOR SOIL AND ROCK ANALYSES
Global level
uuo
q0+∆q
q0
A BOverrelaxation
A
+=
A
B
Standard setting: 1.2
Absolute maximum: 2.0
Low friction angles (<20°): 1.5 acceptable
• Initial stress method + Over relaxation
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PLAXIS Standard Course Universti Teknologi Malaysia, Johor
May 14-16,2007
Presented by GOUW Tjie-Liong
[email protected] 10
PLAXISFINITE ELEMENT CODE FOR SOIL AND ROCK ANALYSES
Global level
uuo
q0+∆q
q0
Arc
q0+∆q
Arc-length control
• Initial stress method + arc-length control
PLAXISFINITE ELEMENT CODE FOR SOIL AND ROCK ANALYSES
Global level
uuo
q
e
unbalance
=|q
e-q
c|
qc
qe = “external“ load
(including weights)
qc = internal reaction forces
(integral of σc)
Convergence requirement:
Global error = Tolerated error
Standard setting:
Tolerated error = 0.01
| || |
| || |
load
unbalance Error Global =
• Global error
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PLAXIS Standard Course Universti Teknologi Malaysia, Johor
May 14-16,2007
Presented by GOUW Tjie-Liong
[email protected] 11
PLAXISFINITE ELEMENT CODE FOR SOIL AND ROCK ANALYSES
Global level
| || |
||| |
load
unbalance Error Global =
||||
||||c
eqc
Error Local σ
σσ −=
Convergence requirements
• Accuracy reached if:
• Global error = Tolerated error
• Inaccurate stress points = 3 + (pl. soil points)/10
• Inaccurate interface points = 3 + (pl. intf.
points)/10
PLAXISFINITE ELEMENT CODE FOR SOIL AND ROCK ANALYSES
Load advancement
u
qScaling up
Scaling down
Scaling up
• Converged within desired minimum number of iterations:
• Scaling up by a factor 2
• Not converged within desired maximum number of iterations:
• Scaling down by a factor 2
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PLAXIS Standard Course Universti Teknologi Malaysia, Johor
May 14-16,2007
Presented by GOUW Tjie-Liong
PLAXISFINITE ELEMENT CODE FOR SOIL AND ROCK ANALYSES
Load advancement
u
q
Reaching prescribed
ultimate level
X
u
q
Reaching final step
X
u
q
Failure beforereachingprescribed ultimate
level
X
No. of steps procedure: • Plastic calculation, incr. Multipliers• Phi – c reduction (safety analysis)
Ultimate level procedure: Plastic calculation: • Staged construction• Total multipliers