PressureDependMultiYield-Example 11
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Input File
# saturated, undrained single BbarBrick element with pressure dependent material.
# subjected to 1D sinusoidal base shaking
wipe
set friction 31.40 ;#friction angle
set phaseTransform 26.50 ;#phase transformation angle
set E1 93178.4 ;#Young's modulus
set poisson1 0.40 ;
set G1 [expr $E1/(2*(1+$poisson1))] ;
set B1 [expr $E1/(3*(1-2*$poisson1))] ;
set gamma 0.600 ;# Newmark integration parameter
set dt 0.01 ;# time step for analysis, does not have to be the same as accDt.
set numSteps 1600 ;# number of time steps
set rhoS 1.973 ;# saturated mass density
set rhoF 1.00 ;# fluid mass density
set densityMult 1. ;# density multiplier
set Bfluid 2.2e6 ;# fluid shear modulus
set fluid1 1 ;# fluid material tag
set solid1 10 ;# solid material tag
set accMul 2 ;# acceleration multiplier
set pi 3.1415926535 ;
set inclination 0;
set massProportionalDamping 0.0 ;
set InitStiffnessProportionalDamping 0.001;
set bUnitWeightX [expr ($rhoS-$rhoF)*9.81*sin($inclination/180.0*$pi)*$densityMult] ;# buoyant unit weight in X direction
set bUnitWeightY 0.0 ;# buoyant unit weight in Y direction
set bUnitWeightZ [expr -($rhoS-$rhoF)*9.81*cos($inclination/180.0*$pi)] ;# buoyant unit weight in Z direction
set ndm 3 ;# space dimension
model BasicBuilder -ndm $ndm -ndf $ndm
nDMaterial PressureDependMultiYield $solid1 $ndm [expr $rhoS*$densityMult] $G1 $B1 $friction 0.1 80 0.5 \
$phaseTransform 0.17 0.4 10 10 0.015 1.0 ;# 27 0.6 0 0 0 101 0.630510273
nDMaterial FluidSolidPorous $fluid1 $ndm $solid1 $Bfluid
node 1 0.00000 0.0000 0.00000
node 2 0.00000 0.0000 1.00000
node 3 0.00000 1.0000 0.00000
node 4 0.00000 1.0000 1.00000
node 5 1.00000 0.0000 0.00000
node 6 1.00000 0.0000 1.00000
node 7 1.00000 1.0000 0.00000
node 8 1.00000 1.0000 1.00000
element bbarBrick 1 1 5 7 3 2 6 8 4 $fluid1 $bUnitWeightX $bUnitWeightY $bUnitWeightZ
updateMaterialStage -material $solid1 -stage 0
updateMaterialStage -material $fluid1 -stage 0
fix 1 1 1 1 0 0 0
fix 2 0 1 0 0 0 0
fix 3 1 1 1 0 0 0
fix 4 0 1 0 0 0 0
fix 5 1 1 1 0 0 0
fix 6 0 1 0 0 0 0
fix 7 1 1 1 0 0 0
fix 8 0 1 0 0 0 0
# equalDOF
# tied nodes around
equalDOF 2 4 1 3
equalDOF 2 6 1 3
equalDOF 2 8 1 3
set nodeList {}
for {set i 1} {$i <= 8 } {incr i 1} {
lappend nodeList $i
}
set elementList {}
for {set i 1} {$i <= 1 } {incr i 1} {
lappend elementList $i
}
# GRAVITY APPLICATION (elastic behavior)
# create the SOE, ConstraintHandler, Integrator, Algorithm and Numberer
system ProfileSPD
test NormDispIncr 1.D-10 25 2
constraints Transformation
integrator LoadControl 1 1 1 1
algorithm Newton
numberer RCM
analysis Static
analyze 2
# switch the material to plastic
updateMaterialStage -material $fluid1 -stage 1
updateMaterialStage -material $solid1 -stage 1
updateMaterials -material $solid1 bulkModulus [expr $G1*2/3.];
analyze 2
setTime 0.0 ;# reset time, otherwise reference time is not zero for time history analysis
wipeAnalysis
############# create recorders ##############################
eval "recorder Node -file allNodesDisp.out -time -node $nodeList -dof 1 2 3 -dT 0.01 disp"
eval "recorder Node -file allNodesAcce.out -time -node $nodeList -dof 1 2 3 -dT 0.01 accel"
eval "recorder Element -ele $elementList -time -file stress1.out -dT 0.01 material 1 stress"
eval "recorder Element -ele $elementList -time -file strain1.out -dT 0.01 material 1 strain"
eval "recorder Element -ele $elementList -time -file press1.out -dT 0.01 material 1 pressure"
eval "recorder Element -ele $elementList -time -file stress5.out -dT 0.01 material 5 stress"
eval "recorder Element -ele $elementList -time -file strain5.out -dT 0.01 material 5 strain"
eval "recorder Element -ele $elementList -time -file press5.out -dT 0.01 material 5 pressure"
eval "recorder Element -ele $elementList -file backbone.out -dT 1000 material 1 backbone 80 100 200 300"
############# create dynamic time history analysis ##################
pattern UniformExcitation 1 1 -accel "Sine 0 10 1 -factor $accMul"
rayleigh $massProportionalDamping 0.0 $InitStiffnessProportionalDamping 0.
integrator Newmark $gamma [expr pow($gamma+0.5, 2)/4]
constraints Penalty 1.e18 1.e18 ;# can't combine with test NormUnbalance
test NormDispIncr 1.0e-5 25 0 ;# can't combine with constraints Lagrange
#algorithm Newton ;# tengent is updated at each iteration
algorithm ModifiedNewton ;# tengent is updated at the begining of each time step not each iteration
system ProfileSPD ;# Use sparse solver. Next numberer is better to be Plain.
numberer Plain ;# method to map between between equation numbers of DOFs
analysis VariableTransient ;# splitting time step requires VariableTransient
############# perform the Analysis and record time used #############
set startT [clock seconds]
analyze $numSteps $dt [expr $dt/64] $dt 15
set endT [clock seconds]
puts "Execution time: [expr $endT-$startT] seconds."
MATLAB Plotting File
clear all;
a1=load('allNodesAcce.out');
d1=load('allNodesDisp.out');
s1=load('stress1.out');
e1=load('strain1.out');
s5=load('stress5.out');
e5=load('strain5.out');
p1=load('press1.out');
p5=load('press5.out');
fs=[0.5, 0.2, 4, 6];
accMul = 2;
%integration point 1 p-q
po=(s1(:,2)+s1(:,3)+s1(:,4))/3;
for i=1:size(s1,1)
qo(i)=(s1(i,2)-s1(i,3))^2 + (s1(i,3)-s1(i,4))^2 +(s1(i,2)-s1(i,4))^2 + 6.0* s1(i,5)^2 + 6.0* s1(i,6)^2 + 6.0* s1(i,7)^2;
qo(i)=sign(s1(i,7))*1/3.0*qo(i)^0.5;
end
figure(1); clf;
%integration point 1 stress-strain
subplot(2,1,1), plot(e1(:,7),s1(:,7),'r');
title ('Integration point 1 shear stress \tau_x_y VS. shear strain \epsilon_x_y');
xLabel('Shear strain \epsilon_x_y');
yLabel('Shear stress \tau_x_y (kPa)');
subplot(2,1,2), plot(-po,qo,'r');
title ('Integration point 1 confinement p VS. deviatoric q relation');
xLabel('confinement p (kPa)');
yLabel('q (kPa)');
set(gcf,'paperposition',fs);
saveas(gcf,'SS_PQ1','jpg');
%integration point 5 p-q
po=(s5(:,2)+s5(:,3)+s5(:,4))/3;
for i=1:size(s5,1)
qo(i)=(s5(i,2)-s5(i,3))^2 + (s5(i,3)-s5(i,4))^2 +(s5(i,2)-s5(i,4))^2 + 6.0* s5(i,5)^2 + 6.0* s5(i,6)^2 + 6.0* s5(i,7)^2;
qo(i)=sign(s5(i,7))*1/3.0*qo(i)^0.5;
end
figure(4); clf;
%integration point 5 stress-strain
subplot(2,1,1), plot(e5(:,7),s5(:,7),'r');
title ('Integration point 5 shear stress \tau_x_y VS. shear strain \epsilon_x_y');
xLabel('Shear strain \epsilon_x_y');
yLabel('Shear stress \tau_x_y (kPa)');
subplot(2,1,2), plot(-po,qo,'r');
title ('Integration point 5 confinement p VS. deviatoric q relation');
xLabel('confinement p (kPa)');
yLabel('q (kPa)');
set(gcf,'paperposition',fs);
saveas(gcf,'SS_PQ5','jpg');
figure(2); clf;
%node 3 displacement relative to node 1
subplot(2,1,1),plot(d1(:,1),d1(:,5),'r');
title ('Lateral displacement at element top');
xLabel('Time (s)');
yLabel('Displacement (m)');
set(gcf,'paperposition',fs);
saveas(gcf,'D','jpg');
s=accMul*sin(0:pi/50:20*pi);
s=[s';zeros(1000,1)];
s1=interp1(0:0.01:20,s,a1(:,1));
figure(3); clf;
%node 3 acceleration
subplot(2,1,1),plot(a1(:,1),s1+a1(:,5),'r');
title ('Lateral acceleration at element top');
xLabel('Time (s)');
yLabel('Acceleration (m/s^2)');
set(gcf,'paperposition',fs);
saveas(gcf,'A','jpg');
figure(5); clf;
%integration point 1 excess pore water pressure
subplot(2,1,1),plot(p1(:,1),-p1(:,2),'r');
title ('Integration point 1 excess pore pressure');
xLabel('Time (s)');
yLabel('Excess pore pressure (kPa)');
subplot(2,1,2),plot(p1(:,1),p1(:,3),'r');
title ('Integration point 1 excess pore pressure ratio');
xLabel('Time (s)');
yLabel('Excess pore pressure ratio');
set(gcf,'paperposition',fs);
saveas(gcf,'EPWP','jpg');
Displacement Output File
Stress-Strain Output File (Integration Point 1 & Integration Point 3)
Excess Pore Pressure Output File
Acceleration Output File
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