PressureDependMultiYield02-Example 1

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Solid-fluid fully coupled (u-p) plane-strain 9-4 noded element: saturated soil element with pressure dependent material, subjected to 1D sinusoidal base shaking


Input File

# Written by Jinchi Lu and Zhaohui Yang (May 2004)

wipe
set matOpt   1          ;# 1 = pressure depend; 
                        ;# 2 = pressure independ; 
set fmass  1            ;# fluid mass density
set smass  2.0          ;# saturated soil mass density
set G     9.0e4     
set B     2.2e5    
set bulk   2.2e6                        ;#fluid-solid combined bulk modulus
set vperm  5.e-6        ;#vertical permeability (m/s)
set hperm  [expr $vperm]        ;#horizontal permeability (m/s)

set accGravity  9.81    ;#acceleration of gravity
set vperm  [expr $vperm/$accGravity/$fmass]  ;#actual value used in computation
set hperm  [expr $hperm/$accGravity/$fmass]  ;#actual value used in computation
set loadBias 0.0                        ;# Static shear load, in percentage 
                                        ;# of gravity load (=sin(inclination angle))

set accMul  2.          ;# acc. multiplier
set period   1.0        ;# Period for applied Sine wave
set deltaT   0.01       ;# time step for analysis
set numSteps 2500       ;# number of time steps
set gamma    0.6        ;# Newmark integration parameter

set massProportionalDamping   0. ;
set InitStiffnessProportionalDamping 0.002;

#############################################################
# BUILD MODEL

#create the ModelBuilder
model basic -ndm 2 -ndf 3
node 1 0 0
node 2 2.5 0
node 3 2.5 2
node 4 0 2

fix 1 1 1 0 
fix 2 1 1 0
fix 3 0 0 1
fix 4 0 0 1
equalDOF 3 4 1 2

model basic -ndm 2 -ndf 2
node 5 1.25 0.
node 6 2.5 1
node 7 1.25 2
node 8 0 1
node 9 1.25 1

fix 5 1 1
equalDOF 3 7 1 2
equalDOF 6 8 1 2
equalDOF 6 9 1 2

set gravY [expr -$accGravity]  ;#calc. gravity
set gravX [expr -$gravY*$loadBias]

# define material and properties
switch $matOpt {
  1 {
    nDMaterial PressureDependMultiYield02 1 2 1.8 $G $B 32 .1 80 0.5\
                                          26. 0.067 0.23 0.06 0.27 
  }
  2 {
    nDMaterial PressureIndependMultiYield 2 2 1.8 4.e4 2.e5 40 .1
  }
}

              #    ele#                     thick maTag    bulk  mDensity  perm1  perm2  gravity       
element 9_4_QuadUP  1     1 2 3 4 5 6 7 8 9  1.0   1       $bulk $fmass  $hperm  $vperm $gravX $gravY    

#set material to elastic for gravity loading
updateMaterialStage -material $matOpt -stage 0  

#recorder for nodal variables along the vertical center line.
set SnodeList {}
for {set i 0} {$i < 9} {incr i 1} {
  lappend SnodeList [expr $i+1]
}

set FnodeList {}
for {set i 0} {$i < 4} {incr i 1} {
  lappend FnodeList [expr $i+1]
}

#############################################################
# GRAVITY APPLICATION (elastic behavior)

# create the SOE, ConstraintHandler, Integrator, Algorithm and Numberer
numberer RCM
system ProfileSPD
test NormDispIncr 1.0e-8 30 0
algorithm KrylovNewton
constraints Penalty 1.e18 1.e18
set nw 1.5
set nw2 [expr pow($nw+0.5, 2)/4]
integrator Newmark $nw $nw2
analysis Transient 

analyze 10 5e3

updateMaterialStage -material $matOpt -stage 1

analyze 100 1.e0

# rezero time
wipeAnalysis
setTime 0.0
#############################################################
# NOW APPLY LOADING SEQUENCE AND ANALYZE (plastic)

#   base input motion                     
pattern UniformExcitation  1  1    -accel "Sine 0. 10. $period -factor $accMul"

eval "recorder Node -file disp  -time -node $SnodeList -dof 1 2 -dT $deltaT disp"
eval "recorder Node -file  pwp -time -node $FnodeList -dof 3 -dT $deltaT vel"
eval "recorder Node -file acc  -time -node $SnodeList -dof 1 2 -dT $deltaT accel"
recorder Element -ele 1  -time -file stress1  -dT $deltaT material 1 stress
recorder Element -ele 1  -time -file strain1  -dT $deltaT material 1 strain
recorder Element -ele 1  -time -file stress5  -dT $deltaT material 5 stress
recorder Element -ele 1  -time -file strain5  -dT $deltaT material 5 strain
recorder Element -ele 1  -time -file stress9  -dT $deltaT material 9 stress
recorder Element -ele 1  -time -file strain9  -dT $deltaT material 9 strain


constraints Penalty 1.e18 1.e18
test NormDispIncr 1.e-4 25 0
numberer RCM
algorithm KrylovNewton
system ProfileSPD
integrator Newmark $gamma  [expr pow($gamma+0.5, 2)/4]  
rayleigh $massProportionalDamping 0.0 $InitStiffnessProportionalDamping 0.0
analysis VariableTransient 

set startT [clock seconds]
analyze $numSteps $deltaT [expr $deltaT/100] $deltaT 15
set endT [clock seconds]
puts "Execution time: [expr $endT-$startT] seconds."

wipe  #flush ouput stream


MATLAB Plotting File

clear all;

a1=load('acc');
d1=load('disp');
p1=load('pwp');
s1=load('stress1');
e1=load('strain1');
s5=load('stress5');
e5=load('strain5');
s9=load('stress9');
e9=load('strain9');

fs=[0.5, 0.2, 4, 6];
fs2=[0.5, 0.2, 4, 3];
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;
   qo(i)=sign(s1(i,5))*1/3.0*qo(i)^0.5;
end

figure(1); close 1; figure(1);
%integration point 1 stress-strain
subplot(2,1,1), plot(e1(:,4),s1(:,5),'r');
title ('shear stress \tau_x_y VS. shear strain \epsilon_x_y at integration point 1');
xLabel('Shear strain \epsilon_x_y');
yLabel('Shear stress \tau_x_y (kPa)');
subplot(2,1,2), plot(-po,qo,'r');
title ('confinement p VS. deviatoric stress q at integration point 1');
xLabel('confinement p (kPa)');
yLabel('q (kPa)');
set(gcf,'paperposition',fs);
saveas(gcf,'SS_PQ_p1','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;
   qo(i)=sign(s5(i,5))*1/3.0*qo(i)^0.5;
end

figure(5); close 5; figure(5);
%integration point 5 stress-strain
subplot(2,1,1), plot(e5(:,4),s5(:,5),'r');
title ('shear stress \tau_x_y VS. shear strain \epsilon_x_y at integration point 5');
xLabel('Shear strain \epsilon_x_y');
yLabel('Shear stress \tau_x_y (kPa)');
subplot(2,1,2), plot(-po,qo,'r');
title ('confinement p VS. deviatoric stress q at integration point 5');
xLabel('confinement p (kPa)');
yLabel('q (kPa)');
set(gcf,'paperposition',fs);
saveas(gcf,'SS_PQ_p5','jpg');

%integration point 9 p-q
po=(s9(:,2)+s9(:,3)+s9(:,4))/3;
for i=1:size(s1,1)
    qo(i)=(s9(i,2)-s9(i,3))^2 + (s9(i,3)-s9(i,4))^2 +(s9(i,2)-s9(i,4))^2 + 6.0* s9(i,5)^2;
   qo(i)=sign(s9(i,5))*1/3.0*qo(i)^0.5;
end

figure(6); close 6; figure(6);
%integration point 9 stress-strain
subplot(2,1,1), plot(e9(:,4),s9(:,5),'r');
title ('shear stress \tau_x_y VS. shear strain \epsilon_x_y at integration point 9');
xLabel('Shear strain \epsilon_x_y');
yLabel('Shear stress \tau_x_y (kPa)');
subplot(2,1,2), plot(-po,qo,'r');
title ('confinement p VS. deviatoric stress q at integration point 9');
xLabel('confinement p (kPa)');
yLabel('q (kPa)');
set(gcf,'paperposition',fs);
saveas(gcf,'SS_PQ_p9','jpg');

figure(2); close 2; figure(2);
%node 3 displacement relative to node 1
plot(d1(:,1),d1(:,6));
title ('Lateral displacement at element top');
xLabel('Time (s)');
yLabel('Displacement (m)');
set(gcf,'paperposition',fs2);
saveas(gcf,'Disp','jpg');

s=accMul*sin(0:pi/50:20*pi);
s=[s';zeros(3000,1)];
s1=interp1(0:0.01:40,s,a1(:,1));

figure(3); close 3; figure(3);
%node acceleration
a = plot(a1(:,1),s1+a1(:,6),'r');
title ('Lateral acceleration at element top');
xLabel('Time (s)');
yLabel('Acceleration (m/s^2)');
set(gcf,'paperposition',fs2);
saveas(gcf,'Acc','jpg');

figure(4); close 4; figure(4);
a=plot(p1(:,1),p1(:,2));
title ('Pore pressure at base');
xLabel('Time (s)');
yLabel('Pore pressure (kPa)');
set(gcf,'paperposition',fs2);
saveas(gcf,'EPWP','jpg');


Displacement Output File

Stress-Strain Output File (integration point 1)

Stress-Strain Output File (integration point 5)

Stress-Strain Output File (integration point 9)

Excess Pore Pressure Output File

Acceleration Output File


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