PressureDependMultiYield-Example 14

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Inclined (4 degrees), saturated, undrained soil column (user defined modulus reduction curve) with pressure dependent material


Input File

#Created by Zhaohui Yang (zhyang@ucsd.edu)
#
#plane strain,  shear-beam type mesh with single material,  
#dynamic analysis,  SI units (m, s, KN, ton)
#input motion may be from a file, or a sinusoidal wave. 
#
#USER DEFINED YIELD SURFACES
#
wipe
#
#some user defined variables
# 
set matOpt   2      ;# 1 = drained, pressure depend;  2 = undrained, pressure depend; 
                    ;# 3 = undrained, pressure independ; 4 = elastic 
set mass  2.0      ;# saturated mass density
set fmass 1.0      ;# fluid mass density
set G     6.e4     ;
set B     2.4e5    ;
set press   0.    ;# isotropic consolidation pressure on quad element(s)
set accMul  2.       ;# acc. multiplier (m/s/s)
set accNam  myACC      ;# acc. file name if imposed motion is read from file 
                       ;# - YOU MUST CHANGE IT TO THE RIGHT NAME
set accDt   0.0166     ;# dt for input acc.
set loadBias .07     ;# Static shear load, in percentage of gravity load (=sin(inclination angle))
set period   1.0      ;# Period if imposed motion is Sine wave
set deltaT   0.01    ;# time step for analysis, does not have to be the same as accDt.
set numSteps 2000    ;# number of time steps
set gamma    0.6     ;# Newmark integration parameter

set massProportionalDamping   0.0 ;
set InitStiffnessProportionalDamping 0.002;

set numXele 1      ;# number of elements in x (H) direction
set numYele 10      ;# number of elements in y (V) direction
set xSize 1.0       ;# x direction element size
set ySize 1.0       ;# y direction element size

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

#create the ModelBuilder
model basic -ndm 2 -ndf 2

# define material and properties
switch $matOpt {
  1 {
    nDMaterial PressureDependMultiYield 1 2 $mass $G $B  31.4 .1 80 0.5 \
                                        26.5 0.1 0.4 10 10 0.015 1.0 -11\
                                  1e-6 0.999  3e-6 0.995  1e-5 0.99  3e-5 0.96  1e-4 0.85 3e-4 0.64 \
                                  1e-3 0.37   3e-3 0.18   1e-2 0.08  3e-2 0.03  1e-1 0.01
    
    set gravY [expr -9.81*$mass]  ;#gravity
    set gravX [expr -$gravY*$loadBias]
  }
  2 {
    nDMaterial PressureDependMultiYield 1 2 $mass $G $B  31.4 .1 80 0.5 \
                                        26.5 0.1 0.4 10 10 0.015 1.0 -11\
                                  1e-6 0.999  3e-6 0.995  1e-5 0.99  3e-5 0.96  1e-4 0.85 3e-4 0.64 \
                                  1e-3 0.37   3e-3 0.18   1e-2 0.08  3e-2 0.03  1e-1 0.01
    nDMaterial FluidSolidPorous 2 2 1 2.2e6
    
    set gravY [expr -9.81*($mass-$fmass)]  ;# buoyant unit weight
    set gravX [expr -$gravY*$loadBias]
  }
  3 {
    nDMaterial PressureIndependMultiYield 1 2 $mass 4.e4 2.e5 20 .1 0 100 0. -11\
                                  1e-6 0.999  3e-6 0.995  1e-5 0.99  3e-5 0.96  1e-4 0.85 3e-4 0.64 \
                                  1e-3 0.37   3e-3 0.18   1e-2 0.08  3e-2 0.03  1e-1 0.01
    nDMaterial FluidSolidPorous 3 2 1 2.2e6
   
    set gravY [expr -9.81*($mass-$fmass)]  ;# buoyant unit weight
    set gravX [expr -$gravY*$loadBias]
  }
  4 {
    nDMaterial ElasticIsotropic 4 2000 0.3 $mass
    set gravY [expr -9.81*$mass]  ;#gravity
    set gravX [expr -$gravY*$loadBias]
  }
}

# define the nodes
set numXnode  [expr $numXele+1]
set numYnode  [expr $numYele+1]

for {set i 1} {$i <= $numXnode} {incr i 1} {
  for {set j 1} {$j <= $numYnode} {incr j 1} {
    set xdim [expr ($i-1)*$xSize]
    set ydim [expr ($j-1)*$ySize] 
    set nodeNum [expr $i + ($j-1)*$numXnode] 
    node $nodeNum $xdim $ydim 
  }
}

# define elements
for {set i 1} {$i <= $numXele} {incr i 1} {
  for {set j 1} {$j <= $numYele} {incr j 1} {
    set eleNum [expr $i + ($j-1)*$numXele] 
    set n1  [expr $i + ($j-1)*$numXnode] 
    set n2  [expr $i + ($j-1)*$numXnode + 1] 
    set n4  [expr $i + $j*$numXnode + 1] 
    set n3  [expr $i + $j*$numXnode] 
                                    #     thick  material        maTag  press density gravity    
    element quad $eleNum $n1 $n2 $n4 $n3  1.0  "PlaneStrain"   $matOpt $press 0.0  $gravX $gravY 
  }
}  

updateMaterialStage -material 1 -stage 0
updateMaterialStage -material 2 -stage 0
updateMaterialStage -material 3 -stage 0

# fix the base 
for {set i 1} {$i <= $numXnode} {incr i 1} {
  fix $i 1 1
}

# tie two lateral sides
for {set i 1} {$i < $numYnode} {incr i 1} {
  set nodeNum1 [expr $i*$numXnode + 1]
  set nodeNum2 [expr ($i+1)*$numXnode]
  equalDOF $nodeNum1 $nodeNum2 1 2
}

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

# create the SOE, ConstraintHandler, Integrator, Algorithm and Numberer
system ProfileSPD

test NormDispIncr 1.e-5 10 0
algorithm ModifiedNewton  
constraints Transformation
integrator LoadControl 1 1 1 1
numberer RCM

# create the Analysis
analysis Static 
analyze 2

# switch material stage from elastic (gravity) to plastic
  switch $matOpt {
   1 {
    updateMaterialStage -material 1 -stage 1
    updateMaterials -material 1 bulkModulus [expr $G*2/3.]
   }
   2 {
    updateMaterialStage -material 1 -stage 1
    updateMaterialStage -material 2 -stage 1
    updateMaterials -material 1 bulkModulus [expr $G*2/3.]
   }
   3 {
    updateMaterialStage -material 1 -stage 1
    updateMaterialStage -material 3 -stage 1
   }
   4  ;# do nothing
  }


#############################################################
# NOW APPLY LOADING SEQUENCE AND ANALYZE (plastic)

# rezero time
setTime 0.0
wipeAnalysis

#                                    
#Sinusoidal motion, comment next line if using input motion file
pattern UniformExcitation    1    1    -accel "Sine 0 10 $period -factor $accMul"

#decomment next line if using input motion file
#pattern UniformExcitation    1    1  -accel "Series -factor $accMul -filePath $accNam -dt $accDt"

#recorder for nodal displacement along the vertical center line.
set nodeList {}
for {set i 0} {$i < $numYnode} {incr i 1} {
  lappend nodeList [expr $numXnode/2 + $i*$numXnode]
}
eval "recorder Node -file disp  -time -node $nodeList -dof 1 2 -dT $deltaT disp"
eval "recorder Node -file acc  -time -node $nodeList -dof 1 2 -dT $deltaT accel"

#recorder for element output along the vertical center line.
set name1 "stress";   set name2 "strain";   set name3 "press"
for {set i 1} {$i < $numYnode} {incr i 1} {
  set ele [expr $numXele-$numXele/2+($i-1)*$numXele] 
  set name11 [join [list $name1 $i] {}]
  set name22 [join [list $name2 $i] {}]  
  set name33 [join [list $name3 $i] {}] 
  recorder Element -ele $ele  -time -file $name11 material 1 stress
  recorder Element -ele $ele  -time -file $name22 material 1 strain
  if { $matOpt == 2 || $matOpt == 3 } {   ;#excess pore pressure ouput
    recorder Element -ele $ele -time -file $name33 material 1 pressure
  }
}

constraints Transformation
test NormDispIncr 1.e-5 10 0
numberer RCM
algorithm Newton 
system ProfileSPD
rayleigh $massProportionalDamping 0.0 $InitStiffnessProportionalDamping 0.0
integrator Newmark $gamma  [expr pow($gamma+0.5, 2)/4]  
analysis VariableTransient 

#analyze 
set startT [clock seconds]
analyze $numSteps $deltaT [expr $deltaT/100] $deltaT 5
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('press1');
s1=load('stress1');
e1=load('strain1');
p6=load('press6');
s5=load('stress5');
e5=load('strain5');
p10=load('press10');
s9=load('stress9');
e9=load('strain9');

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;
   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 10 m depth');
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 10 m depth');
xLabel('confinement p (kPa)');
yLabel('q (kPa)');
set(gcf,'paperposition',fs);
saveas(gcf,'SS_PQ_10m','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 6 m depth');
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 6 m depth');
xLabel('confinement p (kPa)');
yLabel('q (kPa)');
set(gcf,'paperposition',fs);
saveas(gcf,'SS_PQ_6m','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 2 m depth');
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 2 m depth');
xLabel('confinement p (kPa)');
yLabel('q (kPa)');
set(gcf,'paperposition',fs);
saveas(gcf,'SS_PQ_2m','jpg');

figure(2); close 2; figure(2);
%node 3 displacement relative to node 1
subplot(2,1,1),a=plot(d1(:,1),d1(:,8),'r');
hold on
subplot(2,1,1),b=plot(d1(:,1),d1(:,14),'g');
hold on
subplot(2,1,1),c=plot(d1(:,1),d1(:,22),'b');
title ('Lateral displacement wrt base');
xLabel('Time (s)');
yLabel('Displacement (m)');
legend([a,b,c],'8m depth','4m depth', 'Surface',2)
set(gcf,'paperposition',fs);
saveas(gcf,'Disp','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); close 3; figure(3);
%node acceleration
subplot(3,1,1),a=plot(a1(:,1),s1+a1(:,22),'r');
legend(a,'at surface',4);
title ('Lateral acceleration');
xLabel('Time (s)');
yLabel('Acceleration (m/s^2)');
subplot(3,1,2),a=plot(a1(:,1),s1+a1(:,14),'r');
legend(a,'4 m depth',4);
xLabel('Time (s)');
yLabel('Acceleration (m/s^2)');
subplot(3,1,3),a=plot(a1(:,1),s1+a1(:,8),'r');
legend(a,'8 m depth',4);
xLabel('Time (s)');
yLabel('Acceleration (m/s^2)');
set(gcf,'paperposition',fs);
saveas(gcf,'Acc','jpg');


figure(4); close 4; figure(4);
%integration point 1 excess pore water pressure
subplot(3,1,1),a=plot(p10(:,1),-p10(:,2),'r');
legend(a,'1 m depth',4);
title ('Excess pore pressure');
xLabel('Time (s)');
yLabel('Excess pore pressure (kPa)');
subplot(3,1,2),a=plot(p6(:,1),-p6(:,2),'r');
legend(a,'5 m depth',4);
xLabel('Time (s)');
yLabel('Excess pore pressure (kPa)');
subplot(3,1,3),a=plot(p1(:,1),-p1(:,2),'r');
legend(a,'10 m depth',4);
xLabel('Time (s)');
yLabel('Excess pore pressure (kPa)');
set(gcf,'paperposition',fs);
saveas(gcf,'EPWP','jpg');


Displacement Output File

PD Ex21Disp.jpg


Stress-Strain Output File (2 m depth)

PD Ex21SS PQ2m.jpg


Stress-Strain Output File (6 m depth)

PD Ex21SS PQ6m.jpg


Stress-Strain Output File (10 m depth)

PD Ex21SS PQ10m.jpg


Excess Pore Pressure Output File

PD Ex21EPP.jpg


Acceleration Output File

PD Ex21Accel.jpg


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