Dear all,
It's the first that I use OpenSees in site response analysis..
First of all, I tried to analyze a soil column, I used the input file provided by the website (http://opensees.berkeley.edu/wiki/index ... _Analysis)) and by doing some modifications I found the modes of the soil.
My basic question is why the soil column has only one element along the long. dimension? Also, I don't understand the reason why there are no BCs at the two vertical lateral surfaces of the elements (restrain the x displacement or Lysmer dashpots..)
Moreover, according to the theory, I think that the 1st mode of the soil column should be equal to 4*H/vs=4*40/250=0.64sec but I take 0.9sec..
Obviously, I am missing something.
Could you please help me?
Many thanks in advance,
Olympia
I also copy the tcl file
wipe
#-------------------------------------------------------------------------------------------
# 1. DEFINE ANALYSIS PARAMETERS
#-------------------------------------------------------------------------------------------
#---SOIL GEOMETRY
# thicknesses of soil profile (m)
set soilThick 40.0
#---MATERIAL PROPERTIES
# soil mass density (Mg/m^3)
set rho 1.7
# soil shear wave velocity (m/s)
set Vs 250.0
# soil shear modulus (kPa)
set G [expr $rho*$Vs*$Vs]
# poisson's ratio of soil
set nu 0.0
# soil elastic modulus (kPa)
set E [expr 2*$G*(1+$nu)]
# soil bulk modulus (kPa)
set bulk [expr $E/(3*(1-2*$nu))]
# soil cohesion (kPa)
set cohesion 95.0
# peak shear strain
set gammaPeak 0.05
# soil friction angle
set phi 0.0
# reference pressure
set refPress 80.0
# pressure dependency coefficient
set pressCoeff 0.0
# bedrock shear wave velocity (m/s)
set rockVS 760
# bedrock mass density (Mg/m^3)
set rockDen 2.4
#---GROUND MOTION PARAMETERS
# time step in ground motion record
set motionDT 0.005
# number of steps in ground motion record
set motionSteps 7990
#---WAVELENGTH PARAMETERS
# highest frequency desired to be well resolved (Hz)
set fMax 100.0
# wavelength of highest resolved frequency
set wave [expr $Vs/$fMax]
# number of elements per one wavelength
set nEle 10
#---RAYLEIGH DAMPING PARAMETERS
set pi 3.141592654
# damping ratio
set damp 0.02
# lower frequency
set omega1 [expr 2*$pi*0.2]
# upper frequency
set omega2 [expr 2*$pi*20]
# damping coefficients
set a0 [expr 2*$damp*$omega1*$omega2/($omega1 + $omega2)]
set a1 [expr 2*$damp/($omega1 + $omega2)]
puts "damping coefficients: a_0 = $a0; a_1 = $a1"
#---ANALYSIS PARAMETERS
# Newmark parameters
set gamma 0.5
set beta 0.25
#-------------------------------------------------------------------------------------------
# 2. DEFINE MESH GEOMETRY
#-------------------------------------------------------------------------------------------
# trial vertical element size
set hTrial [expr $wave/$nEle]
# trial number of elements
set nTrial [expr $soilThick/$hTrial]
# round up if not an integer number of elements
if { $nTrial > [expr floor($soilThick/$hTrial)] } {
set numEleY [expr int(floor($soilThick/$hTrial)+1)]
} else {
set numEleY [expr int($nTrial)]
}
puts "number of verticl elements: $numEleY"
# final vertical size of elements (m)
set sizeEleY [expr $soilThick/$numEleY]
puts "vertical size of elements: $sizeEleY"
# define horizontal size of elements (m)
set sizeEleX $sizeEleY
puts "horizontal size of elements: $sizeEleX"
# number of nodes in vertical direction
set numNodeY [expr 2*($numEleY + 1)]
#-------------------------------------------------------------------------------------------
# 3. DEFINE NODES FOR SOIL ELEMENTS
#-------------------------------------------------------------------------------------------
# soil nodes are created in 2 dimensions, with 2 translational dof
model BasicBuilder -ndm 2 -ndf 2
set yCoord 0.0
set count 0
# loop over nodes
for {set j 1} {$j <= $numNodeY} {incr j 2} {
node $j 0.0 [expr $yCoord + $count*$sizeEleY]
node [expr $j+1] $sizeEleX [expr $yCoord + $count*$sizeEleY]
set count [expr $count+1]
}
puts "Finished creating all soil nodes..."
#-------------------------------------------------------------------------------------------
# 4. DEFINE DASHPOT NODES
#-------------------------------------------------------------------------------------------
#node 2000 0.0 0.0
#node 2001 0.0 0.0
#puts "Finished creating dashpot nodes..."
#-------------------------------------------------------------------------------------------
# 5. DEFINE BOUNDARY CONDITIONS AND EQUAL DOF
#-------------------------------------------------------------------------------------------
# define fixity of base nodes
fix 1 1 1
fix 2 1 1
# define fixity of dashpot nodes
#fix 2000 1 1
#fix 2001 0 1
# define equal DOF for simple shear deformation of soil elements
for {set k 3} {$k <= $numNodeY} {incr k 2} {
equalDOF $k [expr $k+1] 1 2
}
# define equal DOF for dashpot and base soil nodes
#equalDOF 1 2 1
#equalDOF 1 2001 1
puts "Finished creating all boundary conditions and equalDOF..."
#-------------------------------------------------------------------------------------------
# 6. DEFINE SOIL MATERIALS
#-------------------------------------------------------------------------------------------
nDMaterial PressureIndependMultiYield 1 2 $rho $G $bulk $cohesion $gammaPeak \
$phi $refPress $pressCoeff 25
puts "Finished creating all soil materials..."
#-------------------------------------------------------------------------------------------
# 7. DEFINE SOIL ELEMENTS
#-------------------------------------------------------------------------------------------
set wgtX 0.0
set wgtY [expr -9.81*$rho]
# loop over elements
for {set j 1} {$j <= $numEleY} {incr j 1} {
set nI [expr 2*$j - 1]
set nJ [expr $nI + 1]
set nK [expr $nI + 3]
set nL [expr $nI + 2]
element quad $j $nI $nJ $nK $nL 1.0 "PlaneStrain" 1 0.0 0.0 $wgtX $wgtY
}
puts "Finished creating all soil elements..."
#-------------------------------------------------------------------------------------------
# 8. DEFINE MATERIAL AND ELEMENTS FOR VISCOUS DAMPERS
#-------------------------------------------------------------------------------------------
# dashpot coefficient
#set mC [expr $sizeEleX*$rockDen*$rockVS]
# material
#uniaxialMaterial Viscous 4000 $mC 1
# elements
#element zeroLength 5000 2000 2001 -mat 4000 -dir 1
#puts "Finished creating dashpot material and element..."
#-------------------------------------------------------------------------------------------
# 8. CREATE GRAVITY RECORDERS
#-------------------------------------------------------------------------------------------
# record nodal displacments, velocities, and accelerations at each time step
recorder Node -file Gdisplacement.out -time -nodeRange 1 $numNodeY -dof 1 2 disp
recorder Node -file Gvelocity.out -time -nodeRange 1 $numNodeY -dof 1 2 vel
recorder Node -file Gacceleration.out -time -nodeRange 1 $numNodeY -dof 1 2 accel
# record stress and strain at each gauss point in the soil elements
recorder Element -file Gstress1.out -time -eleRange 1 $numEleY material 1 stress
recorder Element -file Gstress2.out -time -eleRange 1 $numEleY material 2 stress
recorder Element -file Gstress3.out -time -eleRange 1 $numEleY material 3 stress
recorder Element -file Gstress4.out -time -eleRange 1 $numEleY material 4 stress
recorder Element -file Gstrain1.out -time -eleRange 1 $numEleY material 1 strain
recorder Element -file Gstrain2.out -time -eleRange 1 $numEleY material 2 strain
recorder Element -file Gstrain3.out -time -eleRange 1 $numEleY material 3 strain
recorder Element -file Gstrain4.out -time -eleRange 1 $numEleY material 4 strain
puts "Finished creating gravity recorders..."
#-------------------------------------------------------------------------------------------
# 9. APPLY GRAVITY LOADING
#-------------------------------------------------------------------------------------------
constraints Transformation
test NormDispIncr 1e-5 30 1
algorithm Newton
numberer RCM
system ProfileSPD
integrator Newmark $gamma $beta
analysis Transient
analyze 10 5.0e2
puts "Finished with elastic gravity analysis..."
# update material to consider elastoplastic behavior
#updateMaterialStage -material 1 -stage 1
# plastic gravity loading
#analyze 40 5.0e2
#puts "Finished with plastic gravity analysis..."
#-------------------------------------------------------------------------------------------
# 10. CREATE POST-GRAVITY RECORDERS
#-------------------------------------------------------------------------------------------
# reset time and analysis
setTime 0.0
wipeAnalysis
# record nodal displacments, velocities, and accelerations at each time step
recorder Node -file displacement.out -time -dT $motionDT -nodeRange 1 $numNodeY -dof 1 2 disp
recorder Node -file velocity.out -time -dT $motionDT -nodeRange 1 $numNodeY -dof 1 2 vel
recorder Node -file acceleration.out -time -dT $motionDT -nodeRange 1 $numNodeY -dof 1 2 accel
# record stress and strain at each gauss point in the soil elements
recorder Element -file stress1.out -time -dT $motionDT -eleRange 1 $numEleY material 1 stress
recorder Element -file stress2.out -time -dT $motionDT -eleRange 1 $numEleY material 2 stress
recorder Element -file stress3.out -time -dT $motionDT -eleRange 1 $numEleY material 3 stress
recorder Element -file stress4.out -time -dT $motionDT -eleRange 1 $numEleY material 4 stress
#recorder Element -file strain1.out -time -dT $motionDT -eleRange 1 $numEleY material 1 strain
recorder Element -file strain2.out -time -dT $motionDT -eleRange 1 $numEleY material 2 strain
recorder Element -file strain3.out -time -dT $motionDT -eleRange 1 $numEleY material 3 strain
recorder Element -file strain4.out -time -dT $motionDT -eleRange 1 $numEleY material 4 strain
puts "Finished creating all recorders..."
# PROCEDURE TO VISUALISE THE MODEL BEFORE RUNNING THE ANALYSIS
source DisplayPlane.tcl;
source DisplayModel3D.tcl;
# procedure for displaying 3D perspectives of model
# Define DISPLAY -------------------------------------------------------------
set xPixels 1000; # height of graphical window in pixels
set yPixels 500; # height of graphical window in pixels
set xLoc1 300; # horizontal location of graphical window (0=upper left-most corner)
set yLoc1 400; # vertical location of graphical window (0=upper left-most corner)
set dAmp 100; # scaling factor for viewing deformed shape, it depends on the dimensions of the model
DisplayModel3D NodeNumbers $dAmp $xLoc1 $yLoc1 $xPixels $yPixels
DisplayPlane NodeNumbers $dAmp XY
set numModes 10;
file mkdir modes;
# Define RECORDERS -------------------------------------------------------------
for { set k 1 } { $k <= $numModes } { incr k } {
recorder Node -file [format "modes/mode%i.out" $k] -nodeRange 1 $numNodeY -dof 1 2 3 4 5 6 "eigen $k"
}
# perform eigen analysis
#-----------------------------
set lambda [eigen $numModes];
# calculate frequencies and periods of the structure
#---------------------------------------------------
set omega {}
set f {}
set T {}
set pi 3.141593
foreach lam $lambda {
lappend omega [expr sqrt($lam)]
lappend f [expr sqrt($lam)/(2*$pi)]
lappend T [expr (2*$pi)/sqrt($lam)]
}
puts "periods are $T"
# write the output file cosisting of periods
#--------------------------------------------
set period "modes/Periods.txt"
set Periods [open $period "w"]
foreach t $T {
puts $Periods " $t"
}
close $Periods
DisplayModel3D ModeShape $dAmp 300 10 800 500 1
integrator LoadControl 0 1 0 0
test EnergyIncr 1.0e-10 100 0
algorithm Newton
numberer RCM
constraints Transformation
system ProfileSPD
analysis Static
analyze 1
site response analysis
Moderator: Moderators