radiation damping in QzSimple1 material

[ZVaghefi]

Hi,

I have built a model of soil-structure allowed to uplift using QzSimple1 material for soil elements.
Unexpectedly, changing radiation damping ratio (i.e. Crad) as the input of this material, doesn't affect the responses!
Does this mean that QzSimple1 material does'nt consider the radiation damping?!! Am I right?
Why does this occur? and, how does the model react changing Crad?
I searched in QzSimple1 source code and other references, but I didn't find any reason for this problem.

I appreciate any help.
Many thanks.

[skamalzare]

Hi,

There can be multiple reasons why you are not seeing any differences. You need to explain your problem in more details. How are your waves reaching these elements? These elements are installed in vertical direction, if you have horizontal waves hitting them, my expectation is that you should not see any damping.

Regards,
Soheil

[ZVaghefi]

Thanks a lot for your reply.

The model is subjected to horizontal seismic excitation. You said that if only horizontal waves hit springs, we should not see any damping. You are right; I changed excitation and saw that responses change with changing Crad. But my problem has not been solved yet.

I should explain more about the model. The model is soil structure system which is composed of a SDOF structure as super-structure and beam on nonlinear winkler foundation (BNWF as used in PEER 2007/04 report) as sub-structure. The stiffness of vertical distributed springs their spacing are determined in such a way as to produce proper stiffness for the rocking motion of surface foundations. If the spring behavior is elastic, I use elastic material for them and add dashpot elements parallel to vertical springs in order to provide radiation damping. The damping of each dashpot is calculated in such a way as to produce proper damping for the rocking motion (same as damping proposed by Wolf). If the springs are nonlinear, I use QzSimple1 for springs and remove dashpots. In fact, I think that Crad in the QzSimple1 material should provide damping for rocking motion, so even when only horizontal excitation is exerted on the system Crad should affect the responses. Is it correct? If not, how can damping of rocking motion be considered in case of using QzSimple1 material?

If the above descriptions are not enough, I can explain more.

Thanks in advance.

[skamalzare]

When you were using elastic materials with parallel (vertical) dashpots, were you able to see proper performance from the dashpots?

QzSimple1 material is designed to represent soil behavior at tip of a pile. I don't have a clear idea how they will work for a shallow foundation. These elements are usually coupled with P-Y elements. P-Y elements have the horizontal dashpots that absorb the horizontal radiation. You might not get proper hz radiation damping by only using QzSimple1 materials.

Why don't you add a horizontal dashpot to your model and see how it affects the behavior.

Regards,
Soheil

[ZVaghefi]

Thanks indeed for your response. Firstly, I apologize for the long passage.

In the first case, when I use elastic materials with parallel vertical dashpots, a rigid tensionless spring (ENT material) is also used in series with each pair of vertical spring–damper to allow foundation uplift. The sway stiffness of the soil is modeled by a pair of spring and damper, with coefficients kx and cx, respectively. As I pointed in previous post, the radiation damping is also provided by vertical dashpots having viscous damping to produce Cϴ (proposed by Wolf). The response of your first question is that in this case, horizontal and vertical dampers provide horizontal and rocking radiation damping (cx and Cϴ), so vertical dampers affect the responses even in the absence of vertical excitation (because of rocking motin).

According to the PEER 2005/04, although QzSimple1 material was intended to model the behavior of a pile tip under cyclic loading, the mechanisms of local response below the shallow foundation are quite similar, so another case is using QzSimple1 material instead of each set of vertical series-parallel springs (three vertical elements) above, and PySimple instead of each pair of horizontal spring-damper. In both cases (paragraph 1 &2), the stiffness of vertical and horizontal springs are the same, but the implementation of radiation damping differs. In the latter one, the radiation damping is produced by Crad. Based on the source code of QzSimple1 material, this element utilizes an elastic, plastic, and gap component in series as generally (shown in Figure 2.4. of PEER 2007/04*). Radiation damping may be modeled through a dashpot added in parallel to the elastic component of the material. Now, when this set of springs (QzSimple &Py material) are subjected to horizontal excitation, changing Crad doesn’t change the responses yet!!

It should be said that in the second case, I used the code generated by Raychowdhury (from the appendix of his thesis**) which is also brought in the appendix of PEER 2007/04, in more details.

In fact, my main purpose is to verify my model with PEER model described in the first and second paragraph, respectively. Both of them are under horizontal excitation. In the case of elimination of radiation damping in my model (i.e. zero cx and Cϴ), the responses of two models are very close; but in the presence of radiation damping, the responses of PEER model don’t change, and therefor the results aren’t comparable!!

I really appreciate any ideas or comments on this issue. Is there any references comparing responses of model having QzSimple1 & Py material for several amounts of radiation damping (Crad)?

Thanks a lot.
__________________________________________________________________________________________________________________________
* Numerical Models for Analysis and Performance-Based Design of Shallow Foundations Subjected to Seismic Loading(by Gajan et.al. ,2008)
** Nonlinear Winkler-based shallow foundation model for performance assessment of seismically loaded structures (by Raychowdhury, Prishati,2008)

[ZVaghefi]

Hi,

Any idea on the problem mentioned in my posts?

This is the script of the second case (i.e. using QzSimple & Py materials).
In this script, radiation damping (CradSoil) is assumed 0.05. You can try other amounts and see that the responses don't change under horizontal excitation!
This is the script of Example#1 of Raychowdhury thesis.
______________________________________________________
##--Example # 1 - "A shear wall supported by a strip footing"
#--Written by Prishati Raychowdhury (UCSD)
#--units: N,m
wipe
wipeAnalysis
# Create ModelBuilder
model BasicBuilder -ndm 2 -ndf 3
# Set wall and footing dimensions
set LengthWall 0.5;
set WidthWall 0.2;
set HeightWall 5.0;
# Set structural nodes
node 1 0. 0.
node 2 0. $HeightWall
# set wall properties
set AWall [expr $WidthWall*$LengthWall]
set EWall [expr 2.15*pow(10,10)]; #----[N/m^2] concrete
set IWall [expr $WidthWall*pow($LengthWall,3)/12.]
uniaxialMaterial Elastic 1 $EWall
# set geometric transformation

geomTransf Linear 1
#geomTransf Corotational 1
#geomTransf PDelta 1

# set wall element
#element elasticBeamColumn $eleTag $iNode $jNode $A $E $Iz $transfTag
element elasticBeamColumn 1 1 2 $AWall $EWall $IWall 1
# set wall mass
set MWall 1200.0; #---mass of structure (kg)
mass 2 $MWall $MWall 1
##
#-------------------------------------------------
# Use ShallowFoundationGen command to
# attach shallow foundation with Foundation tag=1
# at node 1
#--------------------------------------------------
##
set FoundationTag 1
######################################################################################
# #
# This is an intermediate file generated by the command ShallowFoundationGen. #
# Source it after the ShallowFoundationGen command. #
# Use this file to check shallow foundation nodes, elements, fixity details #
# ShallowFoundationGen.cpp is developed by Prishati Raychowdhury (UCSD) #
# #
######################################################################################
# Foundation Tag =1
# Foundation Base Condition Tag =5

#node $NodeTag $Xcoord $Ycoord
node 1001 -0.5 0
node 100001 -0.5 0
node 1002 -0.4 0
node 100002 -0.4 0
node 1003 -0.3 0
node 100003 -0.3 0
node 1004 0 0
node 100004 0 0
node 1005 0.3 0
node 100005 0.3 0
node 1006 0.4 0
node 100006 0.4 0
node 1007 0.5 0
node 100007 0.5 0
node 100008 0.5 0
node 100009 0.5 0

#equalDOF $rNodeTag $cNodeTag $dof1 $dof2 $dof3
equalDOF 1 1004 1 2 3

#Materials for shallow foundation

#uniaxialMaterial QzSimple2 $matTag $SoilType $Qult-end-extreme $z50-end <TpSoil> <CradSoil>
uniaxialMaterial QzSimple2 101 1 5e+007 3.59211 0 0.05

#uniaxialMaterial QzSimple2 $matTag $SoilType $Qult-end $z50-end <TpSoil> <CradSoil>
uniaxialMaterial QzSimple2 102 1 1e+008 3.59211 0 0.05

#uniaxialMaterial QzSimple2 $matTag $SoilType $Qult-mid $z50-mid <TpSoil> <CradSoil>
uniaxialMaterial QzSimple2 103 1 3e+008 17.9605 0 0.05

#uniaxialMaterial PySimple2 $matTag $SoilType $Pp $xp50 Cd <CradSoil>
uniaxialMaterial PySimple2 105 1 102000 0.0145067 0.0 0.05

#uniaxialMaterial TzSimple2 $matTag $SoilType $Tult $xt50 <CradSoil>
uniaxialMaterial TzSimple2 106 1 1000 0.000142222 0.1 0.05

#uniaxialMaterial Elastic $matTag $Kx
# uniaxialMaterial Elastic 104 5.625e+007

#Vertical spring element connectivity
#element zeroLength $eleTag $iNode $jNode -mat$matTag -dir $dir
element zeroLength 100001 100001 1001 -mat 101 -dir 2
element zeroLength 100002 100002 1002 -mat 102 -dir 2
element zeroLength 100003 100003 1003 -mat 103 -dir 2
element zeroLength 100004 100004 1004 -mat 103 -dir 2
element zeroLength 100005 100005 1005 -mat 103 -dir 2
element zeroLength 100006 100006 1006 -mat 102 -dir 2
element zeroLength 100007 100007 1007 -mat 101 -dir 2

#Horizontal spring element connectivity
#element zeroLength $eleTag $iNode $jNode -mat$matTag -dir $dir
element zeroLength 100008 1007 100008 -mat 105 -dir 1
element zeroLength 100009 1007 100009 -mat 106 -dir 1

# element zeroLength 100008 1007 100008 -mat 104 -dir 1
#fix 1 1 0 0

# geomTransf Linear $transfTag <-jntOffset $dXi $dYi $dXj $dYj>
geomTransf Linear 10

#foundation element connectivity
#element elasticBeamColumn $eleTag $iNode $jNode $A $E $Iz $transfTag
element elasticBeamColumn 1001 1001 1002 0.25 2.15e+010 0.00130208 10
element elasticBeamColumn 1002 1002 1003 0.25 2.15e+010 0.00130208 10
element elasticBeamColumn 1003 1003 1004 0.25 2.15e+010 0.00130208 10
element elasticBeamColumn 1004 1004 1005 0.25 2.15e+010 0.00130208 10
element elasticBeamColumn 1005 1005 1006 0.25 2.15e+010 0.00130208 10
element elasticBeamColumn 1006 1006 1007 0.25 2.15e+010 0.00130208 10

#fixity
fix 100001 1 1 1
fix 100002 1 1 1
fix 100003 1 1 1
fix 100004 1 1 1
fix 100005 1 1 1
fix 100006 1 1 1
fix 100007 1 1 1
fix 100008 1 1 1
fix 100009 1 1 1

set endFootNodeL_1 1001
set endFootNodeR_1 1007
set endSprEleL_1 100001
set endSprEleR_1 100007
set midSprEle_1 100004

set MassFooting 1200.0
mass 1 $MassFooting $MassFooting 1
#-------------------------------
# Eigen Value Analysis
#-------------------------------
set PI 3.1415926
set lambdax [eigen 1]
set lambda [lindex $lambdax 0]
set omega [expr pow($lambda,0.5)]
set Tn [expr 2*$PI/$omega]
set fn [expr 1/$Tn]
puts "1st mode, Tn=$Tn sec, fn=$fn Hz"

##############################
## Rayleigh damping
##############################
set damping 0.05
set lambdax [eigen 2]
#set w1 [expr sqrt([lindex $lambdax 0])]
#set w2 [expr sqrt([lindex $lambdax 1])]
set wn [expr 2*$PI*$fn*2]
set w1 $wn
set w2 0.0
set am [expr $damping*2.0*$w1*$w2/($w1+$w2)]
set bk [expr $damping*2.0/($w1+$w2)]
set bkinit 0.0
set bklast 0.0
rayleigh $am $bk $bkinit $bklast
puts "$w1 $w2 $am $bk"
#-------------------------------

#-------------------------------
# Recorder
#-------------------------------
###-wall
recorder Node -time -file WallRoofdisp.dat -node 2 -dof 1 2 3 disp
recorder Element -file WallElementforce.dat -time -ele 1 localForce


recorder Node -time -file WallShear.dat -node 2 -dof 1 reaction
recorder Node -time -file WallRoofaccel.dat -node 2 -dof 1 accel

###-Spring
recorder Node -time -file EndSprLdisp.dat -node $endFootNodeL_1 -dof 1 2 3 disp
recorder Element -file EndSpringLforce.dat -time -ele $endSprEleL_1 force
#-----------------------
# Gravity LOAD PATTERNS
#-----------------------
set gacc 9.87
set FSv 5.0
set deadLoad [expr ($MassFooting+$MWall)*$gacc*$FSv]; #---total gravity load on footing (footing+wall)
#puts $deadLoad
pattern Plain 1 "Linear" {
load 2 0. [expr -$deadLoad] 0.
}
#--------------------
# gravity analysis
#--------------------
system UmfPack
constraints Plain
test NormDispIncr 1.0e-8 40 0
algorithm Newton
numberer RCM
integrator LoadControl 0.1
analysis Static
analyze 10; #use 10 analysis steps
#--------------------
# Pushover analysis
#--------------------
#loadConst
loadConst -time 0.0

#----------------------------------------------------
# Seismic load
#----------------------------------------------------
set dt 0.005
set factorx 9.81
set t 30
set accel "Series -dt $dt -filePath newRecords/RECh01.txt -factor $factorx
"
pattern UniformExcitation 3 1 -accel $accel
set dte 0.005
constraints Plain
numberer Plain
system BandGeneral
test NormDispIncr 1.e-6 20
algorithm Newton
integrator Newmark 0.5 0.25
analysis Transient
analyze [expr int($t/$dte)] $dte
puts "groundmotion done!. End Time:[getTime]"
_____________________________________________

Regards,
Vaghefi

[skamalzare]

Dear Vaghefi,

My understanding is that when you have a vertical damper, it absorbs the vertical motions (e.g. p-waves). In your case, when the foundation rocks, it hits the elements in vertical direction. The p-waves generated by this impact are absorbed by the dampers inside the QZ materials. These generated and absorbed motions are separate from the earthquake motion. In your code, earthquake loads are applied in horizontal direction. They generate shear waves (s-waves). To absorb these waves you need horizontal dampers. Otherwise, they will reflect back from your fix boundaries.

Saying this, I believe, if you are modeling for earthquake and rocking foundation, you need to implement two sets of horizontal and vertical dampers.

Regards,
Soheil

[ZVaghefi]

Dear Soheil,

Thanks a lot for the clear and worth information.
Fortunately, the problem was solved. You are right, both horizontal and vertical springs should be used in the model; and so I did. The main and simple point that I understood after try and error was that the amount of “Crad” or “C” as the last input parameter of QzSimple1, Py and Tz material should not be in fraction (e.g. 0.05). It should be the amount of viscous damping (as proposed by Wolf or others) in N.s/m. Exact looking at these material source codes proves this evidence. In fact, the radiation damping in fraction is meaningless. This misunderstanding is due to not clear explanation in these materials command-manuals. Unfortunately, in “ShallowFoundationGen” command, a new implementation in Opensees, Crad is also defined in fraction which is not correct. I hope this will be improved.
Thanks for your time and very useful guidance in your posts.

Best Regards,
Vaghfei

[Danielaait]

Dear ZVaghefi,

In your previous post, you stated the following idea:

"If the spring behavior is elastic, I use elastic material for them and add dashpot elements parallel to vertical springs in order to provide radiation damping. The damping of each dashpot is calculated in such a way as to produce proper damping for the rocking motion (same as damping proposed by Wolf)."

I want to model elastic Soil-Structure interaction using BNWF model. I used elastic foundation case, which is Foundation condition = 3 in ShallowFoundationGen command.

I didn't see a damping term in the generated file from ShallowFoundationGen command. How can I consider material and radational damping of the soil foundation?



Thank you
Daniel