Ibarra Krawinkler Deterioration Model- warning

[EQpkm]

Hi,

Could you please help me about this non convergence and warning!
Thanks

(i also copied my script.)


Ec = 30769.358811184036
Modified Ibarra-Medina-Krawinkler Model with Bilinear Hysteretic Response

T = 0.22599913714961264
Model Built
2e-3 Is Done
-4e-3 Is Done
2e-3 Is Done
-4e-3 Is Done
2e-3 Is Done
-4e-3 Is Done
4e-3 Is Done
-8e-3 Is Done
4e-3 Is Done
-8e-3 Is Done
4e-3 Is Done
-8e-3 Is Done
6e-3 Is Done
-12e-3 Is Done
6e-3 Is Done
-12e-3 Is Done
6e-3 Is Done
-12e-3 Is Done
12e-3 Is Done
-24e-3 Is Done
12e-3 Is Done
-24e-3 Is Done
12e-3 Is Done
-24e-3 Is Done
18e-3 Is Done
-36e-3 Is Done
18e-3 Is Done
-36e-3 Is Done
18e-3 Is Done
-36e-3 Is Done
24e-3 Is Done
-48e-3 Is Done
24e-3 Is Done
-48e-3 Is Done
24e-3 Is Done
-48e-3 Is Done
24e-3 Is Done
-48e-3 Is Done
30e-3 Is Done
WARNING: CTestNormDispIncr::test() - failed to converge
after: 6 iterations
NewtnRaphson::solveCurrentStep() -the ConvergenceTest object failed in test()
StaticAnalysis::analyze() - the Algorithm failed at iteration: 0 with domain at
load factor 183367
OpenSees > analyze failed, returned: -3 error flag
Trying Newton with Initial Tangent ..
CTestNormDispIncr::test() - iteration: 1 current Norm: 9.04171e-014 (max: 1e-006
, Norm deltaR: 9.41761e-006)
CTestNormDispIncr::test() - iteration: 1 current Norm: 9.04374e-014 (max: 1e-006
, Norm deltaR: 5.44865e-006)
CTestNormDispIncr::test() - iteration: 1 current Norm: 9.04171e-014 (max: 1e-006
, Norm deltaR: 1.83251e-005)
CTestNormDispIncr::test() - iteration: 1 current Norm: 9.04374e-014 (max: 1e-006
, Norm deltaR: 5.62993e-006)
CTestNormDispIncr::test() - iteration: 1 current Norm: 9.04171e-014 (max: 1e-006
, Norm deltaR: 8.34329e-006)
CTestNormDispIncr::test() - iteration: 1 current Norm: 9.04374e-014 (max: 1e-006
, Norm deltaR: 1.55582e-005)
CTestNormDispIncr::test() - iteration: 1 current Norm: 9.04171e-014 (max: 1e-006
, Norm deltaR: 2.79088e-006)
CTestNormDispIncr::test() - iteration: 1 current Norm: 9.04374e-014 (max: 1e-006
, Norm deltaR: 1.2219e-005)
CTestNormDispIncr::test() - iteration: 1 current Norm: 9.04171e-014 (max: 1e-006
, Norm deltaR: 1.26447e-005)
CTestNormDispIncr::test() - iteration: 1 current Norm: 9.04374e-014 (max: 1e-006
, Norm deltaR: 2.20568e-006)
CTestNormDispIncr::test() - iteration: 1 current Norm: 9.04171e-014 (max: 1e-006
, Norm deltaR: 1.508e-005)
CTestNormDispIncr::test() - iteration: 1 current Norm: 9.04374e-014 (max: 1e-006
, Norm deltaR: 7.74869e-006)
CTestNormDispIncr::test() - iteration: 1 current Norm: 9.04171e-014 (max: 1e-006
, Norm deltaR: 5.12613e-006)
CTestNormDispIncr::test() - iteration: 1 current Norm: 9.04374e-014 (max: 1e-006
, Norm deltaR: 1.80006e-005)
CTestNormDispIncr::test() - iteration: 1 current Norm: 9.04171e-014 (max: 1e-006
, Norm deltaR: 4.84302e-006)
CTestNormDispIncr::test() - iteration: 1 current Norm: 9.04374e-014 (max: 1e-006
, Norm deltaR: 8.04671e-006)
CTestNormDispIncr::test() - iteration: 1 current Norm: 9.04171e-014 (max: 1e-006
, Norm deltaR: 1.48118e-005)
CTestNormDispIncr::test() - iteration: 1 current Norm: 9.04374e-014 (max: 1e-006
, Norm deltaR: 1.93749e-006)
CTestNormDispIncr::test() - iteration: 1 current Norm: 9.04171e-014 (max: 1e-006
, Norm deltaR: 1.29265e-005)
CTestNormDispIncr::test() - iteration: 1 current Norm: 9.04374e-014 (max: 1e-006
, Norm deltaR: 1.18912e-005)
CTestNormDispIncr::test() - iteration: 1 current Norm: 9.04171e-014 (max: 1e-006
, Norm deltaR: 3.07842e-006)
CTestNormDispIncr::test() - iteration: 1 current Norm: 9.04374e-014 (max: 1e-006
, Norm deltaR: 1.58214e-005)
CTestNormDispIncr::test() - iteration: 1 current Norm: 9.04171e-014 (max: 1e-006
, Norm deltaR: 8.07496e-006)
CTestNormDispIncr::test() - iteration: 1 current Norm: 9.13111e-014 (max: 1e-006
, Norm deltaR: 0.116057)
WARNING: CTestNormDispIncr::test() - failed to converge
after: 6 iterations
NewtnRaphson::solveCurrentStep() -the ConvergenceTest object failed in test()
StaticAnalysis::analyze() - the Algorithm failed at iteration: 0 with domain at
load factor 183967
OpenSees > analyze failed, returned: -3 error flag
Trying Newton with Initial Tangent ..
CTestNormDispIncr::test() - iteration: 1 current Norm: 9.04363e-014 (max: 1e-006
, Norm deltaR: 5.19557e-006)
CTestNormDispIncr::test() - iteration: 1 current Norm: 9.04171e-014 (max: 1e-006
, Norm deltaR: 9.71562e-006)
CTestNormDispIncr::test() - iteration: 1 current Norm: 9.04374e-014 (max: 1e-006
, Norm deltaR: 1.51116e-005)
CTestNormDispIncr::test() - iteration: 1 current Norm: 9.04171e-014 (max: 1e-006
, Norm deltaR: 2.55802e-007)
CTestNormDispIncr::test() - iteration: 1 current Norm: 9.04374e-014 (max: 1e-006
, Norm deltaR: 1.26213e-005)
CTestNormDispIncr::test() - iteration: 1 current Norm: 9.04171e-014 (max: 1e-006
, Norm deltaR: 1.21979e-005)
CTestNormDispIncr::test() - iteration: 1 current Norm: 9.04374e-014 (max: 1e-006
, Norm deltaR: 2.65264e-006)
CTestNormDispIncr::test() - iteration: 1 current Norm: 9.04171e-014 (max: 1e-006
, Norm deltaR: 1.5527e-005)
CTestNormDispIncr::test() - iteration: 1 current Norm: 9.04374e-014 (max: 1e-006
, Norm deltaR: 7.30165e-006)
CTestNormDispIncr::test() - iteration: 1 current Norm: 9.04171e-014 (max: 1e-006
, Norm deltaR: 5.54334e-006)
CTestNormDispIncr::test() - iteration: 1 current Norm: 9.04374e-014 (max: 1e-006
, Norm deltaR: 1.72556e-005)
CTestNormDispIncr::test() - iteration: 1 current Norm: 9.04171e-014 (max: 1e-006
, Norm deltaR: 4.38108e-006)
CTestNormDispIncr::test() - iteration: 1 current Norm: 9.04374e-014 (max: 1e-006
, Norm deltaR: 1.0415e-005)
CTestNormDispIncr::test() - iteration: 1 current Norm: 9.04171e-014 (max: 1e-006
, Norm deltaR: 1.43648e-005)
CTestNormDispIncr::test() - iteration: 1 current Norm: 9.04374e-014 (max: 1e-006
, Norm deltaR: 1.12083e-006)
CTestNormDispIncr::test() - iteration: 1 current Norm: 9.04171e-014 (max: 1e-006
, Norm deltaR: 1.33579e-005)
CTestNormDispIncr::test() - iteration: 1 current Norm: 9.04374e-014 (max: 1e-006
, Norm deltaR: 1.05365e-005)
CTestNormDispIncr::test() - iteration: 1 current Norm: 9.04171e-014 (max: 1e-006
, Norm deltaR: 3.53711e-006)
CTestNormDispIncr::test() - iteration: 1 current Norm: 9.04374e-014 (max: 1e-006
, Norm deltaR: 1.71662e-005)
CTestNormDispIncr::test() - iteration: 2 current Norm: 1.95455e-014 (max: 1e-006
, Norm deltaR: 7.749e-007)
CTestNormDispIncr::test() - iteration: 1 current Norm: 4.40793e-016 (max: 1e-006
, Norm deltaR: 1.48055e-006)
CTestNormDispIncr::test() - iteration: 1 current Norm: 4.51168e-016 (max: 1e-006
, Norm deltaR: 5.96047e-007)
CTestNormDispIncr::test() - iteration: 1 current Norm: 4.50888e-016 (max: 1e-006
, Norm deltaR: 1.39149e-006)
CTestNormDispIncr::test() - iteration: 1 current Norm: 4.5121e-016 (max: 1e-006,
Norm deltaR: 4.76837e-007)
CTestNormDispIncr::test() - iteration: 1 current Norm: 4.51124e-016 (max: 1e-006
, Norm deltaR: 1.36994e-006)
CTestNormDispIncr::test() - iteration: 1 current Norm: 4.51071e-016 (max: 1e-006
, Norm deltaR: 3.57628e-007)
CTestNormDispIncr::test() - iteration: 1 current Norm: 4.51166e-016 (max: 1e-006
, Norm deltaR: 1.25205e-006)
CTestNormDispIncr::test() - iteration: 1 current Norm: 4.51113e-016 (max: 1e-006
, Norm deltaR: 2.38419e-007)
CTestNormDispIncr::test() - iteration: 1 current Norm: 4.51217e-016 (max: 1e-006
, Norm deltaR: 1.21607e-006)
CTestNormDispIncr::test() - iteration: 1 current Norm: 4.51155e-016 (max: 1e-006
, Norm deltaR: 1.78814e-007)
CTestNormDispIncr::test() - iteration: 1 current Norm: 4.51259e-016 (max: 1e-006
, Norm deltaR: 1.06624e-006)
CTestNormDispIncr::test() - iteration: 1 current Norm: 4.51218e-016 (max: 1e-006
, Norm deltaR: 2.91038e-010)
CTestNormDispIncr::test() - iteration: 1 current Norm: 4.51315e-016 (max: 1e-006
, Norm deltaR: 1.15e-006)
CTestNormDispIncr::test() - iteration: 1 current Norm: 4.51007e-016 (max: 1e-006
, Norm deltaR: 1.1921e-007)
CTestNormDispIncr::test() - iteration: 1 current Norm: 4.51358e-016 (max: 1e-006
, Norm deltaR: 1.21607e-006)
CTestNormDispIncr::test() - iteration: 1 current Norm: 4.5107e-016 (max: 1e-006,
Norm deltaR: 2.98023e-007)
CTestNormDispIncr::test() - iteration: 1 current Norm: 4.51402e-016 (max: 1e-006
, Norm deltaR: 9.99601e-007)
forrtl: error (200): program aborting due to control-C event
Image PC Routine Line Source
OpenSees.exe 01D2EA9A Unknown Unknown Unknown
OpenSees.exe 01CB3AA4 Unknown Unknown Unknown
OpenSees.exe 01CC2288 Unknown Unknown Unknown
KERNELBASE.dll 77ADDCD5 Unknown Unknown Unknown
KERNEL32.DLL 7607919F Unknown Unknown Unknown
ntdll.dll 77D5B5AF Unknown Unknown Unknown
ntdll.dll 77D5B57A Unknown Unknown Unknown
CTestNormDispIncr::test() - iteration: 1 current Norm: 4.51091e-016 (max: 1e-006
, Norm deltaR: 2.07335e-006)
Terminate batch job (Y/N)?

##===============================================================================================================
##################################################################################################################################
wipe all;

set DataDir SDOF-SpecimenBG6-Ibarra-Krawinkler-results; # set up name of data directory (can remove this)
file mkdir $DataDir; # create data directory

model BasicBuilder -ndm 2 -ndf 3;
source rotSpring2DModIKModel.tcl; # procedure for defining a rotational spring (zero-length element)

# Define Building Geometry, Nodes, and Constraints-------------------------------------------------------------------
# define structure-geometry parameters
# number of frame bays (excludes bay for P-delta column)
# calculate joint offset distance for beam plastic hinges--------------------------------------------------------

set phlat23 [expr 0.0]; # lateral dist from beam-col joint to loc of hinge on Floors

# calculate nodal masses -- lump floor masses at frame nodes------------------------------------------------------
set g 9806; # acceleration due to gravity (mm/s2)
set P [expr 1900e3]; # Axial Load (N)

set Mass2 [expr ($P)/$g]; # total member mass of Floor 2
set Negligible 1e-9; # a very smnumber to avoid problems with zero

# define nodes and assign masses to beam-column intersections of frame---------------------------------------------

node 11 0.0 0.0;

node 12 0.0 1645.0; # mm


mass 12 $Mass2 1e-9 0.0; # node#, Mx My Mz, Mass=Weight/g, neglect rotational inertia at nodes

# define extra nodes for plastic hinge rotational springs
# columns--------------------------------------------------------------------------------------------------------------

# column hinges at bottom of Story 1
node 117 0.0 0.0;

mass 117 $Negligible $Negligible 0.0; # node#, Mx My Mz, Mass=Weight/g, neglect rotational inertia at nodes

# assign boundary condidtions-----------------------------------------------------------------------------------------
fix 11 1 1 1;

# Define Section Properties and Elements-------------------------------------------------------------------------------
# define material properties------------------------------------------------------------------------------------------
set fc 34;
set Ec [expr 8200*pow($fc,0.375)];
puts "Ec = $Ec"
set n 10;
set m 1;
set Es 2.1e5;
# define column section C35x35 for Story 1 & 2 & 3

set Acol [expr 350*350]; # cross-sectional area (mm^2)
set Icol [expr ($m*350*350*350*350)/ 12]; # moment of inertia (mm^4)



# set up geometric transformations of element----------------------------------------------------------------------------
set PDeltaTransf 1;

geomTransf PDelta $PDeltaTransf; # PDelta transformation

# define beam & column elements-----------------------------------------------------------------------------------------
# command: element elasticBeamColumn $eleID $iNode $jNode $A $E $I $transfID

# Columns Story 1
element elasticBeamColumn 111 117 12 $Acol [expr $Ec*1e1] [expr 0.6*$Icol] $PDeltaTransf;

#-----------------------------------------------------------------------------------------------------------------

# Define Rotational Springs for Plastic Hinges (Ibarra et al., 2005)-------------------------------------------------------------------------
# constants
set McMy 1.21;
set LS 10.0;
set LD 10.0;
set LK 10.0;
set LA 1000.0;
set cS 1.0;
set cK 1.0;
set cA 1.0;
set cD 1.0;
set DP 1.0;
set DN 1.0;
set ResP 0.0;
set ResN 0.0;
set th_pcP 0.225; # this value is due to lack of data in the post-capping region, Haselton et al., 2011.
set th_pcN 0.225; # this value is due to lack of data in the post-capping region, Haselton et al., 2011.
set th_pP 0.06;
set th_pN 0.06;

set My 3.462725e8; # N.m (KN.mm)

set Icol_mod [expr $Icol*($n+1.0)/$n]; # modified moment of inertia for columns in Story 1 & 2
set Ks_col [expr $n*6.0*$Es*$Icol_mod/1645.0]; # rotational stiffness of Story 1 column springs


set a_mem [expr ($n+1.0)*($My*($McMy-1.0)) / ($Ks_col*$th_pP)]; # strain hardening ratio of spring
set b [expr ($a_mem)/(1.0+$n*(1.0-$a_mem))]; # modified strain hardening ratio of spring (Ibarra & Krawinkler 2005, note: Eqn B.5 is incorrect)

#------------------------------------------------------------------------------------------------------------------------------------------------
# Define column springs--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
# rotSpring2DModIKModel id ndR ndC K asPos asNeg MyPos MyNeg LS LK LA LD cS cK cA cD th_p+ th_p- th_pc+ th_pc- Res+ Res- th_u+ th_u- D+ D-

# column springs at Story 1 (corner columns)
# rotSpring2DModIKModel 1 11 117 [expr $My/0.013] 0.0455 0.0455 $My [expr (-1)*$My] $LS $LK $LA $LD $cS $cK $cA $cD 0.06 0.06 $th_pcP $th_pcN $ResP $ResN 0.298 0.298 $DP $DN;
rotSpring2DModIKModel 1 11 117 $Ks_col $b $b $My [expr (-1)*$My] $LS $LK $LA $LD $cS $cK $cA $cD $th_pP $th_pN $th_pcP $th_pcN $ResP $ResN 0.298 0.298 $DP $DN;

#............................................................................................................................................................................................................................
# create region for frame column springs-------------------------------------------------------------------------------------------------------------------------------------
# command: region $regionID -ele $ele_1_ID $ele_2_ID...

region 1 -ele 1;

#-------------------
source SDOF_Records.tcl

# Eigenvalue Analysis--------------------------------------------------------------------------------------------------

# Define & apply damping
set xDamp 0.02;
set Lambda [eigen 1];
set omega [expr pow($Lambda,0.5)];
set alphaM 0.0;
set betaKcurr 0.0;
set betaKcomm [expr 2.*$xDamp/($omega)];
set betaKinit 0.0;
rayleigh $alphaM $betaKcurr $betaKinit $betaKcomm;

set PI 3.14;
set T [expr 2.0*$PI/$omega];
puts "T = $T";

# Gravity Loads & Gravity Analysis-------------------------------------------------------------------------------------

#
# define GRAVITY -------------------------------------------------------------
pattern Plain 101 Constant {
load 12 1.0 -$P 0.0
}



# Gravity-analysis: load-controlled static analysis--------------------------------------------------------------------
set Tol 1.0e-6; # convergence tolerance for test
constraints Plain; # how it handles boundary conditions
numberer RCM; # renumber dof's to minimize band-width (optimization)
system BandGeneral; # how to store and solve the system of equations in the analysis (large model: try UmfPack)
test NormDispIncr $Tol 6; # determine if convergence has been achieved at the end of an iteration step
algorithm Newton; # use Newton's solution algorithm: updates tangent stiffness at every iteration
set NstepGravity 10; # apply gravity in 10 steps
set DGravity [expr 1.0/$NstepGravity]; # load increment
integrator LoadControl $DGravity; # determine the next time step for an analysis
analysis Static; # define type of analysis static or transient
analyze $NstepGravity; # apply gravity

# maintain constant gravity loads and reset time to zero
loadConst -time 0.0
puts "Model Built"


# assign lateral loads and create load pattern: use ASCE 7-10 distribution
set lat2 1.0; # force on each frame node in Floor 2
pattern Plain 200 Linear {
load 12 $lat2 0.0 0.0;
}

## Set up analysis parameters
constraints Plain;
numberer RCM ;
system BandGeneral ;
analysis Static ;

set controlnode 12
set loaddirection 1
set currentDisp 0.0
set Tol 1e-6;

foreach Dincr {2e-3 -4e-3 2e-3 -4e-3 2e-3 -4e-3 4e-3 -8e-3 4e-3 -8e-3 4e-3 -8e-3 6e-3 -12e-3 6e-3 -12e-3 6e-3 -12e-3 12e-3 -24e-3 12e-3 -24e-3 12e-3 -24e-3 18e-3 \
-36e-3 18e-3 -36e-3 18e-3 -36e-3 24e-3 -48e-3 24e-3 -48e-3 24e-3 -48e-3 24e-3 -48e-3 30e-3 -60e-3 30e-3 -60e-3 36e-3 -72e-3 36e-3 -72e-3 36e-3 -72e-3 36e-3 -72e-3 \
42e-3 -84e-3 42e-3 -84e-3 42e-3 48e-3 -96e-3 48e-3 -96e-3 54e-3 -108e-3 54e-3 -108e-3 60e-3 -120e-3 60e-3 -120e-3 66e-3 -122e-3 66e-3 -122e-3 72e-3 -144e-3\
72e-3 -144e-3 78e-3 -156e-3 78e-3 -156e-3 84e-3 -168e-3 84e-3 -168e-3 90e-3 -180e-3 90e-3 -180e-3 96e-3 -192e-3 96e-3 -192e-3 100e-3 -200e-3 100e-3 -200e-3\
105e-3 -210e-3 105e-3 -210e-3 110e-3 -220e-3 110e-3 -220e-3 120e-3 -240e-3 120e-3 -240e-3 130e-3 -260e-3 130e-3 -260e-3 140e-3 -280e-3 140e-3 -280e-3\
150e-3 -300e-3 150e-3 -300e-3 160e-3 -320e-3 160e-3 -320e-3 170e-3 -340e-3 170e-3 -340e-3 180e-3 -360e-3 180e-3 -360e-3 200e-3 -400e-3 200e-3 -400e-3\
210e-3 -420e-3 210e-3 -420e-3 220e-3 -440e-3 220e-3 -440e-3 240e-3 -480e-3 240e-3 -480e-3 260e-3 -540e-3 260e-3 -540e-3 280e-3 -560e-3 280e-3 -560e-3\
300e-3 -600e-3 300e-3 -600e-3 320e-3 -640e-3 320e-3 -640e-3 340e-3 -680e-3 340e-3 -680e-3 360e-3 -720e-3 360e-3 -720e-3 380e-3 -760e-3 380e-3 -760e-3\
400e-3 -800e-3 400e-3 -800e-3 420e-3 -840e-3 420e-3 -840e-3 440e-3 -880e-3 440e-3 -880e-3} {


##
integrator DisplacementControl $controlnode $loaddirection $Dincr
analysis Static
set nSteps 1000
if { $Dincr > 0 } {
set Dmax [expr $Dincr*$nSteps]
set ok 0
while {$ok == 0 && $currentDisp < $Dmax} {
set ok [analyze 1]
if {$ok != 0} {
puts "Trying Newton with Initial Tangent .."
test NormDispIncr $Tol 2000 0
algorithm Newton -initial
set ok [analyze 1]
test NormDispIncr $Tol 6 2
algorithm Newton
}
if {$ok != 0} {
puts "Trying Broyden .."
algorithm Broyden 8
set ok [analyze 1 ]
algorithm Newton
}
if {$ok != 0} {
puts "Trying NewtonWithLineSearch .."
algorithm NewtonLineSearch 0.8
set ok [analyze 1]
algorithm Newton
}
set currentDisp [nodeDisp $controlnode $loaddirection]
}
} elseif { $Dincr < 0 } {
set Dmax [expr $Dincr*$nSteps/2]
set ok 0
while {$ok == 0 && $currentDisp > $Dmax} {
set ok [analyze 1]
if {$ok != 0} {
puts "Trying Newton with Initial Tangent .."
test NormDispIncr $Tol 2000 0
algorithm Newton -initial
set ok [analyze 1]
test NormDispIncr $Tol 6 2
algorithm Newton
}
if {$ok != 0} {
puts "Trying Broyden .."
algorithm Broyden 8
set ok [analyze 1 ]
algorithm Newton
}
if {$ok != 0} {
puts "Trying NewtonWithLineSearch .."
algorithm NewtonLineSearch 0.8
set ok [analyze 1]
algorithm Newton
}
set currentDisp [nodeDisp $controlnode $loaddirection]
}
}

puts "$Dincr Is Done"
}

puts "*****************************************"
puts "Cyclic Analysis For Is Successfully Done!"
puts "*****************************************"
##
#

[fmk]

not exactly sure why you THINK you have a problem with what you are showing ... the warnings are that it failed to converge for a step .. the analysis steps after appear to be WORKING until YOU issued the control-c .. the reason for all the output is that the active convergence test during these working steps has a 2 flag.

[EQpkm]

shear force - drift curve looks wrong! strength and stiffness deterioration is not observed!?
but backbone curve (moment-curvature) seems right!!

[EQpkm]

Following parameters make an important role in analysis results. So how can i be sure which value is suitable to be considered for each one?
(As an example i compared LS1 = 1.0 and LS2 = 1000
LS1 result no deterioration)

set LS 1000.0; # basic strength deterioration (a very large # = no cyclic deterioration)
set LK 1000.0; # unloading stiffness deterioration (a very large # = no cyclic deterioration)
set LA 1000.0; # accelerated reloading stiffness deterioration (a very large # = no cyclic deterioration)
set LD 1000.0; # post-capping strength deterioration (a very large # = no deterioration)

[andy0071]

According to the Dissertation of D. Lignos 2008, Λs,c,a,k should be close to 1.0 depending on fc , ρsh,eff, sn and some other parameters.
Besides, in the Dissertation, he mentioned that "use of the same Λ value for all four deterioration modes usually provides adequate description of each deterioration mode"
I think, you can calibrate the parameters of the I-M-K model by your experiment results or even the finite element analysis results for a rational value to your model.