3.4.2.12. SANISAND-MS Material

Code Developed by: Haoyuan Liu (Norwegian Geotechnical Institute (NGI), formerly TUDelft), José A. Abell (UANDES, Chile), Andrea Diambra (University of Bristol), and Federico Pisanò (TU Delft).

This command is used to construct a multi-dimensional SANISAND-MS (SAniSandMS) material, which is an extension of the Manzari-Dafalias (SAniSand) model with cyclic ratcheting control using the memory-surface (MS) concept. This allows capturing the ratcheting effects in sands that occur in high-cyclic loading in the presence of a static stress field or in the case of assymetric loading.

../../../../_images/SAniSandMS-fig0a.png

TCL command:

nDMaterial SAniSandMS $matTag $G0 $nu $e_init $Mc $c $lambda_c $e0 $ksi $P_atm $m $h0 $ch $nb $A0 $nd $zeta $mu0 $beta $Den $fabric_flag $flow_flag $intScheme $TanType $JacoType $TolF $TolR

Please report bugs as an issue on the main OpenSees repositoy and tag @jaabell

Where,

Argument

Type

Description

$matTag

integer

unique tag identifying material

$G0

float

dimensionless shear modulus constant

$nu

float

Poisson ratio

$e_init

float

initial void ratio

$Mc

float

critical state stress ratio

$c

float

ratio of critical state stress ratio in extension and compression

$lambda_c

float

critical state line constant

$e0

float

reference critical void ratio at p = 0

$ksi

float

critical state line constant

$P_atm

float

atmospheric pressure

$m

float

yield locus opening parameter (radius of yield surface in stress ratio space)

$h0

float

hardening parameter

$ch

float

hardening parameter

$nb

float

bounding surface void ratio dependence parameter $nb ≥ 0

$A0

float

intrinsic dilatancy parameter

$nd

float

dilatancy surface parameter $nd ≥ 0

$zeta

float

memory surface shrinkage parameter

$mu0

float

ratcheting parameter

$beta

float

dilatancy memory parameter

$Den

float

mass density of the material

$fabric_flag

integer

(deprecated)

$flow_flag

integer

(deprecated)

$intScheme

integer

constitutive integration method (3: Runge-Kutta 4th order with error control (the only one currently implemented))

$TanType

integer

type of tangent stiffness to report (0: elastic stiffness | 1: continuum elastoplastic stiffness )

$JacoType

integer

placeholder (not used in explicit methods)

$TolF

float

tolerance for yield surface intersection calculation (stress units)

$TolE

float

(adimensional) relative error for explicit integrator

The current implementation on SANISAND-MS uses fourth-order Runge-Kutta with error control for constitutive integration. The strain coming from a finite-element containing SANISAND-MS is applied incrementally by subdividing automatically to keep the constitutive integration error below the parameter $TolE. The integration error \(e\) is defined as:

\[\begin{split}e = \max\left\lbrace e_{\sigma},\, e_{\alpha} \right\rbrace \\ e_{\sigma} = \dfrac{\Vert \sigma^5 - \sigma^4 \Vert}{\Vert \sigma^4 \Vert} \\ e_{\alpha} = \dfrac{\Vert \alpha^5 - \alpha^4 \Vert}{\Vert \alpha^4 \Vert}\end{split}\]

And \(\sigma^p\) is the stress prediction using a \(p\)-th order integration formula, and likewise for the backstress \(\alpha^p\). Thus, in the code a 5-th order formula to approximate and bound the integration error, while integration advances using the fourth-order equation (RK45).

../../../../_images/SAniSandMS-fig0b.png

The above equations differ from those in the main reference by Liu et al. (2019) in that the use of the yield back-stress ratio \(\alpha\) is resumed here, as in Dafalias and Manzari (2004), to avoid certain numerical inconveniences.

Citation information

If you use SANISAND-MS in your published research work, please cite the main reference ([SANISAND-MS]) and also inform jaabell (at miuandes dot cl), to update the list of published articles and works that use the code.

Naming convention

In text documents we use the spelling SANISAND-MS, but the OpenSees implementation uses SAniSandMS to accomodate coding conventions in OpenSees.

Available formulations

The material formulations for the SAniSandMS object are “ThreeDimensional” and “PlaneStrain”

Recorder queries

Valid Element recorder queries are:

  • stress returns stress tensor

  • ``strain``returns strain tensor

  • alpha for \(\mathbf{\alpha}\), the back-stress ratio tensor for the yield surface

  • alphaM for \(\mathbf{\alpha^M}\), the back-stress ratio tensor for the memory surface

  • alpha_in for \(\mathbf{\alpha_{in}}\)

  • MM size of memory surface

  • estrain elastic strain tensor

recorder Element -eleRange 1 $numElem -time -file stress.out  stress

#. Elastic or Elastoplastic response could be enforced by
   Elastic:   updateMaterialStage -material $matTag -stage 0
   Elastoplastic:   updateMaterialStage -material $matTag -stage 1

Example

This example, provides an asymetric drained triaxial test of the constitutive model to show the effect of ratcheting. First the sample is compressed isotropically to 200KPa, then a cyclic deviator stress is applied.

set test_type "drained_triaxial_cyc" ;# Used in recorders.tcl

wipe
 
# Create a 3D model with 4 Degrees of Freedom
model BasicBuilder -ndm 3 -ndf 3
 
# Confinement Stress
set pConf -200.0

# Increment of q added at constant p0 (will be the average during cyclic loading)
set delta_qav -75.0; 

# Amplitude of cyclic deviatoric stress
set delta_qcyc -60.0; 


set G0        110.  ; # [Adimensional]
set nu        0.05  ; # [Adimensional]
set e_init    0.72  ; # [Adimensional]
set Mc        1.27  ; # [Adimensional]
set c         0.712 ; # [Adimensional]
set lambda_c  0.049 ; # [Adimensional]
set e0        0.845 ; # [Adimensional]
set ksi       0.27  ; # [Adimensional]
set P_atm     101.3 ; # [kPa]
set m         0.01  ; # [Adimensional]
set h0        5.95  ; # [Adimensional]
set ch        1.01  ; # [Adimensional]
set nb        2.0   ; # [Adimensional]
set A0        1.06  ; # [Adimensional]
set nd        1.17  ; # [Adimensional]
set z_max     4     ; # For SAniSand [Adimensional]
set cz        0     ; # For SAniSand [Adimensional]
set mu0       260.  ; # For SAniSand [Adimensional]
set zeta      0.0005; # For SAniSand [Adimensional]
set beta      1     ; # For SAniSand [Adimensional]
set w1        0.5   ;
set w2        2     ;
set Den       1.584 ; # [Mg/m^3]
set intScheme 3     ; # Corresponds to Modified-Euler integration scheme
set TanType   1     ; # 0: elastic stiffness, 1: continuum elastoplastic stiffness
set JacoType  1     ; # Not used in explicit methods
set TolF      1.0e-6; # Tolerances, not used in explicit
set TolR      1.0e-6; # Tolerances, not used in explicit

#Reference atmospheric pressure
set P_ref $P_atm
 
# Create material   
nDMaterial SAniSandMS  1 $G0 $nu $e_init $Mc $c $lambda_c $e0 $ksi $P_atm $m $h0 $ch $nb $A0 $nd $zeta $mu0 $beta $Den  $intScheme $TanType $JacoType $TolF $TolR
set type "RK"


# Create nodes
node 1  1.0 0.0 0.0
node 2  1.0 1.0 0.0
node 3  0.0 1.0 0.0 
node 4  0.0 0.0 0.0
node 5  1.0 0.0 1.0
node 6  1.0 1.0 1.0
node 7  0.0 1.0 1.0
node 8  0.0 0.0 1.0
 
# Create Fixities
fix 1   0 1 1 
fix 2   0 0 1 
fix 3   1 0 1 
fix 4   1 1 1 
fix 5   0 1 0 
fix 6   0 0 0 
fix 7   1 0 0 
fix 8   1 1 0 
 
 

# Create element
#       SSPbrickUP  tag    i j k l m n p q  matTag  fBulk  fDen    k1    k2   k3   void   alpha    <b1 b2 b3>
element SSPbrick   1     1 2 3 4 5 6 7 8    1
 
recorder Element -file ${type}_${test_type}_stress.out -ele 1  -time stress
recorder Element -file ${type}_${test_type}_strain.out -ele 1 -time strain


# Create analysis
constraints Transformation
test        NormDispIncr 1.0e-4 20 0
algorithm   Newton
numberer    RCM
system      BandGeneral
integrator  LoadControl 0.0001
analysis    Static
 
 
# Apply confinement pressure
set pNode [expr $pConf / 4.0]
pattern Plain 1 {Series -time {0 1 100} -values {0 1 1} -factor 1} {
    load 1  $pNode  0.0    0.0    
    load 2  $pNode  $pNode 0.0    
    load 3  0.0     $pNode 0.0    
    load 4  0.0     0.0    0.0    
    load 5  $pNode  0.0    $pNode 
    load 6  $pNode  $pNode $pNode 
    load 7  0.0     $pNode $pNode 
    load 8  0.0     0.0    $pNode 
}
analyze 10000
 



loadConst


puts "Starting monotonic analysis"


# Apply confinement pressure
set delta_sigma_a [expr $delta_qav*2./3.]
set delta_sigma_r [expr -$delta_sigma_a/2]
set pNode2 [expr $delta_sigma_r / 4.0 ]
set pNode1 [expr $delta_sigma_a / 4.0]
pattern Plain 3 {Series -time {1 2 100} -values {0 1 1} -factor 1} {
    load 1  $pNode2  0.0     0.0    
    load 2  $pNode2  $pNode2 0.0    
    load 3  0.0      $pNode2 0.0    
    load 4  0.0      0.0     0.0    
    load 5  $pNode2  0.0     $pNode1 
    load 6  $pNode2  $pNode2 $pNode1 
    load 7  0.0      $pNode2 $pNode1 
    load 8  0.0      0.0     $pNode1 
}


integrator LoadControl 0.0001
analyze 10000
 



loadConst




puts "Starting cyclic analysis"


set Ncyc 1000
set NcycActuallyDo 1000
set dT      [expr 0.001]
set tmax    [expr $NcycActuallyDo]
set numStep [expr int(2.0*$tmax / $dT)]
 







set qlist [list 0]
set timelist [list 2]

for {set i 1} {$i <= $Ncyc} {incr i} {
   lappend qlist [expr $delta_qcyc/4.0] [expr -$delta_qcyc/4.0]     
   lappend timelist [expr 2*$i + 1] [expr 2*$i + 2]
}

set tsq "{Series      -time {$timelist} -values {$qlist} }" ;#-factor 1}"
puts $tsq

# return


eval "pattern Plain 4 $tsq { load 5  0 0 1.0;  }"
eval "pattern Plain 5 $tsq { load 6  0 0 1.0;  }"
eval "pattern Plain 6 $tsq { load 7  0 0 1.0;  }"
eval "pattern Plain 7 $tsq { load 8  0 0 1.0;  }"





# Analyze and use substepping if needed
set remStep $numStep
set success 0
integrator  LoadControl $dT
proc subStepAnalyze {dT subStep} {
    if {$subStep > 10} {
        return -10
    }
    for {set i 1} {$i < 3} {incr i} {
        puts "Try dT = $dT"
        # set success [analyze 1 $dT]
        integrator  LoadControl $dT
        set success [analyze 1]
        if {$success != 0} {
            set success [subStepAnalyze [expr $dT/2.0] [expr $subStep+1]]
            if {$success == -10} {
                puts "Did not converge."
                return success
            }
        } else {
            if {$i==1} {
                puts "Substep $subStep : Left side converged with dT = $dT"
            } else {
                puts "Substep $subStep : Right side converged with dT = $dT"
            }
        }
    }
    return success
}
 
puts "Finished static Start analysis"
set startT [clock seconds]


set startTime  [getTime]
while {$success != -10} {
    set subStep 0
    integrator  LoadControl $dT
    set success [analyze $remStep  $dT]
    if {$success == 0} {
        puts "Analysis Finished"
        break
    } else {
        set curTime  [getTime]
        puts "Analysis failed at $curTime . Try substepping."
        set success  [subStepAnalyze [expr $dT/2.0] [incr subStep]]
        set curStep  [expr int(($curTime-$startTime)/$dT + 1)]
        set remStep  [expr int($numStep-$curStep)]
        puts "Current step: $curStep , Remaining steps: $remStep"
    }
}
set endT [clock seconds]
puts "loading analysis execution time: [expr $endT-$startT] seconds."





wipe

The script produces an output that can be visualized as follows.

../../../../_images/SAniSandMS-fig1.png
../../../../_images/SAniSandMS-fig2.png
../../../../_images/SAniSandMS-fig3.png

Main references

SANISAND-MS

Liu, H. Y., Abell, J. A., Diambra, A., & Pisanò, F. (2019). Modelling the cyclic ratcheting of sands through. Géotechnique, 69(9), 783-800.

PhDThesis

Liu, H.Y. (2020). Constitutive modelling of cyclic sand behaviour for offshore foundations (Doctoral dissertation, Delft University of Technology).

List of works using SANISAND-MS

1

Liu, H. Y., & Pisano, F. (2019). Prediction of oedometer terminal densities through a memory-enhanced cyclic model for sand. Géotechnique Letters, 9(2), 81-88.

2

Liu, H. Y., Kementzetzidis, E., Abell, J. A., & Pisanò, F. (2021). From cyclic sand ratcheting to tilt accumulation of offshore monopiles: 3D FE modelling using SANISAND-MS. Géotechnique, 1-16.

3

Liu, H.Y., & Kaynia, A. M. (2021). Characteristics of cyclic undrained model SANISAND-MSu and their effects on response of monopiles for offshore wind structures. Géotechnique, 1-39.