This work presents a new staggered multilevel material identification procedure for phenomenological critical state plasticity models. The emphasis is placed on cases in which available experimental data and constraints are insufficient for calibration. The key idea is to create a secondary virtual experimental database from high-fidelity models, such as discrete element simulations, then merge both the actual experimental data and secondary database as an extended digital database (EDD) to determine material parameters for the phenomenological macroscopic critical state plasticity model. The calibration procedure therefore consists of two steps. First, the material parameters of the discrete (distinct) element method (DEM) simulations are identified via the standard optimization procedure. Then, the calibrated DEM simulations are used to expand the experimental database with new simulated loading histories. This expansion of database provides additional constraints necessary for calibration of the phenomenological critical state plasticity models. The robustness of the proposed material identification framework is demonstrated in the context of the Dafalias–Manzari plasticity model.

References

1.
DiMaggio
,
F. L.
, and
Sandler
,
I. S.
,
1971
, “
Material Model for Granular Soils
,”
J. Eng. Mech. Div.
,
97
(
3
), pp.
935
950
.
2.
Finn
,
W. L.
,
Lee
,
K. W.
, and
Martin
,
G.
,
1977
, “
An Effective Stress Model for Liquefaction
,”
Electron. Lett.
,
103
, pp.
517
533
.
3.
Prevost
,
J. H.
,
1985
, “
A Simple Plasticity Theory for Frictional Cohesionless Soils
,”
Int. J. Soil Dyn. Earthquake Eng.
,
4
(
1
), pp.
9
17
.
4.
Bardet
,
J.
,
1986
, “
Bounding Surface Plasticity Model for Sands
,”
J. Eng. Mech.
,
112
(
11
), pp.
1198
1217
.
5.
Anandarajah
,
A.
,
1993
, “
VELACS Project: Elasto-Plastic Finite Element Prediction of the Liquefaction Behavior of Centrifuge Models Nos. 1, 3 and 4a
,”
International Conference on the Verification of Numerical Procedures for the Analysis of Soil Liquefaction Problems
, Balkema, Rotterdam, The Netherlands.
6.
Oka
,
F.
,
Adachi
,
T.
, and
Yashima
,
A.
,
1995
, “
A Strain Localization Analysis Using a Viscoplastic Softening Model for Clay
,”
Int. J. Plast.
,
11
(
5
), pp.
523
545
.
7.
Borja
,
R. I.
,
Chao
,
H.
,
Montáns
,
F.
, and
Lin
,
C.
,
1999
, “
Nonlinear Ground Response at Lotung LSST Site
,”
J. Geotech. Geoenviron. Eng.
,
125
(
3
), pp.
187
197
.
8.
Jeremic
,
B.
,
Runesson
,
K.
, and
Sture
,
S.
,
1999
, “
A Model for Elastic-Plastic Pressure Sensitive Materials Subjected to Large Deformations
,”
Int. J. Solids Struct.
,
36
(
31
), pp.
4901
4918
.
9.
Nemat-Nasser
,
S.
, and
Zhang
,
J.
,
2002
, “
Constitutive Relations for Cohesionless Frictional Granular Materials
,”
Int. J. Plast.
,
18
(
4
), pp.
531
547
.
10.
Lashkari
,
A.
, and
Latifi
,
M.
,
2008
, “
A Non‐Coaxial Constitutive Model for Sand Deformation Under Rotation of Principal Stress Axes
,”
Int. J. Numer. Anal. Methods Geomech.
,
32
(
9
), pp.
1051
1086
.
11.
Yang
,
Z.
, and
Elgamal
,
A.
,
2008
, “
Multi-Surface Cyclic Plasticity Sand Model With Lode Angle Effect
,”
Geotech. Geol. Eng.
,
26
(
3
), pp.
335
348
.
12.
Andrade
,
J. E.
, and
Ellison
,
K. C.
,
2008
, “
Evaluation of a Predictive Constitutive Model for Sands
,”
J. Geotech. Geoenviron. Eng.
,
134
(
12
), pp.
1825
1828
.
13.
Li
,
L.
,
Aubertin
,
M.
, and
Shirazi
,
A.
,
2010
, “
Implementation and Application of a New Elastoplastic Model Based on a Multiaxial Criterion to Assess the Stress State Near Underground Openings
,”
Int. J. Geomech.
,
10
(
1
), pp.
13
21
.
14.
Roscoe
,
K. H.
,
Schofield
,
A.
, and
Wroth
,
C.
,
1958
, “
On the Yielding of Soils
,”
Geotechnique
,
18
(
1
), pp.
22
53
.
15.
Schofield
,
A.
, and
Wroth
,
P.
,
1968
,
Critical State Soil Mechanics
,
McGraw-Hill
,
London
.
16.
Roscoe
,
K. H.
, and
Burland
,
J.
,
1968
,
On The Generalized Stress-Strain Behaviour of Wet Clay
,
Cambridge University Press
,
London
.
17.
Nova
,
R.
, and
Wood
,
D. M.
,
1979
, “
A Constitutive Model for Sand in Triaxial Compression
,”
Int. J. Numer. Anal. Methods Geomech.
,
3
(
3
), pp.
255
278
.
18.
Manzari
,
M. T.
, and
Dafalias
,
Y. F.
,
1997
, “
A Critical State Two-Surface Plasticity Model for Sands
,”
Geotechnique
,
47
(
2
), pp.
255
272
.
19.
Jefferies
,
M.
,
1993
, “
Nor-Sand: A Simple Critical State Model for Sand
,”
Géotechnique
,
43
(
1
), pp.
91
103
.
20.
Borja
,
R. I.
, and
Lee
,
S. R.
,
1990
, “
Cam-Clay Plasticity, Part 1: Implicit Integration of Elasto-Plastic Constitutive Relations
,”
Comput. Methods Appl. Mech. Eng.
,
78
(
1
), pp.
49
72
.
21.
Borja
,
R. I.
, and
Andrade
,
J. E.
,
2006
, “
Critical State Plasticity. Part VI: Meso-Scale Finite Element Simulation of Strain Localization in Discrete Granular Materials
,”
Comput. Methods Appl. Mech. Eng.
,
195
(
37
), pp.
5115
5140
.
22.
Gao
,
Z.
,
Zhao
,
J.
,
Li
,
X.-S.
, and
Dafalias
,
Y. F.
,
2014
, “
A Critical State Sand Plasticity Model Accounting for Fabric Evolution
,”
Int. J. Numer. Anal. Methods Geomech.
,
38
(
4
), pp.
370
390
.
23.
Tanaka
,
M.
, and
Dulikravich
,
G. S.
,
1998
,
Inverse Problems in Engineering Mechanics
,
Elsevier
,
Amsterdam
.
24.
Chaparro
,
B. M.
,
Thuillier
,
S.
,
Menezes
,
L. F.
,
Manach
,
P. Y.
, and
Fernandes
,
J. V.
,
2008
, “
Material Parameters Identification: Gradient-Based, Genetic and Hybrid Optimization Algorithms
,”
Comput. Mater. Sci.
,
44
(
2
), pp.
339
346
.
25.
Yang
,
Z.
, and
Elgamal
,
A.
,
2003
, “
Application of Unconstrained Optimization and Sensitivity Analysis to Calibration of a Soil Constitutive Model
,”
Int. J. Numer. Anal. Methods Geomech.
,
27
(
15
), pp.
1277
1297
.
26.
Blaheta
,
R.
,
Hrtus
,
R.
,
Kohut
,
R.
,
Axelsson
,
O.
, and
Jakl
,
O.
,
2012
, “
Material Parameter Identification With Parallel Processing and Geo-Applications
,”
Parallel Processing and Applied Mathematics
,
Springer
,
Berlin, Heidelberg
, pp.
366
375
.
27.
Feng
,
X.-T.
,
Chen
,
B.-R.
,
Yang
,
C.
,
Zhou
,
H.
, and
Ding
,
X.
,
2006
, “
Identification of Visco-Elastic Models for Rocks Using Genetic Programming Coupled With the Modified Particle Swarm Optimization Algorithm
,”
Int. J. Rock Mech. Min. Sci.
,
43
(
5
), pp.
789
801
.
28.
Ghaboussi
,
J.
,
Pecknold
,
D. A.
,
Zhang
,
M.
, and
Haj-Ali
,
R. M.
,
1998
, “
Autoprogressive Training of Neural Network Constitutive Models
,”
Int. J. Numer. Methods Eng.
,
42
(
1
), pp.
105
126
.
29.
Li
,
X.
,
2005
, “
Calibration of an Anisotropic Sand Model
,”
Calibration of Constitutive Models
,
ASCE
, pp.
1
12
.
30.
Dafalias
,
Y. F.
, and
Manzari
,
M. T.
,
2004
, “
Simple Plasticity Sand Model Accounting for Fabric Change Effects
,”
J. Eng. Mech.
,
130
(
6
), pp.
622
634
.
31.
Papadimitriou
,
A. G.
, and
Bouckovalas
,
G. D.
,
2002
, “
Plasticity Model for Sand Under Small and Large Cyclic Strains: A Multiaxial Formulation
,”
Soil Dyn. Earthquake Eng.
,
22
(
3
), pp.
191
204
.
32.
Shahir
,
H.
,
Pak
,
A.
,
Taiebat
,
M.
, and
Jeremic
,
B.
,
2012
, “
Evaluation of Variation of Permeability in Liquefiable Soil Under Earthquake Loading
,”
Comput. Geotech.
,
40
, pp.
74
88
.
33.
Choi
,
C.
,
Arduino
,
P.
, and
Harney
,
M. D.
,
2005
, “
Two-Surface Soil Constitutive Model Calibration for Coarse Granular Materials
,” Calibration of Constitutive Models,
ASCE
, pp.
1
15
.
34.
Mahnken
,
R.
, and
Stein
,
E.
,
1994
, “
The Identification of Parameters for Visco-Plastic Models Via Finite-Element Methods and Gradient Methods
,”
Modell. Simul. Mater. Sci. Eng.
,
2
(
3A
), pp.
597
616
.
35.
Mahnken
,
R.
, and
Stein
,
E.
,
1996
, “
A Unified Approach for Parameter Identification of Inelastic Material Models in the Frame of the Finite Element Method
,”
Comput. Methods Appl. Mech. Eng.
,
136
(
3
), pp.
225
258
.
36.
Rechenmacher
,
A. L.
, and
Medina-Cetina
,
Z.
,
2007
, “
Calibration of Soil Constitutive Models With Spatially Varying Parameters
,”
J. Geotech. Geoenviron. Eng.
,
133
(
12
), pp.
1567
1576
.
37.
Arnold
,
S. M.
,
Holland
,
F.
, and
Bednarcyk
,
B. A.
,
2014
, “
Robust Informatics Infrastructure Required for ICME: Combining Virtual and Experimental Data
,” 55th
AIAA/ASMe/ASCE/AHS/SC
Structures, Structural Dynamics, and Materials Conference
.
38.
Broderick
,
S. R.
,
Aourag
,
H.
, and
Rajan
,
K.
,
2011
, “
Data Mining of Ti–Al Semi-Empirical Parameters for Developing Reduced Order Models
,”
Phys. B
,
406
(
11
), pp.
2055
2060
.
39.
Feng
,
X. T.
, and
Yang
,
C.
,
2004
, “
Coupling Recognition of the Structure and Parameters of Non‐Linear Constitutive Material Models Using Hybrid Evolutionary Algorithms
,”
Int. J. Numer. Methods Eng.
,
59
(
9
), pp.
1227
1250
.
40.
Alexandrov
,
N. M.
,
Lewis
,
R. M.
,
Gumbert
,
C. R.
,
Green
,
L. L.
, and
Newman
,
P. A.
,
1999
, “
Optimization With Variable-Fidelity Models Applied to Wing Design
,”
AIAA
Paper No. 2000-0841.
41.
Alexandrov
,
N. M.
,
Dennis
,
J. E.
, Jr.
,
Lewis
,
R. M.
, and
Torczon
,
V.
,
1998
, “
A Trust-Region Framework for Managing the Use of Approximation Models in Optimization
,”
Struct. Optim.
,
15
(
1
), pp.
16
23
.
42.
Cundall
,
P. A.
, and
Strack
,
O. D.
,
1979
, “
A Discrete Numerical Model for Granular Assemblies
,”
Geotechnique
,
29
(
1
), pp.
47
65
.
43.
Sun
,
W.
,
Kuhn
,
M. R.
, and
Rudnicki
,
J. W.
,
2013
, “
A Multiscale DEM-LBM Analysis on Permeability Evolutions Inside a Dilatant Shear Band
,”
Acta Geotech.
,
8
(
5
), pp.
465
480
.
44.
Jäger
,
J.
,
1999
, “
Uniaxial Deformation of a Random Packing of Particles
,”
Arch. Appl. Mech.
,
69
(
3
), pp.
181
203
.
45.
Jaeger
,
J.
,
2005
,
New Solutions in Contact Mechanics
,
WIT Press/Computational Mechanics
,
Southampton, MA
.
46.
Kuhn
,
M. R.
,
2011
, “
Implementation of the Jäger Contact Model for Discrete Element Simulations
,”
Int. J. Numer. Methods Eng.
,
88
(
1
), pp.
66
82
.
47.
Liu
,
Y.
,
Sun
,
W.
,
Yuan
,
Z.
, and
Fish
,
J.
,
2015
, “
A Nonlocal Multiscale Discrete-Continuum Model for Predicting Mechanical Behavior of Granular Materials
,”
Int. J. Numer. Methods Eng.
(submitted).
48.
Christoffersen
,
J.
,
Mehrabadi
,
M.
, and
Nemat-Nasser
,
S.
,
1981
, “
A Micromechanical Description of Granular Material Behavior
,”
ASME J. Appl. Mech.
,
48
(
2
), pp.
339
344
.
49.
Satake
,
M.
,
1978
, “
Constitution of Mechanics of Granular Materials Through the Graph Theory
,”
Continuum Mechanical and Statistical Approaches in the Mechanics of Granular Materials
,
Gakuzutsu Bunken Fukyukai
,
Tokyo
, pp.
47
62
.
50.
Pastor
,
M.
,
Zienkiewicz
,
O.
, and
Chan
,
A.
,
1990
, “
Generalized Plasticity and the Modelling of Soil Behaviour
,”
Int. J. Numer. Anal. Methods Geomech.
,
14
(
3
), pp.
151
190
.
51.
Pestana
,
J. M.
, and
Whittle
,
A.
,
1995
, “
Compression Model for Cohesionless Soils
,”
Géotechnique
,
45
(
4
), pp.
611
631
.
52.
Ling
,
H. I.
, and
Yang
,
S.
,
2006
, “
Unified Sand Model Based on the Critical State and Generalized Plasticity
,”
J. Eng. Mech.
,
132
(
12
), pp.
1380
1391
.
53.
Jefferies
,
M.
, and
Been
,
K.
,
2000
, “
Implications for Critical State Theory From Isotropic Compression of Sand
,”
Géotechnique
,
50
(
4
), pp.
419
429
.
54.
Wood
,
D. M.
,
1990
,
Soil Behaviour and Critical State Soil Mechanics
,
Cambridge University
,
New York
.
55.
Li
,
X.-S.
, and
Wang
,
Y.
,
1998
, “
Linear Representation of Steady-State Line for Sand
,”
J. Geotech. Geoenviron. Eng.
,
124
(
12
), pp.
1215
1217
.
56.
Been
,
K.
, and
Jefferies
,
M. G.
,
1985
, “
A State Parameter for Sands
,”
Géotechnique
,
35
(
2
), pp.
99
112
.
57.
Nazzal
,
M. D.
,
Abu-Farsakh
,
M. Y.
, and
Mohammad
,
L. N.
,
2010
, “
Implementation of a Critical State Two-Surface Model to Evaluate the Response of Geosynthetic Reinforced Pavements
,”
Int. J. Geomech.
,
10
(
5
), pp.
202
212
.
58.
Andrade
,
J. E.
,
Ramos
,
A. M.
, and
Lizcano
,
A.
,
2013
, “
Criterion for Flow Liquefaction Instability
,”
Acta Geotech.
,
8
(
5
), pp.
525
535
.
59.
Conn
,
A. R.
,
Gould
,
N. I.
, and
Toint
,
P. L.
,
2000
, Trust Region Methods,
MPS/SIAM Series on Optimization
,
SIAM
,
Philadelphia, PA
.
60.
Marquardt
,
D. W.
,
1963
, “
An Algorithm for Least-Squares Estimation of Nonlinear Parameters
,”
J. Soc. Ind. Appl. Math.
,
11
(
2
), pp.
431
441
.
61.
Fish
,
J.
,
2013
,
Practical Multiscaling
,
Wiley
,
New York
.
62.
Arulmoli
,
K.
,
1992
,
Velacs Verification of Liquefaction Analyses by Centrifuge Studies Laboratory Testing Program: Soil Data Report
,
Earth Technology Corporation
,
Irvine, CA
.
63.
Kammerer, A. M., Wu, J., Pestana, J. M., Riemer, M., and Seed, R. B.,
2000
, “
Cyclic Simple Shear Testing of Nevada Sand for PEER Center Project 2051999
,” Dept. of Civil and Environmental Engineering, Univ. of California, Berkley, CA, Geotechnical Engineering Rep. No. UCB/GT/00- 01.
64.
Kuhn
,
M. R.
,
2008
, “
OVAL and OVALPLOT: Programs for Analyzing Dense Particle Assemblies With the Discrete Element Method
,” http://faculty.up.edu/kuhn/oval/oval.html
65.
Viggiani
,
G.
,
Andò
,
E.
,
Takano
,
D.
, and
Santamarina
,
J. C.
,
2015
, “
Laboratory X-Ray Tomography: A Valuable Experimental Tool for Revealing Processes in Soils
,”
Geotech. Test. J.
,
38
(
1
), pp.
61
71
.
66.
Charalampidou
,
E.-M.
,
Hall
,
S. A.
,
Stanchits
,
S.
,
Lewis
,
H.
, and
Viggiaini
,
G.
,
2011
, “
Characterization of Shear and Compaction Bands in a Porous Sandstone Deformed Under Triaxial Compression
,”
Tectonophysics
,
503
(
1
), pp.
8
17
.
67.
Sun
,
W.
,
Andrade
,
J. E.
,
Rudnicki
,
J. W.
, and
Eichhubl
,
P.
,
2011
, “
Connecting Microstructural Attributes and Permeability From 3D Tomographic Images of In Situ Shear‐Enhanced Compaction Bands Using Multiscale Computations
,”
Geophys. Res. Lett.
,
38
(
10
), p. L10302.
68.
Sun
,
W.
,
Andrade
,
J. E.
, and
Rudnicki
,
J. W.
,
2011
, “
Multiscale Method for Characterization of Porous Microstructures and Their Impact on Macroscopic Effective Permeability
,”
Int. J. Numer. Methods Eng.
,
88
(
12
), pp.
1260
1279
.
69.
Boon
,
C.
,
Houlsby
,
G.
, and
Utili
,
S.
,
2012
, “
A New Algorithm for Contact Detection Between Convex Polygonal and Polyhedral Particles in the Discrete Element Method
,”
Comput. Geotech.
,
44
, pp.
73
82
.
70.
Lim
,
K. W.
, and
Andrade
,
J. E.
,
2014
, “
Granular Element Method for Three‐Dimensional Discrete Element Calculations
,”
Int. J. Numer. Anal. Methods Geomech.
,
38
(
2
), pp.
167
188
.
71.
Kuhn
,
M. R.
,
Renken
,
H.
,
Mixsell
,
A.
, and
Kramer
,
S.
,
2014
, “
Investigation of Cyclic Liquefaction With Discrete Element Simulations
,”
J. Geotech. Geoenviron. Eng.
,
140
(
12
), p.
04014075
.
72.
Salot
,
C.
,
Gotteland
,
P.
, and
Villard
,
P.
,
2009
, “
Influence of Relative Density on Granular Materials Behavior: DEM Simulations of Triaxial Tests
,”
Granular Matter
,
11
(
4
), pp.
221
236
.
73.
Hardin
,
B. O.
,
1985
, “
Crushing of Soil Particles
,”
J. Geotech. Eng.
,
111
(
10
), pp.
1177
1192
.
74.
Cheng
,
Y.
,
Bolton
,
M.
, and
Nakata
,
Y.
,
2004
, “
Crushing and Plastic Deformation of Soils Simulated Using DEM
,”
Geotechnique
,
54
(
2
), pp.
131
141
.
75.
Lade
,
P. V.
,
Yamamuro
,
J. A.
, and
Bopp
,
P. A.
,
1996
, “
Significance of Particle Crushing in Granular Materials
,”
J. Geotech. Eng.
,
122
(
4
), pp.
309
316
.
76.
ASTMD4253
,
2006
, “
Standard Test Methods for Maximum Index Density and Unit Weight of Soils Using a Vibratory Table
,” ASTM International, West Conshohocken, PA.
77.
ASTMD4254
,
2006
, “
Standard Test Methods for Minimum Index Density and Unit Weight of Soils and Calculation of Relative Density
,” ASTM International, West Conshohocken, PA.
78.
Hardin
,
B. O.
,
1978
, “
The Nature of Stress-Strain Behavior for Soils
,”
Earthquake Engineering and Soil Dynamics—ASCE Geotechnical Engineering Division Specialty Conference
, Pasadena, CA, Jun. 19–21.
79.
Wichtmann
,
T.
, and
Triantafyllidis
,
T.
,
2009
, “
Influence of the Grain-Size Distribution Curve of Quartz Sand on the Small Strain Shear Modulus Gmax
,”
J. Geotech. Geoenviron. Eng.
,
135
(
10
), pp.
1404
1418
.
80.
Cho
,
G.-C.
,
Dodds
,
J.
, and
Santamarina
,
J. C.
,
2006
, “
Particle Shape Effects on Packing Density, Stiffness, and Strength: Natural and Crushed Sands
,”
J. Geotech. Geoenviron. Eng.
,
132
(
5
), pp.
591
602
.
81.
Lade
,
P. V.
,
2008
, “
Failure Criterion for Cross-Anisotropic Soils
,”
J. Geotech. Geoenviron. Eng.
,
134
(
1
), pp.
117
124
.
82.
Barreto
,
D.
, and
O'Sullivan
,
C.
,
2012
, “
The Influence of Inter-Particle Friction and the Intermediate Stress Ratio on Soil Response Under Generalised Stress Conditions
,”
Granular Matter
,
14
(
4
), pp.
505
521
.
83.
Yamamuro
,
J. A.
, and
Covert
,
K. M.
,
2001
, “
Monotonic and Cyclic Liquefaction of Very Loose Sands With High Silt Content
,”
J. Geotech. Geoenviron. Eng.
,
127
(
4
), pp.
314
324
.
84.
Kutter
,
B. L.
,
Chen
,
Y.-R.
, and
Shen
,
C.
,
1994
, “
Triaxial and Torsional Shear Test Results for Sand
,” Naval Facilities Engineering Service Center. Port Hueneme, CA, Contract Report CR 94.003-SHR.
85.
Andrade
,
J. E.
,
Lim
,
K.-W.
,
Avila
,
C. F.
, and
Vlahinic
,
I.
,
2012
, “
Granular Element Method for Computational Particle Mechanics
,”
Comput. Methods Appl. Mech. Eng.
,
241–244
, pp.
262
274
.
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