MODELING GEOMATERIALS ACROSS SCALES JOSÉ E. ANDRADE DEPARTMENT OF CIVIL AND ENVIRONMENTAL ENGINEERING AFOSR WORKSHOP ON PARTICULATE MECHANICS JANUARY 2008
COLLABORATORS: DR XUXIN TU AND MR KIRK ELLISON
THE ROADMAP MOTIVATION MULTIPLICITY OF SCALES IN GEOMATERIALS THE THEORETICAL FRAMEWORK MULTISCALE COMPUTATION AND ADVANCED EXPERIMENTAL TECHNIQUES PRELIMINARY RESULTS CONCLUSIONS
MOTIVATION
LIQUEFACTION INSTABILITY, NIIGATA JAPAN, 1964
n SHEAR BANDING IN THE LAB AND IN THE FIELD
CO 2 STORAGE & MONITORING PROCESSES. FROM DOE [2007]
MULTIPLE SCALES IN GRANULAR MATERIALS
LOOSE PACKING SANDSTONE COMPACTION BAND DENSE PACKING FIELD GRAIN SHEAR BAND COMPACTIVE ZONE SAND VOID DILATIVE ZONE SAND PARTICLE LAB HD C-S-H AGGREGATE MACRO PORES HD REGION CONCRETE LD C-S-H AGGREGATE LD REGION GLOBULE FLUID REV LOG (m) >1 0-1 -2-3 -4-6 -9 FAMILY OF GEOMATERIALS ACROSS SCALES
!a P FOOTING GRAIN SHEAR BAND COMPACTIVE ZONE!r FAILURE SURFACE 'HOMOGENEOUS' SOIL DILATIVE ZONE VOID FIELD SCALE LOG (m) >1 SPECIMEN SCALE 0-1 MESO SCALE -2 GRAIN SCALE -3 MULTIPLE SCALES IN SANDS: FROM FIELD TO GRAIN SCALE
WHY MULTISCALE? CAN ACCOUNT FOR INHOMOGENEITIES ACROSS SCALES CAN BYPASS PHENOMENOLOGY FOOTING FAILURE SURFACE P 'HOMOGENEOUS' SOIL CAN LINK MULTIPHISICS AND IMPACT IN MECHANICS LOG (m) FIELD SCALE SPECIMEN SCALE MESO SCALE >1-1 -2
THEORETICAL FRAMEWORK
THEORETICAL FRAMEWORK CONTINUUM MECHANICS CONSTITUTIVE THEORY s x COMPUTATIONAL INELASTICITY X f NONLINEAR FINITE ELEMENTS x 2 x 1 f
THEORETICAL FRAMEWORK CONTINUUM MECHANICS CONSTITUTIVE THEORY COMPUTATIONAL INELASTICITY NONLINEAR FINITE ELEMENTS!$%# ɛ p!$&#!$'#!$!#!$##!%# G = 0!&#!'#!!# β < 0 1 1 µ < 0 G = 0 β > 0 1 1 µ > 0 q ɛ p F = 0 #!!"#!!##!$"#!$##!"# # "# p
THEORETICAL FRAMEWORK CONTINUUM MECHANICS CONSTITUTIVE THEORY F n+1 tr n+1 n+1 F n COMPUTATIONAL INELASTICITY n NONLINEAR FINITE ELEMENTS
THEORETICAL FRAMEWORK CONTINUUM MECHANICS CONSTITUTIVE THEORY COMPUTATIONAL INELASTICITY NONLINEAR FINITE ELEMENTS Displacement node Pressure node
PLANE-STRAIN COMPRESSION SPECIFIC VOLUME CT SCAN FE MODEL
PLANE-STRAIN COMPRESS SPECIFIC VOLUME SHEAR STRAIN AND FLOW FLUID PRESSURE
LIQUEFACTION IN 2D (QUASI-STATIC)
QUASI-STATIC LIQUEFACTION LIQUEFACTION CRITERION DEVIATORIC STRAINS PORE PRESSURES
QUASI-STATIC LIQUEFACTION LIQUEFACTION CRITERION DEVIATORIC STRAINS PORE PRESSURES
QUASI-STATIC LIQUEFACTION LIQUEFACTION CRITERION DEVIATORIC STRAINS PORE PRESSURES
! %"# %## $"# $##!!.#$2/',$2',334',$!(1$52.#! "# "##&$ "##&# "##%$ "##%# "###$!!*#$+,-(.)/'("$0)'.(1! "#### =6;0>7< %""""" 0672$089:;<= $""""" #"""""! "!"#$%&% "'() THE SUBMERGED SLOPE FAILURE
ELASTOPLASTIC FRAMEWORK HOOKE S LAW ADDITIVE DECOMPOSITION OF STRAIN CONVEX ELASTIC REGION σ = c ep : ɛ ɛ = ɛ e + ɛ p F (σ, α) = 0 NON-ASSOCIATIVE FLOW K-T OPTIMALITY CONDITION ɛ p = λg, λf = 0 g := G/ σ λh = F/ α α ELASTOPLASTIC CONSTITUTIVE TANGENT c ep = c e 1 χ ce : g f : c e, χ = H + g : c e : f
THE SIMPLEST PLASTICITY MODEL F (p, q, α) = q + m (p, α) c (α) G (p, q, α) = q + m (p, α) c (α) YIELD SURFACE PLASTIC POTENTIAL DEFINE PLASTIC VARIABLES FRICTION µ = m p, µ = p p, DILATANCY β = m p β = ɛp v ɛ p s!$%# ɛ p!$&#!$'#!$!#!$##!%# G = 0!&#!'#!!# β < 0 1 1 µ < 0 G = 0 β > 0 1 1 µ > 0 q ɛ p F = 0 #!!"#!!##!$"#!$##!"# # "# p
THE SIMPLEST PLASTICITY MODEL f = 1 3 µ1 + 3 2 ˆn g = 1 3 β1 + 3 2 ˆn FRICTION AND DILATION AFFECT VOLUMETRIC RESPONSE F µ µ = λh HARDENING/SOFTENING STRESS-DILATANCY RELATION β }{{} dilation resistance = µ }{{} friction resistance µ cv }{{} residual friction resistance
MULTISCALE FRAMEWORK
GRANULAR SCALE RESPONSE! a MACRO SCALE RESPONSE! a UPSCALING OR HOMOGENIZATION! r! r DEM MATERIAL RESPONSE FEM STRESS RATIO 1.6 1.2 0.8 0.4 FEM DEM 0 5 10 15 20 MAJOR STRAIN, % 1(23%4,)-5*+,)&-./*0 #" #! "! 64% 74% *!"! " #! #" $! $" %&'()*+,)&-./*0 * KEY IDEA: INFORMATION PASSING PROBE MICROSTRUCTURE
MULTISCALE FRAMEWORK E, ν ELASTIC CONSTANTS β ɛ v ɛ s µ = β + µ cv APPROXIMATE DILATION APPROXIMATE FRICTION TOTAL NUMBER OF PARAMETERS E, ν, µ cv IF EVOLUTION OF β IS GIVEN
0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 3D GRANULAR SCALE 0.11 0.12 0.13 0.14 0.15 CT & DIC IN TXC PROPERTIES POST-FAILURE ADVANCED EXPERIMENTAL & IMAGING TECHNIQUES
PRELIMINARY RESULTS HOMOGENEOUS AND INHOMOGENEOUS SIMULATIONS
HOMOGENEOUS PREDICTIONS DEM AND TRUE TRIAXIAL
GRANULAR SCALE RESPONSE! a MACRO SCALE RESPONSE! a UPSCALING OR HOMOGENIZATION GIVEN! r! r DILATANCY DEM MATERIAL RESPONSE FEM STRESS RATIO 1.6 1.2 0.8 0.4 FEM DEM 0 5 10 15 20 MAJOR STRAIN, % 1(23%4,)-5*+,)&-./*0 #" #! "! *!"! " #! #" $! $" %&'()*+,)&-./*0 * DILATION RATE 0.2 64% 74% 0 5 10 15 20 25 1 0.8 0.6 0.4 DEVIATORIC STRAIN, % TRIAXIAL COMPRESSION WITH 3D DEM
#"",,#"" %&'()$+ $"" "!$"" (a) (b) $"" "!$"" %&'()$+ B = σ 2 σ 3 σ 1 σ 3!#"",!!""!!""!#""!$"" " $"" #""!"" %&'()*+ -."/" -."/0 -.*/"!#"",!!""!#""!$"" "!!"" %&'()*+ -."/" -."/0 -.1/" 1 GIVEN DILATION EVOLUTION DILATION RATE 0.8 0.6 0.4 0.2 B=0.0 B=0.5 B=1.0 0 1 2 3 4 5 DEVIATORIC STRAIN, % HOMOGENEOUS RESPONSE: TRUE TRIAXIAL EXPERIMENTS
MULTISCALE PHENOMENOLOGICAL 2.5 (a) 2.5 (b) STRESS RATIO 2 1.5 1 0.5 B=0 MODEL B=0 EXPERIMENT B=0.5 MODEL B=0.5 EXPERIMENT B=1 MODEL B=1 EXPERIMENT STRESS RATIO 2 1.5 1 0.5 B=0 MODEL B=0 EXPERIMENT B=0.5 MODEL B=0.5 EXPERIMENT B=1 MODEL B=1 EXPERIMENT 0 1 2 3 4 MAJOR STRAIN, % 0 1 2 3 4 MAJOR STRAIN, % PREDICTIONS: STRESS-STRAIN
2)34&5-*.6+,-*'./0+1 $ # " MULTISCALE >?@ 78!+&)953! 78!+5:;5*.&5/- 78!<=+&)953 78!<=+5:;5*.&5/- 78"+&)953 78"+5:;5*.&5/-!" +! " # $ % &'()*+,-*'./0+1 + 2)34&5-*.6+,-*'./0+1 $ # " PHENOMENOLOGICAL >A@ 78!+&)953! 78!+5:;5*.&5/- 78!<=+&)953 78!<=+5:;5*.&5/- 78"+&)953 78"+5:;5*.&5/-!" +! " # $ % &'()*+,-*'./0+1 + PREDICTIONS: DILATION
INHOMOGENEOUS PREDICTIONS PLANE STRAIN EXPERIMENT WITH SHEAR BAND USING DIC
FEM MODEL & DEV STRAIN 0.45 0.4 0.35 LATERAL LVDT S MEASURED DILATION 0.3 #! =.A>,/0-.84 2 0.25 0.2 0.15 0.1 0.05 7.10-.8420491+52 "& "! &! :87+1;2.43.7+23<=<!& :87+1;28>-3.7+23<=< +?@+,.:+4-2!"!! " # $ % & ' ( ) *+,-./0123-,0.4526 PLANE STRAIN COMPRESSION WITH SHEAR SHEAR BAND
! " # $ % & ' ( ) * +, -. / 0 1 2 3 4 5 6 7 8 9 : ; < = >? @ A B C D E F G H I J K L M N O P Q R S T U V W X Y Z [ \ ] ^ _ ` a b c d e f g h i j k l m n o p q r s t u v w x y z { } ~! " # $ % & ' ( ) * +, -. / 0 1 2 3 4 5 6 7 8 9 : ; < = >? @ A B C D E F G H I J K L M N O P Q R S T U V W X Y Z [ \ ] ^ _ ` a b c d e f g h i j k l m n o p q r s t u v w x y z { } ~ STRESS RATIO 1.5 1 0.5 BIFURCATION MODEL EXPERIMENT 0 1 2 3 4 5 6 7 VERTICAL STRAIN, % 06./010/,*+/012,+/-3415,-./0123)38296):5 "*# "))!*+!*'!*%!*#!!&!"! 768*09:;;*+ 768*0906<*+ *=;*+-7*3,9:;;*+ *=;*+-7*3,906<*+ 1!"&! " # $ % & ' ( BIFURCATION ;05-)<-4= 182.4-)<-4= BIFURCATION )*+,-./012,+/-3415 )!))! " # $ % & ' ( ) COARSE MESH 1 FINE MESH,-./0123)4/.2056)7 PREDICTIONS COMPARED WITH OBSERVATIONS
CONCLUSIONS THE GRAIN SCALE CAN BE `PROBED TO EXTRACT MATERIAL BEHAVIOR DILATANCY PLAYS A KEY ROLE DICTATING THE BEHAVIOR OF GRANULAR MATERIALS THE MULTISCALE FRAMEWORK FULLY EXPLOITS THE FEM ARCHITECTURE THE MULTISCALE FRAMEWORK IS PREDICTIVE UNDER MONOTONIC QUASI-STATIC LOADING PERFORMANCE UNDER DYNAMIC CONDITIONS TBD...