MODELING GEOMATERIALS ACROSS SCALES JOSÉ E. ANDRADE DEPARTMENT OF CIVIL AND ENVIRONMENTAL ENGINEERING EPS SEMINAR SERIES MARCH 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]
EXPERIMENTAL OBSERVATION FIELD OBSERVATION PHYSICAL PHENOMENON NUMERICAL SIMULATION THEORETICAL FRAMEWORK PUZZLE TO UNDERSTANDING (GEO)PHYSICAL PHENOMENA
EXPERIMENTAL OBSERVATION FIELD OBSERVATION PHYSICAL PHENOMENON NUMERICAL SIMULATION THEORETICAL FRAMEWORK OUR FOCUS IN THE PUZZLE
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
LOOSE PACKING COMPACTION BAND c ep? k? DENSE PACKING FIELD SCALE SPECIMEN SCALE MESO SCALE GRAIN SCALE LOG (m) >1 0-1 -2-3 MULTIPLE SCALES IN SANDSTONES: DEFORMATION BANDS
WHY MULTISCALE? CAN ACCOUNT FOR INHOMOGENEITIES ACROSS SCALES! a SHEAR BAND IMPOSE CURRENT MACRO-STATE UPSCALING PERMEABILITY k LB COMPUTATION INACTIVE LATTICE ACTIVE LATTICE CAN BYPASS PHENOMENOLOGY CAN LINK MULTIPHISICS AND IMPACT IN MECHANICS! r FEM COUPLED SOLID-FLUID COMPUTATION SPECIMEN SCALE UPSCALE c ep k MESO SCALE c ep UPSCALING CONSTITUTIVE TANGENT! 11! 12 DEM COMPUTATION GRAIN SCALE GRAIN! 22 PORE
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 BALANCE OF MASS φ ṗ K f + v = q σ + γ = 0 BALANCE OF MOMENTUM
THEORETICAL FRAMEWORK CONTINUUM MECHANICS CONSTITUTIVE THEORY q = k h σ = c ep : ɛ DARCY HOOKE COMPUTATIONAL INELASTICITY NONLINEAR FINITE ELEMENTS k PERMEABILITY TENSOR CONTROLS FLUID FLOW c ep MECHANICAL STIFFNESS CONTROLS DEFORMATION
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 COMPRESSION 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
CONSTITUTIVE THEORY
PERMEABILITY k
SYNCHROTRON CT IMAGE CASTLEGATE SANDSTONE KOZENY-CARMAN 1 φ3 2 k= d 180 (1 φ)2 POROSITY Permeability, m 2 1.E-10 1.E-11 1.E-12 1.E-13 Synthetic: lab Synthetic: numerical Natural: lab Natural: numerical (3.34 micron) Natural: numerical (1.67 micron) Kozeny-Carman 1.E-14 FREDRICH ET AL (2006) 1.E-15 0 EXPERIMENTS VS. CALCS 10 20 30 40 Porosity, % PERMEABILITY: LATTICE BOLTZMANN OR KOZENY-CARMAN?
STIFFNESS c ep
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 0.11 0.12 0.13 0.14 0.15 3D GRANULAR SCALE CT & DIC IN TXC 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 EXISTING MODELING ARCHITECTURE THE MULTISCALE FRAMEWORK IS PREDICTIVE UNDER MONOTONIC DRAINED QUASI-STATIC LOADING MULTI-PHYSICS PERFORMANCE TBD...