MODELING GEOMATERIALS ACROSS SCALES JOSÉ E. ANDRADE DEPARTMENT OF CIVIL AND ENVIRONMENTAL ENGINEERING EPS SEMINAR SERIES MARCH 2008

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1 MODELING GEOMATERIALS ACROSS SCALES JOSÉ E. ANDRADE DEPARTMENT OF CIVIL AND ENVIRONMENTAL ENGINEERING EPS SEMINAR SERIES MARCH 2008

2 COLLABORATORS: DR XUXIN TU AND MR KIRK ELLISON

3 THE ROADMAP MOTIVATION MULTIPLICITY OF SCALES IN GEOMATERIALS THE THEORETICAL FRAMEWORK MULTISCALE COMPUTATION AND ADVANCED EXPERIMENTAL TECHNIQUES PRELIMINARY RESULTS CONCLUSIONS

4 MOTIVATION

5 LIQUEFACTION INSTABILITY, NIIGATA JAPAN, 1964

6 n SHEAR BANDING IN THE LAB AND IN THE FIELD

7 CO 2 STORAGE & MONITORING PROCESSES. FROM DOE [2007]

8 EXPERIMENTAL OBSERVATION FIELD OBSERVATION PHYSICAL PHENOMENON NUMERICAL SIMULATION THEORETICAL FRAMEWORK PUZZLE TO UNDERSTANDING (GEO)PHYSICAL PHENOMENA

9 EXPERIMENTAL OBSERVATION FIELD OBSERVATION PHYSICAL PHENOMENON NUMERICAL SIMULATION THEORETICAL FRAMEWORK OUR FOCUS IN THE PUZZLE

10 MULTIPLE SCALES IN GRANULAR MATERIALS

11 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) > FAMILY OF GEOMATERIALS ACROSS SCALES

12 LOOSE PACKING COMPACTION BAND c ep? k? DENSE PACKING FIELD SCALE SPECIMEN SCALE MESO SCALE GRAIN SCALE LOG (m) > MULTIPLE SCALES IN SANDSTONES: DEFORMATION BANDS

13 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

14 THEORETICAL FRAMEWORK

15 THEORETICAL FRAMEWORK CONTINUUM MECHANICS CONSTITUTIVE THEORY s x COMPUTATIONAL INELASTICITY X f NONLINEAR FINITE ELEMENTS x 2 x 1 f

16 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

17 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

18 THEORETICAL FRAMEWORK CONTINUUM MECHANICS CONSTITUTIVE THEORY F n+1 tr n+1 n+1 F n COMPUTATIONAL INELASTICITY n NONLINEAR FINITE ELEMENTS

19 THEORETICAL FRAMEWORK CONTINUUM MECHANICS CONSTITUTIVE THEORY COMPUTATIONAL INELASTICITY NONLINEAR FINITE ELEMENTS Displacement node Pressure node

20 PLANE-STRAIN COMPRESSION SPECIFIC VOLUME CT SCAN FE MODEL

21 PLANE-STRAIN COMPRESSION SPECIFIC VOLUME SHEAR STRAIN AND FLOW FLUID PRESSURE

22 LIQUEFACTION IN 2D (QUASI-STATIC)

23 QUASI-STATIC LIQUEFACTION LIQUEFACTION CRITERION DEVIATORIC STRAINS PORE PRESSURES

24 QUASI-STATIC LIQUEFACTION LIQUEFACTION CRITERION DEVIATORIC STRAINS PORE PRESSURES

25 QUASI-STATIC LIQUEFACTION LIQUEFACTION CRITERION DEVIATORIC STRAINS PORE PRESSURES

26 ! %"# %## $"# $##!!.#$2/',$2',334',$!(1$52.#! "# "##&$ "##&# "##%$ "##%# "###$!!*#$+,-(.)/'("$0)'.(1! "#### =6;0>7< %""""" 0672$089:;<= $""""" #"""""! "!"#$%&% "'() THE SUBMERGED SLOPE FAILURE

27 CONSTITUTIVE THEORY

28 PERMEABILITY k

29 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 Porosity, % PERMEABILITY: LATTICE BOLTZMANN OR KOZENY-CARMAN?

30 STIFFNESS c ep

31 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

32 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!$%# ɛ p!$&#!$'#!$!#!$##!%# G = 0!&#!'#!!# β < µ < 0 G = 0 β > µ > 0 q ɛ p F = 0 #!!"#!!##!$"#!$##!"# # "# p

33 THE SIMPLEST PLASTICITY MODEL f = 1 3 µ ˆn g = 1 3 β 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

34 MULTISCALE FRAMEWORK

35 GRANULAR SCALE RESPONSE! a MACRO SCALE RESPONSE! a UPSCALING OR HOMOGENIZATION! r! r DEM MATERIAL RESPONSE FEM STRESS RATIO FEM DEM MAJOR STRAIN, % 1(23%4,)-5*+,)&-./*0 #" #! "! 64% 74% *!"! " #! #" $! $" %&'()*+,)&-./*0 * KEY IDEA: INFORMATION PASSING PROBE MICROSTRUCTURE

36 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

37 D GRANULAR SCALE CT & DIC IN TXC ADVANCED EXPERIMENTAL & IMAGING TECHNIQUES

38 PRELIMINARY RESULTS HOMOGENEOUS AND INHOMOGENEOUS SIMULATIONS

39 HOMOGENEOUS PREDICTIONS DEM AND TRUE TRIAXIAL

40 GRANULAR SCALE RESPONSE! a MACRO SCALE RESPONSE! a UPSCALING OR HOMOGENIZATION GIVEN! r! r DILATANCY DEM MATERIAL RESPONSE FEM STRESS RATIO FEM DEM MAJOR STRAIN, % 1(23%4,)-5*+,)&-./*0 #" #! "! *!"! " #! #" $! $" %&'()*+,)&-./*0 * DILATION RATE % 74% DEVIATORIC STRAIN, % TRIAXIAL COMPRESSION WITH 3D DEM

41 #"",,#"" %&'()$+ $"" "!$"" (a) (b) $"" "!$"" %&'()$+ B = σ 2 σ 3 σ 1 σ 3!#"",!!""!!""!#""!$"" " $"" #""!"" %&'()*+ -."/" -."/0 -.*/"!#"",!!""!#""!$"" "!!"" %&'()*+ -."/" -."/0 -.1/" 1 GIVEN DILATION EVOLUTION DILATION RATE B=0.0 B=0.5 B= DEVIATORIC STRAIN, % HOMOGENEOUS RESPONSE: TRUE TRIAXIAL EXPERIMENTS

42 MULTISCALE PHENOMENOLOGICAL 2.5 (a) 2.5 (b) STRESS RATIO B=0 MODEL B=0 EXPERIMENT B=0.5 MODEL B=0.5 EXPERIMENT B=1 MODEL B=1 EXPERIMENT STRESS RATIO B=0 MODEL B=0 EXPERIMENT B=0.5 MODEL B=0.5 EXPERIMENT B=1 MODEL B=1 EXPERIMENT MAJOR STRAIN, % MAJOR STRAIN, % PREDICTIONS: STRESS-STRAIN

43 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/-!" +! " # $ % &'()*+,-*'./ )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

44 INHOMOGENEOUS PREDICTIONS PLANE STRAIN EXPERIMENT WITH SHEAR BAND USING DIC

45 FEM MODEL & DEV STRAIN LATERAL LVDT S MEASURED DILATION 0.3 #! =.A>,/ "& "! &! :87+1; <=<!& :87+1;28> <=< +?@+,.:+4-2!"!! " # $ % & ' ( ) *+,-./0123-, PLANE STRAIN COMPRESSION WITH SHEAR SHEAR BAND

46 ! " # $ % & ' ( ) * +, -. / : ; < = 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 { } ~! " # $ % & ' ( ) * +, -. / : ; < = 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 BIFURCATION MODEL EXPERIMENT VERTICAL STRAIN, % 06./010/,*+/012,+/-3415,-./0123)38296):5 "*# "))!*+!*'!*%!*#!!&!"! 768*09:;;*+ 768*0906<*+ *=;*+-7*3,9:;;*+ *=;*+-7*3,906<*+ 1!"&! " # $ % & ' ( BIFURCATION ;05-)<-4= )<-4= BIFURCATION )*+,-./012,+/-3415 )!))! " # $ % & ' ( ) COARSE MESH 1 FINE MESH,-./0123)4/.2056)7 PREDICTIONS COMPARED WITH OBSERVATIONS

47 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...