MODELING GEOMATERIALS ACROSS SCALES

Transcription

1 MODELING GEOMATERIALS ACROSS SCALES JOSÉ E. ANDRADE DEPARTMENT OF CIVIL AND ENVIRONMENTAL ENGINEERING AFOSR WORKSHOP ON PARTICULATE MECHANICS JANUARY 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 MULTIPLE SCALES IN GRANULAR MATERIALS

9 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

10 !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

11 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

12 THEORETICAL FRAMEWORK

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

14 THEORETICAL FRAMEWORK CONTINUUM MECHANICS CONSTITUTIVE THEORY COMPUTATIONAL INELASTICITY NONLINEAR FINITE ELEMENTS!$%# ɛ p!$&#!$'#!$!#!$##!%# G = 0!&#!'#!!# β < µ < 0 G = 0 β > µ > 0 q ɛ p F = 0 #!!"#!!##!$"#!$##!"# # "# p

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

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

17 PLANE-STRAIN COMPRESSION SPECIFIC VOLUME CT SCAN FE MODEL

18 PLANE-STRAIN COMPRESS SPECIFIC VOLUME SHEAR STRAIN AND FLOW FLUID PRESSURE

19 LIQUEFACTION IN 2D (QUASI-STATIC)

20 QUASI-STATIC LIQUEFACTION LIQUEFACTION CRITERION DEVIATORIC STRAINS PORE PRESSURES

21 QUASI-STATIC LIQUEFACTION LIQUEFACTION CRITERION DEVIATORIC STRAINS PORE PRESSURES

22 QUASI-STATIC LIQUEFACTION LIQUEFACTION CRITERION DEVIATORIC STRAINS PORE PRESSURES

23 ! %"# %## $"# $##!!.#$2/',$2',334',$!(1$52.#! "# "##&$ "##&# "##%$ "##%# "###$!!*#$+,-(.)/'("$0)'.(1! "#### =6;0>7< %""""" 0672$089:;<= $""""" #"""""! "!"#$%&% "'() THE SUBMERGED SLOPE FAILURE

24 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

25 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

26 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

27 MULTISCALE FRAMEWORK

28 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

29 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

30 D GRANULAR SCALE CT & DIC IN TXC PROPERTIES POST-FAILURE ADVANCED EXPERIMENTAL & IMAGING TECHNIQUES

31 PRELIMINARY RESULTS HOMOGENEOUS AND INHOMOGENEOUS SIMULATIONS

32 HOMOGENEOUS PREDICTIONS DEM AND TRUE TRIAXIAL

33 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

34 #"",,#"" %&'()$+ $"" "!$"" (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

35 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

36 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

37 INHOMOGENEOUS PREDICTIONS PLANE STRAIN EXPERIMENT WITH SHEAR BAND USING DIC

38 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

39 ! " # $ % & ' ( ) * +, -. / : ; < = 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

40 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...