MODELLING SOILS AND GRANULAR MEDIA IAN F COLLINS UNIVERSITY OF AUCKLAND NEW ZEALAND

Transcription

1 THE REMARKABLES QUEENSTOWN NZ MODELLING SOILS AND GRANULAR MEDIA IAN F COLLINS UNIVERSITY OF AUCKLAND NEW ZEALAND

2 OVERALL OBJECTIVES TO GIVE AN OVERVIEW OF EXTANT MODELLING PROCEDURES COMMONLY USED IN GEOTECHNICAL ENGINEERING TO DISCUSS THEIR SHORT COMINGS TO PROPOSE A WAY FORWARD BASED ON MODERN THERMOMECHANICAL FORMULATIONS OF ELASTIC/PLASTIC SOLIDS

3 LECTURE 1 BASIC SOIL PROPERTIES RODIN S THINKER SISLEY S SAND HEAPS

4 HISTORICAL INTRODUCTION

5 Every heap of sand, whether it be on level ground or sloping, will have its base twice the length of its axis. Leonardo da Vinci (Diaries) The strength of sands is determined by certain critical angles!!!

6 σ COULOMB τ τ = c + σ tan φ cohesion friction angle τ c φ σ FAILURE LINES RETAINING WALL

7 Analysed stress system behind retaining walls, and introduced notions of active and passive failures Professor William Rankine (Glasgow) ( )

8 Reynolds, O. On the DILATANCY of media composed of rigid particles in contact,with experimental observations Philosophical Magazine, 20 (S5) , Dec 1885.

9 Reynolds Demonstration

10 A FAMILIAR EXAMPLE OF REYNOLDS DILATANCY

11 OSBORNE REYNOLDS, Second Professor of Engineering in England. (Manchester) Two Books: (c) Sewer gas and how to keep it out of homes (1876). (b) On the Sub-Mechanics of the Universe (1903)

12 Karl von Terzaghi The Father of Soil Mechanics He who said "Erdbaumechanik" in 1923

13 MATHEMATICIANS ARE USEFUL ANIMALS WHO SHOULD BE KEPT IN A GOLDEN CAGE AND FED PROBLEMS JUDICIOUSLY Karl Terzaghi KARL TERZAGHI, , Thoughts occasioned by the centenary of his birth, R. B. Peck, Geotechnique (1983),

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16 JUSTIFICATION OF EFFECTIVE STRESS CONCEPT Pore pressures Contact stress

17 Relative Volume Measures VOIDS RATIO e SPECIFIC VOLUME v POROSITY n VV e=, VS V v= = 1 + e, VS VV n= = e /(1 + e) V

18 PROF ARTHUR CASGRANDE HARVARD (193?) INTRODUCED THE NOTION OF A CRITICAL VOIDS RATIO. ANY SHEARED SAND SAMPLE WOULD EVENTUALLY REACH A CRITICAL VOIDS RATIO IRRESPECTIVE OF INITIAL CONDITIONS.

19 CASAGRANDE τ /σ BEHAVIOUR UNDER SHEAR σ Dense Softening τ (τ / σ ) crit Loose Shear Strain Volume strain Dense (Dilates) e Loose e crit Loose (Contracts) Dense

20 TAYLOR STRESS DILATANCY RELATION INTERLOCKING The serrated block model provides a simple analogy of the effects of volume change and induced dilatancy and anisotopy. σ dx τ dy τ dy = tan(φ + ν ), where tan ν = σ dx

21 THE CAMBRIDGE MODELS 1960 S ROSCOE, SCHOFIELD, WROTH, BURLAND

22 THE COULOMB LINE REPLACED BY THE CRITICAL STATE LINE AN ELASTIC/PLASTIC CRITICAL STATE MODEL

23 MATERIAL PROPERTIES

24 CLAYS-1

25 Kaolinite Illite and Montmorillonite Silica Alumuna Flocculated arrangement of plates forming a Ped Structure of clay plates and particles

26 IILITE

27 PEDS

28 KAOLIN PIPE BOWLS

29 CLAY v SAND CLAY CAN BE REGARDED AS A FINE GRAIN MATERIAL, WHOSE GRAINS HAVE LOW STIFFNESS AND ARE DUCTILE -THEY CAN ALSO ABSORB WATER. SAND IS A COURSE GRAIN MATERIAL, WHOSE GRAINS ARE STIFF AND BRITTLE.

30 GEOSTATICS

31 STRESS IN THE GROUND Vv n= V GROUND LEVEL WATER TABLE Z u = ρ W gh H σ = nρ W gh + (1 n )ρ s gz σ = (1 n )g (ρ S Z ρ W H ) Note : σ as H

32 QUICKSAND If the water table is higher than the local free surface as by a retaining wall, or in a natural depression, the effective pressure can be zero Sherlock Holmes

33 EXPERIMENTAL TECHNIQUES

34 LIMITED NUMBER OF POSSIBLE EXPERIMENTS TRIAXIAL DRAINED TRUE-TRIAXIAL UNDRAINED SHEAR BOX (CENTRIFUGE) SIMPLE SHEAR RING SHEAR (DISCRETE ELEMENT SIMULATION)

35 UoA Standard Triaxial

36 A large Triaxial

37 STANDARD TRIAXIAL CELL

38 SHEAR BOX

39 A CENTRIFUGE

40 NOTATION IN THIS LECTURE WE WILL USE THE STANDARD NOTATION OF TRIAXIAL TESTS ALL STRESSES ARE EFFECTIVE STRESSES. 1 p= 1 3 (σ 1 + 2σ 3 ) and q = (σ 1 σ 3 ) 2 e v = (e1 + 2e 3 ) and e γ = volume strain 2 3 (e1 e 3 ) shear strain 3

41 STANDARD TRIAXIAL TESTS DRAINED TESTS (slow) q UNDRAINED TESTS (fast) q effective stress path total stress path effective stress path total stress path O p Pore pressure Pore pressure p

42 UNDRAINED TESTS ON SAND USING MOIST TAMPING STATIC LIQUEFACTION??

43 BIFURCATIONS IN DENSE AND LOOSE SAND

44 THREE PREPARATION PROCEDURES MOIST TAMPING WATER PLUVIATION AIR PLUVIATION (Experiments by Vaid)

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47 THE RESPONSE IS DEPENDENT ON PREPARATION PROCEDURE In undrained tests, static liquifaction is only obtained using moist tamping

48 DISCRETE ELEMENT SIMULATIONS (DEM)

49 DEM SIMULATION OF SIMPLE SHEAR

50 RING SHEAR TEST (Bob Behringer, Duke University)

51 FORCE CHAIN NETWORK DURING PILE INDENTATION

52 FORMATION OF SAND HEAPS (Bob Behringer, Duke University)

53 EXPLODING GRAIN SILO

54 PARTICLE CRUSHING

55 Thin sleeve of crushed particles immediately adjacent to the pile shaft -Experimental results depicting soil state near the pile - [adapted from Randolph, 2003]

56 ISOTROPIC COMPRESSION AT LARGE STRESSES (PESTANA and WHITTLE)

57 BOLTON-McDOWELL THEORY (1) DISTRIBUTION OF GRAIN SIZES IS FRACTAL: N(L > d ) = Ad 2.5 (3) LARGER PARTICLES PROTECTED. (5) BREAKAGE STRESS VARIES AS d (7) PREDICTS e-ln(p) LINE 2

58 VARIATION OF COORDINATION NUMBER WITH PARTICLE SIZE

59 CONCLUSIONS SOILS ARE 2 OR 3 PHASE MATERIALS STATE VARIABLES ARE NOT OBVIOUS LIMITED RANGE OF EXPERIMENTS DILATANCY, CRUSHING, INTERNAL STRUCTURE, INHERENT AND INDUCED ANISOTROPY ARE ALL IMPORTANT THESE FACTORS POSE MANY CHALLENGES TO THE MATHEMATICAL MODELLER

60 TO BE CONTINUED RAJ AS A HOBBIT