Promotion of the use of Advanced Methods in Practice Sliding/Rolling Constitutive Theory

Transcription

1 Sliding/Rolling Constitutive Theory and Its Generalization By Rajah Anandarajah Johns Hopkins University Promotion of the use of Advanced Methods in Practice Sliding/Rolling Constitutive Theory

2 Promotion of the use of Advanced Methods in Practice Use in situ data to estimate input parameters as much as possible Develop computationally-efficient methods for handling three-dimensional problems Develop physical meaning for parameters

3 Use in situ data to estimate input parameters as much as possible Back-calculate parameters from in situ tests Establish correlations between in situ data and needed parameters

4 Use in situ data to estimate input parameters as much as possible Back-calculate parameters from in situ tests Establish correlations between in situ data and needed parameters

5 Back-calculation of parameters for the anisotropic bounding surface clay model from pressuremeter data Anandarajah, A., and Agarwal, D. (1991). Computer-Aided Calibration of a Soil Plasticity Model. International Journal for Numerical and Analytical Methods in Geomechanics, 15(12):

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8 Back-calculation of parameters for the anisotropic bounding surface clay model from pile-load test A. Anandarajah, J. Zhang and C. Ealy. Calibration of dynamic analysis methods from field test data, Soil Dynamics and Earthquake Engineering, Volume 25, Issues 7-1, August-October 25, Pages

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11 P(t) (lbs) Measured.5 1 t (sec) 1 Measured a(t) (g) t (sec) 1 Calculated FE (56 elem) with.5g max a(t) (g) t(sec). 15G max Disp.-Pile at G-Level (in) Measured Calculated FE (54 elem) with.5g max.5 1 t(t)

12 Use in situ data to estimate input parameters as much as possible Back-calculate parameters from in situ tests Establish correlations between in situ data and needed parameters

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14 Promotion of the use of Advanced Methods in Practice Use in situ data to estimate input parameters as much as possible Develop computationally-efficient methods for handling three-dimensional problems Develop physical meaning for parameters

15 Earthquake Response of a 2-Storey Building Anandarajah, A., Rashidi, H. and Arulanandan, K. (1995). Elasto-Plastic Finite Element Analyses of Earthquake Pile-Soil-Structure Interaction Problems Tested in a Centrifuge. Computers and Geotechnics, 17:

16 Theory Versus Experiment

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19 Complex Soil-Structure System Elevated High way Domains to be analyzed

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21 z(m) 1 5 Elasto-Plastic Equivalent Linear (FE) SAM x (m) Maximum Horizontal Displacement 1% of Pile-Head Maximum Displacement

22 Sliding/Rolling Constitutive Theory and Its Generalization

23 VELACS Predictions: Anandarajah (1992) Data from Arulmoli et al. (1992)

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26 Sliding/Rolling Constitutive Theory and Its Generalization

27 Link 2D Assembly Mechanisms Based on Interparticle Sliding Sliding: F2 = tan( β α) F1 α φ µ β = tan 1 ( S ) + φ µ max v

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29 u p 1 = r sin p 4 θ β u2 = 4rθcosβ vt max vt max

30 ε (2Nθr)cos( β φ 1 p max µ 1 = 1 1 ( β max β min ) σ 1 L1 sin ) β 1 max 1 ( 2Nθr)cos( β max φ ) p µ 1 ε 3 = L1 ( cos β 1 1 ( β β ) σ max min 1 max / 2) ψ = φ µ β = tan 1 ( S ) + φ µ max v σ σ 2 1 = tan( β max φ µ ) β 1 min = 5 β 1 min = 1

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32 6 (a) A 6 (b) A B 4 B q 3 q 3 2 C 2 C p ε(%) q

33 2D TO TRIAXIAL: Discrete Element Method

34 Examples Some Aspects of Anisotropy Anandarajah and Kuganenthira, 1995, Geotechnique

35 Two-Dimensional Analysis Anandarajah, A. (2), Numerical Simulation of One-Dimensional Behavior of Kaolinite. Geotechnique, 5(5):

36 2914 Element Assembly

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40 Consider fcc: Brauns (1968) Hendron (1963)

41 S v = σ σ 3 1 = tan( β φ µ )

42 S v = σ σ 3 1 = 1 2 tan( β φ µ )

43 Future r ij σ ij n ij r ij σ ij n ij σ ij n ij r ij r ij = σ + αn ij ij

44 Conventional S ij rij r ij = S ij + dδ ij δ ij δ ij S ij r ij n ij r ij σ ij σ ij Sliding/Rolling r ij = σ + αn ij ij n ij r ij

45 Generalization of Sliding/Rolling Theory to 3D Loading Using the Bounding Surface Concept Loading Reverse Loading β max = β max = β max = 65 β max = 65 K p [ β ] max β min β max = β = tan 1 ( ) + φ µ 1 β = tan 1 + φ s max s max µ δ L δ UL δ = β = max n ij s ij 2 n I fun( δ ) r ij = σ + αn ij α ij δ

46 J M µ I M a A µ I B α ij A α ij λ & λr A * & ij = α ad ij [ ] a C (1 + ρ δ * λ = C1 exp 2 ) β min = β J [ ] ( p β β exp ) fail + min fail Cβ ε v

47 Triaxial Undrained Monotonic Loading q (kpa) β init = 42.8 β init p (kpa) = q (kpa) β init = 41.7 β init = ε 1 (%)

48 q (kpa) P (kpa) q (kpa) ε 1 (%) -15

49 Triaxial Undrained Cyclic Simulation with β init =

50 Modeling Cyclic Behavior 3 q off = q cyc =28.8 kpa A D 5 q off =17. kpa q cyc =29.4 kpa 2 4 q(kpa) 1-1 B -2 E p(kpa) C q(kpa) p(kpa) Experimental Data for Nevada Sand (VELAS Project, Arulmoli, et al., 1992)

51 Isotropic Anisotropic

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53 Concluding Remarks Calibrate constitutive laws using in situ data as much as possible Develop simpler finite element models for threedimensional problems Develop physical meaning for parameters