Читать книгу Computational Geomechanics - Manuel Pastor - Страница 4

1 Chapter 1Figure 1.1 The Vajont reservoir, failure of Mant Toc in 1963 (9 October): (a...Figure 1.2 Failure and reconstruction of original conditions of Lower San Fe...Figure 1.3 Various idealized structures of fluid-saturated porous solids: (a...Figure 1.4 A porous material subject to external hydrostatic pressure increa...Figure 1.5 Two fluids in pores of a granular solid (water and air). (a) Air ...Figure 1.6 Typical relations between pore pressure head, h _w = p _w /χ _w , sa...

2 Chapter 2Figure 2.1 The soil column – variation of pore pressure with depth for vario...Figure 2.2 Zones of sufficient accuracy for various approximations: Zone 1, Figure 2.3 A partially saturated dam. Initial steady‐state solution. Only sa...Figure 2.4 Test example of partially saturated flow experiment by Liakopoulo...

3 Chapter 3Figure 3.1 Some typical two‐dimensional elements for linear and quadratic in...Figure 3.2 Elements used for coupled analysis, displacement (u) and pressure...

4 Chapter 4Figure 4.1 Behavior of mild steelFigure 4.2 Behavior of soft clayFigure 4.3 Behavior of materials with damageFigure 4.4 General stress–strain behaviorFigure 4.5 Typical hardening behavior of clay. (a) Yield surfaces (b) Stress...Figure 4.6 Ideal plasticity (κ = constant) (a) stress path; (b) stress–...Figure 4.7 Softening behavior (a) stress path; (b) stress–strain curveFigure 4.8 von Mises–Huber yield criterion. (a) In the principal stress spac...Figure 4.9 von Mises criterion for plane stress conditionsFigure 4.10 Tresca yield criterion. (a) In principal stress axes (b) in the ...Figure 4.11 Tresca criterion for plane stress conditionsFigure 4.12 Mohr–Coulomb lawFigure 4.13 Mohr–Coulomb yield surfaceFigure 4.14 Hydrostatic compression stress pathFigure 4.15 Hydrostatic compression test on a normally consolidated clay. (a...Figure 4.16 Open and closed yield surfacesFigure 4.17 Triaxial stress conditionsFigure 4.18 Consolidated drained stress pathFigure 4.19 Consolidated drained stress path in p′ − q planeFigure 4.20 Typical results of CD tests on normally consolidated claysFigure 4.21 Typical results of CU tests on normally consolidated claysFigure 4.22 Predicted (Mohr–Coulomb) and observed behavior in CU testsFigure 4.23 Normal consolidation and Critical State linesFigure 4.24 Constant water content lines as obtained from CD and CU tests (s...Figure 4.25 Yield and plastic potential surfaces of Cam‐Clay modelFigure 4.26 Yield surface of the modified Cam‐Clay modelFigure 4.27 Isotropic compression behavior of sand at four initial densities...Figure 4.28 Isotropic compression behavior of sand.Figure 4.29 Influence of isotropic overconsolidation on shear behavior.Figure 4.30 Drained triaxial tests on dense and loose sandFigure 4.31 Undrained behavior of dense sand in CU triaxial testFigure 4.32 Liquefaction of very loose sand in CU triaxial testFigure 4.33 Behavior of Toyoura sand showing the influence of confining pres...Figure 4.34 CSL plotted in (e, ln p′) (a) and (e, p′ ^ξ ) (b) planes.Figure 4.35 Definition of the state parameter.Figure 4.36 Plastic potential and yield surfaces for (a) loose sands (b) den...Figure 4.37 Dilatancy of soft Bangkok clay.Figure 4.38 Constant p′ test on Bangkok clay.Figure 4.39 Consolidated undrained tests on Bangkok clay.Figure 4.40 Consolidated drained tests on Bangkok clay.Figure 4.41 Behavior of normally consolidated Weald clay.Figure 4.42 Behavior of overconsolidated Weald clay (OCR = 24)Figure 4.43 Behavior of clay under two‐way strain‐controlled triaxial loadin...Figure 4.44 Undrained behavior of Banding sand.Computed results shown by...Figure 4.45 Drained behavior of dense and loose sand.Figure 4.46 Drained behavior of Hostun sand.(a) Compression test; (b) Ex...Figure 4.47 Constant b tests on Reid sand.Figure 4.48 Shear of sand with rotation of principal stress axes.Figure 4.49 Undrained behavior of loose sand under reversal of stress.Figure 4.50 Liquefaction of loose banding sand under cyclic loading. (a, b) ...Figure 4.51 Cyclic mobility of loose Niigata sand. (a, b) Experimental data....Figure 4.52 Interpolation ruleFigure 4.53 Densification of medium‐loose sand under drained cyclic loading...Figure 4.54 Anisotropic behavior of Fuji River sand in triaxial compression ...Figure 4.55 State parameter‐based dilatancy laws for dense and loose sand, t...Figure 4.56 Consolidated undrained tests in Toyoura sand (Verdugo and Ishiha...Figure 4.57 Consolidated drained tests on Toyoura sand (Verdugo and Ishihara...Figure 4.58 Successive yield surfaces for increasing degrees of bounding. Su...Figure 4.59 Isotropic compression test.Figure 4.60 Collapse of very loose granular sands when suction decreases....Figure 4.61 Bounding surface with radial interpolation

5 Chapter 5Figure 5.1 Global to local mapping of a one‐dimensional infinite element.Figure 5.2 Two‐dimensional mapped infinite elements: (a) Lagrangian biquadra...Figure 5.3 Specified motion on the boundaries of a “shaking table box” model...Figure 5.4 A more realistic model of an “infinite” foundation with a specifi...Figure 5.5 A horizontally stratified foundation subject to vertically propag...Figure 5.6 Foundation of Figure 5.5 perturbed by the imposition of a structu...Figure 5.7 Repeatable boundary conditions. Displacement at A = displacement ...Figure 5.8 Two‐dimensional model problem and three meshes (SN, DN, and SW)....Figure 5.9 The problem of Figure 5.8. (a) Time history of horizontal displac...Figure 5.10 Substructure technique for seismic analysis of structuresFigure 5.11 A rigid prismatic foundation embedded in a half‐space subjected ...Figure 5.12 A rigid strip footing embedded in a transversely isotropic half‐...Figure 5.13 First adaptive solution of a purely plastic deformation problem....Figure 5.14 Adaptive solution of the problem of foundation collapse with an ...Figure 5.15 Failure of a rigid footing on a vertical cut. Ideal, von Mises, ...Figure 5.16 Earthquake analysis of lower San Fernando Dam (a) initial mesh; ...Figure 5.17 Discontinuous discretization in time with linear elements.Figure 5.18 Nonuniqueness – mesh size dependence in the extension of a homog...Figure 5.19 Strain softening (H = −5000): comparison of reaction vs. prescri...Figure 5.20 Work dissipation in failure of the material.Figure 5.21 One‐dimensional soil bar in pure compressive loadingFigure 5.22 Plastic strain along the bar using the gradient‐dependent porous...Figure 5.23 Distribution of plastic strain along the bar with different valu...Figure 5.24 Distribution of plastic strain along the bar with different valu...Figure 5.25 Example 1. A saturated soil layer under a periodic load.Figure 5.26 Example 1. Vertical pressure amplitude distribution. Note: Exact...Figure 5.27 Example 2. A saturated soil foundation under transient load; (a)...Figure 5.28 Example 2. Two‐dimensional foundation pressure contours computed...Figure 5.29 Test sample for validating the stabilizing characteristic of the...Figure 5.30 Pore pressures at t = 10 hours (top left), 1 day (top right), an...Figure 5.31 Displacements at t = 10 hours (top left), 1 day (top right), and...Figure 5.32 Pore pressures at different time‐stations.Figure 5.33 Sketch of the soil sample.Figure 5.34 Strain localization on the soil sample: a) contour fills of stra...

6 Chapter 6Figure 6.1 Embankment deformation flow patterns and maximum effective shear ...Figure 6.2 (a) Strip load on a foundation of a weightless c–ϕ mat...Figure 6.3 Layered embankment problem (a) geometry and material properties; ...Figure 6.4 Axisymmetric sample between rough platens. Effect of degree of di...Figure 6.5 The Mohr–Coulomb trace in the mean stress – deviatoric stress pla...Figure 6.6 Load deformation characteristics (undrained conditions) for plane...Figure 6.7 The π plane section of the Mohr–Coulomb surface with ϕ ...Figure 6.8 Load‐deformation curves for ideal associated plasticity for vario...Figure 6.9 A typical example of confined seepage in a submerged structure fo...Figure 6.10 Flow under inclined pile wall in a stratified anisotropic founda...Figure 6.11 Flow under a dam through a highly nonhomogeneous anisotropic fou...Figure 6.12 Vertical section of Acciano dam (Briseghella et al. 1999; Schref...Figure 6.13 Finite element discretization with triangular elements, shades o...Figure 6.14 Contour lines of water pressure after the initial seepage analys...Figure 6.15 Contour lines of water pressure after the initial seepage analys...Figure 6.16 The investigated poroelastic column: geometry, boundary conditio...Figure 6.17 Analytical vs. numerical results for displacement at the top and...Figure 6.18 Continuously varying meshes: an element source is moving from po...Figure 6.19 Percentage errors of the numerical solutions.Figure 6.20 Embedded aquifer in a half‐space.Figure 6.21 Numerical and analytical results for excess pore pressure versus...Figure 6.22 Numerical and analytical results for excess pore pressure versus...Figure 6.23 Analytical solutions for vertical displacements of an isolated a...Figure 6.24 Geometry and discretization of the sample.Figure 6.25 Time steps chosen for the analysis.Figure 6.26 Time history of pressure at the top of the sample for the first ...Figure 6.27 Time history of vertical top displacement (left) and top pressur...Figure 6.28 Energy norms (internal energy, coupling term energy, and total e...Figure 6.29 Time history of maximum vertical displacement (top) and pore pre...Figure 6.30 Variation in time of the applied load and automatic time steppin...Figure 6.31 Energy norms (internal energy, coupling term energy, and total e...Figure 6.32 Definition of cohesive crack geometry and model parameters.Figure 6.33 Fracture energy (a) and loading/unloading law (b) for each homog...Figure 6.34 Fracture energy (a) and loading/unloading law for the interface ...Figure 6.35 Hydraulic crack domain.Figure 6.36 Multiple advancing fracture step at the same time station.Figure 6.37 Nodal forces projection algorithm. (a) Nodal forces at time stat...Figure 6.38 Problem geometry for water injection benchmark and overall discr...Figure 6.39 Crack length time history.Figure 6.40 Crack mouth‐opening displacement (a) and mouth pressure time his...Figure 6.41 Distribution of fluid pressure and cohesive tractions within a f...Figure 6.42 Problem geometry for ICOLD benchmark and calculated crack positi...Figure 6.43 Zoom near the fracture for maximum principal stress contour.Figure 6.44 Zoom for pressure distribution within the crack and fluid lag....Figure 6.45 Principle stress map contours.Figure 6.46 Investigated cross section and loading cases: top pressure loadi...Figure 6.47 Dynamic solutions at the crack tip for fast mechanical loading: ...Figure 6.48 Wave propagation of pressure contour for mechanical loading plot...Figure 6.49 Pressure wave contour plots of dynamic solutions for water press...Figure 6.50 Pressure distribution for the current crack pattern at 0.1 secon...Figure 6.51 Pressure versus time at the injection point.

7 Chapter 7Figure 7.1 Sections through model KVV03 showing dimensions and transducer lo...Figure 7.2 Finite element idealisation.Figure 7.3 (a) Comparison with centrifuge results (top) input motion (bottom...Figure 7.4 Numerical results of excess Pore Pressure at Point I (PPT2628) us...Figure 7.5 Centrifuge model configurations for Class A predictions – VELACS ...Figure 7.6 VELACS Centrifuge model No. 1: (a) instrumentation, finite elemen...Figure 7.7 VELACS Centrifuge model No. 3: (a) instrumentation, finite elemen...Figure 7.8 VELACS Centrifuge model No. 11: (a) instrumentation, finite eleme...Figure 7.9 (a) Schematic model configuration of test MMD1 (Dewooklar et al 2...Figure 7.10 (a) Static deflection of the wall (b) total lateral earth pressu...Figure 7.11 Comparison with centrifuge test MMD1 (Dewooklar et al 2009) (a) ...Figure 7.12 Comparison with centrifuge test MMD1 (Dewooklar et al 2009) (a) ...

8 Chapter 8Figure 8.1 Comparison of the numerical solutions for water pressure (two‐pha...Figure 8.2 Comparison of the two‐phase flow solutions with switching at p _c =...Figure 8.3 Comparison of two‐phase flow solutions with switching at p _c = 2 k...Figure 8.4 Comparison of the two‐phase flow solution with switching at p _c = ...Figure 8.5 Comparison of the gas pressure profiles (the two‐phase flow solut...Figure 8.6 Profiles of vertical displacement (a), water pressure (b), air pr...Figure 8.7 Profile of saturation of air storage modeling in an aquifer with ...Figure 8.8 Vertical settlement versus load level in one‐dimensional elastic ...Figure 8.9 Vertical settlement versus normalized time in the one‐dimensional...Figure 8.10 Vertical settlement vs. normalized time in the one‐dimensional e...Figure 8.11 For the model drawn, vertical settlement, normalized with respec...Figure 8.12 Saturation and relative permeability vs. hydraulic head.Figure 8.13 Water pressure versus time, normalized with respect to applied l...Figure 8.14 (a) Model description and normalized settlement of the top node ...Figure 8.15 Deformed mesh for flexible footing, the fully saturated case: th...Figure 8.16 Deformed mesh for rigid footing, the fully saturated case: the c...Figure 8.17 Deformed mesh for rigid footing, initial partial saturation of 9...Figure 8.18 Pore pressure versus time in the generation phase of the pore pr...Figure 8.19 Horizontal displacements versus time at points A and D for both ...Figure 8.20 Pore pressure versus time in the dissipation phase for the given...Figure 8.21 Vertical displacement versus time in the consolidation phase at ...Figure 8.22 Final pressure distribution over the deformed mesh.Figure 8.23 Saturation distribution over the deformed configuration of the a...Figure 8.24 Vertical (v) and horizontal (h) displacements versus time during...Figure 8.25 Results from the test of a saturated sand column subjected to a ...Figure 8.26 Results from the test of a saturated sand column subjected to a ...Figure 8.27 Results from the test of a saturated sand column subjected to a ...Figure 8.28 3‐D rendering of the subsidence above and around the reservoir R...Figure 8.29 Top: – stress path in the suction – mean effective stress (Equat...Figure 8.30 Top – stress path in the suction‐mean effective stress plane for...Figure 8.31 Inverse subsidence bowl for the recovery phase obtained by numer...Figure 8.32 Vertical subsidence simulated along the reservoir diameter for d...Figure 8.33 Rainfall recorded at the toe of Pizzo d’Alvano massif.Figure 8.34 Geometric and stratigraphic section.Figure 8.35 Capillary pressure–water saturation relationship and relative pe...Figure 8.36 (a) F.E. mesh (2D – plain strain, 8 node element, 1565 nodes, 48...Figure 8.37 Displacement contours at the end of 6 May (lower part of the slo...Figure 8.38 Displacement norm time history at the toe.Figure 8.39 Equivalent plastic strain at the end of 6 May (lower part of the...Figure 8.40 Saturation at the end of 6 May (lower part of the slope).Figure 8.41 Equivalent volumetric strain at the end of 6 May (lower part of ...Figure 8.42 Equivalent plastic strain history of the toe.Figure 8.43 Water pressure time history at the toe.Figure 8.44 Mean effective stress at the toe.Figure 8.45 Mean shear stress at the toe.Figure 8.46 Negative values of the second‐order work contours in terms of ef...

9 Chapter 9Figure 9.1 Obtaining input motion for the structure using the equivalent lin...Figure 9.2 Modeling of soil behavior in compliance with strain‐dependent def...Figure 9.3 Example of liquefaction curve.Figure 9.4 Equivalent shear stiffness G _eq and damping ratio h _eq .Figure 9.5 Flow diagram of the equivalent linear analysis.Figure 9.6 Evaluation of the additive hysteresis damping ratio.Figure 9.7 Dynamic characteristics of deformationFigure 9.8 Comparison with resonance curve of the equivalent linear and nonl...Figure 9.9 Time history of the input wave. Earthquake record El Centro 1940 ...Figure 9.10 Comparison of stress–strain relationship of ELM and nonlinear an...Figure 9.11 Comparison of acceleration of ELM and nonlinear analysis under t...Figure 9.12 Concept of CWEL.Figure 9.13 Excess pore pressure ratio r _u against damage parameter D (a) In ...Figure 9.14 Schematic flow to calculate stiffness under liquefying process....Figure 9.15 Liquefaction strength of sand.Figure 9.16 Secant shear modulus for soil layers.(a) Shear modulus of st...Figure 9.17 Recorded earthquake at Port Island −83.8 m.Figure 9.18 Acceleration at the ground surface.Figure 9.19 Orbit of an observed earthquake record.Figure 9.20 Acceleration of NS, EW, and principal direction.Figure 9.21 Analytical model.Figure 9.22 Response acceleration of NS direction.Figure 9.23 Excess pore pressure ratio (NS).Figure 9.24 Excess pore pressure ratio (EW).Figure 9.25 Excess pore pressure ratio (NS + EW + UD).Figure 9.26 Excess pore pressure ratio (principal direction).Figure 9.27 Maximum response acceleration (a) Horizontal component (b) Verti...Figure 9.28 Profile of maximum response acceleration.Figure 9.29 Time history of pore pressure ratio.Figure 9.30 Liquefaction experiment by blast vibration in a coal mine.Figure 9.31 Three‐dimensional FEA model.Figure 9.32 Stress path on Pi plane.Figure 9.33 Diagram obtained by cyclic shear test and liquefaction test....Figure 9.34 Input motion.Figure 9.35 Excess pore water pressure at GL−1.4 m.Figure 9.36 Acceleration on the surface of the backfill.Figure 9.37 Acceleration at the Base slab.Figure 9.38 Curvature at the pile head.Figure 9.39 Failure and reconstruction of original conditions of the Lower S...Figure 9.40 Idealization of San Fernando dam for analysis: (a) material zone...Figure 9.41 Initial steady‐state solution: (a) pressure (kPa); and (b) satur...Figure 9.42 Deformed shapes of the dam at various times: (i) 15 s (end of ea...Figure 9.43 Horizontal (left) and vertical (right) displacements: (a) at the...Figure 9.44 Excess pore pressure at points (a) to (h) (see Figure 9.40a)Figure 9.45 Results of analysis with increased permeabilities: (a) deformed ...Figure 9.46 Results of analysis with softer materials, showing deformed shap...

10 Chapter 10Figure 10.1 Sketch of the reference axes and main magnitudesFigure 10.2 Definition of auxiliary variables h _s and h _w Figure 10.3 Curvature approximation and the values of E, F, G, L, M, and N a...Figure 10.4 Nodes and numerical integration in an SPH meshFigure 10.5 SPH nodes with FD meshes at solid nodes.Figure 10.6 Injection strategy.Figure 10.7 Deformation of a soil column.Figure 10.8 General view of Thurwieser rock avalanche. Figure 10.9 Thurwieser avalanche after 80 seconds with friction angle 26 : c...Figure 10.10 Shaded relief map of Popocatépetl volcano and surrounding areas...Figure 10.11 Initial conditionsFigure 10.12 Propagation of the lahar along Huilouac gorgeFigure 10.13 Propagation of the 2001 laharFigure 10.14 The aerial view of the debris flow event after the landslide in...Figure 10.15 Results sequence of the debris flow simulation at different pos...Figure 10.16 Computed velocities at times (a) 4s, (b) 13s and (c) 23s.Figure 10.17 Final erosion depths at time 40secondFigure 10.18 Comparison between observed and computed frontal velocities....