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[{"path":"index.html","id":"welcome","chapter":"Welcome","heading":"Welcome","text":"BS4 knit output R Markdown, using bookdown R package.\nPDF file, download cover image .\nWord file, click download.Kyeong Sun Kim\nNovember 2021\nSeoul National University\nFigure 0.1: Paper Outline\n","code":""},{"path":"constitutive-model.html","id":"constitutive-model","chapter":"1 Constitutive Model","heading":"1 Constitutive Model","text":"brief description constitutive models:\n1. Strain—Softening Stiffness—Hardening Model Sakai Tanaka, 1993\n2. Typical Mohr-Coulomb Non-associated Flow\n3. Extended Mohr-Coulomb Model David Muir Wood, 2004","code":""},{"path":"constitutive-model.html","id":"strainsoftening-stiffnesshardening-model","chapter":"1 Constitutive Model","heading":"1.1 Strain—Softening Stiffness—Hardening Model","text":"assumed yield function \\(F\\) defined stress \\(\\vec{\\sigma}\\) soil parameter \\(\\chi\\) (Tanaka Sakai, 1993):\\(F(\\vec{\\sigma},\\alpha(\\chi))=0\\)order avoid numerical instability due singularity non-associated Mohr-Coulomb model, constitutive model based yield function M-C type plastic potential function Draker-Prager type employed.predicting deformations post-peak regime, elastic- strain-softening plastic model developed. yield function given following expression.","code":""},{"path":"constitutive-model.html","id":"yield-function","chapter":"1 Constitutive Model","heading":"1.1.1 Yield function","text":"\\[\n  F(\\vec{\\sigma},\\alpha(\\chi)) = 3\\alpha(\\chi)p'+\\frac{\\sqrt{J_2}}{g(\\theta)}-c(\\chi) = 0\n\\]","code":""},{"path":"constitutive-model.html","id":"plastic-potential-function","chapter":"1 Constitutive Model","heading":"1.1.2 Plastic potential function","text":"\\[\n  G(\\vec{\\sigma},\\alpha'(\\chi)) = 3\\alpha^{'}(\\chi)p'+\\sqrt{J_2}-c(\\chi) = 0\n\\]\\[\n  \\chi = \\int \\delta\\varepsilon^{p}\n\\]\\[\n  (\\delta\\varepsilon^{p})^2 = 2[(\\delta\\epsilon_x^{p})^2+(\\delta\\epsilon_y^{p})^2+(\\delta\\epsilon_z^{p})^2+]+(\\delta\\gamma^{p})^2\n\\]\n, \\(p^{'}\\) mean stress,\\(J_2\\) second invariant deviatoric stress,\\(\\chi\\) soil hardening parameter,\\(c(\\chi)\\) apparent cohesion function,\\(\\delta \\varepsilon_{x,y,z}^{p} , \\delta \\gamma^{p}\\) incremental deviatoric plastic strains.case Mohr-Coulomb model, \\(g(\\theta)\\) given :\\[\n  g(\\theta) = \\frac{3-sin\\phi}{2\\sqrt{3}cos\\theta -2sin\\theta sin\\phi}\n\\]\n, \\(\\theta\\) Lode angle; triaxial compression, \\(=-30 ^{\\circ}\\)\\(\\phi\\) mobilized internal friction angle.","code":""},{"path":"constitutive-model.html","id":"hardening-function","chapter":"1 Constitutive Model","heading":"1.1.3 Hardening function","text":"simple strain-softening functions specified expressed function material constants. (Tanaka Sakai, 1993)\\[\n\\alpha(\\chi) = {(\\frac{2\\sqrt{\\chi }}{\\chi +})}^m \\alpha_p\\; \\\\ (hardening \\; regime;\\; \\chi \\leq ) \n\\]\\[\n\\alpha(\\chi) = \\alpha_r + (\\alpha_p - \\alpha_r) exp\\{-(\\frac{\\chi-}{b})\\}\\; \\\\ (softening \\; regime;\\; \\chi > ) \n\\]\n, \\(, b, m\\) soil parameters.Similar expressions used de Borst (1986).\\[\n\\alpha_p = \\frac{2 sin \\phi_p}{\\sqrt{3}(3-sin\\phi_p)}\n\\]\\[\n\\alpha_r = \\frac{2 sin \\phi_r}{\\sqrt{3}(3-sin\\phi_r)}\n\\]\n, \\(\\phi_{p,r}\\) peak residual friction angle, respectively.","code":""},{"path":"constitutive-model.html","id":"nonassociated-flow-rule-na","chapter":"1 Constitutive Model","heading":"1.2 Nonassociated Flow Rule (NA)","text":"Since may range possible solutions, associated different pattern localization entirely valid, can expected numerical solution sensitive physical imperfections well round-errors exact sequence procedures defining solution scheme carried . end, result load-displacement response tends rather oscillatory.\nFigure 1.1: Load-displacement response strip footing weightless soil (Krabbenhoft et al., 2012)\nbasic idea behind formulation derives structure internal dissipation associated constitutive models. Let us assume yield function type:\\[\nF = Mp+q-c\n\\]\n, \\(p\\) \\(q\\) mean deviatoric stress, \\(M\\) friction coeffcieint, \\(c\\) cohesion.plastic potential function given :\\[\nG = Np +q\n\\]\n, \\(N \\leq M\\) dilation coefficient.\\(p-q\\) triaxial space, plastic strain rates given :\\[\n\\delta \\varepsilon_v^{p} = \\delta \\lambda \\frac{\\partial G}{\\partial p} = \\delta \\lambda N \\\\\n\\delta \\varepsilon_s^{p} = \\delta \\lambda \\frac{\\partial G}{\\partial p} = \\delta \\lambda\n\\]\n, \n\\(\\delta\\) denotes time increment, \\(\\varepsilon_v^{p}\\) \\(\\varepsilon_s^{p}\\) volumetic deviatoric plastic strains conjugate \\(p\\) \\(q\\), respectively.dissipation \\(D\\) given :\\(\\begin{aligned} D &= p \\varepsilon_v^{p} + q \\varepsilon_s^{p} \\\\  &= (Nq+q) \\delta \\lambda \\\\  &= [c-(M-N)p]\\delta \\lambda \\\\  &= [c - (M-N)p]\\varepsilon_s^{p} \\end{aligned}\\)-mentioned parameters related confining pressure, can easily illustraed figure :\nFigure 1.2: Microscopic origins friction plastic shearing asperities. higher confining pressure implies higher degree interlocking asperities thereby higher apparent shear strength (Krabbenhoft et al., 2012)\n","code":""},{"path":"constitutive-model.html","id":"extended-mohrcoulomb-model-emc","chapter":"1 Constitutive Model","heading":"1.3 Extended Mohr—Coulomb Model (EMC)","text":"elastic-perfectly plastic Mohr-Coulomb model widely used geotechnical analysis. provides crude match actual shearing behavior soils. natural extension create hardening version M-C model size yield surface varies nonlinear way development plastic strain. model described hardening linked distortional strain. useful modelling sands , rearrangement rather particles dominates response irrecoverable volumetric changes essentially linked rearrangement particles (Wood, 2004).\nFigure 1.3: Plastic potential curves (solid lines) yield loci (dashed lines) elastic-hardening plastic Mohr-Coulomb modele\nFollowing Taylor’s (1948) proposal link dilatancy mobilized friction shear box test, stress—dilatancy equation expressed terms total strain increments obtained.\nFigure 1.4: Hardening, compaction dilation HMC model\n","code":""},{"path":"constitutive-model.html","id":"comparison-between-associated-and-non-associated-flow-rule-in-plastic-model","chapter":"1 Constitutive Model","heading":"1.3.1 Comparison between associated and non-associated flow rule in plastic model","text":"elastic-perfectly-plastic Mohr-Coulomb model, commonly assumed plastic potential takes form yield surface, slope defined dilation angle \\(\\psi\\) rather friction angle. assumption adopted, dirction plastic strain increment \\(\\delta \\varepsilon^{p}\\) normal set parallel lines dilation angle. normality rule assumed, radical difference slope yield criterion line plastic potental contour observed (J.P. Doherty D. Muir Wood, 2013).\nFigure 1.5: Elastic-perfectly plastic Mohr-Coulomb model () yield failure locus, (b) plastic potentials\n\nFigure 1.6: Elastic-hardening plastic Mohr-Coulomb model () yield locus failure locus separating elastic plastic inaccessible regions stress plane (b) normality applied plastic region\n","code":""},{"path":"constitutive-model.html","id":"yield-function-1","chapter":"1 Constitutive Model","heading":"1.3.2 Yield function","text":"\\[\nF(\\vec{\\sigma}, \\chi) = F(p',q,\\chi)=q - \\eta_y p'=0\n\\]","code":""},{"path":"constitutive-model.html","id":"plastic-potential-function-1","chapter":"1 Constitutive Model","heading":"1.3.3 Plastic potential function","text":"\\[\nG(\\vec{\\sigma}) = q-(M -M') p' ln(\\frac{p_r'}{p'})=0\n\\]\n, \n\\(\\eta_{y,p}\\) stress ratio yield peak, respectively,\\(p_r'\\) chosen s.t. plastic potential gradient passes current stress, .e.,\\(p_r' = p' exp \\{ \\frac{\\eta_y}{M-M'} \\}\\)\\(M\\) material parameter perfect plasticity hardening terminates.\\(M = \\frac{6 sin \\phi}{3 - sin\\phi}\\)\\(M'\\) dilation constant volume line:\\(M' = \\frac{6 sin \\psi}{3 - sin\\psi}\\)\\(M' = M - k \\psi = M-k(v-\\Gamma+\\lambda lnp')\\)\\(k\\) soil constant linking state variable strength.\nCritical State description follows:\\(M' = M - k [(v_0 - \\Gamma + \\lambda ln p_0' + (\\lambda ln \\frac{p'}{p_0'}-v_0 \\varepsilon_p^e)-v_0\\varepsilon_p^p)]\\).","code":""},{"path":"constitutive-model.html","id":"flow-rule","chapter":"1 Constitutive Model","heading":"1.3.4 Flow rule","text":"\\[\n\\frac{\\delta \\varepsilon_{p}^{p}}{\\delta \\varepsilon_{q}^{p}} = M -M'- \\eta_y\n\\]","code":""},{"path":"constitutive-model.html","id":"hardening","chapter":"1 Constitutive Model","heading":"1.3.5 Hardening","text":"\\[\n\\delta \\eta_y = \\frac{1-\\frac{\\eta_y}{M}}{\\beta} \\delta \\varepsilon_q^p\n\\]\n, \\(\\beta\\) model parameter scaling plastic strain,\\(\\beta = \\frac{3}{2}p' \\frac{9-M}{9-(M-M')M ln2 - 3M'} \\frac{1-E_{50}/E_{ur}}{E_{50}}\\) Taylor’s \\(\\sigma-\\psi\\) relation.incremental stress ratio defined :\\(\\delta \\eta_y = \\frac{3 sin \\delta \\phi}{\\sqrt{3}cos\\theta+sin\\theta sin\\delta\\phi}\\)","code":""},{"path":"constitutive-model.html","id":"soil-parameters","chapter":"1 Constitutive Model","heading":"1.3.6 Soil Parameters","text":"","code":""},{"path":"constitutive-model.html","id":"elastic-moduli","chapter":"1 Constitutive Model","heading":"1.3.6.1 Elastic Moduli","text":"elastic moduli estimated modified equation proposed Hardin Black (1968) case sand:\\[\nG = G_0 \\frac{(2.17-e)^2}{1+e}\\sqrt{p'} \\\\\nK = \\frac{1+\\nu}{3(1-2 \\nu)}G\n\\]\n, \\(\\nu\\) Poisson’s ratio,\\(e\\) void ratio,\\(G_0\\) initial shear modulus.","code":""},{"path":"constitutive-model.html","id":"peak-friction-angle","chapter":"1 Constitutive Model","heading":"1.3.6.2 Peak friction angle","text":"peak friction angle \\(\\phi_p\\) estimated empirical relations proposed Bolton (1987):\\[\nI_r = D_r[5-ln(\\frac{p'}{150})]-1, \\; (p' \\geq 150 kN/m^2) \\\\\nI_r = 5D_r -1 , \\; (p' < 150 kN/m^2) \\\\ \n\\phi_p = 3I_r + \\phi_r\n\\]","code":""},{"path":"constitutive-model.html","id":"dilatency-angle","chapter":"1 Constitutive Model","heading":"1.3.6.3 Dilatency angle","text":"dilatency angle \\(\\psi\\) estimated modified Rowe’s stress–dilatency relationship:\\[\nsin\\psi = \\frac{sin\\phi-sin\\phi_r'}{1-sin\\phi sin\\phi_r'} \\\\\n\\phi_r' = \\phi_r[1-\\beta exp\\{-(\\frac{\\chi}{\\epsilon_d})^2\\}]\n\\]\n, \\(\\beta\\) \\(\\epsilon_d\\) stress—dilatency material parameters.\\(E_{50}\\) secant modulus defined :\\(E_{50} = \\frac{\\frac{1}{2}q_{u}}{\\varepsilon_{,50}}\\)\\(E_{ur}\\) unloading/reloading stiffness.","code":""},{"path":"calibration.html","id":"calibration","chapter":"2 Calibration and Validation","heading":"2 Calibration and Validation","text":"\nvalidity finite element tests performed, triaxial elemental test siumlated box union length. set follows:","code":""},{"path":"calibration.html","id":"drained-triaxial-test","chapter":"2 Calibration and Validation","heading":"2.1 Drained Triaxial Test","text":"\nFigure 2.1: Typical triaxial test (Krabbenhoft, 2013)\n\nFigure 2.2: Typical shear-volumetric strain behavior triaxial compression (Krabbenhoft, 2013)\nTwo tests — Triaxial compression extension (TC/TE) — simulated using Multiplier Elasto—plastic analysis axisymmetric conditions indicated Figure .\nfixed loads represent initial axial radial stresses axial Multiplier load increased course analysis reach ultimate limit state.\nFigure 2.3: Setup elemental triaxial compression extension\nprocess trial error, fits shown Figure obtained. data set , information behavior simple shear available value well within range can accommodated isotropic strength option, little reason assume anisotropy.\nnote compression secant modulus compression half extension secant modulus. somewhat unusual, case nevertheless fits data best.","code":""},{"path":"calibration.html","id":"result-of-elemental-triaxial-test-at-100-kpa","chapter":"2 Calibration and Validation","heading":"2.1.0.1 Result of Elemental Triaxial Test at 100 kPa","text":"Triaxial test radial stress 100 kPa simulated using one one block finite elmeent formulation EMC model.\nFigure 2.4: Result Drained Triaxial test 100 kPa\n","code":""},{"path":"calibration.html","id":"result-of-elemental-triaxial-test-at-200-kpa","chapter":"2 Calibration and Validation","heading":"2.1.0.2 Result of Elemental Triaxial Test at 200 kPa","text":"Triaxial test radial stress 200 kPa simulated using one one block finite elmeent formulation EMC model.\nFigure 2.5: Result Drained Triaxial test 200 kPa\n","code":""},{"path":"calibration.html","id":"soil-parameters-1","chapter":"2 Calibration and Validation","heading":"2.2 Soil Parameters","text":"","code":""},{"path":"calibration.html","id":"strainsoftening-stiffnesshardening-model-1","chapter":"2 Calibration and Validation","heading":"2.2.1 Strain—Softening Stiffness—Hardening Model","text":"table presenting model parameters used Sakai Tanaka (1993).","code":""},{"path":"calibration.html","id":"nonassociated-flow-rule-na-1","chapter":"2 Calibration and Validation","heading":"2.2.2 Nonassociated Flow Rule (NA)","text":"table presenting model parameters used Nonassociated (NA) simulations.","code":""},{"path":"calibration.html","id":"extended-mohrcoulomb-model-emc-1","chapter":"2 Calibration and Validation","heading":"2.2.3 Extended Mohr—Coulomb Model (EMC)","text":"table presenting model parameters used Extended Mohr-Coulomb (EMC) simulations.","code":""},{"path":"calibration.html","id":"convergence-criteria","chapter":"2 Calibration and Validation","heading":"2.3 Convergence Criteria","text":"","code":""},{"path":"calibration.html","id":"mesh-convergence","chapter":"2 Calibration and Validation","heading":"2.3.1 Mesh Convergence","text":"table presenting result mesh convergence test NA EMC models.\ngoal mesh convergence test usually seek acceptable range number mesh size.\nHowever, interest present paper differs previously investigated objectives, way object sought .\npresent paper seeks draw detailed analysis failure surface formed soil sheared.\nauthors past described width shear band (Tanaka Sakai, 1993). However, present paper deals limit analysis formulation using Extended Mohr-Coulomb model.","code":""},{"path":"calibration.html","id":"mesh-convergence-results","chapter":"2 Calibration and Validation","heading":"2.3.1.1 Mesh Convergence Results","text":"reulst present investigation determination number mesh elements around 2000.\nHowever, noted studies, outside paper, onto maximum number elements studied, enhance visualization shear band formation, well guidance onto study shear dissipation.\nFigure 2.6: Typical result mesh convergence test (maximum number elements)\n\nFigure 2.7: Result mesh convergence test, confirms 2000 elements acceptable\n\nFigure 2.8: Shear Dissipation mesh convergence test 250, 500, 2000 elements\n\nFigure 2.9: Mesh 250, 500, 2000 elements\n\nFigure 2.10: Shear Dissipation mesh convergence test 5000, 10000, 20000 elements\n\nFigure 2.11: Mesh 5000, 10000, 20000 elements\n","code":""},{"path":"calibration.html","id":"boundary-convergence","chapter":"2 Calibration and Validation","heading":"2.3.2 Boundary Convergence","text":"soil tank width distance anchor soil tank boundary primary condern modeling.\nTherefore, optimized value soil tank width investigated, differing values 10B 3B, , wherein B refers width anchor plate.\nFigure 2.12: Convergence test setup different boundary size: () 10B, (b) 7B, (c) 5B, (d) 3B\nDue reasoning considers method mesh adaptivity, insignificant effect onto extension soil tank width deemed acceptable author. Therefore, result boundary convergence test determined 10B.\nFigure 2.13: Final boundary decision schematic numerical simulations\ntable presenting setup boundary convergence test NA EMC models.","code":""},{"path":"calibration.html","id":"boundary-convergence-results","chapter":"2 Calibration and Validation","heading":"2.3.2.1 Boundary Convergence Results","text":"","code":""},{"path":"result.html","id":"result","chapter":"3 Results","heading":"3 Results","text":"","code":""},{"path":"result.html","id":"parametric-study","chapter":"3 Results","heading":"3.1 Parametric Study","text":"table presenting setup numerical simulations NA EMC models.\ncode refers differing width plate anchor, , whereas number specifies embedment ratio either 1, 2, 3.","code":""},{"path":"result.html","id":"effect-of-embedment-depth-ratio-fracdb","chapter":"3 Results","heading":"3.1.1 Effect of Embedment Depth Ratio \\(\\frac{D}{B}\\)","text":"","code":""},{"path":"result.html","id":"overall-results-with-all-range-of-dense-medium-loose-sands","chapter":"3 Results","heading":"3.1.1.1 Overall Results with All Range of Dense, Medium, Loose Sands","text":"\nFigure 3.1: Effect embedment depth ratio break-factor densities soil\n","code":""},{"path":"result.html","id":"for-different-sand-densities-loose-medium-dense","chapter":"3 Results","heading":"3.1.1.2 For Different Sand Densities: \\(Loose, Medium, Dense\\)","text":"\nFigure 3.2: Effect embedment depth ratio break-factor () loose (b) medium (c) dense\n","code":""},{"path":"result.html","id":"effect-of-width-b","chapter":"3 Results","heading":"3.1.2 Effect of Width \\(B\\)","text":"","code":""},{"path":"result.html","id":"overall-results-with-all-range-of-dense-medium-loose-sands-1","chapter":"3 Results","heading":"3.1.2.1 Overall Results with All Range of Dense, Medium, Loose Sands","text":"\nFigure 3.3: Effect width plate densities soil\n","code":""},{"path":"result.html","id":"shear-dissipation","chapter":"3 Results","heading":"3.1.3 Shear Dissipation","text":"\nFigure 3.4: Effect embedment depth width shear dissipation densities soil\n\nFigure 3.5: Shear dissipation NA model 10 percent maximum value \\(B = 0.04m\\)\n\nFigure 3.6: Shear dissipation NA model 10 percent maximum value \\(B = 0.2m\\)\n\nFigure 3.7: Shear dissipation NA model 10 percent maximum value \\(B = 1.0m\\)\n\nFigure 3.8: Shear dissipation NA model 10 percent maximum value \\(B = 3.5m\\)\n\nFigure 3.9: Shear dissipation NA model 10 percent maximum value \\(B = 4.5m\\)\n\nFigure 3.10: Shear dissipation NA model 10 percent maximum value \\(B = 6.5m\\)\n","code":""},{"path":"result.html","id":"comparison-with-previous-researchers","chapter":"3 Results","heading":"3.2 Comparison with Previous Researchers","text":"\nFigure 3.11: Comparison theories experimental data densities sands\n\nFigure 3.12: Comparison theories experimental data loose dense sands\n","code":""},{"path":"result.html","id":"comparison-of-the-plot-of-the-effect-of-width-on-resistance","chapter":"3 Results","heading":"3.2.0.1 Comparison of the plot of the effect of width on resistance","text":"\nFigure 3.13: Comparison drawn\n","code":""},{"path":"comparison-with-centrifuge-experiment.html","id":"comparison-with-centrifuge-experiment","chapter":"4 Comparison with Centrifuge Experiment","heading":"4 Comparison with Centrifuge Experiment","text":"\nFigure 4.1: Typical numerical test set-\n\nFigure 4.2: Typical mesh numerical simulation; number mesh = 5000\n\nFigure 4.3: Typical result numerical simulation; 1st decile shear dissipation (kJ)\n","code":""},{"path":"comparison-with-centrifuge-experiment.html","id":"results-of-numerical-analysis-for-finding-the-model-that-fits-the-centrifuge-loaddisplacement-curve","chapter":"4 Comparison with Centrifuge Experiment","heading":"4.0.0.1 Results of numerical analysis for finding the model that fits the centrifuge load—displacement curve","text":"\nFigure 4.4: Code name base2; B=6.5m; B/D = 0.915\n\nFigure 4.5: Code name base3; B=6.5m; B/D = 0.615\n\nFigure 4.6: Code name base4; B=4.5m; B/D = 1.044\n\nFigure 4.7: Code name base5; B=4.5m; B/D = 0.744\n\nFigure 4.8: Code name base6; B=4.5m; B/D = 0.444\n\nFigure 4.9: Code name base7; B=3.5m; B/D = 1.314\n\nFigure 4.10: Code name base8; B=3.5m; B/D = 0.101\n","code":""},{"path":"comparison-with-centrifuge-experiment.html","id":"determination-of-model-parameters","chapter":"4 Comparison with Centrifuge Experiment","heading":"4.0.0.2 Determination of model parameters","text":"evaluate difference centrifuge test result model prediction, residual error used:\\[\nError = \\lvert \\frac{y_{actual}-y_{estimated}}{y_{actual}}\\lvert \\times 100\\% \n\\]\ngoal find model best fits (least error) measured data.\ndense sand cases, Model C H, whereas loose sand cases, Model B G chosen studies.\nFigure 4.11: Heat-map errors cetrifuge test model (dense cases); model C H selected among available 10 models\n\nFigure 4.12: Heat-map errors cetrifuge test model (loose cases); model B G selected among 10 available models\n","code":""},{"path":"comparison-with-centrifuge-experiment.html","id":"comparison-of-the-centrifuge-test-results-with-the-chosen-model","chapter":"4 Comparison with Centrifuge Experiment","heading":"4.1 Comparison of the centrifuge test results with the chosen model","text":"\nFigure 4.13: Bar-chart centrifuge test model (cases); left right, 1: B=6.5m,D/B=1.3; 2: B=6.5m,D/B=1; 3: B=4.5m,D/B=1.3; 4: B=4.5m,D/B=1; 5: B=3.5m,D/B=1.6; 6: B=6.5m,D/B=1.3; 7: B=6.5m,D/B=1; 8: B=4.5m,D/B=1.6; 9: B=4.5m,D/B=1.3; 10: B=4.5m,D/B=1; 11: B=3.5m,D/B=1.6; 12: B=3.5m,D/B=1.3\n","code":""},{"path":"comparison-with-centrifuge-experiment.html","id":"result-of-loaddisplacement-curves-of-the-centrifuge-measurement-with-emc-and-na-models","chapter":"4 Comparison with Centrifuge Experiment","heading":"4.1.0.1 Result of load—displacement curves of the centrifuge measurement with EMC and NA models","text":"\nFigure 4.14: Comparison centrifuge data EMC NA models\n","code":""},{"path":"list-of-loaddisplacement-curves.html","id":"list-of-loaddisplacement-curves","chapter":"A List of Load—Displacement Curves","heading":"A List of Load—Displacement Curves","text":"\nFigure .1: Cumulative load-displacement curves uplift plate anchor loose, medium, dense sands; D/B = 1,2,3; B=0.02m\n\nFigure .2: Cumulative load-displacement curves uplift plate anchor loose, medium, dense sands; D/B = 1,2,3; B=0.2m\n\nFigure .3: Cumulative load-displacement curves uplift plate anchor loose, medium, dense sands; D/B = 1,2,3; B=1.0m\n\nFigure .4: Cumulative load-displacement curves uplift plate anchor loose, medium, dense sands; D/B = 1,2,3; B=3.5m\n\nFigure .5: Cumulative load-displacement curves uplift plate anchor loose, medium, dense sands; D/B = 1,2,3; B=4.5m\n\nFigure .6: Cumulative load-displacement curves uplift plate anchor loose, medium, dense sands; D/B = 1,2,3; B=6.5m\n","code":""},{"path":"references-references.html","id":"references-references","chapter":"(REFERENCES) References","heading":"(REFERENCES) References","text":"","code":""},{"path":"references.html","id":"references","chapter":"B REFERENCES","heading":"B REFERENCES","text":"Wood, D. M. (2017). Geotechnical modelling. CRC press.Doherty, J. P., & Muir Wood, D. (2013). extended Mohr–Coulomb (EMC) model predicting settlement shallow foundations sand. Géotechnique, 63(8), 661-673.Gajo, ., & Wood, M. (1999). Severn–Trent sand: kinematic-hardening constitutive model: q–p formulation. Géotechnique, 49(5), 595-614.Krabbenhoft, S., Krabbenhoft, K., & Christensen, R. Limit analysis bearing capacity strip-circular footings layer sand overlying clay.Sakai, T., & Tanaka, T. (2007). Experimental numerical study uplift behavior shallow circular anchor two-layered sand. Journal geotechnical geoenvironmental engineering, 133(4), 469-477.Tanaka, T., & Sakai, T. (1993). Progressive failure scale effect trap-door problems granular materials. Soils Foundations, 33(1), 11-22.Sakai, T., & Tanaka, T. (1998). Scale effect shallow circular anchor dense sand. Soils Foundations, 38(2), 93-99.Sakai, T., & Tanaka, T. (2007). Experimental numerical study uplift behavior shallow circular anchor two-layered sand. Journal geotechnical geoenvironmental engineering, 133(4), 469-477.Riyad, . S. M., Rokonuzzaman, M., & Sakai, T. (2020). Progressive failure scale effect anchor foundations sand. Ocean Engineering, 195, 106496.Kumar, J., & Kouzer, K. M. (2008). Vertical uplift capacity horizontal anchors using upper bound limit analysis finite elements. Canadian Geotechnical Journal, 45(5), 698-704.Riyad, . S. M., Rokonuzzaman, M., & Sakai, T. (2020). Effect using different approximation models exact Mohr–Coulomb material model FE simulation Anchor Foundations sand. International Journal Geo-Engineering, 11(1), 1-21.Riyad, . S. M., Rokonuzzaman, M., & Sakai, T. (2020). Progressive failure scale effect anchor foundations sand. Ocean Engineering, 195, 106496.Roy, ., Chow, S. H., O’Loughlin, C. D., & Randolph, M. F. (2021). Towards simple reliable method calculating uplift capacity plate anchors sand. Canadian Geotechnical Journal, 58(9), 1314-1333.","code":""}]