Numerical limit analysis of three-dimensional slope stability problems in catchment areas

Camargo, Julia T.; Neto, Guenther Schwedersky; Vargas, Edson

doi:10.1007/s11440-016-0459-3

Cited by 41 publications

(29 citation statements)

References 57 publications

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“…We use the mixed-formulation, second-order cone programming implementation of [38] to solve for the stress and velocity distributions in the three-dimensional finite element mesh of our hillslope. The mixed-formulation assumes stresses to be constant within each FE, while velocities in the u; v and w directions are varied linearly between neighboring nodes [50].…”

Section: Numerical Limit Analysismentioning

confidence: 99%

“…A summarizes the NLA method described by Camargo et al [38] and adopted herein for computation of the SF of the hillslope during the 22-day rainfall record.…”

Section: Numerical Limit Analysismentioning

confidence: 99%

“…For each element of the mesh, D i is a 6 Â 6 matrix, while vector d i has dimensions 6 Â 1. In a conic quadratic form, the collapse factor optimization problem now reads [38] maximize k subjet to G Á ðD À1 Á q À D À1 Á dÞ ¼ f þ kf h ; q i 2 K; i ¼ 1; . .…”

Section: ðA:3þmentioning

confidence: 99%

“…Note that it is numerically convenient to use f h in the equilibrium condition as this simplifies considerably our calculations of the SF. Please refer to [38] for a detailed description of the NLA method used in our study.…”

Section: ðA:4þmentioning

confidence: 99%

“…The model was calibrated against a rich data set of distributed bedrock depth measurements using Bayesian inference with the DREAM algorithm [36,37]. Posterior maps of the simulated bedrock depth topography serve as input to a threedimensional finite-element (FE) water flow model of the bedrock-soil domain, and are used to evaluate hillslope stability for a 22-day rainfall record via numerical limit analysis [38] using the ensemble of simulated transient pore water pressures. Our analysis will also consider soil hydraulic parameter uncertainty derived from pedotransfer functions using the Rosetta program [39].…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

The role of uncertainty in bedrock depth and hydraulic properties on the stability of a variably-saturated slope

Gomes

Vrugt

Vargas

et al. 2017

Computers and Geotechnics

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a b s t r a c tWe investigate the uncertainty in bedrock depth and soil hydraulic parameters on the stability of a variably-saturated slope in Rio de Janeiro, Brazil. We couple Monte Carlo simulation of a threedimensional flow model with numerical limit analysis to calculate confidence intervals of the safety factor using a 22-day rainfall record. We evaluate the marginal and joint impact of bedrock depth and soil hydraulic uncertainty. The mean safety factor and its 95% confidence interval evolve rapidly in response to the storm events. Explicit recognition of uncertainty in the hydraulic properties and depth to bedrock increases significantly the probability of failure.

show abstract

Section: Numerical Limit Analysismentioning

confidence: 99%

“…A summarizes the NLA method described by Camargo et al [38] and adopted herein for computation of the SF of the hillslope during the 22-day rainfall record.…”

Section: Numerical Limit Analysismentioning

confidence: 99%

Section: ðA:3þmentioning

confidence: 99%

Section: ðA:4þmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

The role of uncertainty in bedrock depth and hydraulic properties on the stability of a variably-saturated slope

Gomes

Vrugt

Vargas

et al. 2017

Computers and Geotechnics

View full text Add to dashboard Cite

show abstract

Intricacies in three‐dimensional limit analysis of earth slopes

Park

Michałowski²

2018

Num Anal Meth Geomechanics

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Summary Analyses of three‐dimensional slope failures can be elaborate because of the complexity owed to the geometry of the failure mechanism that needs to conform to an admissible kinematics of the slope collapse. This admissibility is imposed by the soil limit state condition, the normality plastic flow rule, and the boundary conditions. The kinematic approach of limit analysis is employed, and a rotational 3D slope failure is revisited. The study leads to the conclusion that some geometric constraints used in previous studies limit the range of admissible mechanisms resulting in overestimating stability factors. A set of results is presented that was obtained using an algorithm that allowed eliminating limitations present in previous studies. The largest improvements in the solutions were found for undrained failures of narrow slopes. For a 30° slope limited in width by the width‐to‐height ratio of 0.6, the stability factor calculated in previous studies overestimated the current calculations by nearly 39%. This overestimation is smaller for drained failures, and it drops significantly with an increase in the width of the failure mechanism.

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Mohr–Coulomb plasticity for sands incorporating density effects without parameter calibration

Choo

2018

Num Anal Meth Geomechanics

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Summary A simple approach is proposed for enabling the conventional Mohr–Coulomb plasticity to capture the effects of relative density on the behavior of dilative sands. The approach exploits Bolton's empirical equations to make friction and dilation angles state variables that depend on the current density and confining pressure. In doing so, the material parameters of Mohr–Coulomb plasticity become void ratios for calculating the initial relative density and the critical state friction angle, all of which are measurable without calibration. A Mohr–Coulomb model enhanced in this way shows good agreement with experimental data of different sands at various densities and confining pressures. In this regard, the proposed approach permits a significant improvement in the conventional Mohr–Coulomb plasticity for sands, without compromising its practical merits.

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Numerical limit analysis of three-dimensional slope stability problems in catchment areas

Cited by 41 publications

References 57 publications

The role of uncertainty in bedrock depth and hydraulic properties on the stability of a variably-saturated slope

The role of uncertainty in bedrock depth and hydraulic properties on the stability of a variably-saturated slope

Intricacies in three‐dimensional limit analysis of earth slopes

Mohr–Coulomb plasticity for sands incorporating density effects without parameter calibration

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