Application of an elastoplastic spectral‐element method to 3D slope stability analysis

Gharti, Hom Nath; Komatitsch, Dimitri; Oye, Volker; Martin, Roland; Tromp, Jeroen

doi:10.1002/nme.3374

Cited by 33 publications

(25 citation statements)

References 108 publications

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“…s Further, the Equation (4) first expresses to weighted integral form and then follows integration by parts and rearranges the expressions simultaneously in the following form [18].…”

Section: Mathematical Foundationmentioning

confidence: 99%

“…The most important issue of SEM is the use of GLL quadrature for spatial integration, using the same points for interpolation and integration, and formation of diagonalized mass matrix. The SEM is a continuous Galerkin method, in which the interpolation function in the Equation (12), we obtain the following relation [18].…”

Section: Mathematical Foundationmentioning

confidence: 99%

“…In this relation,  and  vary from 1 to The elemental mass matrix can be further expressed with the integration based on GLL quadrature over the GLL points as follows [18]. side the elements in which the fields are described.…”

Section: Mathematical Foundationmentioning

confidence: 99%

“…The elemental mass matrix can be further expressed with using the orthogonality of the interpolation function in the following relation [18].…”

Section: Mathematical Foundationmentioning

confidence: 99%

“…To address the different degree of soil saturation and pore-water pressure, the following relation can be applied in aforesaid formulation [18].…”

Section: Mathematical Foundationmentioning

confidence: 99%

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High-Order FEM Formulation for 3-D Slope Instability

Chandra¹,

Prakash²,

Yatabe³

2013

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High-order finite element method (FEM) formulation also referred to as spectral element method (SEM) formulation is currently implemented in this paper for 3-dimensional (3-D) elasto-plastic problems in stability assessment of largescale slopes (vegetated and barren slopes) in different instability conditions such as seismic and saturation. We have reviewed the SEM formulation, and have sought its applicability for vegetated slopes. Utilizing p (high-order polynomial degree or spectral degrees) and h (mesh operation for quality meshing in required elemental budgets) refining techniques in the existing FEM, the complexity of problem domain can be well addressed in greater numerical stability. Unlike the existing FEM formulation, this high-order FEM employs the same integration and interpolation points to achieve a progressive response of the instability, which drastically reduces the computational costs (formation of diagonalized mass matrix) and offers significant benefits to slope instability computations for serial and parallel implementations. With this formulation, we have achieved the following three qualities in slope instability modeling: 1) geometric flexibility of the finite elements, 2) high computational efficiency, and 3) reliable spectral accuracy. A sample problem has also been presented in this paper, which has accommodated all aforesaid numerical qualities.

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“…s Further, the Equation (4) first expresses to weighted integral form and then follows integration by parts and rearranges the expressions simultaneously in the following form [18].…”

Section: Mathematical Foundationmentioning

confidence: 99%

Section: Mathematical Foundationmentioning

confidence: 99%

Section: Mathematical Foundationmentioning

confidence: 99%

“…The elemental mass matrix can be further expressed with using the orthogonality of the interpolation function in the following relation [18].…”

Section: Mathematical Foundationmentioning

confidence: 99%

“…To address the different degree of soil saturation and pore-water pressure, the following relation can be applied in aforesaid formulation [18].…”

Section: Mathematical Foundationmentioning

confidence: 99%

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High-Order FEM Formulation for 3-D Slope Instability

Chandra¹,

Prakash²,

Yatabe³

2013

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A meshed kinematical approach for 3D slope stability analysis

Gong

Tang

et al. 2022

Num Anal Meth Geomechanics

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The limit analysis method has been extensively recognized as an efficient tool for a quick estimate of slope stability. Its common practice is to divide the potential failure domain into one or more standard geometric shapes such as the slice method or horn failure mechanism. However, these methods are difficult to solve the problems with spatially varying soil properties, especially for the variation of soil internal friction angles. To solve this problem, a meshed kinematical approach is proposed in this study for 3D slope stability analysis. The proposed approach takes advantage of the spatial discretization technique to achieve the failure mechanism generation based on soil properties rather than a predetermined geometric shape. It also shares some boundary conditions with the well‐known horn failure mechanism to respect the theoretical framework of limit analysis. The obtained failure mechanism is meshed and composed of a large number of well‐arranged elements, which in turn gives it great flexibility and compatibility in integrating spatially discretized data or combining numerical simulation methods. For verification purposes, the proposed approach is tested by some hypothetical slope stability cases and compared with the horn failure mechanism. Two case studies, respectively, involving a multi‐layer slope and a slope subjected to pore water pressure, are presented to illustrate the practical application of the proposed approach. It is concluded that the meshed kinematical approach is effective for slope stability assessment, which can gain high computation accuracy with much less time consumption compared to the numerical simulations.

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Application of Spectral Element Method (SEM) in Slope Instability Analysis

Tiwari

Bhandary

2023

Progress in Landslide Research and Technology, Volume 1 Issue 1, 2022

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Spectral element framework for slope instability analysis includes Spectral Element Method (SEM) formulation, system requirements for serial and parallel computations, model preparation with hexahedral meshing in Cubit or Trelis, meshing and mapping technique (h- and p-refinement techniques) according to SEM, applying boundary conditions for 2D and 3D, defining inputs for material model, ground water table, seismic loading as well as processing and visualizing the results in Tecplot and ParaView. Within this framework, the safety factor in slope stability is computed and visualized with greater spectral accuracy and stability.

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Application of an elastoplastic spectral‐element method to 3D slope stability analysis

Abstract: International audienc

Cited by 33 publications

References 108 publications

High-Order FEM Formulation for 3-D Slope Instability

High-Order FEM Formulation for 3-D Slope Instability

A meshed kinematical approach for 3D slope stability analysis

Application of Spectral Element Method (SEM) in Slope Instability Analysis

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