Quasi-static collapse of two-dimensional granular columns: insight from continuum modelling

Xue, Zhang; Ding, Yutang; Sheng, Daichao; Sloan, Scott W.; Huang, Wenxiong

doi:10.1007/s10035-016-0643-z

Cited by 30 publications

(21 citation statements)

References 45 publications

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“…As such, the price to pay for the convenience of being able to operate with usual infinitesimal strain theory appears to be very small. It is also notable that the PFEM associated with the infinitesimal strain assumption has already been validated qualitatively as well as quantitatively against both quasi-static and dynamic collapse of granular columns in [22,23]. Furthermore, it succeeds in reproducing a real-world flow-like landslide [31].…”

Section: Particle Finite Element Methodsmentioning

confidence: 78%

“…It is apparent that the KKT conditions (19) - (22) are equivalent to the corresponding incremental equations presented in Appendix A. The last two conditions recover the yield condition and the complementarity condition shown in (A13) when → 0 + , given that the plastic multiplier Δ ⩾ 0, and s n+1 > 0.…”

Section: Generalised Hellinger -Reissner Variational Principlementioning

confidence: 74%

“…To date, a number of challenging problems involving large deformation and free-surface evolution have been tackled by the PFEM. These include the modelling of granular flows [22,23,43,51,52], landslides [31], landslide-generated waves [32,49], multi-fluid flows [53][54][55], fluid-structure interaction [29,56,57], soil -structure interaction [28,44,58], bubble dynamics [59], the melting Figure 4. Steps for the particle finite element method (after [43]).…”

Section: Particle Finite Element Methodsmentioning

confidence: 99%

“…The essential boundary condition (A3) is assumed to hold a priori and thus is not reflected in the KKT conditions. The KKT condition (22) indicates that the newly introduced variable r is the dynamic force.…”

Section: Generalised Hellinger -Reissner Variational Principlementioning

confidence: 99%

“…After finite element discretisation, the resulting problem can be converted into a standard second-order cone programming problem that may be solved efficiently using modern optimisation algorithms (for example, the primal-dual interior point method [18]). Typical advantages of such a solution strategy include the natural treatment of the singularities in the Mohr -Coulomb and Drucker -Prager yield criteria [19][20][21], the straightforward extension from single-surface plasticity to multi-surface plasticity [19], and the forthright implementation of contact between deformable and rigid bodies [22,23]. Additionally, it allows the analysis of the existence, uniqueness, sensitivity and stability of the solution [24].…”

mentioning

confidence: 99%

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Lagrangian modelling of large deformation induced by progressive failure of sensitive clays with elastoviscoplasticity

Xue

Sheng

Sloan

et al. 2017

Numerical Meth Engineering

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International audienceThis paper presents a Lagrangian formulation of elastoviscoplasticity, based on the Particle Finite Element Method, for progressive failure analysis of sensitive clays. The sensitive clay is represented by an elastoviscoplastic model which is a mixture of the Bingham model, for describing rheological behaviour, and the Tresca model with strain softening for capturing the progressive failure behaviour. The finite element formulation for the incremental elastoviscoplastic analysis is reformulated, through the application of the Hellinger-Reissner variational theorem, as an equivalent optimization program that can be solved efficiently using modern algorithms such as the interior-point method. The recast formulation is then incorporated into the framework of the Particle Finite Element Method for investigating progressive failure problems related to sensitive clays, such as the collapse of a sensitive clay column and the retrogressive failure of a slope in sensitive clays, where extremely large deformation occurs

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Section: Particle Finite Element Methodsmentioning

confidence: 78%

Section: Generalised Hellinger -Reissner Variational Principlementioning

confidence: 74%

Section: Particle Finite Element Methodsmentioning

confidence: 99%

Section: Generalised Hellinger -Reissner Variational Principlementioning

confidence: 99%

mentioning

confidence: 99%

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Lagrangian modelling of large deformation induced by progressive failure of sensitive clays with elastoviscoplasticity

Xue

Sheng

Sloan

et al. 2017

Numerical Meth Engineering

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Dynamic modelling of retrogressive landslides with emphasis on the role of clay sensitivity

Xue

Sloan

Oñate

2018

Num Anal Meth Geomechanics

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This paper presents a detailed numerical study of the retrogressive failure of landslides in sensitive clays. The dynamic modelling of the landslides is carried out using a novel continuum approach, the particle finite element method, complemented with an elastoviscoplastic constitutive model. The multiwedge failure mode in the collapse is captured successfully, and the multiple retrogressive failures that have been widely observed in landslides in sensitive clays are reproduced with the failure mechanism, the kinematics, and the deposition being discussed in detail. Special attention has been paid to the role of the clay sensitivity on each retrogressive failure as well as on the final retrogression distance and the final run-out distance via parametric studies. Moreover, the effects of the viscosity of sensitive clays on the failure are also investigated for different clay sensitivities.

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A novel coupled NS‐PFEM with stable nodal integration and polynomial pressure projection for geotechnical problems

Wang

Jin

Yin

et al. 2022

Num Anal Meth Geomechanics

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The node‐based smoothed particle finite element method (NS‐PFEM) offers high computational efficiency but is numerically unstable due to possible spurious low‐energy mode in direct nodal integration (NI). Moreover, the NS‐PFEM has not been applied to hydromechanical coupled analysis. This study proposes an implicit stabilised T3 element‐based NS‐PFEM (stabilised node‐based smoothed particle finite element method [SNS‐PFEM]) for solving fully hydromechanical coupled geotechnical problems that (1) adopts the stable NI based on multiple stress points over the smooth domain to resolve the NI instability of NS‐PFEM, (2) implements the polynomial pressure projection (PPP) technique in the NI framework to cure possible spurious pore pressure oscillation in the undrained or incompressible limit and (3) expresses the NI for assembling coefficient matrices and calculating internal force in SNS‐PFEM with PPP as closed analytical expressions, guaranteeing computational accuracy and efficiency. Four classical benchmark tests (1D Terzaghi's consolidation, Mandel's problem, 2D strip footing consolidation and foundation on a vertical cut) are simulated and compared with analytical solutions or results from other numerical methods to validate the correctness and efficiency of the proposed approach. Finally, penetration of strip footing into soft soil is investigated, showing the outstanding performance the proposed approach can offer for large deformation problems. All results demonstrate that the proposed SNS‐PFEM with PPP is capable of tracking hydromechanical coupled geotechnical problems under small and large deformation with different drainage capacities.

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Quasi-static collapse of two-dimensional granular columns: insight from continuum modelling

Cited by 30 publications

References 45 publications

Lagrangian modelling of large deformation induced by progressive failure of sensitive clays with elastoviscoplasticity

Lagrangian modelling of large deformation induced by progressive failure of sensitive clays with elastoviscoplasticity

Dynamic modelling of retrogressive landslides with emphasis on the role of clay sensitivity

A novel coupled NS‐PFEM with stable nodal integration and polynomial pressure projection for geotechnical problems

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