Second-order cone programming formulation for consolidation analysis of saturated porous media

Xue, Zhang; Sheng, Daichao; Sloan, Scott W.; Krabbenhøft, K.

doi:10.1007/s00466-016-1280-4

Cited by 38 publications

(24 citation statements)

References 67 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Although the problem in this study is simulated under undrained conditions using total stresses, an effective stress analysis can also be performed. This can be achieved by merging the SOCP formulation for consolidation analysis of saturated porous media introduced in [21], where rate-independent models are utilised, with the mixed variational principle presented in this paper. The resulting formulation then can be incorporated into the PFEM for investigating the hydro-mechanical mechanism in the progressive failure of sensitive clays.…”

Section: Discussionmentioning

confidence: 99%

“…We present here the generalised incremental HR variational principle for incremental elastoviscoplastic analysis. Similar to the HR variational principle for elastostatics [21], the HR variational principle for incremental elastoviscoplasticity can be expressed in the form of a min-max programme:…”

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%

“…While it may be solved in a number of ways using either general or specialised methods, it is transformed here into a second-order cone program (SOCP) and then resolved using the high-performance optimisation solver MOSEK [18]. The transformation of programmes of the same type as (37) into a SOCP is straightforward and has been documented in detail in [21,37]. The main operation is to recast the quadratic terms in the objective function to linear ones, subject to a quadratic constraint, and to reform the yield function as a cone.…”

mentioning

confidence: 99%

“…The main operation is to recast the quadratic terms in the objective function to linear ones, subject to a quadratic constraint, and to reform the yield function as a cone. Owing to the attractive advantages presented in the introduction, a variety of mechanics problems have been formulated and solved in such a manner, including computational limit analysis of solids and plates [39][40][41], static/dynamic analysis of elastoplastic frames and solids [19,[42][43][44], analysis of steady-state non-Newtonian fluid flows [45], consolidation analysis [21] and the analysis of granular contact dynamics [38,46,47]. 973…”

mentioning

confidence: 99%

See 4 more Smart Citations

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

Xue

Sheng

Sloan

et al. 2017

Numerical Meth Engineering

Self Cite

View full text Add to dashboard Cite

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

show abstract

Section: Discussionmentioning

confidence: 99%

Section: Generalised Hellinger -Reissner Variational Principlementioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

See 3 more Smart Citations

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

Xue

Sheng

Sloan

et al. 2017

Numerical Meth Engineering

Self Cite

View full text Add to dashboard Cite

show abstract

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

View full text Add to dashboard Cite

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.

show abstract

Geotechnical analysis involving strain localization of overconsolidated soils based on unified hardening model with hardening variable updated by a composite scheme

Tang,

Chen,

Cui

et al. 2024

Num Anal Meth Geomechanics

View full text Add to dashboard Cite

Strain localization simulation of overconsolidated soils with high overconsolidation ratio (OCR) has been a long‐standing challenge. Some critical state soil models, including the modified Cam‐clay (MCC) model, have been widely applied, but they may not predict the shear dilatancy of overconsolidated soils well in some cases. Hence, the unified hardening (UH) model, which may be viewed as a generalized version of the MCC model, is implemented. It has been recognized, nonetheless, that without resorting to the regularization mechanism, the standard finite element method (FEM) or the second‐order cone programming optimized finite element method (FEM‐SOCP) often experiences instability or interruption of calculating the hardening‐softening responses of overconsolidated soils. To resolve the aforementioned difficulty, the UH model is developed and implemented in the framework of FEM‐SOCP based on the micropolar continuum (mpcFEM‐SOCP) to predict strain localizations of overconsolidated soils. Furthermore, to obviate non‐convexity of mpcFEM‐SOCP induced by material softening, an effective composite update scheme of hardening variable pc, which refers to the implicit variable (IV) scheme for the hardening stage and then refers to the explicit variable (EV) scheme for the softening stage, is proposed. Based on one biaxial compression problem and one rigid strip footing problem, numerical analyses disclose that by applying mpcFEM‐SOCP in conjunction with the composite update scheme of pc, the UH model of micropolar continuum can effectively predict the strain localization behavior of overconsolidated soil during its failure stage, and the stable hardening‐softening responses of overconsolidated soils can be readily attained.

show abstract

Second-order cone programming formulation for consolidation analysis of saturated porous media

Cited by 38 publications

References 67 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

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

Geotechnical analysis involving strain localization of overconsolidated soils based on unified hardening model with hardening variable updated by a composite scheme

Contact Info

Product

Resources

About