Evaluation of material point method for use in geotechnics

Sołowski, Wojciech Tomasz; Sloan, Scott W.

doi:10.1002/nag.2321

Cited by 93 publications

(63 citation statements)

References 33 publications

(81 reference statements)

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“…MPM can be seen as an ALE FEM in which all computational variables, including mass, are stored in every single material point. Its application to geotechnical engineering has been discussed and demonstrated by Solowski and Sloan [35]. Its ability to tackle fluid-like behaviours of granular material has been demonstrated by Wieckowski [42].…”

Section: Simulating the Column Collapsementioning

confidence: 99%

“…However, the SPH simulation required a large number of particles to obtain an accurate run-out distance making it computationally more expensive. Solowski and Sloan [34,35] compared MPM simulations with the experimental data of Lube et al [23] and showed that the Mohr-Coulomb model did not dissipate sufficient energy. Hence, the run-out distances were largely overestimated and numerical damping had to be applied in order to match the experimental results.…”

Section: Simulating the Column Collapsementioning

confidence: 99%

“…Many MPM simulations presented in the literature used simple failure criteria such as Mohr-Coulomb (e.g. [1,3,16,34,35]). The model parameters were chosen as being close to the critical state values (u 0 % u 0 cs and w % 0) favouring the large strained areas and neglecting their mechanical behaviour at small strains.…”

Section: Constitutive Modelling For Large Deformationmentioning

confidence: 99%

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The role of constitutive models in MPM simulations of granular column collapses

Fern

Soga

2016

Acta Geotech.

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The granular column collapse is a well-established experiment which consists of having a vertical column of granular material on a flat surface and letting it collapse by gravity. Despite its simplicity in execution, the numerical modelling of a column collapse remains challenging. So far, much attention has been dedicated in assessing the ability of various numerical methods in modelling the large deformation and little to the role of the constitutive model on both the triggering mechanism and the flow behaviour. Furthermore, the influence of the initial density, and its associated dilatancy and strength characteristics, have never been included in the analyses. Most past numerical investigations had relied on simple constitutive relations which do not consider the softening behaviours. The aim of this study is to illustrate the influence of the constitutive model on the on-set of failure, the flow behaviour and the deposition profile using the material point method. Three constitutive models were used to simulate the collapse of two granular columns with different geometries and for two densities. The results of the simulations showed that the constitutive model had a twofold influence on the collapse behaviour. It defined the volume of the mobilised mass which spread along the flat surface and controlled the dissipation of its energy. The initial density was found to enhance the failure angle and flow behaviours and was more significant for small columns than for larger ones. The analysis of the potential energy of the mobilised mass explained the existence of two collapse regimes.

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Section: Simulating the Column Collapsementioning

confidence: 99%

Section: Simulating the Column Collapsementioning

confidence: 99%

Section: Constitutive Modelling For Large Deformationmentioning

confidence: 99%

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The role of constitutive models in MPM simulations of granular column collapses

Fern

Soga

2016

Acta Geotech.

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“…As the mass carried by each material point is assumed unchanged throughout the computation, the conservation of mass is implicitly satisfied. The motion and deformation are assumed to be governed by the momentum equations, and its weak form can be written as:

\int_{Ω} ρ bold-italica \cdot δ bold-italicv d bold-italicx + \int_{Ω} 𝛔 : \nabla δ bold-italicv d bold-italicx = \int_{Ω} ρ bold-italicb \cdot δ bold-italicv d bold-italicx + \int_{\partial normalΩ} 𝛕 \cdot δ bold-italicv d S,

where “·” denotes first‐order vector contraction, “:” represents second‐order tensor contraction, “∇” denotes the gradient operator, ρ is current mass density, a is the acceleration, δ v is an admissible velocity field, σ is the Cauchy stress, b is the body force, τ is the boundary traction, and Ω and ∂ Ω represent the entire current domain of continuum and its boundary, respectively.…”

Section: Hierarchical Coupling Of Mpm and Dem: Formulation And Methodmentioning

confidence: 99%

Multiscale modeling of large deformation in geomechanics

Liang

Zhao

2019

Num Anal Meth Geomechanics

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Summary Large deformation soil behavior underpins the operation and performance for a wide range of key geotechnical structures and needs to be properly considered in their modeling, analysis, and design. The material point method (MPM) has gained increasing popularity recently over conventional numerical methods such as finite element method (FEM) in tackling large deformation problems. In this study, we present a novel hierarchical coupling scheme to integrate MPM with discrete element method (DEM) for multiscale modeling of large deformation in geomechanics. The MPM is employed to treat a typical boundary value problem that may experience large deformation, and the DEM is used to derive the nonlinear material response from small strain to finite strain required by MPM for each of its material points. The proposed coupling framework not only inherits the advantages of MPM in tackling large deformation engineering problems over the use of FEM (eg, no need for remeshing to avoid mesh distortion in FEM), but also helps avoid the need for complicated, phenomenological assumptions on constitutive material models for soil exhibiting high nonlinearity at finite strain. The proposed framework lends great convenience for us to relate rich grain‐scale information and key micromechanical mechanisms to macroscopic observations of granular soils over all deformation levels, from initial small‐strain stage en route to large deformation regime before failure. Several classic geomechanics examples are used to demonstrate the key features the new MPM/DEM framework can offer on large deformation simulations, including biaxial compression test, rigid footing, soil‐pipe interaction, and soil column collapse.

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“…However, the aforementioned computational methods are restricted to the small strain range. If large deformation problems are to be solved, particle or meshfree methodologies arise as suitable alternatives for simulating such problems . The name of “meshfree methods” comes from the fact that they do not rely on meshes but on points to approximate functions and differential operators.…”

Section: Introductionmentioning

confidence: 99%

Optimal transportation meshfree method in geotechnical engineering problems under large deformation regime

Navas

López‐Querol

et al. 2018

Numerical Meth Engineering

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Summary Meshfree methods have been demonstrated as suitable and strong alternatives to the more standard numerical schemes such as finite elements or finite differences. Moreover, when formulated in a Lagrangian approach, they are appropriate for capturing soil behavior under high‐strain levels. In this paper, the optimal transportation meshfree method has been applied for the first time to geotechnical problems undergoing large deformations. All the features employed in the current methodology (ie, F‐bar, explicit viscoplastic integration, and master‐slave contact) are described and validated separately. Finally, the model is applied to the particular case of shallow foundations by using von Mises and Drucker‐Prager yield criteria to find the load at failure in the. The presented methodology is demonstrated to be robust and accurate when solving this type of problems.

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Evaluation of material point method for use in geotechnics

Cited by 93 publications

References 33 publications

The role of constitutive models in MPM simulations of granular column collapses

The role of constitutive models in MPM simulations of granular column collapses

Multiscale modeling of large deformation in geomechanics

Optimal transportation meshfree method in geotechnical engineering problems under large deformation regime

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