Material Point Method Simulations Research Articles

Inrushing failure characteristics of deep shaft structures in soft soils based on material point method simulation

In areas with soft soil, inrushing may occur during the construction of deep shaft structures under high water pressures, causing destructive accidents. Most studies on inrushing have used the finite element method. However, it is difficult to achieve a large deformation simulation because of mesh limitations. The material point method is not constrained by the mesh, and the material properties and motion information of the material are stored at the material points. Therefore, it can be used to effectively simulate large soil deformations. In this study, a numerical model for a deep shaft structure in Shanghai was formulated using the material point method to simulate the evolution of inrushing failure. The likelihood of inrushing damage at different excavation depths was analyzed. Soil heave at the bottom of the pit in the absence of inrushing was examined. The structural and environmental factors affecting the inrushing process are discussed. Strategies have been proposed from different perspectives, such as structure, environment, and construction methods, to reduce the damage caused by inrushing, thereby providing a reference for the safer construction of deep shaft structures.

Material point method simulations of displacement pile and CPT penetration in sand considering the effects of grain breakage

Full displacement installation dramatically alters the stress and strain fields applying around piles and Cone Penetrometer (CPT) probes at sand sites. Calibration chamber tests have indicated that severe particle crushing occurs near to the pile or cone tips and a distinct shear zone may develop that leaves crushed sand adhering to the pile or cone shaft. It is therefore important to investigate how particle breakage affects the stress and deformation fields developed as this process occurs. In this study, installation by monotonic jacking of conically tipped model piles or CPT probes into silica sand is simulated by material point method (MPM) analyses. A thermodynamically consistent model which considers competing grain crushing and dilation is employed to model the sand behavior, while an MPM approach is adopted to cater for the large deformations involved in the penetration process. Particle crushing is predicted beneath the pile tip and around the pile shaft. The numerical results are compared to directly related instrumented pile calibration chamber tests. The numerical results show that the computed stress and displacement fields match key aspects of the experimental results well, especially in reproducing the volumetric compression observed experimentally. The results confirm that combining MPM with suitably sophisticated constitutive models creates new capabilities for analyzing large-deformation problems.

Stabilized mixed material point method for incompressible fluid flow analysis

This paper proposes novel and robust stabilization strategies for accurately modeling incompressible fluid flow problems in the material point method (MPM). To address the modeling of Newtonian fluids with incompressibility constraints, a new mixed implicit MPM formulation is proposed. Here, instead of solving the velocity and pressure fields as the unknown variables like the typical Eulerian computational fluid dynamics (CFD) solver, the proposed approach adopts a monolithic displacement–pressure formulation inspired by the mixed-form updated-Lagrangian Finite Element Method (FEM). To satisfy the inf–sup stability condition, two stabilization strategies are integrated into the formulation: the variational multiscale method (VMS) and the pressure-stabilization Petrov–Galerkin method (PSPG). By concurrently solving the displacement and pressure fields, the developed monolithic solver obviates the need for free-surface detection as well as Dirichlet and Neumann pressure imposition, in contrast to the fractional-step method. This attribute mitigates spurious pressure and velocity oscillations in simulating dynamic and transient flow problems. This study also addresses other prevalent challenges in MPM simulations, such as the pressure oscillations triggered by cell-crossing errors, particle-distribution-induced quadrature errors, and particle-grid information transfer. To resolve these issues, the quadratic B-Spline basis function, the delta-correction method, and the Taylor particle-in-cell method are incorporated into the proposed mixed MPM formulation, thereby enhancing numerical stability. The efficacy of the proposed stabilized incompressible MPM framework is validated through several benchmark cases, comparing the obtained results with other numerical methods and analytical solutions. Furthermore, the method’s capability in simulating real-world problems involving violent free-surface fluid motion is demonstrated through comparisons with experimental results of water sloshing and dam break scenarios.

MPM vs. CEL: Numerical modelling of penetration processes

MPM vs. CEL: Numerical modelling of penetration processes

Research on the Carter Method for the location of sliding surfaces based on a numerical study

In order to investigate the potential location and magnitude of a landslide, the information regarding the location and shape of the sliding surface is important. However, obtaining such information through underground investigations is costly and time-consuming. A method proposed by Carter and Bentley (1985) provides an approach to predict the sliding surface based on ground surface information. With help of advanced techniques such as UAVs and SAR satellites, Carter’s method has been utilized in field sites of potential landslide areas recently. Geophysical surveys and drilling data are commonly used validation data, but the temporal and spatial resolutions of these data are rough and rare. For this problem, this study generated high temporal and spatial resolution data of landslide behaviour by a physically based model and these data were utilized to investigate the capability and limitations of Carter’s method. Firstly, a scenario of slope failure on a 30-degree slope was performed by a numerical model using the material point method (MPM). Next, Carter’s method was applied to predicted the sliding surface using ground surface data obtained from the MPM simulation, and the results were compared with the sliding surface data from the MPM simulation. Finally, we perform an error analysis using the concordance correlation coefficient (CCC) to assess the reliability of Carter’s method. The findings of this study contribute to understanding the capabilities and limitations of Carter’s method in landslide analysis and provide insights for improving landslide risk assessment and mitigation strategies.

Coupled material point and level set methods for simulating soils interacting with rigid objects with complex geometry

The material point method (MPM) is often used to simulate soils that interact with (nearly) rigid objects, such as structures, machines, or rocks. Yet MPM simulations of such problems are quite challenging when the objects have complex shapes. In this paper, we propose an efficient approach for incorporating geometrically complex rigid objects into MPM modeling. The proposed approach leverages the level set method, which can efficiently delineate arbitrary surface geometry, to represent the boundary of a discrete object. For coupling the level set object with the MPM domain, a robust algorithm is developed on the basis of contact mechanics. Through numerical examples of varied complexity, we verify the proposed approach and demonstrate its ability to efficiently simulate challenging problems wherein soils interact with complex rigid objects such as debris-resisting baffles, a vehicle wheel, and basal terrain.

Material Point Simulation Method for Concrete Medium Fracture and Fragmentation under Blast Loading

The nature of the fracture and fragmentation processes in concrete medium under blast loading is the transformation of the medium from continuum to discontinuity. Coupled with the significant rate correlation of concrete medium, its mechanical behavior presents a high degree of complexity. When tackling this problem, the finite element method (FEM) frequently encounters problems such as grid distortion and even negative volume, whereas the material point method (MPM) can efficiently avoid these problems. Furthermore, the original Holmquist-Johnson-Cook (HJC) model does not take the segmented characteristics of the calculation function for the dynamic increasing factor into consideration. As a result, in this article, first, the calculation function for the dynamic increasing factor in the HJC model was modified by the Split-Hopkinson Pressure Bar (SHPB) experiment, and an improved HJC model was proposed; second, an MPM simulation program was developed, and the improved HJC concrete model was embedded into the simulation program; and finally, the simulation program was verified by numerical examples, and the results show that the developed simulation program can better simulate the fracture and fragmentation process of the concrete medium under blast loading, especially the pulverization characteristics of the medium in the near zone of the load.

Face stability analysis of tunnels in saturated soil considering soil-fluid coupling effect via material point method

The stability of the tunnel face has been an important issue investigated by many scholars. To fully study the failure evolution of tunnel face and the hydro-mechanical behavior of surrounding soils in saturated stratum, a two-phase single-point material point method (MPM) considering the fluid–solid coupling effect is adopted to investigate this issue. Firstly, this proposed method is validated by comparing with the results obtained from the existing literatures. Secondly a series of MPM simulations are carried out to study the critical support pressure and failure mechanism of tunnel face in saturated soils. The arching effect range and inclination angle of failure soil in front of tunnel face are analyzed and determined. Finally, the post-failure mechanism of tunnel face is investigated. The run-out distance and the flow-in mass of failed soil in tunnel are calculated through the parametric analysis. The results show that MPM can well predict the whole failure process of tunnel face. The proposed method can provide useful guidance for practical tunnel designs.

Two-Phase MPM Simulation of Surge Waves Generated by a Granular Landslide on an Erodible Slope

A high-speed debris flow sliding into a reservoir can cause a huge disaster. Consequently, predicting landslide movement accurately and its potential interaction with water is crucial. This paper developed a computational model based on a two–layer two–phase material point method (MPM) to simulate surge waves generated by granular landslides on an erodible slope. By comparing granular landslide on a rigid and erodible slope, the effect of the slope erodibility on the process of landslide movement and the waves generated is investigated. The model takes full account of the large deformations, fluidisation and settlement of granular material in soil–water interactions. The numerical model is validated by comparing the simulated results with experimental data. The influences of internal friction angle, density, elastic modulus, Poisson ratio and dilatancy angle on wave height are also studied. The validated model was then used to investigate the surge waves generated by dry and saturated granules sliding along a rigid and erodible slope. The results show that both the erodible slope and saturated granular slide can increase the first wave crest height generated by the landslide.

A Sparse Distributed Gigascale Resolution Material Point Method

In this article, we present a four-layer distributed simulation system and its adaptation to the Material Point Method (MPM). The system is built upon a performance portable C++ programming model targeting major High-Performance-Computing (HPC) platforms. A key ingredient of our system is a hierarchical block-tile-cell sparse grid data structure that is distributable to an arbitrary number of Message Passing Interface (MPI) ranks. We additionally propose strategies for efficient dynamic load balance optimization to maximize the efficiency of MPI tasks. Our simulation pipeline can easily switch among backend programming models, including OpenMP and CUDA, and can be effortlessly dispatched onto supercomputers and the cloud. Finally, we construct benchmark experiments and ablation studies on supercomputers and consumer workstations in a local network to evaluate the scalability and load balancing criteria. We demonstrate massively parallel, highly scalable, and gigascale resolution MPM simulations of up to 1.01 billion particles for less than 323.25 seconds per frame with 8 OpenSSH-connected workstations.

Modelling hydro-mechanical coupled behaviour of unsaturated soil with two-phase two-point material point method

Material point method (MPM) offers an effective approach for analysing large-deformation problems, such as landslides that often involve unsaturated soil. Several MPM formulations for unsaturated soil have been reported in the literature, but they assumed that water retention ability and permeability function are independent of soil deformation. Furthermore, most studies used a single set of material points, so they cannot simulate some processes (e.g., the infiltration of free water into unsaturated soil). To address these problems, a two-point MPM formulation has been extended from saturated to unsaturated soils, considering the influence of porosity change on the water retention curve and permeability function. The information of solid and liquid phases is carried by two individual sets of material points, assuming zero air pressure. The elastoplastic mechanical behaviour is modelled by the Drucker-Prager model using Bishop’s stress. The MPM simulations were compared with the results of physical model tests (for large-deformation problems) and finite element analysis (for small-deformation problems). It is evident that the proposed MPM formulation is able to capture various hydro-mechanical problems well. In particular, the computed failure processes of unsaturated soil slope under rainfall are consistent with results from physical model tests.

Two-layer two-phase material point method simulation of granular landslides and generated tsunami waves

Numerical modeling of the entire process of tsunamis generation by granular landslides is very difficult and challenging as it involves the soil–water interaction, large deformation of soil, and the fluidization and sedimentation of sand. In this study, a computational model based on the two-layer two-phase material point method (MPM) is developed to simulate granular-landslide-generated tsunamis, wherein the soil–water interaction, large deformation of soil, and fluidization and sedimentation of sand are well modeled. The soil behavior is described using a Mohr–Coulomb model with a non-associated flow rule, while the water is considered as weakly compressible. Furthermore, three different benchmark problems are simulated. All computed results well agree with the corresponding analytical solution and laboratory test data, verifying the effectiveness of the proposed two-layer two-phase MPM for modeling the subaerial and submerged granular-landslide-generated tsunamis. Additionally, the influence of different soil material parameters on the water wave generated by the subaerial granular landslide is investigated.

Comparison of Material Point Method and Finite Element Method for Post-Failure Large Deformation Geotechnical Analysis

Finite Element Method (FEM) has been the state-of-the-art method in geotechnical analysis since it first formulated in the 40s. It capable to handle Multiphysics simulation, soil-structure and soil-water interaction, and time history analysis. Though powerful, the standard Lagrangian FEM suffers mesh distortion when handling large strain deformation problem. This mesh entanglement problem makes post-failure analysis is considerably challenging to model if not impossible to do using FEM. The Material Point Method (MPM) then later introduced to solve these large strain deformation problems. Adapted from the Particle in Cell (PIC) method, MPM is a hybrid method that combines Eularian and Lagrangian approach by utilizing moving material points which are moving over spatially fixed computational mesh. This approach enables MPM to calculate not only fluid mechanics such in PIC but also solid mechanics and its intermediatory states. To demonstrate the capability of MPM and its consistency with FEM in geotechnical analysis, this article presents a comparison of FEM and MPM analysis on a hypothetical slope using Mohr-Coulomb constitutive model. The simulation shows that both FEM and MPM analyses are consistent to each other especially in small strain scheme. However, in large strain deformation, MPM is still able to get convergent result while FEM is not. The MPM simulation is also able to animate post failure behavior clearly, calculate post-failure strains and stresses distribution, and present final geometry of the model.

Axisymmetric particle-element coupled method for deformation problems of geomaterial

Although grid-based particle methods are widely used for engineering deformation problems, due to their robustness in large deformation analyses, the computational cost of these methods is quite high compared with mesh-based methods. In 3D problems, the computational cost becomes even higher, whereas some mechanical systems can be regarded as axisymmetric, allowing them to be modeled as two-dimensional axisymmetric entities, resulting in a reduced computation cost. In order to decrease the computational cost further, arbitrary spatial discretization has been introduced to reduce the degrees of freedom in the system. The Particle-Element Coupled Method (PEM), the coupled method of the Material Point Method (MPM) and the Arbitrary Particle Domain Interpolation (APDI) method, enables a system to be discretized in arbitrary spatial resolutions. In this paper, PEM is extended to axisymmetric problems, whose formulation and applicability to geomaterial deformation are presented. Firstly, the axisymmetric MPM simulation of a granular column collapse experiment and its efficiency in computation are reported. Secondly, in the simulation of footing penetration, it is shown that the axisymmetric MPM and the axisymmetric PEM can be used to analyze large deformations that cannot be analyzed by mesh-based methods, such as the Finite Difference Method (FDM). The axisymmetric PEM yields equivalent average pressure–displacement relationships and shear strain distributions, realizing a reduction in the computation cost by half as much.

Relating cone penetration resistance to sand state using the material point method

Cone penetration tests (CPTs) can quantitatively inform about the mechanical state of a sand. However, relating measured cone resistance values to sand state requires complex back-analysis of the processes occurring in the soil during the test. This paper provides new evidence of the value added in this area by modern large-deformation modelling based on the material point method (MPM). It is shown that accurate simulation of the relationship between cone resistance and sand state can be achieved, on condition that the constitutive behaviour of the soil – and especially its critical state features – is adequately modelled over a wide range of confining pressures. This study relies on the predictive capabilities of the critical state NorSand model, and shows how previous calibrations endeavours from the literature (based on triaxial test results) can support the MPM simulation of unrelated CPT results obtained through calibration chamber tests. MPM CPT simulations of ever-increasing quality will positively impact the state of the art of CPT interpretation procedures, to date still largely based on simplified cavity expansion theories.

Fully implicit, stabilised MPM simulation of large-deformation problems in two-phase elastoplastic geomaterials

The Material Point Method (MPM) has been gaining increasing popularity as an appropriate approach to the solution of coupled hydro-mechanical problems involving large deformations. This study extends the implicit GIMP-patch method for coupled poroelastic problems recently proposed by Zheng et al. (2021b) to tackle large-deformation problems in (nearly) isochoric elastoplastic geomaterials, particularly by remedying the numerical inaccuracies caused by volumetric locking, such as spurious stress oscillations and an excessively stiff overall response of the system at hand. To overcome these difficulties in two-phase coupled analyses, the B¯ approach of Hughes (1980) is incorporated into an existing version of the implicit GIMP-patch method. Details regarding the formulation and implementation of the proposed method are provided, while several benchmark problems are numerically analysed to evaluate its performance in the presence of elastoplastic behaviour. Particular emphasis is placed on (i) mitigating effective stress oscillations and (ii) solving several two-phase, coupled, large deformation geotechnical problems. The numerical results confirm the suitability of the implicit B¯ GIMP-patch method for the solution of geotechnical problems spanning weak to strong hydro-mechanical coupling and small to large deformations.

A material point method based investigation on crack classification and transformation induced by grit geometry during scratching silicon carbide

The microcracks and residual stress are commonly regarded as non-negligible obstacles while realizing non-damage surfaces in the grinding of brittle materials. In this paper, with the combination of stress field analysis, material point method simulation and high-speed scratch experiment, a variety of cracks in the classical indentation-induced crack system were decoupled to determine the inducing conditions and coupling modes of different cracks. The tests on pressureless sintered silicon carbide (S–SiC) exhibited that the grit geometry was crucial in inducing different cracks. The Hertzian and lateral crack systems were mainly determined by the rake angle of scratching grit and can transform from one to another near the critical value of −60°. Further, a two-point stress field model was proposed to prove that large contact width is the key factor to induce radial cracks. By contrast, large contact depth is related to the appearance of bottom debris. Furthermore, Raman spectroscopy was used to investigate the velocity effect of grit on cumulative damage. Besides the stacking disorder and residual stress, even chemical disorders such as the fracture of the Si–C bond and the formation of the homonuclear bond were found to be variable at the bottom of the scratch under different contact speeds and depths. Based on the above findings, a multi-layer superposition model was proposed to re-couple the effect of different cracks and predict the workpiece's damage/force state scratched by spherical grits. It proved that blunt grit could also realize low damage machining under specific conditions.

MPM Modeling of Cone Penetrometer Testing for Multiple Thin-Layer Effects in Complex Soil Stratigraphy

Cone penetrometer testing (CPT) is a frequently used soil characterization technique for liquefaction assessment; however, this technique has shortcomings in accurately characterizing very thin soil layers having thicknesses less than two to three times the diameter of the cone. In this study, the material point method (MPM) is used to generate numerical “measured” (or “blurred”) CPT tip resistance (qm) in complex soil profiles. Results show that MPM is capable of accurately simulating qm in soil profiles with layers as thin as 20 mm, even when using basic constitutive models and simplified drainage conditions. It is further shown that MPM simulations are able to replicate the tendency of the CPT to smear the boundaries between very thin, interbedded soil layers in a way that obscures their true thickness and stiffness (typically referred to as thin-layer, transition-zone, or multiple thin-layer effects). While previous numerical studies of CPT have been performed in profiles composed of two or three layers, this study considers highly interlayered profiles with upwards of 27 soil layers. Difficulties of developing and implementing multiple thin-layer corrections are presented. It is shown that a numerical framework like MPM can generate a larger set of data for the development and validation of multiple thin-layer correction procedures with the aim of improving liquefaction severity predictions in complex soil profiles.

Total Lagrangian Material Point Method simulation of the scratching of high purity coppers

In many industries, e.g., mining and agricultural industry, minerals handling, wear in machine elements causes functional surfaces to degrade, eventually leading to material failure or loss of functionality. To understand the abrasive wear resistance of materials scratch tests are sometimes conducted. However, the amount of information that can be obtained from well-defined scratch tests is limited due to the coupling of different physical processes, with a complex stress state. This paper presents a study of the Total Lagrangian Material Point Method (TLMPM) for the simulation of scratch tests. To this end we simulate the scratch of high purity coppers and compare with existing smooth particle hydrodynamics results and experiments. The results show that the TLMPM is stable for any indentation loads considered in the experiments and the results are in excellent agreement with experiments when friction is considered. Moreover, the results show the presence of oscillations in the groove profile at high loads, with and without friction. We show that the origin of these oscillations is linked to both the plastic strain and work hardening rates.

Multi-surfaced elasto-plastic wood material model in material point method

Wood is a naturally occurring material widely used for construction. Due to its natural origin, wood properties vary and its behaviour is complex. This paper shows an implementation of a multi-surface elasto-plastic constitutive material model for wood into a custom explicit material point method code. The constitutive model chosen is one proposed by Schmidt & Kaliske with minor modifications to ensure better internal consistency. The model parameters are chosen based on literature data for spruce. The paper presents two Convected Particle Domain Interpolation Material Point Method simulations of experiments, both performed with the previously established model parameters. The first simulation replicates a compression test of a spruce specimen perpendicular to grain direction, carried out at the Department of Civil Engineering, Aalto University. The second simulation replicates an experiment from literature, in which a spruce specimen with knots is tensioned until failure. The numerical simulations successfully replicate the experimental outcomes qualitatively in terms of the deformation and load-displacement curves. Simulations of the three knotted specimens under tension, with introduced slight variation in wood grain direction, replicate different failure patterns with a similar failure load, resembling the behaviour of natural wooden structural elements. Additionally, one of the obtained failure patterns replicates that of the experiment well.