Research PaperReseeding of particles in the material point method for soil–structure interactions
Introduction
Large deformation problems are frequently encountered in geotechnical practices, which include the impact of submarine landslides on pipelines (Dong et al. 2017), free-falling torpedo anchors penetrating into seabed (Kim et al. 2018), and the dynamic installation of suction caissons (Cox et al. 2014). To avoid excessive mesh distortion in the simulation of large deformation problems, Lagrangian methods seek to remesh periodically and interpolate field variables from the old meshes to the new ones (Hu and Randolph, 1998, Wang et al., 2013, Zhang et al., 2013, Tian et al., 2014); Eulerian methods allow the material to flow through a fixed spatial mesh by decoupling the mesh and material movement (Qiu and Grabe, 2012, Zheng et al., 2014); and arbitrary Lagrangian Eulerian (ALE) methods combine the merits of the Lagrangian and Eulerian approaches (Di et al., 2007, Nazem et al., 2008).
The material point method (MPM), originated from the particle-in-cell method in computational fluid dynamics (CFD) (Harlow 1964) and then extended to solid mechanics (Sulsky et al. 1995), falls into the category of the ALE methods. The material in the MPM is represented by a cloud of discrete particles that inherit history-dependent information such as mass, volume, density, velocities, deformation gradients, and stresses. A fixed Eulerian mesh is used to calculate the governing equations in each incremental step without carrying permanent information. The large deformation of the material can be derived by tracking the particles moving through the background mesh. The MPM has been applied to mimic the flow of granular materials (Bardenhagen et al. 2000), the evolution of subaerial and submarine landslides (Andersen and Andersen, 2010, Soga et al., 2016), the dynamic process of pile driving (Hamad 2016), and the large-amplitude displacement of structural elements through soil (Phuong et al. 2016).
However, the large deformation of the material entangles the particles from the initial uniform arrangement, often causing artificial voids among stretched particles or virtual particle aggregations in compressive domains (Ando et al., 2012, Sołowski and Sloan, 2015, Yue et al., 2015), somehow similar to mesh distortion in the conventional finite element method (Hu and Randolph, 1998, Wang et al., 2013). Also, virtual interpenetration or departure between soil and structure particles may be induced by the ‘penalty’ contact algorithm adopted, although other contact algorithms are also available, such as moving-mesh contact (Ceccato et al. 2016) and generalised frictional contact (Nairn et al. 2018). The varied particle arrangements may introduce numerical noises given the loss of the continuity of the stress field or the singular deformation gradient of the particles. As a result, computational robustness and accuracy tend to be undermined (Steffen et al. 2010). For instance, convergence is not necessarily enhanced with mesh fineness (Liang et al. 2019). Techniques splitting particles in sparse domains and merging particles in dense areas were then developed, Tan and Nairn, 2002, Ma et al., 2009 in the simulation of high-energy explosions as well as Ando et al., 2012, Yue et al., 2015, and Gao et al. (2017) for computer animations. Most of the previous explorations of the rearrangement of particles were based on a qualitative description and limited to visual treatment, which needs to be enhanced for the quantitative analysis of soil–structure interactions in terms of mitigating the fluctuations of contact force.
In this paper, a technique for reseeding particles specialised for soil–structure interactions based on explicit integration is presented. The reseeding operation is performed in elements depending on the number of the accommodated particles and their accumulated deformations. The state variables of the reseeded particles are recovered from their surrounding old counterparts. The stresses of the reseeded particles are adjusted to mitigate the fluctuations of contact force from errors in the state recovery. Then benchmark problems of deep penetration of a wished-in-place T-bar and the dynamic impact of a submarine landslide on a partially buried mudmat are analysed.
Section snippets
Standard material point method
The standard MPM analyses were undertaken using an in-house program, MPM-GeoFluidFlow, which stems from an open-source package, Uintah (Guilkey et al. 2012), and features a novel contact algorithm ‘Geo-contact’ (Ma et al. 2014), as well as a GPU parallel computing strategy (Dong et al., 2015b, Dong and Grabe, 2018). Meshes with identical sizes of square elements were used. The explicit updated Lagrangian calculation in each incremental step was based on the GIMP method presented by Bardenhagen
Tracking of soil boundary
The soil domain needs to be outlined before the reseeding of the particles inside. Previous studies include those by Remmerswaal (2017) based on the support domain of particles and Bing et al. (2019) using the B-spline. A new scheme is used here based on the engagement of elements, which are categorised into inner, boundary and outer individuals. An empty element with no particle inside is seen as an outer element. An engaged element is distinguished as inner if all the surrounding elements
Deep penetration of T-bar
For in-situ geotechnical investigation under deep waters, the T-bar (Fig. 4(a)), a penetrometer with no requirement of extra correlation of the penetration resistance by mobilising the full-flow failure mechanism in the surrounding soil (Fig. 4(b)), has been proven to be more accurate than the conventional vane shear test and cone penetration test (Randolph and Houlsby, 1984, Einav and Randolph, 2005). The shallow penetration of structures (less than half the diameter or width of the structure)
Conclusions
A technique for reseeding particles in an entangled arrangement was presented, specialised for soil–structure interactions. The reseeding operation was performed in inner lattices, i.e. quarter elements, depending on the number of accommodated particles and their deformed lengths. The state variables of the reseeded particles were recovered from their original neighbours. The stresses of the reseeded particles around the structure were adjusted to reduce the errors in the new stress field and
CRediT authorship contribution statement
Y. Dong: Conceptualization, Methodology, Validation, Formal analysis, Writing - original draft, Writing - review & editing.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements
This paper was supported by the National Natural Science Foundations of China (Grant No. 51909248) and the Open Research Fund of State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences (Grant No. Z018011).
This work was also supported by the NVIDIA Corporation with the donation of the GPUs Geforce Titan Xp and GeForce Titan V.
The author would also like to acknowledge the valuable input of Profs. Mark Randolph and Yuxia
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An improved quadrature scheme in B-spline material point method for large-deformation problem analysis
2022, Engineering Analysis with Boundary ElementsCitation Excerpt :The combination of the merits of both Lagrangian and Eulerian methods makes the MPM quite suitable for solving solid mechanics problems with large deformations [3,4], material discontinuity [5,6], and multiphase interaction [7,8] that are challenging for the traditional mesh-based methods such as finite element method (FEM) and finite difference method (FDM), and finite volume method (FVM) [9]. Since the introduction in the 1990s [1,2], the MPM has gained significant progress and been used in many scientific and engineering problems, e.g., penetration and contact [10–12], explosion [13,14], crack propagation [15,16], landslide [17–19], fluid-structure interaction [20–22], thermomechanics [23,24], large deformation elasto-plasticity [25,26], geological engineering [27–29], etc. It has been demonstrated that there exists numerical noise in the original MPM when the particles move across the background cell boundary [30].