Large-displacement landslides based on affine velocity matrix-improved material point method

ZHONG Zu-liang; HE Kai-yuan; SONG Yi-xiang; ZHENG Yong

doi:10.11779/CJGE202209007

Volume 44 Issue 9

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Chinese Journal of Geotechnical Engineering > 2022 > 44(9): 1626-1634. > DOI: 10.11779/CJGE202209007

ZHONG Zu-liang, HE Kai-yuan, SONG Yi-xiang, ZHENG Yong. Large-displacement landslides based on affine velocity matrix-improved material point method[J]. Chinese Journal of Geotechnical Engineering, 2022, 44(9): 1626-1634. DOI: 10.11779/CJGE202209007

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Large-displacement landslides based on affine velocity matrix-improved material point method

1.
College of Civil Engineering, Chongqing University, Chongqing 400045, China
2.
National Joint Engineering Research Center of Geohazard Prevention in Reservoir Area, Chongqing University, Chongqing 400045, China
3.
School of Civil Engineering and Transportation, Hebei University of Technology, Tianjin 300401, China

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Received Date: June 29, 2021
Available Online: September 22, 2022

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Abstract

Abstract

In order to overcome the numerical noise problem of the material point method, the momentum mapping scheme of the affine particle-in-cell method is applied to the classical material point method, that is, in the process of momentum mapping, an additional affine velocity matrix is maintained, and then the velocity field represented by the affine velocity matrix and velocity vector of material point is constructed. It is proved that the affine velocity matrix is the first-order approximation of velocity gradient. The affine velocity matrix greatly simplifies the solving process of spin rate and rate of deformation as well as the computation process in a single time step, so that the computational efficiency is doubled. The Taichi programming language, which can be used for GPU parallel computing, is used for algorithm programming, which improves the solution efficiency hundreds of times. The effectiveness of the improved algorithm to overcome numerical noise, the numerical accuracy and the computational efficiency of the program are verified by simulating the natural stacking of sand columns and the stacking of aluminum rods. By simulating the landslide of a typical shape slope, the applicability and advantages of the algorithm and program in landslide analysis are verified.
- material point method,
- affine particle-in-cell method,
- Taichi programming language,
- landslide

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References

[1]	中国地质环境监测院地质灾害调查与监测室. 地质灾害调查与监测案例[EB/OL]. 中国地质环境信息网. Geological Disaster Investigation and Monitoring Office, Institute of Geological and Environmental Monitoring. Geological Disaster Investigation and Monitoring Cases[EB/OL]. China Geological Environment Information Site. (in Chinese)
[2]	SULSKY D, CHEN Z, SCHREYER H L. A particle method for history-dependent materials[J]. Computer Methods in Applied Mechanics and Engineering, 1994, 118(1/2): 179–196.
[3]	SOGA K, ALONSO E, YERRO A, et al. Trends in large-deformation analysis of landslide mass movements with particular emphasis on the material point method[J]. Géotechnique, 2016, 66(3): 248–273. doi: 10.1680/jgeot.15.LM.005
[4]	BRACKBILL J U, KOTHE D B, RUPPEL H M. FLIP: a low-dissipation, particle-in-cell method for fluid flow[J]. Computer Physics Communications, 1988, 48(1): 25–38. doi: 10.1016/0010-4655(88)90020-3
[5]	张雄, 廉艳平, 刘岩. 物质点法[M]. 北京: 清华大学出版社, 2013. ZHANG Xiong, LIAN Yan-ping, LIU Yan. Material Point Method[M]. Beijing: Tsinghua University Press, 2013. (in Chinese)
[6]	JIANG C, SCHROEDER C, SELLE A, et al. The affine particle-in-cell method[J]. ACM Transactions on Graphics, 2015, 34(4): 1–10. http://www.onacademic.com/detail/journal_1000038155784010_1b19.html
[7]	HARLOW F H. Particle-in-cell computing method for fluid dynamics[J]. Methods Comput Phys, 1964, 3: 319–343. http://www.researchgate.net/publication/247939887_The_Particle-in-Cell_computing_method_for_fluid_dynamics
[8]	HU Y M, FANG Y, GE Z H, et al. A moving least squares material point method with displacement discontinuity and two-way rigid body coupling[J]. ACM Transactions on Graphics, 2018, 37(4): 1–14. http://www.seas.upenn.edu/~cffjiang/research/mlsmpm/hu2018mlsmpm-tech.pdf
[9]	HU Y, LI T M, Anderson L, et al. Taichi: a language for high-performance computation on spatially sparse data structures[J]. ACM Transactions on Graphics, 2019, 38(6): 1–16. http://www.researchgate.net/publication/337118128_Taichi_a_language_for_high-performance_computation_on_spatially_sparse_data_structures
[10]	MAST C M. Modeling Landslide-Induced Flow Interactions with Structures Using the Material Point Method[D]. Washington: University of Washington, 2013.
[11]	JIANG Y, LI M, JIANG C, et al. A hybrid material-point spheropolygon-element method for solid and granular material interaction[J]. International Journal for Numerical Methods in Engineering, 2020, 121(14): 3021–3067. doi: 10.1002/nme.6345
[12]	BARDENHAGEN S G. Energy conservation error in the material point method for solid mechanics[J]. Journal of Computational Physics, 2002, 180(1): 383–403. doi: 10.1006/jcph.2002.7103
[13]	KlÁR G, GAST T, PRADHANA A, et al. Drucker-Prager elastoplasticity for sand animation[J]. ACM Transactions on Graphics (TOG), 2016, 35(4): 1–12. http://web.cecs.pdx.edu/~fliu/seminar/flyer-teran.pdf
[14]	MAST C M, ARDUINO P, MACKENZIE-HELNWEIN P, et al. Simulating granular column collapse using the material point method[J]. Acta Geotechnica, 2015, 10(1): 101–116. doi: 10.1007/s11440-014-0309-0
[15]	BUI H H, FUKAGAWA R, SAKO K, et al. Lagrangian meshfree particles method (SPH) for large deformation and failure flows of geomaterial using elastic-plastic soil constitutive model[J]. International Journal for Numerical and Analytical Methods in Geomechanics, 2008, 32(12): 1537–1570. doi: 10.1002/nag.688
[16]	孙玉进. 岩土大变形问题的物质点法研究[D]. 北京: 清华大学, 2017. SUN Yu-jin. Research on Geotechnical Problems Involving Extremely Large Deformation Using the Material Point Method[D]. Beijing: Tsinghua University, 2017. (in Chinese)
[17]	孙玉进, 宋二祥. 大位移滑坡形态的物质点法模拟[J]. 岩土工程学报, 2015, 37(7): 1218–1225. https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC201507008.htm SUN Yu-jin, SONG Er-xiang. Simulation of large-displacement landslide by material point method[J]. Chinese Journal of Geotechnical Engineering, 2015, 37(7): 1218–1225. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC201507008.htm
[18]	吴方东, 张巍, 史卜涛, 等. 堆载诱发型土质滑坡运动特征物质点法模拟[J]. 水文地质工程地质, 2017, 44(6): 126–134. https://www.cnki.com.cn/Article/CJFDTOTAL-SWDG201706020.htm WU Fang-dong, ZHANG Wei, SHI Bu-tao, et al. Run-out characteristic simulation of a surcharge-induced soil landslide using the material point method[J]. Hydrogeology & Engineering Geology, 2017, 44(6): 126–134. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-SWDG201706020.htm