Citation: | Xia Chengzhi, Shi Zhenming, Li Bo, Zheng Hongchao, Liu Maomao, 2022. Verification and Application of an Improved Smooth Particle Hydrodynamics Method for a Rock Slope under Seismic Conditions. Earth Science, 47(12): 4469-4483. doi: 10.3799/dqkx.2022.318 |
A smooth particle hydrodynamics (SPH) with an improved damage framework was proposed, called kernel-broken smoothed particle hydrodynamics (KBSPH), to simulate the crack propagation and fracture of rock slope under seismic conditions. In KBSPH, an improved damage framework was proposed, which improved the kernel function of damaged particles by introducing a fracture symbol, directly leading to the fracture of the virtual stress bonds of damaged particles. Therefore, the cracks were generated between the virtual bonds, and the crack propagation process of the rock mass is simulated. A double-layer boundary was developed by separating the dynamic boundary from the viscous boundary. Firstly, the dynamic characteristics of KBSPH were verified by thin plate vibration experiments. Secondly, the fracture mechanical properties of KBSPH were verified by a uniaxial compression test of a single fractured rock mass. Finally, the crack propagation process and dynamic response in the multi-joint rock slope under seismic conditions are simulated. The result shows that the thin plate vibration experiment verifies the accuracy of the dynamic characteristics of KBSPH. The uniaxial compression test of single-crack rock mass proves that KBSPH can correctly simulate airfoil cracks at the tip of prefabricated cracks. By comparing the previous numerical simulation methods and field cases, KBSPH correctly reveals the acceleration amplification effect and the crack propagation of the rock slope under earthquake conditions. KBSPH avoids the grid distortion of traditional algorithms and the redistribution of stress components of damaged particles. It reduces the difficulty of programming and improves the running speed. It infers that the KBSPH method is effective and shows promise for applications to more rock slopes under earthquake conditions and understanding of rock fracture mechanisms.
Abdelrazek, A. M., Kimura, I., Shimizu, Y., 2016. Simulation of the Erosion and Seepage Failure around Sheet Pile Using Two⁃Phase WC⁃SPH Method. Journal of Japan Society of Civil Engineers, Ser. A2 (Applied Mechanics (AM)), 72(2): I_495-I_504. https://doi.org/10.2208/jscejam.72.i_495
|
Al⁃Mukhtar, A. M., Merkel, B., 2015. Simulation of the Crack Propagation in Rocks Using Fracture Mechanics Approach. Journal of Failure Analysis and Prevention, 15(1): 90-100. https://doi.org/10.1007/s11668⁃014⁃9907⁃2
|
Antoci, C., Gallati, M., Sibilla, S., 2007. Numerical Simulation of Fluid⁃Structure Interaction by SPH. Computers & Structures, 85(11-14): 879-890. https://doi.org/10.1016/j.compstruc.2007.01.002
|
Bao, Y. J., Huang, Y., Liu, G. R., et al., 2020. SPH Simulation of High⁃Volume Rapid Landslides Triggered by Earthquakes Based on a Unified Constitutive Model. Part I: Initiation Process and Slope Failure. International Journal of Computational Methods, 17(4): 1850150. https://doi.org/10.1142/s0219876218501505
|
Behnia, M., Goshtasbi, K., Marji, M. F., et al., 2014. Numerical Simulation of Crack Propagation in Layered Formations. Arabian Journal of Geosciences, 7: 2729-2737. https://doi.org/10.1007/s12517⁃013⁃0885⁃6
|
Benz, W., Asphaug, E., 1994. Impact Simulations with Fracture. I. Method and Tests. Icarus, 107(1): 98-116. https://doi.org/10.1006/icar.1994.1009
|
Bi, J., Zhou, X. P., 2015. Numerical Simulation of Zonal Disintegration of the Surrounding Rock Masses around a Deep Circular Tunnel under Dynamic Unloading. International Journal of Computational Methods, 12(3): 1550020. https://doi.org/10.1142/s0219876215500206
|
Cao, P., Li, Y. S., Li, Z. L., et al., 2021. Geological Structure Characteristics and Genetic Mechanism of Baige Landslide Slope in Changdu, Tibet. Earth Science, 46(9): 3397-3409(in Chinese with English abstract).
|
Che, A. L., Yang, H. K., Wang, B., et al., 2016. Wave Propagations through Jointed Rock Masses and Their Effects on the Stability of Slopes. Engineering Geology, 201: 45-56. https://doi.org/10.1016/j.enggeo.2015.12.018
|
Crouch, S. L., 1976. Solution of Plane Elasticity Problems by the Displacement Discontinuity Method. I. Infinite Body Solution. International Journal for Numerical Methods in Engineering, 10(2): 301-343. https://doi.org/10.1002/nme.1620100206
|
Cundall, P. A., Strack, O. D. L., 1979. A Discrete Numerical Model for Granular Assemblies. Géotechnique, 29(1): 47-65. https://doi.org/10.1680/geot.1979.29.1.47
|
Fan, H., Huang, D. R., Wang, G., 2021. A Four⁃Way Enhanced Numerical Manifold Method for Crack Propagation and Failure Analysis of Rock Slopes. Applied Mathematical Modelling, 95: 623-643. https://doi.org/10.1016/j.apm.2021.02.025
|
Fortsakis, P., Nikas, K., Marinos, V., et al., 2012. Anisotropic Behaviour of Stratified Rock Masses in Tunnelling. Engineering Geology, 141-142: 74-83. https://doi.org/10.1016/j.enggeo.2012.05.001
|
Gingold, R. A., Monaghan, J. J., 1977. Smoothed Particle Hydrodynamics: Theory and Application to Non⁃Spherical Stars. Monthly Notices of the Royal Astronomical Society, 181(3): 375-389. https://doi.org/10.1093/mnras/181.3.375
|
Gray, J. P., Monaghan, J. J., Swift, R. P., 2001. SPH Elastic Dynamics. Computer Methods in Applied Mechanics and Engineering, 190(49-50): 6641-6662. https://doi.org/10.1016/s0045⁃7825(01)00254⁃7
|
He, C., Tang, H. M., Shen, P. W., et al., 2021. Progressive Failure Mode and Stability Reliability of Strain⁃Softening Slope. Earth Science, 46(2): 697-707(in Chinese with English abstract).
|
Hiraoka, N., Oya, A., Bui, H. H., et al., 2013. Seismic Slope Failure Modelling Using the Mesh⁃Free SPH Method. International Journal of Geomate, 5(1): 660-665. https://doi.org/10.21660/2013.9.3318
|
Huang, D., Cen, D. F., Ma, G. W., et al., 2015. Step⁃Path Failure of Rock Slopes with Intermittent Joints. Landslides, 12(5): 911-926. https://doi.org/10.1007/s10346⁃014⁃0517⁃6
|
Jaeger, J. C., 1971. Friction of Rocks and Stability of Rock Slopes. Géotechnique, 21(2): 97-134. https://doi.org/10.1680/geot.1971.21.2.97
|
Kang, J. T., Wu, Q., Tang, H. M., et al., 2019. Strength Degradation Mechanism of Soft and Hard Interbedded Rock Masses of Badong Formation Caused by Rock/Discontinuity Degradation. Earth Science, 44(11): 3950-3960 (in Chinese with English abstract).
|
Li, Z. S., Ju, N. P., Hou, W. L., et al., 2012. Large⁃Scale Shaking Table Model Tests for Dynamic Response of Steep Stratified Rock Slopes. Journal of Engineering Geology, 20(2): 242-248(in Chinese with English abstract). doi: 10.3969/j.issn.1004-9665.2012.02.013
|
Liao, Z. Y., Ren, M., Tang, C. N., et al., 2020. A Three⁃Dimensional Damage⁃Based Contact Element Model for Simulating the Interfacial Behaviors of Rocks and Its Validation and Applications. Geomechanics and Geophysics for Geo⁃Energy and Geo⁃Resources, 6(3): 1-21. https://doi.org/10.1007/s40948⁃020⁃00171⁃z
|
Libersky, L. D., Petschek, A. G., 2008. Smooth Particle Hydrodynamics with Strength of Materials. In: Trease, H. E., Fritts, M. F., Crowley, W. P., eds., Advances in the Free⁃Lagrange Method Including Contributions on Adaptive Gridding and the Smooth Particle Hydrodynamics Method. Lecture Notes in Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3⁃540⁃54960⁃9_58
|
Libersky, L. D., Petschek, A. G., Carney, T. C., et al., 1993. High Strain Lagrangian Hydrodynamics. Journal of Computational Physics, 109(1): 67-75. https://doi.org/10.1006/jcph.1993.1199
|
Liu, G. R., Liu, M. B., Li, S. F., 2004. Smoothed Particle Hydrodynamics: A Meshfree Method. Computational Mechanics, 33(6): 491. https://doi.org/10.1007/s00466⁃004⁃0573⁃1
|
Ma, G. W., Wang, X. J., Ren, F., 2011. Numerical Simulation of Compressive Failure of Heterogeneous Rock⁃Like Materials Using SPH Method. International Journal of Rock Mechanics and Mining Sciences, 48(3): 353-363. https://doi.org/10.1016/j.ijrmms.2011.02.001
|
Małkowski, P., 2015. The Impact of the Physical Model Selection and Rock Mass Stratification on the Results of Numerical Calculations of the State of Rock Mass Deformation around the Roadways. Tunnelling and Underground Space Technology, 50: 365-375. https://doi.org/10.1016/j.tust.2015.08.004
|
Monaghan, J. J., 1994. Simulating Free Surface Flows with SPH. Journal of Computational Physics, 110(2): 399-406. https://doi.org//10.1006/jcph.1994.1034
|
Monaghan, J. J., 2005. Smoothed Particle Hydrodynamics. Reports on Progress in Physics, 68(8): 1703-1759. https://doi.org/10.1088/0034⁃4885/68/8/R01
|
Shi, G. H., 1991. Manifold Method of Material Analysis. In: Transcations of the 9th Army Confernece on Applied Mathematics and Computing Minneapolis. U. S. Army Research Office, Minnesota, 57-76.
|
Shi, G. H., Goodman, R. E., 1989. Generalization of Two⁃Dimensional Discontinuous Deformation Analysis for Forward Modelling. International Journal for Numerical and Analytical Methods in Geomechanics, 13(4): 359-380. https://doi.org/10.1002/nag.1610130403
|
Sun, L., Grasselli, G., Liu, Q. S., et al., 2022. The Role of Discontinuities in Rock Slope Stability: Insights from a Combined Finite⁃Discrete Element Simulation. Computers and Geotechnics, 147: 104788. https://doi.org/10.1016/j.compgeo.2022.104788
|
VonNeumann, J., Richtmyer, R. D., 1950. A Method for the Numerical Calculation of Hydrodynamic Shocks. Journal of Applied Physics, 21(3): 232-237. https://doi.org/10.1063/1.1699639
|
Wang, J., Zhang, Y., Chen, Y., et al., 2021. Back-Analysis of Donghekou Landslide Using Improved DDA Considering Joint Roughness Degradation. Landslides; 18(5): 1925-1935. doi: 10.1007/s10346-020-01586-1
|
Wu, H., Atangana Njock, P. G., Chen, J. J., et al., 2019. Numerical Simulation of Spudcan⁃Soil Interaction Using an Improved Smoothed Particle Hydrodynamics (SPH) Method. Marine Structures, 66: 213-226. https://doi.org/10.1016/j.marstruc.2019.04.007
|
Xu, G. X., Yao, L. K., Li, Z. H., et al., 2008. Dynamic Response of Slopes under Earthquakes and Influence of Ground Motion Parameters. Chinese Journal of Geotechnical Engineering, 30(6): 918-923(in Chinese with English abstract). doi: 10.3321/j.issn:1000-4548.2008.06.022
|
Yadav, P., Sharan, S., 2019. Numerical Investigation of Squeezing in Underground Hard Rock Mines. Rock Mechanics and Rock Engineering, 52(4): 1211-1229. https://doi.org/10.1007/s00603⁃018⁃1632⁃9
|
Yang, S. Q., Jing, H. W., 2011. Strength Failure and Crack Coalescence Behavior of Brittle Sandstone Samples Containing a Single Fissure under Uniaxial Compression. International Journal of Fracture, 168(2): 227-250. https://doi.org/10.1007/s10704⁃010⁃9576⁃4
|
Yu, S., Ren, X., Zhang, J., et al., 2021a. An Improved Form of Smoothed Particle Hydrodynamics Method for Crack Propagation Simulation Applied in Rock Mechanics. International Journal of Mining Science and Technology, 31(3): 421-428. https://dio.org/10.1016/j.ijmst.2021.01.009 doi: 10.1016/j.ijmst.2021.01.009
|
Yu, S. Y., Ren, X. H., Zhang, J. X., et al., 2021b. An Improved Smoothed Particle Hydrodynamics Method and Its Application in Rock Hydraulic Fracture Modelling. Rock Mechanics and Rock Engineering, 54(12): 6039-6055. https://doi.org/10.1007/s00603⁃021⁃02594⁃w
|
Yu, S. Y., Ren, X. H., Zhang, J. X., et al., 2021c. Numerical Simulation on the Stability of Rock Slope Based on an Improved SPH Method. Journal of Mountain Science, 18 (7): 1937-1950. https://dio.org/10.1007/s11629⁃021⁃6739⁃x doi: 10.1007/s11629-021-6739-x
|
Zhou, X. P., Wang, Y. T., 2016. Numerical Simulation of Crack Propagation and Coalescence in Pre-Cracked Rock-Like Brazilian Disks Using the Non-Ordinary State-Based Peridynamics. International Journal of Rock Mechanics and Mining Sciences, 89: 235-249. https://doi.org/10.1016/j.ijrmms.2016.09.010
|
Zhou, X. P., Wang, Y. T., Qian, Q. H., 2016. Numerical Simulation of Crack Curving and Branching in Brittle Materials under Dynamic Loads Using the Extended Non⁃Ordinary State⁃Based Peridynamics. European Journal of Mechanics: A, 60: 277-299. https://doi.org/10.1016/j.euromechsol.2016.08.009
|
Zhou, X. P., Wang, Y. T., Shou, Y. D., et al., 2018. A Novel Conjugated Bond Linear Elastic Model in Bond⁃Based Peridynamics for Fracture Problems under Dynamic Loads. Engineering Fracture Mechanics, 188: 151-183. https://doi.org/10.1016/j.engfracmech.2017.07.031
|
Zhou, X. P., Zhao, Y., Qian, Q. H., 2015. A Novel Meshless Numerical Method for Modeling Progressive Failure Processes of Slopes. Engineering Geology, 192: 139-153. https://doi: 10.1016/j.enggeo.2015.04.005
|
曹鹏, 黎应书, 李宗亮, 等, 2021. 西藏昌都白格滑坡斜坡地质结构特征及成因机制. 地球科学, 46(9): 3397-3409. doi: 10.3799/dqkx.2020.333
|
何成, 唐辉明, 申培武, 等, 2021. 应变软化边坡渐进破坏模式及稳定性可靠度. 地球科学, 46(2): 697-707. doi: 10.3799/dqkx.2020.058
|
亢金涛, 吴琼, 唐辉明, 等, 2019. 岩石/结构面劣化导致巴东组软硬互层岩体强度劣化的作用机制. 地球科学, 44(11): 3950-3960. doi: 10.3799/dqkx.2019.110
|
李振生, 巨能攀, 侯伟龙, 等, 2012. 陡倾层状岩质边坡动力响应大型振动台模型试验研究. 工程地质学报, 20(2): 242-248. doi: 10.3969/j.issn.1004-9665.2012.02.013
|
徐光兴, 姚令侃, 李朝红, 等, 2008. 边坡地震动力响应规律及地震动参数影响研究. 岩土工程学报, 30(6): 918-923. https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC200806022.htm
|