Verification and Application of an Improved Smooth Particle Hydrodynamics Method for a Rock Slope under Seismic Conditions
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摘要:
开发一种改进损伤框架的粒子流算法，被称为核断裂的光滑粒子流法（kernel⁃broken smoothed particle hydrodynamics，KBSPH），用于模拟地震条件下岩质边坡的裂纹扩展和变形破坏过程.在KBSPH中，提出一种改进的损伤框架，通过引入断裂标志来改进损伤粒子的核函数，使损伤粒子的虚拟应力键直接断裂，裂纹在断裂的应力键间生成，从而模拟岩石的裂纹扩展过程.在地震边界上采用了双层边界，将动力输入边界与黏滞边界分离.首先通过薄板振动实验验证KBSPH的动力特性.其次以单裂隙岩体单轴压缩试验验证KBSPH的断裂力学特性.最后模拟地震条件下多节理岩质边坡中裂纹扩展过程和动力响应.薄板振动实验验证了KBSPH的动力特性的准确性.单裂隙岩体单轴压缩试验，证明了KBSPH可以正确模拟预制裂隙尖端的翼型裂纹.通过对比以往数值模拟方法和现场案例，表明KBSPH正确揭示了加速度放大效应以及地震条件下岩质边坡的裂纹扩展过程.KBSPH避免了传统算法的网格畸变，损伤粒子应力分量重新分配的问题，降低了编程难度，提高了运行速率，可为SPH在地震条件下岩石力学中的应用和理解岩石断裂机理提供一定的参考.
Abstract: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.
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图 1 离散方法和核函数原理示意
Fig. 1. Schematic illustration of the SPH discrete methods and kernel function
图 5 薄板动态位移过程
a.KBSPH模型；b.SPH模型（据Bao et al.，2020）
Fig. 5. Dynamic deformation process of the oscillating plate
图 6 自由端竖向位移的时程曲线
Fig. 6. Time history of vertical displacement for a point on the end of the oscillating plate
图 7 单预制裂隙岩样的模型尺寸和粒子分布
Fig. 7. Model size and base particle distribution of rock cell with a single prefabricated crack
图 8 KBSPH岩样结果及以往试验(Yang and Jing, 2011)对比
Fig. 8. KBSPH result and comparison with experiment result (Yang and Jing, 2011)
图 9 KBSPH边坡模型动力边界以及监测点(a)和粒子分布及岩桥特征(b)
Fig. 9. KBSPH slope model dynamic boundary and monitoring points (a), particle distribution and rock bridge characteristics (b)
图 11 裂隙岩体中坡顶与坡底的水平加速度、速度和位移时程曲线
Fig. 11. Time curves of horizontal acceleration, velocity, and displacements in fractured rock slope
图 12 岩桥水平应力时程曲线(未施加地震水平加速度)
Fig. 12. Time curves of horizontal stress of rock bridge without horizontal seismic acceleration applied
图 13 裂隙岩体的裂纹扩展以及位移云图(未施加地震水平加速度)
Fig. 13. Crack propagation and displacement cloud map of fractured rock mass without horizontal seismic acceleration applied
图 14 岩桥水平应力时程曲线(施加水平地震加速度)
Fig. 14. Time curves of horizontal stress of rock bridge with horizontal seismic acceleration applied
图 15 地震条件下裂隙岩体的裂纹扩展以及位移云图
c.对比IFDEM结果（Sun et al.，2022）；d.现场结果（Huang et al.，2015）
Fig. 15. Crack propagation and displacement cloud diagram of fractured rock mass under seismic conditions
表 1 数值模型与解析解的周期、最大振幅比较
Table 1. Comparison of analytic solution and SPH numerical simulation
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表 2 KBSPH岩坡模型的参数
Table 2. Parameters for KBSPH rock slope model
密度(kg/m3) 弹性模量(GPa) 泊松比 黏聚力(MPa) 内摩擦角(°) 抗拉强度(MPa) 基岩 2 700 10 0.25 1.0 38 0.8 节理 2 300 1 0.35 0.2 24 0.1
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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 -
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