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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