An Improved SPH Method Based on Strength Reduction to Simulate Entire Process of Joint Slope Failure
-
摘要:
裂隙岩质边坡失稳是重大地质灾害，其破坏涉及裂纹萌生、扩展与滑移耦合过程.传统数值方法难以兼顾连续破裂与非连续接触的模拟，且存在网格畸变、参数标定复杂等局限.开发了一种基于强度折减以及核函数改进的三维SPH算法，用于模拟三维裂隙岩体边坡破裂和裂纹扩展以及接触滑移全过程.在改进三维SPH方法中，通过强度折减以及带拉伸截断的摩尔库伦破坏准则实现了裂纹萌芽的判断，通过在改进的核函数内引入损伤标志，实现岩体的裂纹扩展，随后引入了损伤粒子点点三维接触准则，构建完整粒子和断裂粒子三维间接触力.首先采用三维单轴压缩试验来验证算法的可行性，并测定了不同倾角的单裂隙岩体的脆性断裂特征.随后将改进的SPH法以及强度折减理论运用于考虑不同节理倾角的多节理岩质边坡，模拟三维裂隙岩质滑坡破坏过程并评估其稳定性.研究结果表明基于强度折减改进的SPH方法在模拟三维裂隙岩坡破坏以及稳定性问题上具有计算效率高、参数标定少以及准确率高的优点，且该方法可被用于评估其他带结构面的岩质边坡的稳定性.
Abstract:The instability of fractured rock slopes is a major geological disaster, and its failure involves the coupling process of crack initiation, propagation and slip. Traditional numerical methods are unable to simultaneously simulate continuous fracture and discontinuous contact, and they have limitations such as grid distortion and complex parameter calibration. A three-dimensional SPH algorithm based on strength reduction and kernel function improvement is developed to simulate the entire process of fracture, crack propagation and contact slip of three-dimensional fractured rock mass slopes. In the improved three-dimensional SPH method, the determination of crack germination was achieved through strength reduction and the Mohr-Coulomb violation criterion with tensile truncation. The crack propagation of rock mass was realized by introducing damage marks in the improved kernel function. Subsequently, the three-dimensional contact criterion of damage particle dots was introduced to construct the three-dimensional contact force between intact particles and fractured particles. Firstly, three-dimensional uniaxial compression tests were adopted to verify the feasibility of the algorithm, and the brittle fracture characteristics of single-fracture rock masses with different inclinations were determined. Subsequently, the improved SPH method and the strength reduction theory were applied to multi-joint rock slopes considering different joint inclination angles to simulate the failure process of three-dimensional fractured rock landslides and evaluate their stability. The research results show that the improved SPH method based on strength reduction has the advantages of high computational efficiency, less parameter calibration and high accuracy in simulating the failure and stability of three-dimensional fractured rock slopes. Moreover, this method can be used to evaluate the stability of other rock slopes with structural planes.
-
Key words:
- smooth particle hydrodynamics /
- strength reduction /
- rock slope /
- crack propagation /
- contact /
- engineering geology
-
图 4 三维节理岩体模型(a)；单轴压缩的应力-应变曲线(b)；破裂演化(c)；竖向应力演化(d)；形变演化(e)
Fig. 4. Three-dimensional jointed rock mass model (a); stress-strain curve of uniaxial compression (b); rupture evolution (c); vertical stress evolution (d); deformation evolution (e)
图 5 不同预制裂隙角度的岩体破坏过程
a.θ = 60°；b.θ = 30°；c.θ = 0°；d.θ = 90°
Fig. 5. Rock mass failure processes with different prefabricated fracture angles
图 6 考虑不同顺倾角度的三维裂隙边坡构型与粒子分布
Fig. 6. Three-dimensional fracture slope configurations and particle distributions with different forward inclination angles
图 7 多裂隙岩质边坡剖面的阶梯路径破坏及其对应的速度
a.SPH模拟的阶梯路径破坏情况；b.通过SPH模拟得到的对应速度分布（单位：m/s）；c.中国小湾水电站水库边坡的阶梯路径破坏模式的现场观测实例（Huang et al.，2015）；d.加拿大艾希希克河滑坡陡坎边坡的阶梯路径破坏模式的现场观测实例（Brideau et al.，2009）；e.FDEM模拟的阶梯路径破坏情况（Brideau et al.，2009）；f.DEM模拟的阶梯路径破坏情况（Huang et al.，2015）；g.扩展有限元模拟的阶梯路径破坏情况（Zhou and Chen，2019）
Fig. 7. Step path failure and the corresponding velocity of the multi-fracture rock slope profile
图 8 多裂隙岩质边坡的裂纹扩展及完全破坏过程(a)；采用SPH方法对应的速度(b) (单位：m/s)；(c)多裂隙岩质边坡破坏后沉积物现场观测实例(Brideau et al., 2009)
Fig. 8. The crack propagation and complete failure process of multi-fracture rock slopes (a); the velocity corresponding to the SPH method (unit: m/s) (b); field observation examples of sediments after the failure of multi-fractured rock slopes (Brideau et al., 2009) (c)
图 9 岩质边坡的裂纹扩展及滑动面(a)，不同倾角下对应的速度(单位：m/s) (b)
红色和橙色分别代表SPH结果中的剪切裂纹和拉伸裂纹
Fig. 9. Crack propagation and sliding surfaces of rock slopes(a), velocities corresponding to different inclinations (m/s) (b)
图 10 不同节理倾角下岩质边坡的裂纹扩展及完全破坏情况(a)；相应速度场(单位：m/s)(b)；沉积变形量(单位：m)(c)
Fig. 10. Crack propagation and complete failure of rock slopes under different joint inclination angles (a); corresponding velocity field (: m/s) (b); deposition deformation (m) (c)
图 11 不同节理倾角下的FOS变化情况
Fig. 11. The variation of FOS under different joint inclination angles
图 12 不同节理倾角下总位移(a)和总裂纹数量随时间的变化情况(b)
Fig. 12. The total displacement under different joint inclination angles (a) and the variation of the total number of cracks with time (b)
图 13 不同节理倾角下(a)总裂纹数和(b)剪切裂纹数的变化情况
Fig. 13. The variations of the total number of cracks (a) and the number of shear cracks under different joint inclination angles (b)
图 14 采用SPH法和DEM法对块状边坡滑动倾倒破坏的对比
a.SPH法的三维模型；b.DEM法的三维模型；c.SPH法的二维模型；d.DEM法的三维模型
Fig. 14. Comparison of block slope sliding and collapse failure using SPH method and DEM method
表 1 SPH岩体参数
Table 1. Rock mass parameters
物理量 岩石基质 密度(kg/m3) 2 372 弹性模量(GPa) 6.2 泊松比 0.3 粘聚力(MPa) 42 内摩擦角(°) 45 抗拉强度(MPa) 23 
下载: 导出CSV
表 2 SPH岩质边坡模型的物理力学参数
Table 2. Physical and mechanical parameters of rock slope models
物理量 岩石基质 节理 密度(kg/m3) 2 700 2 300 弹性模量(GPa) 4 0.4 泊松比 0.14 0.35 粘聚力(MPa) 20 0.4 抗拉强度(MPa) 15 0.2 内摩擦角(°) 25 15 正常刚度(N/m) 1×108 1×107 摩擦系数 0.25 0.25
下载: 导出CSV
-
Brideau, M. A., Yan, M., Stead, D., 2009. The Role of Tectonic Damage and Brittle Rock Fracture in the Development of Large Rock Slope Failures. Geomorphology, 103(1): 30-49. https://doi.org/10.1016/j.geomorph.2008.04.010 Bui, H. H., Fukagawa, R., Sako, K., et al., 2008. Lagrangian Meshfree Particles Method (SPH) for Large Deformation and Failure Flows of Geomaterial Using Elastic-Plastic Soil Constitutive Model. International Journal for Numerical and Analytical Methods in Geomechanics, 32(12): 1537-1570. https://doi.org/10.1002/nag.688 Cleary, P. W., Pereira, G. G., Lemiale, V., et al., 2016. Multiscale Model for Predicting Shear Zone Structure and Permeability in Deforming Rock. Computational Particle Mechanics, 3(2): 179-199. https://doi.org/10.1007/s40571-015-0073-4 Dehghan, A. N., Khodaei, M., 2022. Stability Analysis and Optimal Design of Ultimate Slope of an Open Pit Mine: A Case Study. Geotechnical and Geological Engineering, 40(4): 1789-1808. https://doi.org/10.1007/s10706-021-01993-8 Deng, S. X., Zheng, Y. L., Feng, L. P., et al., 2019. Application of Design of Experiments in Microscopic Parameter Calibration for Hard Rocks of PFC3D Model. Chinese Journal of Geotechnical Engineering, 41(4): 655-664(in Chinese with English abstract). Do, N. A., Dias, D., Dinh, V. D., et al., 2019. Behavior of Noncircular Tunnels Excavated in Stratified Rock Masses—Case of Underground Coal Mines. Journal of Rock Mechanics and Geotechnical Engineering, 11(1): 99-110. https://doi.org/10.1016/j.jrmge.2018.05.005 Fakhimi, A., Lanari, M., 2014. DEM-SPH Simulation of Rock Blasting. Computers and Geotechnics, 55: 158-164. https://doi.org/10.1016/j.compgeo.2013.08.008 Fukuda, D., Mohammadnejad, M., Liu, H. Y., et al., 2020. Development of a 3D Hybrid Finite-Discrete Element Simulator Based on GPGPU-Parallelized Computation for Modelling Rock Fracturing under Quasi-Static and Dynamic Loading Conditions. Rock Mechanics and Rock Engineering, 53(3): 1079-1112. https://doi.org/10.1007/s00603-019-01960-z Han, Z., Su, B., Li, Y. G., et al., 2019. Numerical Simulation of Debris-Flow Behavior Based on the SPH Method Incorporating the Herschel-Bulkley-Papanastasiou Rheology Model. Engineering Geology, 255: 26-36. https://doi.org/10.1016/j.enggeo.2019.04.013 Hatzor, Y. H., Arzi, A. A., Zaslavsky, Y., et al., 2004. Dynamic Stability Analysis of Jointed Rock Slopes Using the DDA Method: King Herod's Palace, Masada, Israel. International Journal of Rock Mechanics and Mining Sciences, 41(5): 813-832. https://doi.org/10.1016/j.ijrmms.2004.02.002 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 Huang, D., Gu, D. M., 2017. Influence of Filling-Drawdown Cycles of the Three Gorges Reservoir on Deformation and Failure Behaviors of Anaclinal Rock Slopes in the Wu Gorge. Geomorphology, 295: 489-506. https://doi.org/10.1016/j.geomorph.2017.07.028 Huang, M. S., Jia, C. Q., 2009. Strength Reduction FEM in Stability Analysis of Soil Slopes Subjected to Transient Unsaturated Seepage. Computers and Geotechnics, 36(1/2): 93-101. Jia, Q. J., Liu, X. M., Tan, X., 2024. Crack Evolution Mechanism of Stratified Rock Mass under Different Strength Ratios and Soft Layer Thickness: Insights from DEM Modeling. Soils and Foundations, 64(6): 101534. https://doi.org/10.1016/j.sandf.2024.101534 Kazerani, T., Zhao, J., 2010. Micromechanical Parameters in Bonded Particle Method for Modelling of Brittle Material Failure. International Journal for Numerical and Analytical Methods in Geomechanics, 34(18): 1877-1895. https://doi.org/10.1002/nag.884 Lee, H., Jeon, S., 2011. An Experimental and Numerical Study of Fracture Coalescence in Pre-Cracked Specimens under Uniaxial Compression. International Journal of Solids and Structures, 48(6): 979-999. https://doi.org/10.1016/j.ijsolstr.2010.12.001 Li, L., Wang, Y., 2020. Identification of Failure Slip Surfaces for Landslide Risk Assessment Using Smoothed Particle Hydrodynamics. Georisk: Assessment and Management of Risk for Engineered Systems and Geohazards, 14(2): 91-111. https://doi.org/10.1080/17499518.2019.1602877.[LinkOut] Liu, M. B., Liu, G. R., Zong, Z., 2008. An Overview on Smoothed Particle Hydrodynamics. International Journal of Computational Methods, 5(1): 135-188. https://doi.org/10.1142/s021987620800142x Liu, M. M., Shi, Z. M., Li, B., 2024. Analysis of Dynamic Response and Failure Mode of Bedding Rock SlopesSubject to Strong Earthquakes Based on DEM⁃FDM Coupling. Earth Science, 49(08): 2799-2812. Liu, S. Y., Shao, L. T., Li, H. J., 2015. Slope Stability Analysis Using the Limit Equilibrium Method and Two Finite Element Methods. Computers and Geotechnics, 63: 291-298. https://doi.org/10.1016/j.compgeo.2014.10.008 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 Shu, Q., Wang, X. B., Zhao, Y. F., et al., 2020. Numerical Simulation of Failure Processes of Heterogeneous Rock Specimens under Assumption of Invariant Spherical Stress during Stress Drop. Rock and Soil Mechanics, 41(10): 3465-3472. https://doi.org/10.16285/j.rsm.2020.0077 Sun, C. W., Chai, J. R., Xu, Z. G., et al., 2016. Stability Charts for Rock Mass Slopes Based on the Hoek-Brown Strength Reduction Technique. Engineering Geology, 214: 94-106. https://doi.org/10.1016/j.enggeo.2016.09.017 Wang, X. M., Xiao, Y. J., Shi, W. B., et al., 2022. Forensic Analysis and Numerical Simulation of a Catastrophic Landslide of Dissolved and Fractured Rock Slope Subject to Underground Mining. Landslides, 19(5): 1045-1067. https://doi.org/10.1007/s10346-021-01842-y Wang, Y. N., Bui, H. H., Nguyen, G. D., et al., 2019. A New SPH-Based Continuum Framework with an Embedded Fracture Process Zone for Modelling Rock Fracture. International Journal of Solids and Structures, 159: 40-57. https://doi.org/10.1016/j.ijsolstr.2018.09.019 Wang, Y. T., Zhou, X. P., Kou, M. M., 2018. Peridynamic Investigation on Thermal Fracturing Behavior of Ceramic Nuclear Fuel Pellets under Power Cycles. Ceramics International, 44(10): 11512-11542. https://doi.org/10.1016/j.ceramint.2018.03.214 Wang, Z. H., Zhu, Z. M., Zhou, L., et al., 2024. Dynamic Mechanical Properties and Failure Characteristics of Layered Composite Rock Containing a Tunnel-Shaped Hole. Theoretical and Applied Fracture Mechanics, 129: 104217. https://doi.org/10.1016/j.tafmec.2023.104217 Wei, W. B., Cheng, Y. M., Li, L., 2009. Three-Dimensional Slope Failure Analysis by the Strength Reduction and Limit Equilibrium Methods. Computers and Geotechnics, 36(1-2): 70-80. https://doi.org/10.1016/j.compgeo.2008.03.003 Wu, D., Li, H. B., Fukuda, D., et al., 2023. Development of a Finite-Discrete Element Method with Finite-Strain Elasto-Plasticity and Cohesive Zone Models for Simulating the Dynamic Fracture of Rocks. Computers and Geotechnics, 156: 105271. https://doi.org/10.1016/j.compgeo.2023.105271 Wu, D. Y., Yu, L. Y., Su, H. J., et al., 2021. Experimental Study and PFC3D Simulation on Crack Propagation of Fractured Rock-Like Specimens with Bolts under Uniaxial Compression. Rock and Soil Mechanics, 42(6): 1681-1692(in Chinese with English abstract). Xia, C. Z., Shi, Z. M., Kou, H. J., 2024. A Modified Smoothed Particle Hydrodynamics Method Considering Residual Stress for Simulating Failure and Its Application in Layered Rock Mass. Journal of Mountain Science, 21(6): 2091-2112. https://doi.org/10.1007/s11629-023-8362-5 Yang, S. Q., Huang, Y. H., 2017. An Experimental Study on Deformation and Failure Mechanical Behavior of Granite Containing a Single Fissure under Different Confining Pressures. Environmental Earth Sciences, 76(10): 364. https://doi.org/10.1007/s12665-017-6696-4 Yang, Y. T., Sun, G. H., Zheng, H., et al., 2019. Investigation of the Sequential Excavation of a Soil-Rock-Mixture Slope Using the Numerical Manifold Method. Engineering Geology, 256: 93-109. https://doi.org/10.1016/j.enggeo.2019.05.005 Yu, S. Y., Ren, X. H., Zhang, J. X., 2023. Using an Improved SPH Algorithm to Simulate Thermo-Hydro-Mechanical-Damage Coupling Problems in Rock Masses. Case Studies in Thermal Engineering, 47: 103085. https://doi.org/10.1016/j.csite.2023.103085 Zhang, H. J., Wu, S. C., Zhang, Z. X., et al., 2023. Reliability Analysis of Rock Slopes Considering the Uncertainty of Joint Spatial Distributions. Computers and Geotechnics, 161: 105566. https://doi.org/10.1016/j.compgeo.2023.105566 Zhang, W. J., Zheng, H., Jiang, F. Y., et al., 2019. Stability Analysis of Soil Slope Based on a Water-Soil-Coupled and Parallelized Smoothed Particle Hydrodynamics Model. Computers and Geotechnics, 108: 212-225. https://doi.org/10.1016/j.compgeo.2018.12.025 Zhou, X. P., Chen, J. W., 2019. Extended Finite Element Simulation of Step-Path Brittle Failure in Rock Slopes with Non-Persistent En-Echelon Joints. Engineering Geology, 250: 65-88. https://doi.org/10.1016/j.enggeo.2019.01.012 Zhou, Z. Q., Zhao, Y., Bi, J., et al., 2023. Shear Mechanical Properties and Failure Modes of Rock with V-Shaped Intersecting Double-Cracks. Theoretical and Applied Fracture Mechanics, 124: 103755. https://doi.org/10.1016/j.tafmec.2023.103755 邓树新, 郑永来, 冯利坡, 等, 2019. 试验设计法在硬岩PFC3D模型细观参数标定中的应用. 岩土工程学报, 41(4): 655-664. 刘毛毛, 石振明, 李博, 等, 2024. 基于DEM-FDM耦合的顺层岩质边坡强震动力响应及破坏模式分析. 地球科学, 49(8): 2799-2812. doi: 10.3799/dqkx.2023.062 武东阳, 蔚立元, 苏海健, 等, 2021. 单轴压缩下加锚裂隙类岩石试块裂纹扩展试验及PFC3D模拟. 岩土力学, 42(6): 1681-1692. -
点击查看大图
计量
- 文章访问数: 31
- HTML全文浏览量: 20
- PDF下载量: 2
- 被引次数: 0
