Finite discrete element method (FDEM) numerical simulation study on deterioration characteristics of soft-hard interbedded strata landslide-anti-slide pile system under wetting-drying cycles
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摘要:
三峡库区秭归盆地广泛分布以软硬相间地层为主的易滑地层，在长期的库水浸泡冲刷、降雨等作用下，地层岩土体发生劣化损伤，成为降低滑坡稳定和影响工程安全的重要内因。以软硬相间地层岩土体为研究对象，采用有限−离散元法（finite discrete element method，简称FDEM）对不同干湿循环作用下软硬相间地层中硬岩和软岩的力学参数进行了标定，然后通过改进的泰森多边形程序进行了网格重划分，实现了零厚度黏聚力单元的嵌入功能，提出并建立了软硬相间地层滑坡−抗滑桩体系FDEM数值计算模型，最后对不同干湿循环作用下滑坡裂纹的形成过程和抗滑桩的嵌固机理进行了研究。研究结果表明：①滑坡模拟裂纹数量随着干湿循环次数的增加而增多，裂纹宽度也逐渐增大，并与马家沟滑坡现场裂缝进行了对比，模拟结果与现场基本一致；②滑坡−抗滑桩体系的模拟裂纹呈现2种演化模式，一是裂纹从桩顶侧岩土体沿着桩身向下扩展，二是裂纹从抗滑桩周围逐渐向滑体内部延伸，与横向裂纹和竖向裂纹连通，最终形成大型的贯通裂纹；③当干湿循环次数增加时，抗滑桩桩身水平位移、弯矩和剪力也随之增加；④抗滑桩嵌固段的软硬相间地层基岩内的裂纹具有局部化发育特征，而且随干湿循环次数的增加，区域内的应力逐渐减小，位移和应变则逐渐增大，相应的裂纹也愈发密集。研究成果可为不同干湿循环作用下软硬相间地层滑坡防治提供技术支撑。
Abstract:Objective In the Zigui Basin of the Three Gorges Reservoir region, landslide-prone strata mainly composed of soft-hard interbedded strata are widely distributed. Under the long-term action of reservoir water immersion, erosion and rainfall, the formation rock and soil undergo deterioration and damage, which has become a key factor in reducing landslide stability and threatening engineering safety.
Methods Taking rock and soil mass of soft-hard interbedded strata as the research object, finite discrete element method (FDEM) was used to calibrate the mechanical properties of hard and soft rocks in the soft-hard interbedded strata under different wetting-drying cycles. Subsequently, the mesh was redivided using an improved Voronoi diagram program, and the embedding function of zero-thickness cohesive elements was realized. An FDEM numerical model of a landslide-anti-slide pile system in soft-hard interbedded strata was proposed and established. Finally, the formation process of landslide cracks and the working mechanism of anti-slide piles under different wetting-drying cycles were studied.
Results The results showed that: ① The number of simulated landslide cracks increased with the increase in the number of wetting-drying cycles, and the crack width also increased gradually. The simulation results were generally consistent with the field observations of the Majiagou landslide. ② The simulated cracks of the landslide-anti-slide pile system showed two evolutionary patterns: One is that the cracks spread downward from the rock mass on the top side of the pile along the pile body; the other is that the cracks gradually extended from around the anti-slide pile to the inside of the slide body, connecting with transverse cracks and vertical cracks, and finally forming large-scale through cracks. ③ With the increase in the number of wetting-drying cycles, the horizontal displacement, bending moment and shear force of anti-slide pile also increased. ④ The cracks in the soft-hard interbedded strata bedrock of the anti-slide pile showed localized development characteristics; as the number of wetting-drying cycles increased, the stress in the region gradually decreased, the displacement and strain gradually increased, and the corresponding cracks became increasingly dense.
Conclusion The results of this study can provide support for the prevention and control of landslide in soft-hard interbedded strata under different wetting-drying cycles.
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图 1 黏聚力单元的T−S准则[27]
GⅠ，GⅡ分别为Ⅰ型和Ⅱ型断裂能；Kn，Ks分别为黏聚力单元初始法向刚度和初始剪切刚度；$ \sigma_{\mathrm{n}}^0 $，$ \sigma_{\mathrm{s}}^0 $分别为黏聚力单元法向和剪切方向的峰值应力；σ为应力；$ \delta_{\mathrm{n}}^0 $，$ \delta_{\mathrm{s}}^0 $分别为$ \sigma_{\mathrm{n}}^0 $，$ \sigma_{\mathrm{s}}^0 $对应的拉伸位移和剪切位移；$ \delta\mathrm{_{nc}} $，$ \delta\mathrm{_{sc}} $，$ \delta\mathrm{_{np}} $，$ \delta\mathrm{_{sp}} $分别为黏聚力单元的拉伸损伤起始位移、剪切损伤起始位移、拉伸失效位移和剪切失效位移
Figure 1. Traction-separation criterion of cohesive element
图 2 单轴压缩数值模型
D. 模型直径；H. 模型高度；h. 网格边长；v. 加载速率；下同
Figure 2. Numerical model of uniaxial compression
图 3 单轴压缩模拟和试验结果（β. 剪切面破裂角）
Figure 3. Simulation and test results of uniaxial compression
图 4 不同干湿循环作用下单轴压缩结果的应力−应变曲线（E. 弹性模量；n. 干湿循环次数；下同）
Figure 4. Stress-strain curves of uniaxial compression results under different wetting-drying cycles
图 5 侏罗系典型软硬相间地层特征
Figure 5. Characteristic of typical soft-hard interbedded strata in Jurassic
图 6 滑坡−抗滑桩体系有限−离散元法（FDEM）数值计算模型
L. 抗滑桩桩长；DL. 抗滑桩截面直径；α. 硬岩和软岩的倾角
Figure 6. Finite discrete element method numerical model of landslide-anti-slide pile system
图 7 数值模拟结果与现场裂缝分布特征对比（以n=0（天然）为例）
a. 模型整体裂纹分布图; b. 模型局部裂纹分布图; c～e. 现场裂缝图，分别对应b图中区域1、区域2、区域3的模拟裂纹
Figure 7. Comparison of numerical simulation results with field fracture distribution characteristics
图 8 不同干湿循环作用下裂纹的分布情况(b, e, h)与其对应的位移(c, f, i)和应变(d, g, j)云图（以n=0, n=1, n=5为例）
a. 模型整体裂纹分布图；b，e，h. 分别为n=0，1，5时的裂纹云图；c，f，i. 分别为n=0，1，5时的位移云图；d，g，j分别为n=0，1，5时的应变云图. U. 位移；U1. x方向位移；ε. 应变；ε11. x方向应变；下同
Figure 8. Distribution of cracks (b, e, h) and corresponding displacement (c, f, i) and strain cloud maps (d, g, j) under different wetting-drying cycles
图 9 天然条件下滑坡裂纹动态演化过程（step. 模拟运算的步数，下同）
Figure 9. Dynamic evolution process of landslide cracks under natural condition
图 10 5次干湿循环作用后滑坡裂纹动态演化过程
Figure 10. Dynamic evolution process of landslide cracks after five wetting-drying cycles
图 11 不同干湿循环作用下桩周裂纹最终分布状态
Figure 11. Final distribution of cracks around piles under different wetting-drying cycles
图 12 不同干湿循环作用下桩身水平位移(a)、弯矩(b)和剪力(c)分布情况
Figure 12. Distributions of horizontal displacement (a), bending moment (b) and shear force (c) of pile under different wetting-drying cycles
图 13 不同干湿循环作用下桩身嵌固段软硬相间地层的应力（a1～f1）、位移（a2～f2）和应变（a3～f3）分布云图（σ. 应力；σ11. x方向应力；A. 桩前侧基岩顶面应力点；B. 桩底后侧基岩应力点；下同）
Figure 13. Distributions of stress (a1-f1), displacement (a2-f2) and strain (a3-f3) in soft-hard interbedded strata of pile embedded section under different wetting-drying cycles
图 14 不同干湿循环作用下A和B点的应力值
Figure 14. Stress values at A and B points under different wetting-drying cycles
表 1 不同干湿循环作用下硬岩的有限−离散元法（FDEM）单轴压缩模拟输入参数
Table 1. Finite discrete element method uniaxial compression simulation input parameters of hard rock under different wetting-drying cycles
单元
类型参数 干湿循环次数n 0（天然） 1 2 3 4 5 实体
单元密度ρ/(kg·m−3) 2470 2320 2200 2190 2190 2190 弹性模量E/GPa 30 28 27 26 25 24 泊松比ν 0.28 0.28 0.28 0.28 0.28 0.28 黏聚力
单元抗拉强度ft/MPa 5 4 3.5 3 3 2.6 黏聚力c/MPa 10 9 8.5 7.6 7 6.8 内摩擦角φ/(°) 26 24.8 23.5 22.9 22.3 22 Ⅰ型断裂能GI/(J·m−2) 88 60 48 36 36 30 Ⅱ型断裂能GⅡ/(J·m−2) 176 120 96 72 72 60 初始法向刚度En/GPa 60 56 54 52 50 48 初始切向刚度Es/GPa 30 28 27 26 25 24 法向接触刚度Pn/GPa 90 90 90 90 90 90 切向接触刚度Ps/GPa 60 60 60 60 60 60 
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表 2 不同干湿循环作用下软岩的有限−离散元法（FDEM）单轴压缩模拟输入参数
Table 2. Finite discrete element method uniaxial compression simulation input parameters of soft rock under different wetting-drying cycles
单元
类型参数 干湿循环次数n 0(天然) 1 2 3 4 5 实体
单元密度ρ/(kg·m−3) 2260 2100 2050 2030 2020 2020 弹性模量E/GPa 10 8.2 8 7.9 7.5 7 泊松比ν 0.3 0.3 0.3 0.3 0.3 0.3 黏聚力
单元抗拉强度ft/MPa 2 1.7 1.5 1.4 1.35 1.3 黏聚力c/MPa 5 4.2 3.9 3.6 3.2 3 内摩擦角φ/(°) 18 16.5 15.5 15 14.8 14.5 Ⅰ型断裂能GⅠ/(J·m−2) 40 37 30 26 25 25 Ⅱ型断裂能GⅡ/(J·m−2) 80 74 60 52 50 50 初始法向刚度En/GPa 20 16.4 16 15.8 15 14 初始切向刚度Es/GPa 10 8.2 8 7.9 7.5 7 法向接触刚度Pn/GPa 60 60 60 60 60 60 切向接触刚度Ps/GPa 30 30 30 30 30 30
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表 3 计算模型中硬岩−软岩过渡区的有限−离散元法（FDEM）输入参数
Table 3. Finite discrete element method input parameters of hard-soft rock transition zone in the calculation model
单元
类型参数 干湿循环次数n 0(天然) 1 2 3 4 5 黏聚力
单元抗拉强度ft/MPa 1.5 1.4 1.3 1.2 1.1 1 黏聚力c/MPa 4 3.5 3 2.5 2 2 内摩擦角φ/(°) 15 14 13 12 11 10 Ⅰ型断裂能GⅠ/(J·m-2) 30 25 22 20 18 16 Ⅱ型断裂能GⅡ/(J·m-2) 60 50 44 40 36 32 初始法向刚度En/GPa 40 36.2 35 33.9 32.5 31 初始切向刚度Es/GPa 20 18.1 17.5 16.95 16.25 15.5
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表 4 计算模型中的其他参数
Table 4. Other parameters in the calculation model
单元类型 参数 滑体 基岩 抗滑桩 实体单元 密度ρ/(kg·m−3) 2000 3000 2800 弹性模量E/GPa 4 100 25 泊松比ν 0.35 0.2 0.23 黏聚力单元 抗拉强度ft/MPa 1 − − 黏聚力c/MPa 3.5 − − 内摩擦角φ/(°) 22 − − Ⅰ型断裂能GⅠ/(J·m−2) 25 − − Ⅱ型断裂能GⅡ/(J·m−2) 50 − − 初始法向刚度En/GPa 8 − − 初始切向刚度Es/GPa 4 − − 法向接触刚度Pn/GPa 75 − − 切向接触刚度Ps/GPa 45 − −
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