FDEM numerical simulation study on deterioration characteristics of weak-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，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标定，然后通过改进的泰森多边形程序进行网格重划分，实现零厚度黏聚力单元的嵌入功能，提出并建立软硬相间地层滑坡-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。本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支撑。
Abstract:Objective In Zigui Basin of the Three Gorges Reservoir region, prone-sliding strata mainly composed of weak-hard interbedded strata are widely distributed. Under the action of long-term reservoir water immersion, erosion and rainfall, the formation rock and soil bodies deteriorate and become an important internal cause of reducing landslide stability and affecting project safety.
Methods Taking rock and soil mass of weak-hard interbedded strata as the research object, finite discrete element method (FDEM) is used to calibrate the mechanical properties of hard and soft rocks in the weak-hard interbedded strata under different wetting-drying cycles. Then the mesh is redivided by the improved Tyson polygon program, and the embedding function of zero thickness cohesive force unit is realized. The FDEM numerical model of landslide-anti-slide pile system in weak-hard interbedded strata formation is proposed and established. Finally, the formation process of landslide cracks and the embedding mechanism of anti-slide piles under different wetting-drying cycles are studied.
Results The results show that: ① The number of simulated landslide cracks increases with the increase of the number of wetting-drying cycles, and the cracks width also increases gradually. The results of simulation are basically consistent with those of the site of Majiagou landslide. ② The simulated cracks of the landslide-anti-slide pile system show 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 extend from around the anti-slide pile to the inside of the slide body, connecting with the transverse cracks and vertical cracks, and finally forming large through cracks. ③ When the number of wetting-drying cycles increases, the horizontal displacement, bending moment and shear force of anti-slide pile also increase. ④ The cracks in the weak-hard interbedded strata bedrock of the anti-slide pile have the characteristics of localized development, and with the increase of the number of wetting-drying cycles, the stress in the region gradually decreases, the displacement and strain gradually increase, and the corresponding cracks become more and more intensive.
Conclusion The results of this study can provide support for the prevention and control of landslide in weak-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}} $和$ \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 law 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 models 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 under different wetting-drying cycles
图 5 侏罗系典型软硬相间地层特征
Figure 5. Representative characteristic of soft and hard layers of Jurassic strata
图 6 滑坡-抗滑桩体系FDEM数值计算模型
L. 抗滑桩桩长；D. 抗滑桩截面直径；α. 硬岩和软岩的倾角
Figure 6. FDEM 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
Figure 7. Comparison of numerical simulation results with field fracture distribution characteristics (n=0(natural) as an example)
图 8 不同干湿循环作用下裂纹的分布情况与其对应的位移和应变云图（以n= 0, n= 1, n= 5为例）
U. 位移；U1. x方向位移；E. 应变；E11. x方向应变；下同
Figure 8. Distribution of cracks and corresponding displacement and strain cloud maps under different wetting-drying cycles
图 9 天然条件下滑坡裂纹动态演化过程（step. 模拟运算的步数次数，下同）
Figure 9. Dynamic evolution process of landslide cracks under natural conditions
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 of landslide cracks after 5 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、弯矩和剪力分布情况
Figure 12. Distribution of horizontal displacement, bending moment and shear force 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岩层的应力（a1～f1）、位移（a2～f2）和应变（a3～f3）分布云图（E. 应力，E11. x方向应力）
Figure 13. The distribution of stress, displacement and strain in weak-hard interbedded stratum rock of pile embedded section under different wetting-drying cycles
图 14 不同干湿循环作用下A和B 2点处的应力值
Figure 14. Stress values at two points A and B under different wetting-drying cycles
表 1 不同干湿循环作用下硬岩的FDEM单轴压缩模拟输入参数
Table 1. FDEM 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FDEM单轴压缩模拟输入参数
Table 2. FDEM 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FDEM输入参数
Table 3. Calculate FDEM input parameters of the hard-soft rock transition region in the 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. Calculate other parameters in the 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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