Mechanical Characters of Anti-Sliding Piles of Landslide with Double Sliding Zones Based on Finite Difference Method
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摘要: 目前，抗滑桩的变形与内力计算理论多针对单层滑带滑坡，而三峡库区大部分堆积层滑坡发育双层滑带. 鉴于此，考虑双层滑带滑坡的物质组成差异，构建了双层滑带滑坡-抗滑桩相互作用概化模型，提出了双层滑移条件下的滑坡推力计算方法，基于地基系数法和有限差分原理推导了双层滑带滑坡中抗滑桩受力特征的计算公式. 之后，以马家沟滑坡为工程案例，采用数值模拟方法研究了双层滑带滑坡的推力分布规律，并对理论计算方法进行了验证. 结果表明，该计算方法能很好的反映双层滑带滑坡滑移特征，桩身的变形与内力分布具有明显的规律：桩身位移沿桩顶往下逐渐减小，伴有一定反弯现象；桩身剪力和弯矩具有两个极大值和一个极小值，剪力极大值位于滑面处，弯矩极大值位于滑面下方2~3 m，极小值位于深层滑体内. 滑坡推力分布形式和抗滑桩设计参数是影响桩体受力特征的重要因素. 该方法可为双层滑带滑坡的抗滑桩设计提供理论依据.Abstract: Existing theoretical analysis of the deformation and internal force of anti-sliding piles are mostly designed for single-sliding zone landslides, while most of the accumulation layer landslides in the Three Gorges reservoir area develop double sliding zones. Considering the difference in material composition of landslides with double sliding zones, a generalized model for the interaction between landslides with double sliding zones and anti-sliding is constructed. to study the internal force and deformation of anti-sliding piles. Then a calculation method of landslide thrust under double-layer sliding condition is proposed to derive the equations of deformation and internal force of anti-slide pile in landslides with double sliding zones based on the foundation coefficient method and the finite difference principle. Numerical simulation method was used to research the distribution laws of landslide thrust and verify the newly proposed approach via the Majiagou landslide as example. The results of the theoretical and numerical simulation methods well show the sliding characteristics of landslides with double sliding zones. Meanwhile, the distribution of the deformation and internal forces show a great regularity: the displacement of the pile decreases gradually from the top to bottom accompanied by reverse bending phenomenon, the shear force and bending moment of the pile exist two maximum values and one minimum value, and the maximum values of the shear force are located at the sliding surface while the maximum values of the bending moment are located 2~3 m below the sliding surface, and the minimum value is located in the deep sliding body. In addition, the distribution of landslide thrust and the vital design parameters of anti-sliding piles are important factors that affect the mechanical characteristics of the pile. The proposed method can provide a theoretical reference for the design of anti-sliding piles of landslide with double sliding zones.
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图 1 单滑带滑坡抗滑桩受力分析示意图
Fig. 1. Schematic of force analysis of anti-sliding piles in landslide with single sliding zone
图 2 双层滑带滑坡-抗滑桩相互作用概化模型
Fig. 2. Conceptual model of landslide with double sliding zones-anti-sliding pile interaction
图 3 双层滑带滑坡单元划分及受力分析图
a. 双层滑体条块划分；b. 浅层滑体条块受力；c.深层滑体条块受力
Fig. 3. Diagram of division and force analysis of unit of landslide with double sliding zones
图 4 双层滑带滑坡抗滑桩受力分析示意图
Fig. 4. Schematic of force analysis of anti-sliding piles in landslide with double sliding zones
图 5 桩身挠曲和各段差分点划分
a.桩身挠曲；b. h11段；c. h12段；d. h2段
Fig. 5. Diagram showing bending and division of differential points at each section of pile
图 7 马家沟双层滑带滑坡数值计算模型
Fig. 7. Numerical calculation model of Majiagou landslide with double sliding zones
图 10 双层滑带滑坡桩身位移图
a. 桩身位移数值结果；b. 桩身位移分布曲线
Fig. 10. Displacement diagram of anti-sliding piles in landslide with double sliding zones
图 11 双层滑带滑坡桩身剪力图
a. 桩身剪力数值结果；b. 桩身剪力分布曲线
Fig. 11. Shear force diagram of anti-sliding piles in landslide with double sliding zones
图 12 双层滑带滑坡桩身弯矩图
a. 桩身弯矩数值结果；b. 桩身弯矩分布曲线
Fig. 12. Bending moment diagram of anti-sliding piles in landslide with double sliding zones
图 13 不同地基系数下双层滑带滑坡抗滑桩的变形和内力分布图
a. 位移图；b. 剪力图；c. 弯矩图
Fig. 13. Displacement and internal forces diagram of anti-sliding piles in landslide with double sliding zones under different foundation coefficients
图 14 不同截面尺寸的双层滑带滑坡抗滑桩的变形和内力分布图
a. 位移图；b. 剪力图；c. 弯矩图
Fig. 14. Displacement and internal forces diagram of anti-sliding piles in landslide with double sliding zones under different size
图 15 不同桩底支承条件下双层滑带滑坡抗滑桩的变形和内力分布图
a. 位移图；b. 剪力图；c. 弯矩图
Fig. 15. Displacement and internal forces diagram of anti-sliding piles in landslide with double sliding zones under different bearing condition
表 1 滑坡推力分布函数
Table 1. Distribution functions of landslide-thrust
滑坡岩土类型 滑坡推力分布形式 a b 滑坡推力分布函数 岩石 矩形或平行四边形 0 0 $ q\left(z\right)=\frac{{E}_{n}}{{h}_{1}} $ 松散介质（砂土） 三角形 0 2 $ q\left(z\right)=\frac{2{E}_{n}z}{{{h}_{1}}^{2}} $ 介于砂土和粘土 梯形 0 12ζ-6 $ q\left(z\right)=\frac{(12\zeta -6){E}_{n}}{{{h}_{1}}^{2}}z+\frac{(4-6\zeta){E}_{n}}{{h}_{1}} $ 粘土 抛物线形 36ζ-24 18-24ζ $ q\left(z\right)=\frac{(36\zeta -24){E}_{n}}{{{h}_{1}}^{3}}{z}^{2}+\frac{(18-24\zeta){E}_{n}}{{{h}_{1}}^{2}}z $ 
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表 2 滑坡岩土体物理力学参数
Table 2. Physical and mechanical parameters of rock and soil
材料类型 密度(kg/m3) 黏聚力（kPa） 内摩擦角(°) 体积模量（MPa） 剪切模量（MPa） 浅层滑体(碎石土) 2 110 35 27 905 611 深层滑体(砂质泥岩) 2 450 45 42 9 506 6 310 滑床(砂岩) 2 500 70 50 15 000 10 000 浅层滑带土 2 110 11 14 75 32 深层滑带土 2 230 12 15 84 45
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表 3 物理力学参数组合
Table 3. Combination of physical and mechanical parameters
参数滑带 黏聚力(kPa) 内摩擦角(°) 体积模量(MPa) 剪切模量(MPa) 参数1 S1 11 14 75 32 S2 12 15 84 45 参数2 S1 13 16 150 70 S2 12 15 84 45 参数3 S1 9.5 12 40 15 S2 12 15 84 45 参数4 S1 11 14 75 32 S2 14 17 160 90 参数5 S1 11 14 75 32 S2 10 14 40 25
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表 4 推力特征值对比
Table 4. Characteristic value of landslide thrust comparison
P0(kPa) P1(kPa) ζ1 P0’ (kPa) P2(kPa) ζ2 参数1 111.3 190.1 0.54 40.2 482.3 0.64 参数2 1.2 191.5 0.66 15.6 506.7 0.66 参数3 89.7 206.3 0.57 55.5 386.5 0.63 参数4 97.8 217.2 0.56 52.4 389.8 0.63 参数5 44.1 192.7 0.60 10.4 501.2 0.66
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