Calculation method of thrust force of the embedded stabilizing piles under the overtop-sliding failure mode
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摘要: 滑坡推力的确定对于抗滑桩设计极其重要，沉埋桩作为对传统抗滑桩的优化，其受荷段推力的研究目前主要借助于模型试验和数值模拟，缺乏深入的理论分析。为了建立沉埋桩后侧受荷段及桩顶沉埋段滑坡推力计算方法，针对沉埋桩加固的基岩-覆盖层式滑坡，基于潜在越顶破坏模式，由桩顶位置将越顶滑面分为顶部、底部两段，其中，顶部滑面上水平方向合力即为沉埋段推力，可由积分求得，底部滑面上各个方向的力求解方法与此类似；在此基础上，利用刚体极限平衡理论对底部滑面与桩受荷段所围滑体进行受力分析，进而可得受荷段推力计算公式。实例分析表明：理论算法所得沉埋段与受荷段推力值与FLAC3D结果非常接近，其中，受荷段推力、沉埋段推力、设桩位置处总推力随沉埋比的增大而分别非线性减小、增大、减小；沉埋比位于0~0.67范围内时，沉埋段与受荷段推力之比由0缓慢增大到0.30~0.50，随着沉埋比增大到0.8，该比值急剧增大到1.47~2.12；一般沉埋深度下，沉埋段推力小于受荷段推力。沉埋桩推力的理论研究对于桩体内力优化、沉埋深度确定具有重要的现实意义，将有助于该桩型的进一步推广应用。Abstract: Embedded piles act as an optimization structure compared with the traditional stabilizing pile. The determination of the thrust on the loading section is based mainly on the model test and numerical simulation, and there is a lack of in-depth theoretical analysis. For the bedrock-talus landslide reinforced by embedded piles, according to the potential overtop-sliding failure mode, the slide surface can be divided into top and bottom sections by the position of pile top, and the horizontal resultant force of the top section can be obtained by integration, which is the so-called thrust of the embedded section. Similarly, the force on the bottom section of the overtop-sliding surface can also be obtained. Based on the limit equilibrium theory, the force analysis of the sliding mass enclosed by the bottom sliding surface and the load section of the pile can be carried out, and the thrust on the loaded section can also be obtained. Example analyses show that the thrust of the embedded section and the loaded section obtained by the theoretical method are very consistent with the results of FLAC3D, the resultant force of the loading section decreases nonlinearly with the increase of the ratio, while the resultant force of the embedded section presents an opposite trend. With the increase of the embedded ratio from 0 to 0.67, the thrust ratio of embedded section and loading section increases slowly from 0 to 0.3−0.5. With the increase of embedded ratio from 0.67 to 0.8, the ratio increases sharply to 1.47−2.12. Generally, the thrust of embedded section is less than that of loaded section. The theoretical research of the thrust of the embedded pile is of great practical significance for the optimization of the pile internal force and the determination of the pile embedded depth, which will promote the further application of this structure.
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图 1 沉埋桩加固滑坡横截面示意图
Figure 1. Sketch map of the cross section of a landslide reinforced with embedded pile
图 4 沉埋桩加固宝成铁路沿线某滑坡横断面图
Figure 4. Cross section of a practical landslide reinforced with embedded stabilizing piles
图 5 沉埋桩加固滑坡数值模型
Figure 5. Numerical model of the practical landslide reinforced with embedded pile
图 6 数值模拟得到的临界滑动面
Figure 6. Critical slip surface obtained with the shear strength reduction method
图 7 沉埋桩加固滑坡的水平应力云图
Figure 7. Contour of horizontal stress of the reinforced landslide using the embedded pile
图 8 加固后坡体稳定系数随η的变化情况
Figure 8. Variation of stability coefficient of reinforced landslide with the embedded ratio
图 9 受荷段及沉埋段推力随η的变化情况
Figure 9. Variation of the thrust behind the pile and the thrust in the submerged section with the embedded ratio
图 10 设桩处总滑坡推力随η的变化情况
Figure 10. Variation of the total thrust at the section of pile position with the embedded ratio
图 11 沉埋段、受荷段推力之比与η的关系曲线
Figure 11. Variation curve of thrust ratio of the submerged section and the loading section with the embedded ratio
表 1 抗滑桩及坡体主要物理力学参数
Table 1. Main physical and mechanical parameters of the landslide and piles
材料类型 土体重度
/（kN·m–3）黏聚力
/kPa内摩擦角
/（°）弹性模量
/MPa泊松比 碎石土 22 11 20.6 50 0.33 大理岩 23 450 37.0 600 0.25 抗滑桩 25 30 000 0.22 注：抗滑桩视为弹性体，故不考虑其黏聚力和内摩擦角。 
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