Limit analysis of slope stability supported by framed prestressed anchor rods
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摘要: 框架预应力锚杆在边坡工程中应用广泛。在考虑支护结构、锚杆对土体边坡稳定性影响的情况下,基于塑性力学极限分析上限理论的基本原理,推导了其支护边坡的安全系数计算公式。并采用Matlab语言编制算法对推导公式进行全局最优解搜索。对算例采用Flac3d模拟求解其安全系数,和用上限法求得的结果相近。最后采用正交试验设计方法讨论在框架预应力锚杆支护边坡中坡角、坡高、土体性质等内在因素对其稳定性的影响,得出对框架预应力锚杆支护边坡的稳定性影响最大的是坡角,然后再依次为内摩擦角和坡高、黏聚力、坡底支护结构推力设计值、重度,且坡角和内摩擦角对边坡稳定性影响高度显著。Abstract: Framed prestressed anchor rods are widely used in slope engineering.Considering the influences of supporting structures and anchor rods on the stability of soil slopes, the basic principles of the upper limit theory are analyzed, and the formula for calculating the safety factor of supported slope is deduced on the basis of plastic mechanics limit.The algorithm based on Matlab language is adopted to search the global optimal solution.Finally, according to the orthogonal design method, the influences of the internal factors such as slope angle, slope height and soil properties on the stability of prestressed anchor supported slope are discussed.It is concluded that the slope angle has the greatest influences on the stability of the prestressed anchor supported slope, following by the internal friction angle and slope hight, cohesion force, design value of thrust of supporting structures for the slope and soil weight, and the slope height, internal friction angle and slope angle have significant influences on its stability.
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Keywords:
- slope engineering /
- framed prestressed rod /
- stability /
- limit analysis
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图 1 框架预应力锚杆支护边坡模型图
Figure 1. Model for slope supported by framed prestressed anchor rods
表 1 不同极限平衡法所求的安全系数值
Table 1 Values of safety factor calculated by different limit equilibrium methods
Janbu Morgensternprice Spencer Bishop Janbu Generalized 1.270 1.379 1.378 1.380 1.353 
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表 2 关于边坡黏聚力、内摩擦角等的因素水平
Table 2 Factors related to slope cohesion, internal friction angle, soil weight, slope angle, slope height and design value of thrust of supporting structures for slope
水平 黏聚力/kPa 内摩擦角/(°) 重度/(kN·m-3) 坡角/(°) 坡高/m 底部支护结构推力设计值/(kN·m-1) 1 18 20 12 30 6 10 2 21 23 14 40 8 30 3 24 26 16 50 10 50 4 27 29 18 60 12 70 5 30 32 20 70 14 90
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表 3 正交设计组合情况
Table 3 Combined situations of orthogonal design
试验号 黏聚力/kPa 内摩擦角/(°) 重度/(kN·m-3) 坡角/(°) 坡高/m 底部推力设计值/(kN·m-1) 试验结果 1 18 20 12 30 6 10 1.2240 2 18 23 14 40 8 30 1.2250 3 18 26 16 50 10 50 1.1517 4 18 29 18 60 12 70 1.0310 5 18 32 20 70 14 90 0.9062 6 21 20 14 50 12 90 0.9322 7 21 23 16 60 14 10 0.7520 8 21 26 18 70 6 30 1.1593 9 21 29 20 30 8 50 1.7832 10 21 32 12 40 10 70 1.7141 11 23 20 16 70 8 70 0.8876 12 23 23 18 30 10 90 1.4269 13 23 26 20 40 12 10 1.1765 14 23 29 12 50 14 30 1.1735 15 23 32 14 60 6 50 1.7726 16 27 20 18 40 14 50 0.9716 17 27 23 20 50 6 70 1.4204 18 27 26 12 60 8 90 1.4562 19 27 29 14 70 10 10 1.0271 20 27 32 16 30 12 30 1.8385 21 30 20 20 60 10 30 0.8457 22 30 23 12 70 12 50 0.8671 23 30 26 14 30 14 70 1.5460 24 30 29 16 40 6 90 2.0201 25 30 32 18 50 8 10 1.5728
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表 4 正交设计结果
Table 4 Values of orthogonal design
因素 K1 K2 K3 K4 K5 R 黏聚力 1.1076 1.2682 1.2874 1.3428 1.3703 0.2628 内摩擦角 0.9722 1.1383 1.2979 1.407 1.5608 0.5886 重度 1.287 1.3006 1.33 1.2323 1.2264 0.1036 坡角 1.5637 1.4215 1.2501 1.1715 0.9695 0.5943 坡高 1.5193 1.385 1.2331 1.1691 1.0699 0.4494 底部推力设计值 1.1505 1.2484 1.3092 1.3198 1.3483 0.1978
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表 5 各个因素显著性分析
Table 5 Significance analysis of various factors
变异来源 偏差平方和 自由度 方差 F值 Fa 显著水平 黏聚力 0.210 4 0.053 5.177 显著 内摩擦角 1.049 4 0.262 25.864 F0.01(4,4)=15.977 极为显著 坡角 1.048 4 0.262 25.829 F0.05(4,4)=6.388 高度显著 坡高 0.636 4 0.159 15.674 F0.1(4,4)=4.107 显著 推力设计值 0.123 4 0.031 3.033 F0.25(4,4)=2.064 有一定影响 误差e 0.041 4 0.010 总和 3.107
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