摘要
为提高边坡稳定系数的精度、降低其计算复杂度并扩大其应用范围,基于应用较为广泛的极限平衡理论——瑞典圆弧法,转化传统数学模型的连加为积分,得到了积分数学模型;通过对同一边坡在强度折减模型、传统数学模型、积分数学模型这三种不同模型下的稳定系数进行对比,证明了积分公式相对传统公式在精度和计算复杂度上的优越性;并推导出了边坡稳定系数计算的广义数学模型,进而给出了成层土复杂边坡的简化计算方法。结果表明:积分数学模型不用考虑土条划分和预估滑动面形式,其计算值相对强度折减模型仅低4.8%,相对传统数学模型高9.17%;计算时间相对传统数学模型低40%,相对强度折减法仅高20%;广义数学模型在三个假定的前提下,解决了"异形坡面"边坡的稳定系数计算;成层土边坡的简化方法,一定程度上进一步解决了非连续成层土体边坡的稳定系数计算问题。与传统数学模型相比,积分数学模型提高了计算精度并减少了工作量,弥补了传统数学模型因土条宽度选择不当和提出的各种假设所带来的不足,验证了广义数学模型和成层土边坡的简化计算方法对于求解复杂边坡的稳定系数的可行性。
Aiming at improving the accuracy and reducing the computational complexity of slope stability coefficient, and enlarging the application range, thus making the design and construction of slope engineering more practical, the continuous superposition is transformed into integration and the integration mathematical model is obtained based on the widely used theory called Limit Equilibrium Theory—Sweden Circle Method.Then the advantages of the integration formula are shown by computational comparison, the General Mathematical Model is built and the simplified computing method for layered soil slope is given. The results show that: the Integration Mathematical Model is a special example of the General Mathematical Model, and there is no need of soil slice division and prediction of the slide surface under precondition of the four assumptions.Specifically speaking, the value obtained by Integration Mathematical Model is only 4.8% less than the Strength Reduction Model's, while it's 9.17% higher than the Traditional Mathematical Model's, as for the costing time, the Integration Mathematical Model's is 40% less than the Traditional Mathematical Model's, while it's only 20%longer than the Strength Reduction Model's; The General Mathematical Model settles the computation of stability coefficient for the shape-special slope under precondition of the three assumptions; Besides, the simplified method of layered slope can solve the stability coefficient of noncontinuous and layered slope further to some extent. So,the Integration Mathematical Model improves the accuracy and reduces the works, thus offsetting the disadvantages of Traditional Mathematical Model; Besides, the General Mathematical Model and simplified computation method are feasible to deal with the complex slope.
出处
《应用力学学报》
CAS
CSCD
北大核心
2014年第1期162-168,0+14,共7页
Chinese Journal of Applied Mechanics
基金
国家自然科学基金(50978131)
辽宁工程技术大学研究生科研立项(Y201200602)
关键词
瑞典圆弧法
积分
广义数学模型
异形边坡
成层土边坡
Sweden Circle Method
integration
general mathematical model
slope-special slope
layered soil slope.
