基于塑性极限分析上限法在边坡中建立一个合理的速度场,取滑动面为对数螺旋曲面,分别求得边坡滑动体、外荷载所做外功率和滑动面上内能消散率的计算表达式.然后定义材料强度储备安全系数为边坡的稳定安全系数,即边坡中岩土体的c和φ按同一比例折减后边坡达到极限平衡状态,由此可求得边坡处于极限状态时的外功率与内能消散率.再结合虚功率方程得出边坡安全系数的表达式,进而求得其最小上限解,便能确定边坡最不利滑动面的位置以及其最小安全系数.最后,以一个边坡安全系数求解为算例,把本文的计算结果与多种传统方法的计算结果比较,证明本文所提出的方法合理可行.%A reasonable velocity fields in the slope on the base of plastic limit analysis upper bound method was established,and the sliding surface was supposed as logarithmic spiral surface,the computation expression of work rate was calculated by the body forces and surface loads as well as rate of internal energy dissipations of slope can be obtained; then the material safety margin factor was defined as the safety factor of slope,that is c and φ of soil and rock in the slope reduced by the same percentage,and the slope reaches the state of limit balance,the rate of external energy and internal energy dissipations can be gotten while the slope is in the limit state. The expression of safety factor can be obtained via virtual work-rate equation,and its smallest upper bound solution is derived,and the most disadvantageous sliding surface's position and smallest safety factor of the slope are presented. Finally,taking a slope's safety factor solution as an example,the comparisons among the analytical results of various traditional methods were made,then the method proposed by this paper was proved reasonable and feasible.
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