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本文基于毕肖普法和蒙特卡洛法,利用MATLAB编程软件计算了边坡结构的失效概率Pf和对应可靠指标β。在计算上述Pf和对应β时,考虑了土体三个主要基本参数(重度γ、内摩擦角φ、粘聚力c)的随机特性。利用MATLAB程序的计算结果表明,随机变量对边坡可靠度的影响与基本随机参数对抗滑反力的贡献大小有关,即,贡献大的基本随机参数,它的随机波动对结构失效概率Pf的影响也较大,反之亦然。另外,基于MATLAB的算例计算结果还表明:边坡结构失效概率Pf对内摩擦角φ较敏感,而对重度γ和粘聚力c次之。其次,当同时考虑三个随机变量的联合波动对Pf的影响时发现,当它们在小范围内随机波动时,其联合特性对Pf的影响较敏感,但当它们在大范围内随机波动时,Pf主要受敏感随机变量的影响,而三个随机变量联合作用对Pf的影响和敏感随机变量φ单独作用时相差不大。由此可见,在实际边坡工程可靠性分析中,土体内摩擦角起主要作用,不容忽视。
Based on the Bishop method and the Monte Carlo method, this paper calculates the failure probability Pf and the corresponding reliable index β of the slope structure by MATLAB programming software. In calculating the above Pf and corresponding β, the stochastic properties of the three main basic parameters of soil (heavy γ, internal friction angle φ, cohesion c) are considered. The results of MATLAB program show that the influence of random variables on the slope reliability is related to the contribution of basic random parameters to the anti-skid reaction force, ie, the basic random parameter with large contribution, the influence of stochastic fluctuations on the probability of structural failure Pf Also larger, and vice versa. In addition, the calculation results based on MATLAB also show that the failure probability Pf of slope structure is sensitive to the internal friction angle φ, and to the secondary γ and cohesion c. Second, when considering the influence of the joint fluctuations of three random variables on Pf, it is found that their joint properties are more sensitive to Pf when they fluctuate randomly in a small area, but when they fluctuate randomly in a large area, Pf is mainly affected by sensitive random variables, and the effect of the combination of three random variables on Pf is not much different from that of the sensitive random variable φ alone. Thus, in the actual slope engineering reliability analysis, the soil friction angle plays a major role, can not be ignored.