基于振型叠加法的顺层边坡非平稳随机地震响应及动力可靠度分析

为研究非平稳随机地震激励下顺层岩质边坡的动力可靠性问题，采用振型叠加法和虚拟激励法，建立含多层软弱结构面的顺层岩质边坡非平稳随机地震响应的快速算法，根据响应结果，采用首次穿越破坏准则，进一步推导出非平稳地震下顺层岩质边坡动力可靠度计算的解析表达式。在此基础上，通过MATLAB软件平台编写相应的程序以实现计算数据和结果图形的快速输出。算例分析表明：顺层边坡地震响应随时间和频率同时变化，具有明显的非平稳特性；随着边坡岩块高程的增加，其位移响应的离散程度会增大，而其对应结构面上剪切力和法向力响应的离散程度会减小，且法向力响应的离散程度更小；地震过程非平稳随机性会降低顺层岩质边坡的可靠程度，建立的可靠度计算方法能更真实地反映边坡的实际情况，更偏于工程安全。

Non-stationary random seismic response and dynamic reliability analysis of bedding rock slopes based on mode superposition method

To study the dynamic reliability problems of bedding rock slopes under the non-stationary random earthquake excitation, a fast algorithm for the non-stationary random seismic response of bedding rock slopes with multiple weak structural planes was developed based on the mode superposition method and pseudo excitation method. By referring to the calculated results, an analytical expression was derived for dynamic reliability of bedding rock slopes under non-stationary earthquake using the -rst excursion failure criterion. Furthermore, the MATLAB program was coded to achieve the fast output of calculation data and result visualization. The calculation results disclose that the seismic response of bedding slope which changes with time and frequency has obvious non-stationary characteristics. With the increase of the elevation of rock block, the dispersion degree of displacement response increases, while the dispersion degree of shear and normal force responses on the corresponding structural plane decreases, and particularly that of the normal force response appears to be smaller. The non-stationary randomness of seismic process can reduce the reliability of bedding rock slope, and the proposed reliability calculation method can more realistically reflect the actual slopes, beneficial to the engineering safety.