Distribution of the factor of safety,in geotechnical engineering,for independent piecewise linear capacity and demand density functions

In many geotechnical engineering cases, the factor of safety may be defined as the ratio of the capacity, of the geotechnical structure or its support elements, to the pertinent demand. By representing the capacity and the demand as independent piecewise linear random variables, an analytic solution is obtained for the probability density and cumulative distribution functions of the factor of safety. Thus, solutions for the calculation of the mean value, the standard deviation and the minimum and maximum values of the factor of safety, are provided. Application of the developed analytical solutions, to the probabilistic analysis of a published case of rock spalling in a deposition tunnel complex, follows. The methodology allows for the parametric evaluation of the effect of specific design variables to the distribution of the safety factor and to the probability of failure. The closed form solution may be programmed as a computer code that may run easily on a tablet or netbook or even on a smartphone. It proves useful for the probabilistic design of a variety of geotechnical applications, such as foundations, tunneling, mining, underground roof reinforcement, and earth retaining structures, and permits decisions to be taken in terms of risk and reliability.     

深部硬岩剪切边界下应力诱发片帮的机制研究

深部工程开挖现场发现硬岩的剪切破坏过程对地下工程稳定性具有重要影响。深埋硬岩隧洞边墙处片帮或板裂主要为压致拉裂的结果,可通过室内单轴压缩试验来模拟;而拱肩和底角处的片帮或板裂多数是在剪切边界下形成的,需通过室内完整硬岩直剪试验来再现。针对不同类型硬岩压致拉裂型片帮,已进行了相当深入的研究,但对完整硬岩剪切边界下应力诱发型片帮的直接研究还存在着不足。为了深入研究深埋硬岩隧洞片帮或板裂的形成机制,采用FLAC3D软件模拟隧洞不同位置处围岩受开挖扰动的应力调整过程,根据中国锦屏地下实验室二期工程区域的片帮统计结果,将深埋硬岩隧洞片帮划分为压致拉裂型和剪切边界应力诱发型两类,提出剪切边界应力诱发型片帮形成过程的概念模型;利用完整大理岩设计了不同正应力下压剪破裂到剪切滑移的连续性直剪试验,试样典型片帮破坏结果验证了概念模型的合理性。