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中文摘要：
以滑动面可以是任意形状的简布模式为例，分析极限平衡理论下边坡稳定性系数计算的复杂过程和其最终表达式的非线性特征，指出该非线性特征在可靠度分析中造成的障碍。为此，提出以基于结构风险理论的小样本统计学习方法为工具，把低维空间的高度非线性问题转化为高维空间的简单线性问题的解决方法。结合简布模式下的边坡稳定可靠性分析过程，研究推导过渡函数表达式、验算点逐步逼近的迭代方法及可靠度计算等关键步骤，形成基于小样本学习理论的边坡可靠度分析新方法。采用该方法分析发育贯通软弱面的2个边坡工程的稳定可靠性。对比得出，在计算代价上新方法为精确方法的0．6％左右，计算结果绝对差值最大为0．195％，相对差值为1．25％。
英文摘要：
Taking Janbu mode in sliding surface can be random shape for example, the complex calculation process of stability coefficient and nonlinear characteristics of its final expression for slope under limit equilibrium theory are analysed. Obstacle due to nonlinear characteristics for slope stability coefficient when analyzing its reliability is pointed out. To solve above-mentioned problem, a solution in which small samples statistical learning method based on structural risk theory is regarded as tool which transforms high nonlinear problem in low dimensions space into simple linear problem in high dimensions. An analytical process for slope stability coefficient under Janbu mode is used to research and deduce transitional function expression, iterative method for stepwise approach checking point, calculation of reliability and so on. A new analytical method, based on learning theory of small samples for slope stability reliability, is established. Stability for two slopes which have developed a run-through soft surface are analyzed by the new method. It is found that the computation cost of the new method is 0.6% of accurate method; the absolute error of the calculation result is about 0.195% and relative error is 1.25%.
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