基于一阶逆可靠度方法的空间变异土坡坡角设计
Reliability-based design of slope angles for spatially varying slopes based on inverse first-order reliability method
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摘要: 边坡稳定性分析及设计是岩土工程中的经典问题,目前常用的确定性分析(单一安全系数)方法没有量化边坡工程中各种不确定性的影响,概率分析方法则需要进行多次可靠度试算,计算量较大。为此,提出了适合任意坡角的空间变异土坡模型重构方法,基于一阶逆可靠度方法对少量实际试验数据条件下空间变异土坡坡角进行可靠度设计。并以一个代表性的砂土边坡为例对坡角进行可靠度设计,验证了提出方法的有效性。结果表明:提出的方法可以在少量试验数据条件下获得切合工程实际的边坡设计方案,为土坡坡角可靠度设计提供了一条有效途径。对于文中砂土边坡,提出方法仅需进行4,5次迭代计算,便可获得满足目标失效概率的土坡最优坡角。相比之下,确定性分析方法因不能定量地解释边坡工程多种不确定性因素的影响,获得的设计方案与边坡工程实际相差较大。就文中算例而言,对于目标失效概率1×10-4,采用提出方法设计的砂土边坡坡角应小于14.13°;相比之下,采用确定性分析方法设计的边坡坡角与之相差较大。Abstract: Stability analysis and design of soil slopes are a classic problem in geotechnical engineering. The current commonly-used deterministic analysis (e.g., single factor of safety) approach does not quantify the influences of various uncertainties in slope engineering, while the probabilistic analysis approach is time-consuming because it often requires performing multiple rounds of reliability analyses. A slope model reconstruction method that can well adapt to different slope angles is proposed. The reliability-based design of slope angles for spatially varying slopes based on a small amount of test data is carried out using the inverse first order reliability method. To validate the effectiveness of the proposed method, a representative sandy slope is taken as an example, to conduct the reliability-based design of slope angles. The results indicate that the proposed method can obtain a design scheme of slope angle based on a small amount of test data, which is well consistent with engineering practice. It thereby provides an effective tool for the reliability-based design of slope angles for spatially varying slopes. For the sandy slope in this study, an optimized slope angle that achieves various target probabilities of failure can be obtained after 4 or 5 iterative calculations. In contrast, the deterministic analysis method will obtain a biased design scheme since it cannot quantitatively account for the influences of multiple sources of uncertainties in the slope engineering. To yield a target probability of failure of 1×10-4 which is often acceptable for stability evaluation of slopes, the slope angle of the sandy slope designed using the proposed method should be smaller than 14.13°. By contrast, the slope angle designed using the deterministic analysis approach differs significantly from that designed using the proposed method.