考虑参数空间变异结构的结构化交叉约束随机场模拟方法研究

Study of structural cross-constraint random field simulation method considering spatial variation structure of parameters

斜坡岩土体抗剪强度参数的空间变异性具有一定的结构性。为研究岩土体参数空间变异结构对边坡失效概率的影响,依据变异函数的内涵推导出变程与相关距离的数学变换关系,并在此基础上提出了结构化交叉约束随机场模拟方法,用以模拟具有互相关性的参数随机场。建立了结构化交叉约束随机场计算模型,研究不同空间变异结构的抗剪强度参数对边坡失效概率的影响。研究结果表明:结构化交叉约束随机场可用于生成模拟具有复杂各向异性空间变异结构的参数随机场,由于考虑了随机偏差、条件数据和空间变异结构,能较为真实地反映地层实际参数,数据波动较条件参数插值场小。可靠性分析结果表明:不考虑抗剪强度参数空间结构分析易高估边坡的失效概率;考虑c′和φ′互相关性时,失效概率随着相关系数的增加而增加,当参数间呈负相关性时更容易高估边坡的失效概率。

The spatial variability of shear strength parameters of rock and soil mass on slopes is structural. Aimed at studying the effect of spatial variability structure of rock and soil parameters on failure probability of slopes, the transformation relationship between range and correlation distance is deduced based on the mathematical intension of variogram firstly. The simulation method of structural cross-constraint random field is proposed to simulate the cross-correlated parameters random fields. In order to study the effect of shear strength parameters with different spatial variation structures, a slope calculation model of structural cross-constraint random field is established. The results show that the structural cross-constraint random field can reflect real formation parameters by considering random deviation, conditional data and different spatial variation structures. Compared with conditional parameter interpolation field, the proposed method is suitable for parameters with more complex spatial variation structures, i.e. directionality and anisotropy, and the generated data have less fluctuation. The reliability analysis also reveals that the failure probability of slopes is prone to be overestimated without considering the spatial structure parameters. The failure probability increases with the increase of the correlation coefficient when the correlation between the two factors is considered. It is easier to overestimate the slope failure probability under the scenario of negative correlation between c’ and φ’.