基于钻孔资料的耦合马尔可夫链水平方向转移概率矩阵估计

Estimation of Horizontal Transition Probability Matrix for Coupled Markov Chain Based on Borehole Data

地层变异在实际滑坡中广泛存在,其表现为不同类型岩土材料的互相嵌套或一种类型岩土体在另一种较均质岩土体中的随机分布.岩土工程实践中仍缺乏一种有效的地层变异模拟方法.为此,搜集了不同地区的钻孔资料,检验了土体状态转移的一阶马尔可夫性.提出了一种实用的基于钻孔数据的耦合马尔可夫链水平方向转移概率矩阵估计方法.利用给定的水平方向转移概率矩阵进行耦合马尔科夫链模拟以产生虚拟钻孔,通过比较给定的水平方向转移概率矩阵和利用虚拟钻孔估计的水平方向转移概率矩阵评估了所提方法的有效性.最后,利用澳大利亚珀斯市的钻孔资料进行了水平方向转移概率矩阵的估计.结果表明,土体状态转移的一阶马尔可夫性在现实中是广泛存在的;当给定的转移概率矩阵对角占优(矩阵的对角线元素大于非对角元素之和)程度较高时,估计的水平方向转移概率矩阵和给定值有较好的吻合.所提方法使耦合马尔科夫链模型能被有效地用于地层变异的模拟,为在岩土工程中考虑地层变异奠定了基础.

Geological uncertainty widely exists in many landslide cases. It appears in the forms of one soil layer embedded in another or the inclusion of pockets of different soil type within a more uniform soil mass. An effective simulation method for the geological uncertainty is still absent in the geotechnical practice. Hence, borehole data from various sites are collected to verify the first-order Markovian property. A practical method is proposed to estimate the horizontal transition probability matrix （HTPM） for the couple Markov chain （CMC） model. Several virtual boreholes are created by means of simulating realizations of CMC using a prescribed HTPM. The effectiveness of the proposed method is evaluated by comparing the prescribed HTPM and the HTPM estimated from the virtual boreholes. The borehole data from Perth city, Australia is adopted to illustrate the estimation process of the HTPM. The results indicate that first-order Markovian property in soil transitions is quite common in reality. The estimation error of HTPM decreases with the increasing diagonal dominancy of the HTPM or VTPM. The method facilitate the application of the coupled Markov chain model in the simulation of the geological uncertainty. It provides a basis for uncertainty analysis of geotechnical problems considering geological uncertainty.