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为了深入研究不确定因素对立井井壁温度场的影响,将井壁传热区域的导热系数、内热源强度、质量密度及质量比热容等不确定性参数模拟为随机场,基于随机场局部平均理论,采用Monte-Carlo随机有限元法对立井井壁随机温度场求解进行了分析,给出了有限元节点温度响应的均值、方差及变异系数的计算公式,根据计算步骤编写了求解立井井壁随机温度场的Matlab随机有限元程序。通过工程实例,考察了随机场参数对立井井壁温度场随机性响应的影响,并与将各随机参数视为单一随机变量的情况进行了对比。结果表明:基于随机场理论的Monte-Carlo随机有限元法能合理考虑井壁混凝土热学参数空间上的不确定性;编制的Matlab随机有限元程序可直接输出各时刻井壁温度场的统计结果;传统的井壁温度场确定性分析存在缺陷,将井壁混凝土的热学参数模拟为单一随机变量会高估其变异性,采用随机场建模方法显得更加科学合理。
In order to further study the influence of uncertain factors on temperature field of shaft wall, the uncertainty parameters such as thermal conductivity, internal heat source intensity, mass density and mass specific heat capacity are simulated as random fields. Based on the local average theory , The Monte-Carlo stochastic finite element method is used to solve the stochastic temperature field in the shaft wall, and the formulas for calculating the mean value, variance and coefficient of variation of the temperature response of the finite element are given. According to the calculation procedure, Temperature field of Matlab finite element program. Through the engineering example, the influence of random field parameters on the random response of the temperature field in the shaft wall of vertical shaft is investigated. Compared with the case that each random parameter is regarded as a single random variable. The results show that Monte-Carlo stochastic finite element method based on stochastic field theory can reasonably consider the spatial uncertainty of concrete thermal parameters in borehole wall. The prepared Matlab finite element program can directly output the statistical results of borehole temperature field at each moment. The deterministic analysis of the traditional borehole temperature field is flawed. Simulating the thermal parameters of the concrete lining as a single random variable will overestimate the variability, and it is more scientific and reasonable to adopt the stochastic modeling method.