The random field theory is often utilized to characterize the inherent spatial variability of material properties. In order to incorporate sampled data from site investigations or experiments into simulations, a patching algorithm is developed to yield a conditional random field in this study. Comparison is conducted between the proposed algorithm and the conventional Kriging algorithm to underscore the former’s advantages in simulating material properties with limited sampled data. Unlike the Kriging algorithm that interpolates the entire spatial domain, the proposed algorithm restricts the influence domain of sampled data within a reasonable range, which is determined as a function of the scale of fluctuation. The simulated conditional random field via the proposed algorithm is stationary in mean and variance; thus, it would be preferable for situations with a few known data. Additionally, a tunnel excavation model is considered to exemplify the effectiveness of the proposed algorithm. By virtue of Monte-Carlo simulations, maximum tunnel convergence modeled by unconditional and conditional random fields is analyzed in a statistical manner. The results indicate that the proposed algorithm can effectively reduce the uncertainty of prediction in responses. Furthermore, the proposed algorithm is also applicable with a sparse sampling pattern.

随机场理论通常用于表征材料特性的固有空间变异性。为了将来自站点调查或实验的采样数据合并到模拟中，开发了一种修补算法以产生条件随机场在这个研究中。比较了所提出的算法和传统的克里格算法，以强调前者在有限采样数据下模拟材料特性的优势。与Kriging算法对整个空间域进行插值不同，所提出的算法将采样数据的影响域限制在合理范围内，该范围取决于波动范围。通过所提出的算法模拟的条件随机场的均值和方差是平稳的；因此，对于具有少量已知数据的情况将是更可取的。此外，隧道开挖模型被认为可例证该算法的有效性。借助蒙特卡洛模拟，以统计方式分析了无条件和有条件随机场建模的最大隧道收敛性。结果表明，该算法可以有效降低响应预测的不确定性。此外，所提出的算法也适用于稀疏采样模式。