Efficient simulation of conditional random fields and its geotechnical applications

Abstract

Random fields are a powerful tool for modeling spatial variability of geotechnical properties, but they may overestimate variability if field investigation data, such as borehole measurements, are not incorporated. With advancements in testing techniques and the growing availability of high-quality data, reliable spatial variability modeling has become increasingly feasible in geotechnical engineering. This article proposes an efficient and versatile method for simulating conditional random fields (CRFs), aiming to overcome the computational inefficiency of traditional approaches when dealing with large datasets. The proposed method involves three key steps. First, the mean values of CRFs is estimated from observed data by the Kriging interpolation. Then, a conditional covariance matrix of the CRF is constructed by combining the covariance matrix of the unconditional random field with the Kriging interpolation or the Nyström approximation. Finally, the CRF is simulated using the Karhunen–Loève (KL) expansion, which combines the derived eigenvalues and eigenfunctions with random variables. Therefore, this process simulates CRFs effectively by integrating the Kriging interpolation, the conditional covariance modeling and the stochastic expansion. The effectiveness of the proposed method is verified using one-, two-, and three-dimensional geotechnical applications. Numerical results confirm that the proposed method can accurately preserve spatial correlations while significantly reducing the computational effort. Furthermore, it also enables efficient modeling of large-scale geotechnical problems. In these senses, the proposed framework provides a robust tool for spatial variability modeling in geotechnical engineering.