Iron pipes connected by bell-spigot joints are utilized in buried pipeline systems for urban water and gas supply networks. The joints are the weak points of buried iron pipelines, which are particularly vulnerable to damage from excessive axial opening during seismic motion. The axial joint opening, resulting from the relative soil displacement surrounding the pipeline, is an important indicator for the seismic response of buried iron pipelines. The spatial variability of soil properties has a significant influence on the seismic response of the site soil, which subsequently affects the seismic response of the buried iron pipeline. In this study, two-dimensional finite element models of a generic site with explicit consideration of random soil properties and random mechanical properties of pipeline joints were established to investigate the seismic response of the site soil and the buried pipeline, respectively. The numerical results show that with consideration of the spatial variability of soil properties, the maximum axial opening of pipeline joints increases by at least 61.7 %, compared to the deterministic case. Moreover, in the case considering the variability of pipeline-soil interactions and joint resistance, the spatial variability of soil properties remains the dominant factor influencing the seismic response of buried iron pipelines.

The in-situ stress can significant influence the damage caused to rock. A comprehensive analysis of the in-situ stress field is essential for tunnel design, construction and geological monitoring. This study establishes a 3D geologic model using the finite difference method, explicit considering material heterogeneity through random field theory. After conducting 300 simulations, the distribution pattern of the in-situ stress field was statistically analyzed. The inversion accuracy, considering material heterogeneity, is superior to that for homogeneous materials at the measurement points, with smaller relative errors. The extent of in-situ stresses in both the horizontal and vertical directions of the model depend not only the burial depth but also on the physico-mechanical properties of the material. In particular, the distribution of the in-situ stress field exhibits heterogeneity in localized regions, influenced by the material's variability. In the river valley area, the river valley bank slopes are divided into three zones based on the stress force values: the stress release zone, the stress concentration zone, and the virgin rock stress zone. The stress distribution around the tunnel shows significant non-uniformity and irregular fluctuations, with alternating high-stress and low-stress regions. Notably, stress concentration occurs at the crown, sidewalls, and both sides of the tunnel bottom. These in-situ stress fields, which account for the spatial variability of rock parameters, provide a more realistic and accurate reference for engineering practice.

Microscopic properties of granular materials typically exhibit significant heterogeneity. Realistic particle crushing simulation in granular materials requires the use of model that incorporate the spatial heterogeneity of its microscopic properties. This study introduces a novel approach, the Random Field Theory-Discrete Element Method (RFT-DEM) model, to simulate the single-particle crushing behavior of granular materials, considering the spatial heterogeneity of microscopic properties within particles. The material heterogeneity was characterized through Random Field Theory, demonstrating reasonable consistency between simulated and experimental results. The size-dependent characteristics of crushing strength and Weibull modulus were confirmed through a series of single-particle crushing simulations, emphasizing the model's capability to capture such features. Systematic analyses explored the impact of coefficient of variation (COV) and scale of fluctuation (SOF) on single-particle crushing behavior. Increasing COV resulted in reduced characteristic crushing strength and Weibull modulus, with larger particles exhibiting greater sensitivity. Furthermore, increasing SOF initially increased these parameters until a threshold SOF value of 0.0005 m, beyond which they stabilized. Reduced COV or increased SOF diminished the size effect in characteristic crushing strength, and once COV exceeded a threshold of 0.03, the size effect became independent of its variations. These findings contribute to a comprehensive understanding of the intricate interplay between microscopic properties and crushing behavior in granular materials.