Random Finite Element Analysis and Random Factor response Mechanism for Geocell-reinforced Soil Retaining Walls - ZHANG Bingbing; SONG Fei (工程科学与技术, 2025)
ObjectiveAccurate assessment of the strength characteristics and deformation behavior of geocell-reinforced retaining wall structures is crucial for their safety and stability during long-term service. Currently, most of the research methods usually simplify the geocell-reinforced retaining wall and its surrounding soil as homogeneous materials and carry out theoretical calculations and finite element analyses based on such idealized assumptions, which is difficult to fully consider the inherent spatial variability of the soil material and the reinforced structure. For this reason, a finite element analysis method based on random field theory is proposed in this paper, which can more realistically reflect the non-homogeneous characteristics of the reinforced soil retaining wall system by introducing a spatial random distribution model of the soil parameters and the mechanical properties of the geocells, so as to more accurately assess the influence of the spatial variability of the material parameters on the deformation behavior and stability of the retaining wall.MethodsFirstly, in parameter random field modeling, an innovative combination of Latin Hypercube Sampling (LHS) and exponential autocorrelation function is used to construct parameter random fields. The Cholesky decomposition ensures the positive definiteness of the covariance matrix and the strict maintenance of the correlation structure, and the centroid discretization method is adopted to realize the accurate discretization of the uncorrelated Gaussian distribution random field, which not only effectively captures the spatial variability of the soil parameters, but also demonstrates excellent numerical convergence performance. Secondly, a multi-language collaborative automated analysis platform is constructed at the computational implementation level: the random field parameter generation module is developed based on Matlab and the parameter distribution is visualized. The UMAT user subroutine, which considers the mechanical properties of sand and geocells, is written in Fortran. The whole process automation framework was built by Python script to realize the intelligent processing from parameter reading, automatic generation of 500 groups of INP files to the submission of batch calculations and extraction of ODB results. Based on the above method, the random field numerical model of geocell-reinforced soil retaining wall was successfully established, and the probability distribution characteristics of horizontal displacement and vertical settlement of the retaining wall were obtained through large-scale stochastic simulation, and the corresponding cumulative distribution function was constructed. Finally, the global sensitivity analysis method was adopted, focusing on revealing the influence laws of key parameters (K, n, φ0 and PMt), their coefficients of variation and spatial fluctuation ranges on the deformation characteristics of the retaining wall, and quantitatively analyzing the mapping relationship between each parameter and the deformation response of the structure.Results and Discussions Through the in-depth analysis of the random field parameters of foundation soil, backfill soil and geocell-reinforced retaining wall, it is revealed that the soil parameters have significant layering characteristics and the trend of change with depth, which is highly consistent with the layering distribution characteristics of the soil in the actual project, and verifies the reliability of the constructed random field model. Based on 500 sets of finite element simulation results of the random field, the deformation characteristics of the reinforced retaining wall are systematically analyzed: the deterministic analysis results are located near the median of the random calculation results. The stochastic envelope of the horizontal displacement of the top surface of the retaining wall ranges from 6.25 to 32.39 mm (equivalent to 0.46~2.38 times of the deterministic model), while the vertical settlement of the wall shows a greater dispersion, ranging from -31.77 to -7.60 mm (equivalent to 0.53~2.23 times of the deterministic model). Probabilistic statistical analyses showed that both the horizontal displacement at the top of the wall and the wall settlement showed obvious clustering characteristics, with 79.3% and 79.7% of the samples concentrated in the intervals of 8.5~17.5 mm and -16 to -7 mm, respectively. Further, by comparing the stress cloud maps of the deterministic model and the random field model, it is found that the deterministic model presents regular stress gradients and smooth contour transitions, while the random field model exhibits significant irregular stress distribution characteristics. This difference stems from the use of the centroid discretization method to process the cell parameters, which makes each cell have unique mechanical properties, thus reflecting the spatial variability of geotechnical materials more realistically. In addition, the analysis of the response mechanism of parameters with airport reveals that the deformation characteristics of the reinforced soil retaining wall have a significant dependence on the spatial variability characteristics of the key parameters. The global sensitivity analysis by linear normalization treatment shows that the sensitivity ordering of horizontal displacement and settlement to each parameter is consistent, both of which are φ0 > K > n > PMt. In terms of the influence of spatial fluctuation range, it was found that when <alternatives>δh <?fx-imagestate width="2.45533323" height="2.96333337"?> <?fx-imagestate width="2.45533323" height="2.96333337"?> </alternatives>=60 m combined with <alternatives>δv <?fx-imagestate width="2.45533323" height="2.96333337"?> <?fx-imagestate width="2.45533323" height="2.96333337"?> </alternatives> =1.5 m, the deformation response showed a relatively convergent characteristic, and the envelope ranges of horizontal displacement and settlement were 7.92~21.28 mm and -9.15~-20.88 mm, respectively. And when <alternatives>δv <?fx-imagestate width="2.45533323" height="2.96333337"?> <?fx-imagestate width="2.45533323" height="2.96333337"?> </alternatives>=2 m and <alternatives>δh <?fx-imagestate width="2.45533323" height="2.96333337"?> <?fx-imagestate width="2.45533323" height="2.96333337"?> </alternatives>=45 m, the envelope range is slightly expanded (horizontal displacement 7.82~22.40 mm and settlement -8.25~-21.40 mm), indicating that the anisotropy of the fluctuation range has an important influence on the deformation distribution. Particularly noteworthy is that the analysis of parameter coefficients of variation reveals a significant controlling effect of n and PMt on the dispersion of the calculated results: compared with the baseline condition (6.25~32.39 mm), the reduction of the coefficients of variation of n and PMt reduces the upper limit of the horizontal displacements by 31.3% and 27.7% to 8.14~22.26 mm and 7.44~23.42 mm, respectively. Correspondingly, the discretization of vertical settlement shows a similar reduction trend. The random field analysis method established in this study is able to capture the uncertainty of engineering behavior more comprehensively and provides a more reliable prediction tool for the design of reinforced soil structures, which helps to optimize the engineering safety reserve and reduce the risk associated with uncertainty.ConclusionsThe results show that: the random envelope range of horizontal displacement and vertical settlement of reinforced earth retaining wall decreases with the decrease of height of reinforced earth retaining wall (points H-1~H-5) and away from the retaining wall face (points V-1~V-7); the decrease of fluctuation range or coefficient of variation reduces the dispersion of the calculation results, in which the cumulative distribution probability of the parameter φ0 is closer to the random distribution results, while the parameters n and PMt are with the deterministic results The effect of vertical fluctuation range on the failure probability is more significant than that of horizontal direction. The research results can provide reference value for the engineering design and deformation assessment of geocell-reinforced retaining walls.