Analysis of the stability of water-saturated soils under cyclic influence: mathematical models and forecasts

The article discusses the mathematical modeling of soil liquefaction under the influence of dynamic loads, such as seismic, storm, or technogenic cyclic impacts. The liquefaction process, in which soil loses strength and bearing capacity, is critical for assessing the safety of construction objects, especially in areas with increased seismic activity or water-saturated soils. Several approaches were used for modeling, including the following functions: the exponential function from the work of H. Bilge et al. (2009), the logarithmic function from the work of V. Lentini et al. (2018), the power function (polynomial) proposed by C. Guoxing et al. (2018), an additional logarithmic function from the study of E. Meziane et al. (2021), and a hyperbolic function proposed by the authors of this article, which approximated the soil's resistance to cyclic impacts. The study analyzed laboratory test data for various soil types, combined into engineering-geological elements. Each function was analyzed in terms of approximation accuracy using the least squares method, which minimized the deviations between experimental and theoretical values. When evaluating the functions, consideration was given to how each behaves under a large number of loading cycles, which is important for predicting liquefaction under intense and prolonged loads. The selection of the optimal function was made by comparing the MSE and R2 metrics presented in the results tables. The application of the research results has practical significance in geotechnical design, especially for calculating foundations and underground structures in conditions of potentially liquefiable soils. Choosing the most suitable function for modeling soil liquefaction allows predicting soil stability under long-term and intense cyclic loads, minimizing the risk of deformation and destruction of structures.

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