Regression modeling of nonlinear interactions of strength and seepage factors in assessing the stability of earth dams
DOI:
https://doi.org/10.55287/22275398_2026_59_47Keywords:
regression model, levels of variation, interaction of factors, slope stability, earth dam, statistical significanceAbstract
Traditional methods for calculating the slope stability of earth dams are based on deterministic models that fail to account for the stochastic nature of soil properties and their mutual influence. The results of engineering and geological surveys demonstrate significant variability in physical and mechanical characteristics, necessitating the development of regression analysis methods for constructing predictive models. The scientific novelty of this study lies in establishing quantitative patterns of nonlinear interactions between the angle of internal friction, specific cohesion, and permeability using second-order polynomial models verified by statistical criteria. The study utilizes the theoretical foundations of a central composite experimental design (17 runs), least-squares regression analysis, adequacy testing using Fisher's F-test, coefficient significance assessment using Student's t-test, and numerical modeling using the Morgenstern-Price method. Regression models with R² > 0.97 for the stability factor FS and maximum principal stresses σmax were obtained. Specific cohesion was found to contribute 47–51% to the total variance of the response functions. Significant pairwise interactions were revealed: the effect of the internal friction angle increases at low cohesion (interaction coefficient b₁₂ = – 0.019); the effect of seepage on stresses depends on the level of cohesion (b₂₃ = 5.4 kPa). Zones of “plastic failure” of stability were identified for a combination of minimum cohesion (c < 20 kPa) and maximum value of the seepage coefficient (k > 8×10⁻⁵ cm/s).
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