<p>This study investigates the integration of soft computing techniques within a sequential compounding-based framework to evaluate the system reliability of reinforced soil (RS) retaining wall’s structure. External stability was assessed under three failure modes, namely sliding, overturning, and bearing capacity, using deterministic analyses coupled with the First-Order Second-Moment method for estimating probabilities of failure (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">$P_{f})$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>P</mi> <mi>f</mi> </msub> <mrow> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> and reliability indices (<InlineEquation ID="IEq2"> <EquationSource Format="TEX">$\beta )$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>β</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>. Furthermore, system reliability was quantified using the sequential compounding model across various loading scenarios. Results indicated that sliding and overturning failures exhibited negligible <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$P_{f}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>P</mi> <mi>f</mi> </msub> </math></EquationSource> </InlineEquation> (β > 3.0), confirming structural adequacy in these modes. In contrast, bearing capacity governed overall system performance, with <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$P_{f}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>P</mi> <mi>f</mi> </msub> </math></EquationSource> </InlineEquation> ranging from 10.31% to 14.03% and reliability indices between 1.08 and 1.26. The corresponding system reliability indices (<InlineEquation ID="IEq5"> <EquationSource Format="TEX">$\beta_{system}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>β</mi> <mrow> <mi mathvariant="italic">system</mi> </mrow> </msub> </math></EquationSource> </InlineEquation>) were 1.079, 1.173, and 1.264 for the three scenarios of loading, respectively, underscoring the dominant role of bearing capacity in RS wall stability. Soft computing models, namely the Generalized Regression Neural Network (GRNN) and Probabilistic Neural Network (PNN), were developed to predict factor of safety values and corresponding reliability measures. GRNN consistently outperformed PNN, achieving higher predictive accuracy (viz. R<sup>2</sup> values of 0.9827 for sliding, 0.9389 for overturning, and 0.9024 for bearing capacity) and lower RMSE (0.0175–0.0257) in testing stages. In validation, GRNN predictions closely matched the actual probability density and cumulative distribution curves, whereas PNN exhibited noticeable deviations. Moreover, GRNN reliably replicated deterministic <InlineEquation ID="IEq6"> <EquationSource Format="TEX">$\beta_{system}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>β</mi> <mrow> <mi mathvariant="italic">system</mi> </mrow> </msub> </math></EquationSource> </InlineEquation> values in first two loading scenarios and remained closer in third.</p>

External Stability of Reinforced Soil Retaining Wall Using System Reliability-Aided Soft Computing Technique

期刊论文
发表日期：

2025年11月11日

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Md Shayan Sabri,
Amit Kumar Verma,
Ramandeep Singh Malhotra,
Furquan Ahmad

摘要

This study investigates the integration of soft computing techniques within a sequential compounding-based framework to evaluate the system reliability of reinforced soil (RS) retaining wall’s structure. External stability was assessed under three failure modes, namely sliding, overturning, and bearing capacity, using deterministic analyses coupled with the First-Order Second-Moment method for estimating probabilities of failure ( $P_{f})$ $P_{f})$ and reliability indices ( $\beta )$ $β)$ . Furthermore, system reliability was quantified using the sequential compounding model across various loading scenarios. Results indicated that sliding and overturning failures exhibited negligible $P_{f}$ $P_{f}$ (β > 3.0), confirming structural adequacy in these modes. In contrast, bearing capacity governed overall system performance, with $P_{f}$ $P_{f}$ ranging from 10.31% to 14.03% and reliability indices between 1.08 and 1.26. The corresponding system reliability indices ( $\beta_{system}$ $β_{system}$ ) were 1.079, 1.173, and 1.264 for the three scenarios of loading, respectively, underscoring the dominant role of bearing capacity in RS wall stability. Soft computing models, namely the Generalized Regression Neural Network (GRNN) and Probabilistic Neural Network (PNN), were developed to predict factor of safety values and corresponding reliability measures. GRNN consistently outperformed PNN, achieving higher predictive accuracy (viz. R² values of 0.9827 for sliding, 0.9389 for overturning, and 0.9024 for bearing capacity) and lower RMSE (0.0175–0.0257) in testing stages. In validation, GRNN predictions closely matched the actual probability density and cumulative distribution curves, whereas PNN exhibited noticeable deviations. Moreover, GRNN reliably replicated deterministic $\beta_{system}$ $β_{system}$ values in first two loading scenarios and remained closer in third.