T his study is aimed at providing generic equations for the preliminary design of strain-softening slopes across a range of angles (21–75°). A comprehensive series of numerical slope stability analyses was conducted using FEM-based RS2 software on slopes with varied angles and strength characteristics. To align with common engineering practice and software capabilities, the strain-softening behavior was modeled using the Mohr–Coulomb failure criterion with either linear or instantaneous degradation of strength parameters. The model boundaries for the preliminary design were optimized, and results from the FEM models were categorized into six groups for non-linear regression analysis. These analyses led to the development of equations for two types of strain-softening behavior (cr = 0, φr = φp and cr = 0, φr = φp/2). The influence of groundwater on these slopes was also examined, revealing a smaller-than-anticipated influence on the normalized values, confirming the reliability of the proposed equations. Validation using numerous slope failure cases and FDM simulations indicated that the equations for strain-softening where the peak internal friction angle equals the residual internal friction angle are reliable, according to both real-case slope failures and FDM models, within a failure range of unitless ratios <InlineEquation ID="IEq1"> <EquationSource Format="TEX">${c}_{p}/\gamma H\text{tan}({\varphi }_{p})$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>c</mi> <mi>p</mi> </msub> <mo stretchy="false">/</mo> <mi>γ</mi> <mi>H</mi> <mtext>tan</mtext> <mrow> <mo stretchy="false">(</mo> <msub> <mi>φ</mi> <mi>p</mi> </msub> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> ratios (0.005–0.2). However, the second strain-softening behavior did not align with FDM model results, indicating unreliable outcomes for the instantaneous softening in FEM. It is emphasized that the applicability of both the newly proposed and existing equations for strain-softening behavior (e.g., Renani and Martin, Journal of Rock Mechanics and Geotechnical Engineering 12(3), 473–483, 2020) is limited to scenarios where instantaneous degradation is assumed, as commonly implemented in FEM models.

Comprehensive Re-evaluation of Preliminary Design of Strain-Softening Slopes

期刊论文
发表日期：

2025年11月6日

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V. Satar,
H. Ozturk

摘要

T his study is aimed at providing generic equations for the preliminary design of strain-softening slopes across a range of angles (21–75°). A comprehensive series of numerical slope stability analyses was conducted using FEM-based RS2 software on slopes with varied angles and strength characteristics. To align with common engineering practice and software capabilities, the strain-softening behavior was modeled using the Mohr–Coulomb failure criterion with either linear or instantaneous degradation of strength parameters. The model boundaries for the preliminary design were optimized, and results from the FEM models were categorized into six groups for non-linear regression analysis. These analyses led to the development of equations for two types of strain-softening behavior (c_r = 0, φ_r = φ_p and c_r = 0, φ_r = φ_p/2). The influence of groundwater on these slopes was also examined, revealing a smaller-than-anticipated influence on the normalized values, confirming the reliability of the proposed equations. Validation using numerous slope failure cases and FDM simulations indicated that the equations for strain-softening where the peak internal friction angle equals the residual internal friction angle are reliable, according to both real-case slope failures and FDM models, within a failure range of unitless ratios ${c}_{p}/\gamma H\text{tan}({\varphi }_{p})$ $c_{p} / γ H tan (φ_{p})$ ratios (0.005–0.2). However, the second strain-softening behavior did not align with FDM model results, indicating unreliable outcomes for the instantaneous softening in FEM. It is emphasized that the applicability of both the newly proposed and existing equations for strain-softening behavior (e.g., Renani and Martin, Journal of Rock Mechanics and Geotechnical Engineering 12(3), 473–483, 2020) is limited to scenarios where instantaneous degradation is assumed, as commonly implemented in FEM models.