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<p>This study evaluates the stability of re‑excavated rock slopes at the north and south portals of Tunnel 3, Kherrata, Algeria, a seismically active area in jointed marly limestone. An integrated methodology combining kinematic analysis, empirical classification (Slope Mass Rating and Q‑slope), and Finite Element Method–Discrete Fracture Network (FEM–DFN) modeling is applied under static and pseudo‑static seismic loading. Kinematic and empirical analyses indicate high susceptibility to planar and wedge failures, suggesting that slope angles should be reduced below 60°. FEM–DFN simulations confirm that stable conditions can be achieved under static loading (Strength Reduction Factor, SRF = 1.77–1.92), whereas peak ground accelerations (PGA) exceeding 0.25&#xa0;g render the slopes unsafe (SRF &lt; 1.0). To optimize the reinforcement configuration, a multi-factor statistical analysis based on response surface methodology was conducted using SRF values from numerical simulations. The RSM–ANOVA results show that PGA is the dominant factor controlling SRF variability (F = 1390.40, <i>p</i> &lt; 0.0001). Among the support-design parameters, bolt length and bolt spacing are the most influential variables, with F-values of 27.04 and 8.14, respectively, whereas shotcrete thickness has a smaller and statistically non-significant effect within the investigated range of 5–10&#xa0;cm. The response surfaces were then used to identify reinforcement layouts with 4&#xa0;m bolts, spacing ≤ 1.5&#xa0;m, and shotcrete thickness ≥ 10&#xa0;cm that keep SRF above unity for the target peak ground accelerations. The findings demonstrate that response surface methodology-based optimization, coupled with combined FEM–DFN modeling and classical kinematic and empirical tools, provides a robust framework for seismic design of tunnel‑portal rock slopes and offers transferable guidance for similar jointed rock masses.</p> Graphical Abstract <p></p>

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Seismic Stability Assessment of Rock Slopes at Tunnel Portals Using Integrated Numerical and Response Surface Methods

  • 期刊论文

  • 发表日期：

    2026年6月22日

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  • Riadh Boukarm,
  • Mohamed Fredj

摘要

This study evaluates the stability of re‑excavated rock slopes at the north and south portals of Tunnel 3, Kherrata, Algeria, a seismically active area in jointed marly limestone. An integrated methodology combining kinematic analysis, empirical classification (Slope Mass Rating and Q‑slope), and Finite Element Method–Discrete Fracture Network (FEM–DFN) modeling is applied under static and pseudo‑static seismic loading. Kinematic and empirical analyses indicate high susceptibility to planar and wedge failures, suggesting that slope angles should be reduced below 60°. FEM–DFN simulations confirm that stable conditions can be achieved under static loading (Strength Reduction Factor, SRF = 1.77–1.92), whereas peak ground accelerations (PGA) exceeding 0.25 g render the slopes unsafe (SRF < 1.0). To optimize the reinforcement configuration, a multi-factor statistical analysis based on response surface methodology was conducted using SRF values from numerical simulations. The RSM–ANOVA results show that PGA is the dominant factor controlling SRF variability (F = 1390.40, p < 0.0001). Among the support-design parameters, bolt length and bolt spacing are the most influential variables, with F-values of 27.04 and 8.14, respectively, whereas shotcrete thickness has a smaller and statistically non-significant effect within the investigated range of 5–10 cm. The response surfaces were then used to identify reinforcement layouts with 4 m bolts, spacing ≤ 1.5 m, and shotcrete thickness ≥ 10 cm that keep SRF above unity for the target peak ground accelerations. The findings demonstrate that response surface methodology-based optimization, coupled with combined FEM–DFN modeling and classical kinematic and empirical tools, provides a robust framework for seismic design of tunnel‑portal rock slopes and offers transferable guidance for similar jointed rock masses.

Graphical Abstract