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<p>This paper presents a limit analysis-based topology optimization framework for reinforcement design in geotechnical structures.&#xa0;The proposed formulation combines lower-bound limit analysis with a density-based topology optimization and considers two material phases, namely soil and reinforcement, both governed by the Mohr–Coulomb yield criterion. Both relaxed and penalized formulations are used to obtain continuous and near-discrete reinforcement layouts.&#xa0;The successive reweighting procedure ensures a stable transition between relaxed and penalized solutions. A key contribution of the work is its application to geotechnical configurations such as slopes and tunnels, together with the explicit incorporation of implementation cost into the optimization process.&#xa0;In particular, a spatial cost weighting is introduced in the objective function to account for depth-dependent implementation costs. A series of two-dimensional numerical examples is presented&#xa0;to assess the proposed framework.&#xa0;The results show that mechanically&#xa0;consistent reinforcement layouts are obtained&#xa0;and&#xa0;highlight the influence of implementation cost on their spatial distribution.&#xa0;The framework therefore provides a consistent&#xa0;basis for reinforcement design at the ultimate limit state in geotechnical engineering.</p>

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A limit analysis-based topology optimization framework for optimal reinforcement layout in tunnels and slopes

  • 期刊论文

  • 发表日期：

    2026年7月20日

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  • Mohamed Fourati,
  • Zied Kammoun,
  • Hichem Smaoui

摘要

This paper presents a limit analysis-based topology optimization framework for reinforcement design in geotechnical structures. The proposed formulation combines lower-bound limit analysis with a density-based topology optimization and considers two material phases, namely soil and reinforcement, both governed by the Mohr–Coulomb yield criterion. Both relaxed and penalized formulations are used to obtain continuous and near-discrete reinforcement layouts. The successive reweighting procedure ensures a stable transition between relaxed and penalized solutions. A key contribution of the work is its application to geotechnical configurations such as slopes and tunnels, together with the explicit incorporation of implementation cost into the optimization process. In particular, a spatial cost weighting is introduced in the objective function to account for depth-dependent implementation costs. A series of two-dimensional numerical examples is presented to assess the proposed framework. The results show that mechanically consistent reinforcement layouts are obtained and highlight the influence of implementation cost on their spatial distribution. The framework therefore provides a consistent basis for reinforcement design at the ultimate limit state in geotechnical engineering.