A Novel Method for Optimizing the Robustness and Carbon Emissions of Anchored Slopes

Anchored slopes have been widely adopted globally, yet their design faces two critical challenges: the unreliable characterization of geomaterial variability and the urgent need for low-carbon. To address the first challenge, we propose a novel sensitivity index of variability (SIV) formulated through Monte Carlo Simulation (MCS), which systematically quantifies robustness within reliability-based design. Meanwhile, in response to global low-carbon initiatives, carbon emission metrics are innovatively established as the optimization objective for robust geotechnical design (RGD), replacing conventional cost-centric approaches. Building on these methodological advancements, we develop a framework that simultaneously optimizes engineering robustness and environmental sustainability. The operational efficacy of this framework is demonstrated through a case study of a rock slope at the tailwater tunnel outlet of a hydropower station in southwest China. Comparative analysis with the initial design solution reveals that our framework achieves higher robustness while reducing carbon emissions, demonstrating the superior performance of this framework. This study offers a systematic approach to advance both safety and sustainability in geotechnical infrastructure. The proposed methodology is readily adaptable to other earth structures facing similar reliability–environmental trade-offs.