Abstract:The construction of rainfall threshold curves is a crucial foundation for predicting landslides triggered by rainfall and assessing risks. In response to the limitations of traditional empirical threshold methods,which rely on historical disaster data,have limited computational efficiency due to physical model calculations,and lack sufficient interpretability in conventional machine learning models,this study takes the Zhongzhai landslide in Tianshui City,Gansu Province as an example.It proposes a new method for predicting rainfall threshold curves by integrating seepage-stability physical mechanisms with Gene Expression Programming (GEP) symbolic regressiontechniques.First,finite element seepage-stability simulation is used to obtain the unsaturated soil water characteristic curve based on the Van Genuchten model.This curve is then used to simulate the evolution of pore water pressure during rainfall infiltration. Subsequently,the seepage results are incorporated into the stability analysis.Using the Morgenstern–Price limit equilibrium method,response data for the stability coefficient of landslides under different rainfall intensities and duration can be obtained.This model is used to characterize the impact of rainfall infiltration,pore water pressure accumulation, reduced effective stress,and decreased shear strength on the instability of slopes.Based on this,this study constructs a explicit response surface model where rainfall intensity and duration are input variables, and stability coefficients are output variables.The threshold curve for continuous rainfall is determined using the warning criterion of Fs=1.05. The results show that the GEP model can effectively fit the stability response patterns obtained from numerical simulations. The threshold curves derived by the GEP model closely match those of the original numerical simulations. The R² value is 0.997940, the RMSE is 1.198232 mm/d, and the MAE is 0.614462 mm/d. Under the condition of heavy rainfall of 150 mm/d, the warning times predicted by the GEP model are consistent with those from numerical simulations, with a relative error of only 0.66%. This method develops a framework for predicting landslide rainfall thresholds that integrates physical mechanisms with symbolic regression. It can serve as a reference for determining rainfall warning thresholds for individual landslides.