## 1 Introduction  
In recent years, the strength discounting method has seen significant development in slope engineering alongside numerical analysis that applies continuous and discontinuous methods. The ultimate load related to geotechnical engineering is calculated by reducing the strength of the slope and defining the discount factor for the critical instability state as the slope safety factor. This method is essentially the same as the traditional limit equilibrium method. Furthermore, compared with the limit equilibrium analysis method, the numerical analysis can automatically derive the critical slip surface of arbitrary shape and the corresponding minimum safety factor [1; 2; 3]. [PERSON] et al. [4] established a finite element model for strength reduction calculations and compared the results with those of the simplified Bishop method, demonstrating the reliability of the finite element strength reduction method. The application scope of the finite element strength reduction method has been developed continuously, expanding from soil slopes to complex rocky slopes with weak interlayers and structural surfaces, extending from two-dimensional models to three-dimensional models, and changing from a single sliding surface to searching for multilevel secondary sliding surfaces. In this current research on the strength discounting method, the traditional approach of equal proportion discounting of geotechnical strength parameters is used. [PERSON] et al. [5; 6] considered that clayey slopes are damaged and softened with the formation of shear zones, and c (indicating cohesion) decays faster than \(\varphi\) (indicating the angle of internal friction). Further, sandy slopes are prone to shear expansion and softening with the formation of shear zones, and \(\varphi\) decays faster than c. [PERSON] [7] highlighted the deterioration effect of rainfall on the structural surface of slopes. Taking clayey soil slopes as the research object, [PERSON] [8] indicated that a change in water content leads to a deterioration in strength parameters and proposed a method to consider strength reduction under the natural deterioration in mechanical soil parameters. [PERSON] and [PERSON] et al. [9; 10] considered the weakening paths of the strength parameters of soil and discounted the strength parameters c and \(\varphi\) by non-equal proportions on the basis of the Mohr-Coulomb and Hoek-Brown yield criterion, respectively. [PERSON] et al. [11] derived the strength parameter by discounting the scale relationship from the tangent angle based on the critical strength parameter and initial strength parameter of the slope. According to [PERSON] et al. [12], when using the elastic-plastic finite element method to calculate the factor of safety, it is necessary to discount the deformation parameter \(\mu\) (indicating Poisson's ratio) in addition to the strength parameter in order to ensure \(\sin\varphi\geq 1\)-\(2\)\(\mu\) and obtain a more accurate factor of safety. Based on the Duncan-Chang model, [PERSON] et al. [13] proposed adjusting the modulus of elasticity and discounting the strength parameters. [PERSON] et al. [14] undertook cyclic loading and triaxial compression tests on rocks at different stress levels, identifying that at higher stress levels, the triaxial compressive strength of the rock is reduced. Furthermore, the coefficients, including the damping ratio, are inversely proportional to the number of cycles. [PERSON] et al. [15] considered the progressive degradation effect of the structural surface during dynamic loading and evaluated the stability of rocky slopes containing structural surfaces using 3 DEC software. In the progression of this research, although the deformation and strength parameter discount ratio are discussed separately, the effect of tensile strength under dynamic action is neglected. The results of many studies show that, under a static state, the destabilization damage mode of a slope is mostly shear damage [16; 17]. Taking weathered rocky slopes and soil slopes as an example, [PERSON] et al.