###### Abstract  
The shear constitutive model of the slip zone soil can be used to quantitatively describe the relationship between shear stress and shear displacement, which is of great significance for the analysis of deformation mechanism and stability evaluation of landslides. The conventional shear constitutive models were usually proposed based on statistical damage theory with the Weibull distribution function, which is widely used in the field of rock material. However, there are great differences in the structure and mechanical properties of soil and rock; therefore, the suitability of the damage distribution functions for the slip zone soil needs to be further investigated. In this study, eight distribution functions are introduced to describe the damage evolution process of the slip zone soil and applied to two groups of shear stress-shear displacement curves (named shear curves) with different softening characteristics, i.e., strong softening type and weak softening type. The results show that: (1) the applicability of the various damage distribution functions to the two softening types of shear curves is obviously different; (2) the commonly used Weibull distribution is only suitable for the weak softening shear curves; (3) the shear constitutive models based on Gamma, Exponential, and Logistic distributions are the best three models for the strong softening curve; the shear constitutive models based on Gamma, Weibull, and Exponential distributions are the best three models for the weak softening curve; (4) Gamma distribution function is the optimal model in both strong softening and weak softening types of shear curves, and the parameters of the function have clear physical meaning in the shear constitutive model. In general, the Gamma distribution function can more objectively reflect the whole shear damage evolution process of the slip zone soil than other distribution functions. landslide; statistical damage; strain softening; sliding zone soil; ring shear test 202202123493 2022123493 2022123493 202123493 2022123 curves, the hyperbolic model and piecewise linear model were proposed [9; 10; 11]; after the peak of stress-strain curves, strength abruptly falling model [12; 13], linear attenuation model, and hyperbolic attenuation model was proposed [14; 15]. However, these models only reflect the relationship between stress and strain and cannot intuitively represent the characteristics of large deformation of slip zone soil. Recently, a shear constitutive model describing the relationship between shear stress and shear displacement is proposed based on statistical damage mechanics [16; 17; 18]. It has obvious advantages of representing the large deformation mechanics of slip zone soil and providing the basis for dynamic evaluation of landslide stability. Statistical damage mechanics have been widely used in the constitutive models of rock materials [19; 20; 21; 22; 23; 24]. In recent years, the statistical damage mechanics of rock have been introduced into the soil field [16; 17; 18; 25; 26]. Based on statistical damage, the damage variable can be defined as the damage degree of the material. The distribution of damage variables (damage distribution) with displacement in the shear constitutive model represents the damage evolution with shear displacement. However, the damage distribution of soil directly adopts the Weibull distribution function [27], which is widely used in the rock damage mechanical field. In fact, due to the great differences between structural and mechanical properties of soil and rock, the damage distribution function of soil may differ from that of rock. Therefore, the damage distribution function of the slip zone soil needs to be further investigated. A large number of ring shear test results of slip zone soil show that the shear stress-shear displacement curves (named shear curves) can be classified into two types including weak softening curve and strong softening curve.