Abstract：In the research of interaction between dam and its foundation，it is necessary to describe the roughness of the rock surface in order to provide parameters for evaluating the shear mechanical characteristics of the interface. Some issues in the former description of rough surface are analyzed；moreover，it is pointed that the fractal dimensions D may perfectly describe the fine surface such as in the situation of smooth metal friction，but it cannot be directly used in evaluating mechanical properties of rock surfaces where the size of roughness is large-scale. However，with the aid of fractal theory，a new index Rd to describe surface roughness is defined. The index Rd is reasonable because the effect of large-scale roughness is emphasized，which is accord with the fact that the larger the size of roughness is，the more it will affect the rough surface mechanical properties. Meanwhile the value range of Rd is larger than that of fractal dimensions D，which makes it easier to distinguish the roughness of different surfaces. Besides，the Rd value is independent of measuring direction and it is corresponding to the roughness of the area where it describes. Bring the new index Rd into comparison with convention index Ra and fractal dimensions D，the rationality of the new index is testified. However，in the description of the roughness，the rough index should not only have the same value when the rough surface is measured in different directions，but also exhibits that same rough surfaces have different mechanial behaviors when the shear is in different directions. It is pointed out that such two tasks cannot be accomplished with single index. Through theoretical and numerical analysis，a shape factor parameter is proposed. Thus， and Rd make up of a two-parameter system to describe the rough surface. In this system，Rd describes the fine roughness and its value is steady when the measure direction changes，while describes the large size roughness on the surface and its value is varied when the shear direction changes. For the specimen with constant value in its width，the elementary relationship between two-index description system and interface mechanical property is given；and the influence factors are introduced.
