[21] have proposed the Grasselli model which considers 3D roughness on the surface of discontinuity using a number of optical tests and direct shear tests.

And, interpretation of the mechanisms of discontinuity failure with different roughness degrees has not been conducted, for example, shear failure under different loading, failure of heave on the surface of discontinuity, influence of microstructure topography on macroshear strength, and so on.

For natural rock mass discontinuity, the heaves on the surface of discontinuity have the same strength with rock mass under the condition of nonfilling.

Therefore, based on the typical curves of shear strength and shear displacement for two failure modes, the failure of discontinuity presents brittle character when the heaves on the surface of discontinuity are completely cut off from their bottoms, while it presents ductile character when the roughness of discontinuity is decreased due to the shear process.

Under the normal stress influence, shear stress on the surface of discontinuity is not also distributed unequally (Figure 10(c), and the force state of the lower shear box is shown in Figure 10(c)).

This phenomenon can be explained that the asperity height with 8 cm cannot be damaged easily due to the overheight of the heave on the surface of discontinuity under certain normal stress.

Therefore, it can be concluded that the normal stress plays a dominate role to increase the peak shear strength because the significant normal stress will cause close integration of the heaves on the surface of discontinuity which increases the peak shear strength of discontinuity.

In a geometrical sense, the horizontal grazing occurs when the surface of discontinuity has a tangent plane at the grazing point which is parallel to the time axis and the vertical grazing occurs whenever the tangent plane at the grazing point is perpendicular to the time axis.

where [GAMMA] is a cylindrical surface of discontinuity and defined as [GAMMA] = {(t, x)|[PHI](x) = 0, t [member of] R, x [member of] G}.

where the surface of discontinuity is [GAMMA] = {(t,x,x') | x = 0, t [member of] R}, System (2.9) admits 2[pi]-periodie continuous solution of the form [PSI](t) = 1 - cos(t).

Consider a near solution x(t) = x(t, 0, [bar.x]) of (2,28) to [PSI](t) with [bar.x] [not equal to] 0, It is easy to determine that all near solutions intersects the surface of discontinuity [tau](x) = [[tau].sub.0](x).