Abstract: The approximate function of normal stress distribution of symmetrical slope slip surface based on grid element is constructed, which provides a theoretical basis for establishing the limit equilibrium method based on the assumption of normal stress on slip surface in GIS(geographic information systems). Combining GIS's powerful spatial data analysis capabilities, a three-dimensional slope stability analysis model is established based on grid element. Under the assumption that there is no force, the distribution of normal stress on slip surface is deduced. With an analysis example, we can draw a conclusion: in the perspective of the sliding direction of the sliding body, the distribution of the normal stress on slip surface comprises several portions. The largest portion is the dead-weight of the sliding body and the external force, as a known function. The other portion that accounts for a small percentage is consisted of the force between the columns, as an unknown function. Therefore, the approximation function on the distribution of forces between the columns can be performed by a third-order Lagrange polynomials. In the direction perpendicular to the sliding body, the normal stress distribution on slip surface is approximated by parabolic approximation, and then we construct an approximation function of the normal stress distribution of slip surface based on grid element. This kind of approximation function is easily expressed in the GIS. In the end, the rationality of the approximation function is verified by an example.

Key words: three-dimensional slope, limit equilibrium, normal stress on slip surface, approximation function, GIS, grid element