A Universal Mathematical Method for Determining Occurrence of Underground Rock Discontinuity Based on TV Picture of Wall of a Single Borehole

The rock mass mechanical properties and stability of rock engineering are remarkably affected by the occurrence of rock discontinuities. The relative 2D coordinates (d, h) of three non-collinear points at the discontinuity can be accurately derived from setting-out sketch of TV picture of borehole wall. The relative 3D coordinates (x, y, z) of these points and the normal vector of the plane which are determined by them can be obtained using space analytic geometry method., The z-axis and y-axis are rotated toward vertical (z′-axis) and north direction (y′-axis) respectively according to the space geometric relationship of borehole wall and the occurrence of slope and discontinuity without changing the original point and using space coordinate transformation, and the new normal vector of discontinuity in transformed 3D coordinates can also be obtained. Based on the dependency of normal vector, inclination direction and dip angle of discontinuities, a 3D geometrical model can be established, by which the local discontinuity occurrence of any borehole on any flat slope can be determined efficiently.