A Universal Mathematical Method for Determining Occurrence of Underground Rock Discontinuity Based on TV Picture of Wall of a Single Borehole
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摘要: 岩体结构面产状是影响岩体力学性质及工程稳定性的重要地质因素.从钻孔孔壁电视平展图上可较精确地提取结构面迹线上不共线三点的相对二维坐标(d, h)，再利用空间解析几何理论确定其三维空间相对坐标(x, y, z)，并求得结构面法向矢量.根据钻孔孔壁与坡面及结构面产状的空间几何关系，在保持原点不变的情况下，采用空间坐标变换的方法，将三维坐标系z轴和y轴分别转化为竖直方向z′和正北地理方向y′，并确定转化后坐标系空间的结构面法向矢量.再从结构面产状的定义出发，根据结构面法向矢量与结构面倾向、倾角的相关性，建立了一个空间几何模型，通过该模型可求得任意平直坡面上任一钻孔内局部岩体结构面的产状.Abstract: 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.
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图 1 含结构面孔壁及三维直角坐标系
Fig. 1. Borehole wall including discontinuity and its 3D rectangular coordinates
图 2 孔壁电视图平展及二维直角坐标系
Fig. 2. Setting-out TV image of borehole wall and its two-dimensional rectangular coordinates
图 3 含结构面孔壁与斜坡面关系
Fig. 3. Relationship of borehole wall including discontinuity and drilling slope
图 5 结构面法向量在水平面投影示意
Fig. 5. Projection of normal vector of discontinuity in the horizontal plane
图 6 斜坡上倾斜钻孔电视孔壁平展图
Fig. 6. Setting-out TV image of inclined borehole wall of inclined slope
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