ABSTRACT
A main feature of this strategy consists in incorporating information of fracture aperture size in the result of fracture face mapping, because the aperture provides a potential for estimating fracture permeability. As indicated in Figure 4, a selected plane section of medium around a borehole or the cross section between two boreholes is discredited into a two dimensional grid of cells (rectangular elements). As each elongated (straight) fracture (k fracture line) passes through the cells, the corresponding aperture size value is successively summed up in each cell, depending on the fracture length segment Wkj. As mentioned above, the fracture lines are estimated from fracture face mapping algorithm. If the fracture line does not pass through a particular grid element, the segment length Wkj is set to zero. The final value (aperture size value of each cell) Dj derived from all the detected fractures constitutes the fracture aperture density distribution of the selected plane section. (Kim et al., 2002d). That is, the aperture value Dkj in each cell j for k fracture line can be expressed as :
I : total number of grid elements Ak : aperture size value of K fracture line
The final fracture density Dj is then given simply by
4 THREE-DIMENSIONAL PRESENTATION OF FRACTURE MAPPING AND FRACTURE APERTURE DENSITY DISTRIBUTION
As the permeability of hard rock is mainly influenced by fractures, a three-dimensional view of fractures around the test borehole is very helpful to examine some prevailing water flow routes, to envisage a future grouting or excavation plan. This far, the estimated fractures lines are imaged only on the plane section crossing the test hole (see Fig. 3). However, for a three-dimensional presentation, the fracture lines should be determined by intersecting of each fracture plane with an
cated in Figure 5. Figure 6 illustrates the corresponding geometry of fracture plane, arbitrary plane section S and fracture line, with the previous geometry description in Figure 5 in mind. The goal of this algorithm is to find the positions DS1, DS2 which allow determining the
DepDif1(Ds1 DA) and DepDif2 are beforehand calculated. In geometry condition, they are:
Thus, the depths z1, z2 of cross points Ds1, Ds2 are given:
Finally, regarding the geometry relation shown in Figure 7, the horizontal coordinates of Ds1(x1, y1) and Ds2(x2, y2) can be easily computed:
The intersected line, that is, the fracture line from fracture plane and arbitrary plane section apart from the test hole is then determined by two point, Ds1(x1, y1, z1), Ds2(x2, y2, z2) in space. The corresponding fracture
aperture density value in each cell can be also evaluated in the same manner shown in Figure 4.
