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Conventional key block approaches are generally based on the unrealistic assumption of infinite fracture planes defining wedges, and without consideration for the structure of fracture location. A more realistic approach has been developed based on bounded fractures and realistic, geologically based spatial fracture patterns. The fracture patterns can be conditioned to match observed fracture traces, while extrapolating the fracture geometry into the rock.
The to key block analysis is understanding the three dimensional size and interlocking of rock blocks (Hatzor and Goodman, 1992). The primary key-block algorithms currently available are those of Einstein and Glynn (1979), Goodman and Shi (1985), Warburton (1987), and Carvalho et al. (1991). These algorithms were all developed initially for application to infinite fractures. Recently, a number of authors, including Jing and Stephansson (1984) have recognized the need to utilize more realistic fracture patterns.
The algorithm for evaluation of key-block stability is as follow.
The fracture pattern should be generated based on the appropriate geological and geometrical model, based on site data. If possible, the model should be conditioned to fracture mapping or local borehole information. An example fracture pattern based on site data from Sweden is shown in Figure 1. The fracture geometry may include major structural features such as faults and folds, stratigraphie contacts, and spatial variations in fracturing patterns. The first stage of calculation of rock blocks is therefore calculation of fracture intersections based on the equations for intersections of plane polygons in three dimensions.
The first requirement for rock blocks is that they be defined for rock blocks which have at least one face in common with the tunnel being evaluated. The trace map for the fracture intersections with the tunnel is defined by providing the full, three dimensional tunnel geometry, within the same spatial coordinate system used for generating the fracture pattern. The trace maps are calculated using the equations for intersections of plane polygons in three dimensions to generate the two-dimensional line segments which form the trace map for a particular panel of the tunnel structure (Figure 2). Once the tunnel tracemap has been calculated, rock blocks can be constructed by taking fractures which form closed two-dimensional blocks in the tunnel tracemap, forming tracemaps on those fractures and repeating the process until all fractures participating in tracemaps are part of one or more blocks (Jing and Stephansson, 1994). At this stage, we have a collection of faces and connection information. The collection of faces is then processed using an "unfolding" algorithm to form the minimum volume polyhedron which connects to a tunnel face. Checks are made to ensure that the polyhedron generated is closed. Blocks are constructed until all tunnel faces have been tried.
The rock block volume is computed by a process of three-dimensional tessellation. The mass is then determined using this computed volume and the rock-density.
