4.1.4 Tension crack present in the upper slope surface
A tension crack is a void that runs parallel to a slope face (figure 3). It effect on slope stability is considered based on specified location and depth determined by stability charts (Hoek & Bray, 1977), or empirical judgements. Analytical methods are also available for locating the tension cracks along assumed slip surfaces (Sancio & Goodman, 1979; Baker, 1981). If the position of a tension crack is known on the upper surface of a slope, its stability analysis should be based on this existing information. However, when the position of the critical tension crack position is unknown, it becomes necessary to use an optimization approach to locate the position and depth of the tension crack.
Figure 3: Tension crack in upper surface of slope and in the face
The location of the tension crack (figure 4) is expressed by the dimension b (Hoek and Bray, 1981). When the upper surface is horizontal, the transition from one condition to another occurs when the tension crack coincides with the slope crest. The depth of critical tension crack, zc and its location, bc behind the crest can be calculated by the following equations:
If the location of tension crack is known then depth of tension crack can be determined by the following equation.
Where, H is the slope height, α is the slope face angle and Ө is the dip of the sliding plane. The factor of safety is calculated as follows:
Length of discontinuities;
The weight of the block; QUOTE
Factor of safety =
Figure 4: plane failure with tension crack