The probability distribution of fracture data from a rock mechanics test contains information about the effectiveness of the testing procedure and/or about the nature of the operating failure mechanism. The tensile strength of Lac du Bonnet granite forms a bimodal probability distribution when determined through line loading as in the Brazilian test. The same data obtained from three point bends tests are unimodal. The bimodality can in part be removed by distributing the line load over a finite area. Moisture has the anticipated effect in lowering both the average compressive and the average tensile strength of Lac du Bonnet granite. The reduction in strength however is not uniform within the probability distribution; the change is the largest at low and the smallest at high strength. Conversely, long-term loading is more damaging to the high strength members of the distribution. The large scatter of failure times in static fatigue experiments can in part be removed or even utilized when the probability distribution of instantaneous strength is taken into account.
Rock mechanics professionals are all aware of the probabilistic nature of geotechnical measurements and events. They routinely make use of statistical techniques in reducing data and often make statistical inferences about the means based on the assumption of a normal or "student t" distribution. In the process of analyzing fracture data relating to the Lac du Bonnet granite, the comparison of the distributions of fracture data has been yielding more useful information than statistical tests of population means.
The measurement of tensile strength by diametral compression of rock core slices has always been somewhat contraversial. The reason for this is that fracture may not start at the centre, i.e. under the influence of the tensile stress concentration, but at the platen rock contact where high compressive stress concentrations may develop. In the testing of Lac du Bonnet granite, the use of a flat, ungrooved platten (concentrated line loading) results in a probability distribution that is clearly bimodal (Figure 1); the Weibull two-parameter cumulative distribution function (Weibull, 1951) gives a relatively poor fit at the low-strength tail. The source of the bimodal distribution is not the rock itself, because an alternate test, the three point bend test, gives a unimodal form (Figure 1). The use of the recommended finite area loading (Mellor and Hawks, 1971) seems to produce the desired result (Figure 2). The biomodality has not completely disappeared, but the unimodal Weibull fit is much better as quantified by the higher value of the coefficient of codetermination (r2).
The growth of microcracks in a uniaxial compression test is usually demonstrated by tracking the course of the volumetric strain. Alternatively, the intensity of cracking at a certain value of compression may be characterized by the tensile strength of the test specimen with tension applied across diametral planes as in the Brazilian test. Although a large number of specimens are required for meaningful results, there are two advantages.