Rock mechanics engineers are seldom concerned with obtaining the tensile or fracture strength of brittle rock at low mean stresses. The reason for this is twofold. Firstly, the behavior of many excavations in brittle rock is controlled by the inherent discontinuities in the rock mass. Because of the jointing and faulting, tensile strength is usually taken to be negligible. The second reason that tensile strength is seldom obtained in the laboratory is that the technology of utilizing this strength measure in design is undeveloped. Despite the fact that tensile strength of brittle rock is often ignored, there are a number of applications in rock mechanics wherein the knowledge of tensile strength is of fundamental importance. The apparent tensile strength must be known in a hydraulic fracture experiment if the state of in situ stress is to be determined from the initiation of the hydraulically induced fracture. In certain underground situations, the apparent tensile strength of intact rock beams defined by jointing or bedding planes is important in determining required rock bolting. Numerous other situations require a knowledge of apparent tensile strength including such high technology uses of underground space as geothermal energy extraction and LPG storage. Three observations are invariably made when intact rock samples are taken into the laboratory and tested to determine tensile strength.
(1) The apparent tensile strength depends on the sample size (the larger the specimen, the lower the tensile strength)
(2) The apparent tensile strength depends upon the type of test being performed.
(3) With any given test and specimen size, a scatter (usually skewed) about the mean is obtained.
The first dilemma (commonly referred to as the size effect) is also observed with respect to strength at higher (more compressive) mean stresses, although to a lesser extent than with tensile strength. The observation of size effect has prompted many investigators in rock mechanics to recognize that the tensile strength measured at the usual laboratory scale is not a material property. Rather than explaining the differences in strength measured in different types of tests, we readily give adjectives from the test type to label the strength measure. For example, we refer to the Brazilian tensile strength, the direct tensile strength, the Modulus of Rupture (a strength measured in bending), etc. Although the rock mechanics community has not completely come to the realization that the same phenomena occurs in fracture toughness testing, it is becoming popular to refer to the fracture toughness of rock with an adjective taken from the test type (Ouchterlony (1980)). The third observation noted above is often totally neglected in the reporting of test results. Scatter about the mean is often attributed to testing methodology and/or sample-to-sample inhomogeneity. Statistical moments can be useful in understanding the strength characterization of brittle rock and should be reported. The purpose of this paper is to discuss various theories of tensile or fracture strength of brittle rock and to examine critically how these theories address the laboratory observations noted above.