Shearing stresses and normal tensile stresses play both a decisive role in fracturing and brittle of rock material. Based on this hypothesis, a novel strength criterion was developed in one the earlier works of the author. In the criterion, a certain parameter v'' occurs which depends on structure of the material. Originally, the parameter was treated as a constant, which resulted in a linear form of the strength function Fσ1=f(σ3).Although the linear strength criterion is sometimes found to be applicable to various particular rock materials, it is not, in general, of a universal character. Analysis of the triaxial test results for sixteen different volcanic rocks revealed that parameter v'' usually increases in an exponential or linear manner as confining pressure increases, and only in isolated cases does it seem to be independent of the confining pressure. For these three types of dependence v''=f(p) appropriate strength criteria Fσ1=f(σ3=σ2=P)have been given in the present paper. These criteria were used to fit all of the collected empirical data sets. In general, an excellent fit to the data was obtained. Values of the "material constants" that occur in the criteria have been listed, providing a source of input data for rock engineers involved in the design of engineering structures built of or in volcanic rocks.
Ithas generally been accepted that under conditions of triaxial compression, fracturing and failure of rock material occurs as a result of both shearing stresses and normal tensile stresses that are locally generated in the vicinity of microdefects or imperfections. Based on this observation, the author proposed a novel linear strength criterion in one of his earlier works (Kwasniewski 1987; see also Kwasniewski 1989).
The proposition given above has been proven on the basis of an analysis of the conventional triaxial compression test results of several volcanic rocks. Based on an extensive literature search, sixteen empirical data sets [σ1 = f(p)]F have been collected for these rocks, which express the major principal stress at strength failure as a function of confining pressure in the brittle, or at most, transitional field. Samples of these rocks were tested by different investigators at confining pressures that rarely exceeded 100 MPa; it was only Shimada (1986) who tested samples of Yakuno basalt under confining pressure of about 250 MPa (at this pressure the rock still behaved in a brittle manner). When collecting the experimental test results and determining their suitability, only the numerical data taken from original papers and/or reports were taken into account. No attempt was made to read values of the limiting major principal stress (Fσ1)from stress strain curves or from ultimate strength - confining pressure plots. Five data sets have been collected for andesites from the Japanese Islands and from Ontario (Canada), five for basalts from the territory of Japan, Poland, Texas (USA) and Quebec (Canada), two for diabases from Maryland (USA) and Quebec, two for liparites from Japan, one for a rhyolite from Ontario and one for a trachyte from Japan.