A new and very simple method has been used for determining the triaxial strength of rock materials. The test pieces are cylinders 15 mm in diameter and 45 mm in length. The shear strength is determined at different axial pressures. The nonlinear relation between shear strength and axial pressure is well described by a simple two-parameter expression. This expression coincides for small axial pressure with the well known Coulomb-Navier theory but attains a constant value for higher pressures. The shear strength is determined for ten rocks and four ores.
Un procede nouveau et tres simple est applique pour determiner la force triaxiale des mineraux. Les echantillons se composaient de cylindres d'un diamètre de 15mm et d'une longueur de 45 mm. La resistance au cisaillement etait determinee à des pressions axiales differentes. La relation non-lineaire entre la resistance au cisaillement et la pression axiale se definit par une formule simple à deux parametres. A petites pressions axiales, cette formule correspond à la theorie de Coulomb-Navier, à pressions plus elevees, elle arrive à une valeur constante. Les essais ont ete effectues sur quatre minerais et dix roches differentes.
Eine neue und sehr einfache Methode fuer Bestimmung der triaxialen Starke von Bergmaterialen ist angewendet worden. Die Probekarper waren Zylindern - im Durchmesser 15mm und Lange je 45 mm. Die Scherfestigkeit ist bei verschiedenen Axialdruecken festgestellt. Wir haben gefunden, dass die Relation zwischen Scherfestigkeit und Axialdruck durch einen einfachen Ausdruck mit zwei Parametern gut beschrieben werden kann. Der Ausdruck fallt fuer kleine Axialdruecke mit der wohlbekannten Coulomb- Navier-Theorie zusammen und erreicht fuer höhere Druecke einen bestandigen Wert. Die Scherfestigkeit wurde fuer zehn Gesieinsarten und vier Erze festgestellt.
When determining the triaxial strength of rocks it is usual to measure the greatest principal stress at fracture as a function of the least one. With the help of Mohr's circle diagram it is then possible to calculate the shear strength (τn) as a function of the normal pressure on the fracture surfaces (pn). These tests, however, are rather complicated and time consuming. We therefore use a simpler method [5, 6] where we measure the shear strength directly at different normal pressure. The arrangement is seen in figure 1 and consists of two pieces of hardened steel. There is a cylindrical hole through these pieces. The test piece is placed in the hole with very good fitting and is then pressed axially to a certain pressure (pn) between two steel cylinders with the same diameter as the test piece. The test piece is then sheared off and the force from which the shear strength (τn) is calculated is measured. Forces and pressures are measured with an X-Y-recorder, which plots τ and p directly on a diagram. As the test piece is confined, pn can be given values even greater than the uniaxial compression strength. We have used values up to 6 kb which are only limited because of the hydraulic jack. The shear strengths measured are somewhat higher than those from the conventional compression test [5, 6]. This may be due to the fact that in this case fractures arise along definite planes whereas in triaxial compression test, they can choose the weakest paths.
The shear strength is determined for ten rocks and four ores as well as for silver steel. The results are seen in figures 2–15, where the shear strength (τn) is plotted versus normal pressure (pn).
It is well known, however, that these two expressions do not coincide particularly well with the experimental results. Figure 2 shows how the expressions deviate from the experimental results. Some modification of the formulas has been made by Anderson [1] and McClintock-Walsh [7] but they too stated that the strength increases linearly with the normal pressure. This cannot be correct for high normal pressure, however. As μ pn becomes greater than the grain strength the grains must begin to yield and a further increase in the normal pressure will then not increase the strength. We may therefore expect the shear stress to consist of several different parts, including the yield stress of some grains, the friction stress of some, and the shear stress of grains in the unbroken part of the material. When the mean shear stress attains the maximum value the material fails. The problem is, however, to find the strength distribution of the grains. From the figure it is seen that there is very good agreement. The strength of rock materials may now be characterized by the three constants μ, τo and τi,. Table 1 shows these constants for the tested materials. τo is lower than 0.6 kb for all materials except steel, μ varies from 1.0 to 2.5 and the limiting shear strength (τi) has values from 5.6 to 11.7 (20.5) kb.
