The Failure Surface of Isotropic and Anisotropic Rocks under Multiaxial Stresses

Abstract

A newly designed triaxial testing machine was used to investigate the ultimate strength of sandstone and crystalline schists under multiaxial stresses. Each specimen used was 5.5 cubic cm in size, and the capacity of the testing machine was 200 tons vertically and 100 tons in each horizontal axis. The experiments were carried out under stress-controlled condition (8tons/min). Rubber sheets with silicon grease were always used to minimize friction between the specimen and piston plates; thus the coefficient of friction could be reduced to 0.002.The unconfined compressive strength of sandstone was found to be σc=1190kg/cm2 with variation of about ±3.9%. For the sake of non-dimensional representation of multiaxial test data, all the results are expressed as the value divided by σc.Introducing the principal stress parameterλ=2σ2-(σ1+σ3)/σ1-σ3(-1≤λ≤1), experimental results of the axial compression test (λ=-1) with high confining stress are in accordance with Mohr-Coulomb's failure criterion, deriving the strength parameters φ0=33°40' and c0/σc=0.46. The influence of the intermediate principal stress can be expressed by the following extended Mohr-Coulomb's criterion:σ1-σ3/σ1+σ3+2c0cotφ0=sinφ0/1-α*/2√1-λ2=sinφλ, provided we choose the parameter α*=0.07. Under low confining stress, however, the experimental results deviate from the above criterion; we cannot regard them as shear failure.The final representation of the test data is the failure curve on the octahedral stress plane as shown in Fig. 8, indicating a slight influence of the intermediate principal stress on the strength of sandstone.With respect to the multiaxial compression test using schists, attention will be called to the main object which consists in investigating the change in the ultimate strength due to the inclination angle of jointed plane and the variation in these characteristics under high confining pressures.As is clear from uni-axial compression tests on cylindrical specimens, the influence of the inclination of jointed plane on strength is maximum for α≈30° (α: angle between maximum principal stress and jointed plane), the decrease in strength being 75-90% of that for α=90°(see Fig. 10).Failure pattern is generally divided into the cleavage failure along the jointed plane, the shear fracture along it and the shear independent of the jointed plane. From the result of triaxial compression tests on the cubic specimens it is known that the decrease in anisotropy of rock strength cannot be expected to be so large; for α=30°-specimens there occures 50% decrease in strength even under the confining pressure as high as 200kg/cm2 (see Fig. 11).From a series of triaxial compression test under the condition of αoct=const, the failure plane of actual rocks with laminated cracks in the principal stress space is determined as shown in Fig. 13.