Abstract:

Abstract:  Based on elastic mechanics and CoulombMohr fractural theory, we discussed the extremum of shear difference function, i.e., the difference of shearing stress and shearing resistance on an oblique section, in a triaxial unequal stress field by mathematical analysisWe set the stress field in three different states: the triaxial tensile force, the triaxial compressive force and the maximum and minimum principal stress with one tension and one compression, respectivelyThen, we discussed the relationship of trend surface direction of shear fracture to the three principal stress axes and to the inner friction angle and the cohesion of rocksThe potential direction of shear fracture surface was obtained in different stress statesIn the state of triaxial tensile force, the angle between the shear fracture trend surface and the maximum principal stress axis γ=±(45°-φ/2) and the conjugate angle χ=±(90°-φ)In the state of one tension and one compression, ±(45°-φ/2)≤γ≤±45° and the actual value is determined by the ratio of the tensile principal stress to the compressive principal stressThe shear fracture surfaces under the three kinds of unequal principal stresses are plane surfaces parallel to the intermediate principal stress axesThe existence of tectonic tension stress in geological structures is indubitableThrough the analysis of shear fracture trend surface in the state of one tension and one compression, we could solve the question about the fact that the shear surface conjugate angle χ>±(90°-φ) or even close to 90° encountered in the structural geologic investigation.

Key words:

Key words: triaxial unequal stress fields; shear fracture trend surface; shear difference function; CoulombMohr equation; conversion angle of normal tensile and compressive stress