Deep formation rich in the weak plane (bedding, micro-fractures) has strong strength anisotropy and is the internal control factor of frequent wellbore instability of the long horizontal section of shale gas wells, which seriously restricts the realization of improving drilling quality and efficiency. The conventional single plane or multi planes of weakness criterion only considers the pseudo-triaxial loading state (σ2 = σ3) or the loading direction of the intermediate principal stress σ2 coincides with the failure plane of weakness. Based on the theory of elastic mechanics and the Mogi-Coulomb shear failure criterion, this paper establishes the rock strength criterion considering the influence of the weak plane and three-dimensional stress loading. One analyzes the influence of three-dimensional stress on the strength of rock possessing parallel plane of weakness, the variation of equivalent density of wellbore collapse pressure in different time domains, and the influence of wellbore trajectory on wellbore stability considering different occurrences of the weak plane. The results show the obvious influence of intermediate principal stress on the failure of the rock matrix and the weak plane. The strength of the rock matrix first increases and then decreases with the increasing σ2. At a given small dip azimuth angle, the rock strength is controlled by the rock matrix and the weak plane for smaller σ2, while the rock strength is completely controlled by the rock matrix for larger σ2. The strength of the weak plane does not depend on σ2 where the dip azimuth angle coincides with the failure plane of weakness. At a given σ2, the range of failure angle of the weak plane gradually increases with the increasing dip azimuth angle. At a given minimum principal stress σ3, the apparent strength of the rock matrix increases with the increasing σ2. The larger angle between the borehole axis and the normal direction of the weak plane weakens the wellbore stability related to borehole collapse. Besides, the magnitude of the time-dependent equivalent density of collapse pressure descends in short-time, modified instantaneous, long-time, instantaneous, and elastic ones. Introduction of the influence of three-dimensional stress on the strength of rock possessing parallel plane of weakness and time-dependent stress and pore pressure solutions around a borehole is conducive to improving the prediction accuracy of equivalent density of collapse pressure and can help solve the problem of wellbore collapse in complex shale formations.
