Abstract: In order to predict the shear strength of the rock-concrete joints subjected to the constant normal stiffness (CNS), the classical Patton model (idealized as regular triangular asperities) is modified, and the regular triangular asperities are extended to similar ones. The quantitative method for the roughness of rock-concrete joints is also given. Compared with the regular ones, the similar triangular asperities carry different local stresses due to different wavelengths, leading to an asynchronous failure. The collapse load and critical shear displacement of every asperity are identified by the lower-bound solution. On this basis, an evolution equation is proposed to quantify the occurrence of local failure, and the classical Patton model is generalized. The generalized Patton model can predict the shear strength of joints of both the regular and the similar triangular asperities, and the current form can be regressed to the classical form under certain conditions. Finally, the proposed model is validated by the observations from 12 groups of CNS direct shear tests.