<p>This study investigated the time-dependent fracture mechanism of rock–concrete interface under compression–shear state and analyzed the time-dependent fracture behavior of rock foundation–concrete dam interface. First, a compression–shear cohesive constitutive relationship under constant loading was proposed to characterize time-varying cohesive effect of rock–concrete interface, and an improved energy density-based fracture criterion was proposed to judge the fracture state of rock–concrete interface under compression–shear state. Then, taking Greyrock gravity dam as an example, the finite-element method was employed to simulate time-dependent fracture behaviors of the rock foundation–concrete dam interface with respect to different initial crack lengths and constant water levels. The results indicated that, under water level lower than initial cracking water level, the average elastic strain energy density decreased and the initial cracking water level exhibited increasing tendency after undergoing constant loading. Under water level higher than initial cracking water level, the time-dependent crack propagation conditions can be divided into three types: (1) did not propagate; (2) propagated into a certain length and then kept stable; and (3) propagated and then unstable crack propagation occurred. As for the unstable crack propagation, the crack mouth sliding rate under constant loading exhibited obvious two-stage feature, i.e., rapid decreasing stage in primary stage followed by slow increasing stage. A prediction model was proposed to determine the service life of the rock foundation–concrete dam interface using the critical crack mouth sliding rate.</p>