Casing support and zonal isolation are principal objectives in cementing the wells; however, the latter objective always raises the most concern particularly when there is a potential formation fluid migration into the cement sheath. Wellbore integrity is highly dependent upon the integrity of the interfacial bonding between the cement and the formation as well as the bonding between casing and cement. A closer look at the common cement strength test data, performed routinely in the labs, reveals a complicated behavior that cannot be simply modeled using a single parameter, i.e., the interfacial strength. Here, we used cohesive interface constitutive equation to model the behavior of cement interfaces. Formation of microannulus is modeled by utilizing an axisymmetric poroelastic finite element model enriched with cohesive interfaces to simulate initiation of the failure zone and possible broaching of the failure zone along the wellbore to shallower zones. We demonstrated that it is possible to use data produced from routine tests, such as the push-out test, to determine not only the shear strength but also the normal fracture energy and the stiffness of the cement interface. Cohesive interface properties are calibrated such that simulated test results match with the measured response of the specimens. In the next step, we used these parameters to anticipate well-cement behavior for the field-scale problems. A sensitivity analysis is provided to show the role of each parameter in initiation and development of the failure zone. Interestingly, the shear strength, which is commonly measured from push-out tests, is not the only parameter determining the size of the fracture, but other parameters such as normal strength show equally important influence on initiation and propagation of the failure zone. The proposed approach provides a tool for more accurate predictions of cement integrity in the subsurface conditions to quantify the risk of wellbore integrity issues.