Pressure buildup and corrosion at the bottom of the well may result in significantly adverse consequences on the integrity of the cement and casing. Wellbore integrity is highly depending upon the integrity of the interfacial bond between the cement and the formation as well as the bonding between casing and cement. Hence, these interfaces may act as weak paths for failure and potential broaching under the effect of excessive pressure nearby the wellbore. To incorporate the role of the cement sheath on the well integrity, we used cohesive but porous interfacial elements to simulate emergence and possible development of the failure zone. An axisymmetric poroelastic finite element model is built, where cohesive interface elements with zero in-plane thickness are embedded along the interfaces between cement and formation rock and between cement and casing. Nonlinear traction separation law is used to predict fracture initiation. Damage propagation is predicted based on maximum energy release rate criterion, where the parameters for this model could be extracted from the ultrasonic CBL measurements. Using this model, the effects of excessive pore pressure magnitude and positions on wellbore integrity have been shown through some numerical examples. Moreover, the favorable effect of formation permeability on the delamination is investigated. The results show stress and pressure redistribution due to the initiation and propagation of delamination. The proposed approach provides a tool to understand the competition between different interacting physical processes for propagation of failure zone near the wellbore.