ASTM PCC-2 standard provides a series of equations for establishing the composite repair's thickness required for bringing the capacity of dented/damaged pipes, to their original design state. However, the accuracy of the equations' predictions for pipes subjected to various combined loadings has not been fully explored. Moreover, the influence of the state of a pipe/composite wrap (CW) interface (i.e., whether perfectly intact or not intact), in reference to the predictions of the ASTM equations, has not been studied either. In consideration of the above-mentioned issues, a comprehensive finite-element (FE) study is conducted, using the cohesive zone methodology (CZM) to simulate the response of pipes repaired with composite wraps, under single and various combined loading conditions. Moreover, the influence of perfect (or tied) and imperfect (unintact) pipe/CW interface on the load-bearing capacity of repaired pipes is systematically investigated. Finally, the effects of composite repairs' thickness and length on their efficacy are also investigated. The results show that, although the pipe/CW interface state does not have any noticeable effect when the pipe is subjected to a combined loading state of bending moment and internal pressure, it plays a crucial role when the pipe is under a combined internal pressure and uniaxial loading condition. Furthermore, the predicted values calculated according to the ASME standard are compared with the finite-element results, demonstrating that ASTM-based predictions do not provide accurate results when a repaired pipe is subjected to an axial loading condition.