Pavement structures are subject to several deterioration patterns classified in surface or structural failure modes. Structural deteriorations are frequent and lead to heavy and costly maintenance. We restrict our study to the fatigue longitudinal cracks which arise in the underlying layers and growth up to the surface due to traffic repetitive tensile stresses. The characterization of the complete cracking process is very complex because of a large number of covariates and the strong randomness of the environment (climate and traffic loads). Moreover, the current maintenance indicator is a cracking percentage of the road section surface. It gives only partial information onto the underlying racking. In such a context, a condition-based maintenance model on a single variable does not allow to guarantee an optimal maintenance decision. In [10], we have proposed a new model for the longitudinal cracking based on a bivariate stochastic process where the joint probability is a function of the current system state. It allows first to propose a new modeling of imperfect maintenance and then to differentiate maintenance according to their own cracking speed. Nevertheless, one of the main limits is the difficulty of its implementation in operation. The objective of this work is to deepen the model in [10] for improving its applicability for road maintenance while keeping their theoretical properties and advantages. Two directions are developed. First, a new definition of the bivariate deterioration process and the construction of the respective joint probability law based on classical results in Bayesian theory are presented. Then the derivation of the statistical framework for estimating the associated parameters will be proposed. The second direction is in the modeling of the uncertainty in the maintenance impact onto the cracking process.