Probabilistic approach in weighted Markov branching processes

This note provides a new probabilistic approach in discussing the weighted Markov branching process (WMBP) which is a natural generalisation of the ordinary Markov branching process. Using this approach, some important characteristics regarding the hitting times of such processes can be easily obtained. In particular, the closed forms for the mean extinction time and conditional mean extinction time are presented. The explosion behaviour of the process is investigated and the mean explosion time is derived. The mean global holding time and the mean total survival time are also obtained. The close link between these newly developed processes and the well-known compound Poisson processes is investigated. It is revealed that any weighted Markov branching process (WMBP) is a random time change of a compound Poisson process.

Probabilistic modeling of structural deterioration of reinforced concrete beams under saline environment corrosion

For existing reinforced concrete structures exposed to saline or marine conditions, there is an increasing engineering interest in their remaining safety and serviceability. A significant factor is the corrosion of steel reinforcement. At present there is little field experience and other data available. This limits the possibility for developing purely empirical models for strength and performance deterioration for use in structural safety and serviceability assessment. An alternative approach using theoretical concepts and probabilistic modeling is proposed herein. It is based on the evidence that the rate of diffusion of chlorides is influenced by internal damage to the concrete surrounding the reinforcement. This may be due to localized stresses resulting from external loading or through concrete shrinkage. Usually, the net effect is that the time to initiation of active corrosion is shortened, leading to greater localized corrosion and earlier reduction of ultimate capacity and structural stiffness. The proposed procedure is applied to an example beam and compared to experimental observations,including estimates of uncertainty in the remaining ultimate moment capacity and beam stiffness. Reasonably good agreement between the results of the proposed procedure and the experiment was found