Unilateral analysis and damage identification in masonry structures
Georgios A. Drosopoulos
Technical University of Crete
In the present paper direct and inverse analysis procedures are used for the study of masonry arch bridges. As a result of the absence of mortar or its low quality, unilateral contact effects arise in masonry structures. Thus, damage can be developed to the body of the structure, as a pattern of hinges. Suitably modified damage analysis can be used instead. Consequently, reverse analysis problems related to the investigation of the mechanical behaviour of damaged masonry arches, can be formulated.
Two real stone bridges are used as model examples. In principle, within the body of the structure three hinges have been developed, one at the crown and two at the quarter of the span. The damage identification can be seen as a parameter identification procedure. In this framework, an initial geometry of the structure is proposed and analysed with the finite element method. Results are compared with the existing damage pattern.
In particular, a number of assumptions are considered in order to obtain a "potential" initial geometry of the structure. Then, a unilateral contact-friction finite element analysis model is developed, for the estimation of the behaviour of this particular geometry. This is achieved by considering possible load cases and comparing the results with the real existing arch. In this way, the damaged obtained from the computational model is compared with the cracks developed in the real arch.
The finite element analysis model is based on the principles of non-smooth mechanics. The body of the structure is divided into a number of interfaces. A unilateral contact law governs the behaviour in the normal direction of an interface, indicating that no tension forces can be transmitted in this direction. The behavior in the tangential direction takes into account that sliding may or may not occur. The problem is solved using the Newton-Raphson incremental iterative procedure.
From the procedure described above, it can be shown that movement of supports may have led the structure to the present, damaged state. The pattern of hinges which computationally arises is identical with the damage developed in the real arch.
The conclusions obtained from the inverse analysis procedure are used for the study of reinforcement. In particular, the type of the reinforcement must be in accordance with the possible loading conditions which can lead the arch to collapse.
Finally, the uncertainties which arise for this kind of problems make the need for improved inverse analysis procedures, quite demanding. Transformation of the proposed concept into more efficient numerical schemes is a goal for future work.