Gross displacement mechanism analysis of masonry bridges and tunnel linings
Dr Matthew Gilbert
University of Sheffield, UK
The mechanism method of plastic analysis has been applied to masonry structures for many years. When carrying out a mechanism analysis it is typically assumed that the masonry is incapable of resisting tensile stresses and that elastic strains in the masonry can be neglected. The main advantage of the method compared with elastic methods is that the collapse load of a masonry structure can be calculated directly, without prior assumption as to the internal stress state. Complex arrangements of masonry blocks can readily be analysed using computer based methods provided a rigorous solution algorithm is employed. A typical computer based mechanism analysis procedure will involve setting up appropriate geometric constraints together with a governing work equation (both expressed in terms of the problem variables, which are normally the relative rotations and sliding deformations of adjacent blocks). Application of small displacement theory allows a linear programming algorithm to then be used to obtain a solution.
However problems may arise when the method is applied to some common types of masonry structure. In the case of masonry arch bridges, field and laboratory tests carried out over the last decade in the UK have shown that ultimate bridge strength is often considerably enhanced by the presence of horizontal ('passive') backfill pressures, acting to restrain movement of the arch. As standard mechanism analyses use small displacement theory, it has been common to assume that peak backfill pressures will be mobilized by infinitesimal structural displacements. This is rather unrealistic, and will tend to lead to non-conservative predictions of bridge carrying capacity. It has also been found that adoption of this assumption leads to problems when analysing multi-span bridges. For both these reasons the use of an iterative, gross displacement, analysis procedure is investigated. The technique is used to study the behaviour of large-scale model masonry arches and arch bridges, tested in the laboratory. Finally, the capability of the method to assess the stability of multi-ring brickwork tunnel linings in the presence of progressively increasing ground movements is briefly examined.