Structural study of masonry buttresses: the trapezoidal form

Despite its vital importance for the safety of masonry vaulted structures, the stability of buttresses has been the subject of a limited number of investigations. The collapse condition of masonry buttresses subjected to concentrated lateral loads has been analysed by previous researchers for the simple case of a rectangular buttress, and it has been shown that the formation of a crack prior to collapse may strongly influence the overturning resistance. Buttresses of more complex shapes, such as trapezoidal or stepped, are frequently encountered in masonry buildings or retaining walls, and yet a rigorous analysis of their failure conditions has not been developed. In this paper and a companion paper, the collapse analysis accounting for fracturing prior to overturning, as well as for possible sliding, is extended to trapezoidal and stepped geometries. In particular, this paper is devoted to the analysis of trapezoidal buttresses. Analytical formulations are developed for the determination of the fracture shape and location, and for the computation of the horizontal force at collapse. The analytical solution, obtained treating masonry as a continuum with no tension resistance, is compared with predictions obtained numerically with the discrete-element method. The numerical model considers masonry as an assemblage of rigid blocks with no-tension frictional joints, and is based on time-stepping integration of the equations of motion of the individual blocks. The satisfactory agreement between predictions of the two approaches gives confidence in both sets of results.