Earthquakes represent a serious threat to the safety of masonry structures, with failure of these constructions under the influence of seismic action generally occurring via specific, well-documented collapse mechanisms. Analysis and assessment of these collapse mechanisms remains a challenge - while most analysis tools are time-consuming and computationally expensive, typical assessment methods are too simplified and often tend to underestimate the dynamic resistance of the structures. This dissertation aims to bridge the gap between the two through the development of a computational tool for the seismic collapse assessment of masonry structures, which uses rocking dynamics to accurately capture large displacement response, without compromising on computational efficiency. The tool could be used for rapid evaluation of critical mechanisms in a structure in order to prioritise retrofit solutions, as well as for code-based seismic assessment.

The framework of the tool is first presented, wherein the rocking equations of motion are derived for a range of different collapse mechanisms, for any user-defined structural geometry, using as a starting point a geometric model of the structure in Rhino (a 3D CAD software). These equations of motion are then exported for solution to MATLAB. As a number of collapse mechanisms take place above ground level, a methodology to account for ground motion amplification effects is also proposed, while in the case of comparison of multiple different mechanisms, an algorithm to automatically detect critical mechanisms is presented. These developments make it possible to rapidly conduct a seismic analysis of structures with complicated three-dimensional geometries.

However, the rocking equations of motion utilised thus far assume that the interfaces between the masonry macro-elements are rigid, which is not the case in reality. Thus, a flexible interface model is introduced, where the interfaces are characterised by a finite stiffness and compressive strength. This modelling strategy results in an inward shift of the rocking rotation points, and expressions are derived for these shifting rotation points for different interface geometries. The rocking equations of motion are also re-derived to account for the influence of the continuously moving hinges. However, the new equations tend to be highly non-linear - especially in the case of more complex collapse mechanisms. Thus to reduce computational burden, the semi-flexible interface model is proposed, which accounts for the shifting hinges in a more simplified manner than its fully-flexible counterpart. These new analytical models enable more accurate prediction of the seismic response of real-world structures, where interface flexibility tends to have a significant influence on dynamic response, while material damage in the form of crushing of the masonry also reduces dynamic resistance.

The ability of the tool to be used for both seismic analysis and assessment is finally demonstrated by using it to perform a rocking dynamics-based analysis as well as a code-based seismic assessment of the walls of a historic earthen structure.