A Computational Tool for Seismic Collapse Assessment of Masonry Structures

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.Jawaharlal Nehru Memorial Trust Cambridge Commonwealth, European and International Trus

A tool for the rapid seismic assessment of historic masonry structures based on limit analysis optimisation and rocking dynamics

This paper presents a user-friendly, CAD-interfaced methodology for the rapid seismic assessment of historic masonry structures. The proposed multi-level procedure consists of a two-step analysis that combines upper bound limit analysis with non-linear dynamic (rocking) analysis to solve for seismic collapse in a computationally-efficient manner. In the first step, the failure mechanisms are defined by means of parameterization of the failure surfaces. Hence, the upper bound limit theorem of the limit analysis, coupled with a heuristic solver, is subsequently adopted to search for the load multiplier’s minimum value and the macro-block geometry. In the second step, the kinematic constants defining the rocking equation of motion are automatically computed for the refined macro-block model, which can be solved for representative time-histories. The proposed methodology has been entirely integrated in the user-friendly visual programming environment offered by Rhinoceros3D + Grasshopper, allowing it to be used by students, researchers and practicing structural engineers. Unlike time-consuming advanced methods of analysis, the proposed method allows users to perform a seismic assessment of masonry buildings in a rapid and computationally-efficient manner. Such an approach is particularly useful for territorial scale vulnerability analysis (e.g., for risk assessment and mitigation historic city centres) or as post-seismic event response (when the safety and stability of a large number of buildings need to be assessed with limited resources). The capabilities of the tool are demonstrated by comparing its predictions with those arising from the literature as well as from code-based assessment methods for three case studies.This work was partly funded by project STAND4HERITAGE that has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant agreement No. 833123), as an Advanced Grant

Dynamic simulation of one-sided rocking masonry façades using an energy-consistent viscous damping model

Unreinforced masonry façades are specifically vulnerable to seismic actions. Their weak connectivity with adjacent structural members results in their detachment during an earthquake, thus, forming local collapse mechanisms which exhibit one-sided rocking motion. Such mechanisms can accommodate considerable displacements before collapsing/overturning. Hence, their dynamic stability is of great interest. The dynamic response of such collapse mechanisms has been investigated using the classical rocking theory. This is a reliable and fast model that efficiently simulates the dynamic response and energy losses of rocking structures, yet limited to simple structural configurations. As the problem’s complexity increases (e.g. degrees of freedom, boundary conditions, and/or material nonlinearities) numerical modelling of such structures has been recently gaining momentum. However, despite the great advances of such numerical modelling techniques, simulation of energy losses still remains challenging. The present work proposes a novel numerical block-based model that efficiently simulates energy losses during one-sided rocking motion. Specifically, an equivalent viscous damping model is adopted and calibrated in a phenomenological fashion after the classical rocking theory. Importantly, the unilateral dashpot formulation of the proposed viscous damping model allows for an accurate replication of the impulsive nature of impacts. Ready-to-use predictive equations are presented, which are also validated against experimental results from literature

Numerical block-based simulation of rocking structures using a novel universal viscous damping model

Unreinforced masonry structures, particularly façade walls, are seismically vulnerable due to their weak connections with adjacent walls, floors, and/or roofs. During an earthquake, such walls formulate local mechanisms prone to out-of-plane collapse. This behavior has been largely investigated using classical rocking theory, which assumes the structure responds as a rigid body undergoing rocking motion, with energy dissipation at impact. Due to the complexity of the problem, however, e.g., number of degrees of freedom or boundary conditions, numerical block-based modeling is gaining momentum. However, numerical models lack a consistent and reliable treatment of the energy loss at impact. This paper bridges the gap between the well-established energy loss of classical rocking theory and the treatment of damping in numerical modeling. Specifically, it proposes an equivalent viscous damping model through novel ready-to-use predictive equations that capture the dissipative phenomena during both one-sided and two-sided planar rocking motion. The results reveal a satisfactory performance of the proposed model through comparisons with experimental results from literature and highlight its universality and robustness through applications of the model in fundamentally different block-based numerical modeling software.This study has been funded by the STAND4HERITAGE project (New Standards for Seismic Assessment of Built Cultural Heritage) that has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (Grant No. 833123) as an Advanced Gran

An equivalent viscous damping proposal for block-based rocking models

Masonry structures have been observed to display a high vulnerability to failure under seismic action. This stems from the fact that their structural configurations usually lack adequate connections among the distinct elements, resulting in the formation of local mechanisms experiencing Out-Of-Plane (OOP) collapse. In this context, rocking dynamics has proven to be a valuable methodology for the analysis of masonry walls. Classical rocking theory can provide a fast solution to the dynamic phenomena taking place if simple configurations are examined. Nevertheless, as the degrees of freedom and the boundary conditions increase, the complexity increases, and thus the classical rocking theory becomes impractical. In the meantime, recent developments in computational modelling of masonry structures are gaining significant attraction. This includes block-based models which inherently consider the complexity of the problem and enable the solution to be obtained easily in the discretised spatial and time domains. However, despite their widespread use, applications of such models usually lack a reliable treatment of damping. The present work attempts to bridge the gap between the well-established energy loss of the classical rocking theory and the treatment of damping of block-based computational models. To do so, the dynamics of the problem are reviewed and an equivalent viscous damping model is proposed. A unilateral dashpot formulation allows the replication of the impulsive nature of the energy loss at impact. Afterwards, a calibration methodology is adopted for the practical range of the problem's parameters and a ready-to-use equation is provided, which respects energy equivalence. The performance of the proposed damping model is also evaluated through comparisons with experimental results.(undefined