# Thrust Network Optimisation for the Assessment of Vaulted Masonry Structures

Maia Avelino R.
2023
doi: https://doi.org/10.3929/ethz-b-000611351

Masonry structures are ubiquitous in our society, serving as housing for millions worldwide and forming a large part of the world's built heritage. Their assessment and preservation are essential to achieving a more sustainable and resilient built environment.

This dissertation presents a novel computational approach to assess unreinforced vaulted masonry structures. A novel limit-analysis-based framework is developed to search for admissible equilibrium states. The equilibrium solutions considered are represented by compressive thrust networks within the structure's geometry, representing their compressive flow of forces. A modular multi-objective constrained nonlinear optimisation problem is formulated and solved using interior point and sequential least-square quadratic programming techniques to search for admissible networks.

Different objective functions are implemented in the optimisation framework, including the minimum and maximum horizontal thrust states, the maximum Geometric Safety Factor (GSF), maximum vertical and horizontal load multipliers, and the complementary energy minimisation for prescribed foundation displacements. The problem's constraints are formulated to translate the limit analysis admissibility criteria to thrust networks. Gradient vectors and Jacobian matrices are described analytically and computed modularly based on the objective, variables, and constraints selected.

The present formulation requires minimal input, encouraging its future application as a practical numerical tool to assess existing masonry structures. Only the structural envelope, typically obtained through surveys, and the topology and planar geometry of the thrust network are needed for the analysis. The networks' topology is explored, quantifying different patterns. Pattern modification strategies are developed for problems involving different objectives. A new algorithm is described to identify the degrees of freedom in the networks necessary to analyse general topologies. A convex load-path optimisation is formulated and used as starting point for the nonlinear problems.

The framework developed provides a single approach which contributes to three critical open questions in the field:

1. Computing the level of stability of vaulted masonry structures by introducing the stability domain, enabling to compute global safety factors and evaluating the structural robustness.

2. Estimating a lower bound of horizontal and vertical collapse loads by directly maximising a scalar load multiplier, contributing to protecting structures against extreme external actions and evaluating newly imposed loads.

3. Understanding the effects of foundation settlements on crack patterns by investigating minimum energy solutions arising after differential displacements, which can inform the identification and evolution of pathologies in masonry structures.

Throughout the dissertation, several examples are presented to demonstrate the possibilities of the framework. Finally, the implementation is offered as an open-source Python package, enabling future collaboration and further development.

BibTeX

@phdthesis{MaiaAvelino2023,
author      = "Maia Avelino, R. ",
title       = "Thrust Network Optimisation for the Assessment of Vaulted Masonry Structures",
institution = "ETH Zurich",
year        = "2023",
month       = "",
doi         = "https://doi.org/10.3929/ethz-b-000611351",
note        = "",
}

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