This paper presents a methodology to assess the stability of vaulted masonry structures using Thrust Network Analysis (TNA). It offers a new numerical strategy to compute the Geometric Safety Factor (GSF) of a given structure by directly evaluating its minimum thickness. Moreover, it provides an approach for tracing the vault’s stability domain based on its extreme thrust values, which indicates the robustness of the structure. Together, these outcomes represent a proper measure of the safety level of masonry structures. Such results are obtained from constrained nonlinear optimisation problems (NLPs) with appropriate objective functions and constraints enforcing the limit analysis’ admissibility criteria. Networks with fixed horizontal projection are considered, for which the spatial geometry is a function of the independent force densities and the height of the support vertices. A faster, interactive procedure is proposed to improve the selection of such independent force densities. The range of applications of the present method includes arbitrary network topologies and different support conditions. Beyond analytically described geometries, the method can deal with geometries obtained numerically (e.g. from point clouds). The presented strategy is implemented in a Python-based package, and relevant applications illustrate the method’s potential in assessing the stability of three-dimensional historic vaulted structures.

本文提出了一种使用推力网络分析 (TNA) 评估拱形砌体结构稳定性的方法。它提供了一种新的数值策略，通过直接评估其最小厚度来计算给定结构的几何安全系数 (GSF)。此外，它提供了一种基于其极端推力值来追踪拱顶稳定性域的方法，这表明结构的稳健性。总之，这些结果代表了砌体结构安全水平的适当衡量标准。这些结果是从约束非线性优化问题 (NLP) 获得的，具有适当的目标函数和约束，强制执行极限分析的可接受标准。考虑具有固定水平投影的网络，其中空间几何是独立力密度和支撑顶点高度的函数。提出了一种更快的交互式程序来改进这种独立力密度的选择。本方法的应用范围包括任意网络拓扑和不同的支持条件。除了分析描述的几何图形外，该方法还可以处理以数值方式获得的几何图形（例如，从点云）。所提出的策略是在基于 Python 的包中实现的，相关应用说明了该方法在评估三维历史拱形结构稳定性方面的潜力。本方法的应用范围包括任意网络拓扑和不同的支持条件。除了分析描述的几何图形，该方法还可以处理以数值方式获得的几何图形（例如，从点云）。所提出的策略是在基于 Python 的包中实现的，相关应用说明了该方法在评估三维历史拱形结构稳定性方面的潜力。本方法的应用范围包括任意网络拓扑和不同的支持条件。除了分析描述的几何图形外，该方法还可以处理以数值方式获得的几何图形（例如，从点云）。所提出的策略是在基于 Python 的包中实现的，相关应用说明了该方法在评估三维历史拱形结构稳定性方面的潜力。