Abstract Historic buildings and monuments are often composed of carbonate-based stone materials, susceptible to deterioration by the action of acidic substances on its main component, calcite (CaCO3). Today the levels of air pollution that attack heterogeneous structures with a mixture of different materials, usually of complex and articulated geometries, are the main responsible of the damage of calcareous stones. However the mechanisms of degradation of the stone and the factors that affect them cannot be simply specified, due to the sum coupled processes involving physical, chemical and biological changes, associated with capillarity and porosity, on the other hand the management of large number of samples and the cost of characterization analysis, modeling can contemplate a tool for the care and protection of real estate over time. Reason why this work shows a bibliographical review of the mathematical models that aim to describe how the deterioration of the surfaces of these structures varies over time, with particular attention to surface recession of stone, as a function of sets of variables that have been considered determinants in the different cases studied. It has been shown that in the last 30 years the models has had a revealing evolution due to the fact that the phenomenon has been gradually understood, putting in the background variables such as SO2 because of its reduction worldwide, and introducing variables such as HNO3 which has had, on the contrary, increasing values. In addition, it has been shown that linear polynomials, even if they lend themselves well to represent the phenomenon, in the last 10 years have been replaced by equations or systems of differential equations with one or more variables taken into account. Finally, it was revealed the lack of an inclusive model, capable of including all possible deterioration processes, and that time by time can be adapted to different case studies, in different parts of the world and with different conditions nearby, at least for structures with similar materials. Theoretical concepts of how an ideal model should be structured are finally proposed.

中文翻译：

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历史建筑石灰石劣化模拟数学模型综述

摘要 历史建筑和纪念碑通常由碳酸盐基石材组成，易受酸性物质对其主要成分方解石 (CaCO3) 的作用而变质。今天，用不同材料的混合物（通常具有复杂和铰接的几何形状）攻击异质结构的空气污染水平是造成钙质石损坏的主要原因。然而，由于涉及与毛细管和孔隙率相关的物理、化学和生物变化的总和耦合过程，另一方面需要管理大量样品，因此不能简单地指定石材降解的机制和影响它们的因素以及表征分析的成本，建模可以考虑随着时间的推移保护和保护房地产的工具。为什么这项工作显示了数学模型的书目审查，旨在描述这些结构的表面退化如何随时间变化，特别注意石头的表面衰退，作为已被认为是决定因素的变量集的函数在研究的不同案例中。已经表明，在过去的 30 年中，由于这一现象已逐渐被人们了解，模型有了显着的演变，加入了 SO2 等背景变量，因为它在全球范围内减少，并引入了 HNO3 等变量。相反，它具有不断增加的价值。此外，已经表明，即使线性多项式能够很好地表示这种现象，在过去 10 年中，已被考虑一个或多个变量的方程或微分方程组所取代。最后，它揭示了缺乏一个包容性模型，能够包括所有可能的退化过程，并且随着时间的推移可以适应不同的案例研究，在世界不同地区和附近不同条件下，至少对于具有类似的材料。最后提出了如何构建理想模型的理论概念。至少对于具有相似材料的结构。最后提出了如何构建理想模型的理论概念。至少对于具有相似材料的结构。最后提出了如何构建理想模型的理论概念。