In this paper, a new set of non-linear mathematical expressions to calculate the compressive strength and the elastic modulus of masonry prisms with hollow concrete blocks were obtained. The mathematical models were obtained by multifactorial technique model, which has as advantage: the analysis of the variables associated to the models that provide the main influence on the interaction among the different factors analyzed. It also allows obtaining a nonlinear regression model optimized for each response variable (f’_m and E_m). Detailed micro-modeling techniques are adopted to simulate the hollow concrete block masonry, describing the experimental tests for the component materials (blocks and mortar) and block-mortar interface. In addition, the structural behavior of the masonry prisms was obtained experimentally. The numerical models were calibrated and validated based on the experimental tests. A sensitivity analysis was carried out by applying a multifactorial complete design $\left(3^5\right)$ and an optimization analysis of the regression models; the compressive strength and the elastic modulus in masonry prisms were evaluated. The results showed that the compressive and tensile strength of the hollow concrete block and the mortar thickness are the most influential parameters for the maximum compressive strength. The compressive strength of the block and the tensile strength of mortar were the most relevant parameters for the elastic modulus in the masonry prisms. In addition, is concluded that, from the analysis and optimization process, both expressions (f’_m and E_m) are necessarily multifactorial.

本文获得了一套新的非线性数学表达式，用于计算空心混凝土砌块砌体棱镜的抗压强度和弹性模量。通过多因素技术模型获得数学模型，该模型具有以下优点：对与模型相关联的变量进行分析，这些变量对所分析的不同因素之间的交互作用具有主要影响。它也允许获得一个非线性回归模型为每个响应变量优化（F”_米和Ë_米）。采用详细的微模型技术来模拟空心混凝土砌块砌体，描述了组成材料（砌块和砂浆）和砌体砂浆界面的实验测试。另外，通过实验获得了砌体棱镜的结构行为。基于实验测试，对数值模型进行了校准和验证。通过应用多因素完整设计进行敏感性分析$\left(3^5\right)$对回归模型进行优化分析；评估了砌体棱镜的抗压强度和弹性模量。结果表明，空心混凝土砌块的抗压强度和抗拉强度以及砂浆厚度是最大抗压强度的最大影响参数。砌块的抗压强度和砂浆的抗拉强度是砌筑棱镜中弹性模量最相关的参数。此外，得出的结论是，从分析和优化过程中，两个表达式（F”_米和ë_米）必然是多因素的。