Concrete is a kind of composite material that is in a plastic flow state in its initial stage, gradually hardening with the cement hydration reaction and then finally reaching a relatively stable condition. In addition, the compressive strength of concrete is related to not only the curing age but also the curing temperature and humidity. The Kelvin model with a software element is used to describe the growth rule of the compressive strength of concrete. The equivalent age theory is used to consider the coupling effect of the temperature and humidity, and then a fractional-order model of the compressive strength of hydraulic concrete considering this coupling effect is proposed. Next, tests of the compressive strength of concrete under three different curing conditions for different concrete ages are performed, and a fractional-order model of the compressive strength is implemented using the test data. The analysis results show that the fitting effect of the fractional-order model can reach a high level of accuracy with only a few model parameters, and with a better fit than the combinatorial exponential model or combinatorial modified logarithmic model.

混凝土是一种复合材料，在初始阶段处于塑性流动状态，随着水泥的水化反应逐渐硬化，最终达到相对稳定的状态。另外，混凝土的抗压强度不仅与固化年龄有关，而且与固化温度和湿度有关。带软件元素的开尔文模型用于描述混凝土抗压强度的增长规律。利用等效龄期理论来考虑温度和湿度的耦合效应，然后提出考虑这种耦合效应的水工混凝土抗压强度的分数阶模型。接下来，针对不同的混凝土龄期，在三种不同的固化条件下进行了混凝土的抗压强度测试，使用测试数据实现抗压强度的分数阶模型。分析结果表明，分数阶模型的拟合效果仅需几个模型参数即可达到较高的准确度，并且比组合指数模型或组合修正对数模型具有更好的拟合度。