Concrete is a material that is an intermediate between an ideal solid and an ideal fluid. The creep of concrete is related not only to the loading age and duration, but also to its temperature and temperature history. Fractional order calculus is a powerful tool for solving physical mechanics modeling problems. Using a software element based on the generalized Kelvin model, a fractional order creep model of concrete considering the loading age and duration is established. Then, the hydration rate of cement is considered in terms of the degree of hydration, and the fractional order creep model of concrete considering the degree of hydration is established. Moreover, uniaxial tensile creep tests of dam concrete under different curing temperatures were conducted, and the results were combined with the creep test data and complex optimization method to optimize the parameters of a new creep model. The results show that the fractional tensile creep model based on hydration degree can better describe the tensile creep properties of concrete, and this model involves fewer parameters than the 8-parameter model.

混凝土是介于理想固体和理想流体之间的中间材料。混凝土的蠕变不仅与装料年龄和持续时间有关，而且与温度和温度历史有关。分数阶微积分是解决物理力学建模问题的强大工具。使用基于广义开尔文模型的软件元素，建立了考虑装料年龄和工期的分数阶混凝土蠕变模型。然后，根据水化程度考虑水泥的水化速率，建立了考虑水化程度的混凝土分数阶蠕变模型。此外，还对不同固化温度下的大坝混凝土进行了单轴拉伸蠕变试验，然后将结果与蠕变测试数据和复杂的优化方法相结合，以优化新蠕变模型的参数。结果表明，基于水合度的分数阶拉伸蠕变模型可以更好地描述混凝土的拉伸蠕变特性，该模型所涉及的参数少于8参数模型。