中文摘要：

为研究岩土材料的应力、应变和时间的关系，基于分数阶微积分理论，定义含分数阶导数的力学元件（FC元件），推导FC元件的蠕变柔量和松弛模量。与牛顿体元件相比，FC元件能更好地反映流变问题的非线性渐变过程。借鉴经典元件组合模型的建模思路，用FC元件取代整数阶微积分Kelvin-Voigt流变模型中的牛顿体元件，形成基于分数阶微积分的Kelvin-Voigt流变模型。应用离散化求Laplace逆变换的方法以及H-Fox函数，得出分数阶微积分Kelvin-Voigt流变模型的本构方程、蠕变方程、松弛方程、蠕变柔量及松弛模量的解析表达式。采用整数阶微积分Kelvin-Voigt流变模型、整数阶5参数开尔文流变模型和分数阶微积分Kelvin-Voigt流变模型对试验数据拟合的结果表明，分数阶微积分Kelvin-Voigt流变模型不但拟合精度高，能够克服整数阶微积分Kelvin-Voigt流变模型在蠕变初期及蠕变曲线拐点附近与试验数据不能很好吻合的弊端，而且能够在保证拟合精度的条件下，减少本构模型中的参数。

英文摘要：

In order to study the time-dependent relation between the stress and the strain of geotechnical materials, based on fractional calculus theory, the mechanical element with the derivatives of fractional order （FC element） was defined and the creep compliance and the relaxation modulus of FC element were derived. Compared with Newton element, FC element can better reflect the nonlinear gradual change of rheology. In the light of the modeling approach of the classical element combined model, FC element was used to substitute the Newton element in the integer calculus Kelvin-Voigt rheological model to form the frac- tional calculus Kelvin-Voigt theological model. The analytical expressions of the constitutive equation, creep equation, relaxation equation, creep compliance and relaxation modulus for the fractional calculus Kelvin-Voigt rheological model were derived by using the discrete inverse Laplace transform method and H-Fox functions. It is shown by comparing the fitting results of the integer calculus Kelvin-Voigt rheological model, the fractional calculus Kelvin-Voigt theological model and the integer Kelvin rheological model with five parameters that the fractional calculus Kelvin-Voigt rheological model not only overcomes the low fitting precision of the integer calculus Kelvin-Voigt theological model at the initial stage of creep and the inflexion of creep curve, but also reduces parameter in the constitutive model under the condition that the fitting precision is guaranteed.