基于改进分数阶黏滞体的岩石非线性蠕变模型

A nonlinear creep model for rocks based on modified fractional viscous body

通过将表征应力水平对岩石非线性蠕变特性影响的函数引入到常规分数阶黏滞体的本构关系中,提出一种改进的分数阶黏滞体;基于岩石非线性流变力学理论,提出一个能够描述岩石加速蠕变的非线性黏滞体,其黏滞系数随应力水平提高和蠕变时间延长而逐渐减小;将改进的分数阶黏滞体、非线性黏滞体与基本弹性体和塑性体进行组合,建立一个新的4元件非线性黏弹塑性蠕变模型,给出模型的蠕变方程,并利用岩石蠕变试验结果对模型合理性进行验证。研究结果表明:该模型能够较好地描述岩石蠕变全过程的3个阶段,且拟合曲线和试验曲线吻合良好,误差较小。

By introducing a stress influence function to the constitutive relation of the conventional fractional viscous body, a modified fractional viscous body which could reflect the influence of stress level on the creep property of rocks was proposed. Moreover, a new nonlinear viscous body which could describe the tertiary creep of rocks was put forward according to the nonlinear rheology theory, the viscous coefficient of which decreased with the increase of stress and time. Then, through connecting the modified fractional viscous body and the nonlinear viscous body with the traditional elastic and plastic bodies in forms of series and parallel, a new nonlinear viscoelasto-plastic creep model with 4 components for rocks was established, the rationality of which was verified by using creep test data of rocks. The results indicate that the proposed model can well reflect the three stages of rock creep process, and the fitting curves and test curves conform very well to each other.