基于非定常分数阶微积分的岩石蠕变模型研究

分数阶导数引入蠕变模型可较好地模拟蠕变特性,为了解决常规分数阶黏滞体的微分阶次多为定常数,不能用同一元件模拟岩石蠕变的衰减、稳定或加速阶段的问题,基于分数阶微积分理论,提出了一种非定常微分阶次的分数阶黏性元件,将此元件与引入分数阶的理想黏塑性体及理想弹簧串联,建立了新的非线性黏弹塑性蠕变模型,推导了该模型的蠕变方程,并分别利用岩石蠕变试验结果及西原体模型、河海模型对其合理性进行了验证、对比。结果表明:所建模型拟合曲线与试验数据吻合较好,误差较小,具有较高的准确性及合理性,能够较好地模拟岩石蠕变全过程。

Study on rock creep model based on unsteady fractional order calculus theory

By introducing fractional calculus theory to the rock creep model, pronounced effect was obtained in describing the creep property of rock mass. However, the orders of the conventional fractional viscous body almost are almost constant, so a single element cannot be used to simulate the attenuation stage, steady stage or the accelerating stage of rock creep. According to the fractional calculus theory, a modified fractional viscous body with unsteady differential orders was developed. Then, through connecting it and the ideal viscoelastic body that introduced the fractional calculus with the traditional elastic body, a new nonlinear viscoelasto-plastic creep model for rocks was established. In this paper, the creep equation of the model was deduced, and the rationality of which was verified by using creep test data of rocks. What''s more, the paper made a comparison between the proposed model and the Nishihara model, the HoHai model, respectively. The results indicate that the fitting curves and test curves conform very well to each other. The proposed model has high accuracy and rationality and can well reflect the whole stages of rock creep process.