基于分数阶微积分的软弱夹层剪切流变损伤模型

Shear Rheological Damage Model of Weak Interlayer Based on Fractional Calculus

软弱夹层的剪切流变力学特性研究对于保证边坡长期稳定性具有重要意义,建立能够描述软弱夹层剪切流变特性的本构模型是研究的关键。通过分析不同剪切应力水平下的软弱夹层剪切流变试验结果,基于分数阶微积分理论,采用Abel黏壶元件代替传统模型中Kelvin体,并从概率论和统计学的角度出发,进一步引入服从加载时间t的Weibull概率密度分布函数,该函数能够表征软弱夹层统计损伤变量D,从而建立了一个能够全面描述软弱夹层衰减流变、稳定流变和加速流变3个阶段的非线性分数阶剪切流变损伤本构模型。以此为基础,依据FLAC3D所提供的二次开发程序接口,采用VC++编程方法实现了损伤本构模型的二次开发,并对开发的模型进行了验证。结果表明:基于自定义非线性分数阶剪切流变损伤本构模型的FLAC3D数值试验结果与室内剪切流变试验结果较吻合,验证了所建模型的适用性。研究结果可为含软弱夹层边坡长期稳定性研究提供参考。

The study on shear rheological mechanical properties of weak interlayer is of great significance to ensure the long-term stability of slope, and the establishment of constitutive model which can describe the shear rheological properties of weak interlayer is the key to the study. By analyzing the shear rheological test results of weak interlayer under different shear stress levels, the fractional calculus theory was introduced, and the Abel clay pot element was used to replace the Kelvin body in the traditional model. From the perspective of probability theory and statistics, the Weibull probability density distribution function obeying the loading time t was further introduced, which can represent the statistical damage variable D of weak interlayer. Then, a non-linear fractional order shear rheological damage constitutive model was established, which can fully describe three rheology stages of attenuation, stability and acceleration of weak interlayer. On this basis, according to the secondary development program interface provided by FLAC3 D, the secondary development of damage constitutive model was realized by VC + + programming method, and the developed model was verified. The results show that the FLAC3 D numerical test results based on the user-defined nonlinear fractional order shear rheological damage constitutive model were in good agreement with the laboratory shear rheological test results, indicating the applicability of the established model. The results can provide a reference for the long-term stability study of slope with weak interlayer.