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运用Riemann-Liouville的分数阶导数理论及经典模型理论相结合的方法,采用Abel黏壶取代在经典模型理论中的Newton黏壶,得出了分数阶标准线性体模型剪应力松弛的解析表达式。采用不同含水量马兰黄土在不同正压力条件下进行直接剪切松弛试验,并对得到的9组剪应力松弛曲线特征进行了研究。考虑到最小二乘法对分数阶标准线性体模型参数进行拟合无法获得确切的结果,采用Monte Carlo方法对试验结果拟合。拟合结果表明,马兰黄土的松弛特性可由分数阶标准线性体模型有效的表征。确定了马兰黄土的松弛时间和粘滞系数,揭示了马兰黄土在直接剪切试验条件下的松弛特性。
By using the method of fractional derivative theory by Riemann-Liouville and classical model theory, Abel sticky pot is used to replace the Newton sticky pot in classical model theory, and the analytical expression of shear stress relaxation in fractional order linear body model is obtained. Direct shear relaxation tests were conducted under different positive pressure conditions using Malan loess with different water contents. The characteristics of nine groups of shear stress relaxation curves obtained were studied. Considering that the least square method fitting fractional standard linear body model parameters can not get the exact result, Monte Carlo method is used to fit the test results. The fitting results show that the relaxation properties of Malan loess can be effectively characterized by fractional standard linear body model. The relaxation time and viscous coefficient of Malan loess were determined, and the relaxation characteristics of Malan loess under direct shear test were revealed.