马兰黄土剪应力松弛特性研究

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。

Study on Shear Stress Relaxation Properties of Malan Loess

Applying the Riemann-Liouville derivative of factional order theory and the classical model theory,the fractional order of standard linear model for the analytical expression of the shear stress relaxation is given by replacing the traditional Newton dashpot with Abel dashpot.The characteristics of the shear stress relaxation curves of Malan loess are studied based on 9 groups of shear stress relaxation test with different moisture contents under different pressure.Due to the unsatisfied fitting result from using the least squares method for the parameters of fractional order of standard linear model,the Monte Carlo method is used to fit the results.The results show that the shear stress relaxation characteristics of Malan loess can be described by the fractional order of standard linear model efficiently.Based on the fitting results the effective relaxation time and viscosity modulus are determined,and the shear stress relaxation properties is analyzed.