一种新的岩土流变模型元件

A NEW RHEOLOGICAL MODEL ELEMENT FOR GEOMATERIALS

分数阶微积分被发现是一个解决力学建模难题的有力数学工具,利用Riemann-Liouville的分数阶微积分算子及理论,给出一种软体元件及其本构方程,用来模拟介于理想固体和流体之间的土体。该元件能够很好地反映应力松弛和蠕变现象中应力–应变的非线性渐变过程。通过一个软体元件与一个弹簧元件串联或并联,构建2种流变模型,并给出这2种模型的本构方程、松弛模量和蠕变模量。与土的流变实验数据相拟合结果表明,含有软体元件的模型能够更有效地刻画土的流变特性,可以减少参数数量。

A soft-matter element and its constitutive equations were presented by employing the Riemann- Liouville fractional calculus operator theory. The element could be used to simulate the soil of which behaviors were deemed as the materials between perfect solid and fluid; it also could be used to describe the nonlinear slow-variable process of stress-strain in stress relaxation or creep. Two new models were determined when a soft-matter element was parallel to or series connected with an elastic element. The constitutive equations, relaxation modulus and creep modulus could also be obtained. A rheological trial fitting curve of soil was provided The achieved results show that the proposed model with soft-matter element was more efficient in describing the rheological characteristics of soil and could reduce the number of parameters.