基于分数阶微积分的Q2黄土含水损伤蠕变模型

为探索含水Q₂黄土的蠕变特性,对Q₂黄土进行不同含水状态下的三轴蠕变试验,试验结果表明随着含水率的增高,Q₂黄土的流变性能增强。基于分数阶微积分构造的软体元件可描述理想的固体与流体之间材料性质的特性,选用包含软体元件在内的四元件非线性蠕变模型对试验数据进行回归计算拟合求参,并对不同含水率下的模型参数进行分析。结果显示瞬时变形模量E_H与黏弹性系数ξ₁均随含水率增加呈指数形式递减;引入含水损伤变量D_(ω),计算得出各蠕变参数含水损伤演化方程,进而建立考虑含水损伤的非线性蠕变模型,通过应用试验数据对其进行验证,结果表明基于分数阶微积分的含水损伤蠕变模型能够有效地描述Q₂黄土的整体流变特征,模型具有较好的应用前景。

Creep Damage Model of Q2 Loess in Consideration of Moisture Content Based on Fractional Calculus

Triaxial creep tests on Q2 loess of different moisture contents were carried out to explore the creep proper-ties of water-containing Q2 loess.Test results show that the rheological property of Q2 loess strengthens with the in-crease of moisture content.Furthermore,since the soft-matter element built by fractional calculus could simulate the material between ideal solid and ideal fluid,a four-element nonlinear creep model which contains the soft-matter element was applied to fit data,and the model parameters under different moisture contents were analyzed.The re-sults suggest that instantaneous deformation modulus EH and viscoelastic coefficient ξ1 have a negative relationship with moisture content with an exponential decline.A water damage evolution equation of each creep parameter was obtained by introducing the water damage variable D(ω),which was further used to establish a nonlinear creep mod-el in consideration of water damage effect.The nonlinear creep model was verified by test data.It was proved that the nonlinear creep model considering water damage could effectively characterize the overall rheological property of Q2 loess,and has a good application prospect.