冻结黏土分数阶损伤蠕变模型参数确定及验证

为表达介于理想固体和理想流体之间的人工冻土蠕变特性,常用弹簧元件、黏壶元件与滑块元件间的复杂组合来实现。基于分数阶导数理论则可用较简单的模型来表达人工冻土蠕变性质。分析山西某矿井井筒检查孔黏土不同冻结温度下的单轴抗压、蠕变试验曲线,得到温度对冻结黏土单轴抗压应力应变及蠕变特性的影响规律。在Singh-Mitchell模型的基础上,引入分数阶导数理论,建立受冻结温度、加载等级影响的分数阶冻土蠕变模型。通过分析蠕变与时间取对数的拟合曲线发现两者具有线性关系,进而得出与温度有关的模型参数。鉴于建立的分数阶冻土蠕变模型不能反映冻土蠕变加速阶段,将损伤因子引入建立的分数阶蠕变模型,建立人工冻土分数阶损伤蠕变模型。对比分析分数阶蠕变模型计算值与试验值,表明该模型能够很好地反映人工冻结黏土在稳定蠕变阶段、加速蠕变阶段变形发展特点。建立的S-M分数阶蠕变模型参数少、易于确定且有一定的物理意义,便于工程应用。

Parameter determination and verification of fractional damage creep model of clay

In order to express the creep characteristics of artificial frozen soil between ideal solid and ideal fluid, the complex combination of spring element, clay pot element and sliding block element is often used. Based on fractional derivative theory, a simple model can be used to express the creep properties of artificially frozen soil. The uniaxial compression and creep test curves of clay at different freezing temperatures in the manhole of a mine shaft in Shanxi Province are analyzed, and the influence of temperature on the uniaxial compression stress, strain and creep characteristics of frozen clay is obtained. On the basis of Singh-Mitchell model, the fractional derivative theory is introduced to establish a fractional creep model of frozen soil affected by freezing temperature and loading grade. By analyzing the fitting curve of logarithm of creep and time, it is found that there is a linear relationship between them, and then the model parameters related to temperature are obtained. In view of the fact that the established fractional order creep model of frozen soil cannot reflect the accelerated creep stage of frozen soil, the damage factor is introduced into the established fractional order creep model, and the fractional order damage creep model of artificial frozen soil is established. The comparison between the calculated value and the test value of the fractional creep model shows that the model can well reflect the deformation development characteristics of artificially frozen clay in the stable creep stage and the accelerated creep stage. The S-M fractional creep model has few parameters, is easy to determine and has certain physical significance, and is convenient for engineering application.