温度影响下的花岗岩分数阶导数渗透率模型

Fractional derivative permeability modeling approach to the influence of temperature on granite

高放废物地质处置将产生大量衰变热,从而导致处置高放废物硐室的近场围岩温度升高,因此,研究温度对围岩渗透率的影响对评价核素迁移具有重要意义。对北山花岗岩试件进行不同温度场下的三轴压缩渗透试验,获得全应力-应变过程中渗透率的演化过程。在传统压降的指数衰减方程中引入Mittag-Leffler函数,建立分数阶导数型压降衰减模型,较为精确地拟合决定渗透率的流体压降-时间曲线,从而得出分数阶导数渗透率模型。引入裂隙连通度C,通过建立裂隙连通度C与分数阶阶数λ的关系,反映出原始岩样的致密程度和三轴压缩时内部裂隙网络的贯通程度。应用分数阶导数渗透率模型,探讨温度对岩石特性参数的影响,据此得出温度对渗透率演化规律的影响机理,并给出北山花岗岩渗透率与温度变化的定量表达式。

Decay heat generates from the cave of high-level radioactive waste disposal repository,which results in temperature climbing among the surrounding rock.Therefore,the influence of temperature in permeability of surrounding rock plays an important role in evaluating nuclide migration.In this context,the paper represents an evolution of Beishan granite permeability with an experiment of triaxial compression test in vary temperature,in an effort to obtain the evolution of permeability in the process of complete stress-strain curve.The permeability dependent curve of liquid▽p-t is fitting precisely by virtue of pressure drop attenuation model,which introduce the Mittag-Leffler function into the model of the traditional exponential permeability via the fractional derivative approach.By adhibitting fracture connectivity parameter C,the relation between fracture connectivity C and fractional order y is established to reflect the density of original rock sample and the connectivity degree of the fracture network under triaxial compression.In the perspective of permeability model in fractional derivative,the influence of temperature on rock characteristic parameters is discussed,drawing a conclusion on the influence mechanism of temperature on the permeability evolution.Ultimately,the quantitative expression of the permeability of Beishan granite with respect to temperature is given.