基于Navier-Stokes方程幂律型浆液扩散压力

摘要

In order to study the pressure distribution and diffusion radius of slurry throughout fissure section,overcome the shortcomings that the average pressure of the fissure section was obtained by using the average speed,control the slurry flow and the range of diffusion accurately,the diffusion movement of exponential slurry in the horizontal fissures smooth tubular model was theoretically derived based on the Navier-Stokes equations of viscous fluid.Then the effects of law among the viscosity coefficient,rheology index,grouting time,the height of the fracture and diffusion radius or grouting pressure were mainly discussed,which provided theoretical basis for the grouting design of geotechnical fissure.The results show that when the viscosity is smaller,grouting diffusion radius is larger relatively.But the slurry viscosity reaches a certain degree,and the effect of filter is easy to occur under the constant grouting pressure.When the rheological index is smaller,pressure difference Ap has no obvious change.Exceeding a certain value,Ap shows a rapid increase of nonlinear along with the increase of rheological index.The grouting pressure of the interface between the flow core zone and non flow core zone is the maximum.The pressure shows a nonlinear decrease gradually away from the flow core zone (y direction),and then increases rapidly.But the pressure value is always less than the pressure of the interface between the flow core zone and non flow core zone until the crack boundary.With the increase of the grouting time,the diffusion radius of grouting increases with the trend of the non-linear.However,the increasing rate of the diffusion radius is gradually decreased and the diffusion radius tends to reach a certain value finally.%为了研究浆体在裂隙截面各处的压力分布规律和扩散半径,克服以往利用平均速度得到某一截面的平均压力的情况,达到较精确地控制浆体流向和扩散范围,基于黏性流体Navier-Stokes方程,对幂律流体在水平光滑裂隙管状模型内的扩散运动进行理论分析,重点讨论黏度系数、流变指数、注浆时间和裂隙高度方向的距离对注浆压力差和扩散半径的影响规律,从而为岩土裂隙的注浆设计提供必要的理论依据.研究结果表明:当黏度较小时,注浆的扩散半径较大,但当浆体黏度大到一定程度时,恒定注浆压力下容易产生压滤效应;当流变指数较小时,压力差Δp无明显变化,超过某一特定值之后,压力差Δp随着流变指数的增大呈现非线性快速增加;注浆压力在靠近流核区与非流核区界面的压力最大,随着逐渐远离流核区(y方向),其压力呈非线性逐渐减小,到达某一特定位置,然后迅速增大,但直至裂隙边界处其压力始终小于界面处的压力;随着注浆时间增大,浆液的扩散半径不断增大,并且呈现出非线性增大的趋势,但扩散半径的递增率逐渐减小,最终扩散半径趋于某一特定值.