倾斜裂隙中宾汉姆流体非稳定浆液运移机理
Mechanism of inclined fracture slurry transport based on non⁃stable Bingham fluid
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摘要: 水泥基宾汉姆流体浆液在倾斜裂隙中的扩散范围确定直接影响注浆工程参数的选择。 为 研究宾汉姆流体浆液扩散半径计算理论,根据宾汉姆流体浆液运移过程中具有“浆-水”分离的非 稳定特性,建立宾汉姆流体浆液改进的分层充填物理模型,并使用物理模拟方法验证分层充填假设 的可靠性;基于以上改进的物理模型,提出“ 有效扩散半径” 和“ 无效扩散半径” 的概念;利用改进的 分层充填物理模型和 N-S 方程推导了宾汉姆流体浆液在粗糙倾斜裂隙中的有效扩散半径理论公 式,该理论模型考虑了注浆压差、裂隙倾角、裂隙隙宽、裂隙粗糙程度 4 个主控因子对浆液扩散半径 的影响;考虑到注浆工程中通常将沿裂隙走向“ 有效扩散半径” 作为设计依据,进一步推导了对宾 汉姆流体浆液方位角 θ=90°时“有效扩散半径”的解析解;为了验证改进的分层充填物理模型和方 位角 θ=90°时“浆液扩散半径”的解析解的可靠性,将其与常规理论模型进行比较,并使用数值模 拟的方法对“有效扩散半径”的计算值进行验证。 室内浆液扩散试验表明,水泥基宾汉姆浆液运移 时确实有分层分区运移的现象,浆液在平面上的分布可分为 3 个区域:浆液混合区、分层扩散区、分 层扩散前锋面区,这一现象与数值模拟中浆液在最后一层充填时有明显的密度分区现象比较一致; 裂隙中有效扩散半径取决于最后一层充填时裂隙宽度、注浆压差、裂隙粗糙度等参数,而非注浆参 数和裂隙介质参数的初始值;与现有常用模型相比,改进后的宾汉姆流体浆液沿裂隙走向“ 最大有 效扩散半径” 的理论计算值与注浆工程现场经验值更加吻合。Abstract: The determination of the penetration length of cement⁃based Bingham fluid slurry in inclined fractures influ⁃ ences directly the selection of grouting parameters. To calculate the penetration length of Bingham fluid grout,an im⁃ proved physical model of slurry layered filling is established based on the unstable characteristic of “slurry⁃water” separation during slurry transport,and the reliability of the layered filling assumption is verified by using the physical sim⁃ ulation method. Based on this model,the concepts of “effective spread radius” and “ineffective spread radius” are de⁃ veloped. The concept of “effective spread radius” and “ineffective spread radius” is proposed with the improved phys⁃ ical model of layered filling. A theoretical formula for the effective spread radius of Bingham fluid grout in roughly in⁃ clined fractures is derived using the improved physical model and the N-S equation,which considers the effects of four main control factors on the spread radius of the grout,the fracture dip,the fracture gap width,and the fracture roughness. The analytic solution of the “maximum effective spread radius” for the azimuth angle θ=90° of Bingham fluid grout was further derived,given that the values are usually used as the basis for design in grouting projects. To validate the reliability of the improved physical model of layered filling and the analytical solution of the “maximum ef⁃ fective spread radius ” at an azimuth angle of θ = 90°, it is compared with the conventional theoretical model and the calculated value of the “effective spread radius” is verified by using numerical simulations. To validate the re⁃ liability of the improved physical model of layered filling and the analytical solution of the “effective spread radius” at an azimuth angle of θ=90°,it is compared with the conventional theoretical model and numerical simulation models. Indoor grout spread test shows that the cement⁃based Bingham slurry transport does have the phenomenon of layered zoning transport,and the grout distribution on the plane can be divided into three zones:slurry mixing zone,layered spread zone,and layered grout front surface zone. This phenomenon is consistent with the numerical simulation in which the slurry has obvious density zoning phenomenon. The maximum effective spread radius in the fissure depends on the parameters of fissure width,grouting pressure difference,and fissure roughness at the time of last filling, rather than the initial values. Compared with the existing common models,the theoretical calculation of the “effective spread radius” of Bingham’ s fluid grout along the fracture direction is more consistent with the empirical values in grouting projects.