Effective Diffusion Range of Exponential Fluids Based on Navier-Stokes Equation in Collapse Area
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摘要: 为了研究注浆过程水泥浆体在破碎岩体中的扩散范围和压力分布状态，以Navier-Stokes方程为理论基础，在COMSOL平台上建立单裂隙模型，模拟浆体在不规则的单一裂隙面上的流动特征. 在此基础上，建立破碎岩体的平面裂隙模型，同时设置不同的贯通系数，模拟浆体在破碎岩体中的扩散规律. 研究结果表明：当模型中裂隙贯通系数较低时（0.1～0.5），浆体有效扩散范围较小，约为1.5～4.1 m，扩散范围随着压差的增加呈非线性的增加，但是增加率快速降低接近0；当模型中裂隙贯通系数较大时（0.5～1.0），浆体的有效扩散范围显著增加，约为4.1～6.2 m，随着压差的增加也呈非线性增加，增加率呈降低的趋势；当模型中裂隙贯通系数为1.0时，即破碎的岩体中裂隙面全部连通状态，浆体扩散距离随着压差的增加近似呈线性增加，最大扩散距离约为6.2 m. 同时在注浆孔外围6 m处取芯结果能明显观察到浆体固结的破碎岩块，这与模型计算结果一致.
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关键词:
- 幂律型流体 /
- Navier-Stokes方程 /
- 注浆 /
- COMSOL模拟
Abstract: In order to study the diffusion range and pressure distribution of cement paste during grouting in the fractured rock mass, based on the deduced Navier-Stokes equation, a single fracture model is established on the COMSOL platform to simulate the flow characteristics of slurry on irregular single fracture surface. In this regard, a plane fracture model with different penetration coefficients is established to simulate the diffusion law of the slurry in the broken rock mass. The results show that when the crack penetration coefficient is low in the model (0.1−0.5), the effective diffusion range of the slurry is small, about 1.5−4.1 m, and the diffusion distance increases slowly and nonlinearly with the increase of pressure difference, and the increase rate decreases to near 0 quickly. When the fracture penetration coefficient in the model is larger (0.5−1.0), the effective diffusion range of the slurry increases significantly, about 4.1−6.2 m; and it increases nonlinearly with the increase of pressure difference, and the rate of increase decreases gradually. When the fracture penetration coefficient of the model is 1.0, the fractured surface of broken rock is all connected. The diffusion distance of slurry increases approximately linearly with the increase of pressure difference, and the maximum diffusion distance is about 6.2 m. Meanwhile, the results of coring at 6 m around the grouting hole show that the fractured rock mass consolidated by the slurry can be clearly observed, which is consistent with the calculation results of the model.-
Key words:
- power-law fluids /
- Navier-Stokes equations /
- grouting /
- COMSOL simulation
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图 3 主矿体垮塌区滑移面z向应变云图
Figure 3. z direction strain cloud map of slip surface in the collapse area of the main ore body
图 6 注浆体在不规则裂隙表面的流动速度
Figure 6. Flow velocity of a grouting slurry on an irregular fissure surface
图 7 浆体在连通（贯通系数为1）的微裂隙中的流动速度平面矢量图
Figure 7. Plane vector graph of the slurry flow velocity in connected micro fissures with a penetration coefficient of 1
图 8 浆体扩散过程中压差等值线图（贯通系数为1）
Figure 8. Pressure drop contour map of slurry diffusion with a penetration coefficient of 1
图 9 不同裂隙贯穿系数的压差-扩散范围变化曲线
Figure 9. Pressure difference-diffusion range curves for different crack penetration coefficients
表 1 透水率测试表
Table 1. Permeability test results
序号 位置孔号 试验压力/MPa 试验段长/m 吕荣值/Lu 1 Zk1 0.6 16 69.5 2 Zk2 0.6 17 92.0 3 Zk3 0.6 21 118.0 平均值 0.6 18 93.167 
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