Lattice Boltzmann meso-seepage research of reconstructed soil based on the quartet structure generation set
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摘要:
多孔介质模型的重构问题是土体细观渗流机理研究的基础和关键。由四参数随机生长法(QSGS)构建土体模型，采用格子玻尔兹曼方法(LBM)，通过MATLAB自编程序研究重构土在不同条件下的细观渗流机理。结果表明：随模型尺寸增大，孔隙连通程度显著提高，300×300格点大小的模型连通孔隙率增长幅度(34.38%)最大，继续扩大模型尺寸发现增加不明显；流体粒子在孔隙连通性好、孔径大的区域，会形成主渗流通道，且存在指进效应，孔道中间流速最大，可达0.0324，越靠近孔壁流速越小；大孔隙率土的流速比小孔隙率土大，而低孔隙率土中的流速相比大孔隙土更稳定；LBM模拟渗透率与经典K-C公式计算结果对比发现，孔隙率越高计算渗透率越准确(n=0.78，误差为10.22%)；土颗粒越小，渗流孔道越细窄、分布越密集，对应的速度场分布更为均匀，同时流速也更小。该研究成果能较好地揭示重构土的细观渗流机理，也可为现有细观土体孔隙流研究提供一定借鉴。
Abstract:Reconstruction of the porous media model is the basis and key to the study of the meso-seepage mechanism of soil. The soil models are constructed by the quartet structure generation set (QSGS), and the lattice Boltzmann method (LBM) is used to examine the meso-seepage mechanism of the reconstructed soil under different conditions through MATLAB self-programming. The results show that the degree of pore connectivity increases significantly as the model size increases. The 300×300 grid size model has the largest increase in the connected porosity (34.38%). If the model size continues to be expanded, the increase is not obvious. Fluid particles can form the main seepage channel in the area with good pore connectivity and large pore size, and there is a fingering effect. The flow velocity in the middle of the pore channel is the largest, up to 0.0324. The flow velocity is getting smaller and smaller when it gets closer and closer to the pore wall. The velocity of the large porosity soil is larger than that of the small porosity soil, and the velocity of the low porosity soil is more stable than that of the large porosity soil. Comparing the calculation results of LBM simulation permeability with those of the typical K-C formula, it is found that the higher the porosity, the more accurate the calculation of permeability (n=0.78, the error is 10.22%). The smaller the soil particles, the narrower the seepage channels and the denser the distribution. The corresponding velocity field distribution is more uniform, and the flow velocity is also smaller. The research results can better reveal the meso-seepage mechanism of the reconstructed soil, and can also provide a certain reference for the existing meso-soil pore flow research methods.
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Key words:
- Lattice Boltzmann /
- meso-seepage /
- quartet structure generation set /
- soil particle size /
- permeability
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表 1 验证算例参数表 (格子单位)
Table 1. Validation calculation example parameter table (grid unit)
参数 L D δx δt Re pin pout 计算值 10 50 1 1 100 1.0006 1.0000 
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表 2 不同尺寸模型孔隙参数（格子单位）
Table 2. Pore parameters of different size models (grid unit)
模型尺寸 孔隙率n 孔隙数量/个 平均等效孔径 连通孔隙率 
50 0.64 5 10 0.19 100 13 12.5 0.27 200 88 9.6 0.32 300 139 11.5 0.43 400 251 11.4 0.44 500 462 10.5 0.46
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表 3 LBM模拟渗透率与K-C模型计算渗透率对比结果（格子单位）
Table 3. Comparison results of the LBM simulated permeability and K-C model calculated permeability (grid unit)
孔隙率n LBM渗透率 K-C渗透率 误差/% 0.50 0.7658 1.0028 23.63 0.64 2.6856 2.3626 13.67 0.78 5.4187 4.9160 10.22
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