压剪大位移下花岗岩粗糙裂隙渗流场演化矢量算子描述

doi:10.3724/1000-6915.jrme.2024.0513

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摘要岩石粗糙裂隙渗流场的描述一直是难点，平行板流等模型侧重于揭示裂隙纵剖面的流速分布，而裂隙开度几何场与横剖面渗流场密切相关，实现对其的科学描述是建立流速场–几何场关联模型的关键。相对压剪位移超过5%的渗流试验难以开展，因此针对北山深部花岗岩潜在的压剪大位移破坏下的渗流计算问题，基于Reynolds方程建立粗糙裂隙开度几何场–渗流场演化数值计算模型，并通过渗流速率梯度和速度散度，实现对渗流场的场函数微分表征。压剪作用下大位移阶段，每组粗糙裂隙开度模型下的流速场、梯度场和散度场在空间分布上均存在一致性；不同压剪位移下速率、梯度和散度均符合正态分布；随着闭合接触区域的增加，全域渗流向局域渗流转变，梯度和散度矢量算子描述裂隙面流速场演化仍有效。结果表明，流速场的平均梯度和平均散度均趋于0的统计特征意味着低渗条件下粗糙裂隙流可等效为均匀平板流。

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	刘殷彤1
	程建超1
	张辽1
	侯孟冬1
	毛婷婷1
	田金柱1
	高伟琪1
	刘升贵1
	薛东杰1
	2

关键词 ：岩石力学, 粗糙裂隙, 渗流场, 压剪大位移, Reynolds方程, 矢量算子

Abstract：An accurate field description of fracture flow still presents a huge obstacle in flow mechanics. Unlike some classic flow models，i.e. parallel plate flow，focusing on the velocity distribution along the longitudinal section of the fracture，very little attention is paid to the velocity distribution within the fracture cross-section. The spatial distribution of fracture aperture indicates a geometric field，which significantly impacts the flow velocity distribution within the cross-section，while lacking proper correlation models induces a difficult understanding of statistical analysis of geometric field?s effect on fracture flow distribution. To solve the challenge of carrying out a seepage test with relative compression or shear displacement exceeding 5% in lab，the Reynolds equation-based discrete solution of fracture flow considering the large shear-compression displacements for Beishan granite is made，and through the gradient of seepage rate and velocity divergence，the differential characterization of the seepage field's field function was achieved. For the same group of cracks，three fields of flow velocity，gradient and divergence presents a consistent spatial geometric distribution under different shear or compression displacements and nearly all fields conform to the normal distribution. In addition，with the increase in closed aperture and contact area，the full-scale fracture flow turns into local-scale flow and two vector operators of gradient and divergence describing the evolutional distribution of fracture flow are still effective. The results show that in the statistical sense，under low-permeability conditions，a rough fracture flow，characterized by the average gradient and the average divergence of the flow velocity field tend towards 0，can be equivalently treated as uniform flat plate flow with low velocity.

Key words： rock mechanics rough fractures flow velocity fields large compression-shear displacements Reynolds equation vector operators

引用本文:

刘殷彤1，程建超1，张辽1，侯孟冬1，毛婷婷1，田金柱1，高伟琪1，刘升贵1，薛东杰1，2. 压剪大位移下花岗岩粗糙裂隙渗流场演化矢量算子描述[J]. 岩石力学与工程学报, 2025, 44(3): 651-677.
LIU Yintong1，CHENG Jianchao1，ZHANG Liao1，HOU Mengdong1，MAO Tingting1，TIAN Jinzhu1，GAO Weiqi1，LIU Shenggui1，XUE Dongjie1，2. Vector operator-based description of evolutional velocity field for water flow between rough fractures in granite under large compression-shear displacements. , 2025, 44(3): 651-677.

链接本文:

https://rockmech.whrsm.ac.cn/CN/10.3724/1000-6915.jrme.2024.0513 或 https://rockmech.whrsm.ac.cn/CN/Y2025/V44/I3/651

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