水力耦合作用下层间岩体渗透压差衰减时空演化理论模型

doi:10.3724/1000-6915.jrme.2025.0051

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摘要煤矿地下水库下伏层间岩体渗透安全是下压煤层安全开采的重要保障，层间岩体渗透率的精准计算是渗透安全评价的重要依据。低渗岩石常采用瞬态法测试，其核心原理在于渗透压差衰减时间曲线的精确描述，但忽略了渗透压差空间分布的描述，导致渗透率的计算无法摆脱线性达西方程的影响。以大柳塔煤矿地下水库层间岩体为原型，将下压煤层开采等复杂扰动应力路径设计为三阶段：原位应力、采动应力和循环应力，并通过瞬态法对不同水力耦合条件下煤岩、泥岩及砂岩进行全过程特征点多次渗透测试，揭示了层间煤、泥岩和砂岩在采动应力阶段的回弹扩容现象。进一步基于Forchheimer方程、Mittag-Leffler函数对渗透压差衰减平衡曲线弛豫过程非线性进行了描述，验证了Mittag-Leffler函数描述岩石非达西渗流压差衰减过程的有效性。同时，建立水力耦合层间岩样渗透压差时空衰减过程理论模型，指出渗透压差衰减可用流体扩散方程描述，基于分数阶理论实现了对岩石内部渗透压差时空演化的准确描述。并指出瞬态法测试渗透率的原理本质是在空间上满足达西定律，即瞬时均满足稳态测试，在时间演化上满足非达西特征。最后，基于滞后性原理推导了一维分数阶扩散方程的离散格式，完成了水力耦合层间岩样渗透压差衰减时空分数阶方程离散化，通过有限差分法求解并建立了层间岩体渗透压差的时空分布曲面，实现了渗透压差时空分布的可视化，为渗透率空间分布理论求解奠定了基础。

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	程建超1
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	刘殷彤1
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	王路军1
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	侯孟冬2
	张辽2
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	毛婷婷2
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	周生昊2
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	王军5
	薛东杰1
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关键词 ：岩石力学, 水力耦合, 渗透压差, 渗透率, 分数阶, 时空分布

Abstract：The safety evaluation of seepage in interlayer rock beneath the underground water reservoir of coal mines is crucial for the secure extraction of lower coal seams. Accurate calculation of the permeability of interlayer rock serves as a fundamental basis for this seepage safety assessment. The transient testing method is frequently employed to measure permeability in low-permeability rocks, relying on a precise description of the decay curve of the seepage pressure difference. However, the spatial distribution of this seepage pressure difference is often overlooked, leading to permeability calculations being influenced by linear Darcy?s laws. Using the interlayer rock of the underground reservoir in the Daliuta coal mine as a prototype, we designed complex disturbance stress paths associated with lower coal seam mining in three stages: in-situ stress, mining stress, and cyclic stress. Multiple seepage tests were conducted at characteristic points throughout the entire process on coal, mudstone, and sandstone under varying hydraulic-mechanical coupling conditions using the transient method. These tests revealed the phenomenon of rebound expansion during the mining stress stage of the interlayer rock. Furthermore, we describe the nonlinearity of the relaxation process of the seepage pressure difference decay curve based on the Forchheimer equation and the Mittag-Leffler function, validating the applicability of the Mittag-Leffler function in characterizing the differential pressure decay process of non-Darcy seepage in rocks. Subsequently, a spatiotemporal theoretical model for the decay process of the seepage pressure difference in interlayer rock under hydraulic-mechanical coupling was established, demonstrating that this decay can be represented by the fluid diffusion equation. An accurate description of the spatiotemporal evolution of seepage pressure difference in rock is achieved through fractional-order theory. We also emphasize that the principle underlying the transient method for measuring permeability is to satisfy Darcy’s law spatially, indicating that transients conform to steady-state tests in space, while seepage exhibits non-Darcy characteristics over time. Finally, based on the hysteresis principle, we derive the discrete format of the one-dimensional fractional-order diffusion equation and complete the discretization of spatiotemporal fractional-order equations for the decay of seepage pressure difference in interlayer rock under hydraulic-mechanical coupling. Utilizing the finite-difference method, we solve and visualize the spatiotemporal distribution surfaces of seepage pressure difference in the interlayer rock, providing a foundation for theoretical solutions regarding the spatial distributions of permeability.

Key words： rock mechanics hydraulic-mechanic coupling seepage pressure difference permeability fractional derivative spatiotemporal distributions

引用本文:

程建超1，2，刘殷彤1，2，王路军1，3，侯孟冬2，张辽2，4，毛婷婷2，4，周生昊2，4，王军5，薛东杰1，2，4. 水力耦合作用下层间岩体渗透压差衰减时空演化理论模型[J]. 岩石力学与工程学报, 2025, 44(10): 2715-2733.
CHENG Jianchao1, 2, LIU Yintong1, 2, WANG Lujun1, 3, HOU Mengdong2, ZHANG Liao2, 4, MAO Tingting2, 4, ZHOU Shenghao2, 4, WANG Jun5, XUE Dongjie1, 2, 4. Spatiotemporal modelling of decaying evolution of seepage pressure difference in interlayer rock under hydraulic-mechanic coupling. , 2025, 44(10): 2715-2733.

链接本文:

https://rockmech.whrsm.ac.cn/CN/10.3724/1000-6915.jrme.2025.0051 或 https://rockmech.whrsm.ac.cn/CN/Y2025/V44/I10/2715

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