循环应力−孔隙压力耦合作用煤体力学渗流响应及损伤本构模型

Mechanical-seepage responses and damage constitutive model of coal under cyclic stress-pore pressure coupling

  • 摘要: 煤层采动过程中,孔隙瓦斯压力与地应力呈多周期同步加载或卸载的动态耦合特征,两者共同驱动煤体变形及瓦斯运移,诱发矿井煤岩瓦斯动力灾害。为了深入揭示地应力与瓦斯压力多周期耦合作用下的煤体力学渗流响应特征及其主控机制,开展了固定孔隙压力仅应力(stress-only, OS)循环、固定应力仅孔隙压力(pore pressure-only, OPP)循环和应力−孔隙压力耦合(stress-pore pressure coupled,SPPC)循环加卸载的三轴渗流试验,基于统计损伤理论构建了SPPC作用下煤体损伤本构模型。结果表明:应力与孔隙压力对煤体轴向压缩和径向膨胀变形均有促进作用,二者对体积应变影响呈相反的竞争关系,由此导致其对渗流通道的差异化影响(应力促进体积压缩从而抑制瓦斯渗流,孔隙压力导致体积膨胀从而促进瓦斯渗流)。随循环周期增加,3种循环路径煤体轴向应变均呈波动式增长,径向应变波动减小。SPPC循环煤体在应力场与渗流场的耦合作用下,变形响应更敏感、损伤更易累积,至试验结束时,其累积残余应变最大(轴向0.203×10−2,径向−0.059×10−2)。此外,3种循环路径煤体在加载结束时的渗透率随循环周期增加均呈指数型衰减,表明循环损伤累积使孔裂隙难以恢复至初始开度,渗流能力减弱;OS和SPPC循环煤体在卸载结束时的渗透率随循环周期增加逐渐减小,而OPP循环则相反,高压瓦斯将裂隙表面附着的松散煤颗粒或黏土矿物反复冲刷,导致裂隙通道扩展。贡献率数据表明煤体应变演化受应力主控,其在轴向、径向及体积应变中的平均贡献率分别为97.5%、64.9%和79.7%;渗透率演化则由孔隙压力绝对主导,其贡献率 > 97.6%。最后,基于煤体微元强度服从Weibull分布特征,考虑孔隙压力对煤体强度的劣化作用,提出耦合损伤变量,构建了SPPC作用下基于D-P(Drucker-Prager)准则的损伤本构模型,该模型在加−卸载阶段可较好地描述煤体在SPPC作用下的变形响应特征。研究结果为进一步揭示矿井煤岩瓦斯动力灾害的力学作用机理提供了理论支撑。

     

    Abstract: During coal seam mining, pore gas pressure and in-situ stress exhibit dynamic coupling characteristics involving multi-cycle synchronous loading and unloading. Coal deformation and gas migration are jointly driven by these two factors, triggering coal-rock gas dynamic disasters in mines. To further reveal the mechanical-seepage response characteristics of coal and their dominant controlling mechanisms under multi-cycle coupling of in-situ stress and gas pressure, triaxial seepage tests are conducted under three cyclic loading-unloading paths: stress-only (OS) cycling with fixed pore pressure, pore pressure-only (OPP) cycling with fixed stress, and stress-pore pressure coupled (SPPC) cycling. A damage constitutive model for coal under SPPC conditions is developed based on statistical damage theory. The results indicate that stress and pore pressure both promote axial compression and radial expansion of coal, while exerting an opposite competitive relationship on volumetric strain. This leads to their differentiated effects on seepage channels: stress facilitates volumetric compression, thereby inhibiting gas seepage, whereas pore pressure induces volumetric expansion, thus enhancing gas seepage. With an increasing number of cycles, axial strain of coal under all three cyclic paths exhibits a fluctuating increase, whereas radial strain shows a fluctuating decrease. Under the coupled effect of stress and seepage fields, coal subjected to SPPC cycling demonstrates a more sensitive deformation response and greater susceptibility to damage accumulation. By the end of the tests, its cumulative residual strain is the largest (axial 0.203% and radial −0.059%). Additionally, permeability of coal under all three cyclic paths at the end of loading exhibits exponential decay with an increasing number of cycles, indicating that accumulated cyclic damage hinders the recovery of pore-fractures apertures to their initial state, resulting in diminished seepage capacity. Permeability of coal under OS and SPPC cycling at the end of unloading gradually decreases with more cycles, whereas the opposite is observed under OPP cycling. High-velocity gas repeatedly scours loose coal particles or clay minerals adhering to fracture surfaces, facilitating the expansion of fracture channels. Contribution rate analyses reveal that coal strain evolution is dominantly controlled by stress, with average contribution rates of 97.5%, 64.9%, and 79.7% to axial, radial, and volumetric strains, respectively. Permeability evolution is absolutely dominated by pore pressure, with a contribution rate exceeding 97.6%. Finally, based on the characteristic that coal element strength follows a Weibull distribution, and considering the strength degradation effect of pore pressure on coal, a coupled damage variable is proposed, and a damage constitutive model based on the D-P (Drucker-Prager) criterion under SPPC conditions is developed. This model effectively describes the deformation response characteristics of coal under SPPC during loading-unloading stages. The results provide theoretical support for further elucidating the mechanical mechanism of coal-rock gas dynamic disasters in mines.

     

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