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含贯通裂缝岩土体Navier-Stokes流耦合non-Darcy流的拖曳力效应
中文摘要

 岩土体中的贯通裂缝是地下水与地表水相互转换的主要路径,是地下水与岩土体之间水力联系的重要通道,也是岩土体失稳破坏常常追踪的边界条件。然而,当前评价地下水渗流环境下岩土体以及建(构)筑物失稳破坏时,依据现有的规范标准和经典的岩土力学理论,仅考虑岩土体渗流力、孔隙水压力及遭受的软化劣化作用,忽略了伴随贯通裂缝水流的拖曳力效应,而出现难以阐释的困惑。鉴于此,本文从细观尺度入手,建立含贯通裂缝岩土体多孔介质Navier-Stokes流耦合non-Darcy流的非线性数学模型,通过理论计算、试验测试和案例反馈一致性检验,揭示含贯通裂缝多孔介质内的流场特征和流体切应力分布,量化拖曳力对岩土体的力学响应贡献,为科学评价渗流环境下含贯通管缝岩土体的稳定性提供理论基础。论文主要研究内容和创新成果如下: (1)通过构建的Navicr-Stokcs流耦合non-Darcy流理论模型,获得含贯通裂隙岩体渗流流速分布,推求出含贯通裂隙岩体等效渗透系数显式表达;理论上验证了岩体等效渗透系数是受裂缝开度、充填物孔隙率以及渗透率、岩石孔隙率以及渗透率的共同影响;提出的含部分充填裂缝复杂模型可以统一反映含全充填和含无充填裂缝简单模型,由推求的理论表达式可以直接写出经典的开口立方定律,对比前人研究成果,很好地验证了理论模型的正确性;通过室内模型试验对理论分析进行验证,试验结果与理论结果之间的误差小于10%,也很好地验证了理论模型的准确性。 (2)从流体粘性角度出发,基于Newton内摩擦定律,结合含贯通裂隙岩体渗流流速分布,推导出水流拖曳力显式表达式;该理论表达显示拖曳力受裂隙宽度、水流压力差、天然裂隙倾角等参数的影响;当裂隙被充填时,裂隙水流拖曳力还与岩石基质和充填介质的渗透率以及孔隙率有关。对于无充填裂隙岩体拖曳力,该力一方面源于压力水头作用,另一方面受水体自重作用,这与天然水体运动的原因一致,该表达式的简化结果得到前人理论结果的验证。 (3)建立降雨条件下坡面径流和坡体渗流耦合分析模型,推导出渗流和径流的流速分布,获得坡面水流拖曳力显式表达式。将流速表达式代入水流冲刷颗粒拖曳力表达式,对坡面松散颗粒进行分析,建立了松散颗粒滑动、滚动启动判据;将拖曳力表达式嵌入刚体极限平衡理论,对顺坡向浅层边坡稳定性进行分析,量化了拖曳力对浅层边坡稳定性的影响。成果应用于四川南江县浅层土质滑坡群,通过对坡面径流拖曳力进行参数敏感性分析,发现:坡体较薄时,坡面径流拖曳力效应对斜坡稳定系数的影响可以达到10%;随着坡体厚度增加,坡面径流对斜坡稳定系数的影响逐渐下降;尽管与降雨入渗土体软化作用相比,拖曳力对斜坡宏观不稳定性的贡献较小,但是当斜坡稳定性在近乎临界状态时,实践中常被忽略的拖曳力会导致边坡失稳,起到决定性作用。 (4)引入断裂力学理论,针对裂隙静水压力效应,分析岩质边坡裂隙起裂扩展机理,得到了岩体裂隙起裂的临界水深。当超过临界水深,后缘裂隙扩展至岩质斜坡软弱结构面,发生高水头作用下的裂隙渗流;将渗流模型引入岩质边坡渗流分析,得到相应的渗流拖曳力表达,然后在刚体极限平衡理论中嵌入拖曳力,分析岩质边坡稳定性发现:渗流拖曳力对于斜坡稳定有一定的不利影响,具体体现在裂隙开度、压力水头、裂缝充填物孔隙率等的影响。成果应用于四川“6.24”茂县新磨村滑坡的稳定性分析,计算结果表明:对于大型岩质滑坡,水流拖曳力对斜坡稳定性系数也能发挥一定的作用,具体到反映在茂县新磨村滑坡稳定系数的影响约为1%。相对于降雨入渗对裂隙填充介质的软化劣化效应,尽管拖曳力对于斜坡稳定性的影响相对较小,但是当坡体处于临界稳定状态时却会起到“压死骆驼的最后一根稻草”的作用,引起边坡失稳。 关键词:裂缝流;孔隙渗流;拖曳力;Navier-Stokes方程;Brinkman-extended Darcy方程;边坡稳定性

英文摘要

 The continuous fractures are primary hydraulic channels to transfer surface water into underground water, as well as to connect underground water with rock and soil matrix. The continuous fracture sometimes plays a key role when failure occurs in rock mass and soil. Presently, scholars and engineers in the field of civil engineering only consider pore water pressure, seepage force, softening and deterioration due to water when evaluating stability and safety of the buildings constructed in or on rock mass and soil according to the forced rules and standards and classic theories of rock and soil mechanics. However, this work presents that the effect of drag force widely existing in movement of groundwater should not be neglected in case that the flow in continuous fracture is accompanied by seepage in rock and soil matrix. Accordingly, a nonlinear mathematic model based on micro-scale is used to describe the movement of groundwater in rock mass and soil containing the continuous fracture. This model assumes that Navier-Stokes flow passes through continuous fracture along with non-Darcy seepage in porous rock or soil matrix. Use of the given method revealed the characteristic of flow field and distribution of flow shear stress in rock mass and soil. Meanwhile, the theory methods were validated together with analysis for a series of physical models and project cases. This work made it possible in quantitatively evaluating the contribution of drag force to the mechanical responses of rock mass and soil so as to reasonably calculate the stability and safety of rock and soil in condition of seepage. The major work and innovative conclusions are as follows: (1)By establishing the theoretical model of Navier-Stokes flow coupled with non-Darcy flow, the seepage velocity distribution of rock mass with continuous fracture is obtained, as well as the explicit expression of equivalent permeability coefficient. The result theoretically validated that the equivalent permeability coefficient of fracture rock is influenced by fracture aperture, porosity and permeability of inflllings and rock matrix, et al. The complex model of rock mass with partially filled fracture can reduce to simple models of rock mass with unfilled fracture and rock mass with wholly filled fracture. The classical Open Cube Law could be derived by the theoretical expression. The result could also be verified by comparing with the results of former scholars. Finally, comparisons with experimental data show good agreement, thus verifying the validity of present computations. (2)From view of fluid viscosity, an explicit expression for the flowing fluid's drag force was derived by combining with Newton's law of internal friction and the seepage velocity distribution in fractured rock mass. The expression illustrates that drag force is affected by fracture aperture, hydraulic gradient, the inclination of natural fracture, and so on. When the fracture was infilled, it would also affected by the porosity and permeability of infillings. For the unfilled fractured rock mass, drag force comes from the effect of water pressure and self-weight of water, which is same with reason of causing natural fluid motion. The result was also verified by comparing with the results of former scholars. (3)By establishing the analyzing model of coupling surface runoff with seepage in slope soil under intensive rainfall condition, the seepage velocity and runoff velocity distribution were obtained, as well as the explicit expression of fluid's drag force. By substituting the velocity expression into former expression of particle's drag force, a modified particle's starting criterions of sliding and rolling were obtained. Furthermore, embedding the drag force into the limit equilibrium method and analyzing the stability of shallow soil slope, the drag force effect on the stability of the shallow slope is quantitatively investigated. Then, the research method was applied to the shallow soil landslides occurring in Sichuan Nanjiang, and the results showed that the affecting rate of drag force to the slope stability factor was almost 10 percent while the slope soil layer is comparatively thin, and the effect decreased with the increase of soil depth. Although the effect of drag force to slope stability was small comparing with the softening effect of water infiltration, the drag force would play a key role and cause shallow slope to be failure while the slope was nearly under critical state. (4)By introducing the theory of fracture mechanics, aiming at the hydrostatic pressure effect the mechanism of crack initiation and propagation in rock slope was analyzed and the critical water depth for crack initiation was obtained. While water depth in fracture exceeded the critical water depth, the crack continues to propagate. Once the crack was connected with the former weak layer, it will yield fracture seepage for the high water pressure. Analyzing the seepage characteristics of fractured rock slope, the expression of drag force was derived combining with Newton's law of internal friction. Furthermore, embedding the drag force into the limit equilibrium method and analyzing the stability of rock slope, the drag force effect on the stability of the rock slope is quantitatively investigated. Then, the research method was applied to the stability analysis of “6.24 Xinmo landslide” occurring in Sichuan Maoxian, and the results showed that the affecting rate of drag force to the stability factor of this huge slope was approximately 1 percent for the high water pressure. Although the effect of drag force was small comparing with the softening effect, the drag force would cause slope to be failure and play the key role while the slope was nearly under critical state. Key words: Flow in fracture; Seepage in porous medium; Drag force; Navier-Stokes equation; Brinkman-extended Darcy equation; Slope stability analysis

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