三轴应力下颗粒流失对断层破碎带凝灰岩渗流特征的影响

地下工程施工过程中,处于三向应力状态的断层破碎带凝灰岩在流固耦合作用下发生颗粒流失,继而诱发断层带破碎岩石结构失稳,最终导致断层突水灾害发生。基于此,开展现场断层取样,利用破碎岩石三轴渗透试验系统,研究三轴荷载下不同粒径级配试样颗粒流失规律,进而分析颗粒流失对孔隙结构与渗流流速时变演化规律的影响。研究结果表明:（1）不同三轴应力下,破碎凝灰岩颗粒流失质量与时间满足指数型函数关系,两者间相关系数不低于94%。颗粒流失质量与轴压和围压成反比,且轴向位移越大,颗粒流失质量随围压减小的幅度越小;（2）渗透过程中0～60 s间的孔隙率增长较快,孔隙结构的渗流演变过程与粒径级配有关,随着n (Talbot幂指数) 值的增大,孔隙率整体增大,n值相同时,孔隙率随轴向位移与围压的增大而减小,且孔隙率量级为0.33～0.52;（3）由于试样内部颗粒规律性流失,破碎凝灰岩渗流流速时变演化过程可划分为“平稳渗流、渗流流速突增和近似管流”三个阶段,围压为0.8 MPa时各阶段流速整体大于围压为1.4 MPa时对应阶段的流速。平稳渗流阶段历时短,流速低,其发生次数随n值增加而减少;渗流流速突增阶段流速猛增达到峰值;近似管流阶段保持较高流速,虽然偶尔产生波动,但整体相对平稳。研究成果可为断层突水灾害演化规律研究提供理论依据。      

Effects of the Erosion and Transport of Fine Particles due to Seepage Flow

The gradual erosion and transport of fine particles are among the possible consequences to the subsoil of a severe seepage flow, such as the seepage induced by the artificial lowering of the water table by means of pumping wells. The erosion, in turn, could induce local effects, in terms of reductions in the soil volume and variations in the soil mechanical characteristics, that could be non-negligible when working in an urban area. In this paper, some laboratory tests are presented aimed at investigating the erosion of fine particles from soil samples subjected to a controlled seepage flow. The phenomenon of erosion and transport is then modeled by combining, in a single governing equation, the conservation of mass of moving particles with a suitable law of erosion, which is calibrated on the basis of the seepage tests. This equation, coupled with the equation governing the seepage problem, permits one to evaluate the quantity of particles eroded and transported from the soil mass. The effects of the loss of fine material on the stress–strain distribution within the soil mass are estimated by a finite-element analysis. The proposed model is then adopted for the evaluation of the surface settlements induced by the water pumping from a drainage trench.     

Modeling Flow and Pollutant Removal of Wet Detention Pond Treating Stormwater Runoff

A mathematical model of pollutant removal by wet ponds was developed based on the mass balance principle and the release–storage equation. The release–storage equation can be linear or nonlinear depending on the wet pond shape and the spillway crest features. If the exponent index of the storage relationship (d) is equal to the index of the outflow equation (b), the wet pond hydrological routing model is linear. Otherwise, the model is nonlinear. Substituting the release–storage equation into the continuity equation produces a nonlinear ordinary differential equation (ODE). A Runge–Kutta method was used to solve the resulting nonlinear ODE. When the ratio of indexes d/b = 2/3, the hydrologic wet pond model reduces to a special case that leads to an implicit analytical solution. The pollutant removal and flow routing models were tested with data obtained from an actual wet pond for treating highway runoff. The predicted flow discharges and pollutant concentrations compared well with the observed data.     

Nonlinear Aeroelasticity: Continuum Theory, Flutter/Divergence Speed, and Plate Wing Model

This paper formulates flutter/divergence instability problems using continuum models for structure and air flow as coupled nonlinear partial differential equations. The structure model is a Kirchoff CFFF thin plate allowing for nonzero thickness and camber bending. The aerodynamics is modeled by the transonic small disturbance potential equation. The aeroelastic boundary conditions are derived for nonzero angle of attack. A central result is the time domain model as a nonlinear convolution/evolution equation in a Hilbert space. Flutter speed is characterized as a Hopf bifurcation point, completely determined by the linearized equations. The main tool in solving the linear equations is the Possio equation for nonzero angle of attack. Divergence speed is shown to be determined by an eigenvalue problem for linear operators. The corresponding stationary (steady state) solutions are more regular in the transonic range (as M goes to one) if the angle of attack is nonzero.     

中国页岩气开发理论与技术研究进展

中国的页岩气田属于非常规气藏,采用体积压裂工程技术才可以实现有效开采。不过,页岩储层与一般储层的性质不同,纳米级孔隙大量分布,其孔隙和渗透率十分微小,同时还分布有微裂缝,气体在其中的流动具有解吸、扩散、滑脱和渗流等多种微观机理,并且呈现出基质?微裂缝?人工裂缝的跨尺度多流态流动。常规的油气开发理论与技术并不适用于页岩气藏,因此需要有针对性的研究,并建立页岩气开发的理论与技术,才能实现我国页岩气藏的高效地开发。从页岩气流动的基本规律出发,总结了页岩气流动的多流态?多尺度?多场耦合输运机理和渗流规律,归纳了考虑解吸?扩散?滑移?渗流的多尺度非线性渗流统一方程,给出了多尺度全流态图版。通过页岩气多级压裂水平井多区耦合非线性渗流理论、多场耦合非线性渗流理论,形成页岩气藏流场区域储量动用与开发动态变化规律,针对我国页岩气特点构建了页岩气产量递减模型。基于上述理论提出了开发设计方法,提出了我国储层分级评价及优选目标评价方法,并且建立了适合我国储层的分级评价及优选目标方法与指标,对中国页岩气压裂开发工艺适应性技术进展进行了归纳总结。在此基础上,对未来页岩气高效开发理论的发展方向进行了展望,以期对我国页岩气理论和技术研究提供指导。      

渗流作用下风化壳淋积型稀土矿细观孔隙结构演化特征

为研究风化壳淋积型稀土矿浸出过程中溶液渗流作用对孔隙结构的影响,以去离子水为溶浸液开展浸矿实验。对浸出前后矿样进行显微CT扫描,获取了试样内部结构图像,利用阈值分割算法得到了浸出前后稀土矿样的孔隙结构图像。进而,研究了溶液渗流作用下试样孔隙结构的变化特征,分析了渗流作用对试样孔隙率、孔隙体积、孔隙长度、孔隙宽度和孔隙方位角等参数的影响。结果表明:稀土矿孔隙形状和尺寸在渗流作用下发生显著变化,且在粗细颗粒接触区最为明显;溶液渗流作用使得稀土矿孔隙率增大,孔隙总数量减少,孔隙总体积增大。渗流作用下矿样中小孔隙数量减少,大孔隙数量增多,各尺寸区间的孔隙数量变化率随孔隙尺寸的增大呈现先增大后减小的趋势。溶液渗流作用下孔隙长宽比分布更加集中,孔隙方位角在各角度区间的分布更加均匀,孔隙各向异性增强。      

Coupled Creep and Seepage Model for Hybrid Media

The permeability coefficient of a rock mass depends mainly on the aperture of the joint and the porosity of the block, which may alter with time when creep of the rock mass is taken into account. Therefore, a coupled creep and seepage model for hybrid media is proposed in this paper. Large-scale and strongly permeable joints are simulated according to their spatial distributions, while other discontinuities are treated as equivalent continuum. Based on the fundamental mechanism of creep effects on the permeability of the rock mass, together with empirical equations for hydraulic conductivity, coupled creep and seepage equations for filled joints, rough joints, and equivalent continuum are proposed. By application of these equations, governing equations for the coupled creep and seepage model are deduced. A simplified numerical solution is proposed to solve the coupled creep and seepage model. The coupled model is shown to simulate the evolvement of seepage, deformation, and stress field in a gravity dam. By comparing the results derived by coupled and uncoupled models, it is concluded that the coupling between creep and seepage should be taken into account when performing engineering design of large dams.     

Design of Minimum Seepage-Loss Nonpolygonal Canal Sections

Analytical solutions exist for the problem of determination of seepage loss from polygonal sections such as a triangle, a rectangle, and a trapezoid. In this investigation, seepage from circular and exponential sections has been calculated by a finite-difference-based numerical solution of the differential equation governing the seepage flow. The phreatic boundaries of the flow domain were described in terms of two parameters that are estimated by a minimization process. Such seepage computations were performed for a large number of independent dimensionless variables of the section geometry. Subjecting the computed seepage to regression analyses explicit equations for seepage loss from canals having circular and exponential cross sections have been obtained. Using these seepage-loss equations, the design variables for minimum seepage loss of circular and exponential canal sections have been obtained. The use of the design equations has been illustrated by design examples.     

多相混合渗流理论研究

针对现有多相渗流理论假设各相均为连续相、无相间交换,不能表征相对渗透率端点附近出现非连续相,未能考虑多相混合、界面作用、相间传质传输等多相掺混复杂流动的问题,本文把多相渗流流体作为一个总体即混合流体,研究多相流体在多孔介质中传输,包含不相溶、相界面变化、相间传质传输、混合相,搞清各相间交换关系和流动机制,即多相混合流动规律.首先基于平衡热力学第一、第二定律,考虑渗流过程中的多相体系平衡条件,推导出了渗流过程中多相体系平衡热力学关系式,之后运用多相流体全质量守恒定律和渗流过程中多相体系平衡热力学公式,建立了多相流体混合渗流理论模型,分析了多相混合渗流理论与传统多相渗流理论的关系,提出了多相混合渗流的理论.指出多相体系流体总的渗流速度不仅与压力梯度成正比,还与多相体系混合渗流程度有密切关系,其中混合渗流程度是饱和度、界面张力、压力梯度和孔隙度的函数.研究结果表明,多相混合渗流理论深刻地反映了多相流体混合渗流的本质,揭示了多相流体混合渗流的内在作用变化规律,弥补了多相渗流理论用单相达西定律推广到了多相渗流中的不足,多相混合渗流理论涵盖了传统多相渗流理论,具有重大的理论意义和应用价值.     

Stochastic Model for Time-Dependent Compression of Particulate Media

The volumetric creep of loose granular materials, in absence of pore fluid pressure, is modeled as a stochastic process of diffusion-convection for excess porosity under sustained, applied loading. The analogy of the underlying concepts, with the theory of sedimentation in Brownian motion, and differences with the earlier contribution of Marsal (1965) are discussed. The analytical formulation and numerical solution are presented for a 1D compression with finite strain and moving boundary surface. The results represent the time evolution of the spatial distribution of the material porosity and the rate of settlement. The compression versus time relationship is normalized in dimensionless form to facilitate the determination of the governing equation coefficients from test data. Examples of determination and comparisons with the model response are presented. According to the model, final settlement is reached asymptotically with equilibrium porosity. At transient states, the spatial distribution of porosity is not necessarily uniform, even when both initial and final distribution are uniform.     

Design of Minimum Seepage Loss Canal Sections with Drainage Layer at Shallow Depth

This paper presents an analytical solution for the quantity of seepage from a rectangular canal underlain by a drainage layer at shallow depth. The solution has been obtained using inverse hodograph and conformal mapping. Using the solution for the rectangular canal and the existing analytical solutions for triangular and trapezoidal canals, simplified algebraic equations for computation of seepage loss from these canals, when the drainage layer lies at finite depth, have been presented, which replace the cumbersome evaluation of complex integrals. Using these seepage loss equations and a general uniform flow equation, simplified equations for the design variables of minimum seepage loss sections have been obtained for each of the three canal shapes by applying a nonlinear optimization technique. The optimal design equations along with the tabulated section shape coefficients provide a convenient method for design of the minimum seepage loss section. A step-by-step design procedure for rectangular and trapezoidal canal sections has been presented.     

Green-Ampt One-Dimensional Infiltration from a Ponded Surface into a Heterogeneous Soil

Saturated hydraulic conductivity and wetting front pressure head (as soil properties) on an abrupt Green-Ampt front are assumed to increase and decrease with depth of a porous heterogeneous soil subject to a constant ponding or infiltration-evaporation depleted ponding on the surface. The corresponding Cauchy problem for a nonlinear ordinary differential equation describing the wetting front propagation in the soil profile is solved by computer algebra routines. Sensitivity of the cumulative infiltration to variation of hydraulic conductivity and capillarity is studied. A concave-convex infiltration graph is obtained for some values of parameters of the assumed exponential growth/decay of conductivity/capillarity. Texture of soil samples collected from a pedon is used for calculation of conductivity from a pedotransfer function. Synthesis of heterogeneity resulting in a specified front dynamics is discussed.     

地下矿山充填料岩石区域非均质一维渗流规律

以地下矿山采场为对象建立了充填料岩石渗流模型,根据实际情况确立初始条件和边界条件,推导出水在充填料和岩石中的渗流压力和流量公式,在此基础上分析了地下充填料岩石中的渗流规律及影响因素.通过分析得出:在充填料中,流量在初始阶段增长较快,达到一个峰值后逐渐下降;压力随时间逐渐降低,最后趋于稳定;渗透率越大,流量和压降越大;高度越高,流量越小而压降越大;孔隙度越小,压力越大,孔隙度对流量的影响在不同阶段各不相同.在岩石中,渗流压力与其渗透率无关,但受充填料渗流的影响较大,随时间降低,渗流流量则只与岩石的渗透率有关.      

Numerical Model of Sedimentation∕Thickening with Inertial Effects

A numerical model of gravity sedimentation and thickening was developed from the governing two-phase flow equations for the liquid and solid phases. The inertial and gravity terms in the solid and liquid momentum equations were retained in the gravity sedimentation and thickening model. An implicit, space-staggered finite-difference algorithm was developed for the resulting coupled partial differential equations. Constitutive relationships describing the physical properties of the slurry were required to solve the numerical model. These constitutive properties describing the relationship between effective stress and porosity and between permeability and porosity were determined experimentally and by model calibration. The model was calibrated and verified using the data of dynamic porosity profiles of gravity sedimentation and thickening of kaolin suspensions in distilled water.     

Multiscale Modeling of Flood-Induced Piping in River Levees

A three-dimensional transient fully coupled fluid-particle model is utilized to simulate flood-induced piping under river levees and taking into account the effects of soil-fluid-structure interactions. The porous soil medium is modeled as a mixture of two phases, namely the fluid phase (water) and the particulate solid phase. The fluid is idealized as a continuum by using an averaged form of Navier–Stokes equations that accounts for the presence of the solid particles. These particles are modeled at a microscale using the discrete element method. The interphase momentum transfer is modeled using an established relationship that accounts for the dynamic change in porosity and possible occurrence of nonlinear losses. The hydraulic structure (levee) is modeled as an impervious rigid block and its motion is described by a combination of external and internal forces from the surrounding fluid and solid particles. A computational simulation is conducted to investigate the response of a granular deposit when subjected to a rapidly increasing head difference. The simulation provided information at the microscale level for the solid phase as well as at the macroscopic level for the pore-water flow. The settlement and failure mechanism of the structure were captured as the hydraulic head difference gradually increased and the solid phase underwent subsequent deformations. The results suggest that failure of such structures may occur suddenly and at hydraulic gradients well below the critical gradient. The proposed computational framework for analyzing river and flood-protection levees would provide a new dimension to the design of such vital geotechnical systems. The technique can be effectively used to investigate failure mechanisms under complex loading and flow conditions.     

Kinetics of simultaneous two-phase precipitation in the Fe-C system

A theoretical approach for the interpretation of the kinetics of simultaneous stable and metastable phase precipitation in a binary system is proposed. The model, based on the nucleation and growth theory, defines a critical size different for each phase. The size of the clusters evolves by adding or substracting a single atom one at a time. A set of coupled differential equations is obtained for the chemical rate whose solution reproduces the kinetics of thermoelectric power measurements in the Fe-C multiphase system. Suppositions about the growing and dissolution rate constants reduce the size of the equation system with a gain in computation time.     

Simulation of Ground-Water Flow in Steep Basin with Shallow Surface Soil

A coupled ground-water∕channel flow distributed model has been developed for continuous simulation in a 123-km2 basin. The aim was to analyze the streamflow generation processes in natural vegetated environments. Finite-difference schemes have been used to solve conservation equations of the 2D saturated subsurface flow and the 1D kinematic surface flow. Because of the high hydraulic conductivity of the surface soil, only the saturation excess mechanism of runoff production has been considered. Parameter sensitivity analysis showed the overriding influence of soil storage capacity and conductivity. A grid discretization >100 m produces a hydraulic conductivity greater than physically meaningful, which considerably increases as the space-grid step increases. Results indicate that the model can satisfactorily simulate the water-flow behavior of the catchment after fitting the three parameters of surface hydraulic conductivity, effective porosity, and evapotranspiration losses. These are done after calculating the conductivity as a function of the height of the water table. The simulation efficiency has varied from 87% in the first 5-year calibration period to 85.8% in the subsequent 5-year validation period.     

Engineering Model of Dilute Pneumatic Conveying

We introduce a simple model of gas–particle flow in a pipeline, which can be used as a tool in engineering design. A chaotic particle motion due to the particle–particle and particle–wall collisions is modeled by analogy with the motion of gas molecules. The pressure gradient is calculated as a sum of particles drag forces per unit volume. As a result, the problem of pressure losses is reduced to the solution of one nonlinear algebraic equation. The gas viscous friction losses are found by the Colebrook–White approximation. The model is validated by testing it against the experimental data and other, more sophisticated, models known in the literature.     

Time-Centered Split Method for Implicit Discretization of Unsteady Advection Problems

A new method for implicit solution of unsteady nonlinear advection equations is presented. This time-centered split (TCS) method uses a nested application of the midpoint rule to computationally decouple advection terms in a temporally second-order accurate time-marching discretization. The method requires solution of only two sets of linear equations without an outer iteration, and is theoretically applicable to quadratically nonlinear coupled equations for any number of variables. The TCS algorithm is compared to other nonlinear solution methods (local linearization, Picard iteration, and Newton iteration) and applied to the Crank-Nicolson discretization of the one-dimensional Burgers’ equation. The temporal accuracy and practical stability of the method is confirmed using an unsteady flow test case with an analytical solution. The method is shown to require computational effort similar to local linearization, but does not require discrete computation of a functional Jacobian for solution.     

Furrow Irrigation Advance Simulation Using a Surface–Subsurface Interaction Model

A model for the simulation of furrow irrigation advance was developed based on the Saint-Venant equations for the one-dimensional surface flow and the two-dimensional Richards equation for porous media flow. Solutions are computed numerically using finite differences for the surface flow and finite elements for the subsurface flow. Computations are internally coupled through an iterative procedure. Infiltration is computed with the Richards equation every five nodes used in the surface flow computations and by linear interpolation at the remaining nodes. In addition, the Richards equation is solved at the boundaries of the surface flow domain and in the vicinity of the wave front. The time step is calculated using the Courant–Friedrich–Lewy condition and a stability criterion that accounts for friction effects. This combined criterion prevents numerical instabilities and convergence problems, especially in cases of high friction coefficient, low discharge rates, and/or high infiltration rates resulting generally in low flow depth and slow irrigation advance. The model was evaluated against an approach involving high resolution correspondence used in both surface and subsurface flow, using different soil types, inflow discharge, and stability criteria.