Differential equations governing slip-induced pore-pressure fluctuations in a water-saturated granular medium

Macroscopic frictional slip in water-saturated granular media occurs commonly during landsliding, surface faulting, and intense bedload transport. A mathematical model of dynamic pore-pressure fluctuations that accompany and influence such sliding is derived here by both inductive and deductive methods. The inductive derivation shows how the governing differential equations represent the physics of the steadily sliding array of cylindrical fiberglass rods investigated experimentally by Iverson and LaHusen (1989). The deductive derivation shows how the same equations result from a novel application of Biot's (1956) dynamic mixture theory to macroscopic deformation. The model consists of two linear differential equations and five initial and boundary conditions that govern solid displacements and pore-water pressures. Solid displacements and water pressures are strongly coupled, in part through a boundary condition that ensures mass conservation during irreversible pore deformation that occurs along the bumpy slip surface. Feedback between this deformation and the pore-pressure field may yield complex system responses. The dual derivations of the model help explicate key assumptions. For example, the model requires that the dimensionless parameterB, defined here through normalization of Biot's equations, is much larger than one. This indicates that solid-fluid coupling forces are dominated by viscous rather than inertial effects. A tabulation of physical and kinematic variables for the rod-array experiments of Iverson and LaHusen and for various geologic phenomena shows that the model assumptions commonly are satisfied. A subsequent paper will describe model tests against experimental data.     

紫坪铺水库造成孔隙弹性耦合变化及其对2008年汶川地震触发作用

位于川西地区龙门山断裂带附近的紫坪铺水库于2005年9月开始蓄水.约2.7年后,2008年5月12日,M_w7.9级汶川地震在龙门山断裂带上发生,两事件在时间和空间上的接近,揭示其可能相互关联,但前人的诸多研究给出了不同甚至是相反的结果.本研究基于完全耦合孔隙弹性理论,利用二维有限元模型(FEM),模拟水库蓄水造成的区域孔隙压力场和应力场的演化过程,基于库仑应力演化探讨其对龙门山断裂带活动的影响.模拟结果显示紫坪铺水库蓄水打破了原来的区域孔隙压力平衡,形成孔隙压力梯度源,向周围地壳传播;进而造成龙门山断裂带上库仑应力正值范围不断扩大,由浅入深影响到整条断层,尤其对浅层范围的加载作用明显,达上百千帕,为整个断层面的失稳提供了基础.震源区域库仑应力呈持续增长趋势,汶川地震发震前,增长了约数千帕~数十千帕,即使初期库仑应力为负,在未来某时刻库仑应力仍可能由负转正,并不断增大.通过计算汶川地震震源及其附近区域内相对于多种可能断层倾角的库仑应力,发现库仑应力随断层倾角增大而增加.因此整体来看,紫坪铺水库蓄水对龙门山断裂带起加载作用,有可能触发地震.对紫坪铺库区周围的小震分析也显示,蓄水以来小震明显增多、且不同时段小震发生密集区与水库距离逐渐增大,与孔隙压力扩散趋势一致.以上结果表明紫坪铺水库的蓄水增加了汶川地震的危险性.     

稠油蒸汽热采区声波资料异常现象的物理解释及应用

针对稠油蒸汽热采区常见的声波资料异常现象, 根据双相多孔介质声波传播理论及相关实验结果,对于这一特殊的声波测井响应特征进行了解释,认为注入蒸汽的影响导致了纵波速度的低异常及幅度的强衰减, 而使声波测井资料显现出异常高时差值或出现“跳变”现象.据此总结了利用声波资料评价蒸汽波及范围与蒸汽前缘的解释方法,并进行了多井评价实验, 取得了满意结果.同时,也为利用孔隙介质弹性波动理论评价地下蒸汽分布范围的适用性提供了新的现场实际例证.     

Triggered earthquakes as stress gauge: Implication for the uppercrust behavior in the Grenoble area,France

A sequence of moderate shallow earthquakes (3.5M _L5.3) was located within the Vercors massif (France) in the period 1961–1984. This subalpine massif has been a low seismic area for at least 5 centuries. During the period 1962–1963, 12 shallow earthquakes occurred in the neighborhood (10 km) of the Monteynard reservoir, 30 km south of the city of Grenoble. The latest fourM _L4.0 earthquakes occurred in 1979–1984 either at larger distance (35 km) or greater depth (10 km) from the reservoir. Two triggering mechanisms are suggested for this sequence: (i) the direct effect of elastic loading through either increased shear stress or strength reducing by increased pore pressure at depth; (ii) the pore pressure diffusion induced by poroelastic stress change due to the reservoir filling.The weekly water levels, local balanced geological cross sections, and focal mechanisms argue for two types of mechanical connection between the earthquake sequence and the filling cycles of the Monteynard reservoir. The seismic sequence started with the 1962–1963 shallow earthquakes that occurred during the first filling of the reservoir and are typical of the direct effect of elastic loading. The 1979 deeper earthquake is located at a 10 km depth below the reservoir. This event occurred 16 years after the initial reservoir impoundment, but one month after the previous 1963 maximum water level was exceeded. Moreover the yearly reservoir level increased gradually in the period 1962–1979 and has decreased since 1980. Accordingly we suggest that the gradual diffusion of water from reservoir to hypocentral depths decreases the strength of the rock matrices through increased pore pressure. The transition between the two types of seismic response is supported by the analysis ofM _L3.5 earthquakes which all occurred in the period 1964–1971, ranging between 10 and 30 km distance from the reservoir. The three other delayed earthquakes of the 1961–1984 seismic sequence (M _L4 during the 1979–1984 period) are all located 35 km away from the reservoir. Based on the seismic activity, the estimates for the hydraulic diffusivities range between 0.2–10 m²/s, except for the first event that occurred 30 km north of the reservoir, the filling just started. The lack ofin situ measurements of crustal hydrological properties in the area, shared by most of the Reservoir-Induced-Seismicity cases, prevents us from obtaining absolute evidence for the triggering processes. These observations and conceptual models attest that previous recurrence times for moderate natural shocks (4.5M _L5.5) estimated within this area using historical data, could be modified by 0.1–1 MPa stress changes. These small changes in deviatoric stress suggest that the upper crust is in this area nearly everywhere at a state of stress near failure. Although the paucity of both number and size of earthquakes in the French subalpine massif shows that aseismic displacements prevail, our study demonstrates that triggered earthquakes are important tools for assessing local seismic risk through mapping fault zones and identifying their possible seismic behavior.     

Generalized poroelastic wellbore problem

This paper presents a novel analytical solution to the transient, z‐dependent, and asymmetric problem of an infinite wellbore drilled into a fluid‐saturated porous medium. The formulations are based on Biot's linear theory of poroelasticity, in which the dependency of poroelastic field variables to spatial coordinates as well as time domain is considered in the most general form. This gives flexibility to the solution in cases that cannot be analyzed using the conventional plane strain or symmetric models. One such case is when calculating the stress variations around an inclined wellbore where the far‐field stresses are acting over a finite vertical section. The results of our solution to this case with a three‐dimensional state of far‐field stress are used to analyze the stability of inclined wellbores passing through abnormally stressed formations. The presented solution is capable of finding expressions for fundamental solutions with stress or flow boundary conditions at the wellbore. These solutions are here adopted to analyze the pressure disturbances generated by multiprobe formation tester, a standard wireline device that is designed for downhole fluid sampling as well as estimating the directional permeabilities of subsurface earth formations. A comparison with the conventional solution for the relevant pressure diffusion equation indicates that the poroelastic effect is relatively significant in relation to the transient response of the pore pressure. Further, it is shown that the finite dimensions of sink probe would, to a great extent, contribute to the formation's pore pressure variations at its immediate proximity. Copyright © 2013 John Wiley & Sons, Ltd.     

Delineation and interpretation of spatial coseismic response of groundwater levels in shallow and deep parts of an alluvial plain to different earthquakes: A case study of the Kumamoto City area,southwest Japan

Coseismic changes in groundwater levels have been investigated throughout the world, but most studies have focused on the effects of one large earthquake. The aim of this study was to elucidate the spatial patterns of level changes in response to several earthquakes, and the relationship of the patterns to shallow and deep groundwater in the same area. We selected the Kumamoto City area in southwest Japan, a region with one of the richest groundwater resources in Japan, as our study site. Data from hourly measurements of groundwater levels in 54 wells were used to characterize the coseismic responses to four earthquakes that occurred in 2000, 2001, 2005, and 2008. Although the distance to the hypocenter (12–2573 km), and seismic energy (M_w = 5.0–8.0) of these earthquakes varied, systematic groundwater level changes were observed in the range of 0.01–0.67 m. Spatial patters of the level changes were clarified by interpolating the point data by a spline method. The zones where coseismic rises were observed were generally wider for deep groundwater than for shallow groundwater, probably as a result of an increase in compressive stress. General trends in the changes in groundwater levels, and calculated pressure changes, were clarified to be consistent in the deep groundwater, but the coseismic increases or decreases in compressive stress in the shallow groundwater were variable, depending on the distance to the earthquake epicenter. We developed a conceptual model of the mechanism underlying this phenomenon by assuming permeability enhancement induced by elastic strain and pore-pressure change over the depth range. In addition, the importance of local geology was identified, because levels in the area of Togawa lava (a porous andesite) tended to change more in magnitude, and more quickly, with a shorter recovery time, than levels measured in the area outside the lava.     

An anisotropic damage–plasticity model for saturated quasi‐brittle materials

This article is devoted to numerical modeling of anisotropic damage and plasticity in saturated quasi‐brittle materials such as rocks and concrete. The damaged materials are represented by an isotropic poroelastic matrix containing a number of families of microcracks. Based on previous works, a discrete thermodynamic approach is proposed. Each family of microcracks exhibits frictional sliding along crack surfaces as well as crack propagation. The frictional sliding is described by a Coulomb–Mohr‐type plastic criterion by taking into account the effect of fluid pressure through a generalized effective stress concept. The damage evolution is entirely controlled by and coupled with the frictional sliding. The effective elastic properties as well as Biot's coefficients of cracked porous materials are determined as functions of induced damage. The inelastic deformation due to frictional sliding is also taken into account. The procedure for the identification of the model's parameters is presented. The proposed model is finally applied to study both mechanical and poromechanical responses of a typical porous brittle rock in drained and undrained compression tests as well as in interstitial pressure controlled tests. The main features of material behaviors are well reproduced by the model. Copyright © 2012 John Wiley & Sons, Ltd.     

A finite element porothermoelastic model for dual-porosity media

An existing dual-porosity finite element model has been extended to include thermo-hydro-mechanical coupling in both media. The model relies on overlapping distinct continua for the fluid and solid domains. In addition, conductive and convective heat transfers are incorporated using a single representative thermodynamics continuum. The model is applied to the problem of an inclined borehole drilled in a fractured formation subjected to a three-dimensional state of stress and, a temperature gradient between the drilling fluid and the formation. A sensitivity analysis has been carried out to study the impact of thermal loading, effect of heat transport by pore fluid flow and, the effect of parameters of the secondary medium used to represent the fractures. Copyright © 2004 John Wiley & Sons, Ltd.     

Modelling poroelastic hollow cylinder experiments with realistic boundary conditions

A general poroelastic solution for axisymmetrical plane strain problems with time dependent boundary conditions is developed in Laplace domain. Time‐domain results are obtained using numerical inversion of the Laplace transform. Previously published solutions can be considered as special cases of the proposed solution. In particular, we could reproduce numerical results for solid and hollow poroelastic cylinders with suddenly applied load/pressure (Rice and Cleary, Rev. Geophys. Space Phys. 1976; 14 :227; Schmitt, Tait and Spann, Int. J. Rock Mech. Min. Sci. 1993; 30 :1057; Cui and Abousleiman, ASCE J. Eng. Mech. 2001; 127 :391). The new solution is used to model laboratory tests on thick‐walled hollow cylinders of Berea sandstone subjected to intensive pressure drawdown. In the experiments, pressure at the inner boundary of the hollow cylinder is observed to decline exponentially with a decay constant of 3–5 1/s. It is found that solutions with idealized step‐function type inner boundary conditions overestimate the induced tensile radial stresses considerably. Although basic poroelastic phenomena can be modelled properly at long time following a stepwise change in pressure, realistic time varying boundary conditions predict actual rock behaviour better at early time. Experimentally observed axial stresses can be matched but appear to require different values for α and ν than are measured at long time. The proposed solution can be used to calculate the stress and pore pressure distributions around boreholes under infinite/finite boundary conditions. Prospective applications include investigating the effect of gradually changing pore pressure, modelling open‐hole cavity completions, and describing the phenomenon of wellbore collapse (bridging) during oil or gas blowouts. Copyright © 2004 John Wiley & Sons, Ltd.     

Stochastic computational modelling of highly heterogeneous poroelastic media with long‐range correlations

The compaction of highly heterogeneous poroelastic reservoirs with the geology characterized by long‐range correlations displaying fractal character is investigated within the framework of the stochastic computational modelling. The influence of reservoir heterogeneity upon the magnitude of the stresses induced in the porous matrix during fluid withdrawal and rock consolidation is analysed by performing ensemble averages over realizations of a log‐normally distributed stationary random hydraulic conductivity field. Considering the statistical distribution of this parameter characterized by a coefficient of variation governing the magnitude of heterogeneity and a correlation function which decays with a power‐law scaling behaviour we show that the combination of these two effects result in an increase in the magnitude of effective stresses of the rock during reservoir depletion. Further, within the framework of a perturbation analysis we show that the randomness in the hydraulic conductivity gives rise to non‐linear corrections in the upscaled poroelastic equations. These corrections are illustrated by a self‐consistent recursive hierarchy of solutions of the stochastic poroelastic equations parametrized by a scale parameter representing the fluctuating log‐conductivity standard deviation. A classical example of land subsidence caused by fluid extraction of a weak reservoir is numerically simulated by performing Monte Carlo simulations in conjunction with finite elements discretizations of the poroelastic equations associated with an ensemble of geologies. Numerical results illustrate the effects of the spatial variability and fractal character of the permeability distribution upon the evolution of the Mohr–Coulomb function of the rock. Copyright © 2004 John Wiley & Sons, Ltd.