Numerical modeling of porosity waves in the Nankai accretionary wedge décollement,Japan: implications for aseismic slip

Seismic and hydrologic observations of the Nankai accretionary wedge décollement, Japan, show that overpressures at depths greater than ～2 km beneath the seafloor could have increased to near lithostatic values due to sediment compaction and diagenesis, clay dehydration, and shearing. The resultant high overpressures are hypothesized then to have migrated in rapid surges or pulses called ‘porosity waves’ up the dip of the décollement. Such high velocities—much higher than expected Darcy fluxes—are possible for porosity waves if the porous media through which the waves travel are deformable enough for porosity and permeability to increase strongly with increasing fluid pressure. The present study aimed to test the hypothesis that porosity waves can travel at rates (kilometers per day) fast enough to cause aseismic slip in the Nankai décollement. The hypothesis was tested using a one-dimensional numerical solution to the fluid mass conservation equation for elastic porous media. Results show that porosity waves generated at depths of ～2 km from overpressures in excess of lithostatic pressure can propagate at rates sufficient to account for aseismic slip along the décollement over a wide range of hydrogeological conditions. Sensitivity analysis showed porosity wave velocity to be strongly dependent on specific storage, fluid viscosity, and the permeability–depth gradient. Overpressure slightly less than lithostatic pressure could also produce porosity waves capable of traveling at velocities sufficient to cause aseismic slip, provided that hydrogeologic properties of the décollement are near the limits of their geologically reasonable ranges.     

Hydro-micromechanical modeling of wave propagation in saturated granular crystals

Biot theory predicts wave velocities in a saturated granular medium using the pore geometry, viscosity, densities, and elastic moduli of the solid skeleton and pore fluid, neglecting the interaction between constituent particles and local flow, which becomes essential as the wavelength decreases. Here, a hydro-micromechanical model, for direct numerical simulations of wave propagation in saturated granular media, is implemented by two-way coupling the lattice Boltzmann method (LBM) and the discrete element method (DEM), which resolve the pore-scale hydrodynamics and intergranular behavior, respectively. The coupling scheme is benchmarked with the terminal velocity of a single sphere settling in a fluid. In order to mimic a small amplitude pressure wave entering a saturated granular medium, an oscillating pressure boundary on the fluid is implemented and benchmarked with the one-dimensional wave equation. The effects of input waveforms and frequencies on the dispersion relations in 3D saturated poroelastic media are investigated with granular face-centered-cubic crystals. Finally, the pressure and shear wave velocities predicted by the numerical model at various effective confining pressures are found to be in excellent agreement with Biot analytical solutions, including his prediction for slow compressional waves.     

Transient solution for a plane‐strain fracture driven by a shear‐thinning,power‐law fluid

This paper analyses the problem of a fluid‐driven fracture propagating in an impermeable, linear elastic rock with finite toughness. The fracture is driven by injection of an incompressible viscous fluid with power‐law rheology. The relation between the fracture opening and the internal fluid pressure and the fracture propagation in mobile equilibrium are described by equations of linear elastic fracture mechanics (LEFM), and the flow of fluid inside the fracture is governed by the lubrication theory. It is shown that for shear‐thinning fracturing fluids, the fracture propagation regime evolves in time from the toughness‐ to the viscosity‐dominated regime. In the former, dissipation in the viscous fluid flow is negligible compared to the dissipation in extending the fracture in the rock, and in the later, the opposite holds. Corresponding self‐similar asymptotic solutions are given by the zero‐viscosity and zero‐toughness (J. Numer. Anal. Meth. Geomech. 2002; 26 :579–604) solutions, respectively. A transient solution in terms of the crack length, the fracture opening, and the net fluid pressure, which describes the fracture evolution from the early‐time (toughness‐dominated) to the large‐time (viscosity‐dominated) asymptote is presented and some of the implications for the practical range of parameters are discussed. Copyright © 2006 John Wiley & Sons, Ltd.     

Limestone mechanical deformation behavior and failure mechanisms: a review

In this paper, several mechanical deformation curves of limestone are reviewed, and the effects of temperature, confining pressure, and fluid are discussed. Generally, Mohr–Coulomb is used for limestone brittle fracture. The characteristic of low temperature cataclastic flow and the conditions and constitutive equations of intracrystal plastic deformation such as dislocation creep, diffusion creep, and superplastic flow are discussed in detail. Specifically, from the macroscopic and microscopic view, inelastic compression deformation (shear-enhanced compaction) of large porosity limestone is elaborated. Compared with other mechanics models and strength equations, the dual porosity (macroporosity and microporosity) model is superior and more consistent with experimental data. Previous research has suffered from a shortage of high temperature and high pressure limestone research; we propose several suggestions to avoid this problem in the future: (1) fluid-rock interaction research; (2) mutual transition between natural conditions and laboratory research; (3) the uniform strength criterion for shear-enhanced compaction deformation; (4) test equipment; and (5) superplastic flow mechanism research.     

双相多孔介质中体波传播特性影响参数研究

基于修正的Biot理论,通过数值计算分别研究了3种体波（P1、P2、S波）的波速和衰减与固体颗粒压缩性、频率、孔隙率、流体黏滞系数、动力渗透系数等参数之间的关系。分析结果表明：（1）P1、P2波的波速和衰减与固体颗粒压缩性之间近似呈线性变化关系,而S波则几乎保持不变,并通过定量比较发现,能否忽略固体颗粒压缩性的影响取决于固体骨架体变模量( )与固体颗粒体变模量( )的比值;（2）孔隙率对P1、S波波速的影响较为显著,并且预测当孔隙率接近于1.0时,P1、P2波之间发生相互转换;（3）3种体波的波速和衰减均随流体黏滞系数和动力渗透系数而变化,且在这两个参数下的变化规律基本相反;（4）3种体波的波速和衰减均随频率的增大而增大,其中,频率对P2波的影响较大。     

动荷载作用下岩石非线性弹性响应研究

岩石是一种典型的颗粒孔隙介质。在冲击荷载下,即便是在作用荷载比较低的阶段,由于岩石内部自然缺陷的存在,应力波随着传播距离延伸,其幅值有较大的衰减。文中对饱油和饱水的砂岩、大理岩进行SHPB冲击试验,研究结果表明:对于同种岩石试样,饱油岩样的衰减系数比饱水样品的小;对于不同的岩样,孔隙率大的岩样相应的衰减系数大。应力波在饱和介质中的衰减与介质中液体的粘滞系数有关。同时,材料中的孔隙和液体的存在对应力波的弥散特征也有一定的影响。然后基于Preisach-Mayergoyz(P-M)空间模型对冲击荷载比较低的阶段,岩石内部应力波的衰减和弥散问题进行了较详细的分析,得到了一些初步结论。本研究对于石油开采、物探以及岩土工程有一定的意义。     

渗透系数极端情况下饱和土中压缩波波速及其物理本质

目前对渗透系数取极端值情况下饱和土中两类压缩波物理本质的理解尚不够清晰,比如文献中对渗透系数无穷大情况下饱和土中两类压缩波波速的求解有不同的结果。结合Zienkiewicz给出的土动力学基本方程,深入讨论了流体运动方程的建立,推导了饱和土一维压缩弹性问题的动力控制方程及其 - 、 - 形式,进而得出渗透系数取0和取无穷大这两种极端情况下饱和土中压缩波的波速,解释了其物理意义。提出了惯性耦合力的概念,指出两相体动力分析时土骨架和孔隙水之间的相互作用包含渗透力和惯性耦合力两项,并重点讨论了衡量惯性耦合力的参数孔隙度对压缩波波速的影响。     

可压缩流体饱和孔隙介质中孔隙压力波传播数值分析

首次将高精度时空守恒元/解元方法推广到可压缩流体饱和孔隙介质中孔隙压力波传播的数值计算中。将孔隙度梯度从源（汇）项中分离,直接引入流通量,改进了理论模型。通过对孔隙介质激波问题的数值模拟,验证了方法的精度和有效性。在此基础上,提出了孔隙介质中二维黎曼问题,并揭示了孔隙压力波存在接触间断、激波、膨胀波、压缩波等复杂的结构特征。该成果对二氧化碳地质封存、二氧化碳提高石油采收率、页岩气压裂开采以及地震破裂过程的研究具有重要的理论与应用意义。     

饱和冻土中弹性体波传播特性影响参数研究

基于Leclaire对饱和双相孔隙弹性介质Biot模型的扩展,研究含有两种不同固相组分的三相多孔弹性介质中体波的传播特性。以饱和冻土为例,分析了各相体积分数、颗粒形状,接触参数等因素对波动方程中惯性参数、黏性参数、刚度参数的影响;对该三相介质模型进行了退化,分析了孔隙中只含液态水或固态冰时体波的特性;以饱和冻土为例,通过数值计算,探讨了饱和冻土中体波的相速度和衰减系数与胶结参数、接触参数、频率、饱和度、孔隙率等参数的关系。结果表明：与一般的饱和土不同,饱和冻土中存在5种体波,即3种纵波和2种横波;5种体波均具有弥散性和衰减性,且P1波、S1波弥散性和衰减性远小于P2、P3、S2波;胶结参数、饱和度、孔隙率对5种体波的传播特性影响显著,接触参数对传播特性影响较小。     

Inverse modeling of velocities and inferred cause of overwash that emplaced inland fields of boulders at Anegada, British Virgin Islands

A combination of numeric hydrodynamic models, a large-clast inverse sediment-transport model, and extensive field measurements were used to discriminate between a tsunami and a storm striking Anegada, BVI a few centuries ago. In total, 161 cobbles and boulders were measured ranging from 1.5 to 830?kg at distances of up to 1?km from the shoreline and 2?km from the crest of a fringing coral reef. Transported clasts are composed of low porosity limestone and were derived from outcrops in the low lying interior of Anegada. Estimates of the near-bed flow velocities required to transport the observed boulders were calculated using a simple sediment-transport model, which accounts for fluid drag, inertia, buoyancy, and lift forces on boulders and includes both sliding and overturning transport mechanisms. Estimated near-bed flow velocities are converted to depth-averaged velocities using a linear eddy viscosity model and compared with water level and depth-averaged velocity time series from high-resolution coastal inundation models. Coastal inundation models simulate overwash by the storm surge and waves of a category 5 hurricane and tsunamis from a Lisbon earthquake of M 9.0 and two hypothetical earthquakes along the North America Caribbean Plate boundary. A modeled category 5 hurricane and three simulated tsunamis were all capable of inundating the boulder fields and transporting a portion of the observed clasts, but only an earthquake of M 8.0 on a normal fault of the outer rise along the Puerto Rico Trench was found to be capable of transporting the largest clasts at their current locations. Model results show that while both storm waves and tsunamis are capable of generating velocities and temporal acceleration necessary to transport large boulders near the reef crest, attenuation of wave energy due to wave breaking and bottom friction limits the capacity of storm waves to transport large clast at great inland distances. Through sensitivity analysis, we show that even when using coefficients in the sediment-transport model which yield the lowest estimated minimum velocities for boulder transport, storm waves from a category 5 hurricane are not capable of transporting the largest boulders in the interior of Anegada. Because of the uncertainties in the modeling approach, extensive sensitivity analyses are included and limitations are discussed.     

One‐dimensional analytical solution for mesoscopic flow induced damping in a double‐porosity dual‐permeability material

Heterogeneities, such as fractures and cracks, are ubiquitous in porous rocks. Mesoscopic heterogeneities, that is, heterogeneities on length scales much larger than typical pore size but much smaller than the wavelength, are increasingly believed to be responsible for significant wave energy loss in the seismic frequency band. When a compressional wave stresses a material containing mesoscopic heterogeneities, the more compliant parts of the material (e.g., fractures and cracks) respond with a greater fluid pressure than the stiffer portions (e.g., matrix pores). The induced fluid flow, resulting from the pressure gradients developed on such scale, is called mesoscopic flow. In the present study, the double‐porosity dual‐permeability model is adopted to incorporate mesoscopic heterogeneities into rock models to account for the attenuation of wave energy. Based on the model, the damping effect due to mesoscopic flow in a one‐dimensional porous structure is investigated. Analytical solutions for several boundary‐value problems are obtained in the frequency domain. The dynamic responses of infinite and finite porous layer are examined. Numerical calculations show that the damping effect of mesoscopic flow is significant on the pore pressure response and the resulting effective stress. For the displacement, the effect is seen only at the very low frequency range or near the resonance frequencies. Copyright © 2017 John Wiley & Sons, Ltd.     

The influence of pumping parameters in fluid‐driven fractures in weak porous formations

In this work, we investigate the main pumping parameters that influence a fluid‐driven fracture in cohesive poroelastic and poroelastoplastic weak formations. These parameters include the fluid viscosity and the injection rate. The first parameter dominates in the mapping of the propagation regimes from toughness to viscosity, whereas the second parameter controls the storage to leak‐off dominated regime through diffusion. The fracture is driven in weak permeable porous formation by injecting an incompressible viscous fluid at the fracture inlet assuming that the fracture propagates under plane strain conditions. Fluid flow in the fracture is modeled by lubrication theory. Pore fluid movement in the porous formation is based on the Darcy law. The coupling follows the Biot theory, whereas the irreversible rock deformation is modeled with the Mohr–Coulomb yield criterion with associative flow rule. Fracture propagation criterion is based on the cohesive zone approach. Leak‐off is also considered. The investigation is performed numerically with the FEM to obtain the fracture opening, length, and propagation pressure versus time. We demonstrate that pumping parameters influence the fracture geometry and fluid pressures in weak formations through the viscous fluid flow and the diffusion process that create back stresses and large plastic zones as the fracture propagates. It is also shown that the product of the propagation velocity and fluid viscosity, µv that appears in the scaling controls the magnitude of the plastic zones and influences the net pressure and fracture geometry. These findings may explain partially the discrepancies in net pressures between field measurements and conventional model predictions for the case of weak porous formation. Copyright © 2014 John Wiley & Sons, Ltd.     

流体饱和多孔隙垂向非均匀固体的弹性波传播理论

建立含有可压缩粘滞流体的多孔隙垂向非均匀弹性固体内之应力波传播理论。论述了其中的一个问题。即当Ｐｏｉｓｅｕｉｌｌｅ流动假设成立的低频率范围且流体与固体的质量密度可相比拟（例如含水饱和岩石之类）时，流体与固体间虽有相对运动但无摩擦的情形。在一定的近似条件下，可以存在两类膨胀波和一类旋转波，它们都存在频散     

Depression and elevation tsunami waves in the framework of the Korteweg–de Vries equation

Although tsunamis in the deep ocean are very long waves of quite small amplitudes, as they propagate shorewards into shallow water, nonlinearity becomes important and the structure of the leading waves depends on the polarity of the incident wave from the deep ocean. In this paper, we use a variable-coefficient Korteweg–de Vries equation to examine this issue, for an initial wave which is either elevation, or depression, or a combination of each. We show that the leading waves can be described by a reduction of the Whitham modulation theory to a solitary wave train. We find that for an initial elevation, the leading waves are elevation solitary waves with an amplitude which varies inversely with the depth, with a pre-factor which is twice the maximum amplitude in the initial wave. By contrast, for an initial depression, the leading wave is a depression rarefaction wave, followed by a solitary wave train whose maximum amplitude of the leading wave is determined by the square root of the mass in the initial wave.     

Analytical solutions of long nonlinear internal waves: Part I

The Gardner equation is an extension of the Korteweg–de Vries (KdV) equation. It exhibits basically the same properties as the classical KdV, but extends its range of validity to a wider interval of the parameters of the internal wave motion for a given environment. In this paper, we derive exact solitary wave solutions for the generalized Gardner equation that includes nonlinear terms of any order. Unlike previous studies, the exact solutions are derived without assuming their mathematical form. Illustrative examples for internal solitary waves are also provided. The traveling wave solutions can be used to specify initial data for the incident waves in internal waves numerical models and for the verification and validation of the associated computed solutions.     

扭转导波在锚固锚杆中传播的数值模拟

采用有限元数值模拟的方法研究了扭转导波在锚固锚杆中的传播性质。建立了自由锚杆和锚固锚杆的有限元模型,在锚杆顶端激发20～60 kHz扭转导波信号,计算得到导波在自由锚杆和锚杆锚固段的传播速度值与理论值吻合很好,证明了扭转导波数值模拟方法的有效性。数值模拟结果表明：随着激发波频率的增大,扭转导波在自由锚杆和锚杆锚固段中的衰减值均呈线性递增趋势,导波在锚杆锚固段上界面的反射回波逐渐减弱;扭转导波在锚杆锚固段的衰减值较大,无法在锚杆顶端采集到锚杆底端反射回波信号,所以扭转导波不适用于锚杆长度的检测;随着锚固介质弹性模量的增大,同一频率扭转导波在锚杆锚固段上界面的反射波逐渐增强。通过检测扭转导波在锚杆锚固段上界面的反射回波,可以确定锚固介质弹性模量的大小。     

Wave propagation in a general anisotropic poroelastic medium: Biot’s theories and homogenisation theory

Anisotropic wave propagation is studied in a fluid-saturated porous medium, using two different approaches. One is the dynamic approach of Biot’s theories. The other approach known as homogenisation theory, is based on the averaging process to derive macroscopic equations from the microscopic equations of motion. The medium considered is a general anisotropic poroelastic (APE) solid with a viscous fluid saturating its pores of anisotropic permeability. The wave propagation phenomenon in a saturated porous medium is explained through two relations. One defines modified Christoffel equations for the propagation of plane harmonic waves in the medium. The other defines a matrix to relate the relative displacement of fluid particles to the displacement of solid particles. The modified Christoffel equations are solved further to get a quartic equation whose roots represent complex velocities of the four attenuating quasi-waves in the medium. These complex velocities define the phase velocities of propagation and quality factors for attenuation of all the quasi-waves propagating along a given phase direction in three-dimensional space. The derivations in the mathematical models from different theories are compared in order to work out the equivalence between them. The variations of phase velocities and attenuation factors with the direction of phase propagation are computed, for a realistic numerical model. Differences between the velocities and attenuations of quasi-waves from the two approaches are exhibited numerically.     

Fluid convection and mass transfer in porous sandstones—a theoretical model

When porous, fluid-saturated, bodies of geologic dimensions are subjected to temperature gradients on the order of the normal geothermal gradient (25°C/km) it is shown that large (km) scale eddy currents will spontaneously arise and persist in these bodies. The velocity of these fluid currents is on the order of 1 meter per year, but taken over a period of several million years, the mass flux accompanying the fluid flow is large enough to produce significant porosity changes. It is shown that diffusive mass transfer is generally a negligible component of the total mass flux when characteristic distances are greater than grain diameters and it is concluded that most post-depositional reservoir cementation is due to slowly circulating fluids. In terms of a broad perspective, reservoir diagenesis can be regarded as a low heat flow analogue of hydrothermal alteration, occupying the low fluid flow regime of the spectrum, and passing into the hydrothermal regime as the heat flow and fluid velocities increase.     

深部岩体多孔介质流变模型的研究

考虑到传统流变模型在反映载荷水平影响和描述加速蠕变阶段方面的缺陷,在改进传统流变元件模型的基础上,引入非理想黏性元件,建立了在数学上能体现载荷水平影响并能描述加速蠕变的新的改进流变模型;同时从定义出发,考虑到孔隙度的动态性,对孔隙度和通用有效应力公式进行修正;鉴于岩体的孔隙性和不均匀性,把岩体看作多孔介质,应用多孔介质理论中的有效应力代替改进岩土流变模型中的恒应力,计入温度和孔隙压的影响,最终建立了深部（高温度、高地压和高孔隙压）岩体多孔介质流变模型。     

The dynamics of magma-mixing during flow in volcanic conduits

The production of mixed magmas (streaky pumice) during flow in a volcanic conduit has been modelled in the laboratory by studying the flow of two miscible fluids of differing viscosity passing concentrically through a vertical pipe. In the experiments reported in this paper, the outermost fluid is the more viscous, as would be the case when two magmas are simultaneously tapped from a zoned chamber in which silicic magma overlies mafic magma. At a Reynolds number (Re) which is much less than that required for turbulence in isoviscous pipe flow, the interface between two liquids of different viscosity can become unstable. Growth of the instability and mixing proceed when Re, based on the properties of the inner, less viscous fluid (Re _i), is greater than approximately 3 if between 10% and 90% of the flowing fluid is composed of the more viscous fluid. Outside this range of flow rate ratios, higher Re _i and viscosity ratios are required to ensure mixing. When the viscosity ratio U10 the unstable flow takes the form of an asymmetric, sinusoidal wave and at higher viscosity ratios axisymmetric, bead-like waves are the dominant instability. Entrainment across the boundaries of these wavy interfaces results in the production of streaky mixtures of the two liquids. The degree of mixing increases with Re ₁, U and distance downstream. Application of experimental results to magmatic situations shows that mixing will be possible in eruptions which tap layers of different viscosity from a stratified chamber. If a volcanic feeder is allowed to become lined by silicic magma before a mafic magma layer is drawn up from the chamber then a mixed pumice (or lava) sequence will ensue. Alternatively, if draw-up occurs when the feeder is still propagating away from the chamber, the slower flowing silicic magma may be overtaken by the faster flowing mafic magma. The advancing conduit will then have mafic or hybrid chilled margins enclosing a silicic interior, i.e. the usual arrangement in composite dykes and sills. Simultaneous tapping of silicic and underlying mafic magmas from a chamber can thus lead to magma mixing and to the emplacement of either mixed pumice sequences or composite intrusions, depending on the history of magma withdrawal and the dynamics of flow in the conduit.