衬砌隧道中移动轴向激励作用下两相多孔介质动力响应

为了研究衬砌隧道中地铁振动在饱和地层中的传播情况,采用移动轴向激励模拟技术,建立了隧道-衬砌-两相介质的动力分析模型;利用波函数展开法、傅里叶变换法等,推导了频域内衬砌隧道移动轴向激励作用下两相多孔介质动力响应的解析解,并给出了两相多孔介质临界速度的经验公式;通过离散快速傅里叶逆变换得到了时-空域内两相介质的动力响应。结果表明：无衬砌隧道中移动的轴向常激励作用下,两相介质临界速度只与介质的剪切模量和密度有关,且数值接近其剪切波速的1.1倍;对于衬砌隧道,介质的临界速度随着衬砌剪切模量的增大而增大,随着衬砌密度的增大而减小,衬砌对振动向介质中的传播有一定的削弱作用,衬砌剪切模量与介质剪切模量相差越大,削弱越明显;动力响应频率越接近激振频率,其幅值越大,所对应的临界速度越小。     

Large‐scale poroelastic fractured reservoirs modeling using the fast multipole displacement discontinuity method

An effective approach to modeling the geomechanical behavior of the network and its permeability variation is to use a poroelastic displacement discontinuity method (DDM). However, the approach becomes rather computationally intensive for an extensive system of cracks, particularly when considering coupled diffusion/deformation processes. This is because of additional unknowns and the need for time‐marching schemes for the numerical integration. The Fast Multipole Method (FMM) is a technique that can accelerate the solution of large fracture problems with linear complexity with the number of unknowns both in memory and CPU time. Previous works combining DDM and FMM for large‐scale problems have accounted only for elastic rocks, neglecting the fluid leak‐off from the fractures into the matrix and its influence on pore pressure and stress field. In this work we develop an efficient geomechanical model for large‐scale natural fracture networks in poroelastic reservoirs with fracture flow in response to injection and production operations. Accuracy and computational performance of the proposed method with those of conventional poroelastic DDM are compared through several case studies involving up to several tens of thousands of boundary elements. The results show the effectiveness of the FMM approach to successfully evaluate field‐scale problems for the design of exploitation strategies in unconventional geothermal and petroleum reservoirs. An example considering faults reveals the impact of reservoir compartmentalization because of sealing faults for both geomechanical and flow variables under elastic and poroelastic rocks. Copyright © 2015 John Wiley & Sons, Ltd.     

A Reservoir–Geomechanical Model to Study the Likelihood of Tensile and Shear Failure in the Caprock of Weyburn CCS Project with Regard to Interpretation of Microseismic Data

According to poroelastic theory and also field observations, an increase in reservoir pore pressures can result in a decrease in horizontal stresses in the seal layers. This reduction is in favor of hydrofracture initiation and reactivation of weak planes and has to be studied in caprock integrity analyses. In this paper, a field scale reservoir–geomechanical (GEM-FLAC3D) model is developed for the Phase IB area of the Weyburn (Canada) CCS project that is located in Williston sedimentary basin. A one-way coupling has been conducted between the two codes for the period of CO₂ injection in Phase IB area from 2000 to 2010. Therefore, the reservoir pore pressures at selected timesteps are unidirectionally fed to the FLAC3D. In order to study the likelihood of tensile and shear failure in the seal layer on top as a result of stress transfer due to poroelastic effects, two margin ratios are defined for tensile and shear failure and their variations are studied above the reservoir upon changes in pore pressures within the reservoir. The results show that overall; the likelihood of shear failure has been about 25% greater than that of tensile failure in Weyburn. However, between 2008 and 2009, the pressures were high enough to trigger both tensile and shear mechanisms above the reservoir. A discussion is also presented on relevance of this study for interpretation of microseismic data with regard to failure margin ratios, magnitudes and distribution of events recorded in each year.     

盐岩油气储库介质地质力学模型相似材料的研制

以江苏金坛盐岩地下油气储库为示范工程,以精铁粉、重晶石粉、石英砂、一级松香和医用酒精为原料,根据相似原理以及金坛盐岩油气储库地层中盐岩、泥岩和盐岩夹层的实测物理力学参数,开展了各种配比条件下材料的单轴压缩、三轴压缩、直剪和巴西劈裂试验,通过原岩和模型材料的重度、泊松比、弹性模量、抗压强度、抗拉强度、黏聚力、内摩擦角等基本物理力学参数以及相应变形特征和强度破坏特性的对比分析,研制出基本满足相似条件要求的盐岩油气储库介质（盐岩、泥岩和盐岩夹层）的地质力学模型相似材料,为开展盐岩地下油气储库运营的变形与失效破坏地质力学模型试验提供了可靠的材料保证。     

材料状态对干砂小应变特性的影响

利用注能虚拟质量(EIVM)共振柱系统进行了干砂小应变特性试验,研究了有效平均正应力、土样密度、剪应变幅值以及荷载往复次数对剪切模量和阻尼比的影响。试验结果表明,剪切模量随有效平均正应力与土样密度的增加而增加,而阻尼比的变化规律则与之相反,并且有效平均正应力对干砂小应变特性的影响程度比土样密度的影响程度大得多;随着剪应变的增加,剪切模量越来越小,而阻尼比越来越大;荷载往复次数对剪切模量基本没有影响,而对阻尼比有较大影响。     

Determination of the poroelasticity of shale

Shales play important roles in various civil, energy and environmental engineering applications. Shales are categorized as poroelastic materials due to their tight and very stiff structure, and reliable poroelastic properties are required when dealing with shales. This paper presents simple procedures to determine the poroelastic properties of rocks using oedometer and triaxial consolidation tests. The procedures, which avoid the difficulty to perform determination of the unjacketed bulk modulus of the rock minerals, are demonstrated on a North Sea shale. The experimentally obtained Biot coefficient α and the drained bulk modulus K of the shale range from 0.95 to 0.99, and from 0.17 to 2.00 GPa, respectively. The Biot coefficient α and the drained bulk modulus K values determined from the oedometer and triaxial tests are compared and show good agreement and consistency between the two test procedures. The Skempton’s coefficient B-value of the triaxial samples was also experimentally measured prior to the triaxial consolidation tests. The theoretically predicted B-value varies from 0.81 to 0.96 which is, on the average, only about 10% higher than the experimentally obtained B-value which range from 0.80 to 0.85.

     

A modified rock physics model for analysis of seismic signatures of low gas-saturated rocks

In seismic applications, the bulk modulus of porous media saturated with liquid and gas phases is often estimated using Gassmann's fluid substitution formula, in which the effective bulk modulus of the two-phase fluid is the Reuss average of the gas and liquid bulk moduli. This averaging procedure, referred to as Wood's approximation, holds if the liquid and gas phases are homogeneously distributed within the pore space down to sizes well below the seismic wavelength and if the phase transfer processes between liquid and gas domains induced by the pressure variations of the seismic wave are negligible over the timescale of the wave period. Using existing theoretical results and low-frequency acoustic measurements in bubbly liquids, we argue that the latter assumption of “frozen” phases, valid for large enough frequencies, is likely to fail in the seismic frequency range where lower effective bulk modulus and velocity, together with dispersion and attenuation effects, are expected. We provide a simple method, which extends to reservoir fluids a classical result by Landau and Lifshitz valid for pure fluids, to compute the effective bulk modulus of thermodynamically equilibrated liquid and gas phases. For low gas saturation, this modulus is significantly lower than its Wood's counterpart, especially at the crossing of bubble point conditions. A seismic reflector associated to a phase transition between a monophasic and a two-phase fluid thus will appear. We discuss the consequences of these results for various seismic applications including fizz water discrimination and hydrocarbon reservoir depletion and CO₂ geological storage monitoring.     

干砂弹性参数测定的弯曲-伸展元试验

利用安装在共振柱测试系统中的弯曲-伸展元,开展了干砂中P波（压缩波）和S波（剪切波）的室内试验,详细地分析了干砂中P波和S波的信号特征,研究了输入频率、土体密实度和有效围压对输出信号的影响。对比各种信号分析方法,并参考共振柱试验结果确定了S波的传播时间。根据实测波速和波动理论,确定了土体的弹性参数,包括剪切模量,侧限模量和泊松比。研究结果表明,P波和S波的输出信号频率在一定程度上随输入信号频率、土体密实度和有效围压的增加而增加,且P波信号比S波信号更容易确定波的传播时间;土体的弹性模量随土体密实度和有效围压的增加而增加,但剪切模量增长比侧限模量快;土体的泊松比并非一个常数,随着土体密实度和有效围压的增加而下降。初步探讨了利用剪切模量估算泊松比,以方便实际工程应用。     

一种基于弹性应变能的裂隙岩体等效弹性模量评价方法

基于线弹性断裂力学裂隙面张开位移及剪切位移理论公式,考虑裂隙存在常法向和常切向刚度情况,研究了含单个裂隙岩体加载过程中由于裂隙存在而附加的弹性应变能。基于应变能等效方法并假设两种裂隙变形模型--非均匀变形模型和均匀变形模型,研究了二维非贯通裂隙岩体的等效杨氏模量和等效剪切模量解析表达式。研究结果表明,对于贯通裂隙规则分布情况,均匀变形模型得到的解析解与Amadei等的结果一致;对于非贯通裂隙正态分布情况,考虑裂隙相互作用的非均匀变形模型解明显低估裂隙岩体的等效杨氏模量和等效剪切模量,而考虑裂隙相互作用的均匀变形模型解与有限元数值解的偏差在10%以内。得到的解析表达式在一定条件下可以作为裂隙岩体等效弹性模量评价方法之一。     

Poromechanical response of borehole in excavation disturbed zone

This paper presents time-dependent response of a cylindrical borehole in a poroelastic medium with an excavation disturbed zone. The general solutions are derived based on Biot’s theory of poroelasticity by employing Laplace and Fourier transforms. Both shear modulus and permeability coefficient are assumed to be changed from their original values in the disturbed zone. The general solutions are employed to formulate boundary value problems corresponding to a borehole subjected to axisymmetric loading applied at its surface, and contact problems of a rigid cylindrical plug in a borehole. Selected numerical results are presented to portray the influence of poroelastic effects and the excavation disturbed zone.     

列车荷载下轨道系统-层状横观各向同性饱和地基动力响应

基于Biot波动理论,构建列车荷载-轨道系统-双层状横观各向同性饱和地基模型,将模型分为上覆路轨系统和地层系统。对上覆路轨系统和地层系统处理,并利用双重Fourier变换技术,在变换域中将横观各向同性饱和地基动力响应的求解简化为求解一个6阶控制方程的特征值问题,进而得到了列车荷载作用下双层横观各向同性饱和地基力响应的解析结果。利用离散Fourier逆变换得到数值计算结果,重点分析了上下土层的刚度和泊松比对位移和孔隙水压力和剪切应力响应的影响,结果表明,上、下土层刚度差异对地基动力响应有较大影响,土层各向异性参数中模量的影响较泊松比大。计算结果可为软土路基加固深度的确定提供理论依据。     

准各向同性裂隙岩体中有效动弹性参数与弹性波速关系的研究

从弹性波在介质中传播的特点和弹性波法在岩体工程中的实际应用情况方面,分析了弹性波在含裂隙岩体介质中的传播特征。将岩体中裂隙呈随机分布的裂隙岩体似为准各向同性裂隙岩体,根据能量平衡原理、岩石断裂力学理论和卡氏最小功能定理(Castiglano’s theorem),确定了准各向同性裂隙岩体的有效动弹性参数( 、 、 )与裂隙密度参数(Xv)的数学关系。在此基础上,根据各向同性介质中传播的弹性波理论,建立了准各向同性裂隙岩体中弹性波速( 、 )和 / 与裂隙密度参数(Xv)之间的关系。理论研究表明,在此裂隙岩体中,有效动弹性参数和弹性波速与裂纹密度参数之间相互的关系均近似成倒数函数的非线性关系;裂隙密度参数增加,有效动弹性模量( )也减少,弹性波速( , )也减小;在裂隙密度参数较小时,此裂隙岩体的有效弹性模量和弹性波速随裂隙密度参数的变化较大,说明裂隙体的有效弹性参数和弹性波速对裂隙体非常敏感。     

强风化花岗岩动力学参数的试验研究

地震反应分析通常采用等效非线性模型,动剪切模量G和阻尼比λ是该模型的两个重要参数。为研究目前在大型工程建设中遇到越来越多的强风化花岗岩的动力特性,利用固定-自由型共振柱（GDS RCA）对强风化花岗岩的剪切模量和阻尼比进行试验研究。GDS RCA为一种国际上广泛应用的共振柱,具有良好的性能,利用其控制试样的固结围压和孔隙水压力,可以测得试样在不同有效应力状况下的动剪切模量和阻尼比。对比研究不同有效应力下共振频率、动剪切模量和阻尼比随剪应变的变化情况,给出其变化曲线。按照Hadin-Drnevich[1]所提出的双曲线模型,拟合动剪切模量比和阻尼比随剪应变的变化曲线。利用摩擦理论,对试样阻尼的产生机制进行探讨。试验结果表明,随着剪应变的增加,试样系统的共振频率随之减小,试样阻尼比随之增大;试样的动剪切模量和阻尼比皆与试样固结时的有效应力有关,而试样阻尼比也受孔隙水压力的影响。     

The Effects of Temperature and Pressure on the Porosity Evolution of Flechtinger Sandstone

A porosity change influences the transport properties and the elastic moduli of rock while circulating water in a geothermal reservoir. The static and dynamic elastic moduli can be derived from the slope of stress–strain curves and velocity measurements, respectively. Consequently, the acoustic velocities were measured while performing hydrostatic drained tests. The effect of temperature on static and dynamic elastic moduli and porosity variations of Flechtinger sandstone was investigated in a wide range of confining pressure from 2 to 55 MPa. The experiments were carried out in a conventional triaxial system whereas the pore pressure remained constant, confining pressure was cycled, and temperature was increased step wise (25, 60, 90, 120, and 140 °C). The porosity variation was calculated by employing two different theories: poroelasticity and crack closure. The porosity variation and crack porosity were determined by the first derivative of stress–strain curves and the integral of the second derivative of stress–strain curves, respectively. The crack porosity analysis confirms the creation of new cracks at high temperatures. The porosity variation was increasing with an increase in temperature at low effective pressures and was decreasing with a rise in temperature at high effective pressures. Both compressional and shear wave velocities were increasing with increasing pressure due to progressive crack closure. Furthermore, the thermomechanical behavior of Flechtinger sandstone was characterized by an inversion effect where the sign of the temperature derivative of the drained bulk modulus changes.     

Effective elastic properties of the double‐periodically cracked plates

In this paper, the interaction of double‐periodical cracks is accurately solved based on the isolating analysis procedure, superposition principle, pseudo‐traction method, Chebyshev polynomial expansion and crack‐surface collocation technique. The jump displacement crossing crack faces, the average additional strain and therefore the effective compliance of the double‐periodically cracked plate are directly determined. The numerical results for axial‐symmetrically distributed double‐periodical cracks, general double‐periodical cracks with one collinear direction as well as two sets of double‐periodical cracks with same size and square distribution are given in this paper. And the partial typical numerical results are compared with the previous works. The analysis shows that the anisotropy induced by the general double‐periodical cracks is generally not orthogonal anisotropy. Only when the double‐periodical cracks are axial‐symmetrically distributed, is the anisotropy orthogonal. In this special cases, the effective engineering constants (consist of effective elastic modulus, the effective Poisson's ratio, the effective shear modulus) of cracked plate versus crack spacing, in the plane stress and plane strain conditions, respectively, are analysed. Copyright © 2005 John Wiley & Sons, Ltd.     

Propagation of Rayleigh waves in fluid‐saturated non‐homogeneous soils with the graded solid skeleton distribution

The propagation characteristic of Rayleigh waves in a fluid‐saturated non‐homogeneous poroelastic half‐plane is addressed. Based on Biot's theory for fluid‐saturated media, which takes the inertia, fluid viscosity, mechanical coupling, compressibility of solid grains, and fluid into account, the dispersion equations of Rayleigh waves in fluid‐saturated non‐homogeneous soils/rocks are established. By considering the shear modulus of solid skeleton variation with depth exponentially, a small parameter, which reflects the relative change of shear modulus, is introduced. The asymptotic solution of the dispersion equation expressing the relationship between the phase velocity and wave number is obtained by using the perturbation method. In order to analyze the effects of non‐homogeneity on the propagation characteristic of Rayleigh waves, the variation of the phase velocity with the wave number is presented graphically and discussed through numerical examples. Copyright © 2016 John Wiley & Sons, Ltd.     

The method of fundamental solution for 3‐D wave scattering in a fluid‐saturated poroelastic infinite domain

By using a complete set of poroelastodynamic spherical wave potentials (SWPs) representing a fast compressional wave P_I, a slow compressional wave P_II, and a shear wave S with 3 vectorial potentials (not all are independent), a solution scheme based on the method of fundamental solution (MFS) is devised to solve 3‐D wave scattering and dynamic stress concentration problems due to inhomogeneous inclusions and cavities embedded in an infinite poroelastic domain. The method is verified by comparing the result with the elastic analytical solution, which is a degenerated case, as well as with poroelastic solution obtained using other numerical methods. The accuracy and stability of the SWP‐MFS are also demonstrated. The displacement, hoop stress, and fluid pore pressure around spherical cavity and poroelastic inclusion with permeable and impermeable boundary are investigated for incident plane P_I and SV waves. The scattering characteristics are examined for a range of material properties, such as porosity and shear modulus contrast, over a range of frequency. Compared with other boundary‐based numerical strategy, such as the boundary element method and the indirect boundary integral equation method, the current SWP‐MFS is a meshless method that does not need elements to approximate the geometry and is free from the treatment of singularities. The SWP‐MFS is a highly accurate and efficient solution methodology for wave scattering problems of arbitrary geometry, particularly when a part of the domain extends to infinity.     

Deformation modulus of heavily jointed–sheared and blocky greywackes by pressuremeter tests: Numerical, experimental and empirical assessments

Deformability of rock masses influencing their behavior is an important geomechanical property for the design of rock structures. Due to the difficulties in determining the deformability of jointed rock masses at the laboratory-scale, various in-situ test methods such as pressuremeter, dilatometer, plate loading tests etc. have been developed. Although these techniques are currently the best and direct methods, they are time-consuming and expensive, and present operational difficulties. In addition, the influence of the test volume on deformation modulus depending on the method employed is also important. For these reasons empirical equations to indirectly estimate the deformation modulus have also been recommended by several investigators as an alternative approach. In this study; the geomechanical quality of weak, heavily jointed, sheared and/or blocky greywacke rock masses, on which very concentrated civil works are continuing at the southern and southwestern parts of Ankara (Turkey), was assessed. The deformation modulus was determined by pressuremeter tests, the possible effects of variables on the derived deformation modulus from the pressuremeter test were evaluated by numerical methods, and the comparisons between the deformation modulus of the greywackes obtained from the pressuremeter tests and their geomechanical quality (GSI and RMR) were made. Numerical simulations revealed that the presence of a disturbed annulus around the borehole causes underestimation of the deformation modulus, while the effect of length to diameter ratio of the pressuremeter probe on the deformation modulus is minor. Based on the geo-engineering characterization assessments, mainly two greywacke rock masses with different geomechanical qualities were identified. Geotechnical quality of one of these rock masses was verified by the back analysis of two slope failures. The empirical equations to indirectly estimate the deformation modulus of the greywackes using their GSI and RMR values yielded high coefficients of correlation.     

构造应力对裂缝形成与流体流动的影响

裂缝是低渗透储层流体流动的主要通道,控制了低渗透油气藏的渗流系统。低渗透储层裂缝的形成与流体密切相关,高流体压力引起岩石内部的有效正应力下降,导致岩石剪切破裂强度下降,使岩石容易产生裂缝。高孔隙流体压力还造成某一点的应力摩尔圆向左移动,可以使其最小主应力(σ3)由压应力状态变成拉张应力状态,从而在岩石中形成拉张裂缝。裂缝的渗透性受现今应力场的影响,通常与现今应力场最大主压应力近平行分布的裂缝呈拉张状态,连通性好,开度大,渗透率高,是主渗透裂缝方向。构造应力对沉积盆地流体流动的影响主要表现在三个方面:(1)构造应力导致的岩石变形,不仅提供了流体流动的通道,而且还改变了岩石的渗透性能;(2)在构造强烈活动时期,构造应力的快速变化是流体流动的重要驱动力;(3)岩石中应力状态影响多孔介质的有效应力,从而影响介质中的渗流场。当作用在含流体介质上的构造应力发生改变时,岩石孔隙体积变小,构造应力首先由岩石的骨架来承担;当岩石孔隙体积减小到一定程度时,构造应力由孔隙流体来承担,从而影响岩层渗流场的变化。