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1.
Naturally occurring fold systems are typically irregular. Although such systems may sometimes be approximated by a periodic geometry, in reality they are commonly aperiodic. Ord (1994) has proposed that naturally occurring fold systems may display spatial chaos in their geometry. Previous work has indicated that linear theories for the formation of fold systems, such as those developed by Biot (1965), result in strictly periodic geometries. In this paper the development of spatially chaotic geometries is explored for a thin compressed elastic layer embedded in a viscoelastic medium which shows elastic softening. In particular, it is shown that spatially localized forms of buckling can develop and the evolution of these systems in the time domain is presented. A nonlinear partial differential equation, fourth order in a spatial variable and first order in time, is found to govern the evolution. A related nonlinear fourth-order ordinary differential equation governs an initial elastic phase of folding. The latter equation belongs to a class with spatially chaotic solutions. The paper reviews the implications of localization in the geological framework, and draws some tentative conclusions about the development of spatial chaos. Crudely arrived-at, yet plausible, evolutionary time plots under the constraint of constant applied end displacement are presented. Emphasis throughout is on phenomenology, rather than underlying mathematics or numerics. 相似文献
2.
Pavlos Nomikos Reza Rahmannejad Alexandros Sofianos 《Rock Mechanics and Rock Engineering》2011,44(5):553-564
An exact closed form solution is derived for the mechanical behaviour of a linear viscoelastic Burgers rock around an axisymmetric tunnel, supported by a linear elastic ring. Analytical formulae are provided for the displacement of the rock/lining interface and for the pressure exerted by the rock on the lining, taking into account the stiffness and its installation time. Results calculated from these formulae do validate the corresponding numerical results of a 2D finite differences code. Further, comparison to previous existing solutions for the same viscoelastic model indicates similarities and differences. A parametric study is performed to investigate the effect of the viscoelastic constants, the stiffness and installation time of the support. The derived closed form solution is used to construct the time-dependent Supported Ground Reaction Curves of the viscoelastic rock, i.e. the time contour plots on the convergence confinement diagram. The importance of the effect of the support on the restrained rock creep and the exerted pressure on the lining, during the design life of a structure, is examined. 相似文献
3.
The formulation of viscoelastic solutions from elastic equations using the ‘correspondence principle’ and an inverse Laplace transform has been discussed extensively in the literature. Because this method has been developed, many time-dependent solutions can be obtained from closed form elastic solutions and conditions have been delineated in which the ‘quasi-elastic’ approximation of the viscoelastic solution is within acceptable tolerance. This communication shows the feasibility of the application of these methods to formulate approximate nonlinear viscoelastic solutions with nonlinear stress-strain materials, and for want of a specific nonlinear model to demonstrate this, the hyperbolic model was selected. The ‘power law’ is used to model the relaxation modulus of the viscoelastic materials. There are five related development that are discussed here using a simple numerical example to illustrate each of them and they are: (1) a linear elastic solution, (2) a linear viscoelastic solution, (3) a nonlinear elastic solution, (4) a nonlinear viscoelastic solution and finally, (5) a ‘regression’ approximation of the nonlinear viscoelastic solution which is suggested by the series form of the elastic solution. All of these are related to one another and each provides an acceptably accurate solution of the problem it addresses. The latter is of particular practical interest since it can be used to provide answers to problems involving nonlinear viscoelastic materials while requiring only very small calculation times. The problem used as an example is the calculation of the displacement of a circular hole in an infinite plate made of a material with a nonlinear time-dependent stress-strain relationship. The nonlinear elastic form of the solution was developed by matching results from nonlinear finite element analysis. 相似文献
4.
A Study of Stress Change and Fault Slip in Producing Gas Reservoirs Overlain by Elastic and Viscoelastic Caprocks 总被引：3，自引：2，他引：1
Geomechanical simulations were conducted to study the effects of reservoir depletion on the stability of internal and boundary faults in gas reservoirs overlain by elastic and viscoelastic salt caprocks. The numerical models were of a disk-shaped gas reservoir with idealized geometry; they mimic the structure of a gas field in the northern Netherlands which has experienced induced seismicity during gas production. The geomechanical simulations identified the area of the internal fault most sensitive to fault reactivation as coinciding with the epicenters of the largest seismic events associated with gas production. Depletion-induced shear slip is initiated at the depth of the reservoir, in the fault areas where the vertical fault throw ranges between 0.5 and 1.5 times the reservoir thickness. The extent of reactivated area differs depending on whether the caprock is viscoelastic or elastic: when it is viscoelastic, there is more down-dip shear displacement. High initial horizontal stresses in the rock salt and lower stresses in the elastic side-seal and the reservoir promote unloading of the internal and reservoir-bounding faults even before the reservoir is depleted. Particularly prone to fault reactivation are the fault zones along the interface between the reservoir rock and the salt caprock, which may already be critically stressed before depletion and are likely to be reactivated early during gas production. Stress relaxation and associated geomechanical changes affecting fault stability and ground surface deformation may continue long after production has ceased, due to the viscous behavior of the salt. 相似文献
5.
P-wave velocity and gradient images beneath the Okinawa Trough 总被引：1，自引：0，他引：1
To investigate the influence of spatial change of viscosity on postseismic deformation associated with the interplate 1946 Nankai earthquake (M 8.0) at the Nankai Trough, southwest Japan, we newly constructed a realistic viscoelastic structure model, taking into account temperature- and depth-dependent viscosity of materials. For this purpose, we first compiled leveling and triangulation data during postseismic periods and clarified characteristics of the amount and spatial patterns of postseismic vertical displacement and principal strain fields. Then, we calculated the spatial distributions of viscosity from temperature and flow fields, which were obtained from 2D subduction models. By incorporating the obtained viscosity structure into 3D viscoelastic finite element models, we constructed a temperature- and depth-dependent viscosity structure model (MODEL P2). Based on MODEL P2, we constructed a viscoelastic structure model, taking into account Poisson's ratio for the oceanic plate and low-velocity regions and the existence of low-viscosity materials beneath the Shikoku and Chugoku districts (MODEL P3), which were revealed from seismic tomography. We also constructed a conventional layered viscoelastic structure model (MODEL L1) and plate subduction model (MODEL P1) with constant viscosity for each region and evaluated the effects of different viscoelastic structures on postseismic surface deformations, using the coseismic slip distribution obtained by inversion analyses of geodetic data. We also compared the calculated surface deformations with the observed postseismic crustal deformations in and around Shikoku. The results show that postseismic surface deformation fields for the newly constructed MODEL P2 are rather different from those for MODELs L1 and P1. Landward horizontal displacements for MODEL P2 are smaller than those for MODELs L1 and P1, seaward horizontal displacements are negligible, and vertical displacement is characterized by small subsidence over Shikoku. The postseismic horizontal principal strain field for MODEL P2 is characterized by contractions in the N–S to NW–SE directions at amounts smaller than those for MODELs L1 and P1. Postseismic surface deformations for MODEL P3 are almost the same as those for MODEL P2. The observed postseismic vertical displacement and horizontal principal strain fields could not be explained by the viscoelastic response for the realistic viscoelastic structure models P2 and P3. This indicates that the effects of elastic and viscoelastic responses due to interplate coupling on the plate interface, after-slip at the extension of the coseismic slipped region, and poroelasticity should be taken into account to precisely estimate postseismic surface deformation. This also suggests that, in order to evaluate postseismic crustal deformations derived from a large interplate subduction zone earthquake, it is essential to use realistic temperature- and depth-dependent viscoelastic structure models. 相似文献
6.
粘弹性准饱和土中球空腔的动力响应 总被引：2，自引：0，他引：2
从工程实际出发,采用粘弹性两相介质模型,考虑土骨架的粘性以及流体与固体之间的耦合作用,利用Laplace变换求解了粘弹性准饱和土中球空腔的动力响应问题,得到了变换域内的解析解。借助数值Laplace反变换,数值分析了粘弹性准饱和土中球空腔动力响应的位移、应力及孔压的变化规律。为分析地下结构动力响应提供了一种有效的方法,模型符合工程实际,有一定的工程应用价值。 相似文献
7.
刚性承压板下深部岩体压缩蠕变参数反演 总被引：4，自引：1，他引：3
为获得岩体深部的压缩蠕变力学参数,进行了现场刚性承压板中心孔变形试验。推导出了圆形刚性承压板在均布荷载作用下中心孔深部岩体广义Kelvin模型的瞬时弹性变形。基于黏弹性理论,经过拉普拉斯变换和逆变换,进一步得到了黏弹性变形的计算公式。采用了以瞬时弹性模量、黏弹性模量和黏弹性系数为反演值的迭代优化反演法,并将计算公式程序化。该方法应用于一大型水电站坝区边坡工程,有效获得了坝区软弱岩体深部的压缩蠕变力学参数,克服了以往仅以岩体表面位移进行力学参数反演的缺陷。 相似文献
8.
The viscoelastic deformation behavior of a sedimentary rock under different loading rates is numerically modeled and investigated by the numerical manifold method (NMM). By incorporating a modified 3-element viscoelastic constitutive mode in the NMM, crack initiation and propagation criteria, and crack identification and evolution techniques, the effects of the loading rates on the cracking behavior of a sedimentary rock, such as crack open displacement, crack sliding displacement, crack initiation, crack propagation and final failure mode, are successfully modeled. The numerical results reveal that under a high loading rate (>1,000 MPa/s), due to the viscoelastic property of the sedimentary rock, not only the structural behavior deviates from that of elastic model, but also different cracking processes and final failure modes are obtained. 相似文献
9.
我国海上稠油资源比较丰富,但由于受到海上条件等因素限制,聚合物驱成为提高海上稠油采收率的主要方法.因此深化聚合物溶液驱稠油微观渗流机理对于进一步提高采收率具有十分重要的意义.目前关于粘弹性聚合物渗流机理的理论研究主要局限于弹性聚合物溶液的单相流体在微观孔道内流动特征研究,而针对粘弹性聚合物、油两相流体渗流机理的研究甚少,特别是针对稠油聚合物驱的相关研究未见报道.为此,借助于计算方法较为成熟的OpenFOAM开源平台开展了聚合物驱稠油两相流体渗流机理的研究;以收缩孔道为微观物理模型,建立了粘弹性聚合物溶液、普通稠油两相渗流连续性方程、运动方程及本构方程,并采用VOF（volume of fluid）界面追踪方法建立两相界面相方程;以OpenFOAM开源平台为基础,开发了粘弹性流体、幂律流体两相流体求解器;绘制了不同弹性聚合物溶液在微观孔道内驱油的饱和度分布、速度分布及应力分布特征.结果表明,相对于水驱,纯粘性聚合物溶液前缘突破时间慢,波及面积大,驱油效率高.相比于同等粘度的纯粘性聚合物溶液,粘弹性聚合物的弹性有助于挖潜凸角内的残余油,聚合物溶液的弹性越大,稠油驱油效率越高.随着聚合物溶液弹性的增强,第一法向应力增大,当聚合物溶液进入到孔道突变处时,其弹性发挥的作用最大,法向应力的值最大.研究结果可为矿场实施聚合物驱设计、筛选聚合物溶液提供重要的理论支持. 相似文献
10.
移动荷载下黏弹性半空间体上双层板的动力响应 总被引：1，自引：0，他引：1
采用黏弹性半空间体上无限大双层板模型模拟路面结构,通过三重Fourier积分变换得到单位脉冲荷载作用下路面动力响应的Green函数。根据线性系统的叠加原理,利用广义Duhamel积分推导出移动荷载作用下路面动力响应的解析解。采用自适应Simpson法编制了计算奇异、振荡函数的广义积分计算程序,完成了路面动力响应从波数-频率域到时间-空间域的转换。结合算例,对移动荷载作用下路面的振动规律进行研究,讨论上、下层板厚度和板材料的弹性模量对路面动力响应的影响,明确了路面结构的振动特性,研究结果可为路面结构的设计、施工提供理论指导。 相似文献
11.
The dynamic response due to a spherical source of radius a embedded in an elastic and viscoelastic full-space is investigated at a distance R from the source. Previous solutions to the elastic case are extended to incorporate realistic source pressure functions. The elastic solution is then cast in a scale independent form in order to generalize the application. The results show that the near-field of the spherical source may be defined by R/a < 5. For this region the particle velocity and displacement decrease as R?2, and the risetime decreases as R?1. However. in the far-field region (R/a > 5) the particle velocity and displacement decrease as R?1, and the risetime is independent of R. A non-constant Q model is developed to model viscoelastic attenuation and a complete analytical solution for wave propagation is obtained by cascading the separate mechanisms of geometric attenuation and viscoelastic attenuation. A comparison of our analytical model with the results of dynamic finite element modelling shows excellent agreement. This suggests that the method of cascading the separate transfer functions is a valid approach for wave propagation in viscoelastic media. 相似文献
12.
The problem of the coseismic deformation of an earth model consisting of an elastic layer of uniform thickness overlying an
elastic half-space due to a very long tensile fault in the layer is solved analytically. Integral expressions for the surface
displacements are obtained for a vertical tensile fault and a horizontal tensile fault. The integrals involved are evaluated
approximately by using Sneddon’s method of replacing the integrand by a finite sum of exponential terms. Detailed numerical
results showing the variation of the displacements with epicentral distance for various source locations in the layer are
presented graphically. The displacement field in the layered half-space is compared with the corresponding field in a uniform
half-space to demonstrate the effect of the internal boundary. Relaxed rigidity method is used for computing the postseismic
deformation of an earth model consisting of an elastic layer of uniform thickness overlying a viscoelastic half-space. 相似文献
13.
P. C. Hsieh 《国际地质力学数值与分析法杂志》2006,30(12):1201-1212
In many instances soils can be assumed to behave like viscoelastic materials during loading/unloading cycles, and this study is aimed at setting up a viscoelastic model to investigate the dynamic response of a porous soil layer of finite thickness under the effect of periodically linear water waves. The waves and homogeneous water are described by potential theory and the porous material is described by a viscoelastic model, which is modified from Biot's poroelastic theory (1956). The distributions of pore water pressures and effective stresses of various soils such as silt, sand, and gravel are demonstrated by employing the proposed viscoelastic model. The discrepancies of the dynamic response between the simulations of viscoelastic model and elastic model are found to be strongly dependent on the wave frequency. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
14.
An analytical solution is developed in this paper to investigate the dynamic response of a large‐diameter end‐bearing pipe pile subjected to torsional loading in viscoelastic saturated soil. The wave propagation in saturated soil and pile are simulated by Biot's two‐phased linear theory and one‐dimensional elastic theory, respectively. The dynamic equilibrium equations of the outer soil, inner soil, and pile are established. The solutions for the outer and inner soils in frequency domain are obtained by Laplace transform technique and the separation of variables method. Then, the dynamic response of the pile is obtained on the basis of the perfect contacts between the pile and the outer soil as well as the inner soil. The results in this paper are compared with that of a solid pile in elastic saturated soil to verify the validity of the solution. Furthermore, the solution in this paper is compared with the classic plane strain solution to verify the solution further and check the accuracy of the plane strain solution. Numerical results are presented to analyze the vibration characteristics and illustrate the effect of the soil parameters and the geometry size of the pile on the complex impedance and velocity admittance of the pile head. Finally, the displacement of the soil at different depth and frequency is analyzed. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
15.
假定土骨架服从标准线性固体黏弹性本构关系,研究了深埋圆形隧洞的饱和黏弹性土-弹性衬砌耦合系统在轴对称爆炸作用下的瞬态动力响应。首先,基于饱和土的Biot模型和衬砌的弹性理论,通过引入势函数和Laplace变换,利用弹性衬砌和饱和黏弹性土界面处的连续性条件以及边界条件,得到饱和黏弹性土体和弹性衬砌位移、应力和孔隙水压力等在Laplace变换域中的解析解。其次,利用Laplace数值Crump逆变换得到耦合系统在时间域的动力响应,数值分析了不同土体模型下土体-衬砌耦合系统的径向位移和环向应力以及土体孔隙水压力等。结果表明：对不同土体模型的土体-衬砌耦合系统,其在爆炸载荷作用下的动力响应性态基本一致,但动力响应的振动周期和幅值等具有明显的差异。同时,对于饱和黏弹性土-弹性衬砌系统,土体黏性参数对土体径向位移和孔隙水压力有明显的影响,但对土体环向应力影响较小。 相似文献
16.
为研究深部洞室围岩的分区破裂化机制,建立了厚壁筒三维线弹性解析模型。逐步减小厚壁筒均布内压,模拟洞室静力开挖。逐步增加厚壁筒轴向均布压力,模拟洞室开挖导致洞室轴向应力集中。逐步增加厚壁筒外周非均布压力系数,模拟洞室开挖导致洞室水平应力的重分布和集中效应。根据弹性力学知识和边界条件,确定洞室开挖引起的弹性应力场、应变场及位移场。从拉压域、应变梯度及径向压拉蓄能等3个方面入手,分别研究了内压静力卸荷、水平应力重分布、围压均匀部分及轴压对深部洞室围岩分区破裂的作用机制。结果表明：径向弹性拉伸能和径向弹性压缩能的相对变化反映了围岩能量释放速率和释放量。水平应力重分布和轴压是围岩出现分区破裂现象的主要因素,但两者作用机制不同。该模型可为研究高地应力深部洞室围岩破坏提供一个较统一的理论工具,也为深部工程设计提供了理论依据。 相似文献
17.
Euclides Mesquita Marco Adolph Edson Rodrigues Carvalho Edivaldo Romanini 《国际地质力学数值与分析法杂志》2009,33(18):1933-1952
In this article a numerical solution for a three‐dimensional isotropic, viscoelastic half‐space subjected to concentrated surface stress loadings is synthesized with the aid of the Radon and Fourier integral transforms. Dynamic displacement and stress fields are computed for points at the surface and inside the domain. The analysis is performed in the frequency domain. Viscoelastic effects are incorporated by means of the elastic–viscoelastic correspondence principle. The equations of motion are solved in the Radon–Fourier transformed domain. Inverse transformations to the physical domain are accomplished numerically. The scheme used to perform the numerical inverse transformations is addressed. The solution is validated by comparison with results available in the literature. A set of original dynamic displacement and stress solutions for points within the half‐space is presented. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
18.
三维黏弹性介质人工边界研究 总被引：1，自引：0，他引：1
为了得到适于分析非线性结构-地基相互作用问题的人工边界,结合弹性波理论与黏弹性理论,推导出了适于模拟三维黏弹性远场介质辐射阻尼的人工边界,并对其模拟远场地基辐射阻尼的性能及相应地震波动输入方法进行了研究。结果表明：在结构-地基动力相互作用问题中,得到的黏弹性人工边界模拟计算域外远场黏弹性介质的辐射阻尼具有理想精度;不论是简谐波还是非简谐波,地震波动输入都取得了理想结果;在黏弹性介质条件下自由地表处的总场位移幅值n是输入波幅值的 倍。 相似文献
19.
针对岩质或黄土浅埋隧道,考虑岩土体黏弹性流变特性和支护效应,给出斜坡下进行隧道施工时的全域时效解答。根据一般黏弹性问题求解方法,采用复变函数方法、Laplace变换、黏弹性叠加关系,用随时间和空间变化支护力体现管片支护效应,导出适用于任意黏弹性模型岩体、任意时刻施加支护的应力与位移。解答与相同模型有限元结果一致,根据解答分析了广义Kelvin黏弹性模型岩体中浅埋隧道开挖时侧压力系数、斜坡倾角、埋深对稳定地表沉陷大小和范围、洞周时效位移、应力的影响,给出可按深埋问题处理时的埋深范围。解答可用于岩质和黄土隧道初步设计中,并为隧道与地下结构相互作用分析两阶段法提供自由位移场。 相似文献
20.
基于常Q模型的解耦分数阶拉普拉斯算子粘滞波动方程,可以分开模拟振幅衰减和相位错动。但该方程拉普拉斯算子的阶数是随空间变化的,因此数值求解存在一定困难。这里基于截断的泰勒展开,经过一系列近似,推导出拉普拉斯算子的阶数与空间无关的解耦分数阶粘滞弹性波动方程。采用中心差分计算时间导数,使用交错网格伪谱法计算空间导数。数值算例表明,新的方程在处理非均匀介质时具有精度高,计算简便的优点。 相似文献