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1.
The dynamic response of a tunnel buried in a two-dimensional poroelastic soil layer subjected to a moving point load was investigated theoretically. The tunnel was simplified as an infinite long Euler–Bernoulli beam, which was placed parallel to the traction-free ground surface. The saturated layer was governed by Biot’s theory. Combined with the specified boundary conditions along the beam and saturated poroelastic layer, the coupled equations of the system were solved analytically in the frequency–wavenumber domain based on Fourier transform. The time domain responses were obtained by the fast inverse Fourier transform. The critical velocity of the considered structure was determined from the dispersion curves. The different dynamic characteristics of the elastic soil medium and the saturated poroelastic medium subjected to the underground moving load were investigated. It is concluded that, for coarse materials or fine materials subjected to the high-velocity loading, models ignoring the coupling effects between the pore fluid and the soil skeleton may cause errors. The shear modulus and the permeability coefficients of the saturated soil as well as the load moving velocity had significant influence on the displacement and pore pressure responses. 相似文献
2.
Stress distribution in the vicinity of a permeable cylindrical cavity surface (borehole wall) arising due to modal vibrations of an internal cylindrical radiator of infinite extent is studied. Biot phenomenological model is used to represent the behavior of sound in the fluid-saturated elastic porous medium and closed-form solution in the form of an infinite series is developed. A numerical example for the infinite cylindrical surface excited in vibrational modes of zeroth and first order while immersed in a water-filled cavity embedded within a water-saturated Ridgefield Sandstone environment is presented and several limiting cases are examined. Effects of axial and radial vibration frequencies, porosity, frame stiffness, and interface permeability condition on stress distribution at the borehole surface are presented and discussed. 相似文献
3.
基于Fourier-Bessel级数展开法,研究深埋圆形三层复合式衬砌洞室在平面P波入射下的动应力集中问题,并给出三层衬砌洞室动应力集中系数级数解析解;依托某IX度地震区管道隧道实际工程,分析不同衬砌刚度组合和厚度组合对洞室动应力集中系数的影响。研究表明:注浆加固洞室围岩和设置减震层都可以降低二次衬砌动应力集中系数;增大围岩注浆区弹性模量和厚度,有利于减小衬砌动应力集中系数,最优围岩注浆区厚度为1倍洞室净空半径;减震层弹性模量降低,减震层厚度增大,二次衬砌动应力集中系数变小,减震层弹性模量宜低于围岩弹模1/20,最优减震层厚度宜取1/50的洞室内净空半径。最后针对实际管道隧道抗减震技术,考虑围岩稳定性,提出"围岩-加固圈-减震层-衬砌"新型减震结构,分析结果表明:对比其他三种抗减震措施,新型减震结构的减震效果最好。 相似文献
4.
By the theories of potential flow and structural vibration, the formulae for evaluating the ‘wet’ (with water) frequencies and mode shapes of the beam‐supported aqueduct are derived through a simplified fluid‐structure interaction analysis. The time‐history formulae of structural responses to the vertical seismic excitation are obtained. Applying the response‐spectrum principle, the equivalent vertical earthquake load exerted on the beam and the corresponding effects are also derived. Several illustrative examples are conducted. The analytical results show that: (i) The ‘wet’ frequencies of the structure are lower than the corresponding ‘dry’ (without water) frequencies due to the participating water mass, but the ‘wet’ mode shapes are identical to the corresponding ‘dry’ ones. (ii) The water mass plays an important role in the vertical seismic response, which varies with the different geological sites. For the different seismic inputs, the deeper the water is, the greater are the structural responses. (iii) The vertical seismic effects on the beam are generally not too small to be neglected and should be considered in the structural designs of a beam‐supported aqueduct. Copyright © 2002 John Wiley & Sons, Ltd. 相似文献
5.
This paper presents a new formulation for critical damping of structures with elastically supported visco‐elastic dampers.Owing to the great dependence of damper performance on the support stiffness, this model is inevitable for reliable modelling of structures with visco‐elastic dampers. It is shown that the governing equation of free vibration of this model is reduced to a third‐order differential equation and the conventional method for defining the critical damping for second‐order differential equations cannot be applied to the present model. It is demonstrated that the region of overdamped vibration is finite in contrast to that (semi‐infinite) for second‐order differential equations and multiple critical damping coefficients exist. However, it turns out that the smaller one is practically meaningful. Copyright © 2001 John Wiley & Sons, Ltd. 相似文献
6.
半无限空间中稳态P波在衬砌周围的散射 总被引：8，自引：0，他引：8
本文采用多级坐标和复变函数方法针对半无限空间中P波在一衬砌周围的散射问题提出了一种近似求解分析方法。具体做法是利用一个半径很大的圆来逼近半空间的直边界，将待解问题转化为全空间中P波在一圆孔和一衬砌周围的共同散射问题。我们预先写出问题波函数的一般形式解，利用边界条件并借助复数傅立叶级数展开把问题化为求解波函数中未知系数的无穷线性代数方程组，进而讨论了衬砌内外边界处动应力集中系数针对不同条件组合的分布和变化情况。算例结果表明：本文方法对于研究与P波（SV波）有关的散射问题是可行的。 相似文献
7.
Routine amplitude‐versus‐offset or amplitude‐versus‐angle (AVA) analysis is founded on the predicted reflectivity of a planar boundary between isotropic homogeneous half‐spaces, yet many real boundaries of interest to hydrocarbon exploration may violate these assumptions. Here, we evaluate consequences of boundary roughness, i.e. small‐scale, sub‐resolution topography, on the reflecting boundary, to find whether sub‐resolution topography can deceive routine AVA analysis and produce misleading hydrocarbon indicators. We use noise‐free synthetic CMP and stacked‐section seismograms, generated with a Kirchhoff‐integral method, for offsets up to 4000 m. The reflecting boundary was at 2000 m depth below a single overburden layer, and comprised isolated mounds or channels (sinusoidal cross‐section, 5–40 m high and 100–750 m wide), and more complex roughness (simulated with seven 1.5–2 km long bathymetric profiles across modern‐day river‐beds, with dune and bar features up to approximately 20 m or 20 ms TWT vertical relief, and 10–100 m or more lateral extent). Flat‐boundary responses were taken as the ‘reference’ against which to compare waveforms and amplitudes through semblance analysis, AVA intercept A and slope B cross‐plots, and inferred Poisson's ratios. Physical properties of the media were based on shales and brine‐ or oil‐sands from an offshore UK oilfield. For the CMP centred on the topographic feature, isolated mounds and channels produced correlated excursions of A and B from the flat‐boundary response (by approximately 35–200%), simulating the familiar ‘background trend’ but sometimes oblique to it. Inferred Poisson's ratios were around 0.3, but for some channels often fell as low as 0.2, potentially interpretable as gas sand. For complex boundary topographies on a shale/brine‐sand model, AVA parameters were extracted for 29 CMPs, 100 m apart along each of seven profiles. On a cross‐plot, they spanned the flat‐boundary response on a linear trend B = (0.01 ± 0.02) – (1.72 ± 0.09)A, similar to reported real data and a realistic ‘mudrock trend’ but with outliers both above and below it that could be interpreted as ‘real’ weak anomalies. Poisson's ratios were 0.30 ± 0.01, between the expected values for brine‐ and oil‐sand. This suggests that boundary roughness may contribute to observed trends on cross‐plots and possibly small, but potentially laterally extensive, false AVA anomalies may also be induced. 相似文献
8.
Camilo Valencia Juan Gomez Juan Jaramillo Mario Saenz Juan Vergara 《Studia Geophysica et Geodaetica》2017,61(1):93-114
The problem of diffraction of cylindrical and plane horizontally polarized shear waves (SH waves) by a finite crack embedded in a plane bidimensional elastic full-space is revisited. Particularly, we construct an approximate solution by the addition of independent diffracted terms. In our method the derivation of the fundamental case of a semi-infinite crack obtained as a degenerate case of a generalized wedge is first considered. This result is then used as a building block to compute the diffraction of the main incident waves. The interaction between the opposite edges of the crack is later considered in terms of a series, one term at a time until a desired tolerance is reached. Moreover, we propose a procedure to determine the number of required interactions as a function of frequency. The solution derived with the superposition technique is shown to be effective at low and high frequencies and as shown by comparisons with a direct boundary element method software, highly accurate solutions are obtained after retaining just a few terms of the infinite series. 相似文献
9.
Based on the plane complex variable theory and the image technique, an analytical solution is presented for scattering of plane harmonic P, SV or Rayleigh waves by a shallow lined circular tunnel in an elastic half space. The major contribution of this study is the treatment of the orthogonality of the boundary conditions along the half surface and the cavity wall. In terms of the image technique, the scattered waves by the half surface are simulated as transmitting from the image source of the origin of the tunnel. Using two different conformal mapping functions, we obtained the complex-valued stresses and displacements of the elastic medium and the liner in the image domain, respectively. The boundary value problem results in a set of infinite algebraic equations. The accuracy of the present approach is verified by comparing the present solution results with the available published data. Parametric study indicates that the embedment depth, the shear modulus and the thickness of the liner have significant influences on the dynamic response of the liner and the medium. 相似文献
10.
Detailed echo‐sounder and acoustic Doppler velocimeter measurements are used to assess the temporal and spatial structure of turbulent flow over a mobile dune in a wide, low‐gradient, alluvial reach of the Green River. Based on the geometric position of the sensor over the bedforms, measurements were taken in the wake, in transitional flow at the bedform crest, and in the internal boundary layer. Spatial distributions of Reynolds shear stress, turbulent kinetic energy, turbulence intensity, and correlation coefficient are qualitatively consistent with those over fixed, two‐dimensional bedforms in laboratory flows. Spectral and cospectral analysis demonstrates that energy levels in the lee of the crest (i.e. wake) are two to four times greater than over the crest itself, with minima over the stoss slope (within the developing internal boundary layer). The frequency structure in the wake is sharply defined with single, dominant peaks. Peak and total spectral and cross‐spectral energies vary over the bedform in a manner consistent with wave‐like perturbations that ‘break’ or ‘roll up’ into vortices that amalgamate, grow in size, and eventually diffuse as they are advected downstream. Fluid oscillations in the lee of the dune demonstrate Strouhal similarity between laboratory and field environments, and correspondence between the peak frequencies of these oscillations and the periodicity of surface boils was observed in the field. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
11.
半无限空间中圆形孔洞周围SH波的散射 总被引：14，自引：5，他引：14
建立了求解在含有圆形孔洞的弹性半空间中SH波散射与圆形孔洞附近动应力集中问题的解析方法。利用SH波散射的对称性和多极坐标的方法，构造了一个可以预先满足半空间自由表面上应力自由边界条件的圆形孔洞对SH波散射的波函数。利用这一波函数，则可将该问题转化成对一个圆形孔洞散射的求解问题。该问题的解答最终又可归结为对一组无究代数方程组的求解问题，并可利用截断有限项的方法对其进行计算，最后给出了有关圆形也洞附近动应力集中问题的算例和数值结果，并讨论了波数与圆孔至自由边界距离变化对动应力集中的影响。 相似文献
12.
This work examines the propagation of time harmonic, horizontally polarized shear waves through a naturally occurring heterogeneous medium that exhibits viscous behaviour as well as random fluctuations of its elastic modulus about a mean value. As a first step, the governing equation, which is a heterogeneous Helmholtz equation, is solved using algebraic transformations and the relevant Green's function is obtained for two sets of boundary conditions, one corresponding to a finite depth layer and the other to an infinite layer. Viscous material behaviour is introduced by considering the depth-dependent elastic modulus to be a complex quantity. Subsequently, material stochasticity in the medium is handled through the perturbation approach by assuming that the elastic modulus has a small random fluctuation about its mean value. The final results are closed-form expressions for the mean value and covariance matrix of both the wave speed profile in the medium and the corresponding Green's function. In Part II, (Soil Dynam. Earth. Engng, 1996,15, 129-39), two examples concerning seismic wave propagation in soft topsoil and in sandstone serve to illustrate the methodology and comparisons are made with Monte Carlo simulations. 相似文献
13.
This paper proposes an online test technique that employs mixed control of displacement and force. Two types of mixed control, ‘displacement–force combined control’ and ‘displacement–force switching control’ are proposed. In displacement–force combined control, one jack is operated by displacement‐control, and another is operated by force‐control. Validity of the combined control technique is demonstrated by a series of online tests applied to a base‐isolated structure subjected to horizontal and vertical ground motions simultaneously. The substructuring technique is employed in the tests, and the base‐isolation layer is tested, with the rest of the structure modeled in the computer. Displacement‐control and force‐control were adopted for simulating the horizontal and vertical response, respectively. Both displacement‐ and force‐control were implemented successfully despite interference between the two jacks. Earthquake responses of the base‐isolated structure involving the effects of varying axial forces on the horizontal hysteretic behavior of the base‐isolation layer were simulated. In the displacement–force switching control, the jack was operated by displacement‐control when the test specimen was flexible but switched to force‐control once the specimen became stiff. Validity of the switching control technique was also checked by a series of online tests applied to the base‐isolated structure subjected to vertical ground motions. Switching between displacement‐control and force‐control was achieved when the axial force applied to the base‐isolation layer changed from tension to compression or from compression to tension. Both the displacement‐ and force‐control were successful even with many rounds of switching. The test revealed that large accelerations occurred on the floor immediately above the base‐isolation layer at the instants when the axial force of the base‐isolation layer changed from tension to compression. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
14.
In this paper, a finite element model of a soil island is coupled to both a consistent transmitting boundary and a paraxial boundary, which are then used to model the propagation of waves in semi-infinite elastic layered media. The formulation is carried out in the frequency domain while assuming plane strain conditions. It is known that a discrete model of this type, while providing excellent results for a wide range of physical parameters in the context of a half-space problem, may deteriorate rapidly at low frequencies of excitation. This is so because at low frequencies the various waves in the model eventually attain characteristic wavelengths which exceed the distance of the bottom boundary, which then causes that boundary to fail. Also, the paraxial boundaries themselves break down at very low frequencies. In this paper, this difficulty is overcome and the model׳s performance is improved upon dramatically by incorporating an artificial buffer layer sandwiched between the bottom of the soil medium and the underlying elastic half-space. Applications dealing with rigid foundations resting on homogenous or layered half-space media are shown to exhibit significant improvement. Following extensive simulations, clear guidelines are provided on the performance of the coupled model and an interpretation is given on the engineering significance of the findings. Finally, clear recommendations are provided for the practical use of the proposed modelling strategy. 相似文献
15.
Based on the u–p formulation of Biot equation with an assumption of zero permeability coefficient, a high-order transmitting boundary is derived for cylindrical elastic wave propagation in infinite saturated porous media. By this transmitting boundary the total stresses on the truncated boundaries of a numerical model, such as a finite element model, are replaced by a set of spring, dashpot and mass elements, with some additionally introduced auxiliary degrees of freedom. The transmitting boundaries are incorporated into the DIANA SWANDYNE II program and an unconditionally stable implicit time integration algorithm is adopted. Despite the assumption made in the derivation of the transmitting boundary, numerical examples show that it can provide highly accurate results for cylindrical elastic wave propagation problems in infinite saturated porous medium in case the u–p formulation is applicable. Although the direct applications of the proposed transmitting boundary to general two dimensional wave problems in infinite saturated porous media are not highly accurate, acceptable accuracy can still be achieved by placing the transmitting boundary at relatively large distance from the wave source. 相似文献
16.
In order to investigate the response of structures to near‐fault seismic excitations, the ground motion input should be properly characterized and parameterized in terms of simple, yet accurate and reliable, mathematical models whose input parameters have a clear physical interpretation and scale, to the extent possible, with earthquake magnitude. Such a mathematical model for the representation of the coherent (long‐period) ground motion components has been proposed by the authors in a previous study and is being exploited in this article for the investigation of the elastic and inelastic response of the single‐degree‐of‐freedom (SDOF) system to near‐fault seismic excitations. A parametric analysis of the dynamic response of the SDOF system as a function of the input parameters of the mathematical model is performed to gain insight regarding the near‐fault ground motion characteristics that significantly affect the elastic and inelastic structural performance. A parameter of the mathematical representation of near‐fault motions, referred to as ‘pulse duration’ (TP), emerges as a key parameter of the problem under investigation. Specifically, TP is employed to normalize the elastic and inelastic response spectra of actual near‐fault strong ground motion records. Such normalization makes feasible the specification of design spectra and reduction factors appropriate for near‐fault ground motions. The ‘pulse duration’ (TP) is related to an important parameter of the rupture process referred to as ‘rise time’ (τ) which is controlled by the dimension of the sub‐events that compose the mainshock. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
17.
Gin-Show Liou 《地震工程与结构动力学》1989,18(5):667-686
The total system studied in this paper is a layered soil stratum with a rigid bedrock and a cylindrical cavity on the surface. Analytic solutions for the layered medium with prescribed harmonic displacement time history on the surface of the cylindrical cavity are presented. The whole soil domain is divided into interior and exterior domains. The interior domain is the projection of the cylindrical cavity down to the rigid bedrock, whereas the exterior domain is then the soil medium complement to the interior domain. The displacement and stress fields in both domains are expanded as an infinite series of Fourier components with respect to the azimuth. For each Fourier component in the infinite series, the solutions for both domains are found independently by solving the general differential equations of wave propagation satisfying the boundary conditions of the top surface and the lower rigid boundary. Displacement and stress continuity conditions are then imposed on the vertical interface between the two domains using the formulation of a weighted residual. For the soil-structure interaction problem, the impedance matrix at the interface between the structure and the soil medium can be easily generated using the analytic solutions, which can then be combined with the finite element model of the structure. A simple example is presented to demonstrate the effectiveness of the procedure presented. 相似文献
18.
The problem of harmonic wave diffraction by tunnels in an infinite poroelastic saturated soil obeying Biot's theory is studied numerically under conditions of plane strain and the effect of poroelasticity on the response is assessed through some parametric studies. The method is based on the theory of Mei and Foda, which considers the total field to be approximated by the superposition of an elastodynamic problem with modified elastic constants and mass density for the whole domain and a diffusion problem for the pore fluid pressure confined to a boundary layer at the free boundaries. Both problems are solved numerically by the boundary element method in the frequency domain. Results dealing with the response of a circular tunnel with and without an elastic concrete liner in an infinite poroelastic medium to incident harmonic P and SV plane waves are provided and compared against analytical ones as well as to those corresponding to linear elastic soil behaviour. Copyright © 2002 John Wiley & Sons, Ltd. 相似文献
19.
An absorbing boundary for saturated porous media is developed that can be used for transient analyses in the time domain. The elastic constitutive equations for the saturated porous media follow Bowen's formulation. The method consists of applying viscous tractions along the artificial boundary. The absorbing boundary behaviour is assumed linear and isotropic. Hadamard's conditions provide the speeds of the dilatational and shear waves that propagate in saturated porous media. Since these expressions are frequency independent, the intensities of the viscous tractions are evaluated in the time domain, and the two dilatational waves are accounted for. The viscous tractions are defined from the drained characteristics, assuming an infinite permeability, at variance with the traditional ‘undrained’ method based on undrained characteristics and a null permeability. Solid media and materials with low permeability are also retrieved as subcases. The results show that, at no additional cost, this ‘drained’ method is more accurate for all permeabilities than the ‘undrained’ method, which disregards the existence of the second dilatational wave. Copyright © 2003 John Wiley & Sons, Ltd. 相似文献
20.
基于Biot饱和多孔介质动力学理论,运用Laplace变换和波函数展开法,根据饱和土体与衬砌结构交界面的连续条件和衬砌结构内边界上的应力自由条件,得到饱和土中深埋圆柱形衬砌洞室对瞬态平面P波和SV波散射问题的解答,该解答可以退化成为饱和土中深埋圆柱形空穴或弹性夹塞物的情形,并很容易转换成为对稳态波散射的解.通过与已有的相关问题的解析解答进行对比,验证了该解答的正确性.同时利用Laplace逆变换的数值方法,给出了饱和土和衬砌中应力和位移场在时域内的数值解,通过算例,分析了衬砌厚度、刚度对衬砌内边界处应力集中因子的影响. 相似文献