Vertical dynamic response of a disk on a saturated poroelastic half-space

This paper considers the vertical dynamic response of a disk on a saturated poroelastic half-space. Firstly the pressure-solid displacement form of the harmonic equations of motion for a poroelastic solid are developed from the form of the equations originally presented by Biot. These equations are solved by a new method. Then the mixed boundary value problem for the vertical harmonic vibration of a disk on a poroelastic half-space is studied. The two types of drainage conditions at the surface of the poroelastic half-space are considered: (a) the surface of the poroelastic half-space is assumed to be completely pervious both within and exterior to the plate; (b) The interface between the plate and the poroelastic half-space is assumed to be impervious and the exterior region is assumed to be pervious. By using the Hankel transform techniques, the paper develops the governing dual integral equations. These governing integral equations are further reduced to systems of standard Fredholm integral equations of the second kind by Abel transform.     

Note on the flow of a stratified fluid over a stationary obstacle in a channel

Abstract

A new method is introduced to produce a uniform stratified flow over a stationary obstacle in an open channel. The flow is achieved by discharging the flow from the channel through a sink. The details of the sink are unimportant. The flow speed is limited only by the sink capacity. Selective withdrawal at lower densimetric Froude numbers is effectively eliminated through the use of a contraction. The standing, free-surface, long wave arising from the initiation of the flow is also eliminated by the contraction. Experiments are conducted for flow over a sphere for a range of Reynolds numbers from O(10²) to O(10³) and a range of Richardson numbers from O(10^?1) to O(10). Dye and neutrally buoyant droplets are used for quantitative analysis of the wake structure. The wake is also probed by a hot-film anemometer. The frequency of vortex shedding is obtained. Comparison with data from towed experiments is also presented.     

Dynamic response of a pair of walls retaining a viscoelastic solid

Making use of a previously reported, simple, approximate method of analysis, a critical evaluation is made of the dynamic pressures and forces induced by horizontal ground shaking on a pair of infinitely long, parallel walls retaining a uniform viscoelastic solid. The walls are presumed to be rigid but elastically constrained against rotation at their base. The effects of both harmonic and earthquake-induced excitations are examined. The accuracy of the method is assessed by comparing its predictions for the special case of fixed-based walls with those obtained by an exact method, and comprehensive numerical data are presented which elucidate the underlying response mechanisms, and the effects and relative importance of the parameters involved. The parameters examined include the characteristics of the ground motion, the ratio of the distance between walls to the height of the contained material, and the flexibility of the rotational wall constraints. In addition to valuable insights into the responses of the systems investigated, the results presented provide a convenient framework for the analysis of more complex systems as well.     

Horizontal vibrations of a disk on a poroelastic half-space

This paper analytically examines the horizontal vibration of a rigid disk on a saturated poroelastic half-space. The pressure-solid displacement form of the harmonic equations of motion for asymmetric dynamic problem are developed from the form of the equations originally presented by Biot. Making use of a new method the solution of the above equations is obtained. According to the mixed boundary -value conditions, the dual integral equations of the horizontal vibration of a rigid disk on a saturated poroelastic half-space are established. By appropriate transforms, it is shown that the dual integral equations can be reduced to a pair of Fredholm integral equations of the second kind, whose solutions are then computed. Numerical results for the horizontal dynamic compliance coefficient are given at the end of this paper.     

无破碎带断层场地对SH波的散射

在层状半空间精确动力刚度矩阵和斜线荷载动力格林函数的基础上建立间接边界元方法,在频域内求解无破碎带断层场地对入射平面SH波的散射。为方便求解,将总波场分解为自由波场和散射波场,自由波场由直接刚度法求得,断层两侧的散射波场通过在断层面上分别对两侧施加均布斜线荷载产生的动力响应来模拟,虚拟荷载的密度可通过引入断层表面的边界条件确定,最后叠加自由波场和散射波场求得总波场。以有落差断层和无落差断层模型为例进行数值计算,分析断层落差、断层倾角以及断层两侧介质的刚度比对散射效应的影响。研究表明,断层落差与波长相当时,断层对SH波的放大作用最大;地表位移幅值随着断层倾角的增大逐渐增大;若断层无落差且其两侧刚度不同时,一般刚度较小一侧地表位移幅值较大且振荡更为剧烈,波从刚度较小一侧入射时位移幅值放大尤为显著。     

A Tool for Forecasting the Arrival Time of a Tracer or a Pollutant at a Karst Spring

Karst aquifers are a groundwater resource of global importance. Protection and contamination of karst water resources are often tackled by means of land-use planning and monitoring of physico-chemical and microbial water properties coupled to early-warning systems. However, these solutions of management do not integrate observational data on karst hydrodynamic, for example, tracer tests. Thus, this technical note aims at introducing a straightforward method for forecasting the arrival time of a tracer or a pollutant at a karst spring. Deliverables from the proposed method can assist professionals in the case of a pollution involving a swallow hole of the karst network. The approach is based on repeated tracer testing, gauging of spring flow rate and mathematical curve fitting. Tracer tests and gauging of spring flow rates are repeated under low, middle, and high flow periods. Arrival times of tracer from a given swallow hole of the network are plotted as a function of measured flow rates at the karst spring. The observational data are finally fitted by a mathematical function. Flow rate monitoring at high-temporal resolution at the karst spring and the mathematical functions allow forecasting the arrival of a tracer or a pollutant at the spring in the case of an accident involving a swallow hole of the network or estimating the duration of a pollution if hydrodynamic conditions do not change abruptly. The applicability of the method is documented by three study sites in Switzerland.     

Truncated model of a barotropic atmosphere with a periodic forcing

The effect of variations in time of the zonal flow is investigated by the study of a simplified truncated model of a barotropic atmosphere in the presence of an oscillating zonal forcing. Long-time numerical simulations of a triadic model in spherical geometry are carried out for various values of both the frequency and the amplitude of the oscillating part of the zonal forcing. It is found that the reaction of the system to simple sinusoidal forcing is characterized, as happens for strongly nonlinear systems, by complicated trajectories in the phase-space and that the spectrum of the zonal component is much more complicated than that of the forcing function, with interesting relative maxima in the range of very low climatological frequencies. Moreover it is shown that, for proper values of both the frequency and the amplitude of the sinusoidally oscillating part of the forcing function, our simplified model of the large-scale planetary circulation oscillates between an essentially zonal regime (a flow pattern dominated by the zonal flow component) and a wave regime (a flow pattern characterized by significant values of the meridional component of the velocity field associated with the wave components). The transitions between the two regimes are strongly asymmetric: in fact, the time needed for a wave-like flow to evolve into an essentially zonal one is, in the limit of our model, typically 4 to 5 times greater than that needed for the inverse transition. The results are intuitively interpreted in the limit of very long periods of the oscillations of the forcing function. Other interesting features of the results are considered.     

The maximum depth of a river as a stochastic process

The maximum depth of a river section is schematized as a non‐stationary continuous‐parameter continuous stochastic process, with a three‐parameter lognormal distribution. Two processes, represented by a first‐order and a second‐order differential equation, are considered. Non‐stationarity is accounted for by the mean, the other parameters being assumed constant. The continuous processes are then discretized as AR(1) and ARMA(2,1) processes respectively, and used for computing the conditional probability (which is of practical interest) for a given maximum depth not to be exceeded in a period of given length. The models are applied to the River Po (Italy) and the AR(1) model is found to be preferable. An analysis of the effect of discretizing the parameter is also carried out, considering the second‐order model and the conditional probability, for which analytical results for the continuous‐parameter model are available. Copyright © 2002 John Wiley & Sons, Ltd.     

Transient electromagnetic response of a sphere in a layered medium

The integral equation for the electromagnetic response of a sphere in a layered medium may be solved as follows. First, the unknown time harmonic electric field in the sphere is expanded in spherical vector waves. Secondly, the coefficients for these wave functions are found by a set of equations. The equations are found by multiplying the integral equation throughout by each wave function and integrating over the spherical conductor.Once the unknown coefficients have been determined, then the transient response may be found by taking the inverse Fourier transform. In carrying out the Fourier transform one learns that for most of the time range used in prospecting, only the lowest order vector wave function is significant. A study of the singularities of the spectrum of the transient shows that, for the time range considered, only a single branch cut is significant. There are no pole type responses. That is, the field does not decay exponentially. Previous studies of a sphere in free space reported only pole type responses. That is, at the later stages, the field decays exponentially. This study shows that, in order to model satisfactorily the effect of the host rock on transient electromagnetic fields, the sphere must be placed in layered ground.     

Steady-state harmonic response of a rigid plate bearing on a liquid-saturated poroelastic halfspace

Soil–structure interaction problems are typically modelled by assuming subgrade behaviour to be either elastic or viscoelastic. Herein, compliance functions that may be used to solve soil–structure interaction problems are evaluated by treating the subgrade as a liquid-saturated poroelastic material whose behaviour is governed by Biot's theory. The compliances are evaluated for the harmonic rocking and vertical motions of rigid permeable and impermeable plates bearing on a poroelastic halfspace. Comparisons are made with elastic solutions which assume the subgrade to be either completely drained or undrained. Also, solid and fluid contact stresses are reported for the poroelastic case and compared to the solid contact stresses for the elastic cases.     

柱面波在半空间中洞室周围的散射

采用一种间接边界积分方程法求解了柱面波在半空间中洞室周围的散射问题。通过边界条件的验算以及退化解答与精确解的比较,验证了本文方法的计算精度。文中主要分析了入射波频率、波源与洞室距离等参数对洞室附近地表位移响应和洞室动应力集中的影响,得出了一些有益的结论。     

Behavior of a seismically isolated bridge crossing a fault rupture zone

The effect of the fault rupture zone traversing a seismically isolated bridge is investigated utilizing a finite element model of a section of the Bolu Viaduct and a set of synthetic broadband strong ground motions simulated for the Bolu Viaduct site due to the 1999 Duzce earthquake. Both the original and a potential retrofit seismic isolation system designs are considered in the analyses. The results show double isolation system demands when fault crossing is considered, as compared to the case where fault crossing is ignored. The pier drift demands, however, remain comparable in both cases. Furthermore, the location of fault crossing along the bridge length, as well as the fault orientation with respect to the bridge longitudinal direction are shown to influence substantially the response of the seismically isolated bridge. Isolation system permanent displacements are greatly influenced by the restoring force capability of the isolation system when fault crossing effects in the excitations are ignored. In the case of fault crossing, the permanent displacements of the isolation system are dominated by the substantial permanent tectonic displacement along the fault trace which is imposed upon the structure. The results of this study contribute to developing a better understanding of how seismically isolated bridges respond when traversed by fault rupture zones. The lack of analyses and design guidelines for bridges crossing faults in international standards renders this study a useful reference for the profession.     

Response of a harbour opened to a sea of variable depth

Wave-induced oscillations in a circular harbour with protruding breakwaters and narrow mouth are analytically investigated by using a variational method. The effects of the bottom topography of the contiguous external sea are studied, especially as far as Helmholtz resonance is concerned; it has been found that the amplitude of the resonance peak is quite sensitive to the depth variation, while the related resonance wavenumber is more stable.     

Dynamic response of a piecewise circular tunnel embedded in a poroelastic medium

Recently, considerable efforts have been devoted to evaluation of seismic dynamic response of a circular tunnel. Conventional approaches have considered integral liners embedded in an elastic medium. In this study, we re-examine the problem with piecewise liners embedded in a porous medium. Surrounding saturated porous medium of tunnels is described by Biot's poroelastic theory, while the liner pieces and the connecting joints are treated as curved beams and characterized by curved beam theories. The scattered wave field in the porous medium is obtained by the wave function expansion method. The differential equations governing the vibration of a curved beam is discretized by the General Differential Quadrature (GDQ) method. The domain decomposition method is used to establish the global discrete dynamic equations for the piecewise tunnel. The surrounding soil and the tunnel are coupled together via the stress and the displacement continuation conditions which are implemented by the boundary collocation method. Numerical results demonstrate that the stiffness difference between the liner piece and the connecting joints has a considerable influence on the internal forces of the liner piece.     

Is a type of low frequency ULF magnetic disturbance a kind of earthquake precursors?

A type of relatively low frequency ULF magnetic disturbance has been generally observed by the magnetic induction-meter since it’s operation at Baijiatuan observatory in Beijing. As the amplitudes and frequencies of such disturbance signals change with time and are different from the disturbances produced by some man-made magnetic sources, therefore they are usually taken as a kind of earthquake precursors for ULF electro-magnetic emission. However, a comparative analysis with magnetic storms on the magnetogram obtained by variometerat the same station indicates that such signals always occur in the period of magnetic storm occurrence and so far we have not found the cases where such signals occur with no magnetic storms, therefore this kind of ULF magnetic disturbances should not be taken as a ULF earthquake precursors of the electromagnetic emission at present. The main features of such signals are as follows: the signals occur discontinuously during storms and the duration of each time section with such signals and the occurrence rates of the sections and the disturbance amplitudes are usually related to the types and intensities of storms. The wave form characteristics of the ULF disturbance are also related to the types of storms. Generally, the amplitudes and durations for SC storms are stronger and longer respectively than those for GC stroms, and if a storm is with largerK index, then relatively large amplitudes and higher rates and longer durations as well as variable frequencies will be observed andvice versa. Most of the start time and the time section with strongest disturbance recorded by the ULF unit and by the variometer are not consistent with each other, and the same one is only about 44%. The periods and intensities of such disturbance signals are in the ranges of few to several seconds and 0.04–8 nT respectively. The predominant frequency is about 0.06 Hz and certain energies are also distributed on the harmonic frequencies. Contribution No. 95A0063, Institute of Geophysics, SSB, China.     

Periodic response of a rigid block resting on a footing subjected to harmonic excitation

This study presents the dynamic behaviour of a rigid block which rests on a footing supported by a spring and a dashpot on a rigid base. The response of the rigid body is examined carefully when the base is excited by a harmonic force. It is found that a periodic motion appears in three different modes: stick-stick, stick-slip and slip-slip. The conditions that initiate the stick-stick and slip-slip modes are derived in explicit forms and the maximum sliding displacement is also obtained analytically. Useful dimensionless parameters are proposed for the presentation of the dynamic behaviour. The accuracy of results is confirmed by the response history computed by the Nigam-Jennings method.     

充液井中多极声源的辐射效率

利用反射声场探测井外地质构造的声波远探测方法已逐渐成为石油测井的一门重要应用技术.在远探测测井中声源常采用单极、偶极和四极等.为了考察各种声学辐射器的辐射性能,本文从辐射声场和井孔声场的能流密度出发,提出了一种利用辐射器向井外辐射的能量与沿井筒传播的能量比的大小来评价其辐射效率的方法,考察了不同声源激发的沿井传播的导波能流、地层辐射波能流及声源辐射效率随频率的变化规律.计算结果表明:不同声源的辐射效率和优势激发频段各不相同.单极声源在低频下的辐射效率很低,因为此时声源激发的能量几乎全部被斯通利波带走,相比之下,偶极声源在低频时的辐射效率远大于单极声源.本文的结果说明了偶极声源作为低频远探测声源要优于单极声源.     

Quasi-static deformation of a viscoelastic half-space by a displacement dislocation

The correspondence principle is used to get the Laplace transformed solution of the problem of the quasi-static deformation of a viscoelastic half-space by a shear displacement dislocation from the corresponding static elastic results. The transformed solution is inverted for the Voigt and the Maxwell viscoelastic models. It is shown that, for a vertical dip-slip fault, the surface displacements for the viscoelastic case are identical with the elastic displacements. In the case of a vertical strike-slip fault, detailed numerical results are obtained for both a point source and a finite rectangular source. It is found that the results for the viscoelastic models differ significantly from the corresponding elastic results.     

Nitrate as a tracer of groundwater flow in a fractured multilayered aquifer

Abstract

Knowledge of the processes that control nitrate migration and its geochemical evolution in the subsurface are fundamental for the regional management of polluted aquifers. In this paper, the spatial distribution and transient variations of nitrate concentrations, associated with manure fertilization, are used to depict hydrogeological dynamics within the sedimentary aquifer system of la Plana de Vic in the Osona region of Spain. Flow systems are identified from geological, hydraulic head, hydrochemical and isotopic data, and by considering nitrate itself as a tracer that indicates how flow paths are modified by human pressures. In this area, nitrates move through fractured aquitards in flows induced by groundwater pumping. Moreover, the lack of casing in the boreholes permits a mixing of groundwater from distinct layers inside the wells, which negates any benefits from the low-nitrate groundwater found in the deepest aquifer layers. Therefore, impacts on groundwater quality are related to intensive manure fertilization as well as to inadequate well construction and exploitation strategies.

Citation Menció, A., Mas-Pla, J., Otero, N. & Soler, A. (2011) Nitrate as a tracer of groundwater flow in a fractured multilayered aquifer. Hydrol. Sci. J. 56(1), 108–122.     

Application of a long range transport model to a mount Etna plume

A long range transport model and its application to an Etna plume are described. The model is a classical segmented plume lagrangian trajectory model. Firstly, air mass trajectories are computed by using the actual winds observed at the E.C.M.W.F. (Reading U.K.). The model then determines 5-day trajectories starting every 3 hours and made of 3-hour segments. Vertical movements of air parcels are taken into account by using the vertical component of the synoptic wind. Secondly, diffusion, SO₂ to SO₄ transformation and dry deposition are calculated for each trajectory segment. Sensitivity tests are presented and the results of the simulation for an experimental field period (21–25 september 1983) are examined.