地下衬砌洞室对Rayleigh波的放大作用

本文利用波函数展开法,给出了半空间中圆形衬砌洞室引起的Rayle igh波散射问题的一个级数解,并通过对求解技术的改进,获得了高频解答。论文通过入射波长、洞室直径、衬砌刚度和埋置深度等参数分析,研究了地下洞室对Rayle igh波的放大作用。数值结果表明,地下洞室情况下地表位移幅值可以达到无洞室情况的2.6倍以上;多数情况下,柔性衬砌洞室情况地表位移幅值最大,无衬砌洞室情况次之,刚性衬砌情况最小。     

On the propagation of magneto-elastic waves

Summary The electromagnetic equations of Maxwell, equations of elasticity have been used to solve the problem of propagation of waves for a one-dimensional magneto-elastic problem. The frequency equation has also been set forth.     

地震作用下大型地下洞室群应力传播特征研究

选用攀枝花-会理地震波,通过基线校正和高频滤波,作为实际地震动输入,利用FLAC3D软件对某水电站大型地下洞室群进行了地震作用下应力传播特性的研究。数值分析结果表明,洞室群周围应力时程的变化趋势与输入加速度时程的变化趋势相似,但由于地震波的传播需要一定的时间,因此存在一定的滞后效应。洞室边墙出现了一定面积的拉应力区,随着输入加速度的增大,拉应力区的范围有所扩展,但是扩展的范围不大。所得结果对大型地下洞室群地震动传播特征问题的研究具有一定的参考意义。     

On the propagation of topographically trapped waves

Abstract

In the context of ageostrophic theory in a homogeneous ocean, a nondimensional number is determined which corresponds to the Ursell number for long gravity waves. It is defined as Q = NL ²/h ³, where N is the amplitude of the wave travelling along the long length-scale direction, L is its length and h (which for gravity waves is the water depth) is given by h=(l ⁴ f ²/g)^1/3. where l is the short length-scale, f the Coriolis parameter and g the acceleration due to gravity. The physical meaning of Q is as follows: if Q? O(1) the free evolution of the wave is linear and weakly dispersive, if Q = O(1) nonlinear and dispersive effects balance out and finally if Q ?O(1) the evolution is nonlinear and non-dispersive. Expressions for the time scales for the development of dispersive and nonlinear effects are also determined. These results apply to topographically trapped waves, namely barotropic continental shelf and double Kelvin waves travelling along a rectilinear topographic variation.     

On the generation of capillary-gravity waves due to two-dimensional sources

Summary With the aid of the generalized function method, a study is made of the linearized theory of transient development of capillary-gravity waves in an inviscid, incompressible and homogeneous liquid of finite and infinite depth due to an arbitrary oscillating source situated at a finite depth below the undisturbed free surface of the liquid. The initial value problem is solved by using Laplace-Fourier transforms combined with asymptotic methods. The asymptotic solution is found to consist of the steady state and the transient components which are independently modified by surface tension. The latter decays more rapidly as timet due to the presence of surface tension than in the case where surface tension is neglected. It is predicted that the principal effect of surface tension is to increase both the phase and group velocity of the waves and make the energy more readily available among the rapidly travelling progressive surface waves. In addition to the effects of surface tension on the physical properties of the wave motions, our method of solution provides an interesting illustration of the applicability of generalized functions in water wave phenomena.     

Note on the propagation of waves from a spherical cavity in an infinite solid

Summary The present note, as its title implies, is concerned with the investigation of disturbances in an infinite elastic medium containing an initial magnetic field in the axial direction. The equations ofMaxwell, those of elasticity have been effectively made use of to solve the problem.     

On propagation of love-type waves on a spherical model with rigidity and density both varying exponentially with the radial distance

Summary The propagation of Love type waves on a spherical model' in the mantle of which the rigidity and density vary exponentially with the radial distance while in the core they remain constant — has been investigated. The frequency equation that has been worked out has been examined in detail for the existence of root in the particular cases when they involve Bessel Functions of smallest and largest orders.     

On the disturbance due to a spherical distortional pulse in an elastic medium

Summary Theoretical expressions are derived for the displacement, velocity and stress in the time domain induced by an axially symmetric shearing stress applied at the inner surface of a spherical cavity in a hornogeneous, isotropic, elastic medium of infinite extent. Theoretical seismograms are computed for a step source and for three sources with exponential decay in time. A satisfactory time-dependence of the source can be obtained by combining the step source with one or more exponentially decaying sources.     

A series solution for surface motion ampli-fication due to underground group cavities: Incident P waves

Introduction In recent years some big cities in China commonly build subways in central urban areas to improve crowded surface transportation, and the subways usually are large-scale group cavities composed by two parallel cavities. Construction of large-scale group cavities will certainly affect the design ground motion near the cavities, and further affect seismic safety of the existing build-ings nearby. So it is of significance to estimate this effect on seismic design of the buildings. H…     

A series solution for surface motion amplification due to underground twin tunnels: incident SV waves

A series solution of displacement response of the ground surface in the presence of underground twin tunnels subjectcd to excitation of incident plane SV waves is derived by using Fourier-Bessel series expansion method. The numerical parametric study shows that underground twin tunnels significantly amplify the nearby surface ground motion. It is suggested that the effect of subways on ground motion should be considered when the subways are planned and designed.     

On the disturbances in a viscoelastic medium due to blast inside a spherical cavity

Summary In this paper we have considered the disturbances in a viscoelastic medium due to a blast of intensityP and durationT sec inside a spherical cavity.     

On the random error propagation in relatively large networks

Summary A relatively large network is one which covers a large area whereas each observation only involves points within a small local area. For such networks an efficient method is described to establish the lower bounds for the spectral norm of the covariance matrix of the rigorously adjusted co-ordinates. The method utilizes a classification of observations and networks which is thought to be interesting in itself. The weakness of pure angular networks is revealed to stem from the fact that such networks offer little resistance to conformal distortions of the network. A numerical example is given. Asymptotic results for block-type networks are obtained which apply among others to photogrammetric bundle block networks.     

On the frequency equation for love waves due to abrupt thickening of the crustal layer

Summary The effect of thickening of the crustal layer in mountainous region on the dispersion curve of Love waves has been studied. Perturbation method has been applied to obtain the modified frequency equation for Love waves through the surface of separation between a semi-infinite material and a layer the thickness of which abruptly increases throughout a certain length of the path. The effect is to decrease the phase velocity of the waves particularly in the low period range. It has been pointed out that by proper study, the amount of thickening may be obtained.     

Note on the propagation of waves in infinite spherically-aeolotropic medium produced by a blast in a spherical cavity

Summary By using the Laplace transform method, solution has been obtained for the elastodynamic problem due to blast pulse on the inner surface of a spherical cavity in an infinite spherically aeolotropic elastic solid. Both types of blast producing radial and rotational waves have been considered.     

On the propagation of Rayleigh waves in three dimensions in alluvial soils

Summary The propagation of Rayleigh waves in three dimensions in alluvial soils which do not behave like ordinary isotropic elastic solids have been discussed in this paper. The frequency equation has been solved for different soil constants.     

Modeling undertow due to random waves

A numerical model of undertow due to random waves is developed. The model includes three sub-models: (i) a model for multi-directional and multi-frequency random wave transformation, (ii) a surface roller evolution model, and (iii) a model for calculating the vertical distribution and the mean value of the undertow velocity. The calculation of wave trough level is performed based on a theory for the wave asymmetry. The model was successfully validated against small- and large-scale laboratory experiments. Thus, the model is expected to provide reliable input for the modeling of sediment transport and morphological change due to waves and currents.     

On the reynolds stress and lateral eddy viscosity due to transient oceanic Rossby waves

Summary From numerical solutions of a wind-driven homogeneous ocean model, anegative lateral eddy viscosity of the order 10⁴ cm² sec^–1 is inferred from the large-scale time-dependent currents in the interior of an enclosed shallow basin. The transient Rossby waves in this region produce a systematic convergence of eddy momentum at the latitude of the maximum average eastward current, and thus effect a transfer of zonal momentum from the large-scale eddies to the mean flow. In this sense they are analogous to the Rossby waves in the atmospheric general circulation, and it is speculated that such waves may help to maintain the mean zonal ocean currents. Although this negative viscosity induced by the large-scale transients is relatively small compared with the prescribed lateral viscosity of 10⁸ cm² sec^–1 and should be given a quite different physical interpretation, it is evidently an important viscous effect for the mean flow in the interior of the basin. The prescribed viscosity, on the other hand, is effective in controlling the model's simulated sub-grid scale dissipation, which occurs almost entirely in the nearby steady boundary currents.