Earthquake Wave Propagation Research Articles

ANALYSIS METHODS OF STOCHASTIC MODEL

The difficulty of modeling underground structures is a bottleneck in quantitatively studying earthquake phenomena. Stochastic modeling that accounts for the uncertainty of modeling is an alternative, and the authors have been developing two analysis methods for a stochastic model. This paper presents these methods in a unified manner, emphasizing the efficiency of numerical computation. The earthquake wave propagation and the surface earthquake fault formation are solved as examples, and the results are compared with observed data to examine the validity and limitation of the analysis methods of the stochastic model.

ANALYSIS METHODS OF STOCHASTIC MODEL:<br> APPLICATION TO STRONG MOTION AND FAULT PROBLEMS

The difficulty of modeling underground structures is a bottleneck in quantitatively studying earthquake phenomena. Stochastic modeling that accounts for the uncertainty of modeling is an alternative, and the authors have been developing two analysis methods for a stochastic model. This paper presents these methods in a unified manner, emphasizing the efficiency of numerical computation. The earthquake wave propagation and the surface earthquake fault formation are solved as examples, and the results are compared with observed data to examine the validity and limitation of the analysis methods of the stochastic model.

Reliability methods in earthquake engineering

AbstractMethods for seismic reliability assessment are selectively reviewed, on the basis of their capability of providing, in their present form or in their foreseable state of development, a realistic measure of the total risk. Realism starts with description of the seismic input, which must be related to the main parameters of earthquake generation and wave propagation. It then involves structural models, which must be sufficiently accurate to incorporate physical measures of structural performance, to describe the actual sources of uncertainty, and to detect all important modes of failure. Finally, realism implies a degree of complexity of the method and computation which are acceptable to advanced engineering practice. As regards the input, it is argued that properly selected recorded accelerograms (and, in the future, possibly, synthetic accelerograms) satisfy the requirement of realism to a much higher degree than random processes and samples. The consequence of the use of accelerograms is that, whatever risk evaluation method is adopted, simulation is always necessary, in order to take account of sample‐to‐sample variability. Three main categories of method are distinguished: simulation‐based, FORM‐based (First Order Reliability Methods), and response‐surface‐based, although the boundaries between the three are often blurred. A number of different proposals for implementation exist in the literature within each category. A subjective selection has been made of two or three of these proposals for each category, as a means of describing the general approach in more detail and for discussing their essential limitations. The opinion is offered that the subject area of seismic risk assessment still presents great opportunities for development, both of a fundamental and an applied nature. It is encouraging to note that large efforts are being made internationally on both aspects, and that the profession is showing increasing consciousness of the importance of the approach and a willingness to introduce it into common engineering practice.

Study on prediction method of sea-shock response of floating structure considering the characteristics of propagation of earthquake waves in water and seabed (First Report)

The purposes of present study are to develop the powerful numerical method for sea shock phenomenon and to clarify the characteristics of sea shock responses on very large floating structure.The present numerical method has been considered the characteristics of propagation earthquake waves in water and seabed. Numerical computations have been carried out very large floating structures in the cases of several seabed conditions.From the comparisons of computational results, it is that the numerical results by present method are greatly different of the results with the rigid seabed condition.

Two‐dimensional reconstruction of the surface ground motions of an earthquake: The September 21, 1999, Chi‐Chi, Taiwan earthquake

The observed time history and spatial dependence of the surface ground motions of the September 21, 1999, Chi‐Chi, Taiwan earthquake over the entire island are presented. For the first time, this report presents an analysis of time‐dependent spatial ground motions at both near‐source and local distances using strong motion records. The two‐dimensional ground motions of the Chi‐Chi earthquake were reconstructed from more than 400 free‐field strong motion records after being corrected for absolute times. The reconstructed seismic wavefields can be considered as a new type of observed data, named “3‐D seismograms” here. Results of this study offer some insight into the study of earthquake source and wave propagation based on 3‐D numerical modelling and greatly compliment our ability to distinguish wave generations due to sources and/or structures.

Domain Decomposition Based Parallel Contact Algorithm and Its Implementation to Explicit Finite Element Analysis Code.

Computer simulations are about to replace experiments in various fields related to dynamic problems, such as crashworthiness of vehicles, vibration of a nuclear reactor in earthquake and ultrasonic wave propagation in solid with cracks for nondestructive evaluation. For solving such large scale problems, the parallel processing has become a key technology. In this paper, a parallel contact algorithm suitable for a domain decomposition technique is proposed, and implemented on a dynamic finite element analysis code based on an explicit time integration scheme. Parallel efficiency of the code is tested through sample analyses on a PC cluster.

A simplified input output relation method using AR model for earthquake wave propagation analysis

This paper introduces a Simplified Input Output Relation Method (SIORM) using multiple-variable autoregression (AR) model which can be used to determine ground wave propagation properties. Using the AR model, a method is developed to establish the basis for the formulation of SIORM. The degree of accuracy of this method is evaluated. SIORM is applied to actual ground acceleration records taken at Minamisuna and Etchujima sites in Japan and its results are discussed in this paper.

A simplified input output relation method using AR model for earthquake wave propagation analysis

This paper introduces a Simplified Input Output Relation Method (SIORM) using multiple-variable autoregression (AR) model which can be used to determine ground wave propagation properties. Using the AR model, a method is developed to establish the basis for the formulation of SIORM. The degree of accuracy of this method is evaluated. SIORM is applied to actual ground acceleration records taken at Minamisuna and Etchujima sites in Japan and its results are discussed in this paper. © 1997 John Wiley & Sons, Ltd.

Reconnaissance report on highway damage from the 18 June 1994, Arthurs Pass earthquake

The magnitude M 6.5 earthquake on 18 June 1994 centred about 20 km southwest of Arthurs Pass, caused considerable damage to State Highway 73 through Arthurs Pass National Park, closing the highway for several days and restricting traffic for more than a week. The most serious damage occurred in the Upper Otira Gorge where a large (5-10,000 m3) rock slide covered the road and partially dammed the Otira River. Other damage affecting the highway consisted of debris and rockfalls, and slumping along the edge of poorly compacted fills. Bridges and other structures were not damaged.
 Damage to the highway appears to be associated with site specific factors rather than proximity to the epicentre. The pattern of ground damage may be due to the effects of topography on the propagation of earthquake waves, and variations in rock mass quality and destressing of valley slopes.

Stochastic Seismic Ground Motion Modelling With Imperfectly Stratified Earth Medium

Earthquake wave propagation in an imperfectly stratified linear elastic earth medium, generated by a buried seismic dislocation source, is investigated. Using a first order perturbation approach, it is shown that the total wave field may be obtained as a superposition of a mean wave field and a scattered wave field. Both the mean and the scattered wave fields exist in the same perfectly stratified earth medium, without the presence of the irregular interface. The mean wave field is associated with a buried seismic dislocation source, while the scattered wave field is associated with a set of fictitious discontinuity sources distributed on the fictitious mean interface, which has the same effect as the interface irregularities and can be obtained in terms of the mean wave field. The response in the mean wave field can be obtained using the finite integral transform approach. The response in the scattered wave field may be constructed by the fundamental solution with a sinusoidal interface, which may be obtained using the same approach as the mean wave field. With knowledge of the fundamental solution and its corresponding properties, the statistical properties of the ground motion with an imperfectly stratified earth medium may be evaluated. Finally, a numerical example is carried out for illustration purposes.

Earthquake wave propagation in layered media by boundary integral methods : Soil Dynam Earthq Engng V10, N3, April 1991, P130–140

Abstract The authors have previously presented work on the use of boundary methods to solve steady-state wave scattering problems in two-dimensional homogenous systems and on the use of these solutions with Fourier transforms to solve problems of transient input waves. This paper extends that work to nonhomogeneous systems. The methodology is now applicable to profiles with various material parameters in media bounded by irregularly shaped interfaces subjected to transient or periodic incident waves of any form. The profiles which can be solved are layers of finite extent, layers of infinite extent, cavities, inclusions of different materials, lenses, cases of three media and three interfaces meeting at a single point, and any combination thereof. The paper presents the basic equations of wave propagation in a single medium, the extension of these equations to multiple media, and the methodology of correcting for the truncation of the numerical portions of a problem. Using these techniques, several simple geometries are solved and the solutions are computed to closed-form solutions when available. Th comparisons are good and the value of correcting for the truncation is verified. The methodology is then applied to a test case of real data taken from real earthquake records, to wit: the response of the Santa Felicia earth dam to the San Fernando (1971) earthquake. The comparison is good in the time domain but in the frequency domain shows some inaccuracy at the higher frequencies. This loss of quality is attributed to the fact that a linear elastic system is not a good model for soil response. The final section an initial attempt to examine the effects of some simple damping schemes. Great improvement is shown in the attempt to reproduce numerically the response of the Santa Felicia earth dam.

Earthquake wave propagation in layered media by boundary integral methods

The authors have previously presented work on the use of boundary methods to solve steady-state wave scattering problems in two-dimensional homogenous systems and on the use of these solutions with Fourier transforms to solve problems of transient input waves. This paper extends that work to nonhomogeneous systems. The methodology is now applicable to profiles with various material parameters in media bounded by irregularly shaped interfaces subjected to transient or periodic incident waves of any form. The profiles which can be solved are layers of finite extent, layers of infinite extent, cavities, inclusions of different materials, lenses, cases of three media and three interfaces meeting at a single point, and any combination thereof. The paper presents the basic equations of wave propagation in a single medium, the extension of these equations to multiple media, and the methodology of correcting for the truncation of the numerical portions of a problem. Using these techniques, several simple geometries are solved and the solutions are computed to closed-form solutions when available. Th comparisons are good and the value of correcting for the truncation is verified. The methodology is then applied to a test case of real data taken from real earthquake records, to wit: the response of the Santa Felicia earth dam to the San Fernando (1971) earthquake. The comparison is good in the time domain but in the frequency domain shows some inaccuracy at the higher frequencies. This loss of quality is attributed to the fact that a linear elastic system is not a good model for soil response. The final section an initial attempt to examine the effects of some simple damping schemes. Great improvement is shown in the attempt to reproduce numerically the response of the Santa Felicia earth dam.

Propagation of Earthquake Waves in Buildings with Soft First Floor

Simplified response of buildings with a soft first floor and excited by propagating wave motion at the base are studied, so that the physical phenomena associated with phased input excitation can be characterized. Analytical solutions are obtained for two‐dimensional continuous building models, neglecting the soil‐structure interaction, and for monochromatic antiplane excitation. It is shown that the wave energy does not always propagate from the ground into the building, depending on the value of the horizontal phase velocity of the ground motion. There is a possibility that it propagates only into the “soft” first floor, which then acts as an “isolation layer” for the upper floors. However, this is at the expense of very large deformations of the columns of the first floor, that are not considered in the conventional analysis of buildings. Also, the out‐of‐phase motion of the base may excite torsional vibrations with large amplitudes. It is concluded that the design for P‐delta effects in the soft first...

Earthquake Ground Motions

In this review, we discuss some of the many phenomena that can determine the nature of strong ground motion. Some of these phenomena have been inferred from the study of existing ground-motion records, and others are inferred from theoretical models of earthquake sources and wave propagation.

Evaluation of deformation of tunnel structure due to Izu‐Oshima‐Kinkai earthquake of 1978

AbstractDue to the Izu‐Oshima‐Kinkai earthquake of 1978, the Inatori tunnel, a single‐track railway tunnel in Japan, was severely damaged. This damage was mainly caused by the main fault and a subsidiary fault which is estimated to have traversed the tunnel. The objective of this paper is to evaluate the performance of available mathematical models of earthquake wave propagation by taking advantage of the actual damage data of this tunnel. This paper has also the purpose of contributing to the earthquake‐resistant design procedure of the tunnel in the source region by estimating its deformation using the fault mechanical model. In this paper using a set of fault parameters previously proposed by seismologists for the Izu‐Oshima‐Kinkai earthquake, the longitudinal, transverse and vertical displacements of the tunnel axis are computed. These computed results are then compared with the surveyed residual deformation. For each of three deformation components a similar trend can be recognized, and the comparison indicates that a reasonably good correlation exists between these surveyed and computed displacements.

An earthquake engineering wave propagation model

A finite element model for the seismic behaviour of soils requires the definition of suitable boundary conditions to simulate the surrounding soil. These conditions are here analyzed theoretically under the only assumption that the boundary soil behaves elastically. Their application requires the definition of the wave direction. The one of impinging waves is known, being an input datum; the one of the outcoming waves is in general not known a priori. The amount of errors involved is discussed. Analogous problem was previously dealt with for sources of disturbances interiors to the represented portion of the space.

Some Problems on the Propagation of Earthquake Waves

Some Problems on the Propagation of Earthquake Waves

Societies and Academies

Societies and Academies

The propagation of earthquake waves

1. A complete understanding of the propagation of earthquake disturbances demands a solution of the problem of the vibrations of an elastic sphere in which the mutual gravitational attraction of the parts is taken into account, as well as the variation of the physical constants of the earth’s material with distance from the centre. The classical solution of Lamb applied only to a sphere in which gravitation is supposed negligible, and in which the physical constants have uniform values throughout. In a subsequent discussion of certain aspects of the general problem, I tried to take gravitation into account, but was only able to make progress by introducing the quite artificial assumption of a permanent field of force exactly annulling the gravitational field of the sphere in its undisturbed state. In a valuable critical note on this paper, the late Lord Rayleigh indicated a method which opened up possibilities of progress while avoiding this very artificial restriction. In the present note, I have availed myself of Lord Rayleigh’s suggestion, and have treated the problem in certain of its aspects which seem to have a direct seismological importance. A summary and discussion of results will be found at the end (§ 18). 2. We assume the earth to be spherical in shape and to be arranged in spherical layers, so that all the physical constants are functions of a single variable, r , the distance from the centre. In the absence of earthquake disturbances, the stress system at any point is assumed to reduce to a simple hydrostatic pressure, p . This will be connected with the density and the ρ gravitational potential V by the usual equations ∂ p /∂ x = ρ ∂V/∂ x , etc. in which p, ρ and V are functions of r only.

Societies and Academies

LONDON Royal Society, November 23.—Sir Charles Sherrington, president, in the chair.—T. E. Stanton: On the characteristics of cylindrical journal lubrication at high values of the eccentricity. The arc of contact of the film was limited in extent in the experiments and the intensity of pressure was considerably higher than in normal practice; the arcs of contact varied from 14 to 35 degrees and the maximum intensities of pressure from 14 to 35 tons per sq. inch. In all the cases observed, the pressure distribution in the film has been in accordance with the hydrodynamical theory of Osborne Reynolds. By means of a careful determination of the pressure distribution in the film, and a measurement of the radius difference of bearing and journal, sufficient data have been obtained to calculate the viscosity of the lubricant and the attitude and eccentricity of the bearing. The values of the viscosity of the lubricant so calculated were in good agreement with those determined in a viscometer, and it was concluded that the calculated values of the eccentricity were trustworthy. In the case of a journal 2.5 cm. diameter, the least distance apart of the surfaces was found to vary from 0.0024 to 0-0024 mm.—J. H. Jeans: The propagation of earthquake waves. Earthquake waves are regarded as being compounded of a number of free vibrations of a non-homogeneous gravitating earth. In 1885, Lord Rayleigh discussed a certain type of surface waves which would travel over the earth's surface with a velocity of about 0.92√(μ/p). It is now shown that there are additional, and far more numerous, surface waves which travel with velocities √(μ/p) and √(λ+2μ)/p). If such waves are generated by an earthquake at any point close to the earth's surface, they will refocus themselves upon this point after intervals which are integral multiples of 2π√(φ/(λ+2μ)) and 2√(φ/(λ + 2μ)), the numerical values of these quantities being about 223 and 126 minutes respectively. In 1917, two series of earthquakes, each originating from the same centre, had their times given approximately by formulæ of the type