Ruichong Zhang

Modeling, synthetics and engineering applications of strong earthquake wave motion

State of the art in modeling, synthetics, statistical estimation, and engineering applications of strong ground motion is reported in this paper. In particular, models for earthquake wave motion are presented, in which uncertainties both in the earth medium and the seismic source are taken into consideration. These models can be used to synthesize realistic strong earthquake ground motion, specifically near-field ground motion which is quite often not well recorded in real earthquakes. Statistical estimation techniques are also presented so that the characteristics of spatially-correlated earthquake motion can be captured and consequently used in investigating the seismic response of such large scale structures as pipelines and long-span bridges. Finally, applications of synthesized strong ground motion in a variety of engineering fields are provided. Numerical examples are shown for illustration.

Seismic Waves in a Laterally Inhomogeneous Layered Medium, Part I: Theory

Seismic waves in a layered half-space with lateral inhomogeneities, generated by a buried seismic dislocation source, are investigated in these two consecutive papers. In the first paper, the problem is formulated and a corresponding approach to solve the problem is provided. Specifically, the elastic parameters in the laterally inhomogeneous layer, such as P and S wave speeds and density, are separated by the mean and the deviation parts. The mean part is constant while the deviation part, which is much smaller compared to the mean part, is a function of lateral coordinates. Using the first-order perturbation approach, it is shown that the total wave field may be obtained as a superposition of the mean wave field and the scattered wave field. The mean wave field is obtainable as a response solution for a perfectly layered half-space (without lateral inhomogeneities) subjected to a buried seismic dislocation source. The scattered wave field is obtained as a response solution for the same layered half-space as used in the mean wave field, but is subjected to the equivalent fictitious distributed body forces that mathematically replace the lateral inhomogeneities. These fictitious body forces have the same effects as the existence of lateral inhomogeneities and can be evaluated as a function of the inhomogeneity parameters and the mean wave field. The explicit expressions for the responses in both the mean and the scattered wave fields are derived with the aid of the integral transform approach and wave propagation analysis.

Seismic Waves in a Laterally Inhomogeneous Layered Medium, Part II: Analysis

Seismic wave scattering representation for the layered half-space with lateral inhomogeneities subjected to a seismic dislocation source has been formulated in the companion paper with the use of first-order perturbation (Born-type approximation) technique. The total wave field is obtained as a superposition of the mean and the scattered wave fields, which are generated, respectively, by a series of double couples of body forces equivalent to the seismic dislocation source and by fictitious body forces equivalent to the existence of the lateral inhomogeneities in the layered half-space. The responses in both the mean and the scattered wave fields are found with the aid of an integral transform technique and wave propagation analysis. The characteristics of the scattered waves and their effects on the mean waves or corresponding induced ground and/or underground mean responses are investigated in this paper. In particular, coupling phenomena between P-SV and SH waves and wave number shifting effects between the mean and the scattered wave responses are presented in detail. With the lateral inhomogeneities being assumed as a homogeneous random field, a qualitative analysis is provided for estimating the effects of the lateral inhomogeneities on the ground motion, which is related to a fundamental issue: whether a real earth medium can or cannot be approximately considered as a laterally homogeneous layer. The effects of the lateral inhomogeneities on the ground motion time history are also presented as a quantitative analysis. Finally, a numerical example is carried out for illustration purposes.

Synthesis of Acoustic-Emission Wave Propagation in Multi-Layer Media

This paper presents synthesis of acoustic-emission (AE) wave propagation in multi-layer materials and simulation of AE wave responses at free surface. In particular, the AE source is modelled as an arbitrary-orientation dislocation over an inclined-to-surface fault within one layer or at the layer-to-layer interface, while the materials are assumed as multi-layer media, each of which is homogeneous, isotropic and linearly elastic. With the use of the integral transformation approach, the three-dimensional wave propagation in the materials is solved in transformed or frequency-wavenumber domain. Subsequently, a closed-form solution for wave responses at free surface is found, which can then be converted in time-space domain. Numerical examples are finally provided for illustration.

Acoustic-Emission Wave Response to a Dislocation Source in Layered Media

This paper presents synthesis of acoustic-emission (AE) wave propagation in multi-layer materials and simulation of AE wave responses at free surface. In particular, the AE source is modelled as an arbitrary-orientation dislocation over an inclined-to-surface fault within one layer or at the layer-to-layer interface, while the materials are assumed as multi-layer media, each of which is homogeneous, isotropic and linearly elastic. With the use of the integral transformation approach, the three-dimensional wave propagation in the materials is solved in transformed or frequency-wavenumber domain. Subsequently, a closed-form solution for wave responses at free surface is found, which can then be converted in time-space domain. Numerical examples are finally provided for illustration.

RE-EXAMINATION OF THICKNESS-RESONANCE- FREQUENCY FORMULA FOR STRUCTURAL INTEGRITY APPRAISAL AND DAMAGE DIAGNOSIS

This study examines rationale of correction factor β in the formula of thickness resonant frequency, fundamental to the thickness estimation of impact-echo (IE) approach in nondestructive testing (NDT) for integrity appraisal and damage diagnosis of infrastructure systems. It shows the role of the factor in the formula from the perspective of testing equipment setup, wave propagation, and resonant frequency identification, much broader than what was first introduced empirically for shape correction of a structure under test. Emphasis is laid in wave-based interpretation of resonant frequency, typically obtained from traditional fast Fourier transform (FFT) data analysis of IE recordings. Since the FFT data analysis provides average, not true, characteristic of resonant frequency shown in the nonstationary IE recordings, it typically distorts the thickness estimation from the formula if the correction factor is not used. An adaptive time-frequency data analysis termed Hilbert–Huang transform (HHT) is then introduced to overcome the shortage of FFT analysis in identifying the resonant frequency from noise-added IE recordings. With FFT and HHT analyses of five data sets of sample IE recordings from sound and damaged concrete structures and comparison with referenced ones, this study reveals that the proposed IE approach with HHT data analysis not only eliminates the subjective use of correction factor in the formula, but it also improves greatly the accuracy in the thickness estimation.

MODAL PARAMETER IDENTIFICATION OF TSING MA BRIDGE DURING TYPHOON VICTOR: EMD-HT APPROACH

Publisher Summary There are several methods available for identifying modal parameters of a civil structure from its field measurement data. This chapter identifies the modal parameters of the Tsing Ma Bridge (TMB) from the bridge responses measured during Typhoon Victor using the newly-emerged empirical mode decomposition (EMD) method in conjunction with the Hilbert-transform (HT) technique. In the chapter, natural frequencies and modal damping ratios identified by the EMD-HT approach are first compared with those obtained by the traditional fast Fourier transform (FFT) method. The EMD-HT approach is then used to examine bridge modal parameters identified from different sensors at different locations. Finally, the EMD-HT approach is used to investigate variations of natural frequency and total modal damping ratio of the Bridge with vibration amplitude and mean wind speed. It is demonstrated that the EMD-HT approach is applicable to modal parameter identification of large civil structures using field measurement data, and the EMD-HT approach is better than the FFT method. The results show that the EMD-HT approach and the FFT method produce almost the same natural frequencies but the FFT method gave higher modal damping ratios than the EMD-HT approach in most cases. The consistent modal parameters are identified from different sensors at different locations. The results also demonstrate that the natural frequencies of the bridge decrease slightly with the increase of mean wind speed and vibration amplitude. The total damping ratios, however, exhibits an increasing trend with the increase of vibration amplitude and mean wind speed.