Shock and Vibration

Volume 2016 (2016), Article ID 6841836, 8 pages

http://dx.doi.org/10.1155/2016/6841836

## Seismic Damage Analysis of Concrete Gravity Dam Based on Wavelet Transform

^{1}School of Civil Engineering, Nanjing Forestry University, Nanjing 210037, China^{2}College of Mechanics and Materials, Hohai University, Nanjing 210098, China

Received 6 October 2015; Revised 20 January 2016; Accepted 7 February 2016

Academic Editor: Mario Terzo

Copyright © 2016 Dunben Sun and Qingwen Ren. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The key to the dam damage assessment is analyzing the remaining seismic carrying capacity after an earthquake occurs. In this paper, taking Koyna concrete gravity dam as the object of study, the dynamic response and damage distribution of the dam are obtained based on the concrete damage plastic constitutive model. By using time-frequency localization performance of wavelet transform, the distribution characteristics of wavelet energy for gravity dam dynamic response signal are revealed under the action of different amplitude earthquakes. It is concluded by numerical study that the wavelet energy is concentrated in low-frequency range with the improving of seismic amplitude. The ultimate peak seismic acceleration is obtained according to the concentration degree of low-frequency energy. The earthquake damage of the dam under the moderate-intensity earthquake is simulated and its residual seismic bearing capacity is further analyzed. The new global damage index of the dam is proposed and the overall damage degree of the dam can be distinguished using defined formula under given earthquake actions. The seismic bearing capacity of the intact Koyna dam is 591 gal considering the dam-water interaction and its residual seismic bearing capacity after simulating earthquake can be calculated.

#### 1. Introduction

Under earthquakes with the intensity greater than moderate level, the concrete dam may crack and its strength as well as stiffness will decrease. The continuum damage mechanics is an effective way to accurately model the degradation in the mechanical properties of concrete dam. Lee and Fenves [1, 2] proposed the plastic damage constitutive model of concrete and simulated failure processes of concrete structures as well as the Koyna dam under earthquake and acquired the consistent results with the actual earthquake damage. A lot of results have been achieved in analyzing the damage of concrete dams under the action of earthquake [3–5], in which the plastic damage models were used. To assess the structural damage state simulated using numerical methods, many kinds of damage indexes have been proposed [6–9]. Usually the damage index uses a set of structural response parameters that can be used to evaluate the damage to structures. These response parameters, which are generally used for damage assessment of buildings, can be portrayed as deformations, stiffness, energy dissipations, or their combination. For damage assessment of concrete dam, there are limited works in the field of global damage indexes [10, 11]. However, these indexes cannot reflect the residual bearing capacity of the structure.

Structural damage usually causes a reduction in the stiffness of structure and will directly influence the dynamic response of the structure, in which the frequency components of vibration signal change with the stiffness reduction. Wavelet analysis has an excellent localized performance in time-frequency domain, which may be used to analyze a signal in an arbitrary resolution in time-frequency domain. Wavelet analysis is generally utilized in damage detection of structures [12–15] but is rarely used in seismic response analysis of structure [16]. So far, almost no article has been found to research the dynamic loading capacity of concrete dam by using wavelet analysis theory.

In this paper, the damage distribution characteristics of an intact concrete gravity dam, the Koyna dam, are analyzed under the action of the same earthquake with different amplitudes, and the corresponding vibration signals of dam crest are extracted. By means of wavelet analysis, the energy change rule of vibration signals in low-frequency band is obtained with the improvement of earthquake amplitudes, from which the seismic bearing capacity of the intact dam is acquired. Subsequently, the damage distribution of the dam is simulated under moderate-intensity earthquakes and the residual seismic bearing capacity of an earthquake damaged dam is further calculated. The global damage index of the dam is proposed and the overall seismic damage degree of the dam is calculated.

#### 2. Wavelet Analysis Theory

##### 2.1. The Concept of Wavelet Transforms

Supposing , is square-integrable real-valued space, the continuous wavelet transform is defined as follows: where is wavelet mother function or basic wavelet, is scale factor, and is translation factor, and the value of can be positive or negative.

For the structures engineering, discrete time series signals are usually attained. To facilitate the application, it is necessary to use the discrete wavelet transform. For continuous wavelet , scale factor and translation factor can be expressed in discrete form by setting , , , is integer domain. The discrete wavelet base function can be expressed as The discrete wavelet transform is expressed as

##### 2.2. The Concept of Relative Wavelet Energy

Wavelet transform (WT) is a time-frequency transform operation, which converts a time-domain signal into the time-scale plane according to (1). It provides us with a tool to inspect the relatively narrow frequency bands over a relatively short time window. The WT algorithm can be expressed by the tower-style decomposition as Figure 1. The analysis phase of the wavelet transform decomposes a signal into frequency bands that are localized in time and scale. The window size (sale) used in wavelet transform is chosen to be shot at high frequencies and long at low frequencies, providing good time resolution at high-frequency and good frequency resolution at low frequencies. Because of this localization property, wavelets are very good in isolating singularities and irregular structures in signals.