1、Dynamic response of gravity dam model with crack anddamage detectionWANG ShanShan it is very dangerous if the crack slopes downstream. The whole failure processes of the two possible failure modes of the cracked dam, i.e., overturning or sliding of the top separated block during earthquakesunder abn
2、ormal conditions, were also simulated. Some important phenomena such as the bounce of the top block and the relationship of the sliding and overturning were examined in detail. Bayraktar et al. used the Lagrangian approach to investigate the effect of base-rock characteristicson the stochastic dynam
3、ic response of dam-reservoir-foundation system subjected to different earthquake input mechanisms. Calayir et al. investigated the earthquake damage response of the concrete gravity dams. Zhu et al. studied the seismic behavior of concrete gravity dams with cracks that penetrated the monoliths. Arab
4、shahi et al. studied various possibilities of natural isolation occurring along the dam-foundation interface during an earthquake in order to evaluate the seismic response of an existing gravity dam. Long et al. conducted comparative studies to investigate the seismic response of a 160 m high gravit
5、y dam with and without reinforcement. Because many gravity dams are being constructed in the high seismic risk zones, the earthquake is a challenge to these dams. Therefore, in these previous works, most of the studies concentrated onthe safety of dam subjected to earthquake, and provide relatively
6、little information on vibration response of structure with crack. Few works focused on variation of structural dynamic behavior brought by structural damage. Many gravity dam structures, exposed to various external loadsduring their lifetime, have suffered damage and deterioration such as crack. Van
7、landuit et al. pointed out that damage in the structures alters the structural dynamic properties and response, such as stiffness, mass, damping, natural frequency, mode shape, vibration signal response, etc.Damage can seriously affect structural performance and may eventually lead to catastrophic f
8、ailure. Thus, maintaining safety and integrity of the structures and avoiding loss of human life due to the catastrophic failure of undetected damage structures require a better understanding of relationship between crack and structural dynamic response. In this paper, in order to study the dynamic
9、behavior of gravity dam with damage, the sweep vibration responses of the gravity dam with and without damage are investigated. Due to earthquakes or other reasons, gravity dams normally have damage such as cracks in practical service. The assessment of the safety of gravity dam with crack is very i
10、mportant in many engineering applications. In this case, the structural damage detection method for the gravity dam with crack plays an important role in analyzing the safety of the structure. Significant research has been conducted in the area of dynamic response-based damage detection techniques.
11、Some studies questioned the suitability of modal data for damage detection, arguing that the modal information was a reflection of global system properties while damage was a local phenomenon. For example, Todorovska et al. illustrated that most of the structural health- monitoring methods for civil
12、 engineering structures were physically based on detecting changes in the modal parameters of the structure, which were global properties, depending on the overall stiffness of the structure. Hence, they changed little when the damage was localized, and they were also sensitive to environmental infl
13、uences (e.g., temperature)and changes in the boundary conditions (e.g., soil-foundation system), which were difficult to separate and might produce similar effects as damage on the record response. Wang et al. presented a new structural damage detection method called the local damage factor (LDF), w
14、hichwas capable of determining the presence, severity, and location of a structural local damage at the same time. By including the dynamic information of the local intact structure in the LDF method, the influence of structural nonlinearity, imperfection, and system noise were considered, so that t
15、he accuracy of damage detection was improved. The experimental results demonstrated that the proposed local damage factor technique could be efficiently used in local damage detection and structural health monitoring of structures. Because the weight and volume of gravity dam are very huge, it is di
16、fficult to excite or vibrate the structure. In recent years, there has been a growing interest in the damagedetection in structures subject to base excitation 11. Besides evaluating the dynamic response of the gravity dams subjected to the base excitation, the other goal of model experiment of gravi
17、ty dam is to test the efficiency of local damage factor based on base excitation for the sake of damage detection of gravity dam.2 Dynamic response of gravity dam model withcrack2.1 Theoretical backgroundThe equations of motion of a structure with N degrees of freedom and viscous damping coefficient
18、s can be expressed as ; (1)tftxKtDtM/xwhere M, D, and K represent the nn mass, damping, and stiffness matrices, respectively. 、 and x are the acceleration, velocity, and /displacement vectors, respectively.f(t) is the time-dependent applied force vector. For a harmonic input, the external force and
19、displacement can beexpressed as； (2)tjeFtf； (3)XxSubstituting eqs. (2) and (3) into eq. (1) yields；(4)tjtjeFeXKDjM2From the above equation, the frequency response functionmatrix is defined asH； (5)12jThen, eq. (4) can be expressed as； (6)FXDamage in the structure alters the structural parameters. As
20、suming that damage in the structure usually causes a change in the mass M , damping D and stiffness K of the intact structure, respectively we have：； (7)Md； (8)； (9)KdIn many studies, the proportional viscous damping is used for dynamic analysis, and it is expressed as：； (10)KcMKccDddd 212121where c
21、1 and c2 are constants.From eqs. (5), (7), (9) and (10), the frequency response function matrix of the structure with damage dHis obtained as：； (11)12 ddd KDjMHThen, the vibration response of the structure with damage can be expressed as：(12)FXddThese equations also illustrate that there is a close
22、relation between the structural damage and dynamic behavior.2.2 Experimental procedureThe objective of the experimental study was to validate the variety of dynamic responses between the intact structure and damaged structure. The number 5 section model of the Jiananqiao gravity dam was considered,
23、and the test specimen is shown in Figure 1. This section of the Jiananqiao gravity dam has the dimensions of 112.0m86.7m30.0m, and the scale of the model is 1: 200. The model is made of gypsum. Six accelerators were used as the transducers to acquire the structural dynamic responses. A conceptual sk
24、etch of the location of transducers is shown in Figure 2. The structural damage on the structure was simulatedby saw-cutting a crack with a 20 mm depth on the top part of the model (see Figure 3). The excitation equipment was an electric-magnetic vibration system controlled by a COMET shaker control
25、 system. The data acquisition and analysis were performed using a dynamic analyzer with a parallel multi-channel function. In order to validate the relationship between the damage and structural dynamic behavior accurately, the dynamic responses of structure with and without damage were measured usi
26、ng the same excitation level.Figure 1 Test specimen.Figure 2 Arrangement of transducersFigure 3 Crack on the structure2.3 Experimental results and discussionThe test was conducted by vibrations of the shaking table along the selected horizontal direction (see Figure 1). The excitation force was intr
27、oduced as a sine sweep with a frequency bandwidth between 130 and 170 Hz and a constant acceleration level between 5 and 10 m/s2. The typical amplitude vs. time histories of the acceleration transducers for the dynamic responses of structures with and without crack were plotted in Figures 4 and 5, r
28、espectively. According to the amplitude vs. time histories of the acceleration transducers, the peak-peak values of structural dynamic responses were obtained and summarized in Table 1 and Figure 6 for the constant exciting acceleration level of 5 m/s2 (Case A). Similarly, the peak-peak values of st
29、ructural dynamic responses were also obtained and summarized in Table 2 and Figure 7 for the constant exciting acceleration level of 10 m/s2 (Case B). Table 1 and Figure 6 demonstrate that the peak-peak acceleration responses all increase for the structure with crack for Case A. The maximum peak-pea
30、k acceleration response difference between the intact and damaged structures is 29.1%. As shown in Table 2 and Figure 7, the values of peak-peak acceleration responses have a similar trend for Case B, and the maximum peak-peak acceleration response difference between the intact and damaged structure
31、s is 24.8%. Figure 4 Typical acceleration time history for intact structureFigure 5 Typical acceleration time history for damage structureTable 1 The peak-peak values of structural dynamic responses (m/s2)2 forCase ANumber of testing point1 2 3 4 5 6Intact structure 91.6 43.6 67.1 90.6 109.7 127.3Da
32、maged structure118.3 47.8 72.4 96.5 116.3 134.1Figure 6 Peak-peak responses for Case A.Table 2 The peak-peak values of structural dynamic responses (m/s2)2 forCase BNumber oftesting point1 2 3 4 5 6Intact structure 178.0 85.9 128.7 167.5 201.3 231.1Damaged structure222.1 89.0 133.4 174.0 210.3 241.0
33、Figure 7 Peak-peak responses for Case B3 Damage detection of gravity dam3.1 Theoretical backgroundDamage in a structure alters its dynamic characteristics. The nonlinear response feature can be used as an indicator of structural damage. In a dynamic structural system, x(t) is defined as one random v
34、ibration signal in the entire structure and y(t) is the other random vibration signal in thelocal structure or component of a structure. All the random processes considered are stationary and erratic. or expresses the auto-xSyspectral density, and denotes the cross-spectral density. Then, a xySdamag
35、e indicator, the local damage factor (LDF) is defined as ：(13)ydxyx SSLDF)(2/where , 、 and are the auto-spectral densities and cross-spectral xS/y/xyS/density of the intact structure, respectively, while 、 ydSand xyd are xthe auto-spectral densities and cross-spectral density of the damaged structur
36、e, respectively. If the damage is present in the structure, it changes the value of LDF. The LDF value is used to determine the presence, severity and location of structural damage. The influence of structural nonlinearity and system noise are included in the LDF method, so that the accuracy of dama
37、ge detection can be improved.3.2 Experimental procedureThe objective of the experimental study was to demonstrate the effectiveness of the local damage factor (LDF) method in gravity dam damage detection. The same model and structural damage in the above dynamic response study was considered in this
38、 study, as shown in Figure 1. The direction of excitation force as well as the location of transducersmeasuring the vibration responses wer also shown in Figure 2. The excitation force was introduced as random vibration with bandwidth between 100 and 300 Hz and a constant 0.1 (m/s2)2/Hz acceleration
39、 PSD level. In this study, two cases were experimentally investigated: (C) intact (undamaged); (D) with a 20 mm deep crack. In this experiment, the base excitation was used as the vibration signal in the entire structure.3.3 Experimental damage detection results and discussionIn Figures 8 and 9, the
40、 typical amplitude/time histories of the base excitation and structural response are plotted. For each case, by using the vibration data received by these two transducers, LDFs were calculated based on eq. (13). The LDF values of the two cases (Cases C and D) are shown in Figures 10 and 11. As expec
41、ted, the LDF value of the intact structure (Case C) in Figure 10 is equal to 0, since there is no damage in the structure and the nonlinear severity effects of structure itself (e.g., imperfection) and system noise are eliminated. The LDF distribution of the 20 mm deep crack (Case D) is given in Fig
42、ure 11, and the maximum value of LDF is about 10%; it took place at the frequency of 127.9 Hz which is a little smaller that the first natural frequency of the intact structure (Case C). The reduction of the first natural frequency in the structure with the 20 mm deep crack is due to the introductio
43、n of damage. Hence, the LDF method can be used a damage index and is capable of evaluating both the presence and relative severity of gravity dam damage.4 ConclusionsThe varieties of dynamic responses of the intact gravity dam and gravity dam with crack were studied in this paper. The experiment of
44、gravity dam model was investigated, and both the intact and damage dynamic responses were evaluated. The test conducted by the excitation force was introduced as a sine sweep with a frequency bandwidth between 130 and 170 Hz and a constant acceleration level between 5and 10 m/s2. The experimental re
45、sults showed that the peak-peak acceleration responses all increase for the structure has a crack. The same model and structural damage used in dynamic response study was considered in the study of gravity dam damage detection. Excitation force was introduced as random vibration with bandwidth betwe
46、en 100 and 300 Hz and a constant 0.1 (m/s2)2/Hz acceleration PSD level. In the experiment, the base excitation was used as vibration signal in the entire structure. Based on the experimental observation in this study, it is concluded that the nonlinear response feature can be used as an indicator of
47、 structural damage. The LDF method can be used as damage index and is capable of evaluating both the presence and relative severity of structural damage. Furthermore, the LDF method can be used as a viable condition assessment and damage identification technique to detect and quantify the damage in the gravity dam.
