# Damage Evolution Analysis in a \"Spaghetti\" Bridge Model Using the Acoustic Emission Technique
## 4 Results
### Comparison with the Bundle Model  
Three histograms were computed to compare the AE-test results with the Bundle Model predictions: with the first 50% of observed signals, with the first 75% of signals, and with all signals. Figure 14 depicts the corresponding results. This information is complemented by Figure 15, which illustrates a typical acceleration pattern being observed throughout the tests. Because of measurement noise, a threshold \(\log(0.2)=-0.7\) is used for computing the AE-signals. In Figure 14, this implies the nearly horizontal distribution that was obtained for small amplitudes: as small avalanches are undistinguished from measurement noise, the counting of AE-signals remains constant. Comparing the results in Figure 14 to the theoretical predictions that are given by the Bundle Model in Figure 6a,b, it is possible to observe that:  
1. The experimental results agree with the general shape predicted by the model, with a central part tending to a linear curve in the bi-log graph. This evidences that the damage process tends to occur according to an exponential function, but its characteristic exponent is different. The data are also consistent with the theoretically expected deviations towards both magnitude extremes. 2. Reducing the sample size for drawing the distribution does not affect AE-events distribution only at the magnitude extremes: when only the first 50% of the data are used, the intermediate linear range reduces in amplitude, and the angular coefficient is also affected. 3. The results that are presented here suggest that the damage process occurs according to a general pattern that is similar to the one predicted by the Bundle Model. However, this tendency suffers in varying degrees from the effects of measurement noise, the structure's external geometry, the boundary conditions applied to it, and the internal organization of the system's elements. The influence that is exerted by these factors  
Figure 14: \(N(A)\) —histograms from the AE— test results, taking into account 50%, 75%, and 100% of observed events. Figure 15: The acceleration pattern typically acquired during the tests, with the amplitude threshold that defined actual AE-signals. is illustrated schematically in Figure 16. The two extreme cases correspond to the predictions given by the Bundle Model when all fibers are aligned in parallel (a) or almost entirely in series (f), whereas cases (b)-(e) represent several combinations of geometry and externally applied loads, which appear as intermediate arrangements within the context of the model. Thus, the spaghetti bridge configuration studied here is closer to the quasi-serial Bundle Model (case (f)), which is more prone to localization effects than the other cases. Finally, all profiles tend to a \"platea\" for small-amplitude events due to the need to apply a threshold value for negating measurement noise effects. The following three examples reinforce the hypothesis presented in item (3):  
1. In seismology [45; 46] state that seismic events may result in any intermediate form between the extreme-case histograms depending on several characteristics of the region where the event occurs. 2. The behavior that is noted by [45] is also observed in the seismic behavior in the region of Angra dos Reis, Brazil, as evidenced by the corresponding histogram of seismic events shown in Figure 17.
3. In [47], a comparative analysis is made between a prismatic specimen under uniaxial compression and a pre-fissured beam under flexion on three points. Both of the structures were made from concrete, and the comparison was carried out by both numeric and experimental means. The results are summarized in Figure 18, making it clear that geometry and boundary conditions significantly influence structural behavior. For instance, the histogram for the beam tends to horizontal for small magnitudes, because new ruptures tend to occur at the extremities of the pre-fissures, favoring the localization of avalanches and connection between events.