13th International Conference on Fracture June 16–21, 2013, Beijing, China -6- on the classical method is introduced in the following part. The basic idea of the localization in masonry is the same as that in concrete. But propagation delay due to the layers in the masonry structures makes the homogeneous assumption is unavailable here. Modifications for propagation delay are implemented. The geometry distance ds is still taken as the calculated path, since the detailed knowledge of the actual wave path , is not possible to be known. But modification can be made for the time-delay according to the velocity property in Fig. 3 to reduce the effect of inhomogeneous property. In the modified model, the classical model result in Eq. (5) is modified into: 2 2 2 1 10 0 1 1 2 2 ( ) n n i i i i i i r x x k t t v , (8) where 1 / i i k d d is the modified factor, which is used to modify the effects of the inhomogeneity or propagation delay. The parameter ξ, denoted as degree of the inhomogeneity, in ki reflects the inhomogeneous degree of the material. The degree of the inhomogeneity ξ is determined from the result of the pencil-lead break wave velocity test, shown in Fig. 3. It reflects the relationship between the calculated velocity and the wave propagation distance. In strictly homogeneous materials, the value is 0 since the wave velocity is a constant value and does not changes with travelling distance. If the material is not homogeneous, value will theoretically increases with the degree of the heterogeneity. The degree of the inhomogeneity in our research is 0.14, which is taken from the relation between the velocity and travelling distance shown in Fig. 3. 4.2. Sensor distribution The results of the locations are shown in Fig. 4 for both the modified and classical methods. It can be noted that the location accuracy varies with the position of the breaks. The break points can be approximately divided into three groups. The points 3~8 inside the central area of the sensor covered region (the dashed line in Fig. 4) have the best crack source monitoring result for both classical and the modified methods. In the second group, including points 2, 9, 10, 11, 12, points are distributed on the nearby region of the sensor covered region. The rest of the points, far from the sensor network, are in the third group. For points in the first group, both methods give the ideal result, all the errors are smaller than 6 mm, and most of the crack events can be monitored. For the second group, the modified model shows better results than the classical method. The errors (a value in Fig. 4) in the classical method are about 15~75 mm, whereas the counterparts (b value in Fig. 4) can be reduced to about 6~27 mm in the modified method. In this condition, about half of the break events can be detected according to the c value in Fig. 4. The result from the classical method for the third group is barely acceptable for its exaggerated errors, whereas modified method is still in good conditions. Although the errors were slightly large, about three or four centimeters, the results are still acceptable considering the entire size scale of the surface. Three representative points, 4, 10 and 17 respectively, of the three
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