Perkowski Zbigniew, Tatara Karolina
Faculty of Civil Engineering and Architecture, Department of Physics of Materials, Opole University of Technology, Katowicka 48, 45-061 Opole, Poland.
Materials (Basel). 2020 Jan 23;13(3):551. doi: 10.3390/ma13030551.
The accuracy of transmission ultrasonic tomography for the detection of brittle damage in concrete beams can be effectively supported by the graph theory and, in particular, by Dijkstra's algorithm. It allows determining real paths of the fastest ultrasonic wave propagation in concrete containing localized elastically degraded zones at any stage of their evolution. This work confronts this type of approach with results that can be obtained from non-local isotropic damage mechanics. On this basis, the authors developed a method of reducing errors in tomographic reconstruction of longitudinal wave velocity maps which are caused by using the simplifying assumptions of straightness of the fastest wave propagation paths. The method is based on the appropriate elongation of measured propagation times of the wave transmitted between opposite sending-receiving transducers if the actual propagation paths deviate from straight lines. Thanks to this, the mathematical apparatus used typically in the tomography, in which the straightness of the fastest paths is assumed, can be still used. The work considers also the aspect of using fictitious wave sending-receiving points in ultrasonic tomography for which wave propagation times are calculated by interpolation of measured ones. The considerations are supported by experimental research conducted on laboratory reinforced concrete (RC) beams in the test of three-point bending and a prefabricated damaged RC beam.
图论，尤其是迪杰斯特拉算法，可以有效地支持透射超声层析成像检测混凝土梁中脆性损伤的准确性。它能够确定在含局部弹性退化区混凝土中，超声波在其演化的任何阶段传播的最快实际路径。这项工作将这种方法与从非局部各向同性损伤力学中获得的结果进行了对比。在此基础上，作者开发了一种减少纵波速度图层析重建误差的方法，这些误差是由于采用最快波传播路径为直线的简化假设而产生的。该方法基于以下情况：如果实际传播路径偏离直线，则对在相对的发射 - 接收换能器之间传输的波的测量传播时间进行适当延长。由此，通常在层析成像中使用的、假设最快路径为直线的数学工具仍可使用。这项工作还考虑了在超声层析成像中使用虚拟波发射 - 接收点的方面，其波传播时间通过对测量值进行插值计算得到。这些考虑得到了在实验室钢筋混凝土（RC）梁三点弯曲试验以及预制受损RC梁上进行的实验研究的支持。
