【文章內(nèi)容簡(jiǎn)介】 ximum wave amplitude in this case may be affected by such noises. It is therefore critical to develop a suitable analysis method to analyze the attenuation of ultrasonic waves and to get meaningful results.In this paper, a method to calculate the amplitude ratio using the average amplitude over a time interval is suggested as follows:= (5)where is the time interval centered at the maximum amplitude of a wave packet, is the recorded wave amplitude, i=1 is for the ?rst arrival, and i=2 is for the echo, k is a material constant.The parameters , , and their de?nitions are illustrated in Fig. 3. Because this method considers the average amplitude across intervals of equal lengths of time for the ?rst arrival and the echo, the effects of errors and noises on the maximum amplitude will be minimized. To evaluate the effects of the time interval length and on the accuracy of the results, the amplitude ratios in free bolts—those in which the boundary between the ?rst arrival and the echo was very clear—were calculated with different time intervals as a percentage of the whole waveforms of the ?rst arrival and the echo. The results for sample 1 at different frequencies are shown in Fig. clear that if the time interval is too small (., less than 25% of the whole waveform), the amplitude ratio as determined by Eq. (5) varies with the length of the timeinterval. When the time interval is greater than 25% of the whole waveform, the results vary very little and are nearly the same as that at 100% (the whole waveform).In the following, == 100 were used in calculation of the average amplitude for all tests. With an input signal of 25 kHz, this time interval corresponded to 45% f the whole waveform in free bolts, and at 100 kHz, it covered 95% of the whole waveform. It is apparent that although a small part of the whole waveform has not been considered in this method, the calculated amplitude ratio can still re?ect the total energy loss in a rock bolt. This method however makes it much easier in practice to estimate the energy loss, especially when the boundary between the ?rst arrival and the echo in grouted rock bolts is dif?cult to identify because of dispersion.. Group velocity estimationThe wave travel time in the rock bolt is de?ned as the time lapse from the beginning of the excitation signal, which was recorded from the input end of the bolt, to the ?rst arrival, which was recorded from the other end of the bolt. However, determination of the beginning of the ?rst arrival and the echo is often plicated by the dispersion character of the guided wave. Dispersion increases with frequency. The recorded raw waveforms therefore need to be ?ltered ?rst by a band ?lter to narrow the frequency band around each testing frequency [5]. This was achieved by using a ?ltering program designed in Matlab. All the recorded waveforms were ?ltered using this program to give a narrow band of 75 kHz. The arrival time determined by the ?ltered waveforms is found to be more representative of the anticipated actual wave travel time at a speci?c frequency. With the bolt length and the travel time determined using this method, the group velocity of guided ultrasonic waves can be calculated. The calculated group velocity is found to follow different trends in the free and the grouted bolts, as explained later. For partially grouted bolts, the group velocity in the free segment is considered the same as that in the free bolts.4. Effects of frequency and bolt length on the behavior ofguided waves in free boltsExperiments were conducted on free bolts using frequencies from 25 to 100 kHz. Fig. 5a) shows the typical waveform recorded in sample 1 at an input frequency of 25 kHz. It was observed during data analysis that with the increase of the input frequency, the travel time of the ?rst arrival and the echo reaching the receiving end increased slightly, and the wave amplitude reduction of the echo from the ?rst arrival is almost the same at all input frequencies.. Attenuation in free boltsThe measured amplitude ratio, Rm, determined from the two free bolts (samples 1 and 2) are shown in Fig. 6. It can be concluded from the chart that the total attenuation in the free bolts did not change with frequency. The average amplitude ratio is for sample 1 and for sample 2. Thus it is also clear that the amplitude ratio is not affected much by the bolt length and that the very small difference for the two bolts is negligible. This con?rms that the dissipative attenuation can be ignored for rock bolts because of the short traveling distance. Since there is little or no dispersion in waveforms, nor is there energy leakage to other mediums, the DISP attenuation, which was expected to change with frequency and distance, is negligible in the free bolts.The energy loss for both free bolts was nearly constant and did not change with frequency or bolt length. As discussed earlier, this part of the energy loss has a ?xed amount, and is mainly caused by setup loss, mostly from refraction at the contact surfaces of the bolt samples with other objects. The setup loss is however expected to change for different test setups.If the amplitude ratio after the DISP attenuation is assumed as R1 and after the setup loss as R2, then the measured amplitude ratio, Rm, according to Eq. (2), will be: (6)As can be seen, the attenuation relationship de?ned in Eq. (1) applies only to R1, not to the directly measured Rm, since R2 is independent from travel distance.For a free bolt R1≈, the main energy loss will be the setup loss and Rm≈R2. It can be inferred that for grouted rock bolts, the nongrouted free length will have very little effect on the result of attenuation because of its short length and the major energy loss will be in the grouted length. It can also be reasonably concluded from Fig. 6 that the amplitude ratio, R2, after the setup loss (approximately 20%) for