【正文】 s, as well as receiving and digitizing the received wave signals. Sinusoidal ultrasonic input signals were used to excite the transmitter at the nongrouted end of the bolt. The received signal at the other end was ampli?ed before being digitized. The puter was used to record, display, and process the signals.The transducers used were piezoelectric, types R6 and R15, from Physical Acoustics Corporation. Both ends of the test bolts were smoothed and vacuum grease was used to provide good contact with the transducers.The experiments were conducted by exciting a transmitter (R6) with input signals at different frequencies into the nongrouted end of a bolt sample. The signal arriving at the other end was picked up by a transducer (R15) and the whole waveform was recorded digitally. During each test, the input frequency ranged from 25 to 100 kHz.3. Experiment data analysis methodIn the following, ‘?rst arrival’ refers to the ?rst wave packet that arrived at the receiving end and ‘echo’ refers to the same wave packet that reached the receiving end for a second time after it was re?ected back from the input end. The attenuation was estimated by assessing the wave amplitude ratio of the echo over the ?rst arrival.. Attenuation estimationAs explained earlier, wave attenuation is not only related to the grout quality but also to the frequency and other factors. The amplitude ratio of a wave packet that has traveled some distance has an inverse logarithm relationship, as shown in Eq. (1), with the attenuation higher the attenuation, the greater the energy loss, and the lower the amplitude ratio. Therefore the measured amplitude ratio, Rm as de?ned below, is used as an indirect measurement of attenuation in this study: (4)where A1 is the average amplitude of the ?rst arrival and A2 is the average amplitude of the echo as de?ned below.It is understood that good grout quality results in higher energy loss along the rock bolt due to energy leakage and dispersion. It is therefore very dif?cult to study wave attenuation in grouted bolts because the recorded waveform is often very weak and is affected by a lot of noises. The received waveform sometimes may not be very clear, making it dif?cult to identify the boundary between the ?rst arrival and the echo. This bees more problematic when the bolt is short or when dispersion is serious. The maximum 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 th