【正文】 f the measured amplitude ratio, Rm, for the grouted bolts at different frequencies are shown in Fig. is already known from the experiment results of free bolts in Fig. 6 that the amplitude ratio after the setup loss, R2,is and is independent from frequency. Because the equipment setup and test conditions for the grouted rock bolts are the same as those for the free bolts, it is assumed that the amplitude ratio, R2, is also in the grouted bolts. Thus the amplitude ratio R1 after the DISP attenuation can be calculated by rewriting Eq. (6) as R1=Rm/R2. Rm can be calculated from the recorded waveforms following the same procedure as for free bolts.The results of R1 of the grouted rock bolts with different frequencies are shown in Fig. 9. It can be seen that the ratio, R1, of the grouted rock bolts varies inversely with frequency and grouted length. At frequencies less than 65 kHz, R1 decreased linearly with frequency and it also decreased with grouted length. It is noticeable that at frequencies higher than 65 kHz, the data were scattered and the linear trend became unclear. The explanation is that both dispersive and spreading attenuation increased with frequency. The higher the frequency, the greater the energy loss. Hence, the received signal became very weak when the input frequency was above 75 kHz. The weak signal not only introduces more measuring errors, but also aggravates the effects of noises, making the results less reliable.. Group velocity in grouted rock boltsFor the grouted bolts, the results of group velocity calculated from the raw waveform data were totally meaningless. Only after ?ltering could meaningful results be obtained. The ?ltering method and the arrival time estimation method are the same as those previously discussed for the free bolts.The group velocity in the grouted length of a partially grouted rock bolt was calculated using the travel time in the grouted length only. The travel time in the grouted length was determined by subtracting the travel time in the free length, which is assumed to have the same velocity as the free bolt, from the total travel time. The measured group velocity in the grouted length for samples 3–5 are shown in Fig. 7, together with that from the free bolts.It can be seen from Fig. 7 that the results of the three grouted bolts are consistent to each other. The group velocity in the grouted bolts followed an opposite trend as did that in the free bolts。 Group velocity1. IntroductionRock bolts are widely used in underground and surface excavations in mining and civil engineering for ground reinforcement and stabilization. In many applications, rock bolts are grouted in the ground with cement or resin. Testing of the grout quality and monitoring of the bolt tension of rock bolts has long been a challenge in the ?eld. Conventionally, grout quality is assessed by pullout test and overcoring. Both methods are destructive and time consuming. The usefulness of pullout test results as a measure of the grout quality can be limited by the critical length of grout beyond which the steel bolt will fail ?rst. Therefore, other methods, such as nondestructive testing methods using ultrasonic waves have bee attractive. In recent years, research in this area has been very active. It is noticed that properties of guided waves, such as velocity and attenuation, are functions of the input wave frequency. Although the guided ultrasonic wave seems to be a promising method for monitoring rock bolts, research in this area is still in the early stage and many technical problems remain to be solved. In a grouted bolt, wave behavior is not only related to the grout quality but also to the wave frequency. The grouted length and the properties of materials surrounding the bolt may all play an important role.One of the important characteristics of a guided wave is that its velocity not only depends on the material properties but also on the thickness of the material and the wave frequency. Unlike a bulk wave, the guided wave propagates as a packet, which is made up of a band of superimposed ponents with different frequencies. It is the group velocity that de?nes the speed at which the ‘envelope’ of the packet moves along. It has been shown that in a rock bolt, the rate of energy transfer is identical to the group velocity. Our recent research examined the effects of wave frequency and the curing time of grout on the group velocity of guided ultrasonic waves in rock found that the wave group velocity is much lower in grouted bolts than in free bolts. The lower the frequency, the lower the velocity. Our test results indicated that the input frequency for rock bolt testing below 100 kHz would provide better resolution and clearer signals. This observation is supported by the results discussed further on in this paper.Attenuation is another important characteristic of a guided wave. In general, attenuation refers to the total reduction in the signal strength. Attenuation occurs as a natural consequence of signal transmission over a distance due to wave energy loss. There have been extensive research and experiments on attenuation of bulk waves. Wave attenuation is de?ned by an attenuation coef?cient. For example, the pwave amplitude decay can be expressed as a function of travel distance. (1)where Aa is the amplitude at location a, Ab is the amplitude at location b, is the attenuation coef?cient, constant, L is the distance from locations a to b, R is the amplitude ratio, R=Ab/Aa.However, there has been little research on attenuation of guided waves, especially in grouted rock bolts. Wave attenuation in grouted rock bolts is very plicated and is often affected by many factors including the grouting material and the grout quality. Each of these factors may cause some attenuation.In general, the observed wave attenuation may have several ponents, some of which may be frequenc