【正文】 rmation is calledenergy dispersion.(c) Spreading attenuation: An energy loss which occurs at the interface between the bolt and the grouting material. As a guided wave reaches the interface, not all of the wave energy can be re?ected at the interface. Part of the energy passes through the interface and is transmitted into the grouted material, a phenomenon called energy leakage.Therefore, it can be reasonably assumed that attenuation in grouted rock bolts consists of two major ponents。dispersive and spreading attenuation, both of which are frequencydependent. The total attenuation in grouted rock bolts should thus be the sum of the two ponents and in future will be referred to as DISP attenuation.It should be pointed out however, that as observed during our laboratory tests, the amplitude decay and the energy loss of guided waves recorded during tests of rock bolts in laboratory are not solely from the DISP attenuation. Another important ponent is the energy loss due to refraction at the contact surfaces between the bolt sample and the equipment. Theoretically, when a wave reaches an interface adjoining a medium which does not transmit mechanical waves (., vacuum or air), no refraction occurs and all energy is re?ected rock bolt test, transducers are attached to the bolt sample, which is in contact with the testing frame (., a table or a rack). It is at these contact surfaces that some energy is inevitably refracted, causing energy loss. This type of energy loss, as shown later, is expected to be constant and is of a ?xed quantity for a speci?c type of test setup. In future it will be called setup energy loss. As a result, the recorded amplitude decay and energy loss during rock bolt tests will be greater than what is actually caused by the DISP attenuation.An ongoing research program at Dalhousie University is aimed at studying the characteristics of guided waves in grouted rock bolts. Effects of wave frequency and grouted length on the behavior of guided ultrasonic waves in free bolts and grouted bolts have been studied. The achieved results are strikingly convincing. The details are given below.2. Experiments of guided ultrasonic wave testsAn understanding of the ultrasonic wave characteristics in free bolts (nongrouted bolts) is essential to the study of the behavior of guided ultrasonic waves in grouted bolts. In this research, both free bolts and grouted bolts were tested.. Test samplesThe test samples included two free bolts and three grouted bolts of various lengths. The free bolts were bare steel bars. The grouted bolts were made by casting a cylindrical concrete block around a steel bar to simulate the grouted rock bolts in the ?eld (). In these tests the bolts were not tensioned. The sample sizes and other descriptions are given in Table 1. The two free bolts (samples 1 and 2) were used to study the effects of bolt length and frequency on the behavior of guided ultrasonic waves, particularly the setup energy loss due to equipment setup. The three grouted bolts (samples 3–5) with varying grouted lengths were used to investigate the effects of frequency and grouted length on the attenuation of guided ultrasonic waves.. Test instruments and experiment descriptionThe instruments used in the study included a Handyscope HS3 (a data acquisition device with a wave generator), an ampli?er, two transducers, and a puter. The equipment setup is illustrated in . The HS3 unit has the capability of generating ultrasonic signals with varying frequencies, 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 ma