外文翻译---频率和锚固长度对超声波在锚杆中传播行为的影响.docx

英文原文Effects of frequency and grouted length on the behavior of guided ultrasonic waves in rock boltsD.H. Zoua, Y. Cui, V. Madengaa, C. ZhangAbstractExperiments were conducted to study the behavior of guided waves in free and grouted rock bolts. Ultrasonic waves with frequencies from 25 to 100 kHz were used as excitation inputs. Tests were rst conducted on free bolts to help understand the behavior of guided waves in non-grouted bolts. The effects of wave frequency and grouted length on the group velocity and attenuation of the guided ultrasonic waves were then evaluated. The test results indicated clear but different trends for the group velocity in the free and the grouted bolts. The attenuation in free bolts was not affected by bolt length and frequency. However, in grouted bolts it increased with frequency and grouted length. It was also found that the two main sources of attenuation are the setup energy loss, which has a xed quantity for a specic type of test setup, and the dispersive and spreading energy loss which varies with frequency and bolt length.2007 Elsevier Ltd. All rights reserved.Keywords: Rock bolts; Guided waves; Attenuation; Amplitude; 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 pull-out test and over-coring. Both methods are destructive and time consuming. The usefulness of pull-out 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 non-destructive testing methods using ultrasonic waves have become 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 components with different frequencies. It is the group velocity that denes 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 bolts.We 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 observa-tion 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 dened by an attenuation coefcient. For example, the p-wave 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 coefcient, 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 complicated 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 components, some of which may be frequency-dependent and some frequency-independent. The total attenuation is the sum of the contributions of all inuencing factors 14, and this relationship applies to both bulk waves and guided waves: (2)where is the attenuation coefcient of the ith component caused by the ith factor, is the travel distance affected by the ith factor, is the amplitude ratio after attenuation of the ith component, If is the same for all factors, then wehave or (3)where is the total attenuation coefcient.According to the cause, attenuation may be grouped into the following categories:(a) Dissipative attenuation: An energy loss due to non-elastic resistance of the medium. It increases with thewave travel distance and may become profound over a long distance depending on the material property. This type of attenuation in steel is generally very low compared to that in rocks. As shown later, it can beignored in practice for guided waves traveling in rock bolts due to the low resistance of steel and the short bolt length (13 m).(b) Dispersive attenuation: An energy loss due to deforma-tion of waveform during wave propagation, a char-acteristic that distinguishes guided waves from bulk waves. The phenomenon of wave deformation 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 reected 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 components;dispersive and spreading attenuation, both of which are frequency-dependent. The total attenuation in grouted rock bolts should thus be the sum of the two components 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 attenua-tion. Another important component 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 (e.g., vacuum or air), no refraction occurs and all energy is reected back.Ina rock bolt test, transducers are attached to the bolt sample, which is in contact with the testing frame (e.g., 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 specic 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 (non-grouted 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.2.1. 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 (Fig.1). 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 35) with varying grouted lengths were used to investigate the effects of frequency and grouted length on the attenuation of guided ultrasonic waves.2.2. Test instruments and experiment descriptionThe instruments used in the study included a Handy-scope HS-3 (a data acquisition device with a wave generator), an amplier, two transducers, and a computer. The equipment setup is illustrated in Fig.2. The HS-3 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 non-grouted end of the bolt. The received signal at the other end was amplied before being digitized. The computer was used to record, display, and process the signals.The transducers used were piezo-electric, 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 transmit-ter (R6) with input signals at different frequencies into the non-grouted 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 reected back from the input end. The attenuation was estimated by assessing the wave amplitude ratio of the echo over the rst arrival.3.1. 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 relation-ship, as shown in Eq. (1), with the attenuation coefcient.The higher the attenuation, the greater the energy loss, and the lower the amplitude ratio. Therefore the measured amplitude ratio, Rm as dened 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 dened 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 difcult to study wave attenuation in grouted bolts because the recorded wave-form is often very weak and is affected by a lot of noises. The received waveform sometimes may not be very clear, making it difcult to identify the boundary between the rst arrival and the echo. This becomes 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 denitions 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 boltsthose in which the boundary between the rst arrival and the echo was very clearwere 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. 4.Itis clear that if the time interval is too small (e.g., 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 reect 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 difcult to identify because of dispersion.3.2. Group velocity estimationThe wave travel time in the rock bolt is dened 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 complicated 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 specic 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 fre-quencies 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.4.1. 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 0.79 for sample 1 and 0.81 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 conrms 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 dened in Eq. (1) applies only to R1, not to the directly measured Rm, since R2 is independent from travel distance.For a free bolt R11.0, the main energy loss will be the setup loss and RmR2. It can be inferred that for grouted rock bolts, the non-grouted 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 ca