顾桥矿井1.5Mta新井设计含5张CAD图-采矿工程.zip
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翻译部分 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. ZhangAbstract:Experiments 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: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).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.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 can also be reasonably concluded from Fig. 6 that the amplitude ratio, R2, after the setup loss (approximately 20%) for the test setup in this research is about 0.8.4.2. Group velocity in free boltsAs indicated above, before estimating the arrival time, the raw waveforms were ltered with a band lter.A typical ltered waveform of sample 1 is illustrated in Fig. 5b), which shows a more well-dened signal than the raw waveform. The determined group velocities for the two free bolts (samples 1 and 2) are shown in Fig. 7 together with the theoretical group velocity solution, which was determined from Achenbachs solution in a steel bar of 19.5 in diameter 3. It can be seen in the chart that the results from the ltered data t well with the theoretical solution in the tested frequency range. As the frequency changed from 25 to 100 kHz; the group velocity dropped by about 10%. The group velocity was apparently not affected by the bolt length.5. Effects of frequency and grouted length on behavior of guided wavesExperiments were also conducted on the grouted rock bolts using frequencies from 25 to 100 kHz. The typical raw waveform for sample 4 at an input frequency of 35 kHz is displayed in Fig. 3. It was observed from the recorded data that the waveforms in grouted bolts showed dispersion, apparently more serious at higher frequency ranges. At the same time, as the input frequency increased the lengths of time for the rst arrival and the echo to reach the receiving end decreased signicantly, following an opposite trend from that observed in the free bolts. The wave amplitude reduction of the echo from the rst arrival also becamemore severe.5.1. Attenuation in grouted rock boltsThe results of the measured amplitude ratio, Rm, for the grouted bolts at different frequencies are shown in Fig. 8.It is already known from the experiment results of free bolts in Fig. 6 that the amplitude ratio after the setup loss, R2,is 0.8 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 0.8 in the grouted bolts. Thus the amplitude ratio R1 after the DISP attenuation can be calculated by re-writing 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.5.2. Group velocity in grouted rock boltsFor the grouted bolts, the results of group velocity calcu-lated 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 35 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; and its value was not affected by the grouted length, but by the frequency. It is interesting to note that at the low frequency end (i.e., 25 kHz), the group velocity in the grouted bolts was about half of that in the free bolts; at frequencies higher than 75 kHz the velocity increase in the grouted bolts slowed down, and at the highfrequency end (i.e., 100 kHz), the velocity was approaching that of the free bolts. In fact, at high frequencies, it was more difcult to separate the grouted length and the free length from the recorded signals. Therefore, frequencies higher than 75 kHz are not recommended for the test.6. Discussions and conclusionsThis research examined the attenuation and group velocity of the guided ultrasonic waves in rock bolts. The test results showed variations with frequency and grouted length. It was determined that due to the short length of rock bolts used in the eld, the dissipative attenuation can be ignored.In free bolts, the dispersive and spreading attenuation along the bolt is negligible and the main source of attenuation is from the setup loss of energy, which reduced the amplitude by 20% in one round trip for the equipment setup in this research. The setup loss is considered to be independent from frequency and bolt length, but depen-dent upon the specic equipment setup. The group velocityin the free bolts decreased by about 10% as the frequency increased from 25 to 100 kHz.In grouted bolts, the setup loss is assumed to be the same as that in the free bolts because the test setup was the same. However, the dispersive and spreading (DISP) attenuation increased with frequency and grouted length, and it was moresevere than that from the setup loss. The amplitude ratio due to the DISP attenuation decreased as the frequency and grouted length increased. The group wave velocity in the grouted length of the test bolts increased steadily as the frequency increased to 75 kHz while the increase slowed down at a higher frequency. However, at 25 kHz, the group velocity wasnearly 50% lower in the grouted length than that in the free bolts. As the frequency approached 100 kHz, the velocity difference between the free bolts and the grouted length was reduced to less than 10%.As indicated earlier, the experiments in this study were conducted using a transmission-through setup (i.e., with sensors on both ends of the tested bolts). This type of setup is not applicable to the eld where only one end of a rock bolt is accessible. The next step of this research will be to conduct similar tests using a transmission-echo setup (i.e., with a sensor at one end only). This will require a different testing device, which is being custom-built for the specic testing requirements. During the next stage of research, tension will also be applied to the bolt samples to study the tension effects. The ultimate goal of this research will be to develop a non-destructive testing device using guided ultrasonic waves for eld monitoring of grouted rock bolts, particularly the grout quality, grouted length, bolt failure, and bolt tension.AcknowledgmentsThis research was supported by a research grant from the Natural Sciences and Engineering Research Council of Canada.中文译文频率和锚固长度对超声波在锚杆中传播行为的影响D.H. Zoua, Y. Cui, V. Madengaa, C. Zhang摘 要：以频率从25至100千赫的超声波作为励磁输入，研究超声波在自由和锚固锚杆中传播的特性。首先对自由锚杆进行实验来了解导波在非锚固时的行为。从波的频率和锚固长度上对群速度和衰减超声导波的影响进行评估。实验结果表明，在自由和锚固锚杆中，群速度有不同的趋势。在自由锚杆中，波的衰减不受锚杆长度和波频的影响。但是，在锚固锚杆中衰减随着频率和锚固长度的增加而增加。同时还发现设置能量损失引起衰减的两个主要来源，一是对某一特定类型的测试体系的一个固定量，二是色散和传播能量损耗随波的频率和锚杆长度的变化而变化。关键词：岩石锚杆；导波；衰减；振幅；群速度1 引言锚杆被广泛应用在采矿和土木工程中的地下和地表开挖后加固和稳定地面。在许多应用中，锚杆用水泥或树脂锚固。测试锚杆锚固质量和监测锚杆预紧力长期以来一直是该领域中的一个挑战。通常用拉拔实验和应力解除法来测试锚固质量。这两种方法都是破坏性和耗时的实验。用拉拔实验结果来衡量锚固质量，受锚杆初次破坏后关键锚固长度的限制。因此，像利用超声波这种非破坏性测试方法已经受到了关注。近年来，这一领域的研究已经非常活跃。导波的性质，如速度和衰减，受输入波频率的作用影响。虽然超声导波是一个很有前景的监测锚杆的方法，但是在这一领域的研究仍尚处于初期阶段，许多技术问题仍待解决。在锚杆中，波的行为不仅与锚固的质量，而且与波的频率有关，也受锚杆周围岩体的特性和锚固长度的影响。导波的一个重要的特征是其速度不仅取决于材料性能，而且取决于材料的厚度及波的频率。导波不像体波，而是由一个束具有不同频率的成分波叠加组成。群速度决定其传播速度，波整体以该速度传播。在锚杆中，能量传递速率与群速度相同。我们最近研究测试锚杆中波的频率和固化时间对超声导波群速度的影响。我们发现群速度在锚固锚杆中低于在自由锚杆中。频率越低，速度越低。实验结果表明，为锚杆实验输入低于100千赫的频率会提供更好的分辨率和更清晰的信号。本文将进一步讨论这个实验结果。导波的另一个重要特点是衰减。一般来说，衰减是指信号强度的减弱。衰减是信号长距离传输过程中波能损失的自然结果。在体波的衰减方面已经有广泛的研究和试验。波的衰减是由一个衰减系数定义的。举例来说，纵波振幅衰减可以表示为一个距离函数。 (1)其中Aa，Bb分别是位置a，b处的振幅；是衰减系数且是常数；L是从a到b的距离；R 是振幅比率，R=Ab/Aa。然而,很少有研究导波的衰减，特别是在锚杆锚固方面。在锚固锚杆中波的衰减是非常复杂并且常常受包括锚固材料和锚固质量在内的多种因素的影响。这些因素都可能造成一些衰减。通常，波的衰减可能有几个部分组成，其中一些随频率变化一些与频率无关。总衰减是所有因素影响的结果，这也适用体波和导波： (2)其中是受第i个因素影响的第i个分量的衰减系数；是受第i个因素影响的距离；Ri是第i个分量衰减后振幅的比；如果对所有的因素都相同，则有 或 (3)其中是所以衰减系数的和。根据起因，衰减可分为以下几类：(a) 耗散衰减：一种由非弹性介质阻碍引起的能量损耗。它随波的传播距离的增加而增加，并可能根据物质的性质在长距离传播时成为很显著的原因。这类型的衰减在钢材中跟在岩石中相比普遍很低，如后面所述，在实践中由于钢的低阻力和锚杆长度(13 m),导波在锚杆中传播时,这种衰减可以被忽视。(b) 色散衰减：一种由于传播过程中波形变形导致的能量损耗。这也是导波在波传播中区别于体波的一个特点。这种波变形的现象称为能量色散。(c) 传播衰减：一种发生在锚杆与锚固材料界面间的能量损失。作为一个导波的到达界面，并不是所有的波能都可以在界面上反射的。一部分能量会穿过界面，并传到锚固材料，这种现象称为能量泄漏。因此，可以合理地假设在锚固锚杆中衰减由两部分组成:色散衰减和传播衰减，这两者都是跟频率密切相关的。锚杆中的总衰减就是这两种衰减的总和，以后将统称为色散衰减。需要指出的是：正如我们在实验中观察到的，在测试锚杆实验室中记录的导波的振幅衰减和能量损失并不仅仅来源于色散衰减。另一个重要组成部分，是在锚杆样品及设备的接触面之间折射的能量损失。理论上说，当一个波到达毗邻另一不传送机械波的界面（例如真空或空气），没有折射发生，所有能量都被反射回去。在锚杆实验中，传感器被放在接触测试框架的锚杆样品上（例如，一张桌子或机架）。正是在这些接触面上，有些能源不可避免地折射，造成能量损失。如后面所述，这类能量损失预计将是不间断的，作为特定类型的试验装置这是一个固定的数量值,下面称为安装能量损失。结果表明，记录的此类振幅衰减和能量损失在锚杆测试中将大于真正由色散衰减所致。在达尔豪西大学正在进行的研究项目，旨在研究导波在锚杆中传播的特征。对波频率和锚固长度对超声导波在自由及锚固锚杆中传播的影响进行了研究。得到的结果具有很强的说服力，详情如下文。2 超声导波测试的实验了解超声波在自由锚杆（非锚固）中的特点 ，是研究超声导波在锚固锚杆中行为所必不可少的。在这项研究中，分别对自由锚杆和锚固锚杆进行了试验。2.1 试验样本试验样本包括2个自由锚杆和3个长度不同的锚固锚杆。自由锚杆是裸露的钢筋。锚固锚杆在现场是用圆柱混凝土在钢筋周围砌成块状来模拟该锚固锚杆的(图1)。在这些测试中锚杆没有被拉紧。样本的大小及其他说明见表1。2个自由锚杆（试件1和2）被用来研究锚杆长度和频率对导波的影响，尤其是由于设备安装导致的安装能量损耗。3个具有不同锚固长度的锚杆（试件35）被用来观察频率和锚固长度对导波衰减的影响。表1锚杆试件的几何特征样品锚杆长度/mm锚杆直径/mm锚固长度/mm锚固直接/mm1240019.5002100019.5003120019.53001604120019.5500160580019.57501602.2 试验仪器和实验描述在研究中所用的工具，包括一个手提示波器HS-3(有产生波的数据采集器)，一个放大器，两个传感器和一台电脑。设备安装的说明图，见图2。单一的手提示波器HS-3有发不同频率的超声波信号的能力，以及接收和数字化接收波的信号。超声波正弦输入信号被用来激发在锚杆非锚固末端的发射机。在另一端接收到的信号先是被扩增，然后被数字化。电脑被用来记录，显示和处理信号。传感器是来自物理声学公司R6和R15类型的压阻式电动机。两端测试锚杆均是平滑的，真空润滑脂被用来提供传感器间的良好接触。实验的进行通过激发一个发射机（R6），在锚杆样品非锚固的末端输入不同频率的输入信号,在信号到达的另一端被一个传感器（R15）接收，整个波形被数字化录入。在每次试验中，输入频率的范围介于25至100千赫。3 实验数据的分析方法在下文中，“首次到达”指第一束波第一次到达接收端，“回声”指同一束波到达接收端，“反射波”是指上述的波束到达接收端后反射回输入端。衰减估计是比较首次到达波和回声的振幅比。3.1 衰减估计如前面所解释的，衰减不仅和锚固性质，而且和频率及其他因素有关，和一个传播了若干距离的波束的振幅有一个逆对数关系，如（1）式衰减系数所示。衰减越高，能量损失越大，振幅比越低。因此实测振幅比Rm，在这一研究中作为衰减的一种间接测量： (4)其中A1是首次到达的平均振幅，A2是回声的平均振幅。据了解，好的锚固质量由于能量泄漏及色散导致沿锚杆更高的能量损失。因此很难研究在锚固锚杆中波的衰减，因为波形记录往往很薄弱，而且受很多噪音的影响。收到的波形有时会很不清楚，使首次到达和回声的界线难以确定。当锚杆很短或严重分散时这个问题更加突出，在这种情况下波的最大波幅可能会受这类噪音的影响。因此，建立一种有效的分析方法来分析超声波的衰减和获得有意义的结果非常关键。本文提出了一种计算振幅比的方法，就是利用一定的时间间隔内的平均振幅来计算，公式如下： i=1，2 （5）其中是最大振幅间的时间间隔，是波的振幅，i=1表示首次到达，i=2表示回声；k是材料常数。参数、和它们的含义如图3所示。因为这个方法考虑两个相同时间间隔中首次到达和回声的平均振幅，所以误差和噪音对最大振幅的影响最小。为了说明时间间隔的长度对结果准确度的影响，用不同时间间隔计算自由锚杆中的振幅比(首次到达和回声的界限很明显)，用百分比表示。模型一在不同频率下的结果如图4所示。从图中可清楚的看出：当时间间隔很小时(通常小于整个波形的25%)，由方程5得到的振幅比随间隔时间的长短而变化。当时间间隔超过这个波形的25%时，结果变化就非常小，几乎达到100%。下面的实验都用t1=t2=100us的时间间隔来计算。输入25khz的信号，自由锚杆中的时间间隔包含整个波形的45%，当输入100khz是，时间间隔占整个波形的95%。尽管这个方法没有考虑整个波形的一小部分，但是计算出的振幅比仍能反映锚杆中的能量损失。而且这个方法在实践中非常容易算出能量的损失，尤其是在色散导致锚固锚杆中首次到达和回声的界限很难分辨的时候。3.2 估算群速度从记录锚杆输入端的励磁信号到锚杆另一端的首次到达之间的延时定义为波在锚杆中的传播时间。但是，确定首次到达和回声的开始常常受到色散特性的影响。色散随着频率增加而增加。所以首先需要把记录的原始波形滤波来约束每次实验频率的频带。在matlab中通过一个滤波程序就可以实现。所有记录的波形都可以用这个程序滤波到一个5khz的窄频带。我们发现，用过滤的波形确定到达时间更能代表某种频率的实际波的传播时间。根据锚杆长度和用这种方法确定的传播时间，可以计算出超声导波的群速度。计算得到的群速度在自由锚杆和锚固锚杆中有不同的趋势，具体在下文介绍。对部分锚固锚杆，自由部分的群速度跟在自由锚杆中的群速度相同。4 自由锚杆中频率和锚杆长度对导波行为的影响用25khz到100khz的频率在自由锚杆中实验表明试件1中输入25kzh频率的典型波形。由数据分析可看出，随着输入频率的增加，首次到达的时间和回声到达接收端的时间缓慢增加，而由首次到达产生的回声的降幅在任何输入频率下都相同。4.1 自由锚杆中的衰减对自由锚杆1和2的实测振幅比Rm如图6所示。由图表可知:自由锚杆中的总衰减不随频率而变化。试件1的平均振幅比是0.79，试件2的平均振幅比是0.81。因此，振幅比受锚杆长度的影响不大，两锚杆的细微差别可以忽略。由于传播距离很短，所以锚杆中的色散衰减可以忽略。既然在波形中没有或有很少的色散，能量也就不会泄露到其他介质中，跟频率和传播距离有关的色散衰减在自由锚杆中也就可以忽略。对两个自由锚杆的能量损失不随频率和锚杆长度而变化，而是接近一个常数。如前所述，这部分能量损失主要是因为安装损耗，大部分由锚杆和其他物体接触面的反射引起。但是安装损耗在每次不同的实验中都不尽相同。假设色散衰减后的振幅比是R1，安装损耗后的振幅比是R2，则由方程2得到实测振幅比为： (6)可以看出，由方程1定义的衰减关系只适用于R1，而不适用于Rm，因为R2跟传播距离无关。对于自由锚杆R11.0时，主要的能量损失是安装损耗，此时RmR2。据此可推断，锚固锚杆中非锚固端的长度对衰减影响很小，因为距锚杆自由端很短，主要的能量损失在锚固端。从图6中可得出，这项研究中受安装损耗(大约20%)作用后的振幅比和R2大约是0.8。4.2 自由锚杆中的群速度如前所述，在估算到达时间前，要用滤波器对原始波进行滤波。试件1过滤后的波形如图5b所示，比原始波有更好的界定。通过理论计算和直径19.5mm的锚杆实验确定两个自由锚杆的群速度如图7。从图表中可以看出，过滤后的数据结果跟理论计算值都非常吻合。随着频率从25khz到100khz变化，群速度递减大约10%，群速度明显不受锚杆长度的影响。5 频率和锚固长度对导波行为的影响对锚固锚杆的实验频率仍然是从25khz到100khz。对试件4输入35khz得到的波形如图3所示。从记录的数据可以看出，锚固锚杆中的波形有色散，而且频率越高越严重。同时，随着输入频率的增加，首次到达和回声到达接收端的时间明显减少，这跟自由锚杆中的现象不同。首次到达产生的回声的振幅严重减少。5.1 锚固锚杆中的衰减不同频率条件下，锚固锚杆的实测振幅比Rm如图8所示。由自由锚杆的实验结果可知，安装损耗后的振幅比R2是0.8，而且与频率无关。因为对锚固锚杆的实验条
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