1、PDF英文：http:/ Effects of frequency and grouted length on the behavior of guided ultrasonic waves in rock bolts D.H. Zoua, Y. Cui, V. Madengaa, C. Zhang Abstract Experiments were conducted to study the behavior of guided waves in free and grouted rock bolts. Ultrasonic waves with frequencies fro
2、m 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
3、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 sourc
4、es 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 ve
5、locity 1. Introduction Rock 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 bol
6、t 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 o
7、f 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 attenua
8、tion, 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 th
9、e 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
10、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
11、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 tha
12、n in free bolts. The lower the frequency, the lower the velocity. Our test results indicated that theinput 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
13、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 attenu
14、ation 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. ln ln ( )baA RLA (1) where Aa is the amplitude at location a, Ab is the amplitude at location b, is the attenuation coefcient, consta
15、nt, 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 gro
16、uting 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 inuenci
17、ng factors 14, and this relationship applies toboth bulk waves and guided waves: 11 1l n ( ) l n ( )nnni i i iii iL R R (2) where i is the attenuation coefcient of the ith component caused by the ith factor,iL is the travel distance affected by the ith factor, iR is the amplitude r
18、atio after attenuation of the ith component, If iL is the same for all factors, then we have 1niti LL or 1ntii(3) where t is the total attenuation coefcient. According to the cause, attenuation may be grouped into the following categories: (a) Dissipative attenuation: An energy loss due
19、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 guid
20、ed 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 deformat
21、ion 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
22、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
23、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
24、 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
25、), 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 en
26、ergy 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 att
27、enuation. 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 result
28、s are strikingly convincing. The details are given below. 2. Experiments of guided ultrasonic wave tests An 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 samples The test samples included two free bolts and three grouted bolts of various lengths.
