【正文】 e behavior ofguided waves in free boltsExperiments were conducted on free bolts using frequencies 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.. 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 for sample 1 and 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 con?rms 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 de?ned in Eq. (1) applies only to R1, not to the directly measured Rm, since R2 is independent from travel distance.For a free bolt R1≈, the main energy loss will be the setup loss and Rm≈R2. It can be inferred that for grouted rock bolts, the nongrouted 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 .. 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 wellde?ned 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 Achenbach’s solution in a steel bar of 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。 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 (., 25 kHz), the group velocity in the grouted bolts was about half of that in the free bolts。首先對(duì)自由錨桿進(jìn)行實(shí)驗(yàn)來了解導(dǎo)波在非錨固時(shí)的行為。實(shí)驗(yàn)結(jié)果表明，在自由和錨固錨桿中，群速度有不同的趨勢(shì)。但是，在錨固錨桿中衰減隨著頻率和錨固長(zhǎng)度的增加而增加。關(guān)鍵詞：巖石錨桿；導(dǎo)波；衰減；振幅；群速度1 引言錨桿被廣泛應(yīng)用在采礦和土木工程中的地下和地表開挖后加固和穩(wěn)定地面。測(cè)試錨桿錨固質(zhì)量和監(jiān)測(cè)錨桿預(yù)緊力長(zhǎng)期以來一直是該領(lǐng)域中的一個(gè)挑戰(zhàn)。這兩種方法都是破壞性和耗時(shí)的實(shí)驗(yàn)。因此，像利用超聲波這種非破壞性測(cè)試方法已經(jīng)受到了關(guān)注。導(dǎo)波的性質(zhì)，如速度和衰減，受輸入波頻率的作用影響。在錨桿中，波的行為不僅與錨固的質(zhì)量，而且與波的頻率有關(guān)，也受錨桿周圍巖體的特性和錨固長(zhǎng)度的影響。導(dǎo)波不像體波，而是由一個(gè)束具有不同頻率的成分波疊加組成。在錨桿中，能量傳遞速率與群速度相同。我們發(fā)現(xiàn)群速度在錨固錨桿中低于在自由錨桿中。實(shí)驗(yàn)結(jié)果表明，為錨桿實(shí)驗(yàn)輸入低于100千赫的頻率會(huì)提供更好的分辨率和更清晰的信號(hào)。導(dǎo)波的另一個(gè)重要特點(diǎn)是衰減。衰減是信號(hào)長(zhǎng)距離傳輸過程中波能損失的自然結(jié)果。波的衰減是由一個(gè)衰減系數(shù)定義的。 (1)其中Aa，Bb分別是位置a，b處的振幅；是衰減系數(shù)且是常數(shù)；L是從a到b的距離；R 是振幅比率，R=Ab/Aa。在錨固錨桿中波的衰減是非常復(fù)雜并且常常受包括錨固材料和錨固質(zhì)量在內(nèi)的多種因素的影響。通常，波的衰減可能有幾個(gè)部分組成，其中一些隨頻率變化一些與頻率無關(guān)。根據(jù)起因，衰減可分為以下幾類：(a) 耗散衰減：一種由非彈性介質(zhì)阻礙引起的能量損耗。這類型的衰減在鋼材中跟在巖石中相比普遍很低，如后面所述，在實(shí)踐中由于鋼的低阻力和錨桿長(zhǎng)度(1~3 m),導(dǎo)波在錨桿中傳播時(shí),這種衰減可以被忽視。這也是導(dǎo)波在波傳播中區(qū)別于體波的一個(gè)特點(diǎn)。(c) 傳播衰減：一種發(fā)生在錨桿與錨固材料界面間的能量損失。一部分能量會(huì)穿過界面，并傳到錨固材料，這種現(xiàn)象稱為能量泄漏。錨桿中的總衰減就是這兩種衰減的總和，以后將統(tǒng)稱為色散衰減。另一個(gè)重要組成部分，是在錨桿樣品及設(shè)備的接觸面之間折射的能量損失。在錨桿實(shí)驗(yàn)中，傳感器被放在接觸測(cè)試框架的錨桿樣品上（例如，一張桌子或機(jī)架）。如后面所述，這類能量損失預(yù)計(jì)將是不間斷的，作為特定類型的試驗(yàn)裝置這是一個(gè)固定的數(shù)量值,下面稱為安裝能量損失。在達(dá)爾豪西大學(xué)正在進(jìn)行的研究項(xiàng)目，旨在研究導(dǎo)波在錨桿中傳播的特征。得到的結(jié)果具有很強(qiáng)的說服力，詳情如下文。在這項(xiàng)研究中，分別對(duì)自由錨桿和錨固錨桿進(jìn)行了試驗(yàn)。自由錨桿是裸露的鋼筋。在這些測(cè)試中錨桿沒有被拉緊。2個(gè)自由錨桿（試件1和2）被用來研究錨桿長(zhǎng)度和頻率對(duì)導(dǎo)波的影響，尤其是由于設(shè)備安裝導(dǎo)致的安裝能量損耗。表1 錨桿試件的幾何特征樣品錨桿長(zhǎng)度/mm錨桿直徑/mm錨固長(zhǎng)度/mm錨固直接/mm1240000210000031200300160412005001605800750160 試驗(yàn)儀器和實(shí)驗(yàn)描述在研究中所用的工具，包括一個(gè)手提示波器HS3(有產(chǎn)生波的數(shù)據(jù)采集器)，一個(gè)放大器，兩個(gè)傳感器和一臺(tái)電腦。單一的手提示波器HS3有發(fā)不同頻率的超聲波信號(hào)的能力，以及接收和數(shù)字化接收波的信號(hào)。在另一端接收到的信號(hào)先是被擴(kuò)增，然后被數(shù)字化。傳感器是來自物理聲學(xué)公司R6和R15類型的壓阻式電動(dòng)機(jī)。實(shí)驗(yàn)的進(jìn)行通過激發(fā)一個(gè)發(fā)射機(jī)（R6），在錨桿樣品非錨固的末端輸入不同頻率的輸入信號(hào),在信號(hào)到達(dá)的另一端被一個(gè)傳感器（R15）接收，整個(gè)波形被數(shù)字化錄入。3 實(shí)驗(yàn)數(shù)據(jù)的分析方法在下文中，“首次到達(dá)”指第一束波第一次到達(dá)接收端，“回聲”指同一束波到達(dá)接收端，“反射波”是指上述的波束到達(dá)接收端后反射回輸入端。 衰減估計(jì)如前面所解釋的，衰減不僅和錨固性質(zhì)，而且和頻率及其他因素有關(guān)，和一個(gè)傳播了若干距離的波束的振幅有一個(gè)逆對(duì)數(shù)關(guān)系，如（1）式衰減系數(shù)所示。因此實(shí)測(cè)振幅比Rm，在這一研究中作為衰減的一種間接測(cè)量： (4)其中A1是首次到達(dá)的平均振幅，A2是回聲的平均振幅。因此很難研究在錨固錨桿中波的衰減，因?yàn)椴ㄐ斡涗浲鼙∪?，而且受很多噪音的影響。?dāng)錨桿很短或嚴(yán)重分散時(shí)這個(gè)問題更加突出，在這種情況下波的最大波幅可能會(huì)受這類噪音的影響。本文提出了一種計(jì)算振幅比的方法，就是利用一定的時(shí)間間隔內(nèi)的平均振幅來計(jì)算，公式如下： i=1，2 （5）其中是最大振幅間的時(shí)間間隔，是波的振幅，i=1表示首次到達(dá)，i=2表示回聲；k是材料常數(shù)。因?yàn)檫@個(gè)方法考慮兩個(gè)相同時(shí)間間隔中首次到達(dá)和回聲的平均振幅，所以誤差和噪音對(duì)最大振幅的影響最小。模型一在不同頻率下的結(jié)果如圖4所示。當(dāng)時(shí)間間隔超過這個(gè)波形的25%時(shí)，結(jié)果變化就非常小，幾乎達(dá)到100%。輸入25khz的信號(hào)，自由錨桿中的時(shí)間間隔包含整個(gè)波形的45%，當(dāng)輸入100khz是，時(shí)間間隔占整個(gè)波形的95%。而且這個(gè)方法在實(shí)踐中非常容易算出能量的損失，尤其是在色散導(dǎo)致錨固錨桿中首次到達(dá)和回聲的界限很難分辨的時(shí)候。但是，確定首次到達(dá)和回聲的開始常常受到色散特性的影響。所以首先需要把記錄的原始波形濾波來約束每次實(shí)驗(yàn)頻率的頻帶。所有記錄的波形都可以用這個(gè)程序?yàn)V波到一個(gè)177。我們發(fā)現(xiàn)，用過濾的波形確定到達(dá)時(shí)間更能代表某種頻率的實(shí)際波的傳播時(shí)間。計(jì)算得到的群速度在自由錨桿和錨固錨桿中有不同的趨勢(shì)，具體在下文介紹。4 自由錨桿中頻率和錨桿長(zhǎng)度對(duì)導(dǎo)波行為的影響用25khz到100khz的頻率在自由錨桿中實(shí)驗(yàn)表明試件1中輸入25kzh頻率的典型波形。 自由錨桿中的衰減對(duì)自由錨桿1和2的實(shí)測(cè)振幅比Rm如圖6所示。因此，振幅比受錨桿長(zhǎng)度的影響不大，兩錨桿的細(xì)微差別可以忽略。既然在波形中沒有或有很少的色散，能量也就不會(huì)泄露到其他介質(zhì)中，跟頻率和傳播距離有關(guān)的色散衰減在自由錨桿中也就可以忽略。如前所述，這部分能量損失主要是因?yàn)榘惭b損耗，大部分由錨桿和其他物體接觸面的反射引起