LA METHODE DE RESONANCE - APPLICATION D'UNE NOUVELLE METHODE DE MESURE NON-DESTRUCTIVE PAR EGARD A MESURFS D'EPAISSEUR DES ELEMENTS EN BETON MAL ACCESSIBLES
| Figure 1: |
"Multiples" caused by reverberations between
different layers in the upper crust (after Berkhemer )
Besides the detection of damages and inhomogeneities in an object, this technique is also capable of determining the dimensions of elements. This is a well-known problem, i. e. when making researches and expertises of damage at concrete buildings, especially when they are remote, like concrete pavements and catching basins. In these cases, today normally destructive tests are performed, using endoscopy in drill holes or examining drilling cores. In the conventional ultrasonic pulse-echo method, the stress pulse applied on the surface by an ultrasonic impactor is detected by an piezo- electric transducer. The return time of the wave reflected by an interface in the medium gives the information that is needed. In concrete, this method is failing due to the heterogeneity caused by the reinforcement and the large grain size of the Aggregate. Additionally, the wave field radiated by the impactor is disturbing the transducer, so that all further impulses are vanishing in the coda of the primary wave. Attempts have failed to optimize this setup of measuring for the use in concrete . The following studies were motivated by the wish of introducing a nondestructive testing method for these cases. Indeed, it has to be accentuated that this method, after fundamental optimization, also may be applied to other materials like natural stone, metals, wood. First experiences have been made using this new method for detecting spalls and flaws in statuettes of sandstone .
The wave field radiated by the impactor 1 is propagating into the object along spherical wavefronts. After a short travel time t1 the direct wave meets the transducer a. Depending on the distance between impactor and transducer, at a later time also the background echo reaches the transducer. However, this signal is vanishing in the seismic recording of the primary wave due to the strong attenuation in concrete (15-20 dB/m). Besides, a waveform with period T (wavelength L1 = double object thickness 2d) is developing, consisting of a constructive interference. This means, finally a stationary wave is dominating the recording, showing a rather low-frequency signal with frequency Fr. An analysis of the time signal by a fast fourier transform shows the frequency spectrum of the primary wave plus the resonance modes± according to the thickness of the object. This relation yields the following expression:
This fact is illustrated in fig. 3. According to the method we will describe below, a wave has been applied on the surface of a concrete slab. This wave was detected with a piezo-transducer at a distance of 5 cm. Fig. 3 a) shows the complete signal in the time domain. The signal decays after approximately 20 ms. The transformation of this signal into the frequency domain² shows fig. 3 b). The main maximum in the amplitude spectrum near 6,7 kHz is corresponding (using eq. 1) to a thickness of the concrete slab of 30 cm and a wave velocity of 4020 m/s. The period of this wave is according to twice the object thickness.
1 Besides waves with the fundamental mode Fr and the wavelenght L, there are additional waves interfering constructively: (n *Fr) and n = 1,2,3,... . The higher modes n > 1 are of no significance because of the attenuation.
² We used a Fast Hardley Transfom (FHT) with 4092 points taped with a Hanning-window .
3. 1. Measurement of the P-wave velocity
Usually, the P-wave velocity in materials is determined by measuring the travel time of a triggered pulse. Yet the travel distance between impactor and transducer has to be known. In the case of remote objects, this method is not applicable, since only the surface is accessible. At a little higher expenditure, it is possible to measure the P-wave velocity also on the surface of an object. The reason therefore is the propagation of the wave field also along the surface of the object. As shown in fig. 2, this measurement is enabled by an additional transducer at some distance from the other transducer. The signal produced by the impactor is triggering transducer a after a time t, and is reaching transducer b, travelling along the track S2. The travel time measured, the velocity easily can be computed:
3.2. Impactor signal
As this non-destructive testing method uses sound waves, the excitation of these waves is of considerable importance for the success of the measurement. Especially required is a wide range of frequency components in the radiated wave field. This is the only way to make sure that the frequency corresponding to the thickness of the object is stimulated. This is easy to realize by dropping a small spherical steel ball from a certain height down to the surface next to the transducer. Besides it's obvious, that the width of the frequency spectrum is inverse to the contact time of the steel ball on the surface of the object - an idealized delta-peak is producing a white spectrum, the widest spectrum that is possible. Therefore, it is important to use steel balls as small as possible for the excitation. The larger the diameter of the balls, the lower-frequent are the emitted signals, as shown in fig 5. Usually, we used steel balls with diameters of 4-8 mm. Different energies, respectively amplitudes of the impulse may easily be attained by varying the height of fall. Carino & Sansalone suggested to use a steel ball which is hit by a spring bolt as impact source. The advantage of this Arrangement is a better control of the applied energy. But this parameter is not decisive for the aim of our measurements.
3.3. Signal recording
For the use of this measuring technique on structures, it is important to have a user's friendly and robust signal recording system. Also an instant check of the measuring results should be possible. For that reason, a direct A/D-conversion with the option of a fourier transform is indispensable. As described earlier , we are using an 8-channel transient-recorder with a maximum sampling rate of 1 MHz per channel. Each channel has an own 12 bit A/D-converter. An additional use of preamplifiers is required only to improve the signal/noise-ratio. During our tests, the broad band piezo transducers were usually connected directly with the transient-recorder. A suitable software provided the computation of the fourier transform directly after the A/D-conversion of the signals. All results were displayed almost instantaneously on the screen. The data were stored first to the internal storage facility of the transient recorder (256 kbyte RAM per channel). At a typical signal length of 2048 points, thus almost 100 single measurements can be recorded. Of course, it is possible to shift the measurement data to the 100 Mbytes hard disk drive.
4. 1. Measurements on different specimen
First the method has been tested on specimen in the laboratory. Two concrete plates of 30 cm thickness had been designed, one of them reinforced (plate B), the other plain (plate A). For avoiding resonance effects coming from the short sides of the plates, a rather large base (150x80 cm) had been chosen. Fig. 6 explains the experimental setup. The plates rested on three small wooden beams for reaching a clear background echo. The point of the measurement was carefully chosen, thus an interface concrete-air was provided.
First of all, the average P-wave velocity was determined by using the through-transmission pulse-velocity method (with an ultrasonic transmitter of 20 kHz resonance frequency). Altogether, 600 single tests at different points and with different transmitter-transducer configurations have been analysed. They are summarised in line 1 of tab. 1. The standard deviation is according to a relative error of only 3 %. Although we supposed a higher vp-value in reinforced concrete, this could not be confirmed within measurement accuracy. The results presented in the second line we obtained by measuring v. at the surface of the two plates. It was found that these velocities were distinctly slower than the ultrasonic pulse velocities. The measurements of the frequency spectrum did not present similar difficulties. An example is shown in fig. 3. The frequency maximum of every fourier spectrum has been extracted and is shown in line 3 of tab. 1. The frequency values were remarkably reproducable and their scatter was far below the measuring accuracy of the speed measurement. The thickness of the concrete plate is computed using eq. 3 and referring to the speed measured on the surface of the plates (line 4).
Table 1: Measurements of the thickness and the P-wave-velocities at two different slabs.
|A: not reinforced slab||standard deviation||B: reinforced||standard deviation|
|1||vp (ultrasonic pulse) [10^3 m/s ]||4.18||+/- 0.11||4.26||+/- 0.13|
|2||vp (measured on the surface) [10^3 m/s]||4.01||+/- 0.10||4.06||+/- 0.05|
|3||resonance frequency [Hz]||6.50||+/- 0.03||6.88||+/- 0.03|
|4||thickness (acc. eq. 1) [cm]||29.6||+/- 0.5||29.5||+/- 0.5|
|5||vp (with resonance method) [10^3 m/s]||3.90||+/-0.14||4.13||+/-0.16|
The ultrasonic pulse velocities are rather high compared to those obtained by measuring on the surface of the plates. The bleeding in the upper areas of concrete plates, this means the segregation of the Aggregate grains during the compaction process, may be a reason for this discrepancy. For our interests, this effect seems to be equalized by the fact that in the resonance measurements occur slower velocities as well. Thus we are able to calculate the "correct" thickness (30 cm). Going the opposite way, this is easy to see: presuming the thickness as well-known, the P-wave velocity can be calculated with high precision, as shown in line 5. It is nice to see that these vp-values correspond to those measured on the. surface. An explanation therefore is hard to find. Already Carino & Sansalone [6, page 137; 1, page 117] have reported this effect. According to their researches, the difference between the two measurement methods comes to approximately 10 % of the ultrasonic pulse velocity. It was important for our considerations to see that the velocities measured on the surface produced quite useful results which lead to very exact values of the plate thickness. This fact was confirmed during the following field tests.
4.2. Tests at a retaining wall with the interface concrete-soil
The experimental setup described in chapter 4.1 is little exemplary as far as the inter-face concrete-air represents an idealized case with a high reflectivity. In practice, we have to deal with a different medium adjoining to the remote side of the concrete object. Because of that, we performed another experiment at a retaining wall of reinforced concrete. The thickness of the wall could be measured on the top side with values between 23,5 and 24,5 cm. In tab. 2 the results are shown. Once more, the P-wave velocity has been determined both using the transmission method and measuring it on the surface. The resonance frequencies have been measured on five different points. We computed the thickness of the wall using vp measured on the surface (line 2) as well as the pulse velocity (line 3). Four of the five spectra are presented in fig. 7, giving an impression of the analysis of the resonance peaks. The similarity of the spectra is easy to recognize. The variations of the main frequency are probably representing variations of the thickness differing from point to point. The absolute values of the thickness are determined exactly according to eq. 1, although the v.-values measured on the surface are distinctly slower than pulse velocities. Obviously the determination of the vp-velocity on the surface contains an systematic error of the same order (see above).
Table 2: Measurements at a retaining wall.
|1. measure.||2.measure.||3.measure.||4.measure.||5.measure.||mean||vp [m/s]|
|1.||resonance frequencies [kHz]||8.81||8.88||8.69||8.63||9.00||8.80||Z]|
|2.||thickness [cm] (vp surface)||23.3||23.1||23.6||23.8||22.8||23.3||4.11* 10^3|
|3.||thickness [cm] (vp direct)||25.6||25.5||26.0||26.2||25.1||25.7||4.52. 10^3|
4.3. Test-measurements on a concrete floor
For testing the suitability of the method on structures with unknown dimensions, a blank test has been performed. A concrete floor of unknown thickness has been tested using the resonance method (see fig. 8). To begin with, in an area of ca. 2 m² the P- wave velocity has been determined and systematically the resonances of the background echoes have been measured. While the vp-measurements delivered average values of 4200 m/s, the resonance measurements showed unexpected pictures. A selection of them is shown in fig. 9. Two differently significant peaks at about 7000 resp. 11 000 Hz are easy to perceive. Using the determined vp, these peaks are corresponding to a reflection horizon of ca. 20 res. 30 cm. We decided to drill a hole at the position represented by fig. 9 e). At this position, the reflections determined by the resonance method should be near 18.9 cm (7200 Hz) resp. 28.3 cm (11 000 Hz), the first value representing the main maximum.
After that, a hole of 24 mm diameter has been drilled and examined using an endoscope. At approximately 18.5 cm we saw a boundary layer between the concrete slab and a layer of lean concrete. This layer of poor concrete had in fact a thickness of 10 cm, which we did not expect. It was found that the resonance method could very successful predict the depths of reflecting interfaces within measurement accuracy. Obviously, different reflection contrasts between the two layers of concrete at different positions have caused the differences in the amplitudes of the main maxima.
4.4. Estimation of the measurement accuracy and the systematic and statistic errors
Although the measurements provided quite satisfying results, a number of disturbing effects have to be considered. First, it is obviously essential, that the reflectivity at the back surface (resp. at the reflecting interfaces) is high enough. This means, there has to be a sufficient difference of the material in which the wave is propagating, and the one at which the wave is being reflected. But as we found out, there were no problems, neither at the interface concrete-soil (chapter 4.2), nor at the interface concrete-gravel or concrete-lean concrete (chapter 4.3). Besides, already tests have been successful using this method for the detection of flaws in concrete (with horizontal cracks of some tenths of a millimeter of width) [6, 7] and spalls in sandstone . Cracks in elements of finite thickness are appearing in the frequency spectrum as side maxima with higher frequencies than the main maximum (produced by the background echo).
For a correct interpretation of the frequency spectrum, all the geometric effects are to be known. Especially the lateral boundaries of the objects have to be considered, because they could cause side or even main maxima. By a boundary, for example, additional modes are produced and show up in the frequency spectrum according to the lateral dimensions of the object. As far as these effects are known and do not superpose the frequency area of interest, the measurement is not affected by these problems.
It is important to take into account that the resonance method is not an integral but a point-focal NDT-method. The thickness will be tested at that point, where the transducer is put on. To produce a two-dimensional image of the specimen one have to scan the object with the test equipment. Of cause the expense could be significantly higher according to the intended accuracy. Under the assumption that the calculation of vp is not necessary at every point (see below), a single measurement requires about two minutes. Local inhomogeneities and thickness variations between the test points will not be measured. On the other hand, heterogeneities in the tested part of the object like voids or reinforcement may influence the results.
The error of measurement must be calculated by the law of error propagation. For an experiment, the error function of a determined quantity F(xi)which is related to some directly measured quantities xi, is given by Equation 4. In our case the main error of the determination of the thickness is calculated according to eq. 3 with:
The distance s between the two transducers on the concrete slab surface was fixed to 30 cm. With an accuracy of one millimeter this leads to a relative error of 0.4%. The accuracy of the frequency analysis is strongly depending on the geometry of the object, which effects the setup for the test. A very important boundary condition is the minimum depth din, from while a reflection is expected. The maximum bandwidth of the frequency Fmax, is related to:
For instance: to measure a thickness of at least 5 cm at a velocity of vp = 4000 m/s the bandwidth must be 40 kHz or more. This corresponds to a sampling rate of 80 kHz respectively a time base of 12.5 µs or less. Generally we choose at our measurements a time base of 10 µs (100 kHz). )with a recording interval of 40 ms this is corresponding to approximately 4 kWords of data for one measurement. The frequency resolution of the fourier transform is fixing the error of the resonance calculations. To achieve an error of less than 1 % the resolution Fmin, of the frequence determination should be around 66.7 Hz (according to chap. 4. 1: thickness 30 cm and vp= 4000 m/s). Actually we obtained a resolution of 25 Hz at a recording interval of 40 ms. This is related to an error of only 0.4 % at frequencies of 6700 Hz. Obviously the error of the frequency measurements is far below the other errors. Especially the P-wave velocity, measured with the travel time differencies Delt t (see eq. 5), is incorrect in a dimension higher. The transient recorder offers a time resolution of 1 µs (1 MHz) in maximum, what is related to an error of 2 µs (at a thickness of about 30 cm and with an velocity of 4000 m/s) res. 2.7 % at least. In fact the error will be even higher, because of the statistic deviation and the systematic errors like shown in chapter 3. 1: the travel path of the signals used for vp-measurements at the surface is different from that, used for the resonance method. It is difficult to estimate the influence of this error. We found that the effect is in the same order as the error regarding the calculation of vp with the resonance method (chap. 4.1). At other investigations this effect have to be taken into account. To draw a conclusion - by using equation 5 - we found an overall error of about 4 According to the last paragraph this figure have to be corrected. In our experience it is better to calculate with values of 3-6 % for the error of the thickness measurements. Of cause these values depend on the circumstances and the equipment, so the measuring error have to be calculated for every new experiment.
At present, this method is being improved at the FMPA. To increase the handiness, a shockproof industrial standard laptop equipped with a transient recorder plug-in board has been purchased. This plug-in board enables measurements with 12-Bit resolution and a maximum sampling rate of 5 MHz. Using two parallel inputs, a maximum sampling rate of 2 MHz for each channel is provided. Thereby, above all the determination of the compression wave velocity could have been improved. This has the largest influence to the total error, as shown above. Further researches aim at an improvement of the impact source.
|Prof. Dr.-Ing. H.W. REINHARDT , born in 1939, studied Civil Engineering and made
a thesis on photoelastic investigation of three-dimensional transient thermal stresses. Today he is Professor for Civil engineering materials at Stuttgart Univerity and Managing director of Otto-Graf-Institute (FMPA - Material Testing Research Institute) , Stuttgart, Germany.
Dipl.-Geophys. C.U. GROSSE born in 1961, studied Geophysics at the University of Karlsruhe. Today he procceed on his thesis
(Deadline for July 1996) and is a research member at the Institute of Construction Materials, University of Stuttgart, Germany. |
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