I appreciate Dr. Grosse's statement concerning the importance of focusing on the scientific aspects of impact-echo and other NDT methods, and not on advertising for commercial purposes. When the scientific and practical aspects of the impact-echo method become better understood, increased commercial use will follow.

In his message dated 2/6/98 Dr. Grosse presented three questions:

First Question: 'How can we be sure of the number of P-wave reflections?' Dr. Grosse goes on to state that experience and calculations in his laboratory and elsewhere show that stress waves are rapidly attenuated in concrete (about 30 dB/meter) and that under these conditions 3 or 4 wave reflections in a 0.3m thick slab will be difficult to detect.

Answer: The two on-line reports cited in Dr. Grosse's Forum message of 2/6/98 describe computer simulations of the propagation of stress waves in concrete samples with and without small air inclusions comparable in size to grains of sand (0.4 to 0.6mm). These simulations show that stress waves with wavelengths of the order of these inclusions (frequencies 6 to 10 MHz) are rapidly attenuated by scattering. This expected result is not relevant to the discussion of impact-echo, because the wavelengths of the stress waves used in this method are far greater than the size of a grain of sand. At a frequency of 6.3 kHz and a wave speed of 3996 m/s (see Figure 1 below) the wavelength is greater than 600mm. Because this wavelength is far greater than the dimensions of the natural inhomogeneities, (air inclusions, mortar/aggregate interfaces, micro-cracks, etc.) the response of the concrete approximates that of a homogeneous medium, and the attenuation is due mainly to spreading of the spherical wave. The use of impact-generated stress waves of low frequency (up to about 70 kHz) and relatively long wavelength (50mm to about 2000mm) is the characteristic of the impact-echo method that distinguishes it from traditional ultrasonic methods, and that makes it especially well suited to testing a heterogeneous material like concrete. Long wavelength stress waves are reflected by flaws (cracks, voids, honeycombing, etc.) and internal interfaces (such as concrete/steel) with dimensions equal to or greater than the wavelength, and by external surfaces. Multiple reflections of P-waves excite short-lived natural resonances in the structure in the vicinity of the impact. In impact-echo testing the modes of vibration that are of principal interest are thickness, flexural, and cross-sectional modes. The frequencies of the principal modes, and in some cases higher modes, of vibration are measured using impact-echo, and used to calculate dimensions or the depth of flaws and internal interfaces.

The distribution of frequencies in stress waves generated by the impact of small steel spheres is a function mainly of the sphere diameter. This is explained in Chapter 3 of the book on impact-echo by Sansalone and Streett: http://www.impact-echo.com/Impact-Echo/bullbrie.htm .

The smaller the sphere diameter, the higher the maximum useful frequency (the maximum frequency for which the energy in the stress waves is sufficient for impact-echo testing). For a 12mm diameter sphere, the maximum useful frequency is about 25 kHz. For a 4mm diameter sphere, the maximum useful frequency is about 73 kHz.

In this discussion we restrict our attention to plate structures - those for which the lateral dimensions are large relative to the thickness. If the plate is solid, the P-waves produced in impact-echo tests are reflected back and forth between the two surfaces, and for the first few milliseconds they receive no interference from waves reflected from the lateral boundaries. The result is a waveform that takes on the appearance of a decaying sine wave, with a period equal to the time required for a stress wave to travel from the impact surface to the opposite side of the plate and back again. In answer to the first question of Dr. Grosse, it is a simple matter to observe, and count, the number of cycles in the recorded waveform.

Figure 1. Waveform (upper graph) and spectrum from an impact-echo test on a 315mm thick concrete plate (the wall of a railway tunnel). In this case the waveform consists of 2048 data points at intervals of 2u-s. Twenty-five P-wave reflections are present in the waveform (the maximum points). The dominant frequency is found from the spectrum (calculated by Fast Fourier Transform) to be 6.35 kHz. Figure 2. Impact-echo results from the same test shown in Figure 1, with the first half of the signal removed. The vertical scale in the waveform has been expanded, to show that the structure remains well defined up to the very end of the test (about 4 milli-seconds after the impact).

Figure 1 shows the results of an impact-echo test, performed as part of a systematic study of wall thickness in a railway tunnel, using a commercial impact-echo test instrument. In this test 2048 data points were recorded at intervals of 2 u-s, for a total time of 4096 u-s. The upper graph is the time-displacement waveform and the lower graph is the amplitude spectrum calculated using a Fast Fourier Transform. A low-frequency component present in the original waveform (at about 1.0 to 1.2 kHz), caused by the natural resonance of the transducer element, has been removed by digital filtering.

Each maximum on the waveform marks the approximate arrival time at the transducer of a reflected P-wave. In this example 25 P-wave arrivals are visible. This represents a travel path of more than 15 meters in a plate that is a little more than 0.3 meters thick. The time difference between the two cursors on the waveform, which are 10 cycles apart, is 1948 - 358 = 1590 u-s. The period of this "sine wave" is approximately 159.0 u-s, which corresponds to a frequency of 6.30 kHz. The dominant peak in the spectrum, calculated using a Fast Fourier Transform, is 6.35 kHz. The wave speed was found from independent measurements to be 3996 m/s. The expected thickness frequency, f, is calculated from the simple equation f = Cp/(2t), where Cp is the wave speed in m/s and t is the thickness in meters. In this example the thickness was unknown in the beginning, and was estimated to be 0.4m, from which the expected frequency was calculated: f=3996/(2 x 0.4) = 4995 Hz or about 5.0 kHz. From the observed thickness frequency of 6.35 kHz, the true thickness is calculated: t = 3996/(2 x 6350) = 0.315m. (In cases where the thickness is known, but the wave speed is unknown, an estimate of the wave speed is used in the first test, and the observed frequency and the known thickness are used to calculate the true wave speed.)

Figure 2. To illustrate the point that long wavelength P-waves are slowly attenuated in concrete, Figure 2 shows only the second half of the waveform (recorded between 2048 and 4096 u-s after the beginning of the test) and the corresponding spectrum. The vertical scale of the waveform has been expanded to show that oscillations in the signal are still clearly defined at the end of the waveform. The 6.3 kHz peak in the spectrum is even sharper than that in Figure 1. It is clear that if the signal had been recorded for more than 4096 u-s, many more P-wave arrivals could be detected.

It is useful to point out here that computer simulations of stress wave propagation using finite element methods (not the same as finite difference methods) carried out by Professor Sansalone on a 315mm thick concrete plate, produce a waveform very similar to that shown in these figures. She has also demonstrated that finite element simulations of a plate structure produce a waveform that is virtually identical to the Green's function solution for an infinite plate. (See References 31, 33, 40 and 41from the book on impact-echo by Sansalone and Streett. These references appear in the article on impact-echo in this month's NDTnet journal.)

Summary: Stress waves with wavelengths greater than about 50 mm travel long distances in solid concrete without severe attenuation. They are reflected by flaws (cracks, voids, etc.) and internal interfaces (such as concrete/steel interfaces) that have dimensions equal to or greater than the wavelengths of the stress waves, and by external surfaces. If a transducer that responds to small surface displacements is used to detect P-wave arrivals at the impact surface, it is possible to record multiple P-wave reflections and to determine the frequencies of transient resonances in the vicinity of the impact point. The depths from which the P-waves are reflected can then be calculated. In practice a single impact-echo test can be completed in less than 30 seconds, often in less than 10 seconds.

Second Question: What is the influence of the condition of the surface of the tested material when using an impact source?

Answer: If the concrete surface is especially rough it is sometimes necessary to grind a small spot smooth. We use a battery-powered electric grinder for this purpose. It is seldom needed for concrete surfaces produced by wooden forms or exposed horizontal surfaces that have been smoothed, such as floors and decks.

Third Question: How important is the frequency response of the receiving transducer to the results? Do you document the frequency response as well as the phase response of the transducers you use with your equipment?

Answer: The frequency response of the transducer is extremely important. The transducer used in Professor Sansalone's original instrument and in our commercial instrument is a conical, broadband, displacement transducer, originally developed for acoustic emission testing of metals by T. M. Proctor at the Ultrasonics Division of the U.S. National Bureau of Standards (now called the National Institute of Standards and Technology). For details, see T. M. Proctor, 1982, 'Some Details on the NBS Conical Transducer', Journal of Acoustic Emission, Vol. 1, No. 3, pp.173-78. The transducer consists of a small, conical piezoelectric element attached to a brass backing. The tip of the transducer in contact with the concrete (through a thin lead disk) has a diameter of approximately 0.7mm, and the height of the cone is about 3.5mm. It produces an analog voltage signal in response to surface displacements normal (perpendicular) to the surface, and the response is essentially flat over the range of frequencies of interest in impact-echo (0 to 70 kHz). The frequency response and phase response of the transducer are documented in the paper by Proctor (above).

Prof./Dr. William B. Streett
Cornell University
Ithaca, New York
10 February 1998