Abstract

Scanning impact-echo testing of concrete specimens represents a significant improvement compared to usual single point measurements. Imaging and interpretation of the results in the time-domain (B-Scan) as well as in the frequency-domain (impact-echogram) leads to much more significant and reliable results for thickness and defect location measurements. We present experimental as well as numerical results obtained at a concrete plate containing steel reinforcement and tendon ducts. It is shown that the used imaging techniques lead to new insights for impact-echo testing of finite concrete specimens. Due to reflections of surface and body waves at the lateral boundaries of the specimen geometrical patterns appear in the impact-echogram which turn out to have an important effect on the accuracy of thickness and wave speed measurements, respectively. It is demonstrated that these effects depend not only on the dimensions of the specimen, but also on the location of the actual measuring point and on the duration of the detected time-domain signal.

1. Introduction

Since 1986, when Sansalone and Carino presented their pioneering work [1], the impact-echo method has been successfully used for non-destructive testing of concrete specimens. A low frequency stress wave is introduced into the structure by hammer impact or steel balls. By that, certain resonance modes of the concrete structure under investigation are excited. In particular, thickness modes of vibration are primarily used to identify the back-wall or planar flaws. For that, the time domain-signal of displacement or velocity is usually detected a few cm beside the impact point. Performing an FFT then leads to significant peaks in the amplitude spectrum which can be associated with the depth of back-wall or flaws if the effective wave speed of longitudinal waves in the structure is known.

However, practical experience reveals that these single point measurements in concrete are not very reliable and are strongly sensitive to small shifts of source and sensor positions. This is due to the heterogeneity of concrete caused by aggregates, pores and cracks. Thus, a shift of the sensor position can produce significant differences in effective elastic stiffness, yielding remarkable deviations when detecting back-walls and flaws. In the present paper, it is demonstrated that scanning impact-echo testing as first described in [2] is a significant improvement compared to the usual single point measurements.

Another important problem is concerned with the effects of lateral boundaries of the structure under investigation. Impact-echo theory often neglects these boundaries. A plate for example, is often supposed to be infinitely large in lateral direction. However, Sansalone et al. performed numerical studies at finite concrete beams and columns by using the Finite Element Method [3,4]. These studies showed that certain correction factors for effective P-wave speed have to be used if the ratio of height (thickness) to width of the structure can no longer be neglected. These correction factors account for the fact that elastic wave propagation is no longer 'free' and is influenced by the lateral boundaries resulting in a decreased effective wave speed and thus, a lower frequency of the thickness mode of vibration. By using this approach, the correction factor only depends on the overall geometry of the specimen. In this paper it is demonstrated that also the location of the actual measuring point as well as the duration of the detected time-domain signal significantly affects the result of thickness measurements and flaw detection.

2. A laboratory study

For the experimental investigations, a realistic concrete specimen of dimensions 2 m ´ 1.5 m ´ 0.25 m has been used (Fig. 1). It contains a steel reinforcement mesh as well as three unfilled and partly-filled metal tendon ducts located in various depths (60, 80, and 100 mm, respectively). The diameter of the ducts amounts to 40 mm. The concrete contains normal-weight gravel and sand aggregates with a maximum grain size of 32 mm.

The measurement frame shown in Fig. 1 (left hand side) was used to perform scanning impact-echo testing along linear scanning lines using a spacing of 1 cm. The hammer used as impact source introduces a stress pulse with a duration of approximately 60 µs resulting in a maximum frequency of about 33 kHz. In a first measurement a scanning line parallel to the tendon ducts and displaced from them was chosen. The results are shown in Fig. 2 in the time-domain (B-Scan) as well as in the frequency-domain. The latter picture gives the amplitude spectrum as a function of the source/sensor location. This B-Scan-like representation in the frequency-domain is called 'impact-echogram' in the following.

	Fig 1: Concrete specimen used for the experimental investigations. In the left picture, the measurement frame is shown which allows scanning impact-echo testing along one-dimensional scanning lines or two-dimensional synthetic apertures. The picture on the right shows a bottom view of the interior of the plate before sealing.
	Fig 2: Experimental results of impact-echo testing along a linear scanning line without effects due to tendon ducts (Left hand side: B-Scan, right hand side: Impact-echogram).

The B-Scan clearly shows the multiple reflections of the longitudinal wave between upper and lower surface of the specimen, visible as horizontal bands. Moreover, significant geometrical effects due to reflections of surface and body waves at the lateral boundaries of the specimen can be seen as tilted structures. In the impact-echogram, the dominant frequency at about 8.2 kHz can be identified, corresponding to an effective P-wave speed of approximately 4100 m/s.

Furthermore, an eye-catching pattern of arches appears in the frequency-domain which is nearly symmetric to the center of the scanning line at y = 72 cm. It superimposes the horizontal band in the impact-echogram which is caused by the dominant back-wall frequencies. For reasons of symmetry this geometrical pattern is obviously caused by the reflections of Rayleigh and shear waves at the lateral boundaries of the specimen.

It is remarkable that superposition of the horizontal structure of back-wall frequencies and the geometrical pattern results in an undulated structure in the frequency-domain that limits the accuracy of thickness measurements compared to the case of an laterally infinite plate without any reflections from the boundaries. In the latter case a perfectly horizontal structure of back-wall frequencies in the impact-echogram can be expected.

In a second measurement a scanning line perpendicular to the tendon ducts was performed. In this region of the plate all three ducts were unfilled and thus, significant reflections were obtained in each case. The results of impact-echo testing are shown in Fig.3.

Fig 3: Experimental results of impact-echo testing along a linear scanning line with significant effects due to tendon ducts (Left hand side: B-Scan, right hand side: Impact-echogram).

The B-Scan shows the geometrical effects from the lateral boundaries again but moreover, also reflections from the tendon ducts appear. They can be seen by branches of hyperbolas being very similar to radar images. Another important fact is that at the location of the ducts the temporal distance between two successive back-wall echoes increases. Therefore, the dominant peaks in the amplitude spectrum shift to lower frequencies. This can clearly be seen in the impact-echogram on the right hand side of Fig. 3. The location of the ducts is x = 45, 85, and 125cm, respectively.

It is also important to point out that at some measuring points, the signal seems to be disturbed which is indicated by the vertical lines in both, B-scan and impact-echogram. From the experimental point of view it is not yet clear if this phenomenon is caused by variations of coupling conditions from one measuring point to another or by other effects, e.g. air-filled pores lying very close to the source/sensor position.

3. Numerical simulations

In order to systematically investigate the geometrical effects described above, comprehensive numerical time-domain studies have been carried out by using the elastodynamic finite integration technique (EFIT, [5]). In contrast to finite element calculations this method allows an easy and explicit consideration of aggregates and pores yielding a much more realistic simulation of impact-echo testing of concrete specimens [6].

3.1 Three-dimensional simulation of impact-echo testing
In Fig. 4, a three-dimensional discrete model of the concrete specimen shown in Fig. 1 is presented. It consists of 1.2 million grid cells and contains a steel reinforcement mesh and three metal tendon ducts. It is filled with normal-weight aggregates (gravel and sand) according to a standardised grading curve with a maximum grain size of 32 mm. The material parameters used for the simulations were r = 2050 kg/m³, c_P = 4000 m/s, c_S = 2400m/s for the cement matrix and r = 2670 kg/m³, c_P = 4435 m/s, c_S = 2640 m/s on average for the aggregates. For steel reinforcement and tendon walls, the material parameters of steel were used, i.e. r = 7800 kg/m³, c_P = 5900 m/s, c_S = 3200m/s. Dissipative absorption was neglected in each material. In addition to the aggregates, air-filled pores in the mm and cm range were also implemented into the model. They were approximated by voids with stress-free boundaries.

Fig 4: Three-dimensional discrete EFIT model of the concrete specimen shown in Fig. 1. It contains a steel reinforcement mesh and three metal tendon ducts and is filled with gravel and sand aggregates with a maximum grain size of 32 mm. The picture on the right shows a snapshot of the elastic wave field taken 0.241 ms after impact excitation at a position lying somewhat beside the utmost right duct. The whole numerical model consists of 1.2 million grid cells.

In Fig. 5, the results of a single point impact-echo simulation are shown. The time-domain signal of particle velocity on the left was calculated for a duration of 4 ms. Performing an FFT leads to the amplitude spectrum shown on the right hand side. A dominant peak at about 8 kHz can clearly be observed indicating the location of the back-wall.

Fig 5: Calculated time-domain signal of particle velocity at the sensor position (left hand side) and corresponding amplitude spectrum (right hand side) of the impact-echo simulation described in Fig. 4.

3.2 Simulation of impact-echo testing along scanning lines
In order to calculate B-Scans and impact-echograms as shown in Figs. 2 and 3, a set of simulations with various locations of source and sensor along a linear scanning line must be performed. Especially in three dimensions memory requirements and computation times are large. Thus, a first goal was to demonstrate that the geometrical effects described in the previous section are predominantly caused by reflections at outer boundaries lying perpendicular to the scanning line and therefore, two-dimensional simulations with significantly less computation costs are sufficient to model the overall effects.

In Fig. 6, the calculated B-Scan and impact-echogram for a linear scanning line using a three-dimensional model with somewhat smaller lateral dimensions as given in Fig. 4 are presented. In order to show the pure geometrical reflections from the boundaries, tendon ducts and steel reinforcement as well as aggregates and pores were neglected here.

Fig 6: B-Scan (left hand side) and impact-echogram (right hand side) calculated by using a linear scanning line in a 3-D homogeneous concrete model with dimensions of 1.3 x 1.5 x 0.25 m3 without steel reinforcement and tendon ducts. Note that compared to Figs. 2 and 3, the duration of the calculated time-domain signals amounts to 2 instead of 1 ms. Moreover, the point of origin of the vertical time axis is located at the bottom side of the B-Scan representation, whereas in Figs. 2 and 3 it is located at the top.

Fig 7: B-Scan (left hand side) and impact-echogram (right hand side) calculated by using a linear scanning line in a 2-D homogeneous concrete model without steel reinforcement and tendon ducts. The resulting patterns are very similar to the 3-D case shown in Fig. 6.

The B-Scan shows the multiple reflections of the back-wall echo as well as the reflections from the outer boundaries. Up to 1 ms, the observed patterns are very similar to those shown in Fig.2. In the impact-echogram nearly the same pattern of arches being symmetric to the centre of the scanning line can be seen. Further simulations clearly revealed that these patterns are caused by the reflections of Rayleigh, shear and pressure waves at the outer boundaries including mode converted echoes. However, the dominant parts are based on Rayleigh wave echoes.

Fig. 7 gives the same pictures for a 2-D cross-sectional model of the specimen considering the lateral boundaries only. It is remarkable that the overall patterns are very similar to the 3-D case. Especially for the time interval between 0 and 1 ms the agreement of the B-Scans is very good. For larger times, some quantitative differences can be observed due to reflections from the corners of the three-dimensional specimen which are absent in the 2-D case. However, the results demonstrate that obviously 2-D simulations are already adequate to investigate the geometrical effects in finite specimens.

3.3 Geometrical effects and their impact on thickness measurements
We now take a closer look on the results of thickness measurements in the frequency-domain. The left picture in Fig. 8 shows the B-Scan of a 2-D simulation in a homogeneous concrete model without tendon ducts and reinforcement. The length of the scanning line is 2 m according to the specimen shown in Fig. 1. The time interval of the signals amounts to 1 ms and thus, the picture can be directly compared to the left picture in Fig. 2. One can clearly see that the reflections from the lateral boundaries consist of various contributions from different wave modes, i.e. Rayleigh, shear and longitudinal waves directly scattered and indirectly generated by mode conversion at the boundaries.

Fig 8: Calculated B-Scan (left hand side) and impact-echogram (right hand side) using a two-dimensional homogeneous concrete model without tendon ducts and steel reinforcement. The time slice of the B-Scan data ranges from 0 to 1 ms. The length of the scanning line is 2 m.

As already mentioned in Sec. 2, the geometrical effects produce curved bands in the impact-echogram (picture on the right). This results in an undulated horizontal structure indicating that the back-wall frequency peaks change from one measuring point to another depending on the position of the bands. This is demonstrated in Fig. 9, where the dominant back-wall frequency is given as a function of position along the scanning line.

Fig 9: Back-wall frequency f0 as a function of position x along the scanning line.

Of course the curve in Fig. 9 is symmetric to the centre of the scanning line at x = 100cm. At this point the curve reaches a minimum of f₀ = 7.53 kHz. The difference to the local maxima at x = 22 and x = 188 cm, where f₀ = 7.96 kHz, is nearly 5.5 % ! This is an important result. It means that even if the P-wave speed is exactly known, results of thickness measurements at an arbitrary position of the plate fluctuate by ± 0.7cm (the thickness of the plate is 25 cm in this case), because the measured value strongly depends on the location of the actual measuring point.

It has been proven by further simulations that the curve progression given in Fig. 9 and thus, the uncertainty in thickness determination strongly depends on the length of the time-domain window used for FFT calculation. To the best of our knowledge these important results have not been described in impact-echo literature so far. They throw new light on the problem of correction factors for effective wave speed as introduced by Sansalone et al. [3,4]. As a conclusion it can be summarised that the correction factors depend not only on the overall geometry of the specimen, but also on the duration of the detected time-domain signal as well as on the location of the actual measuring point.

3.4 The effect of aggregates and pores
The frequencies typically used for impact-echo testing are small and the corresponding wavelengths are large compared to the size of aggregates and pores. Thus, heterogeneity of concrete is often neglected in impact-echo testing. However, previous numerical simulations revealed that in some cases things are not that easy, in particular if air-filled pores with dimensions of some mm or cm exist [7]. In order to investigate the influence of aggregates and pores, further simulations using an extended model have been carried out. The results are shown in Fig. 10.

Fig 10: Calculated B-Scan (left hand side) and impact-echogram (right hand side) using a two-dimensional heterogeneous concrete model without tendon ducts and steel reinforcement. The porosity due to air-filled pores amounts to 0.5 %.

Compared to the results given in Fig. 8, additional scattering noise can be observed in the time-domain but the dominant reflections are still visible. The patterns shown in the impact-echogram are also nearly unchanged indicating that heterogeneity does not influence the thickness determination very much. However, vertical dark lines at certain measuring points appear in the frequency-domain data. These disturbances can also be found in the B-Scan at the same positions.

The vertical lines look very similar to those found in the experimental data as shown in Fig. 3. Because in the simulation coupling conditions are always constant for each measuring point, one can conclude that the disturbances in the measurements are also - if not predominantly - caused by air-filled pores lying very close to the impact point and/or sensor position.

3.5 Indirect detection of tendon ducts
A very challenging task in impact-echo testing is the detection of filled or unfilled tendon ducts. In contrast to planar flaws, the scattered waves from the ducts undergo a large geometrical spreading, i.e. the multiple reflections between the measuring surface and the ducts are significantly smaller than between planar parallel surfaces. As a consequence, in many cases tendon ducts cannot be detected directly by using the impact-echo method. However, it is possible to detect them indirectly by observing changes in the back-wall frequency. This is demonstrated in the following by numerical simulations in a concrete model with three unfilled tendon ducts. The depth of the tendons is in accordance with the values given in Sec. 2.

In the B-Scan the three reflection hyperbolas caused by the ducts can be clearly identified. Further investigations revealed that the branches of the hyperbolas are mainly caused by shear wave reflections and only the central regions around the apex are due to longitudinal wave echoes. This is an important fact although the results are not very surprising. It is well known that the main part of the acoustic energy introduced by low-frequency hammer impact is transferred into the shear and Rayleigh waves propagating sideways. Only a relatively small portion can be found in the pressure wave running in forward direction.

Moreover it can be seen from the B-Scan in Fig. 11 that the back-wall echo at the position of a duct is significantly influenced by the scattering process. The impact-echogram shows that the corresponding back-wall peaks are shifted to lower frequencies. The simplest time-domain explanation for this behaviour would be to argue that the waves have to walk around the duct and thus, the traveling distance increases which in turn results in a lower frequency in the spectrum. A closer look to the problem reveals that it is better to replace this travel time model by an effective medium approach in which the shift of the frequency peaks is explained by a reduced effective stiffness of the plate in regions affected by the duct. Unfortunately, these problems are beyond the scope of this paper and cannot be discussed in further detail here.

	Fig 11: Calculated B-Scan (left hand side) and impact-echogram (right hand side) using a two-dimensional homogeneous concrete model with three tendon ducts at x = 45, 85, and 125 cm. The depth of the ducts is, from left to right, d = 60, 100, and 80 mm, respectively.
	Fig 12: B-Scan (left hand side) and impact-echogram (right hand side) as a result of subtraction of Fig. 11 from Fig. 8.

In order to better demonstrate the effects of the tendon ducts on impact-echo testing as described above, the pictures in Figs. 8 and 11 were subtracted yielding a difference representation in the time- and frequency-domain as shown in Fig. 12. In the B-Scan the reflection hyperbolas of the ducts can be seen much more clearly now. Moreover, the delayed back-wall echoes behind the first duct reflection are evident. Thus, the impact-echogram shows significant peaks at the three duct locations.

Similar to the model without ducts, the impact of aggregates and pores on the results has also been investigated here. For this, a heterogeneous 2-D concrete model including the three tendon ducts as well as aggregates and pores has been used. It is shown in Fig.13. The results of the corresponding simulation are shown in Fig. 14.

	Fig 13: Two-dimensional concrete model including aggregates, pores and three unfilled tendon ducts. The porosity due to air-filled pores amounts to 1 % in this case.
	Fig 14: Calculated B-Scan (left hand side) and impact-echogram (right hand side) using a two-dimensional heterogeneous concrete model with tendon ducts as shown in Fig. 13. The porosity due to air-filled pores amounts to 1 %.

In contrast to the simulation in Fig. 10, a somewhat higher porosity has been used in this case. The signal-to-noise ratio in the time-domain is obviously worse. Especially attenuation of shear and Rayleigh waves seems to be higher than that of the pressure waves due to their smaller wavelengths. Nevertheless, apart from the vertical lines at certain positions the overall appearance of the impact-echogram did not change dramatically. The shifted frequency peaks at the position of the ducts can still be seen.

The qualitative agreement between the simulation results shown in Fig. 14 and the experimental results presented in Fig. 3 is pretty good. All important phenomena in the measurements can also be found in the simulations. Even the scattering noise due to aggregates and pores can obviously be modeled in a very realistic way.

4. Conclusions

The numerical and experimental investigations presented in this paper show that even 17 years after Sansalone et al. presented their pioneering work about the impact-echo method there are still interesting new phenomena to investigate. The realisation of scanning impact-echo testing and imaging of the results in B-Scan-like manner offers new insights into the method and leads to much more reliable and significant results compared to the ordinary used single point measurements.

The geometrical effects caused by reflections of wave fronts at the outer boundaries of the specimen produce systematic errors in thickness and flaw depth determination. These uncertainties must be taken into account if the measurements are performed at specimens with lateral boundaries lying in the vicinity of the measuring point.

It has further been demonstrated that the presence of unfilled tendon ducts can be verified by determining the frequency shift of the back-wall echo. Further investigations not presented here reveal that it seems to be possible to determine the depth of the ducts also. This and the problem of filled tendon ducts with injection faults is part of ongoing research and will be presented in a forthcoming paper.

The elastodynamic finite integration technique (EFIT) has proven to be a very effective, powerful, and flexible method for time-domain simulation of impact-echo tests. In contrast to the finite element method, aggregates and pores can be implemented explicitly and thus, their influence on the time- and frequency-domain results can be investigated systematically. The numerical calculations turned out to be an important tool for a better interpretation of the received signals, for determination of the physical possibilities and limits of the method as well as for development and optimisation of imaging algorithms.

Acknowledgement

This work was supported by the 'Deutsche Forschungsgemeinschaft' (DFG) within the scope of the 'Forschergruppe FOR 384' (Non-destructive evaluation of concrete structures using acoustic and electro-magnetic methods), which is gratefully acknowledged. We dedicate this paper to the memory of Regine Lausch. It was not granted to her to further support our joint work but her ideas will live on.

References

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