International Symposium (NDTCE 2003) NonDestructive Testing in Civil Engineering 2003  
Start > Contributions >Posters > Tendon Ducts: 
Comments on void depth detection in tendon duct with the impact echo method based on finite element computationsOdile ABRAHAMLCPC  BP 4129  F44340 Bouguenais Cedex  France Odile.abraham@lcpc.fr ABSTRACTThe impact echo method can be used to detect void in tendon duct in certain condition of void depth and void size. It has been stated that a void causes a decrease of the thickness frequency of the slab as well as the appearance of a frequency peak indicative of the depth of the void that is different by a factor around two of that of a filled duct. The second phenomenon does not appear to be easily observed in the field. To gain insight in the limits of detection of this void depth frequency, and in order to understand the physics of the multiple reflections that exist between the surface and the circular void, some finite element modelling has been undertaken. The results are presented as frequency profiles in order to reproduce numerically a robust experimental procedure. It is shown that for small void, the void depth frequency can be mislead with multiples of the thickness frequency especially when no frequency profile are carried out. Finally, a procedure that includes a thickness frequency profiles followed by void depth frequency profile is proposed. It is expected that these two profiles, eventually combined with time frequency analysis of the signal, are an efficient way to detect voids in tendon ducts. INTRODUCTIONThe impact echo method was developed in the 1980's for the non destructive testing of concrete structures by the National Institute of Standards Technology (USA) and Cornell University (USA). A extensive bibliography can be found in Sansalone et Streett (1997). The impact echo method relies upon the study of echoes, in the frequency domain, of the Pwave between the surface of a slab and an interface with material exhibiting different mechanical impedance values. As illustrated in Figure 1, the frequency f_{e}, corresponding to the thickness, e, of a concrete slab is:
Where b is a shape factor equal to 0.96 for the case of a solid slab^{2}, and v_{p} is the Pwave speed. If the duct is grouted and filled with steel, the frequency corresponding to the slab thickness will be almost identical. The frequency corresponding to the reflections from the tendons in the filled duct, f_{steel}, is:
Where d is the depth of the duct. If the duct is not grouted, the frequency corresponding to the slab thickness is shifted to a lower value f_{e}' (Abraham & Côte, 2000), and the frequency corresponding to the reflection from the empty duct, f_{void}, equals:
Several papers have been published on the use of the impact echo method for the detection of voids is tendon ducts. They all relate difficulties either to detect a clear peak at f_{steel} or f_{void}(while the thickness frequency shift is often measured). Several factors main may explain this difficulty:
In the following the shift of the thickness frequency and the detection of f_{void} will be discussed with the help of finite element computations. DESCRIPTION OF THE FINITE ELEMENT MODELSThe calculations were performed with the CESAR finite element code (Humbert, 1989). The concrete was assumed to have a density of 2400kgm^{3}, a Young's modulus of 42003MPa and a Poisson's ratio of 0.22, which leads to a v_{p} value of 4470ms^{1}. Material attenuation was neglected: its effect has been discussed elsewhere (Abraham et al., 2000). The 2D models are computed under plane strain conditions with quadratic 6node triangular elements (Fig.1). The slab is 2m long and 0.2m thick. Consequently the thickness resonance frequency is equal to 10.7kHz. Both edges of the slab are clamped. The source is either centred on f_{Ri}=35kHz or f_{Ri}=20kHz. High frequency sources have been selected in order to study f_{void}. The mesh size is smaller than v_{p}/(2max{f_{Ri}})/20, more precisely, less than or equal to 0.006m. The time step is equal to 1ms and the calculation is performed at 512 points, for a total duration of 0.512ms. The signal are always windowed with the same Hanning window whose length is equal to the total duration of the signal in order to lessen the effect of the surface waves (Abraham & et., 2000). The circular void is located in the middle of the slab and in the middle of the thickness. Its diameter is equal to 0.04m (f_{void}=26.8kHz) or 0.06m (f_{void}=30.7kHz). To improve both the repeatability and confidence of impactecho surveys and in order to lessen the need for locating the duct precisely, frequency profiles in the perpendicular direction can be developed. This step consists of performing several impactecho measurements in the vicinity of the duct, at a distance increment ds that is small in comparison with the duct diameter (typically less than D/2), on a line crossing the tendon duct perpendicularly to the long axis (see Fig.2). In the following ds=0.02m and 12 source points on each side of the duct are computed. For each measurement point, the source and the receiver are close to each other (distance less than ds). For each measurement point, the amplitude spectrum is calculated and results are plotted in a 3D frame of reference (Bscan). If the location of the duct is known, the measurement points following the duct can obviously be processed in the same fashion provided they have been spaced closely enough.
FINITE ELEMENT RESULTSWith no void Figure 3 shows the finite element results when there is no duct for the two sources. It is a frequency profile (or Bscan): the xaxis is the distance from the centre of the slab (Fig.2), the yaxis is frequency, and the colours are representatives of the normalised amplitude of the Fourier spectrum of the signal. Of course the spectra are the same as x varies, that is when the source is moved along the slab, for there is no void. When the source is centred on 20kHz, the thickness resonance frequency f_{e} is dominant. Some multiples of the resonance frequency are even though visible. When the source is centred on 35kHz the third multiple is now dominant. Those results again emphasise that the choice of the source is a primordial factor influencing impact echo results (Abraham et al, 2000, Abraham et al., 2002b). With a void Figure 4 and Figure 5 show the results for the two void diameters. The first thing to be noticed is the shift of the thickness frequency towards a lower value. This shift is an efficient way to detect a void (Abraham & Côte, 2002a) as far as the thickness of the slab is known. It is affecting the thickness frequency over a quite large zone that extends outside the void diameter. In Abraham & Côte 2002a it has been shown that to diagnose separately two tendon ducts, they should be distant of at least 4 time their diameter.
The expected f_{void} frequencies are indicated by white dashed lines on the frequency profiles (f_{void}=26.8kHz for D=0.04m and f_{void}=30.7kHz for D=0.06m). When looking where the energy is located in the spectrum, nothing can be seen near those f_{void} frequencies. Nonetheless the effect of the void on the higher part of the frequency profiles is clearly seen especially around the multiples of the thickness frequency f_{e}. The patterns observed are quite complicated: more work is required to understand the interaction of the wave field generated with an impact on the surface of the slab with a void located underneath. Note that to avoid bias, the sources are centred on frequencies that do not correspond to the f_{void} frequencies themselves. The source frequency is either smaller or larger for both void sizes. In all cases, the second multiple becomes more energetic with regards to the thickness resonance frequency and its multiples comparing to the case with no void. When the source is centred on 20kHz the effect of the void on the second multiple is larger for the larger void. This effect remains located near the expected value of the second multiple. Discussion For instance the coefficientb used in the calculus of f_{void} still need to be confirmed and explained. The influence of the shape of the void should be studied: the void depth should be unchanged as well as its horizontal extension (from a circle to a rectangle for instance). Note as well that a common depth for a tendon duct is around the middle of the slab which means that the second multiple of the resonance frequency is located nearby the frequency f_{void}. Proposed procedure
It should be noticed, the shift of the thickness frequency is often seen with the high frequency source so that one frequency profile might be enough.
ConclusionThe objective of this paper was to put into relief some questions about the detection of voids in tendon duct with the impact echo method that still need to be addressed. It has been stated that the shift of the thickness frequency is a reliable tool to detect void and that the appearance of the thickness resonance frequency above a void might come from complex phenomena that modify the relative energy of the second multiple of the thickness frequency. REFERENCES

