TABLE OF CONTENTS

Summary Introduction Simulation Interpretation Conclusions Acknowledgements References

Summary

The elastic wave-propagation of ultrasonic signals in concrete with varying percentage of air inclusions is simulated in two dimensions using finite-difference-methods. Snapshots of the wave explain their different behaviour in several kinds of inhomogenous models with varying contrasts in their elastic parameters. The received A- and B-Scans show the negative influence of size-effects and air inclusions on the data and the induced problem to detect a flaw inside the concrete.

Zusammenfassung. Simulation von US-Rißdetektion in Beton mit unterschiedlichem Luftgehalt
Die aktive Durchschallung von Beton wird an zweidimensionalen Betonmodellen mit unterschiedlichem Luftgehalt mit Hilfe einer Finiten-Differenzen-Methode simuliert. Momentaufnahmen der Wellenausbreitung im Medium ergeben Aufschluß über das unterschiedliche Vehalten der Welle in dem inhomogenen Medium mit verschieden großen Kontrasten in den elastischen Parametern. Die empfangenen A- und B-Scans werden daraufhin untersucht, inwieweit die Lufteinschlüsse und Randeffekte die Daten negativ beeinflussen bzw. die Detektion eines Risses erschweren.

Résumé: Simulation des Éxperiments Ultrasonique dans Béton armé avec des Inclusion d'Air à des Pourcentages différents
Nous avons simulée la propagation des ondes élastiques en béton armé avec des inclusions d'air à des pourcentages différents en deux dimensions avec des méthodes à différences finies. Instantanés des ondes nous donnent des explications de leur conduire dans des matériaux avec des inhomogenités différents. Les données recu nous montrent les influences négatives des inclusions d'air et celles du bord du modèle. Nous avons la possibilité d' évaluer les problèmes qui resultent pour l' inversion et qui resultent pour la détection d' une rupture dans le béton.

Keywords: finite-difference simulation, elastic wave-propagation,scattering, air inclusions, ultrasound, non-destructive testing

Introduction

The motivation for this simulation are the difficulties occuring during the interpretation of ultrasonic data obtained in the non-destructive testing of concrete. The main problems arise because of air inclusions and size-effects. The wave-propagation depending on these parameters is to be investigated with this simulation.

This simulation is one of the first with the new finite-difference-grid investigated at the Geophysical Institute of the University of Karlsruhe [ Karrenbach, 1995] [Gold, 1997] which can cope with the problems that arise when FD-schemes solve the elastic wave equation for big contrasts in the elastic parameters (like air inclusions). The wave-propagation is computed up to eighth order. Because of that the f-d-allgorithm is more suitable than the finite-integration-algorithm that only can cope with second order [Fellinger, 1995].

Simulation

Fig. 1: Twodimensional concrete model with elliptic inclusions and fractal flaw in 5cm depth Fig. 2: Input wavelet, convolved with the frequency response function of the ultrasonic receiver.

A special medium program has been developed for producing models of of fiber-reinforced materials or concrete interactively, used as input for the FD-program. The chosen model (fig 1) exists of 500*500 gridpoints representing 10cm * 10cm concrete. Each gridpoint provides the three elastic parameters density, speed of pressure- and shear-wave for the finite difference simulation. The parameters are taken from the measurements of Weiler [Weiler, 1995]. The structure of the model is similar to specimen concreted according DIN 1045. Ellipses with different sizes are placed randomly into the matrix-material cement, representing the stuffing material: 22.54% aggregates with 4 -8 mm diameter, 24.05% aggregatesd with 2 - 4mm diameter, 14.85% aggregates with 1 - 2 mm diameter and sand with 0.4 - 0.6 mm diameter.

The different models have 0%, 2% and 4% ellipses representing the air inclusions with the same diameter as the sand ellipses. So the smallest objects take at least six gridpoints in our model. A fractal flaw is placed horizontally in the middle of the model in a depth of 5cm and with a length of approximately 3cm and a diameter of 0.2mm. Surrounding the model there is a frame of ten gridpoints including the parameters of air for getting total reflections on all sides and taking them into account as size-effects.

The wavelet (fig 2) is produced by breaking a pencil on an ultrasonic receiver. There is also the possibility to use synthetic wavelets with given frequencies and shapes. The used method has the advantage, that the input signal is already convolved with the frequency response function of the receiver [Weiler, 1995]. The shape of the wavelet is very similar to the one given by a piezo-transducer. After converting the signal into the propriate data format, it is send within a point source through the model. (Alternatively we would have been able to use a line source, but for our purposes the point source was sufficient .)

Because of its sampling rate in the dimension of Megahertz, it takes about 10 000 timesteps to propagate the signal through the model. One simulation with the highly parallelized FD-program (written in High Performance Fortran) takes up to ten hours on 32 nodes of the intel Paragon parallel-computer of the University of Stuttgart.

Interpretation

Fig. 3: Left: Snapshot of the wave propagating through concrete without any air- inclusions. Right: Concrete with 4% air inclusions, causing scattering of the waves and attenuation of high frequencies. [You can access to animated images (each about 500KB) at the Author's homepage: 0% - 2% - 4% air inclusions]

The output of the finite-difference-program allows several possibilities of interpreting the simulations. First there is to mention the visualization of the wave propagating through the model with so called snapshots. Second there is the possibility get the output of horizontal receiverlines. These datasets can be divided into B-Scans and A-Scans.

Snapshots of the propagating elastic wave inside the concrete are explaining the different behaviour of the wave in concrete with and without air inclusions. The higher the percentage of air inhomogenities, the more scattering and mode conversion of the wave leads to an energy losses of the primary wave. The informations about air inclusions and flaws are shifted into the coda of the wave. This causes significant problems to extract and analyse them. The scattering of the stuffing materials is of low order compared to the described effect.

In the snapshots it can also be seen, that lower frequencies propagate through the concrete with air inclusions without getting scattered. Only wavelengths that have the size of the air inclusions are attenuated by scattering. Their energy concentrates in the upper part of the model. The lower frequencies can be used to detect the flaw. If a model with bigger sizes of air-ellipses would be used, these low frequencies would also be attenuated. The information about the flaw is hidden, as soon as the size of the air ellipses tends to be of the size of the flaw.

Fig. 4: B-Scan's from the simulations, taken from a receiverline at the top of the model. Left: Concrete without any air inclusions. The reflection hyperbel is detected after 30ms, (white arrow). Right: Concrete with 4% air inclusions, no reflection hyperbel can be seen.

In the following simulations one receiverline is placed on the top of the model, which records the A-Scans and B-Scans of pointlike receivers. In order to get an A-Scan of a commercial transducer, all A-Scans in between the diameter of the receiver (2 cm) has to be averaged. This stack influences the quality of the data because the waves scattered at the air inclusions (<<2cm) are eliminated out of the data by this averaging procedure. Only the coherent wavefield is detected considering a receiver with a diameter bigger than the correlation length of the scattering objects [Ishimaru, 1987]. In other words: A pointlike receiver doesn't detect the flaw as well as a receiver that has the length of the flaw.

Looking at the B-Scans it's obvious, that the influences of size-effects in simple shaped models (like the quadratic example) are also of a low order. The reflection hyperbel of the flaw can be well seen in the concrete with 0% air inclusions. The waves propagating along the edges cross the hyperbel sometimes, but there is less noise then in the examples with air inclusions.

The stacked A-Scans explain the possibility to detect a flaw in concrete with different percentages of air inclusions using only one A-Scan of a commercial receiver. With rising percentage of air inhomogenities, the energy of the transmitted signal decreases, it gets attenuated and the reflection of the flaw gets superimposed by the coherent noise of the scattering.

Fig. 5: Both A-Scans were taken from the simulations investigating concrete without air inclusions. Left: A-Scan of a pointlike receiver. Right: Several pointlike receivers inbetween the diameter of 2 cm were averaged. The reflection of the flaw can be detected after 30 m 2%

Fig. 6: Left: A-Scan of a receiver with 2 cm diameter, obtained on the top of a concrete model with 2% air inclusions. Right: 4% air inclusions. The reflection of the flaw at 30m. 2%

Conclusions

The finite-difference-program and the medium program, are two powerful tools to simulate the elastic wave-propagation in concrete. So there is the possibility to get more information about the behaviour of the wave inside different kind of concrete and with various kind of source wavelets. Additionally there is the possibility to estimate the different influences on the wave. Those influences are for instance due to size effects when using other kinds of surfaces and shapes of the concrete block.

The investigated B-Scans can be used to invert the data. With the help of this method informations are extracted out of the data about the structure of the examined model, (see also the following article "Application of a modified SAFT-Algorithm on synthetic B-scans of coarse grained Materials"). The described algorithms are also implemented to test inversion-algorithms. Their appliability in coarse grained materials and the imaging quality of the programs using data with different signal to noise ratio can be tested comparing the output "image" with the input medium of the FD-program presented in this paper.

Future enhancements are the compilation of the FD-program on the new supercomputers CRAY T3E/512 and NEC SX-4/32 of the University of Stuttgart to cope with bigger 2D-models and to perform 3D-simulations.

Acknowledgements

We gratefully acknowledge funding of our work the Deutsche Forschungsgemeinschaft (DFG) in part A6 of the special research program SFB 381 "Charakterisierung des Schädigungsverlaufes in Faserverbundwerkstoffen mittel zerstörungsfreier Prüfung."
Special appreciation must be expressed to Martin Karrenbach and Norbert Gold [7] from the Geophysical Institute of Karlsruhe, who made the FD-simulations possible.

References

1. Gold, N. (1997): Theoretical description of the propagation of elastic waves in 2-D and 3-D random media. Phd-Thesis, University of Karlsruhe.
2. Ishimaru, A. (1987): Wave Propagation and Scattering in Random Media. Vols 1 and 2. New York: Academic Press.
3. Karrenbach, M. (1995): Elastic tensor wave fields. Phd-Thesis, Department of Geophysics, Stanford University.
4. Fellinger, P., Marklein, R., Langenberg, K.J., Klaholz, S. (1995): Numerical Modeling of elastic wave propagation and scattering with EFIT - elastodynamic finite integration technique. Wave Motion 21, S.47-66
5. Weiler, B. (1995): Elastic constants - their measurements and calculation. Otto-Graf-Journal. Vol. 6.
6. Weiler, B., Grooße, C. (1995): Calibration of ultrasonic transducers - a comparative study of different methods. Otto-Graf-Journal. Vol. 6.
7. Internet Sites of Martin Karrenbach and Norbert Gold

Authors

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. email: reinhardt@po.uni-stuttgart.de	Dr. C.U. GROSSE born in 1961, studied Geophysics at the University of Karlsruhe. He finished his thesis in July 1996 and is a research member at the Institute of Construction Materials, University of Stuttgart, Germany. email: christian.grosse@po.uni-stuttgart.de Author's Home Page: http://www.uni-stuttgart.de/UNIuser/fmpa/grosse/grosse.html
Eberhard Burr is a research member at the Otto-Graf-Institute. Main topics of his Phd-thesis are the forward modelling of elastic waves in concrete with F-D-Methods. Email: burr@po.uni-stuttgart.de. Homepage: http://www.uni-stuttgart.de/UNIuser/fmpa/burr/frames.html.
Norbert Gold from the Geophysical Institute of Karlsruhe. Homepage: http://www-gpi.physik.uni-kalrsruhe.de/pub/wit/resall.html#gold