International Symposium (NDT-CE 2003)Non-Destructive Testing in Civil Engineering 2003
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The use of laser-interferometry (ESPI) in analysis of reinforced concrete structuresJosef, Hegger, Institute of Structural Concrete (IMB), University of Technology, Aachen, Germany;
Stephan, Görtz, Zerna, Köpper & Partner Ingenieurgesellschaft für Bautechnik, Bochum, Germany;
Jörg, Niewels, Institute of Structural Concrete (IMB), University of Technology, Aachen, Germany
AbstractWhereas the ultimate limit state of structural concrete can be described realistically by mechanical models, the phase of early crack formation is widely unknown. Due to the low adhesive tensile strength of the concrete matrix the formation of microcracks already starts under comparable low stresses, especially concerning the contact zones to the aggregate and the reinforcement. Therefore a highly nonlinear structural behaviour emerges very early. The crack formation is a ductile process creating continuous macrocracks by the accumulation of microcracks.
By using laser interferometry it is possible to visualize the strains of the concrete surface already during the formation of microcracks. In addition, the nonlinear stress-redistribution of the concrete matrix can be derived from the strains measured in a very early state of loading.
1. IntroductionThe load bearing capacity and the deformation behaviour of reinforced concrete is characterized by the bond between cement matrix, reinforcement and aggregates. For the reinforcement the relation between stress and strain can be assumed as bilinear. In contrast to this the stress-strain curve for concrete consisting of cement matrix and aggregate is nonlinear under compression as well as tension (Fig. 1). Due to the very little tensile strength of the concrete (less than 10 % of the compression strength) the tensile forces in reinforced concrete structures are taken by the reinforcement. To activate the load bearing capacity of the reinforcement, crack formation is necessary. The occurring stress-redistributions are influenced by the longitudinal reinforcement and the stirrups: For a low shear reinforcement ratio extensive nonlinear stress rearrangements occur already before the actual macrocracking. They are not negligible for the further structural behaviour. This influence of the reinforcement on the crack-processing was analysed using the laser-interferometry. Shear tests on girder webs with different shear reinforcement ratios were carried out .
Concrete is - different from glass, for example - a quasi-brittle not a perfect-brittle material. In the linear-elastic fracture mechanics the tensile failure of a perfect brittle material occurs abruptly by crack-formation. In concrete a crack is formed by the accumulation of very fine microcracks. These occur before the actual macrocracking in the fracture process zone, which is not visible for one´s eyes. By increasing the load of the fracture process zone continuous microcracks form up and combine to visible macrocracks (Fig. 1).
According to the microcracking the fracture process zone becomes less stiff. The stresses are redistributed nonlinear to stiffer parts of the structure. The first microcracks are exclusively influenced by the stress trajectories calculated for the uncracked system (crack initiation). Concerning the posterior macrocrack the course and the direction can deviate from the direction of crack initiation. Although the direction of the main stresses is the same at crack initiation, structural elements with low shear reinforcement ratio show smaller crack angles than those with a higher shear reinforcement ratio. An abrupt failure within the crack formation is avoided by the stress-redistributions. In  it is assumed that the actual course of the macrocrack does not depend on the stress trajectories which led to crack initiation as well.
The process of redistributions during microcracking is characterized by very little strain. By using the laser-interferometry it is possible to measure small displacements areawise on the surface of a structure. In this way the proceeding of nonlinear redistributions up to the formation of macrocracks can be visualized. Hariri already gained good results in the experimental analysis of the fracture process zone of concrete structures without reinforcement .
2. Use of the laser-interferometryThe functioning of the laser-interferometry (ESPI - Electronic Speckle Pattern Interferometry) is based on the interference of reflected waves of the coherent laser light. The surface which has to be analysed (measuring-area) is illuminated by a laser from two different positions (Fig. 2).
The light waves are reflected on the uneven surface of the concrete in a diffuse way which is characteristic for each discrete load step. The reflected waves are overlaying and produce a speckle picture (Fig. 3) recorded by a CCD-camera. By subtracting two speckle pictures taken at different load levels, a picture of interference is received. The stripes in this picture of interference can be interpreted as level curves of the one-dimensional relative displacements of the points in the measuring-area. By using a software of the GOM-company the graduations of the grey colour in the picture of interference are digitally collected and the coordinates of the displacements are calculated. The displacement of each point is not relative to its original position but to its position in the picture taken the load step before. In order to calculate the displacements of several load steps it is necessary to add up the relative displacements of each load step.
The sensitivity of the laser-interferometry is in a range of accuracy from 10-6 - 10-8 m. It has to be regarded that the displacements from one load step to another must not be more than 2·10-5 m. Therefore the measuring system is not suitable to record the proceeding macrocracks. It is useful to keep the measuring-area shaded because otherwise the superposition of daylight and laser light can affect the results. Furthermore even very little vibrations of the measuring equipment must be avoided, as they would lead to wrong results.
The ESPI measuring system was used to analyse three shear tests on beams made of high strength lightweight concrete . The beams were loaded by two single loads positioned in the third of the beam length (four-point-bending test). They were increased until the formation of shear cracks had come to an end. Two beams (LWAC 3L/5L) had a very low shear reinforcement ratio in the range of minimum shear reinforcement ratio. The third beam was highly shear reinforced near the range of diagonal strut failure. The measurements were taken in an area of 20 x 25 cm at the web of the beam. Finally in this area the shear cracks occurred. It was necessary to connect the measuring equipment with the specimen using a steel girder as shown in Fig. 2 in order to avoid the influence of global deflections. Thus even small relative displacements between measuring equipment and measuring-area could nearly be eliminated. As the measuring was only possible in the x- or the y-direction it was necessary to turn round the equipment by 90 degrees in order to take the photo of the other direction. This process took about two seconds. Via an analogue force-signal the height of the load could be saved together with the appropriate photo and the analysed direction.
The files containing the displacement measurements were prepared at the University of Technology Eindhoven by Mr. ing. H.L.M. Wijen of the Institut Constructief Ontwerpen. By the finite element system ORPHEUS which was developed at the Institut für Massivbau (IMB) the results were visualized. Therefore the measuring-area on the concrete surface is represented by a panel of finite elements. After editing the displacement files the measured displacements were applied in each node of this panel structure. In addition, assuming the modulus of elasticity the principle stress can be derived from the strains. Using the graphical surface of ORPHEUS the principal strain as well as the principal stresses and the displacements were be visualized.
3. Application of the laser-interferometry and results
For the observer apparently at the same time crack 1 and crack 2 occured in the area of the nonlinear strain increase. They were nonparallel shear cracks immediately reaching across the complete height of the web (Fig. 5). After relieving the specimen and reloading it, crack 3 occurred nearly at the same load as the cracks before. By increasing the load, another crack occurred parallel to crack 2 and 3 (not illustrated), leading to the later failure of the specimen. In contrast to this crack 1 was without meaning for the further load bearing behaviour.
From the comparison of the load at the beginning of the nonlinear behaviour with the load at macrocracking it can be derived that the nonlinear rearrangements start at 80 to 95 % of the load where the first visual macrocracks occur. Microcracking is determined by the trajectories of the uncracked system. For this reason the inclination of crack 1 is in good accordance within the linear elastic calculation of the specimen. After this first damage there are stress-redistributions coming to an end during the actual crack formation. By this a change from the macroscopic homogeneous concrete specimen was performed to the cracked specimen containing reinforcement between the cracks (truss model).
For low shear reinforcement ratios a flatter inclined crack occured in order to transfer the forces from the concrete to the reinforcement. Crack 2, actually occuring immediately after crack 1, showed an apparently flatter angle. Increasing the load the truss model dominated the load bearing behaviour without influence of the trajectories of the uncracked system. For this reason the following cracks were parallel to crack 2. These general conclusions are confirmed by test LWAC 5L. Specimen LWAC 5R had a higher shear reinforcement ratio. The macrocracking occurred with less audible noise and less rapidly. The shear cracks did not immediately reach across the complete height of the web. Apparently the tension stresses which could not be sustained by the concrete were gradually redistributed to the reinforcement. According to the higher shear reinforcement ratio less strain was necessary in order to activate sufficient high tension forces. This resulted in a more fluently changeover from the microcracking to the macrocracking.
The nonlinear rearrangements mentioned above could be confirmed by conventional measuring techniques (strain gauges). Before the macrocracks became visible, a disproportional increase of the strain of the stirrups and a rotation of the strut angle could be observed.
4. SummaryShear tests at the Institut für Massivbau point out a correlation between the crack angle and the shear reinforcement ratio. The laser-interferometry was used as measuring technique to investigate the influence of nonlinear redistributions on the crack angle before macrocracking. This technique enables displacement-measurements areawise with a grade of accuracy between 10-6 - 10-8 m. The principal strains and their directions can be specified from the displacements. The following conclusions can be drawn from the measurements: - Testing specimens of low shear reinforcement ratio the shear cracks ran flatter than according to a linear elastic calculation for an uncracked specimen. The reason lies within the stress redistributions. - There are nonlinear processes before the visible crack formation. They begin at about 85 % of the load of the visible macrocrack. - The stress-redistributions have a non negligible influence on the inclination of the cracks. The crack inclination is not only determined by the trajectories of the uncracked system but also by the inner structural system during the period of crack formation.