Application of the Digital-Image-Correlation Technique to Measure the Deformation of a Seismic Retrofitted Column of a Two-Storey Building

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Abstract

In this research the digital-image-correlation (DIC) technique is used to measure the column deformation of an in situ test. A push-over test is organized on July 26 2007 on a two-storey building of Guan-Miao elementary school in Tainan, Taiwan. The columns of this building are seismic retrofitted with steel plate.

The measurement result shows that the DIC technique can successfully measure the relative displacement of the column. Because we can determine the relative displacement of many points of the column, not only the deformation curve but also the rotation and curvature can be determined using interpolation method. The curvature shows that the plastic hinge is happened at about 2% storey drift ratio. It shows that the DIC technique can be applied to the measurement of a full scale in situ test.

Keywords: digital-image-correlation technique, full scale in situ test, push-over test, non-contact measurement technique.

1 Introduction

The Chi-Chi earthquake, which occurred on September 21 1999, caused a great damage. Many buildings are destroyed or damaged. About 40% of them are the buildings of the elementary or junior high schools. Because of the growth of the student number and the safety reason a few old school buildings is planed to be pulled down. Therefore a series of push-over tests on such buildings are carried out in the past years to verify the effectiveness of various retrofit techniques.

A push-over test is organized on July 26 2007 on a two-storey building of Guan-Miao elementary school in Tainan, Taiwan. The columns of this building are seismic retrofitted with steel plate. The traditional measurement technique is used to measure the deformation of the building. The measurement instruments are installed inside the building. Because of the safety reason they will be removed from the

Paper 289

Application of the Digital-Image-Correlation Technique to

Measure the Deformation of a Seismic Retrofitted Column for a

Two-Storey Building

S.H. Tung1, M.H. Shih2 and Y.S. Yang3

1 Department of Civil and Environmental Engineering

National University of Kaohsiung, Taiwan

2 Department of Construction Engineering

National Kaohsiung First University of Science and Technology, Taiwan

3 National Center for Research on Earthquake Engineering, Taipei, Taiwan ©Civil-Comp Press, 2008

Proceedings of the Ninth International Conference on Computational Structures Technology, B.H.V. Topping and M. Papadrakakis, (Editors), Civil-Comp Press, Stirlingshire, Scotland

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building at a certain deformation. Therefore the column deformation can no more be measured using the traditional measurement technique at larger deformation.

The DIC technique is developed during the 1980s [1-3]. It has been applied to analyze various problems. e.g. French scholars Raffard et al. [4] applied DIC technique to measure the deformation of mortar, providing a further insight into mortar mechanics. Dost et al.[5, 6] acquired nano-images using an atomic force microscope, which help them not only find out the profiles of nano materials, but also analyze nano-displacement and nano-crack by integrating DIC technique. Kuo et al. [7, 8] use DIC technique to investigate the deformation of Aluminum Bicrystals. Shih et al. [9] apply DIC technique to observe the crack development in masonry wall. The advantage of DIC technique is that it is a measurement technique without contact with the test specimen. The digital camera can be installed outside the building. Therefore the DIC technique is applied in this test in order to evaluate the measurement capability in such a full scale in situ test.

2 Digital-Image-Correlation Method

Y, Y* X, X* △y* △y* △x △x* P Q Q* P* △y yQ yP yQ* yP* xP xQ xP* xQ* ▽ Area of Scanning Undeformed Subimage Deformed Subimage Pixel Location Sampling Grid

Figure 1: Schematic drawing of relative location of sub-images of deformed and undeformed images on surface. [2]

Digital-image-correlation method is widely applied to the field of image identification technique. By comparing local correlation of two images, the relationship (under assumption of parameter’s functional relationship) between undeformed and deformed images could be identified. As shown in Figure 1, central point prior to deformation is point P, and then changed to point P* after deformation, the relationship between P and P* can be expressed as

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* * ( , ) ( , ) x x u x y y y v x y = + = + (1)

For undeformed images, the concept of finite element method (FEM) is used to divide the images into several sub-images (as shown in Figure 2). Assuming undeformed image is A and deformed image B, the correlation coefficient (equation 2) [2] is used to define the relationship between image A and B.

2 2 ij ij ij ij g g COF g g Σ = Σ ⋅Σ   (2)

Where, g and ij g~ij is grey scale of image A on coordinate (i, j) and image B on

coordinate (i, j ), respectively. And, coordinate (i, j ) of image B corresponds to

coordinate (i,j) of image A.

Figure 2: Schematic Drawing of Sub-images (Grids) on Surface

If optimum function parameter for every sub-image is recognized by an optimization procedure, the corresponding coordinate of every undeformed and deformed sub-image could be obtained. Accordingly, displacement vector and displacement field can be individually computed.

3 The Full Scale Push-Over Test

The specimen of this test is an old building of Guan-Miao elementary school in Tainan, Taiwan. It’s a two-storey reinforced concrete building. Four test specimens are planed in this project. This research focuses on the specimen no. 1, which is retrofitted with the steel plate.

The test arrangement is shown in figure 3. If we observe the building from the front side, the specimen no. 1 is composed of the four classrooms at the left end of the building. The specimen is separate from the rest of the building by cutting the floor, roof and walls. It is pushed at the position of the beams from the right side of

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the specimen. Four actuators are installed on the beams of the right building. Therefore the right building will offer the necessary reaction force. Six steel braces are installed in the right building to avoid the happening of large deformation.

Figure 3: Schematic drawing of the test arrangement

The outside size of the specimen is shown in figure 4. The beams and the columns A2 and A4 (both sides of the specimen) are retrofitted with the steel plate. The rest columns are unchanged. The specimen is pushed at the right side. The ratio of the force at the beam of the first floor to the force at the beam of the ground floor is kept at 2.

The specimen is pushed from the right side. The test pauses at the storey drift ratio of 0.25%, 0.5%, 0.75%, 1.0%, 1.25%, 1.5%, 1.75%, 2.0% and 3.0%. The storey drift ratio is defined as the ratio of lateral displacement of roof to the height of the roof. The cracks are marked during the pause. At the 3% storey drift ratio, the traditional measurement instruments are removed from the specimen. Therefore only the measurement technique based on the DIC method can be used to measure the deformation in the following test. After 3% storey drift ratio, the test pauses at 4%, 5% and 6% storey drift ratio for only a short time. Then the specimen is pushed over.

Figure 4: Schematic drawing of specimen no. 1.

specimen no. actuato steel

A1 A2 A3 A4 A5 2 3P 1 3P 3.5 m 3.5 m 9 m 9 m

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4 Method of Image Acquisition and Analysis

4.1 Image Acquisition Method

Figure 5(a) is the image of column A4. It is marked with both the regular signs (as shown in figure 5(b)) and painted irregular signs (figure 5(c)). To avoid disturbing the observation of other research teams, the distribution of marks on the surface of column A4 is not very dense.

Figure 5: (a) Image of marked column A4, (b) regular signs, (c) irregular signs The Canon EOS 300D DSLR camera with SIGMA 18-200mm F3.5-6.3 DC lens is used to capture the digital images of column A4. The camera stands before the column A4 at a distance about 10 m from the column. Figure 6 shows the images of column A4 at the storey drift ratio of 0%, 1%, 2% and 3%.

4.2 Image Analysis

Because the column surface is not fully paved with the speckles, the single point tracing mode of DIC technique is used to analyze the column deformation. The position of every mark is traced. Two parallel observation lines on the surface of column (as shown in figure 7) are chosen. There are 181 equal spaced points in each line. The positions of these points are calculated using B-Spline interpolation

(c) (b)

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function based on the positions of the traced points. Then we can use these data to evaluate the lateral displacement, storey drift ratio, rotation and curvature of the column A4.

(a) 0% (b) 1.0%

(c) 2.0% (d) 3.0%

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Figure 7: The locations of two observation lines.

5 Analytical Results of Digital Images

Figure 8 shows the relative lateral displacement of column A4 at different height. It is the average displacement of both observation lines. The reference point is the lower end point of left observation line. All the lateral displacement is relative to this point. The difference of theoretical storey drift ration between two adjacent curves is 0.5%. Figure 8 shows that the lateral displacement differences between every two adjacent curves at the same height are almost the same before 2% storey drift ratio. The increment of lateral displacement is obviously bigger after the storey drift ratio reach 2%. It shows that the plastic hinge seems to be formed in the column A4 at about 2% storey drift ratio.

If the lateral displacement difference of the two end points of the observation line divides by the vertical distance of these two points, we can get the measured storey drift ratio of ground floor. The relationship between measured and scheduled storey drift ratio is shown in figure 9 (the blue line). The slope of the blue line is different from 1 because the length of the observation line is not equal to the height of the ground floor.

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0 500 1000 1500 2000 2500 3000 0 20 40 60 80 100 120 140 160 X (mm) H ei gh t (m m ) 0.5%1.0% 1.5% 2.0% 2.5% 3.0%

Figure 8: The lateral displacement of column A4 at different storey drift ratio

0% 1% 2% 3% 4% 5% 6% 0% 1% 2% 3% 4% 5% 6%

Scheduled storey drift ratio

Mea su red Sto rey d rift ratio original modified

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The rotation angles at different height of various storey drift ratios are shown in figure 10. Because of the constraint of beam and foundation beam the rotation angles of top and bottom of column A4 is smaller than that of the mid part of the column. Before 2% storey drift ratio the rotation angles of both end of the observation line are almost the same. After that the rotation angle at column bottom is obviously bigger than the rotation angle of column top. From the picture we can find that the ground near column bottom heaves. It shows that the foundation beam-column joint is damaged. This situation is more serious at 3% storey drift ratio.

0 500 1000 1500 2000 2500 3000 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07

Rotation angle (rad)

H ei gh t (m m ) 0.5%1.0% 1.5% 2.0% 2.5% 3.0%

Figure 10: The rotation angle of column A4 at different storey drift ratio

The difference method is used to calculate the curvatures of every interpolation points of both observation lines. The results are shown in figure 11. It shows that the noise is not small. But all the curves at the column height between 50 and 200 cm are almost linear. Near the height of 30 and 250 cm the variations of curvature are quite large. This means that the plastic hinge occurs at these two positions. It also can be found that the plastic hinge is already formed at about 1% storey drift ratio. And the plastic hinge range spreads as the storey drift ratio changes from 1% to 3%. The length of the plastic hinge increases about from 30 cm to 50 cm. And the length of the plastic hinge near the column bottom is smaller than that near the column top.

The results of figure 10 and 11 can be used to explain why the slope of the blue line in figure 9 diverges from 1 and why the slope increases rapidly after 2% storey drift ratio. The length of the observation line is 253.5 cm and the height of this storey is 350 cm. Therefore the difference between the observation line length and the storey height is about 1 m. We can find that there is still small rotation at both ends of the observation line, and the rotation angle at lower end of the observation

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line is greater than that at upper end of the observation line. The lower end of the observation line is not far from the bottom of the column. If we ignore the difference of the rotation angle between the both ends of the observation line and use the product of the rotation angle at upper end of the observation line and the difference between the storey height and the length of the observation line to modify the horizontal displacement of the ceiling relative to the ground. The modified storey drift ratio can be calculated by dividing the modified horizontal displacement by the storey height (350 cm). The relationship between the modified and the scheduled storey drift ratio is shown in figure 9 as the red line. It shows that the slope of the red line is about equal to 1 before the storey drift ratio reach 2%.

0 500 1000 1500 2000 2500 3000

-1.0E-04 -5.0E-05 0.0E+00 5.0E-05 1.0E-04 1.5E-04 Curvature H ei ght (m m ) 0.5%1.0% 1.5% 2.0% 2.5% 3.0%

(a) Left observation line.

0 500 1000 1500 2000 2500 3000

-1.0E-04 -5.0E-05 0.0E+00 5.0E-05 1.0E-04 1.5E-04

Curvature He ig ht (m m ) 0.5%1.0% 1.5% 2.0% 2.5% 3.0%

(b) Right observation line.

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Figure 11 shows that the plastic hinge is really occurred. The resistance of the ground floor is reduced after the occurrence of plastic hinge. This causes the recovery of deformation of the first floor. Therefore almost all the deformation will occur in the ground floor. This makes the lateral displacement increase rapidly. The slope of the lines in figure 9 increases obviously since 2% storey drift ratio. But even all the deformation occurs in the ground floor, the slope of the lines in figure 9 should not be greater than 2. This situation can be explained with the following two reasons. First, as said above, the deformation recovery of the first floor makes the lateral displacement of the ground floor increases obviously. Second, we use the rotation angle at the upper end of the observation line to modify the horizontal displacement. But after the occurrence of the plastic hinge the rotation angle in the region higher than the upper end of the observation line varies continuously. If we inspect the picture, we can find that the rotation angle near the beam is already very small. Therefore the modified horizontal displacement of the ground floor is overestimated. The combination of these two reasons causes the slope of the modified line in figure greater than 2.

6 Conclusions

The DIC technique is applied to the measurement of a full scale in situ test. The following conclusions can be drawn according to the results in the above section: 1. The modified measured storey drift ratio is almost the same as the scheduled

storey drift ratio before 2% storey drift ratio. It shows that the accuracy of the DIC technique is very good. The DIC technique can be successfully applied to measure the deformation in a full scale test.

2. The occurrence of the plastic hinge can be determined and the position and length of the plastic hinge can also be found out.

3. Because the column is only marked at a few points, we can only trace the position of these points. Therefore we have to calculate the coordinates of the points in the observation line by interpolating. If the column surface can be fully paved with the speckles, then the point position can be directly determined. This can increase the accuracy. The noise shown in figure 11 should be able to be reduced.

References

[1] W.H. Peters and W.F. Ranson, “Digital Imaging Techniques in Experimental Stress Analysis”, Optical Engineering, Vol. 21 (3), 427-432, 1982.

[2] T.C. Chu, W.F. Ranson, M.A. Sutton and W.H. Peters, “Application of Digital-Image-Correlation Techniques to Experimental Mechanics”, Experimental Mechanics, 25(3), 232-244, 1985.

[3] M.A. Sutton, J.L. Turner, H.A. Bruck and T.A. Chae, “Full-field Representation of Discretely Sampled Surface Deformation for Displacement and Strain Analysis”, Experimental Mechanics, Vol. 31, 168-177, 1991.

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[4] D. Raffard, P. Ienny and J.-P. Henry, “Displacement and Strain Fields at a Stone/Mortar Interface by Digital Image Processing”, Journal of Testing and Evaluation, Vol. 29 (2), 115-122, 2001.

[5] M. Dost, D. Vogel, T. Winkler, J. Vogel, R. Erb, E. Kieselstein,“How to detect Edgar Allan Poe’s ‘purloined letter’ - or: Cross correlation algorithms in digitised video images for object identification, movement evaluation and deformation analysis”, Nondestructive Detection and Measurement for Homeland Security, Proceedings of SPIE Vol. 5048, 2003.

[6] M. Dost, N.Rümmler, E. Kieselstein, R. Erb, V. Hillmann, V. Großer, “Correlation Analysis at Grey Scale Patterns in an in-situ Measuring Module for Microsystem Technology”, Materials Mechanics – Fracture Mechanics – Micromechanics, Eds. T. Winkler, A. Schubert, pp. 259-266, Berlin/ Chemnitz, 1999.

[7] J.C. Kuo, S. Zaefferer, Z. Zhao, M. Winning and D. Raabe, “Deformation Behavior of Aluminum Bicrystals”, Advanced Engineering Materials, 5, 563-566, 2003.

[8] S. Zaefferer, J.C. Kuo, Z. Zhao, M. Winning and D. Raabe, “On the influence of the grain boundary misorientation on the plastic deformation of aluminum bicrystals”, Acta Materialia, 51, 4719-4735, 2003.

[9] Ming-Hsiang Shih, Shih-Heng Tung, Jui-Chao Kuo and Wen-Pei Sung, “Application of Digital Image Correlation Method for Crack Observation”, The Eighth International Conference on Computational Structures Technology, Las Palmas de Gran Canaria, Spain, September 12-15, 2006.

數據

Figure 1: Schematic drawing of relative location of sub-images of deformed and  undeformed images on surface

Figure 1:

Schematic drawing of relative location of sub-images of deformed and undeformed images on surface p.2
Figure 2: Schematic Drawing of Sub-images (Grids) on Surface

Figure 2:

Schematic Drawing of Sub-images (Grids) on Surface p.3
Figure 4: Schematic drawing of specimen no. 1.

Figure 4:

Schematic drawing of specimen no. 1. p.4
Figure 3: Schematic drawing of the test arrangement

Figure 3:

Schematic drawing of the test arrangement p.4
Figure 5: (a) Image of marked column A4, (b) regular signs, (c) irregular signs  The Canon EOS 300D DSLR camera with SIGMA 18-200mm F3.5-6.3 DC lens  is used to capture the digital images of column A4

Figure 5:

(a) Image of marked column A4, (b) regular signs, (c) irregular signs The Canon EOS 300D DSLR camera with SIGMA 18-200mm F3.5-6.3 DC lens is used to capture the digital images of column A4 p.5
Figure 6: Images of the column A4 at different storey drift ratio

Figure 6:

Images of the column A4 at different storey drift ratio p.6
Figure 7: The locations of two observation lines.

Figure 7:

The locations of two observation lines. p.7
Figure 8: The lateral displacement of column A4 at different storey drift ratio

Figure 8:

The lateral displacement of column A4 at different storey drift ratio p.8
Figure 9: The relationship between the measured and scheduled storey drift ratio

Figure 9:

The relationship between the measured and scheduled storey drift ratio p.8
Figure 10: The rotation angle of column A4 at different storey drift ratio

Figure 10:

The rotation angle of column A4 at different storey drift ratio p.9
Figure 11: The curvature at different height of column A4

Figure 11:

The curvature at different height of column A4 p.10

參考文獻