Dam Deformation Measurements with GPS

TECHNICAL ARTICLE Deformation Monitoring in Steel Arch Bridges Through Close-Range Photogrammetry and the Finite Element Method L. Taşçi Department of Geodesy and Photogrammetry (Geomatic) Engineering, Firat University, Elaziğ, Turkey Keywords Bridge, Deformation, Photogrammetry, Finite Element Method Correspondence L. Taşçi, Department of Geodesy and Photogrammetry (Geomatic) Engineering, Firat University, Elaziğ, Turkey Email: ltasci@firat.edu.tr Received: October 19, 2012; accepted: February 27, 2013 doi:10.1111/ext.12022 Abstract Deformation measurements are performed periodically to prevent death and injuries in case of the damage or collapse of manmade structures such as dams, tunnels, bridges, high-rise buildings, and other natural landslide regions. Deformations and displacements in such structures can occur if structures are not built on solid ground and they are subjected to huge static loadings, which causes hazardous shaking due to the motion of the ground beneath. To reduce losses, it is very important to make continuous observations using various measurement methods to detect changes and to analyze the scales of these changes using various analysis techniques. The aim of this study is to determine the behavior of a steel arch bridge under a static load by measuring and analyzing potential deformations and displacements using four different measurement methods. The graphs depicting the result of each measurement method show that the results of the four different measurement methods coincide with each other. Introduction The observation of engineering structures over time in case of any damage caused by a disaster or the age of the structure is referred to as structural health monitoring (SHM), and it is crucial to develop observation methods to detect deformations and analyze the movements of buildings to ensure that civil structures are reliable and usable. For SHM, contact and noncontact methods are employed. In addition, the finite element method (FEM) has also been used in this study. Contact methods are performed with high-accuracy instruments such as dial gauges, extensometers, linear variable differential transformers (LVDTs), and fiber optics. These devices give results in real time with a high geometrical precision and reliability; however, they can only detect one-dimensional (1-D) displacements on a single point where they are mounted. Therefore, these techniques are not appropriate for the measurement of an entire surface, which requires large number of points scattered on the surface of an object.1 – 3 Noncontact methods provide the opportunity to measure a large number of points scattered on the Experimental Techniques (2013)  2013, Society for Experimental Mechanics surface of an object in three dimensions, with respectable results related to the required accuracy. For measuring tasks over short and long time frames with a large number of points scattered on the surface of an object, close-range photogrammetry may be used.3 With the advent of high-resolution digital cameras, photogrammetry has been widely used in many different engineering disciplines. Due to the flexibility, portability, and speed of cameras based on charge-coupled device (CCD) and complementary metal-oxide semiconductor (CMOS) during image data acquisition and the capability of automated in-house data-reduction, digital photogrammetric techniques provide a cost-effective alternative or supplement for deformations monitoring.4 Photogrammetric measurement refers to a method that allows three-dimensional (3-D) evaluation using a two-dimensional (2-D) image of an object.5,6 Threedimensional evaluation of an object can be performed if at least two images of the same object (stereo images) are taken from two different locations; thus, photogrammetric techniques provide 3-D deformation measurements.3,7 One advantage of photogrammetric techniques is that deformations can be detected by a device that is not in contact with the object. This 1 Deformation Monitoring L. Taşçi Historical Overview Figure 1 Principle of the single-camera deformation measurement.7 eliminates the setup and sighting error.1,8,9 Depending on the size of the observed structure, a single camera might be sufficient for the determination of 1-D or 2-D deformations (Fig. 1). As a numerical method, FEM is used more frequently than the other structural analysis methods because it is suitable for computer programming. According to FEM, various engineering structures are assumed to be comprised of finite elements connected with each other at nodal points. Provided that the load–displacement correlations are known, it is possible to examine the behaviors of engineering structures through available calculation methods. FEM is widely used for the analyses of stress and strains in structures under external loads. For detailed information about this method, see Refs. 10 and 11. The purpose of this study is to determine displacements at two points of a steel arch bridge under an external load by using different measurement methods. In this study, a steel arch bridge, designed by the Civil Engineering students at Firat University for the ‘‘Design and Construct’’ competition held at Boğaziçi University in 2010 was used. A geodetic test network consisting of 17 reference points was produced for the photogrammetric analysis method. The geodetic test network was measured by using a reflectorless total station, and coordinates were measured in a local coordinate system. Stereo images before and after the loading were taken from two different positions using a professional digital single-lens reflex (DSLR) camera. The reactions of the bridge to test loads were also measured by means of two comparators placed on the bridge where the maximum displacements were expected. The nodal displacements in the bridge were calculated through FEM using the SAP2000 finite element program and by analyzing digital images using Photomodeler software. Subsequently, the displacement results obtained from the comparators and reflectorless Total Station have been compared with results obtained from the Photomodeler software and the SAP2000 Finite element analysis program. 2 According to Jáuregui,5 photogrammetry was used by Scott (1978) to measure local buckling deformations in a curved, steel box-girder bridge. The continuous bridge was a 1:12 scale model tested to failure over 11 days. Approximately 4000 targets were attached to the compression flange steel plate close to an interior support; however, only 1800 were used for measurement purposes. Accuracy of 0.2 mm (0.008 inch) was achieved using a stereometric camera, but at a high cost compared with dial indicators. Whiteman et al.9 describes the use of digital photogrammetry measurements of deflections in concrete beams during destructive testing. Two video camera systems were used to measure vertical deflections with a precision of ±0.25 mm (1◦ ). Maas and Hampel1 utilized photogrammetric techniques on the water reservoir wall of Nalps in the Swiss Alps. The wall has a length of 480 m and a height of 100 m on the air side. A total of 60 points were signalized. The 3-D coordinates of the targets were determined in a photogrammetric network, based on a total of 41 images acquired by an off-the-shelf 3000 × 2000 pixel still video camera. A self-calibrating bundle adjustment based on the 41 images and an average of 14 image rays per point yielded a standard deviation of 2–3 mm in all threecoordinate directions, which could be confirmed by geodetic reference measurements. Shirkhani et al.12 tested the capabilities of photogrammetry on the spillover of Marun dam (245.7 × 62.8 m). During the experience, an accuracy of 4.25 mm was achieved. In this project, a total accuracy of 4.2175 mm and a precision of 1.8877 mm are obtained. Peterman13 used three nonmetric Canon EOS 5 Mk II cameras to calculate deformations. The number of fixed points was increased to 14, and there was a total of more than 200 signalized points on each panel. Additionally, there were eight fixed control points placed around the frame. This time, three midrange, 10 megapixel consumer digital photo cameras were used. The distances between the cameras and the points were approximately 3 m. The fixed point positions were measured with a Leica 2003 tachymeter. The comparison showed that smaller deformations could be measured more accurately. Based on this comparison, the accuracy of the deformation measurements was assessed to be between 0.5 and 1.0 mm, 0.7 mm on average. Detchev et al.14 reviewed the advantages and disadvantages of using remote sensing methods, such Experimental Techniques (2013)  2013, Society for Experimental Mechanics L. Taşçi as terrestrial laser scanning and digital close-range photogrammetry, for the purposes of precise 3-D reconstruction and the estimation of deflections in structural materials. It is also shown how a low-cost setup of multiple digital cameras and projectors can be used for the monitoring of concrete beams subjected to different loading conditions by a hydraulic actuator. Preliminary Studies Deformation Monitoring (a) (b) The studied bridge The bridge was designed as a river bridge. The span of the bridge was 6.90 m, with a 0.90 m width and a 1.60 m maximum height. The bridge deck is between the upper and lower arches and is 1.20 m in height. Plates with thicknesses of 6 and 8 mm were employed at the connection points. The horizontal ‘‘e’’ distance among the bolts was 3.5d min, and they were designed to form minimum ‘‘2d’’ distance to the corners. All the profilers chosen have ST-37 strength, as stipulated in the competition rules. General views of the bridge are given in Fig. 2. Network design It is revealed from preliminary studies that determination of the dimension of the target signs is very important. For the points close to the camera, if large target signs are used, the pixel dimensions are unnecessarily increased. In the same way, for the points far from the camera, if small target signs are used, the pixel dimension is decreased, and finding the center of the target signs is very difficult. Therefore, in this study, small target signs for the points close to the camera and large target signs for the points far from camera are used. In any photogrammetric project, this step is the most important one for reaching the expected accuracy. Therefore, in the laboratory environment, 17 reference points at different heights and distances were designed. These reference points were established on stable surfaces (e.g. columns, beams, and walls of the laboratory) well removed from the bridge. For good visibility of the reference points in the images, a bull’s-eye-shaped target figure is placed on each reference point, as illustrated in Fig. 3. Deformation Measurement Test This study investigates the structural behaviors of a steel arch bridge under various external loads using geodetic and nongeodetic methods. Because the available laboratory conditions do not allow Experimental Techniques (2013)  2013, Society for Experimental Mechanics (d) (c) Figure 2 General views of the bridge: (a) view of top of the steel bridge; (b) front view; (c) view of 3D of the steel bridge; (d) side view. for the bridge to be loaded through bridge deck diagonals in the direction of gravity, I-cross-section horizontal elements that have rigid cross-sections were used to transfer the displacements to the bridge through a hydraulic jack. While placing the hydraulic jack on the I-cross-sections, a load cell was inserted, and the hydraulic jack was limited through the beam of the laboratory. I-cross-section horizontal elements were set on the upper chord elements in the middle span of the bridge. With this I-cross-section horizontal truss element located in the midspan of the bridge, vertical displacements were loaded on the upper chord elements. The resistance to these displacements by the bridge was measured by means of a load cell. The bridge was exposed to a step-by-step deformation through the hydraulic jack. To determine the deformations on the bridge under loading, two object points were chosen (O_U and O_A) (see Fig. 4) and two comparators were located on these points. Figure 4 illustrates the general view and experimental design. Before applying an external load to the bridge, the positions of object points were measured using comparators and the total station. Simultaneously, at a distance of 3 m from the bridge, stereo images with a 30 cm base were taken with a Canon EOS 50D DSLR camera. These measurements were used as the reference measurements (0 epoch). After loading the bridge, the same process was repeated for the same points under different loadings. 3 Deformation Monitoring L. Taşçi Figure 3 Geodetic reference network and coded target. Figure 4 The experimental design of the bridge and object points. Photogrammetric Techniques Camera calibration The photogrammetric techniques include camera calibration, measurements, data acquisition at the laboratory, data processing, and compilation of deformation diagrams. The procedure is given below. Using photogrammetric techniques, this study focuses on detecting the displacement of a steel arch bridge under an external load. In close-range photogrammetry, using a metric camera is essential to determine 4 Experimental Techniques (2013)  2013, Society for Experimental Mechanics L. Taşçi Deformation Monitoring taken at two pre-identified points 3 m away from the bridge; stereo images of the bridge were taken as eight different external loads were applied. The horizontal distance between these two points was approximately 30 cm. Data processing Figure 5 Calibration test area. 3-D coordinates on an object. A metric camera is a special camera such that its interior orientation parameters (i.e. focal distance, principal point coordinates, and distortions) are known. These parameters are determined by the camera calibration. The camera used in this study was calibrated using Photomodeler software and 12 test images taken for this purpose. These images contain 100 test points such that 4 out of these 100 points are geodetic control points whose geodetic coordinates are known (Fig. 5). The mathematical model utilized during the calibration process was the collinearity equations (Eq. 1) that are the basic mathematical equations in photogrammetry15 : [m11 (X −X0 ) + m12 (Y −Y0 ) + m13 (Z−Z0 ] [m31 (X −X0 ) + m32 (Y −Y0 ) + m33 (Z−Z0 ] [m21 (X −X0 ) + m22 (Y −Y0 ) + m23 (Z−Z0 ] y = y0 − c [m31 (X −X0 ) + m32 (Y −Y0 ) + m33 (Z−Z0 ] (1) x = x0 − c where c: focal length; x, y: measured photo coordinates; x 0 , y0 : principal point photo coordinates; mij : the coefficients of the rotation matrix; X, Y , Z: ground point coordinates; X 0 , Y 0 , Z0 : projection center coordinates. Data acquisition For the purpose of analyzing the deformations through photogrammetric methods, a Canon EOS 50D SLR with a 15.3 MP resolution was used. The camera was installed on a leveled tripod to ensure stability. Additionally, a remote-controlled shutter button was utilized to prevent possible movement of the camera. With a single camera, images were Experimental Techniques (2013)  2013, Society for Experimental Mechanics Each stereo image pair for each load was analyzed in Photomodeler software separately to assess the deformation amount on the bridge. Relative orientation of the stereo images was performed by selecting six common points on each image pair with a 0.029pixel overall root mean square (RMS) error. The tightness defining light rays intersect of the points is about 0.1%. This process created a 3-D model space with 1.74 mm precision in which all the points in the test area could be observed. According to this precision, it can be stated that the accuracy of the measurement was obtained with the 95% probability or higher. Additionally, absolute orientation was applied to each image pair for the transformation of model coordinates to the predetermined geodetic coordinate system. In this study, the positions of the reference points that were measured using a reflectorless total station in the local coordinate system are assumed to be the ground truth.16 The photogrammetric points are evaluated based on these points. This process made it possible to obtain 3-D coordinates of every single detail identified in the model area. Thus, for each different load session case, the displacement amount at each test point on the bridge was determined by measuring the 3-D coordinates of the test points. All the steps explained so far were carried out through Photomodeler software. Finite Element Method FEM was used to design the 3-D model of the steel bridge used by selecting optimum profiles, and the FEM of the bridge was analyzed through the SAP2000 software package. There were differences in some connections of the bar elements in the construction project and the actual constructed version of the bridge; therefore, these bar connection elements were updated in the FEM model of the bridge during 3-D model creation. The bridge used in this study was designed such that the elevation of the bridge deck (z) was 120 cm. Horizontal truss elements were designed diagonally, and they were connected to the bridge truss system to provide rigid behavior against vertical loads and pin connections against horizontal loads. The loads 5 Deformation Monitoring L. Taşçi Figure 7 View of cross-sections of bridge. Figure 6 Three-dimensional views of the bridge in FEM. were transferred from the horizontal truss elements to the vertical and diagonal elements and then through the upper and lower chords to the vertical elements, namely, the bridge piers. The upper and lower elements of the truss system are rigidly connected to each other. Both the vertical and diagonal elements that form the truss system placed between the upper and lower chord elements are pinned to upper and lower chord elements. The total span of the bridge is 690 cm, and its width is 90 cm. The highest elevation of the bridge is 160 cm, and the lowest level is 80 cm. Figure 6 presents 3-D and 2-D views of the FEM of the bridge. Cross-sections for all the elements, including bridge piers constituting vertical elements, upper and lower chord elements and diagonals of the truss system, and diagonal elements forming the deck slab, are demonstrated in Fig. 7. The cross-sections of these elements are summarized in Table 1. All the elements of the bridge are made of BC-I steel and appropriate material properties are defined in FEM (see Table 2). Numerical analysis of the bridge was done for two object points identified on the bridge where the maximum displacements were expected. The load–displacement behaviors at these points were calculated through FEM using the SAP2000 finite element program. It is observed that measurements are comparable with each other for the point reflectorless theodolite, comparator, and photogrammetric methods. Figures 8 and 9 present the results of both numerical analyses and the experiments. The results have separately been shown for two object points identified on the bridge. Figure 8 displays the load applied to the midspan of the bridge versus displacements of the reference point at the upper chord, 6 Table 1 Cross-section of bridge bar elements Bar element Cross-section Size (mm) Material b1 Circular pipe BC-I h1 Circular pipe h2 Circular pipe v1 Circular pipe v2 Circular pipe c Square-box φ = 30 t=3 φ = 30 t=3 φ = 25 t=2 φ = 25 t=2 φ = 25 t=2 a = 80 t=3 BC-I BC-I BC-I BC-I BC-I Table 2 Steel material properties The unit weight Elasticity modulus Poisson ratio Minimum yield stress Minimum tensile stress Effective yield stress Effective tensile stress γs Es ν fy fu fye fyu 7.697 × 10 –5 200,000 0.3 235 340 352.5 374 N/mm3 N/mm2 N/mm2 N/mm2 N/mm2 N/mm2 whereas Fig. 9 displays the displacement of the reference point at the lower chord under a vertical load. In addition, as seen in Figs. 8 and 9, the differences between the results of FEM analyses and the experimental program stems from the reductions that occur in bar cross-sections during the connection of bar elements. The lower rigidity of the system also causes the aforementioned difference. Furthermore, the relative differences between the real objects/model and the material and cross-section properties and the accepted limits contributed to this difference. Experimental Techniques (2013)  2013, Society for Experimental Mechanics L. Taşçi • With the photogrammetric method, it is possible to Comparator Total Station FEM Photogrammetry 10 Load (kN) Deformation Monitoring • 5 0 0 5 10 15 Displacement (mm) • Figure 8 Displacement of the upper chord under the vertical loading. Comparator Total Station FEM Photogrammetry Load (kN) 10 • 5 • 0 0 5 10 15 determine the deformations in each of the three directions and at all the points on the object, while comparators measure the displacement in one direction at a certain point. As seen in this research, the diameter of the targets is crucial when the distance between the camera and the object is considered. For this reason, the diameters of the targets are twice as large as those computed in the network design to obtain better results. It is concluded that photogrammetry has the advantage of being able to directly measure noncontact points in a short period of time. As a result, photogrammetry can be used as an acceptable measurement tool in deformation measurements. The results obtained from all the methods agree in terms of detecting displacements. This reveals that photogrammetry can be used as a surveying technique, especially when a quick and accurate analysis is required. The use of photogrammetry method can be advantageous when it is tough to measure big-scale engineering structures. Displacement (mm) References Figure 9 Displacement of the lower chord under the vertical loading. Conclusions This research aimed to present the comparableness of measurements collected via close-range photogrammetry method. To present the comparableness, the photogrammetric method, comparator measurements and reflectorless total station measurements were used to perform deformation measurements on a steel arch bridge. The behavior of the steel arch bridge is also compared with numerical results generated by using FEM. By comparing these methods and processing the data obtained from photographs taken during the test carried out in the laboratory, we have reached the following conclusions: • In this article, the major advantages of the proposed procedure are the calculation of displacements in three dimensions and the achievement of high accuracies in the monitoring of two points on the steel arch bridge by using a noncontact method. • This study emphasizes that a single camera is enough to determine deformations with the photogrammetric method, although two-camera systems were used in previous studies. Experimental Techniques (2013)  2013, Society for Experimental Mechanics 1. Maas, H.G., and Hampel, U., Photogrammetric Techniques in Civil Engineering Material Testing and Structure Monitoring, Photogrammetric Engineering and Remote Sensing 72(1):39–45 (2006). 2. 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EM 1110-1-100, ‘‘Engineering and Design Photogrammetric Mapping,’’ Department of the Army U.S. Army Corps of Engineers. Washington, DC, 20314-1000 (2003). 16. Valença, J., Júlio, E.N.B.S., and Araújo, H.J., Application of Photogrammetry to Structural Assessment, Experimental Techniques 36(5), 71–81 (2012). doi:10.1111/j.1747-1567.2011.00731.x. Experimental Techniques (2013)  2013, Society for Experimental Mechanics