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Abstract: This paper presents the results from shaking table tests of a one-tenth-scale reinforced concrete (RC) building model. The test model is a protype of a building that was seriously damaged during the 1985 Mexico earthquake. The input ground excitation used during the test was from the records obtained near the site of the prototype building during the 1985 and 1995 Mexico earthquakes. The tests showed that the damage pattern of the test model agreed well with that of the prototype building. Analytical prediction of earthquake response has been conducted for the prototype building using a sophisticated49404
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3-D frame model. The input motion used for the dynamic analysis was the shaking table test measurements with similarity transformation. The comparison of the analytical results and the shaking table test results indicates that the response of the RC building to minor and the moderate earthquakes can be predicated well. However, there is difference between the predication and the actual response to the major earthquake. Keywords: RC building; shaking table test; seismic response; inelastic dynamic analysis 1 Introduction Both shaking table tests and nonlinear response analysis are important approaches in earthquake engineering research and design of building structures. The results of shaking table tests are affected by the size and the similarity design of the test model, the properties of model materials, the input and control of vibration, the data acquisition and treatment, and other similar factors. Thus, it is difficult to evaluate the test results. Nonlinear response analysis plays a very important role in seismic design of building structures. The newly issued "Code for Seismic Design of Buildings (GB50011-2001)" (Chinese National Standard, 2001) emphasizes the necessity of nonlinear response analysis for high-rise buildings. As is well-known, the results obtained from inelastic dynamic response analysis are highly dependent on many factors, such as the structural modeling, the evaluation of structural member behaviors, the input of earthquake ground motions, the numerical methods and so on. Hence, the reliability of Correspondence to: Ye Xianguo, Hefei University of Tech- nology, Hefei 230009, China Tel: 0086-0551-3441036 E-mail: yexiang@mail.hf.ah.cn *Professor; ~Doctor Supported by: National Natural Science Foundation of China Under Grant No.59978013 Received date: 2003-11-04; Accepted date: 2004-10-24 the nonlinear dynamic response analysis needs to be examined carefully, which can be done by comparing it to the real structural seismic response or to the shaking table test results from the model structure. The actual structural seismic response under strong ground motion may not be easy to obtain from instrumented buildings during the actual earthquake; however, shaking table tests can be used to provide valuable data for evaluation purposes. This paper describes a shaking table test program of a building model in reduced scale. The structural prototype of the model was a 10-story reinforced concrete (RC) building(Ye, 1996) made in one-tenth scale. The test was carried out by using the three- directional shaking table facility in the State Key Laboratory for Disaster Reduction at Tongji University, Shanghai, China, and a total of 11 runs of shaking table tests were conducted. For comparison purposes, an inelastic dynamic response analysis of the prototype building structure by using a 3-D model was performed. The acceleration time- history records obtained on the shaking table surface were used as the input to the numerical analysis. 2 Overview of shaking table tests Shaking table tests of a reduced-scale RC building model were conducted under recorded three-directional input seismic motions. The main objectives were to: (1) simulate the seismic damage to a real RC building to validate current shaking table test technology; (2) comprehensively understand the nonlinear dynamic performance of RC building structures under earthquakes of different intensities; and (3) verify the reliability of earthquake response predication by means of inelastic dynamic response analysis. 2.1 Test model The structure prototype of the test model is a 10- story RC frame-wall official building in Mexico City, constructed in 1970. It had a regular rectangular shape consisting of five frames spanning 9.0 meters in the longitudinal direction (X-direction), and four frames with the bay of 6.0m in the transverse direction (Y- direction). In the transverse direction, four shear-walls were symmetrically placed in the two end-frames. The total height of the building was 39.05m. The building was designed for a base shear coefficient of 0.078 in the longitudinal direction and 0.104 in the transverse direction. The material strength was about 24 MPa for concrete in cubic compression and 400 MPa for steel bars in tension yielding respectively. The building was damaged in the 1985 Mexico Michoacan earthquake. The peak acceleration of the earthquake was only 0.171 g, but it lasted about 180s with peak velocity of 61 cm/s, and its predominant vibration period was 2s. The fundamental period of the building was 1.2s in the longitudinal X-direction. The performance of the building in the 1985 Mexico earthquake is described in Meli (1992). It was characterized by plastic hinging at the ends of several longitudinal beams, from the first to the sixth floors. The concrete was crushed at the top and bottom of the section and the longitudinal reinforcement buckled in several cases. Some diagonal cracking in the columns from the third to the sixth floors and some evidence of hinging at the column bases of the ground floor were found in the longitudinal direction. No sign of damage attributable to the shaking in the transverse direction could be found. Due to the limited capacity of the shaking table facility, the specimen had to be designed at a reduced 1/10 scale and the maximum weight could not meet the requirement of similarity of artificial mass. Therefore, the test model was designed according to the general similitude law (Zhang, 1997) that considers the effect of the short of artificial mass. Table 1 lists the similarity ratios based on the general similitude law. The specimen weighed 5.8t, and the base plate was 2.8t. Iron pieces were evenly distributed on each floor slab to serve as additional artificial mass. The total weight of the test model was 15t. Fig. l(a) shows the view of the specimen on the table. Figure l(b) shows the floor plan and the arrangement of beam-column-shear wall members of the test model. The cross-section of columns was 50mmx80mm, 50mmx90mm, 50mmx70mm and 50mmx60mm, and the cross-section of beams was 40mm• and 30mm• The thickness of the shear-walls was altered from 40mm to 25mm. The floor slab was made in thickness of 20mm instead of 10mm in the one-tenth scale model. The unmatched slab thickness was for the feasibility of reinforcement detailing and for the capacity to support the artificial mass. The base plate of the test model was attached firmly to the shaking table surface with bolts. The specimen was cast using fine gravel concrete and galvanized steel wires. Generally, #8 steel wires were used for columns, #10 for beams, #12 for walls, #14 for floor slabs, and #16 used as hoops bars of beams and columns. Samples of the concrete and steel wire were retained during the construction of the specimen and were tested to obtain their mechanical properties. Table 2 lists the material properties of the concrete and steel wire. The reinforcement details of the test model were as similar as possible with the prototype building. Construction of the test model was executed story by story using the following procedures: (1) arranging the reinforcement; (2) molding; (3) concrete casting filling vertically; (4) natural curing for three days; and (5) de- molding. The construction joint was on the top of each of the floor slabs. The .galvanized steel wires in columns were extended 120mm above the floor slab and banded with the wires from the upper story columns for the next story construction. The construction was completed within one month. The test was carried out two months later. 2.2 Excitation program The three-directional acceleration records SCT85 and SCT95, obtained near the site of the prototype building during the 1985 and 1995 Mexico earthquakes, given in Table 3, were used as the input seismic motion. The duration of SCT85 and SCT95 were compressed to 23.94s and 27.66s, respectively, to achieve the similarity ratio S, for the shaking table test excitation. The SCT85 input was repeated, increasing the acceleration peak value gradually. This was done to study the dynamic response and performance of the model in a wide range from elastic to elasto-plastic. The excitations in the series are shown in Table 4. The major excitation direction was in X direction to study the seismic performance of the RC frames. Before and after each seismic excitation, white noise waves at low peak acceleration were inputted, to monitor the changes in the natural vibration characteristics of the model. 2.3 Response measurement The responses of the specimen during shaking were measured using acceleration sensors and displacement transducers. The points of the sensors/ transducers installed are shown in Fig.1. There were a total of 33 measurement points including 31 for accelerations and 2 for displacements. Three sensors were placed on the table surface and every two floor levels including the roof to measure the acceleration response in the X, Y and Z directions, respectively, and two sensors were mounted on each level of the rest of the floors to detect the acceleration in X and Y directions. The two transducers were installed on the table surface and on the roof to measure the displacements only when the X- direction vibration tests were performed. 3 Test results 3.1 Crack development and failure mode As the peak acceleration of excitation increased from 0.15g to 0.4g (SCT85-1 to SCT85-6), very small cracks appeared at the construction joints of the columns from the first to fourth stories in the exterior line 44-frame, as well as some cracks at the end of the X-directional beams. During this stage, only a slight change in the natural period was found. This indicated that the model performed basically in the elastic state. As the amplitude of the excitation was increased to 0.6g (SCT85-7 and SCT85-8) in the longitudinal frame direction (X-direction), obvious cracks due to bending and shear developed at the ends of many beams and at the top of lower story columns, and diagonal cracks appeared in most beam-column joints. Meanwhile, small cracks extended into the connection area of the floor slabs with the transverse beams and shear walls. Furthermore, concrete crushes began at the base of the first-story columns. Also, fine cracks were found at the end of some coupling beams between the shear walls The excitation was increased and reached the target PGA at the run of SCT85-10 after two attempts using SCT85-8 and SCT85-9 (see Table 4). At this stage, the test model was subjected to severe damage in the X- directional frames. Diagonal shear cracks on lower-story columns and some beam-column joints were observed. Flexural yielding also occurred at X-directional beams in all stories from the first to the sixth floor level. At the base of the first-story columns, cover concrete spalled off, core concrete crushed and steel wires buckled. This also happened at the middle-height or top-end of some middle-story columns where diagonal or incline cracks appeared. As the cover concrete spalling off, the damage to the beam-column joints increased. In the final run of the excitation SCT95-11, almost no further damage was found. This was attributed to the relatively low intensity of the excitation. The above damage pattern generally conformed to the observed seismic damage to the prototype building (Meli, 1992). 3.2 Natural frequency and vibration mode Table 5 lists the natural frequencies of the model measured during the test. The natural frequency decreased with the development of damage to the model. Under low excitation up to 0.4g (SCT85-1- SCT85-6), the natural frequency only changed slightly. Apparent changes in the natural frequency were observed after the SCT85-8 and SCT85-9 excitations. This confirmed the damage and the severe damage to the test model, respectively. Figure 2 ( where f0 (i=1, 2, 3 and 4) denotes the initial natural frequency) shows the changes in the first four natural frequencies with increasing excitation intensity. The changes in the first vibration mode shape of the test model (in X-direction) is shown in Fig.3 for the cases after each excitation. The mode shape also changed gradually as the excitation intensity increased. 3.3 Measured acceleration time histories The difference between the target input and the measurement of the excitation PGAs was noticed, and attributed to the limited precision of the shaking table facility. The acceleration time history curves measured on the roof and the 6th floor level can be observed from Fig.4-Fig.7, which show the measured values pided by the similarity factor Sa (for comparison to the analytical simulation). The ratio of peak response acceleration to the input PGA at selected floor levels is shown in Fig. 8. The change of the ratio (peak response acceleration/peak ground acceleration, that is, PRA/PGA) corresponded well with the observed damage. That is, in the severely damaged X-direction, the ratio of PRA/PGA obviously was reduced in the strong input SCT85-10, while in the Y-direction, the response was almost elastic and the PRA/PGA ratio remained unchanged. 4 Dynamic response of the prototype buiHing and comparing with the test results To verify the reliability of earthquake response prediction, a time history analysis of the prototype building was performed. The predicted response was compared with the shaking table test results. For comparability, the earthquake response analysis of the prototype building used the input of the test measurements based on the similitude ratio. The analysis was carried out by using the computer program CANNY, which has been reliable in predicting the earthquake response and damage of RC building structures (Li et al., 1999). The program accepts input from multiple components of earthquake excitation in two horizontal directions and in the vertical direction. It offers many options in modeling structures for analysis; including various types of structures using line elements (beam, column, shear wall, cable, truss and spring element, as well as special elements such as isolators and dampers), and the interactions among multi-axial loads. A rich collection of hysteresis models available in the program makes it convenience to simulate the mechanical properties of structural members of concrete and metal materials in various loading conditions. 4.1 Analysis model A 3-D frame structural model, which was based on nonlinear moment-rotation relationships of inpidual structural members, was adopted to carry out the dynamic response prediction of the prototype building. The structural members (beam, column and shear wall) were idealized as line elements, and the floor slabs were treated as a rigid diaphragm having three degrees of freedom; that is, two horizontal translations and one rotation in the slab horizontal plane. Beams and columns were considered rigidly connected. Each structural node was considered as having six displacement degrees of freedom; that is, three translational displacements and three rotations. The two lateral translations of nodes were determined by the rigid movement of the floor slab and the one rotation of nodes was determined by the rotation in the slab plane. The mass was concentrated at the structural nodes. The effect of the gravity load on the lateral displacement (P-D effect) was taken into account in the analysis. Fixed support was assumed at the first-story column base, consistent with the boundary condition of the shaking table test. To account for the interactions between the bidirectional bending and the axial load fluctuation in exterior columns and shear walls, a multi-spring model (MS model) was used to idealize columns and shear walls. Every steel bar in columns and shear walls was treated as a steel spring, and the concrete of the element section was represented by a fairly large number of concrete springs. The spring properties were based on the material stress-strain relationships. The beam element had uniaxial bending in the frame plane and was idealized in a one-component rotational spring model. The nonlinear hysteresis model of moment-rotation relationships had the aspects of strength deterioration, stiffness degradation and pinching effect, as shown in Fig.9. The columns and the shear walls had the flexural and axial deformation idealized by the MS model, and were based on the material stress-strain relationships of concrete and steel. The nonlinear shear behavior of all elements was considered to be proportional to the flexural stiffness degradation. By this simplification, the shear deformation was assumed to be elastic. More information on the details of the analysis models and assumptions can be found from in Li et al. (1999). 4.2 Input for analysis To ensure comparability, the input for the dynamic analysis of the prototype building was the acceleration time history recorded on the shaking table surface. The acceleration values of the records were pided by the similarity ratio 5.659 and the duration was timed by the similarity ratio 7.522 (see Table 1). The observed results from the 11 shaking table tests were combined to form the input acceleration time history in a long duration of 2048s (the acceleration X-component shown in Fig. 10). Therefore, the dynamic analysis could be carried out once to cover all 11 shaking table tests. In this way, the accumulation effect of nonlinear structural damage was reproduced by the analysis. The input directions were taken as the same as the shaking table test in three components of two horizontal directions and vertical direction. The input PGA for the analysis was 1.099 g / 5.659 or 0.194 g in the X-direction. 4.3 Numerical methods In the dynamic analysis, step-by-step numerical integration in the Newmark b-method was employed to solve the equations of motion. The integration was carried out at a time interval of 1/200s against the fundamental period of 1.2s of the prototype building in the X-direction. The mass and stiffness matrices proportional damping assumed a damping constant of 5%. 4.4 Comparison of calculated and measured results The acceleration response results measured from the reduced-scale model and those from the calculated responses of the prototype building were compared over a corresponding vibration time period. The comparison is shown in Fig.4-Fig.7 for the model building roof, and the 6th floor level in the Xand Ydirections. The measured results shown in the figures are the transformed results, that is, they were pided by the similarity factor S. The results are shown in different scales and with the peak response acceleration (PRA) indicated in the figures for easy comparison. For input in relatively lower peak accelerations (up to SCT85-6), the analytical simulation achieved results similar to the actual tests. That is, the major response was in the X-direction and minor in the Y-direction. Moreover, the analysis indicated no cracks under the lower input up to SCT85-3 excitation (PGA 0.025 g), which agreed with the test observation. The results showed that the structure was basically in the elastic stage, and the calculated acceleration responses were close to the measured results both in the wave shape and amplitude. However, considerable differences could be seen between the calculated and the measured results during the strong