FINITE ELEMENT ANALYSIS OF REINFORCED CONCRETE BRIDGE PIER COLUMNS SUBJECTED TO SEISMIS LOADING

Transcription

1 FINITE ELEMENT ANALYSIS OF REINFORCED CONCRETE BRIDGE PIER COLUMNS SUBJECTED TO SEISMIS LOADING By Benjamin M. Schlick University of Massachusetts Amherst Department of Civil and Environmental Engineering 236 Marston Hall Amherst, MA (413) ABSTRACT Many reinforced concrete bridges in Massachusetts have been constructed from the 1950's to the 1970's. These bridges were designed by outdated building codes that did not account for large seismic activities and were designed with typical transverse reinforcement spacing that far exceed today's standards and are therefore insufficient to resist the laterally applied loads. This finite element analysis will involve modeling a scaled version of a reinforced concrete bridge pier column that is being used in Chelmsford Massachusetts. The column will have an axial load applied at the top to simulate the dead loads of the superstructure and will also be subjected to a seismic loading. The cyclic loading will be controlled by the yield displacement, which is calculated using the yield curvature obtained from a computer analysis. The objective of these tests will be to investigate the behavior of the reinforced concrete column, particularly in the plastic hinge region where the failure is predicted. Results will show that spalling of the concrete will occur at the base of the column, which will initiate failure with little energy dissipation. Keywords: Reinforced Concrete, Plastic Hinge, Confinement, Energy Dissipation INTRODUCTION Bridges constructed in the United States between the 1950's to the mid 70's where inadequately designed to resist earthquake loading. After the damaged caused by the 1971 San Fernando earthquake the design requirements have been modified to accommodate the need for columns to achieve sufficient strength and ductility during seismic activity. However, the vulnerability of pre-1971 bridges has been evident in the 1987 Whittier Narrows, the 1989 Loma Prieta, and the 1994 Northridge earthquakes (1). Therefore, repairs to existing bridge substructures must be considered to eliminate further bridge pier failures. There were two main deficiencies with bridge piers designed before 1971: 1) insufficient lap splice length placed at the base of the column and 2) widely spaced transverse reinforcement. Before 1971 the lap splices were designed at the footing of the columns and had a typical length equal to 20 bar diameters. In the existing Building Code Requirements for Structural Concrete, ACI (2), lap splices are required in the center half of the member length. The behavior of a statically indeterminate structure subjected to earthquake loading is such that after the moment strengths at one or more points have been reached, discontinuities develop, commonly known as "plastic hinges", in the elastic curve at those points, which results in an inelastic analysis (2). With the insufficient lap splice length at the base of the column in the plastic hinge region and lack of confinement provided by the transverse reinforcement, the longitudinal reinforcement is not able to develop its desired strength and spalling of the concrete will occur, which will result in debonding and initiate slippage. Ultimately the base of the column can either experience a brittle shear failure, or a brittle pullout failure. BACKGROUND The test specimens used to analyze the effects in the bridge columns were typically designed to react as a cantilever column with single bending. This will provide the largest displacement at the top of the column and produce a linear moment analysis, with the largest moment concentrated at the base of the pier. In the elastic curve of the moment analysis when the moment strengths are reached at one or more points, discontinuities will develop and form plastic hinges, which will result in an inelastic analysis. It is evident in the curvature analysis that there is a plastic hinge region at the base of the column in the inelastic range. The typical setup and diagrams used to demonstrate the effects of cyclic loading on bridge column substructures are shown in figure 1. Lateral Force Plastic Hinge max Deflection Figure 1 Reaction s The bridge pier will be subjected to cyclic loading until failure to determine the performance of the reinforced M max Moment Ф u Curvature Ф y 1 Copyright #### by ASME

2 concrete column, specifically in the plastic hinge region. The results determined from the previous experiments have shown similar deficiencies within the plastic hinge region, which are as follows: 1) Flexural strength short length of lapped reinforcing bars in plastic hinge region. 2) Flexural ductility minimal confinement due to large spacing of transverse reinforcement. 3) Shear strength low shear capacity in plastic hinge region as a result of the reinforcement details. The poor performance of columns tested was a result of insufficient concrete confinement around the base of the column. Without the ability of the longitudinal steel to resist debonding and slippage, the column was not be able to reach sufficient flexural strength and react in a ductile manner. Figure 2 displays the lap-splice in the plastic hinge region. Tensile Stiffness Multiplier = 0.6 (default) The SOLID65 element uses a smeared rebar capability, which involves three different rebar materials orientated in any direction relative to the global coordinate system. The rebar was input to replicate the volumetric ratios and orientation of the longitudinal and transverse reinforcement in the typical bridge column. The material properties chosen for the rebar are as shown: Density = lb/in 3 Modulus of Elasticity E = 29x10 6 psi Yield Strength f y = 40x10 3 psi The modeling of the non-linear properties of the 40 ksi steel was accomplished by developing a stress-strain graph of the multi-linear kinematic hardening properties. Figure 3 displays the stress-strain graph. Lap-Splice of Longitudinal Steel Figure 2 Lap-Splice FINITE ELEMENT ANALYSIS Specimen Geometry The ANSYS finite element analysis program will be used to develop the model geometry and properties designated by a scaled version of a typical bridge built in Chelmsford, Massachusetts. The longitudinal and transverse reinforcement ratio of the bridge columns were approximately 2% and 0.5% of the gross cross-sectional area, respectively and had yield strength of 40 ksi. The cross sectional dimensions were scaled to 1/4 of the originally dimensions to be an 8"x 8" square with a depth of 36". The reinforced concrete column will be meshed using a hexahedral volume element with a 1 in. side length. Figure 3 40 ksi Stress-Strain Graph Modeling Assumptions There are few assumptions that will be made with this model due to the SOLID65 concrete element capabilities. One assumption is that the base of the column will be fixed due to the rigid foundation on the existing column. The model in this analysis will not be used to accurately depict the results of the displacement or applied forces to the existing column. This is a consequence of not having any concept of the placement, size, and number of reinforcing members of steel being used. The reason we cannot predict the longitudinal or transverse steel orientation is due to the smeared reinforcement associated with the SOLID65 element. Figure 4 displays the different moment capacities of the 8"x 8"column due to altered longitudinal steel placement (4 - #4 bars). Modeling Properties The specimen will be modeled using the SOLID65 concrete element, which is used for modeling threedimensional solid models with or without rebar. The element is capable of cracking, crushing, plastic deformation, and creep in tension and compression using the non-linearity material properties. The concrete material properties are as follows: Density = lb/in 3 Modulus of Elasticity E = 3.15x10 6 psi Compressive Strength f ' c = 3000 psi Tensile Strength f ' t = 384 psi Shear Coefficient Open Cracks = 0.7 Shear Coefficient Closed Cracks = " 2.5" #4 bar M u = 8 k-ft M u = 7.5 k-ft Figure 4 Ultimate Moment Capacities 2 Copyright #### by ASME

3 Since there is no way of determining the arrangement of the rebar placed in the column, this analysis will be used to investigate the failure behavior of the reinforced concrete column under cyclic loading rather than the maximum failure loads and displacements. A lap-splice is not an option for this analysis; therefore the model will be analyzed as continuous longitudinal reinforcement. Loading and Constraints The model will have a zero degree of freedom constraint placed at the base, to resemble the existing structure. An axial load will be applied to the top of the column to represent the superstructure dead load of the existing bridge. It is common practice to take an axial load that is a percentage (20%) of the compressive strength of the column. The axial load will be applied as a surface pressure on the top of the column of 600 psi and the calculation is shown as follows: P = 0.2f ' c = 600 psi P = axial load f ' c = 3000psi The seismic loading will be controlled by fractions of the yield displacement. The yield displacement is calculated using a computer program called SEQMC by extracting the yield curvature and applying that to the displacement equation. This however, will not be an accurate yield displacement for the ANSYS model due to the unknown reinforcement arrangement but it is still useful in determining an approximate magnitude of displacement for the model. Using a 2 in. cover to the longitudinal reinforcement a yield curvature was found to equal 5.92x10-4 1/in, which produced a yield displacement of 0.25 in. Figure 5 displays the moment curvature plot and the yield displacement is calculated as follows: 2 ρ y L y = = 0.25 in. 3 y = yield displacement ρ y = yield curvature = 5.92x10-4 1/in L = length of column = 36 in. The yield displacement was imposed onto the column to test how it reacted and the model was found to fail just after 0.1 in. The failure displacement can now be used as a bench mark when applying the cyclic displacements to the column. Solution Analysis Type A full transient dynamic analysis will be utilized to perform a non-linear seismic analysis of the reinforced concrete column. A small displacement transient analysis was required when using a SOLID65 element to gain more accurate results. Automatic time stepping was used and a minimum and maximum time step was specified. The maximum time step requirement is a function of the natural frequency of the system. The column can be thought of as a single degree of freedom model with a large mass at the top, the dead load of 600 psi, and the stiffness of the column. Figure 6 displays the SDF model and the natural frequency calculation is as follows: K Fixed M Figure 6 SDF K ω n = = rad/sec M 3EI K = column stiffness = 3 = 21.1 k/in L EI = EI eff = 2.28x10 3 k-ft 2 (from momentcurvature analysis) 38.4kips M = mass = 2 =.099k-s 2 /in 386in / s The maximum time step is determined as follows: 2 t < t cr = = sec ω n A maximum and minimum time step was specified to equal 0.1 sec to ensure a more accurate solution. The load steps were determined by knowing the failure displacement of the reinforced concrete column to be approximately 0.1 in. The load steps were ramped starting from 0.02 in. loaded cyclically to 0.14 in. Figure 7 and 8 display the loading scheme and the applied loads and constraints to the model, respectively. Displacement vs. Time Displacement (in.) Time Figure 5 Moment-Curvature Plot Figure 7 Loading Pattern 3 Copyright #### by ASME

4 Axial Load (600 psi) Lateral Deflection Integration Points of the Cracks Figure 9 Initial Cracking Figure 8 Loading and Constraints TEST RESULTS Confinement The expected region of failure is in the plastic hinge region, which is located at the base of the column up to approximately 1.5 times the diameter of the column (12 in.). This has been experimentally validated through previous research and they are where discontinuities will begin to form and develop hinges, which will result in an inelastic analysis. Using the ANSYS finite element program with a SOLID65 element there are crushing and cracking capabilities. The first cracks started to occur at time equal to 3.6, the reaction at the base of the column was determined and then the moment at which the crack had occurred was compared to the cracking moment of the model. Figure 9 shows the initial cracks in the plastic hinge region and the moments were calculated as follows: M = PL = 3.98 k-ft M = moment at initial crack P = reaction at time 3.6 = kips L = distance to crack = 36 in M cr = 7.5 M cr = cracking moment f c ' I y Fixed Base = 2.93 k-ft I = moment of inertia = = 341 in 4 The cracking had occurred at a moment that was greater than the cracking moment therefore the results show good accuracy. The column ultimately failed at time equal to 20.8 where the displacement had reached 0.1in., which is were the expected failure would occur due to previous testing earlier in the report. The cracking at failure indicates loss of structural integrity in the plastic hinge region. This is where the cover concrete would begin to spall away from the longitudinal steel. This will ultimately cause the longitudinal steel to buckle due to the slippage between the concrete and steel. The cracking of the concrete is a result from the large stresses imposed in the plastic hinge region. These stresses can be seen exceeding the concrete compressive strength and therefore causing failure at the base of the column. Figures 10 and 11 display the stresses and cracking in the plastic hinge region at failure, respectively. Figure 10 Stress at Failure Plastic Hinge y = distance to extreme fiber = 4 in. 4 Copyright #### by ASME

5 Figure 11 Cracking at Failure Energy Dissipation A reinforced concrete bridge pier must be able to absorb energy into the column during seismic activity to ensure that there is bonding between the concrete and steel reinforcement. The more energy that is dissipated into column will be evidence to show that there is interaction between the steel and concrete and the column is not losing its structural integrity due to debonding and spalling of the concrete. From the results of the finite element model there shows very little energy dissipation, which is a good indicator that the column is forming large cracks in the plastic hinge region and the longitudinal steel is slipping in the concrete. This shows that the concrete is spalling at the base and the column will experience a brittle failure. The energy dissipated is shown by the area in the hysteresis loops, which can be viewed in load vs. displacement figure 12. Load (kips) Plastic Hinge Load vs. Displacement Displacement (in.) Loading Figure 12 Energy Dissipated CONCLUSION The objective of this research was to indicate the failure mode of a reinforced concrete column during seismic activity. The modeling of the bridge column did not replicate the exact structural integrity of the existing column due to the smeared rebar application that was utilized. Therefore, the results will not be used to calculate the moment or ductility capacity of the member; instead the results will be used to determine the triggering effects which caused the column to fail. The results of the full transient analysis indicate that the column experienced significant cracking and crushing in the plastic hinge region, which can be viewed on figures 11. This will lead to spalling of the concrete around the base of the column and ultimately cause the longitudinal steel to debond with the concrete and initiate slippage. This is further investigated by the lack of energy dissipated into the column during the cyclic loading, which can be seen in figure 12. As a final result of this analysis it is evident that the column is deficient in confinement of the reinforcement in the plastic hinge region leading to either a brittle shear failure, or a brittle pullout failure. FURTHER INVESTIGATION The results of this research were used only to determine the failure mode of the column and not the actual capacity of a reinforced concrete column subjected to lateral loading. Therefore research should be done using the SOLID65 element for concrete non-linear behavior without the rebar capability. The reinforcement must be modeled separately with the original steel characteristics and placement in the concrete volume. This could be done with using a three-dimensional structural contact element, which will provide useful information on the slippage effects during the transient loading and can also be used for splices at the base of the column to simulate existing structures. It would also be useful to apply a confining element in the plastic hinge region to further investigate the reinforced concrete column confinement and determine the effectiveness of using a retrofit. A retrofitting scheme that is currently being taken used involves the use of either a steel shell filled with a cement based grout or a fiber reinforcing polymer wrapped around the plastic hinge region. The information collected from the use of these two structural enhancements will be very useful in the future for seismic retrofitting. ACKNOWLEDGMENTS Prof. Ian. R. Grosse Prof. Sergio F. Breña REFERENCES 1. Jaradat, Omar A.; McLean, David I.; Marsh, M. Lee (1998) "Performance of Existing Bridge Columns Under Cyclic Loading Part 1: Experimental Results and Observed Behavior"; ACI Structural Journal, v95, n6, Nov-Dec, 1998, p "Building Code Requirements for Structural Concrete and Commentary (American Concrete Institute ACI ), Farmington Hills, Michigan, August Copyright #### by ASME