Comparison of numerical results of conventional concrete bridge pier. obtained from the uncalibrated model with experimental results for different intensity levels. Comparison of numerical results of HyFRC bridge pier obtained by. uncalibrated model with experimental results for different intensity levels. a) Hysteretic material sample model created using the OpenSees platform.
Introduction
- Background
- Overview
- Hybrid Fibre Reinforced Concrete
- Hybrid Simulation
- Bridge Fragility
- Objectives of Present Study
- Scope of Research
- Experimental study
- Numerical study
- Organisation of Thesis
Calibration of numerical model of the bridge using the detailed experimental output of hybrid simulation. The use of HyFRC in place of conventional concrete is expected to improve seismic performance of the specimen.
Review of Literature
General
Fibre reinforced concrete
- Hybrid fibre reinforced concrete
- Application of FRC and HyFRC in structural members
- Reduction of shear reinforcement
It is also possible to measure the bond strength between polymer fibers and cement or concrete. It was found that the addition of fibers does not increase the compressive strength of the mixture, but increases the modulus of rupture.
Additional features at pier-foundation interface
Experimental evaluation of seismic performance of structural components
- Hybrid simulation
- Experimental studies using hybrid simulation
Unlike pure numerical simulation, the hybrid simulation method combines physical testing of part of the structure, i.e. the validity of the hybrid test results used in the calibration of the numerical model was emphasized.
Bridge fragility analysis
Key issues and limitations of different methods for developing fragility curves for highway bridges. Frankie (2013) developed hybrid fragility curves for a four-span arched bridge using results of hybrid simulation and nonlinear dynamic analysis.
Concluding Remarks
Assessment of Mechanical Properties of Constituent Materials
- General
- Test program (Part I) -Evaluation of volume fractions of steel and polypropylene
- Evaluation of compressive strength
- Evaluation of split cylinder strength
- Four point bending test
- Test program (Part II) –Evaluation of possible reduction in shear reinforcement in
- Details of test specimen
- Loading characteristic and test frame
- Results
- Concluding remarks
The average tensile strength of conventional concrete is found to be 2.6 MPa and that of HyFRC cylinders is 2.83 MPa. Tests for the evaluation of the flexural toughness of conventional concrete and HyFRC specimens with various combinations of fibers are conducted in accordance with ASTM C1018 (1989). The conventional concrete sample shows a very brittle failure mode, while HyFRC samples show a significant improvement in ductility.
The load carrying capacity as well as modulus of rupture of HyFRC samples are also higher than those of conventional concrete samples (Table 3.7).
Numerical Modelling of Bridge
- General
- Numerical Model of Bridge Structure
- Modelling of Superstructure
- Pier modelling
- Results from Numerical Analysis
- Modal analysis
- Nonlinear static analysis
- Nonlinear time history analysis
- Concluding Remarks
The superstructure of a bridge refers to the portion of the bridge above the top of the pier. The cross-sectional characteristics of the deck of the bridge under study are given in Table 4.1. Masses are aggregated at the top by considering the tributary mass of the bridge superstructure.
Differences are observed in the load-deformation curves of the bridge pier modeled with conventional concrete and HyFRC, as shown in Figure 4.7.
Testing of Bridge by Hybrid Simulation
General
Testing procedure by hybrid simulation
- Hybrid simulation framework
- Integration scheme
Mat t + Cv t + r t = f t (5.1) In the above equation, M is the composite mass matrix, C is the composite viscous damping matrix, a t and v t the acceleration and velocity vector, r t the structural restoring force vector and f t the external force vector applied to the system. The state of a system in a subsequent time step is calculated using explicit methods based on the state of the system in the current time step. Implicit methods, on the other hand, find a solution by solving an equilibrium equation that includes both the current state of the system and the subsequent state.
In any case, is greater than or equal to the actual tangent stiffness of the structure, the approximation condition ensures that the integration scheme is unconditionally stable.
Details of test specimen
- Description of material used in construction
- Fabrication of specimen
- Loading characteristic and test frame
- Instrumentation
- Procedure for fixing strain gauge
- Selection of earthquake time history
- Details for cyclic test
For each of the two types of material, three possible details are used at the column-foundation interface. A total of twenty-six electrical strain gauges are attached to the longitudinal and transverse reinforcement in each of the test cases at a predetermined location. Five strain gauges are attached to each of the longitudinal bars C1 and C5, while four strain gauges are attached to each of C2 and C6, as shown in Figure 5.10 (a).
These strain gauges are placed in the core concrete area of the pier, just above the interface of the pier foundation and 10 mm away from the longitudinal reinforcement.
Simulation results
- Observed distribution of damage
- Force-displacement hysteresis
- Cumulative energy dissipation
- Stiffness degradation during cyclic test
- Displacement ductility
- Failure Surface of damaged specimen
- Buckling length of ruptured reinforcement
- Observation of strain distribution in reinforcement and concrete
From Figure 5.15 (e-f), however, it is quite clear that the level of damage in HyFRC-manufactured piers is much less than for conventional concrete samples. a) Conventional concrete tests at the end of 1. level of hybrid testing. However, the degradation rate of the bearing capacity is higher for conventional concrete samples than for HyFRC samples, as can be seen from Figure 5.16 (i-j). In all three detailing types, HyFRC specimens showed delayed growth of stress in the core concrete region compared to their corresponding conventional concrete specimens.
This delayed strain growth resulted in better performance of HyFRC specimens under seismic excitation compared to that of the conventional concrete specimens.
Concluding remarks
The performance of HyFRC bridge piers is better compared to conventional concrete piers when subjected to seismic excitations. Pin reinforcements in bridge piers are effective in removing damage from the pier-foundation interface area. Pin-reinforced piers provide higher energy dissipation capacity compared to bridge piers with normal reinforcement details.
Based on strain measurement, it is determined that the crack initiation is delayed in HyFRC specimens and it is also observed that the presence of special features shifted the damage zone away from the pier-foundation interface.
Calibration of Finite Element Model
- General
- Modelling Assumption
- Comparison of Hybrid Simulation Results with Initial Numerical Model
- Model Calibration Procedures and its Results
- Energy dissipation of calibrated results
- Concluding remarks
The next section shows the comparison of the hybrid simulation result with the initial numerical model. Comparison of the numerical results of HyFRC bridge pile obtained from uncalibrated model with experimental results for different intensity levels. Comparison of the numerical results of conventional concrete bridge pile obtained from a calibrated model with experimental results for different intensity levels.
Comparison of numerical results of the HyFRC bridge pier obtained from the calibrated model with experimental results for different intensity levels.
Seismic Vulnerability Assessment of the Bridge
General
First, a brief overview of the methodology adopted in this study for the development of fragility curves is presented, followed by the identification of different damage states based on the damage pattern observed in the experimental element of the hybrid simulation. Both methods are used to generate fragility curves from dynamic incremental analysis (IDA) data and then compared. This chapter also provides a comparison of the fragility curves obtained from the calibrated and the initial uncalibrated model, emphasizing the importance of model calibration.
This chapter concludes with a comparison of seismic fragility curves for classical concrete bridge piers and HyFRC bridge piers using the calibrated model in each case.
Methodology for Development of Analytical Fragility Curve
- Fragility analysis using PSDM and regression
- Fragility analysis using maximum likelihood estimates
The probability of failure can be calculated from multiple IDA data at each level of the graduated intensity measure (IM) by counting the number of IDA curves that cross the vertical line corresponding to the considered limit state. The ratio of these IDA curves to the total number of IDA curves is the probability of failure or fragility at that IM level. In a similar way, the probability of failure or fragility can be determined for the considered limit state at other IM levels.
The IDA results are used to develop a PSDM, which is then combined with a limit state capacity model to develop seismic fragility curves for the bridge under consideration.
Definition of Damage State using Experimental Results
The probability function takes the form of Bernoulli distribution and is expressed as:. where, FrIMi represents the fragility at IM = IMi based on a specific damage condition and is calculated using Equation 7.5. Total number of sample response points is denoted by n which is the total number of intensity level under which analysis is performed, p is 1 or 0 depending on whether the damage condition k is exceeded or not and q = 1 - p. If measured, maximum strain value in concrete exceeds the cracking stress of 138 µm/m for conventional concrete and 140 µm/m for HyFRC.
In fragility analysis, the maximum drift ratio corresponding to the damage state parameters for each time the history analysis is run under different seismic excitations is monitored and compared with the range of drift ratios indicated in Table 7.2.
Selection of Ground Motions
- Normalization method
- Scaling procedure
FEMA P695 (2009) provisions were considered in selecting ground motions, which are summarized here for completeness. Therefore, some records are factored down and some are factored up, maintaining the overall ground motion strength of the set. The recorded ground motion is adjusted to match the value of the spectral acceleration at the base time period of the structure Sa (T1) (FEMA P695 2009, Vamvatsikos and Cornell 2002).
Recorded ground motions are scaled to match the target spectrum by minimizing the outliers over a range of periods (Bommer and Acevedo 2004, ASCE 43).
Seismic Fragility Curves
- Comparisons of two fragility analysis methods
Therefore, C in Equation 7.3, which indicates spread in limit state capacity in PSDM regressed method, is not considered. A slightly higher R2 value and lower RMSE indicate that Maximum likelihood method gives better results compared to PSDM regressed method for all limit states. However, maximum likelihood method is more computationally intensive as it requires the calculation of new set of parameters (ck and R) at each limit state.
Considering this, only the PSDM regression method is used to develop the fragility curves for further analysis.
Comparisons of fragility curves obtained using calibrated and un-calibrated model
- Comparisons of fragility curves for conventional concrete and HyFRC bridge
Comparison of fragility curves obtained from a calibrated and uncalibrated model for conventional concrete bridge piers. It is observed that an uncalibrated model overestimates the median value of fragility, or in other words, it underestimates the failure probabilities for all considered damage states. For example, a 21% difference in the median value of vulnerability to light damage was observed between the uncalibrated and calibrated models.
Difference in median value and distribution of vulnerability obtained from uncalibrated and calibrated model.
Concluding remarks
The comparison of two methodologies, namely 'PSDM regressed' and 'Maximum likelihood', is carried out in terms of their proximity to direct estimates of fragility, i.e. the importance of model calibration with experimental results is also highlighted by comparing seismic fragility obtained from uncalibrated and calibrated models for conventional concrete, and the results demonstrate the importance of model calibration. For example, a 21% difference in the mean fragility value for the light damage condition is observed for the uncalibrated and calibrated models.
In addition, seismic fragility analysis using experimentally observed damage state and calibrated numerical model shows that HyFRC columns are less vulnerable compared to conventional concrete columns in all damage states.
Conclusions and Recommendation for Future Research
Overview
Summary
For this reason, the current study assumes that hybrid simulation observes the behavior of the interface zone of the pier and the foundation. The effect of HyFRC on improving seismic damage resistance is investigated by hybrid simulation of the entire bridge structure. The stresses at the reinforcement of HyFRC pillars are found to be significantly reduced at all stages of loading and the displacement ductility of HyFRC specimens is improved compared to that of the conventional concrete pillars.
In order to accurately predict the response of the initial numerical model according to the experimental results, modifications are made to the model that include the addition of a translational spring at the column-foundation interface and adjustments to the damping ratio to capture hysteretic damping effects.
Conclusions
In addition, it is also observed that the presence of additional components such as dowel bars, corrugated board near the column-foundation interface zone shifts the damage zone away from the interface region. Columns with dowel reinforcement can exhibit higher energy dissipation capacity than corresponding bridge columns with conventional reinforcement details. The extent of damage at the end of the cyclic test in the column-foundation interface of the HyFRC specimens is significantly smaller than that of the corresponding conventional concrete specimens, so the rehabilitation of such a specimen would be easier.
The application of non-linear spring at the base of the pier has been shown to be quite effective in achieving close agreement between results obtained from calibrated model and hybrid simulation.
Recommendation for future research
Material Testing
IS Method of Mix Design
Sieve analysis result confirms that fine aggregate is from Zone III Specific gravity test result. Fine aggregate: Source-Saigaon, Kukurmara Specific gravity of fine aggregate = 2.59 Water absorption (fine aggregate) = nil Surface moisture (fine aggregate) = nil Step 3: Target average strength.
Load Carrying Capacity of Beam with Four 10 mm ø Longitudinal Reinforcement 159
Because the included shear force Vu is greater than the shear strength to which concrete Vuc resists, the section must be designed for shear reinforcement. However, the minimum specified distance shall be less than the distance required as per clause 26.5 of IS: 456.
Steel for Longitudinal Reinforcement
Steel for Transverse Reinforcement
