Chapter 6 Calibration of Finite Element Model
6.4 Model Calibration Procedures and its Results
0.5MCE intensity level 1MCE intensity level
2MCE intensity level 3MCE intensity level
Figure 6.2. Comparison of the numerical results of HyFRC bridge pier obtained from uncalibrated model with experimental results for different intensity levels
The comparisons of results demonstrate the requirement for substantial improvement in the initial numerical model. The hysteretic behaviour of experimental specimens is used to calibrate the initial numerical model. Procedure for calibration of initial numerical model is presented in next section.
6.4 MODEL CALIBRATION PROCEDURES AND ITS RESULTS
In the previous section, it is shown that there is significant difference in response observed from initial numerical model as compared to the response observed from hybrid simulation.
This is attributed to the assumption made in the numerical model as stated earlier. This section describes the modification made in the initial model in order to accurately predict
the response in line with experimental results. Steps are taken to adjust the response of initial numerical model so that the results from numerical model are in line with the experimental results. These include addition of translational spring at the column base. In the experimental results, rotations are observed at the pier-foundation interface, which clearly contradicts the assumption of fixity at pier base in the initial numerical model. Major cracking at these locations are observed at higher MCE levels resulting in reduced stiffness and increase in displacement. Therefore, a nonlinear zero length translational spring model is introduced to account for stiffness and strength degradation. The sample hysteretic material model used to develop the nonlinear spring is as shown in Figure 6.3 (a).
The properties of nonlinear spring model is developed from the backbone curve of the force-deformation relationship obtained from hybrid simulation. The resulting model is able to capture the stiffness and strength degradation effects at each intensity levels of loading, which is shown in subsequent section. The uniaxial hysteretic material model available in OpenSees platform (McKenna et al. 1997) is used to define the constitutive relationship for the nonlinear spring. Hysteretic material has a predefined trilinear backbone with pinching of force and deformation, damage due to ductility and energy, and degraded unloading stiffness based on ductility. Five parameters are used to define hysteretic behaviour including pinching and stiffness degradation. The input parameter for hysteretic material is shown below-
uniaxialMaterial Hysteretic $matTag $s1p $e1p $s2p $e2p $s3p $e3p $s1n $e1n $s2n $e2n
$s3n $e3n $pinchX $pinchY $damage1 $damage2 <$beta>
where :
$matTag integer tag identifying material
6.4 Model Calibration Procedures and its Results
$s1p $e1p force & deformation at first point of the envelope in the positive direction
$s2p $e2p force & deformation at second point of the envelope in the positive direction
$s3p $e3p force & deformation at third point of the envelope in the positive direction
$s1n $e1n force & deformation at first point of the envelope in the negative direction
$s2n $e2n force & deformation at second point of the envelope in the negative direction
$s3n $e3n force & deformation at third point of the envelope in the negative direction
$pinchx pinching factor for deformation during reloading
$pinchy pinching factor for force during reloading
$damage1 damage due to ductility
$damage2 damage due to energy
$beta
power used to determine the degraded unloading stiffness based on ductility, mu-beta (optional, default=0.0)
(a)
(b)
Figure 6.3. (a) Sample Hysteretic material model created using OpenSees platform (b) backbone curve developed from experimental force-displacement hysteretic response
The first, second and third points on the envelope curve in Figure 6.3 (a) are evaluated with series of hit and trial procedures from the backbone curve of experimental hysteresis loop corresponding to all the intensity level in Figure 6.3 (b). The parameters evaluated are used in defining the zero-length element, which is introduced at the base of bridge pier in the calibrated model framework.
Figure 6.4. Back-bone curve for all the tested specimens
6.4 Model Calibration Procedures and its Results
From Figure 6.4, it can be seen that there is not much difference in the pattern of back-bone curve for all the three specimens (Type 1, 2 and 3) cast with of a particular material type. So, back bone curve for specimen of Type 1 is studied in details for the model calibration in the present study.
Figure 6.5 and Figure 6.6 shows the improvements in the overall response for conventional concrete and HyFRC bridge piers following the implementation of the aforementioned calibration procedure. It is observed that addition of nonlinear translational spring at the base are highly effective in achieving the improved matching of both lateral displacement and force along with dissipated energy in the calibrated model.
0.5MCE intensity level 1MCE intensity level
2MCE intensity level 3MCE intensity level
Figure 6.5. Comparison of the numerical results of conventional concrete bridge pier obtained from calibrated model with experimental results for different intensity levels
0.5MCE intensity level 1MCE intensity level
2MCE intensity level 3MCE intensity level
Figure 6.6. Comparison of the numerical results of HyFRC bridge pier obtained from calibrated model with experimental results for different intensity levels
6.4.1 Energy dissipation of calibrated results
Cumulative energy dissipation at a particular time step is calculated by summing the areas corresponding to preceding time step with energy dissipation of current time step and plot of cumulative energy dissipation with time is shown in Figure 6.7 and Figure 6.8. In all the cases with excitation of different MCE intensity levels, we see that energy dissipation capacity of calibrated model closely matches the experimental capacity for both conventional concrete and HyFRC specimen.
6.4 Model Calibration Procedures and its Results
0.5 MCE intensity level 1MCE intensity level
2 MCE intensity level 3 MCE intensity level
Figure 6.7. Comparison of the energy dissipation for all MCE levels for conventional concrete bridge pier
0.5 MCE intensity level 1MCE intensity level
2 MCE intensity level 3 MCE intensity level
Figure 6.8. Comparison of the energy dissipation for all MCE levels for HyFRC bridge pier