1. Project Goals/Objectives:

The primary goal of this project is the development of improved material models that incorporate cyclic degrading behavior in reinforced concrete members. Efforts will also be directed to the development of damage models based on material and member response information generated during the analysis.

2. Role of this project in supporting PEER’s mission (vision):

The incorporation of enhanced reinforcing bar models and the computation of real-time damage measures will facilitate the identification of post-yield damage states that are central to the PEER performance-based methodology.

3. Methodology Employed:

The ability to model cyclic degradation and predict failure is directly related to the ability of the material models to characterize post-yield softening from a variety of effects: softening of concrete, buckling and low-cycle fatigue of reinforcing bars, fracture of confining reinforcement, etc. Hence, this project will focus first on the development of an advanced reinforcing bar model. This will be complemented with the incorporation of confinement models for concrete and component damage models in the OpenSees platform. Model development will be accompanied by validation studies using experimental data.

4. Brief Description of past year’s accomplishments (Year 6) & more detail on expected Year 7 accomplishments:

Review of Existing Material Models
In general, recent material models developed to simulate the response of mild reinforcing steel tend to be different variations of a bounding surface type formulation. A comprehensive review of different material model formulations was carried out. The most popular implementations appear to be derived from a Menegotto-Pinto formulation used to simulate kinematic hardening under cyclic loading. Dafalias has proposed a more classical bounding surface model capable of modeling both isotropic and kinematic hardening. This model has been developed in a general formulation that allows for the consideration of stress in a 3-d continuum. Balan and Filippou have also proposed a model based on the Menegotto-Pinto formulation, however it uses a slightly different formulation for the kinematic hardening term. The Chang-Mander model, which appeared to be the best-developed model based on the Menegotto-Pinto formulation, was eventually selected as the base model for the proposed development.

Material Model Implementation
The Chang-Mander model was selected because it was well developed and offered good control over the reinforcing bar behavior. Concepts presented in the Balan-Filippou model were used to relate the compressive monotonic curve to the tensile monotonic curve. The implementation of the current model is easy to use, and fairly accurate results can be obtained by specifying only the yield stress, ultimate stress, and the hardening strain. The model was validated with both constant amplitude reversal tests and random cyclic events with generally good agreement with experimental results as shown in Figure 1.

It was noted, however, that after the peak, the model exhibited a tendency to over predict the stress in the reinforcing steel, which is common to bounding surface models. To overcome this, additional memory parameters were added to the original Chang-Mander model. By including 16 reversal memory locations rather than 10, the model is now able to perform very well through an entire random cyclic event as demonstrated in Figure 1. Another feature of the material model is the incorporation of fatigue and strength degradation using an accumulated equivalent cyclic stain counting relationship based on low-cycle fatigue tests of reinforcing bars conducted by Brown and Kunnath.

Work in Progress
Reinforcing Buckling Model

The implementation of the reinforcing buckling model into OpenSees is currently in progress. The buckling effect will be simulated using a force based distributed plasticity element including second order effects. The buckled bar element is adapted from the force-based formulation with distributed plasticity as originally proposed by Spacone and Filippou. Second order effects are derived using a procedure similar to those proposed by Mau and El-Mabsout. The goal is to obtain accurate predictions of buckling behavior while minimizing the number of fibers and integration points along the member. Once this is accomplished, our current material model can be merged with the buckling model for a complete response based on a geometric model rather than an adjustment of the material model.

The concrete fiber section object creates a fiber section object. The properties of the concrete material depend on the particular confinement model selected and the unconfined compressive strength of the concrete. The confinement model determines the effective confinement based on the tie configuration provided. If no ties are provided, the section is assumed to be unconfined. The tie spacing also dictates the buckling behavior of the reinforcing bars.

confinement command
This command is used to select a confinement model to be used on the cross-section. During model calibration, several confinement models may by implemented and compared.

concreteModel command
This command is used to select the concrete model used on the cross-section. Because of its dependency on the confinement model, the concrete material model must be created by the fiber section.

buckling command
This command is used to toggle buckling behavior on or off.

patch
This command is used similar to the fiber section patch only no material tag is assigned. This will require additional consideration during implementation. The goal is to provide the overall size of the section and its discretization in the core and cover. The Concrete Section command will then create the required patches and assign the appropriate confinement models to them.

5. Other Similar Work Being Conducted Within and Outside PEER and How This Project Differs:

Known efforts outside PEER have focused on macromodels that treat cyclic degradation in an equivalent sense through the use of hysteretic force-deformation models. However, none of these projects consider advanced material models to characterize the buckling of reinforcing bars. Similarly, most of the past and current work on damage models has focused on global member response and in the post-processing of response to generate damage indices. The developments related to material modeling will be closely coordinated with the Year 7 project at the University of Washington (PI: Lehman) examining damage models for reinforcing bar buckling and fracture. While preliminary model development will be based on existing experimental data, the enhancement of the model will rely on data generated at UW. This project will also collaborate with another effort at UW on the development of performance criteria for RC columns (PI: Eberhard). The calibration of damage models to be pursued by Eberhard will be based initially on current OpenSees models, however, the refinement of the performance criteria can be facilitated by the improved degrading models to be developed as part of this project. The validation of models will be carried out using data that will become available following the shaking table studies at Berkeley (PI: Mahin). These validation studies will also provide input into refining and improving the proposed models. Interaction with other PEER projects include: ongoing work on assessment of highway over-crossings (Stojadinovic, Berkeley); continuing work on the development of beam-column models (Fenves and Filippou, Berkeley); and the implementation of new OpenSees classes related to implementation of damage models (Deierlein, Stanford).

6. Plans for Year 8 if project is expected to be continued:

The effort to develop cyclic degrading material models incorporating bar buckling and low-cycle fatigue will be largely completed in Year 7. However, the implementation of the models in OpenSees and necessary validation studies will continue into Year 8. The implementation of damage models in OpenSees will also extend into Year 8.

7. Describe any actual instances where you are aware your results have been used in industry:

Not applicable yet, since project is still underway.

8. Expected Milestones & Deliverables: