Project Title/ID Number Modeling of Progressive Collapse in Reinforced Concrete Structural—3432003
Start/End Dates 10/1/03—9/30/04
Project Leader Khalid Mosalam (UCB/F)
Team Members Mohamed Talaat (UCB/GS)

F=faculty; GS=graduate student; US=undergraduate student; PD=post-doc; I=industrial collaborator; O=other

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1. Project Goals/Objectives:

Model the initiation and progression of collapse in reinforced concrete framed structures.

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

The project will have important impact that will support PEER’s mission. These impacts can be summarized in the following:

  1. Reduction of loss of life due to progressive collapse of older construction during major earthquake events by providing the proper computational tools for assessment
  2. Develop viable retrofit methodology to prevent progressive collapse
  3. Allow proper design of new RC frames structures against the undesired limit state of collapse

3. Methodology Employed:

  1. Evaluate existing dynamic analysis capabilities in determining local, progressive, and global collapse for generic reinforced concrete structural systems including:
    a. Older (O) design system susceptible to early deterioration due to reinforcement detailing deficiencies with one unique load path
    b. Retrofitted (R) older design system to achieve certain performance levels which may show an alternate load path prior to collapse
    c. New (N) design system complying with the current state of knowledge allowing the mobilization of variety of alternate load paths during the sequence of progressive collapse
  2. Investigate the influence of several design/behavioral parameters on the selected systems O, R, and N. These parameters will be selected based on findings from previous SDOF study by Ibarra et al. (2003), such as:
    a. Strength and stiffness deterioration due to cyclic effects
    b. Frequency content of ground motion
    c. Ductility capacity
    d. P-? effect
Other specific issues for MDOF systems will be evaluated in the study. Among others, these issues will include the following:
    e. Higher modes of vibration
    f. Spatial variability of strength and stiffness
    g. Boundary conditions and redundancy
    h. 2D versus 3D modeling
    i. Modeling velocity-dependent damping
  1. Evaluate exiting criteria for elimination of failed load carrying elements, particularly columns, in the selected systems: O, R, and N. In that regard, utilization of the findings and development from previous study by Elwood (2002) will be utilized for O and R systems. This will include:
    a. Consideration of the empirical model for the drift at shear failure
    b. Consideration of the shear-friction based model for the drift at axial failure for a shear-damaged column
    c. Development of a generic shear-axial interaction after detecting axial failure where the limit of this interaction is the trigger of the removal criteria of the failed column
    d. Generalization of (a) to (c) above to any type of element, not necessarily older columns
  2. Develop a robust elimination technique of the identified element(s) through the elimination criteria above. This will include:
    a. Direct element elimination where direct modification is conducted for the global system matrix that is assembled from local element matrices. This maybe the most numerically stable approach but it is computationally demanding.
    b. Indirect element elimination where an element is not deactivated but rather its stiffness is multiplied by a severe reduction (penalty) factor. This is computationally cheap but may suffer from numerical stability especially for weak diagonal terms.
    c. Convergence problems are expected to arise with either of the elimination techniques, it is expected that a matrix partitioning to separate damaged elements and variable boundary condition technique to address interface issues should be developed.
  3. New development will focus on practical account for the following interrelated challenging issues:
    a. Effect of strain-rate in the constitutive modeling of the material
    b. Collision behavior of structural elements during failure
The latter issue will require the following:
    1. Develop a practical approach to check for collision between elements accounting for the rigid body motion of the eliminated (failed) elements
    2. Consider contact and collision forces transmitted during contact
    3. Adapt the time increment based on the relative velocity of the collided elements and the transmitted forces during contact
    4. Consider separation, re-contact and collision

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

For year 6: The work conducted by the PI under two projects will be utilize mainly to address different sources of uncertainties in the progressive collapse modeling of the RC frames subjected to severe shaking. Prior accomplishments include:

Fragility Models for RC Structures-3041999 (PI: Der Kiureghian and Mosalam)
Among several publications, the following journal papers and PEER technical report summarize the findings of this project.

  1. Gardoni, P., Der Kiureghian, A., and Mosalam, K.M., “Probabilistic Capacity Models and Fragility Estimates for RC Columns Based on Experimental Observations,” Journal of Engineering Mechanics, ASCE, 128(10), 1024-1038, Oct. 2002.
  2. Gardoni, P., Mosalam, K.M., and Der Kiureghian, “Probabilistic Seismic Demand Models and Fragility Estimates for RC Bridges,” Journal of Earthquake Engineering, 7(1), 79-106, 2003.
  3. Gardoni, P., Der Kiureghian, A., and Mosalam, K.M., “Probabilistic Models and Fragility Estimates for Bridge Components and Systems,” PEER Technical Report 2002/13, June 2002.

Life Sciences Testbed Simulation—3242002 (PI:Mosalam)
The following two refereed conference papers summarize this work.

  1. Lee, T.-H., and Mosalam, K.M., “Probabilistic Fiber Element Modeling of Reinforced Concrete Columns,” Proc. Ninth Int. Conf. on Applications of Statistics and Probability in Civil Eng., ICASP9, San Francisco, July 6-9, 2003.
  2. Lee, T.-H., and Mosalam, K.M., “Sensitivity of Seismic Demand of a Reinforced Concrete Shear-Wall Building,” Proc. Ninth Int. Conf. on Applications of Statistics and Probability in Civil Eng., ICASP9, San Francisco, July 6-9, 2003.

For year 7: refer to item 3 above for specifics. It is intended to document the findings in two PEER reports, one at the end of year 7 and another at the end of year 8. The first report will be aimed towards identifying the generic systems of the study and the investigation of the capabilities of the existing models. On the other hand, the second report will be aimed at the new development of the robust modeling capabilities to remove failed elements, and address specific features of the progressive collapse as described in the scope and project plan above.

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

Engineering Assessment Methodology—3192002 (PI: Krawinkler)
Part of this project focused on simplified procedures that permit approximate performance assessment in terms of collapse. We intend to make full use of the results obtained from this study such as these documented in the following paper.

L. Ibarra, R. Medina and H. Krawinkler, "Collapse Assessment of Deteriorating SDOF Systems," Proc. of the 12th European Conference on Earthquake Engineering, Paper #665, London, Sept. 2001.

RC Frame Validation Tests—5252002 (PI: Moehle)
This project is of direct relevance to the proposed research. We intend to closely collaborate with the researchers of this project and make use of the pervious study documented in the following PhD dissertation.

K.J. Elwood, "Shake Table Tests and Analytical Studies on the Gravity Load Collapse of Reinforced Concrete Frames," Ph.D. Dissertation, Department of Civil and Env. Eng., Univ. of Cal., Berkeley, 2002.

One of the works outside PEER and similar to what is proposed is the elaborate study by Meguro and Tagel-Din which is documented in several publication; four of which are listed below. The focus of this work is on the development of the Applied Element Method for continuum modeling to solve the collapse problem. The proposed work will specifically deal with framed structures in 2D and 3D subjected to severe earthquake loading which is not practically handled in the work of Meguro and Tagel-Din.

  1. K. Meguro and H. Tagel-Din, “Applied Element Simulation of RC Structures under Cyclic Loading,” J. Structural Engineering, ASCE, 127(11), 1295-1305, Nov. 2001.
  2. H. Tagel-Din and K. Meguro, “Applied Element Method for Dynamic Large Deformation Analysis of Structures,” Structural Eng./Earthquake Eng., Int. J. of the Japan Society of Civil Engineers (JSCE), 17(2), 215s-224s, Oct. 2000.
  3. H. Tagel-Din and K. Meguro, “Analysis of a Small Scale RC Building Subjected to Shaking Table Tests using Applied Element Method,” Proc. of the 12th World Conference on Earthquake Engineering, New Zealand, Jan. 30 - Feb. 4, 2000.
  4. H. Tagel-Din and K. Meguro, “Applied Element Simulation for Collapse Analysis of Structures,” Bulletin of Earthquake Resistant Structure Research Center, Institute of Industrial Science, The University of Tokyo, No. 32, March 1999.

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

Refer to items 3 and 4 above where a list of tasks to be conducted in years 7 and 8 are given. At this stage precise separation between year 7 tasks and year 8 tasks is not feasible.

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

None yet.

8. Expected Milestones & Deliverables:

  1. Develop generic systems for old (O), retrofitted (R), and new (N) construction to serve as platform for studying the progressive collapse
  2. Develop and Implement a generic axial-shear interaction model to trigger failed element removal
  3. Implement a robust numerical algorithm to remove failed elements
  4. Develop and implement a practical numerical model to account for debris spread and impact
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