Seismic Performance Reliability of RC Structures: Application of Response Surface Method and Systemic Approach

Document Type : Research Papers


1 Ph.D. Candidate, Department of Civil Engineering, Faculty of Engineering, University of Sistan and Baluchestan, Zahedan, Iran

2 Assisstant Professor, Department of Civil Engineering, Faculty of Engineering, University of Sistan and Baluchestan, Zahedan, Iran


The present study presents an algorithm that models uncertainties at the structural component level to estimate the performance reliability of RC structures. The method calculates the performance reliability using a systemic approach and incorporates the improved response surface method based on sampling blocks using the first-order reliability method and conditional reliability indices. The results of the proposed method at different performance levels were compared to bound techniques and the overall approach. It was shown that the proposed algorithm appropriately estimates the reliability of the seismic performance of RC structures at different damage levels for the structural components. The results indicated that performance reliability indices increased when then on-performance scenarios were examined for high levels of components damage.


ATC-40. (1996). Seismic Evaluation and Retrofit of concrete Buildings, Applied Technology Council, Redwood City, Seismic Safety Commission State of California, Report No. SSC 96-01.
Bucher, C.G. and Bourgund, U. (1990). “A fast and efficient response surface approach for structural reliability problems”, Structural Safety, 7(1), 57–66.
Buratti, N., Ferracuti, B. and Savoia, M. (2010). Response surface with random factors for seismic fragility of reinforced concrete frames”, Structural Safety, 32(1), 42-51.
Der Kiureghian, A. (2004). First- and second-order reliability methods, In Nikolaidis E., Ghiocel D. M., Singhal S., (Eds.), Engineering Design Reliability Handbook, Chapter 14, CRC Press LLC, ISBN0-8493-1180-2.
Dolsek, M. and Fajfar, P. (2007), “Simplified probabilistic seismic performance assessment of plan-asymmetric buildings”, Earthquake Engineering and Structural Dynamics, 36(13), 2021–2041.
Drezner, Z. (1994). “Computation of the trivariate normal integral”, Mathematics of Computation, 62(205), 289–294.
Drezner, Z. and Wesolowsky, G.O. (1990). “On the computation of the bivariate normal integral”, Journal of Statistical Computation and Simulation, 35(1), 101–107.
Ellingwood, B., Galambos T.V., MacGregor J.G. and Cornell, C.A. (1980). Development of a probability based load criterion for American national standard A58: Building code requirements for minimum design loads in buildings and other structures, National Bureau of Standards Special Publication No. 577, Washington D.C.
FEMA. (2000). Pre-standard and commentary for seismic rehabilitation of buildings, Report No. FEMA-356, Federal Emergency Management Agency, Washington D.C.
Gavin, H.P. and Yau, S.C. (2008). “High-order limit state functions in the response surface method for structural reliability analysis”, Structural Safety, 30(2), 162–179.
Genz, A. and Bretz, F. (1999). “Numerical computation of multivariate probabilities with application to power calculation of multiple contrasts”, Journal of Statistical Computation and Simulation, 63(4), 361–378.
Genz, A. and Bretz, F. (2002). “Comparison of methods for the computation of multivariate probabilities", Journal of Computational and Graphical Statistics, 11(4), 950–971.
Gollwitzer, S. and Rackwitz, R. (1983). “Equivalent components in first-order system reliability”, Reliability Engineering, 5(2), 99–115.
Guan, X.L. and Melchers, R.E. (2001). ” Effect of response surface parameter variation on structural reliability estimates”, Structural Safety, 23(4), 429–440.
Hasofer, A.M. and Lind, N.C. (1974). “Exact and invariant second-moment code format”, Journal of Engineering Mechanics, ASCE, 100(1), 111-121.
Hohenbichler, M. and Rackwitz, R. (1983). “First-Order concepts in system reliability”, Structural Safety,1(3), 177–188.
Huh, J. and Haldar, A. (2002). "Seismic reliability of nonlinear frames with PR connections using systematic RSM", Probabilistic Engineering Mechanics, 17(2), 177–190.
Iranian Code of Concrete, (2000). 3rd Edition, Technical Office of Management and Development of Standards, Management and Planning Organization of Iran, (in Persian).
Iranian Code of Practice for Seismic Resistant Design of Buildings, (2005), Standard No. 2800, 3rdEdition, Building and Housing Research Center.
Kang, S.C., Koh, H.M. and Choo, J.F. (2010). “An efficient response surface method using moving least squares approximation for structural reliability analysis”, Probabilistic Engineering Mechanics, 25(4), 365-371.
Kaymaz, I. and McMahon, C.A. (2005). “A response surface method based on weighted regression for structural reliability analysis”, Probabilistic Engineering Mechanics, 20(1), 11–17.
Kent, D.C. and Park, R. (1971). "Flexural members with confined concrete", Journal of Structural Division, ASCE, 97(ST7), 1969-1990.
Khademi, M.H. (2004). Study on scaling of spectral quantities of Iranian accelerograms through magnitude and geological distance of the site, Building and Housing Research Center, 
Research Report BHRC Publication No. R-376, Tehran, Iran.
Kunnath, S.K., Reinhorn, A.M. and Abel, J.F. (1992). “A computational tool for seismic performance of reinforced concrete buildings”, Computers and Structures, 41(1), 157-173.
Liel, A.B., Haselton, C.B., Deierlein, G.G. and Baker, W.B. (2009). “Incorporating modeling uncertainties in the assessment of seismic collapse risk of buildings”, Structural Safety, 31(2), 197-211.
Moller, O., Foschi, R.O., Quiroz, L.M. and Rubinstein, M. (2009). “Structural optimization for performance-based design in earthquake engineering: Applications of neural networks”, Structural Safety, 31(6), 490–499.
Nguyen, X.S., Sellier, A., Duprat, F. and Pons G. (2009). “Adaptive response surface method based on a double weighted regression technique”, Probabilistic Engineering Mechanics, 24(2), 135–143.
Nowak, A.S. and Collins, K.R. (2000). Reliability of Structures, McGraw-Hill, New York.
Park, Y.J., Reinhorn, A.M. and Kunnath, S.K. (1987). IDARC: Inelastic Damage Analysis of Reinforced Concrete frame - shear-wall structures, Technical Report NCEER-87-0008, State University of New York at Buffalo.
Rajashekhar, M.R. and Ellingwood, B.R. (1993). “A new look at the response surface approach for reliability analysis”, Structural Safety, 12(3), 205–220.
Song, J. and Der Kiureghian, A. (2003). “Bounds on system reliability by linear programming”, Journal of Engineering Mechanics, 129(6), 627-636.
Thoft-Christensen, P. and Sørensen, J.D. (1984). “Reliability analysis of elasto-plastic structures”, Proceedings of 11th IFIP Conferences on System Modeling and Optimization, Copenhagen, Springer-Verlag, 556–566.
Valles, R.E., Reinhorn, A.M., Kunnath, S.K., Li, C. and Madan, A. (2005). IDARC 2D Version 6.1: A computer program for inelastic damage analysis of buildings, Technical Report NCEER-96-0010, State University of New York at Buffalo.
Vamvatsikos D. and Cornell C.A. (2002). “Incremental dynamic analysis”, Earthquake Engineering and Structural Dynamics, 31(3), 491-514.
Wen, Y.K., Ellingwood, B.R., Veneziano, D. and Bracci, J. (2003). Uncertainty modeling in earthquake engineering, Mid-America Earthquake (MAE) Center Project, FD-2 Report, University of Illinois.