Simplified seismic loss assessment using limit state loss-intensity models




In an effort to provide practicing engineers with simple means of limiting earthquake-induced losses to buildings, this paper extends a simplified damage-state loss vs. intensity approach for estimation of expected annual losses in two ways. Firstly, modifications to allow consideration of a threshold replacement limit state are provided. Secondly, an equation for simplified loss assessment of buildings characterised with a three-damage state loss-intensity model is presented. Furthermore, recommendations are provided for the simplified models associated parameters’ values.  The proposed approach is trialled for three New Zealand code compliant eccentrically braced frame buildings, and the results compared against those obtained through the PEER framework. It is found that the expected annual loss can be predicted to within 10% of the values obtained via rigorous approaches and opportunities for further research are discussed.


Campbell P (2018). "Proposed low damage design guidance - A NZ Approach". 17th US-Japan-New Zealand Workshop on the Improvement of Structural Engineering and Resilience, Queenstown, NZ, 8 pp.

Pettinga J (2021). "Directing low-damage seismic design with building functionality". Proceedings of the New Zealand Society for Earthquake Engineering Annual Technical Conference.

Pampanin S (2012). "Reality-check and renewed challenges in earthquake engineering: Implementing low-damage systems–from theory to practice". Bulletin of New Zealand Society of Earthquake Engineering, 45(4): 137-160. DOI:

Mayes R, Wetzel N, Weaver B, Tom K, Parker W, Brown A and Pietra D (2013). "Performance based design of buildings to assess damage and downtime and implement a rating system". Bulletin of New Zealand Society for Earthquake Engineering, 46(1): 40-55. DOI:

Daniell JE, Khazai B, Wenzel F and Vervaeck A (2013). “The CATDAT damaging earthquakes database”. Natural Hazards Earth Systems Sciences, 11(8): 2235-2251. DOI:

SEAOC Vision Committee (1995). "Performance-based seismic engineering". Structural Journal of Engineers Association of California, California, USA.

FEMA (2012). “FEMA P-58-1: Seismic Performance Assessment of Buildings Volume 1—Methodology”. Federal Emergency Management Agency and Applied Technology Council (ATC), Redwood City, CA, USA.

Sullivan T (2016). “Use of limit state loss versus intensity models for simplified estimation of expected annual loss”. Journal of Earthquake Engineering, 20(6): 954-974. DOI:

Calvi GM, Sullivan TJ and Welch D (2014). “A seismic performance classification framework to provide increased seismic resilience”. Perspectives on European Earthquake Engineering and Seismology, pp. 361-400. DOI:

Fajfar P and Dolšek M (2012). “A practice‐oriented estimation of the failure probability of building structures”. Earthquake Engineering and Structural Dynamics, 41(3): 531-547. DOI:

Sullivan TJ, Welch DP and Calvi GM (2014). “Simplified seismic performance assessment and implications for seismic design”. Earthquake Engineering and Engineering Vibration, 13(1): 95-122. DOI:

Hwang SH and Lignos DG (2017). “Earthquake‐induced loss assessment of steel frame buildings with special moment frames designed in highly seismic regions”. Earthquake Engineering and Structural Dynamics, 46(13): 2141-2162. DOI:

Orumiyehei A and Sullivan TJ (2021). “Quantifying the likelihood of exceeding a limit state via the displacement-based assessment approach”. Journal of Earthquake Engineering, 26(8): 4346-4364. DOI:

Orumiyehei A and Sullivan TJ (2021). “Displacement-based seismic assessment of the likelihood of failure of reinforced concrete wall buildings”. Buildings, 11(7): 295. DOI:

Porter KA, Beck JL and Shaikhutdinov RV (2002). “Sensitivity of building loss estimates to major uncertain variables”. Earthquake Spectra, 18(4): 719-743. DOI:

Luco N and Cornell CA (1998). “Effects of random connection fractures on the demands and reliability for a 3-story pre-Northridge SMRF structure”. Proceedings of the 6th US National Conference on Earthquake Engineering, 244: 1-12.

O'Reilly GJ and Sullivan TJ (2017). “Quantification of modelling uncertainty in existing Italian RC frames”. Earthquake Engineering and Structural Dynamics, 47(4): 1054-1074. DOI:

Gentile R, Galasso C and Pampanin S (2021). “Material property uncertainties versus joint structural detailing: Relative effect on the seismic fragility of reinforced concrete frames”. Journal of Structural Engineering, 147(4): 04021007. DOI:

Haselton CB, Goulet CA, Mitrani-Reiser J, Beck JL, Deierlein GG, Porter KA, Stewart JP and Taciroglu E (2008). “An assessment to benchmark the seismic performance of a code-conforming reinforced-concrete moment-frame building”. Pacific Earthquake Engineering Research Center.

Kazantzi A, Vamvatsikos D and Lignos D (2014). “Seismic performance of a steel moment-resisting frame subject to strength and ductility uncertainty”. Journal of Engineering Structures, 78: p. 69-77. DOI:

Farag M, Mehanny S, Kohrangi M, Vamvatsikos D and Bakhoum M (2019). “Precast beam bridges with a buffer–gap–elastomeric bearings system: Uncertainty in design parameters and randomness in ground records”. Journal of Bridge Engineering, 24(5): 04019034. DOI:

Fox MJ and Sullivan TJ (2016). “Use of the conditional spectrum to incorporate record‐to‐record variability in simplified seismic assessment of RC wall buildings”. Earthquake Engineering and Structural Dynamics, 45(3): 463-482. DOI:

Baker JW (2010). “Conditional mean spectrum: Tool for ground-motion selection”. Journal of Structural Engineering, 137(3): 322-331. DOI:

Ramirez CM and Miranda E (2009). “Building-specific loss estimation methods and tools for simplified performance-based earthquake engineering”. Stanford University. Report No. 171.

Welch DP, Sullivan TJ and Calvi GM (2012). “Developing direct displacement-based design and assessment procedures for performance-based earthquake engineering”. IUSS Press. Pavia, Italy.

Dhakal RP and Saha S (2017). “Loss optimization seismic design (LOSD): Beyond seismic loss assessment”. Proceedings of 16th World Conference on Earthquake Engineering, Santiago, Chile.

Khakurel S, Dhakal RP, Yeow TZ and Saha S (2020). “Performance group weighting factors for rapid seismic loss estimation of buildings of different usage”. Earthquake Spectra, 36(3): 1141-1165. DOI:

Shahnazaryan D, O’Reilly GJ and Monteiro R (2021). “Story loss functions for seismic design and assessment: Development of tools and application”. Earthquake Spectra, 37(4). DOI:

O’Reilly GJ and Calvi GM (2021). “A seismic risk classification framework for non-structural elements”. Bulletin of Earthquake Engineering, 19: 5471–5494. DOI:

Standards NZ (2004). “NZS 1170.5: Structural Design Actions Part 5: Earthquake Actions–New Zealand”. Standards New Zealand, Wellington, NZ.

Turner CWO, Spooner B and Hanson FMH (2003). Bridge Manual. Transit New Zealand, Wellington, NZ.

Sullivan T, Priestley N and Calvi GM (2012). A Model Code for the Displacement-Based Seismic Design of Structures, DBD12. IUSS Press, Pavia, Italy.

Welch D, Sullivan T and Calvi G (2014). “Developing direct displacement-based procedures for simplified loss assessment in performance-based earthquake engineering”. Journal of Earthquake Engineering, 18(2): 290-322. DOI:

Sullivan TJ and Calvi GM (2013), “Developments in the Field of Displacement-Based Seismic Assessment”. EUCENTRE, Pavia, Italy.

Formisano A, Vaiano G and Fabbrocino F (2019). “A seismic-energetic-economic combined procedure for retrofitting residential buildings: A case study in the province of Avellino (Italy)”. AIP Conference Proceedings. DOI:

Cardone D, Sullivan T, Gesualdi G and Perrone G (2017). “Simplified estimation of the expected annual loss of reinforced concrete buildings”. Earthquake Engineering and Structural Dynamics, 46(12): 2009-2032. DOI:

Krawinkler H, Zareian F, Medina R and Ibarra L (2006). “Decision support for conceptual performance‐based design”. 35(1): 115-133. DOI:

Elwood K, Marquis F and Kim J (2015). “Post-earthquake assessment and reparability of RC buildings: Lessons from Canterbury and emerging challenges”. Proceedings of the Tenth Pacific Conference on Earthquake Engineering: Building an Earthquake-Resilient Pacific.

FEMA (2012). “FEMA P58-2: Seismic Performance Assessment of Buildings: Volume 2 (Implementation)”. Applied Technology Council, Redwood City, CA.

O'Reilly GJ and Calvi GM (2019). “Conceptual seismic design in performance‐based earthquake engineering”. Journal of Earthquake Engineering and Structural Dynamics, 48(4): 389-411. DOI:

Shahnazaryan D and O’Reilly GJ (2021). “Integrating expected loss and collapse risk in performance-based seismic design of structures”. Bulletin of Earthquake Engineering, 19(2): 987-1025. DOI:

Retamales R, Davies R, Mosqueda G and Filiatrault A (2013). “Experimental seismic fragility of cold-formed steel framed gypsum partition walls”. Journal of Structural Engineering, 139(8): 1285-1293. DOI:

ASCE (2014). “ASCE 41-13: Seismic Evaluation and Retrofit Rehabilitation of Existing Buildings”. American Society for Civil Engineers, USA.

Porter KA and Beck JL (2004). “Simplified PBEE to estimate economic seismic risk for buildings”. Proceedings of the International Workshop on Performance-Based Seismic Design, Pacific Earthquake Engineering Research Center, USA. DOI:

Cornell CA, Jalayer F, Hamburger R and Foutch D (2002). “Probabilistic basis for 2000 SAC federal emergency management agency steel moment frame guidelines”. Journal of Structural Engineering, 128(4): 526-533. DOI:

Vamvatsikos D (2012). “Accurate application and second-order improvement of SAC/FEMA probabilistic formats for seismic performance assessment”. Journal of Structural Engineering, 140(2). DOI:

Bakalis K and Vamvatsikos D (2018). “Seismic fragility functions via nonlinear response history analysis”. Journal of Structural Engineering, 144(10). DOI:

O’Reilly GJ and Sullivan TJ (2016). “Direct displacement-based seismic design of eccentrically braced steel frames”. Journal of Earthquake Engineering, 20(2): 243-278.

Haymes K, Sullivan T and Chandramohan R (2020). “A practice-oriented method for estimating elastic floor response spectra”. Bulletin of New Zealand Society for Earthquake Engineering, 53(3): 116-136. DOI:

Standards NZ (2002). “NZS 1170.0: Structural Design Actions, Part 0: General Principles”. Standards New Zealand, Wellington, NZ.

Standards NZ (2007). “NZS 3404: Steel Structures Standard- New Zealand”. Standards New Zealand, Wellington, NZ.

Wilson EL and Habibullah A (2000). Structural Analysis Program SAP2000. Berkeley, California, USA.

Standards NZ (2002) “NZS 1170.2: Structural Design Actions, Part 2: Wind Actions”. Standards New Zealand, Wellington, NZ.

Mazzoni S and McKen F (2006). “The Open System for Earthquake Engineering Simulation (OpenSEES) User Command-Language Manual”.

De Francesco G and Sullivan TJ (2020). “Formulation of localized damping models for large displacement analysis of single-degree-of-freedom inelastic systems”. Journal of Earthquake Engineering, 26(8): 4235-4258. DOI:

O’Reilly GJ and Sullivan TJ (2016). “Direct displacement-based seismic design of eccentrically braced steel frames”. Journal of Earthquake Engineering, 20(2): 243-278. DOI:

Kanvinde A, Marshal K, Grilli D and Bomba G (2014). “Forensic analysis of link fractures in eccentrically braced frames during the February 2011 Christchurch earthquake: Testing and simulation”. Journal of Structural Engineering, 141(5). DOI:

Nascimbene R, Rassati G and Wijesundara K (2012). “Numerical simulation of gusset plate connections with rectangular hollow section shape brace under quasi-static cyclic loading”. Journal of Constructional Steel Research, 70: 177-189. DOI:

Jalayer F and Cornell C (2009). “Alternative non‐linear demand estimation methods for probability‐based seismic assessments”. Earthquake Engineering and Structural Dynamics, 38(8): 951-972. DOI:

Yeow T, Orumiyehei A, Sullivan T, MacRae G, Clifton C and Elwood K (2018). “Seismic performance of steel friction connections considering direct-repair costs”. Bulletin of Earthquake Engineering, 16: 5963-5993. DOI:

Bradley BA (2010). “A generalized conditional intensity measure approach and holistic ground‐motion selection”. Earthquake Engineering and Structural Dynamics, 39(12): 1321-1342. DOI:

O'Reilly GJ and Sullivan TJ (2016). “Fragility functions for eccentrically braced steel frame structures”. Engineering and Structures, 10(2): 367-388. DOI:

Sullivan TJ, Fox M, Keen J and Goebbels S (2021). “Repair methods and costs for earthquake-damaged building components in New Zealand”. DesignSafe-CI.




How to Cite

Orumiyehei, A., & Sullivan, T. (2023). Simplified seismic loss assessment using limit state loss-intensity models. Bulletin of the New Zealand Society for Earthquake Engineering, 56(3), 127–151.