By Tao Lai | October 10, 2019
Blog post illustration

AIR has been using the Capacity Spectrum Method (CSM) for earthquake damage estimation since the 1990s for many models we have developed. This method translates earthquake demands into structural response through a non-linear iterative process using a seismic demand curve, which represents the hazard, and a capacity curve, which represents the behavior of the building. The estimated response is then used to calculate building damage using a building-specific and deformation-based damage function.

In recently updated models, such as the New Zealand earthquake model, as well as in forthcoming updates to the Australia and Caribbean earthquake models, AIR is switching to a more straightforward spectral acceleration-based approach. This directly translates the calculated ground motion intensity at a location into building damage. This blog explains the rationale behind the change.

CSM Was Once Widely Used

The CSM was first introduced in the 1970s as a rapid evaluation procedure in a pilot project for assessing the seismic vulnerability of buildings at the Puget Sound Naval Shipyard (Freeman et al., 1975) when computing resources and sophisticated non-linear time history dynamic analyses were limited. The CSM was adopted as a design procedure in seismic design guidelines in the 1980s (Army 1986).

This method uses a non-linear static pushover analysis to develop a base shear and roof displacement relationship, which is referred to as the building’s capacity curve. When the building’s capacity curve is overlaid with the earthquake demand spectrum, the graphical intersection (i.e., performance point) of the two curves approximates the maximal expected response of the structure.

The CSM has historically been used in engineering seismic design and portfolio earthquake risk assessment. It has the advantage of distinguishing building vulnerability through differentiating buildings’ capacity curves by their material strength and structural system.

This approach is particularly useful when there is a lack of damage observations because it can be implemented using only an engineering analysis of the building of interest. All early versions of AIR’s earthquake models adopted this method, which at one point had been widely used for damage estimation.

An Inherent Limitation

The CSM has an inherent limitation, however, in its ability to correlate the modeled relationships for capacity curves and displacement-based damage functions with observed damage. Specifically, while engineers could quickly document and describe post-earthquake building damage at a particular site, it was almost impossible to comment on the peak deformations that the building had experienced during the earthquake unless that building had been fully instrumented.

This limitation makes it very difficult to develop and validate displacement-based damage functions, which are required for CSM damage estimation. Furthermore, it is very difficult to comment on the building’s strength and capacity without accessing and analyzing the design documents for the building, which are typically not available.

In recent years, as global seismic recording networks have advanced in terms of sensitivity, sophistication, and coverage, more-detailed ground shaking observations have become available after earthquakes. As a result, more recent post-earthquake damage surveys have published damage reports with empirical building vulnerability functions developed in terms of ground motion intensity.

For purposes of model validation, it has become increasingly difficult to compare the modeled performance of the CSM against these published vulnerability functions. The newly developed intensity-based damage functions used in the more recent earthquake models released by AIR, however, can be more easily compared against published vulnerability functions by using the location-level event intensities (LLEI) functionality within Touchstone®.   

More Robust and Consistent Modeling with an Intensity-Based Approach

After the 2011 Tohoku earthquake, AIR received millions of high-quality location-level claims and hundreds of ground motion time history recordings, which allowed AIR engineers to pursue various avenues of research such as the validation of vulnerability functions, assessing the spatial correlation of ground motion, and developing distributions for secondary building damage uncertainty. Another area that AIR engineers investigated was the correlation between ground motion intensity parameters and building damage.

In this last study, AIR engineers calculated common ground motion intensity parameters from recorded ground motions, including peak ground acceleration (PGA), peak ground velocity (PGV), cumulative absolute velocity (CAV), and 0.2-second, 0.3-second, and 1-second spectral accelerations—or Sa(0.2), Sa(0.3), and Sa(1.0), respectively—as well as deformation calculated through CSM. These observed ground motion parameters were correlated with claims data; the correlation between building damage and either spectral accelerations or displacement by CSM give statistically similar correlation coefficients (Lai, et al 2015).

In addition to the direct comparison of vulnerability functions between those found in literature and those developed by AIR, the intensity-based approach leads to a more efficient calculation and a more consistent and intuitive process for determining vulnerability when certain properties of the building are unknown. For these reasons, AIR engineers believe the proposed shift in methodology from CSM to intensity-based damage functions will lead to more robust and consistent modeling as well as an overall better client experience with respect to model evaluation.

For an overview of the enhancements to the hazard module read “Earthquake Risk in New Zealand: A Major Model Update”


Army (1986), Seismic Design Guidelines for Essential Buildings, Departments of the Army (TM 5- 809-10-1), Navy (NAVFAC P355.1), and the Air Force (AFM 88-3, Chapter 13, Section A), Washington, D.C., U.S.A.

Freeman, S.A., Nicoletti, J.P. and Tyrell, J.V. (1975), Evaluations of Existing Buildings for Seismic Risk - A Case Study of Puget Sound Naval Shipyard, Bremerton, Washington”, Proceedings of U.S. National Conference on Earthquake Engineering, Berkeley, U.S.A., pp. 113-122.

Lai, T.; Nasseri, A.; Ghosh J.; Farias, A. and Turel M (2015), A Correlation Study of Building Monetary Loss with Seismic Demands Through Insurance Claims Analyses of 2011 Tohoku Earthquake, SECED 2015 Conference: Earthquake Risk and Engineering towards a Resilient World, 9-10 July 2015, Cambridge UK

Categories: Earthquake

Don't miss a post!



You’re almost done.
We need to confirm your email address.
To complete the registration process, please click the link in the email we just sent you.

Unable to subscribe at this moment. Please try again after some time. Contact us if the issue persists.

The email address  is already subscribed.

You are subscribing to AIR Blogs. In order to proceed complete the captcha below.