AIR's latest earthquake model.
As the landscape of risk transfer alternatives continues to evolve, so has the role and prominence of the catastrophe modeller. Critical to the success of a cat bond issue is the catastrophe modelling undertaken in support of the transaction and, in particular, the reliability of the modelled loss estimates as perceived by rating agencies and potential investors. As the rating agency and investor communities have become more sophisticated with respect to this developing market, so have the models themselves.
Applied Insurance Research (AIR), the Boston-based catastrophe modelling firm, advanced the science and sophistication of earthquake modelling last year with the introduction of the Advanced Component Method ™, or ACM ™, into its US model. Early this year, in time for the Japanese renewals, ACM was made available in AIR's Japan earthquake model. By means of a rigorous, engineering-based analysis of the response of individual structural and non-structural components to the unique vibrational resonance between building and incoming seismic waves, ACM captures a building's response to earthquakes in a far more realistic way than more traditional vulnerability assessment techniques.
Traditional methods are typically based on the performance of the ‘average' building within a large portfolio of buildings. Often, the vulnerability curves (functions that relate the level of damage to the level of earthquake intensity) produced by such models are based on expert opinion. For many years, the mainstay of earthquake vulnerability assessment was a set of vulnerability curves developed by the Applied Technology Council for the State of California; these curves were then mapped to construction types found in other regions. The so-called ATC-13 curves were essentially derived by asking noted structural engineers, builders and the like to estimate the expected percentage of damage that would result to a typical building of a specific construction type if that building was subjected to a particular level of earthquake intensity as defined by MMI. (Introduced before instrumental recordings of earthquakes became commonplace, MMI, or Modified Mercalli Index, is a twelve-point scale based on subjective human responses to ground motion and observed damage.)
A second major effort to develop a methodology for earthquake vulnerability assessment resulted in HAZUS, an interactive software program released by the Federal Emergency Management Agency (FEMA) in 1997. While in HAZUS, as in ACM, objective measures of intensity (spectral displacement and spectral acceleration) replaced the subjective MMI, HAZUS continued to rely on expert opinion and engineering judgment to estimate the state of damage that would result from a given level of intensity. In ACM, reliance on expert opinion and subjective measures of intensity give way to a purely analytical – and objective – approach.
Advanced component method
One striking observation frequently made in the aftermath of earthquakes is that even seemingly similar structures in close proximity to each other are likely to respond quite differently to the same seismic event. Each responds according to its own unique structural configuration and design. In the photograph taken after the 1999 Taiwan earthquake (see next page), one modern building has completely collapsed while others remain intact and an old temple, built without the benefit of seismic design, appears untouched. It is this selectivity exhibited by earthquakes that ACM is designed to capture and that cannot be captured using traditional methods.
The ACM methodology is summarised in figure 1 below. AIR engineers begin by identifying building types typical of the modelled region and defining their general configuration and characteristics. Local design firms are then enlisted to ensure conformity with local and regional construction practices. For its Japan model, AIR worked closely with a leading Japanese design firm, which provided detailed specifications and design documents for representative structures conforming to local Japanese construction practices and code. These design documents include the physical dimensions of each component, as well as their axial, bending, moment and shear capacities, yield strength and other material properties.
ACM addresses and explicitly models uncertainty at every stage of an analysis. Variability in the mechanical properties of building materials, mass and loading patterns is captured by treating these properties, as well as live and dead loadings, as random variables. Using Latin Hypercube sampling techniques and selecting from the probability distributions governing each of these variables, ten similar, yet slightly different, buildings are modelled for each building type.
A seismic analysis is then performed on each ‘virtual' building using SAP2000, a highly reliable engineering software application. Three-dimensional models of buildings are input into the software. Ground motion is modelled as the application of lateral load, which monotonically increases over the height of the building. The amount of load applied is the amount required to horizontally displace, by fixed amounts, every floor of the building. This process is repeated, with incremental displacements, until the building collapses. At each stage, lateral force is distributed to the nodes, or joints, where beams and columns connect. As joints and members fail, the force is redistributed to the elements that remain functional.
Two products come out of the seismic analysis. The first is the building's capacity curve, which describes the mathematical relationship between displacement and the force applied. It is a function of the natural period, stiffness and strength of the building and is non-linear; as joints fail, the building becomes more flexible and, therefore, less force is required to achieve the next inch of displacement.
The second result of the seismic analysis is a component deformation history. As force is applied, the components that comprise the building's frame become deformed. For each incremental displacement of the building, the amount by which components at each of the storeys are deformed will determine what is called the interstorey drift. Finally, the interstorey drift ratio is calculated (see figure 2) and is used as the primary determinant of damage to the building's components, both structural and non-structural.
ACM takes its name from the deconstruction of the modelled building into its components parts – the beams, columns, joints, partitions, etc. – that comprise the structure. Experimental data, as documented in dozens of studies published in refereed journals, are used to estimate damage to each of the building's components as they undergo deformation. The mean damage ratio to the individual component is calculated and, around each mean, a complete probability distribution is estimated.
To combine the damage to all components of a given type, a weighting mechanism is developed such that the importance of each component to total building damage is a function of the storey on which that component resides. For example, gravity load-carrying components such as columns carry the load of all upper storeys, so columns on lower storeys receive a higher weight. More intuitively, if the first floor of a five-storey building collapses, the building is lost; if the fifth floor collapses, only the fifth floor is lost.
Damage ratios for all structural component types are then combined using weights based on the relative importance of each component type to system performance. Separately, a damage function for non-structural components, including partitions, cladding, glazing, suspended ceilings and MEP (mechanical, electrical, plumbing), is estimated.
Estimating monetary damage
Thus far, we have addressed ACM's scientific approach to the estimation of physical damage. But ACM makes a second, major contribution. Through the application of a robust and truly unique cost model based on regional repair costs and regionally appropriate repair strategies, an analysis based on ACM provides detailed information on expected monetary losses.
The traditional approach to estimating monetary damage has been simply to multiply the building damage ratio (derived either through ATC-13 curves or HAZUS damage ratios) by the replacement value of the building. A few modellers employ a subjective mapping algorithm to relate physical to monetary damage. ACM takes a more analytical approach.
ACM's state-of-the-art cost model estimates the cost of repair of each damaged component. Repair costs will depend on regional price indices, construction practices and appropriate repair strategies. In the case of a reinforced concrete column, for example, if damage is negligible or slight, with minor deformations in connections or hairline cracks in a few welds, the recommended action may be a minimal repair or even to do nothing at all. Hence, the repair cost, in this instance, is negligible or zero. There may be alternative methods of repair, each associated with different costs; the appropriate method may depend on the degree of damage and accessibility. At high levels of damage, replacing the affected member may be considered.
Repair costs are determined by identifying the repair strategies for each damaged component on each floor of the building, given the state of physical damage. The cost of inspections, set up costs, demolition and removal of debris are also included.
Estimates of the monetary damage to each individual component are probabilistically combined to achieve an estimate of the monetary damage, or cost of repair, to the building as a whole. It should be noted that the use of hard data on repair and replacement costs guarantees that an ACM analysis can be updated every year using the most current cost information available.
Earthquake intensity is directly linked to individual building performance rather than to the performance of the ‘average' building within a large portfolio of buildings. One implication of this is that damage patterns, as simulated by ACM, will much more closely resemble the pattern and spottiness of damage that is actually observed in the aftermath of earthquakes. In addition, because the focus of ACM is on the response of individual buildings to earthquake intensity, truly objective site-specific analyses can be performed.
ACM is a truly groundbreaking methodology for assessing building vulnerability to earthquakes. ACM is transparent. Its underlying parameters are accessible and the significance of each can be easily grasped by rating agency experts and sophisticated investors. Most importantly, ACM produces far more reliable results than previously available.