Fragility analysis#
One of the most common approaches to define damage in academia is assuming a single damage model per building class. This was the approach followed by GEM in its 2018 release of the global risk model and described in more detail in Martins and Silva (2020). Whilst such a method is well supported it raises some issues when there is a need to estimate losses for the structural, non-structural components and contents separately.
Structural damage#
Damage to structural elements is proportional to the level of displacement with damage initiation stating at the yielding point. Before this the building is assumed to deform elastically, and thus with no significant damage is to be expected. The thresholds for moderate and extensive damage were placed evenly distributed between the onset of damage (Sd_y) and the ultimate displacement capacity (Sd_u).
Table 1. Summary of the damage model for structural elements
Damage state |
Damage threshold |
|---|---|
Slight |
Sd_y |
Moderate |
0.67Sd_y+0.33Sd_u |
Extensive |
0.33Sd_y+0.67Sd_u |
Complete |
Sd_u |
Nonstructural drift sensitive damage#
The category of nonstructural drift sensitive include elements like infill walls, partitions and plumbing. Non-structural components tend to sustain damage before structural components do (e.g. infill walls have a low deformation capacity), therefore we propose an initiation of damage before reaching the yielding displacement of the structure, as described in the Table 2. The thresholds for moderate and extensive damage were placed evenly distributed between the slight damage state and the ultimate displacement capacity.
Table 2. Summary of the damage model for nonstructural drift sensitive elements
Damage State |
Drift-sensitive damage thresholds |
|---|---|
Slight |
0.75Sd_y |
Moderate |
0.50Sd_y+0.33Sd_u |
Extensive |
0.25Sd_y+0.67Sd_u |
Complete |
Sd_u |
Nonstructural acceleration sensitive damage#
For the non-structural components that are acceleration sensitive, we performed a review of the types of components typically found in residential, commercial and industrial facilities using the FEMA P-58 document and several other peer reviewed publications (e.g. Porter et al (2010), Porter et al (2014), Cremen and Baker (2019) and Rashid et al (2021)). These sources of fragility functions provide several models for components such as: shelves, computer equipment, workstations, HVAC and machinery. We also distinguished between components in buildings with no seismic provisions and buildings constructed according to more modern regulations. It is also worth mentioning that for this type of components, the majority of the literature recommends assuming only two damage states (i.e. undamaged or damaged). This assumption is due to the fact that these components (e.g. electronics, furniture, machinery) are unlikely to be classified in different damage states or to even be repaired. Instead, most likely they will be fully replaced.
Table 3. Summary of the damage model for nonstructural acceleration sensitive elements by occupancy and level of seismic design
Occupancy |
Non ductile or low ductility |
Moderate or high ductility |
|---|---|---|
Residential |
0.70g |
1.20g |
Commercial |
0.80g |
1.20g |
Industrial |
0.80g |
1.50g |
References#
Cremen, G. and Baker, J.W. (2019) Improving FEMA P-58 non-structural component fragility functions and loss predictions. Bulletin of Earthquake Engineering, 17(4): p. 1941-1960. DOI: 10.1007/s10518-018-00535-7
Martins, L. and Silva, V. (2020) Development of a fragility and vulnerability model for global seismic risk analyses. Bulletin of Earthquake Engineering. DOI: 10.1007/s10518-020-00885-1.
Porter K., Farokhnia K., Vamvatsikos D. and Cho I.H. (2014) Guidelines for component-based analytical vulnerability assessment of buildings and nonstructural elements, GEM Technical Report 2014-13 V1.0.0, 102 pp., GEM Foundation, Pavia, Italy, DOI: 10.13117/GEM.VULN-MOD.TR2014.13.
Porter, K., Johnson, G., Sheppard, R. and Bachman, R. (2010) Fragility of Mechanical, Electrical, and Plumbing Equipment. Earthquake Spectra, 26(2): p. 451-472. DOI: 10.1193/1.3363847.
Rashid M, Dhakal R, Sullivan T (2021). Seismic design of acceleration-sensitive non-structural elements in New Zealand: State-of-practice and recommended changes. Bulletin of the New Zealand Society for Earthquake Engineering. 54.