1.5. Damage and Loss Estimation

The building performance assessment was performed on a story-level basis using PELICUN ([Zsarnóczay20]), where damage and losses are calculated with story-level fragility functions based on the peak story drift and floor acceleration demands. The story-based damage and loss fragility functions are derived from corresponding building-level damage and loss functions from the HAZUS earthquake model ([FEMA18]) based on the characteristic data for each building (e.g., year of construction, structure type, occupancy type). Specifically, four major states included in this testbed are Slight (DS1), Moderate (DS2), Extensive (DS3), and Complete (DS4), and one None (DS0) damage state. The four major damage states are defined separately for the structural and non-structural damages. More detailed descriptions for the example W1 building are provided below. The full descriptions can be found in [FEMA18]. Collapse safety limit states are evaluated directly from the story drift demands, where a collapse of one or more stories is considered as partial collapse of the entire building.

Note

W1: Wood Light Frame (Structural):

1. Slight: Small plaster or gypsum-board cracks at corners of door and window openings and wall-ceiling intersections; small cracks in masonry chimneys and masonry veneer.

2. Moderate: Large plaster or gypsum-board cracks at corners of door and window openings; small diagonal cracks across shear wall panels exhibited by small cracks in stucco and gypsum wall panels; large cracks in brick chimneys; toppling of tall masonry chimneys.

3. Extensive: Large diagonal cracks across shear wall panels or large cracks at plywood joints; permanent lateral movement of floors and roof; toppling of most brick chimneys; cracks in foundations; splitting of wood sill plates and/or slippage of structure over foundations; partial collapse of “room-over-garage” or other “soft-story” configurations; small foundation cracks.

4. Complete: Structure may have large permanent lateral displacement, may collapse, or be in imminent danger of collapse due to cripple wall failure or the failure of the lateral load-resisting system; some structures may slip and fall off the foundations; large foundation cracks. Approximately 3% of the total area of W1 buildings with Complete damage is expected to be collapsed.

Note

Non-structural Damage (Partition Walls):

1. Slight: A few cracks are observed at intersections of walls and ceilings and at corners of door openings.

2. Moderate: Larger and more extensive cracks requiring repair and repainting; some partitions may require replacement of gypsum board or other finishes.

3. Extensive: Most of the partitions are cracked, and a significant portion may require replacement of finishes; some door frames in the partitions are also damaged and require re-setting.

4. Complete: Most partition finish materials and framing may have to be removed and replaced, damaged studs repaired, and walls refinished. Most door frames may also have to be repaired and replaced.

Note

Non-structural Damage (Suspended Ceilings):

  1. Slight: A few ceiling tiles have moved or fallen down.

2. Moderate: Falling of tiles is more extensive; in addition, the ceiling support framing (T-bars) has disconnected and/or buckled at a few locations; lenses have fallen off some light fixtures and a few fixtures have fallen; localized repairs are necessary.

3. Extensive: The ceiling system exhibits extensive buckling, disconnected T-bars and falling ceiling tiles; the ceiling partially collapses at a few locations and some light fixtures fall; repair typically involves removal of most or all ceiling tiles.

4. Complete: The ceiling system is buckled throughout and/or has fallen and requires complete replacement; many light fixtures fall.

Note

Non-structural Damage (Exterior Wall Panels):

  1. Slight: Slight movement of the panels, requiring realignment.

2. Moderate: The movements are more extensive; connections of panels to the structural frame are damaged, requiring further inspection and repairs; some window frames may need realignment.

3. Extensive: Most of the panels are cracked or otherwise damaged and misaligned, and most panel connections to the structural frame are damaged, requiring thorough review and repairs; a few panels fall or are in imminent danger of falling; some window panes are broken and some pieces of glass have fallen.

4. Complete: Most panels are severely damaged, most connections are broken or severely damaged, some panels have fallen and most are in imminent danger of falling; extensive glass breakage and falling.

Note

Non-structural Damage (Electrical Mechanical Equipment, Piping, Ducts):

1. Slight: The most vulnerable equipment (e.g., unanchored or mounted on spring isolators) moves and damages attached piping or ducts.

2. Moderate: Movements are larger and damage is more extensive; piping leaks occur at a few locations; elevator machinery and rails may require realignment.

3. Extensive: Equipment on spring isolators topples and falls; other unanchored equipment slides or falls, breaking connections to piping and ducts; leaks develop at many locations; anchored equipment indicates stretched bolts or strain at anchorages.

4. Complete: Equipment is damaged by sliding, overturning, or failure of their supports and is not operable; piping is leaking at many locations; some pipe and duct supports have failed, causing pipes and ducts to fall or hang down; elevator rails are buckled or have broken supports and/or counterweights have derailed.

The story drift and floor accelerations from 25 non-linear analyses of each building are used to define multivariate lognormal distributions of peak drifts and accelerations for each story of the building, and the dispersion in the drift and acceleration demands is inflated by 0.22 to account for additional modeling uncertainties not considered in the non-linear dynamic analyses.

Using the distributions of earthquake demands, and damage and loss functions, PELICUN generates 20,000 realizations of damage and losses for each building, and stores statistics of the resulting performance data that are relevant for regional-scale evaluation. The results are output as HDF5 (Hierarchical Data Format) files that can be processed and visualized through MATLAB, Python, Jupyter notebooks, or converted to CSV format.

Zsarnóczay20

Zsarnóczay, A., and Deierlein, G. G. (2020). “PELICUN – A Computational Framework for Estimating Damage, Loss and Community Resilience,” in Proceedings, 17th World Conference on Earthquake Engineering, (Sendai: WCEE).

FEMA18(1,2)

FEMA (2018), HAZUS – Multi-hazard Loss Estimation Methodology 2.1, Earthquake Model Technical Manual, Federal Emergency Management Agency, Washington D.C.