==================
Consequence Models
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Introduction
------------
Consequence models translate structural damage states into economic losses and other impact
metrics. These models are essential for converting fragility analysis results into actionable
risk metrics for decision-making.
Damage-to-Loss Ratios
---------------------
Damage-to-loss ratios map each damage state to an expected loss expressed as a fraction of a
building's replacement cost. The ratios used in this model are:
.. list-table:: Structural Damage-to-Loss Ratios
:header-rows: 1
:widths: 25 25 50
* - Damage State
- Mean Ratio
- Description
* - DS1 (Slight)
- 0.05
- Minor cosmetic repairs
* - DS2 (Moderate)
- 0.15
- Moderate structural repairs
* - DS3 (Extensive)
- 0.60
- Major structural repairs
* - DS4 (Complete)
- 1.00
- Full replacement
Sources and Derivation
~~~~~~~~~~~~~~~~~~~~~~
The damage-to-loss ratios are derived from:
**Empirical Data**
Post-earthquake damage and repair cost surveys (Di Pasquale et al. 2005; Bal et al. 2008)
**Analytical Procedures**
Component-based loss estimation methodologies (Martins et al. 2016; Aljawhari et al. 2023)
Loss Categories
---------------
Structural Losses
~~~~~~~~~~~~~~~~~
Losses associated with damage to the building's lateral load-resisting system and gravity
load-carrying elements.
Non-Structural Loss Functions (SLFs)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Storey Loss Functions (SLFs) relate engineering demand parameters (EDPs) directly to loss ratios
for non-structural components. Two types of SLFs are provided:
* **Drift-sensitive SLFs**: For components sensitive to interstorey drift (partitions, facades, stairs)
* **Acceleration-sensitive SLFs**: For components sensitive to floor acceleration (ceilings, MEP systems)
The SLFs are available for different regions, building materials, component categories, and occupancy types.
**Interactive SLF Viewer**
.. raw:: html
Embodied Carbon Loss Functions
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Carbon SLFs express embodied carbon loss (kg CO₂-eq per unit floor area) as a function of EDP,
for structural and non-structural components. They follow the same region × material × component × occupancy
structure as the non-structural SLFs above.
**Interactive Carbon SLF Viewer**
.. raw:: html
Contents Losses
~~~~~~~~~~~~~~~
Losses from damage to building contents including furniture, fixtures, equipment, machinery,
personal belongings (residential), and inventory (commercial/industrial).
Casualty Consequence Models
---------------------------
Casualty models estimate fatalities and injuries based on building damage and collapse.
The consequence ratios below represent the expected proportion of building occupants
affected at each damage state.
**Fatalities Consequence Ratios**
.. raw:: html
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**Injuries Consequence Ratios**
.. raw:: html
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**Affected Population**
.. raw:: html
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**Displaced Population**
.. raw:: html
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Regional Variations
-------------------
Consequence models may vary by region due to:
* **Construction costs**: Labour and material costs differ globally
* **Repair practices**: Different repair approaches for similar damage
* **Economic factors**: Currency, inflation, and market conditions
* **Building standards**: Code requirements for repairs/retrofits
Uncertainty Quantification
--------------------------
Uncertainty in damage-to-loss ratios is captured through:
**Within-Damage-State Variability**
Coefficient of variation for loss ratio given each damage state
**Between-Building Variability**
Differences in repair costs for buildings of the same class
The uncertainty is propagated through the vulnerability calculation using the formulations
described in the Vulnerability Models section.
References
----------
* Di Pasquale G. et al. (2005). New developments in seismic risk assessment in Italy.
Bulletin of Earthquake Engineering.
* Bal I.E. et al. (2008). Detailed assessment of structural characteristics of Turkish RC
building stock for loss assessment models. Soil Dynamics and Earthquake Engineering.
* Martins L. et al. (2016). Development and assessment of damage-to-loss models for
moment-frame reinforced concrete buildings. Earthquake Engineering & Structural Dynamics.
* Aljawhari K. et al. (2023). Simulation-based consequence models of seismic direct loss
and repair time for archetype reinforced concrete frames. Soil Dynamics and Earthquake
Engineering.
* FEMA (2012). Next-Generation Methodology for Seismic Performance Assessment of Buildings
(FEMA P-58). Washington, D.C.