Methodology & Theoretical Framework

This module is a stochastic spatial decision-support engine that models structural vulnerability and urban mobility loss for a given earthquake scenario. Base collapse probability is looked up from four construction-era bands modelled on FEMA's HAZUS-MH (2003) fragility framework (pre-1985 0.85, 1985-2000 0.60, 2001-2018 0.25, post-2018 0.05), then scaled exponentially by moment magnitude: mag_factor = exp(0.8 x (Mw - 7.0)). A Monte Carlo simulation draws one Bernoulli collapse outcome per building from that probability, producing a dynamic risk envelope that differs slightly on every run unless the seed is fixed. Debris geometry for a collapsed building follows Goretti & Sarli's (2006) empirically calibrated spread ratio (radius = building height x spread coefficient k); the void/solid volume ratio used to convert footprint area into debris volume follows FEMA P-58 (2018) guidance by construction material. A seed parameter is exposed so a given scenario can be reproduced exactly, or re-rolled by changing the seed to sample a different stochastic realisation of the same magnitude.

Input Parameter Guide

Parameter	Description & Recommended Values
Moment Magnitude (Mw)	Earthquake energy. Has an exponential effect on the fragility function (e.g. 7.0 - 7.6).
Debris Spread Coefficient (k)	Fraction of a collapsed building's height thrown horizontally onto adjacent roads (Goretti & Sarli, 2006). Typically 0.30 to 0.50.
Void/Solid Volume Ratio	Fraction of the gross building volume that becomes actual debris (concrete/brick). Per FEMA guidance: • Steel/Glass: 0.10 - 0.20 • Reinforced concrete (RC): 0.25 - 0.35 • Unreinforced masonry: 0.35 - 0.45
Random Seed	Fixes the Monte Carlo draw so results are reproducible run-to-run; change it to sample a different stochastic realization of the same scenario.

Output Schema

[01_Static] Net Logistics Network Topology: Cadastral road/void fabric with building footprints subtracted.
[02_Static] Morphological Conflict: Static form index modelling encroachments onto parcel boundaries as negative vectors.
[03_Dynamic] Stochastic Risk & Volume Index: Point layer with collapse probability, estimated debris volume (m3), and severity class per building.
[04_Dynamic] Macro-Debris Spread Envelope: Dissolved debris polygon covering all collapsed buildings.
[05_Dynamic] Critical Network Blockage Areas: Cumulative debris mass that falls specifically on the road network.
[06_Dynamic] Post-Disaster Active Evacuation Corridors: Remaining accessible routes for search-and-rescue logistics.

How to Read the Results

collapse_prob sorts your retrofit-priority list: buildings above 0.80 under a Mw > 7.0 scenario are pre-code construction and the first candidates for structural assessment.
collapsed (0/1) is this run's Monte Carlo outcome, not a certainty - re-run with a different seed to see how sensitive the network-blockage picture is to the specific draw.
debris_vol_m3 and blocked_area_m2 scale with building height and footprint - a single tall building can outweigh several low ones in total road-blockage impact.
[06] Evacuation Corridors is the headline output for response planning: what survives once [05]'s blockages are subtracted from the network.

Using the Results

Compare Mw 6.5 against Mw 7.5 runs (same seed) to see the exponential, non-linear jump in road loss between a moderate and a major event - this is usually more informative for planning than a single "design" magnitude. Feed [04] Macro-Debris Envelope into Seismic Cascade: Debris -> Network Degradation for the full pre- vs. post-quake accessibility comparison, and [03] Structural Damage Index into Population-Weighted Exposure to translate collapse probabilities into estimated human impact. This is a planning-screening tool, not an engineering-grade structural assessment - do not use individual collapse_prob values to make retrofit funding decisions without a site inspection.