Amr Ghanem · The tool

Locus

A multi-hazard assessment tool. The hazard is an input, not a built-in assumption: Locus predicts how likely a structure is to fail under hazards acting in sequence, and returns a resilience index rather than a pass or a fail.

A locus is the set of all points satisfying a condition — which is exactly what a fragility surface is. The tool computes one.

The work

Why a tool, and why a surface

A code check tells you a building complies. It does not tell you what that building will do when the ground moves, or when water arrives, or when the next hazard nobody planned for arrives. Those are different questions, and answering them takes hundreds of nonlinear analyses per configuration — which is not something anyone does by hand.

So the answer had to be a tool, and the tool had to be general. The hazard is an input, not a built-in assumption, and the output is a surface rather than a curve: a probability exists across the whole parameter space, including for configurations nobody explicitly ran. A probability is something an owner, a city, or a transport agency can decide on. A pass or a fail is not.

What it gives you

Prediction, not just evaluation

A fragility curve answers for the configuration you ran. A surface answers across the whole parameter space at once, so a structure nobody explicitly analysed still has a result — and a change to the design can be tested before it is drawn.
Resilience as a number you can rank

The output is a resilience index, so two different structural systems become directly comparable. That is what turns a set of probabilities into a retrofit priority list.
Hazards assessed together, not one at a time

The hazard is an input, not a hard-coded assumption. The water meets a frame the shaking has already weakened, so assessing earthquake and tsunami separately understates the risk. Earthquake and tsunami are the demonstrated cases, not the limits.
Fed by instrumentation and AI

Assessment is only as good as what it knows about the structure as built. Deep-learning damage detection and multi-sensor fusion on instrumented bridges supply that condition data — the AI reads the structure, the physics computes the failure probability.

How Locus works

Reliability drives the search; nonlinear analysis answers it. Five steps, from a demand to a surface.

01
Sweep
The parameter space is discretised — every hazard intensity and configuration becomes a case.
02
Distribute
Cases are independent, so they run concurrently. Weeks of analysis become hours.
03
Iterate
The coupled loop runs for each case until the design point converges.
04
Fit
A lognormal fitted through those points gives a continuous fragility curve.
05
Surface
The fitted curves join into one continuous surface.
06
Compare
The index reduces a surface to one number, so structures can be ranked.

A trial realisation goes out, a response comes back, the search updates — cycling until the design point converges.

Locus couples reliability analysis to nonlinear structural analysis and extends the pair to sequential multi-hazard loading, driving the established FERUM and ZEUS-NL codes as its solvers.

What it produces

A surface, not a curve — failure probability across two hazards at once. Each marked line is an ordinary fragility curve: hold one hazard fixed and you get one of them. The surface is all of them. Schematic; the hazards are deliberately unnamed, and the capacities are representative rather than from a specific study.

Try it

Set the shaking, set the inundation, and watch the fragility surface and the frame respond.

Ground shaking 0.35 g

Inundation 13.1 ft

Flow velocity, Fr 1.40

Dispersion β 0.50

View -135°

—

P = 1 − (1 − P_eq)(1 − P_ts) · θ_ts reduced by earthquake damage

Forces follow ASCE 7 Chapter 6; capacities are representative for a mid-rise RC frame, not a specific study. See the research page.

What to try

Take the shaking to zero. The probability collapses to the tsunami-only number. That is the coupling switching off.
Leave the shaking at 0.35 g and move the inundation. The readout reports the same tsunami on a damaged frame and on an undamaged one. The gap between them is what assessing the two hazards separately would miss.
Turn the view through a full circle. Axis labels move to whichever edge is nearest you; the probability axis rides the back corner.
Watch the marked point. It is where two ordinary fragility curves cross — one cut at the current inundation, one at the current shaking. Both are drawn, so it reads as an intersection rather than a dot on a sheet.

Source on GitHub

The interactive is open source. The research code — FORM reliability coupled to nonlinear time-history analysis — is not: the repository reproduces the shape of the result in closed form so it runs in a browser.

The papers behind it

Eleven papers, newest first.

Abdelhafeez, M., Park, H., Sherif, M., Ghanem, A., & Moon, D.-S. (2026). “Effects of tsunami wave and bathymetric parameters on hydrodynamic forces and structural fragility” Journal of Building Engineering, 118, Article 115077. https://doi.org/10.1016/j.jobe.2025.115077
Sherif, M. A., Ghanem, A. M., Abdelhafeez, M. H., Jung, D., Kim, D.-J., & Moon, D.-S. (2025). “Fragility curve-based resilience index for structural vulnerability assessment in hazard analysis” Smart Structures and Systems.
Ghanem, A., Lee, Y.-J., & Moon, D.-S. (2024). “Seismic vulnerability of reinforced concrete frame structures: Obtaining plan or vertical mass irregularity from structure use change” Journal of Structural Engineering, 150(3), Article 04023243. https://doi.org/10.1061/JSENDH.STENG-12440
Ghanem, A. (2023). “Integrated framework for multi-hazard resilience assessment of infrastructures” University of Hawaiʻi at Mānoa. https://doi.org/10.13140/RG.2.2.11462.24646
Ghanem, A., Sherif, M., Abdelhafeez, M., Lee, Y.-J., & Moon, D. (2022). “Relationship between seismic redundancy and failure likelihood for mass-eccentric reinforced concrete frame structures” 12th National Conference on Earthquake Engineering (12NCEE), Salt Lake City.
Sherif, M., Ghanem, A., Abdelhafeez, M., & Moon, D. (2022). “Indexing seismic fragility curves of skewed reinforced concrete bridges” 12th National Conference on Earthquake Engineering (12NCEE), Salt Lake City.
Abdelhafeez, M., Ghanem, A., & Sherif, M. (2022). “Probabilistic fragility analysis of reinforced concrete structures under tsunami hydrodynamic loads of the ASCE 7 standard” Ports 2022, 488–497. https://doi.org/10.1061/9780784484395.049
Ghanem, A., Moon, D., & Lee, Y. (2021). “Seismic fragility surface of irregular reinforced concrete frame structures” 17th World Conference on Earthquake Engineering (17WCEE), Sendai, Japan. https://doi.org/10.13140/RG.2.2.10623.38562
Ghanem, A., & Moon, D. (2021). “Seismic fragility assessment of skewed reinforced concrete bridges” 17th World Conference on Earthquake Engineering (17WCEE), Sendai, Japan. https://doi.org/10.13140/RG.2.2.13978.82882
Ghanem, A., & Moon, D.-S. (2021). “Seismic fragility analysis of 3D vertical irregular reinforced concrete structures” Engineering Archive. https://doi.org/10.31224/osf.io/zn9uh
Ghanem, A., Moon, D.-S., & Lee, Y.-J. (2021). “Seismic vulnerability assessment of skewed reinforced concrete bridges” Engineering Archive. https://doi.org/10.31224/osf.io/cy5pj

The full list is on the research page.

Locus

The work

Why a tool, and why a surface

What it gives you

How Locus works

Sweep

Distribute

Iterate

Fit

Surface

Compare

What it produces

Try it

What to try

The papers behind it