LIVEdataset aec-bench@releasetasks 552models 18disciplines 5last submission … · built …

civilwith-tool

Fos Seismic

Computes the factor of safety for embankment or natural slopes subjected to earthquake inertia forces using the pseudo-static infinite slope method per USACE EM 1110-2-1902 and ICOLD Bulletin 148. Applies horizontal and vertical seismic coefficients to the sliding mass, accounts for pore water pressure via the pore pressure ratio ru, and derives the yield acceleration ky at which FoS reaches unity.

with-tool: The model is given an executable Python calculator script.

Standards

ICOLD Bulletin 148 USACE EM 1110-2-1902

How this task is generated

One template produces many comparable benchmark tasks while keeping the scoring contract fixed.

01
Template
The reusable contract shown on this page.
02
Scenario
An archetype and site context are sampled.
03
Difficulty tier
Inputs may be hidden at harder tiers.
04
Task prompt
The model responds with the declared outputs.

Parameters

Inputs the model receives, and the outputs it is scored on.

Inputs

8 inputs

Always given

Included directly in every task prompt.

Slope angle deg
slope_angle_deg
Slope angle beta measured from horizontal
5 – 45 degrees
Slip depth
slip_depth_m
Depth to the slip surface measured vertically from the slope face
1 – 20 m
Pore pressure ratio
pore_pressure_ratio
Pore pressure ratio ru = u / (gamma * z * cos²β)
0 – 0.5
Kh
kh
Horizontal seismic coefficient (fraction of g)
0.05 – 0.4

Derived from scenario

Sampled from the scenario and inferable from its description.

Cohesion
cohesion_kpa
Effective cohesion c' of the embankment material
Derived from the archetype scenario. Hidden at hard difficulty.
0 – 80 kPa
Friction angle deg
friction_angle_deg
Effective friction angle phi' of the embankment material
Derived from the archetype scenario. Hidden at hard difficulty.
0 – 45 degrees
Unit weight
unit_weight_kn_m3
Bulk unit weight of the embankment material gamma
Derived from the archetype scenario. Hidden at hard difficulty.
16 – 22 kN/m³

Optional

Used only when the sampled task needs this part of the contract.

Kv
kv
Vertical seismic coefficient (fraction of g, acts upward for conservative case)
Optional input.
0 – 0.2

Scored outputs

3 outputs

Fos

fos

Factor of safety under pseudo-static seismic loading (dimensionless)

Scores if within ±3% of the reference value.

Yield acceleration ky

yield_acceleration_ky

Yield (critical) horizontal acceleration at which FoS = 1.0 (fraction of g)

Scores if within ±3% of the reference value.

Yield ratio

yield_ratio

Yield acceleration ratio ky / kh (dimensionless)

Scores if within ±3% of the reference value.

Difficulty

Each template is sampled at three tiers. Harder tiers may hide inputs, forcing the model to infer them from the scenario description.

easy

All inputs given

Dry cohesionless slope with no vertical seismic coefficient — simplest case

Pore pressure ratio restricted to: 0

Kv restricted to: 0

medium

All inputs given

Embankment with pore pressure and cohesion, all parameters given

hard

Some inputs hidden

Material properties hidden; agent infers from embankment description and site context

Hidden inputs

Cohesioncohesion_kpa
Friction angle degfriction_angle_deg
Unit weight kn m3unit_weight_kn_m3

Prompt replacement text

The embankment is a {{ archetype.description }} ({{ archetype.site_context }})

Task bundle

The exact instruction and parameter contract used to generate this task, pinned to the published library source.

/workspace

instruction.md
fos-seismic_calc.py

Teal lines show Jinja input conditions, not task visibility policy. A line renders only when that input or tool is visible.

1You are a senior geotechnical/dam engineer specializing in embankment slope stability and seismic assessment.2 3## Problem4 5Calculate the factor of safety of an embankment slope under pseudo-static seismic loading using the infinite slope method, and determine the yield (critical) acceleration.6 7## Given8 9| Parameter | Value | Unit |10|-----------|-------|------|11| Slope angle (β) | {{ slope_angle_deg }} | degrees |12| Depth to slip surface (z) | {{ slip_depth_m }} | m |13{% if cohesion_kpa is defined %}14| Effective cohesion (c') | {{ cohesion_kpa }} | kPa |15{% endif %}16{% if friction_angle_deg is defined %}17| Effective friction angle (φ') | {{ friction_angle_deg }} | degrees |18{% endif %}19{% if unit_weight_kn_m3 is defined %}20| Bulk unit weight (γ) | {{ unit_weight_kn_m3 }} | kN/m³ |21{% endif %}22| Pore pressure ratio (ru) | {{ pore_pressure_ratio }} | - |23| Horizontal seismic coefficient (kh) | {{ kh }} | - |24{% if kv is defined %}25| Vertical seismic coefficient (kv) | {{ kv }} | - |26{% endif %}27{% if archetype_description is defined %}28 29### Site Conditions30 31{{ archetype_description }}32{% endif %}33 34{% if tool_available %}35## Available Tool36 37A pseudo-static slope stability calculation tool is available at `/workspace/fos-seismic_calc.py`. Run it with:38 39```bash40python3 /workspace/fos-seismic_calc.py --help41```42 43You may use this tool to verify your calculations or compute values directly.44{% endif %}45 46## Required47 48Calculate the following:49 501. Factor of safety under pseudo-static seismic loading (FoS)512. Yield acceleration ky — the horizontal seismic coefficient at which FoS = 1.0523. Yield acceleration ratio ky / kh53 54## Applicable Standards55 56- USACE EM 1110-2-1902 — Slope Stability (pseudo-static method)57- ICOLD Bulletin 148 — Selecting Seismic Parameters for Large Dams58 59## Constraints60 61- No internet access is available. Work from engineering knowledge and the provided tool.62- Use the pseudo-static infinite slope method with the following formulation:63  - **Driving shear stress**: T_d = γ·z·[(1 − kv)·sin(β) + kh·cos(β)]·cos(β)64  - **Normal effective stress**: σ'_n = γ·z·[(1 − kv)·cos(β) − kh·sin(β)]·cos(β)65  - **Pore pressure**: u = ru·γ·z·cos²(β)66  - **Resisting shear stress**: T_r = c' + (σ'_n − u)·tan(φ')67  - **Factor of safety**: FoS = T_r / T_d68- The vertical seismic coefficient kv acts upward (reduces effective weight), which is the conservative assumption.69- If kv is not provided, assume kv = 0.70- Yield acceleration ky is solved by setting FoS = 1.0 and solving for kh analytically.71- USACE EM 1110-2-1902 requires FoS ≥ 1.0 for the pseudo-static case; a yield ratio > 1.0 indicates ky exceeds the design kh.72- Typical horizontal seismic coefficients: 0.05–0.15 for low seismicity, 0.15–0.25 for moderate, 0.25–0.40 for high seismicity zones.73 74## Output Format75 76Show your step-by-step working in Markdown, including formulas and intermediate calculations. At the end of your solution, include a JSON block with your final answers in exactly this format:77 78```json79{80  "fos": <numeric_value>,81  "yield_acceleration_ky": <numeric_value>,82  "yield_ratio": <numeric_value>83}84```85 86Write your complete solution to `/workspace/output.md`.87

Scenario archetypes

Each generated task is drawn from one of these realistic scenario bands.

Site contexts ground each scenario in a real locale the model can use to infer hidden values.

Homogeneous earth dam

homogeneous_earth_dam

Homogeneous earth dam with compacted clay core

snowy-mountains-damwivenhoe-spillwaywarragamba-embankment

Parameter ranges

cohesion_kpa: 15 – 40
friction_angle_deg: 18 – 28
unit_weight_kn_m3: 18 – 20
slope_angle_deg: 15 – 25
pore_pressure_ratio: 0.1 – 0.3
kh: 0.05 – 0.15
kv: 0 – 0.05

Zoned rockfill dam

zoned_rockfill_dam

Zoned rockfill dam with gravel shell

thomson-dam-gippslandhinze-dam-gold-coastcotter-dam-act

Parameter ranges

cohesion_kpa: 0 – 10
friction_angle_deg: 35 – 45
unit_weight_kn_m3: 19 – 22
slope_angle_deg: 20 – 35
pore_pressure_ratio: 0 – 0.15
kh: 0.05 – 0.2
kv: 0 – 0.1

Tailings dam

tailings_dam

Tailings storage facility embankment with mine waste fill

bowen-basin-tsfkalgoorlie-tailingshunter-valley-tsf

Parameter ranges

cohesion_kpa: 5 – 20
friction_angle_deg: 20 – 30
unit_weight_kn_m3: 17 – 20
slope_angle_deg: 10 – 20
pore_pressure_ratio: 0.2 – 0.45
kh: 0.08 – 0.25
kv: 0 – 0.08

Road embankment seismic

road_embankment_seismic

Road embankment in a moderate seismic zone

newcastle-road-embankmentadelaide-hills-embankmentlaunceston-highway

Parameter ranges

cohesion_kpa: 5 – 25
friction_angle_deg: 25 – 35
unit_weight_kn_m3: 18 – 21
slope_angle_deg: 18 – 30
pore_pressure_ratio: 0 – 0.2
kh: 0.1 – 0.3
kv: 0 – 0.15

Natural slope seismic

natural_slope_seismic

Natural hillside slope in a seismically active region

blue-mountains-escarpmentcairns-range-hillsideotway-ranges-slope

Parameter ranges

cohesion_kpa: 0 – 15
friction_angle_deg: 28 – 40
unit_weight_kn_m3: 17 – 20
slope_angle_deg: 20 – 40
pore_pressure_ratio: 0 – 0.3
kh: 0.1 – 0.35
kv: 0 – 0.15

Levee seismic

levee_seismic

River levee under earthquake loading

murray-river-leveefitzroy-river-leveehawkesbury-river-levee

Parameter ranges

cohesion_kpa: 10 – 30
friction_angle_deg: 20 – 30
unit_weight_kn_m3: 17 – 19
slope_angle_deg: 10 – 20
pore_pressure_ratio: 0.15 – 0.4
kh: 0.05 – 0.2
kv: 0 – 0.08

Example task

snowy-mountains-dam-homogeneous-earth-dam-preview — hard difficulty, some inputs hidden.

Homogeneous earth dam with compacted clay core. snowy-mountains-dam. Required outputs: fos, yield_acceleration_ky, yield_ratio

The model sees

Scenario context and visible inputs.

slope_angle_deg: 15 to 25 degrees
slip_depth_m: 1 to 20 m
pore_pressure_ratio: 0.1 to 0.3
kh: 0.05 to 0.15
kv: 0 to 0.05

Executable tool: fos-seismic_calc.py

The model must infer

Inputs withheld at this difficulty.

Unit weight kn m3
unit_weight_kn_m3
Cohesion
cohesion_kpa
Friction angle deg
friction_angle_deg

Stand-in text in the prompt

The embankment is a {{ archetype.description }} ({{ archetype.site_context }})

The model must produce

The scored JSON answer schema.

{
  "fos": <number>,
  "yield_acceleration_ky": <number>,
  "yield_ratio": <number>
}

fos · scored within ±3%
yield_acceleration_ky · scored within ±3%
yield_ratio · scored within ±3%

Fos Seismic

How this task is generated

Template

Scenario

Difficulty tier

Task prompt

Parameters

Inputs

Scored outputs

Fos

Yield acceleration ky

Yield ratio

Difficulty

easy

medium

hard

Task bundle

Scenario archetypes

Homogeneous earth dam

Zoned rockfill dam

Tailings dam

Road embankment seismic

Natural slope seismic

Levee seismic

Example task

The model sees

The model must infer

The model must produce