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

civilwith-tool

Hudson Armor Sizing

Determines the required median armor stone weight and nominal diameter for breakwater and revetment stability using Hudson's (1959) formula from the USACE Coastal Engineering Manual and CIRIA C683 Rock Manual. Accounts for design wave height, rock and water densities, structure slope, and the stability coefficient KD which depends on armor type and placement method.

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

Standards

CIRIA C683 Rock Manual USACE CEM

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

5 inputs

Always given

Included directly in every task prompt.

Design wave height
design_wave_height_m
Design wave height H
0.5 – 8 m
Slope angle deg
slope_angle_deg
Structure slope angle alpha from horizontal
18 – 45 degrees

Derived from scenario

Sampled from the scenario and inferable from its description.

Rock density
rock_density_kg_m3
Armor rock density rho_r
Derived from the archetype scenario. Hidden at hard difficulty.
2200 – 3000 kg/m³
Water density
water_density_kg_m3
Water density rho_w
Derived from the archetype scenario. Hidden at hard difficulty.
1000 – 1035 kg/m³
Stability coefficient kd
stability_coefficient_kd
Hudson stability coefficient KD
Derived from the archetype scenario. Hidden at hard difficulty.
1 – 16

Scored outputs

3 outputs

Specific gravity sr

specific_gravity_sr

Specific gravity of rock Sr = rho_r / rho_w

Scores if within ±3% of the reference value.

Armor weight tonnes

armor_weight_tonnes

Median armor unit weight W (tonnes)

Scores if within ±5% of the reference value.

Nominal diameter

nominal_diameter_m

Nominal armor diameter Dn50 (m)

Scores if within ±5% 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

Moderate wave height, all parameters given — straightforward Hudson formula

medium

All inputs given

Larger wave height, steeper slopes — same formula, bigger numbers

hard

Some inputs hidden

Rock density, water density, and KD hidden — agent must infer from site description

Hidden inputs

Rock densityrock_density_kg_m3
Water densitywater_density_kg_m3
Stability coefficient kdstability_coefficient_kd

Prompt replacement text

The armor is {{ 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
hudson-armor-sizing_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 coastal engineer specializing in breakwater and revetment design.2 3## Problem4 5Calculate the required median armor stone weight and nominal diameter for a rubble-mound breakwater using Hudson's equation.6 7## Given8 9| Parameter | Value | Unit |10|-----------|-------|------|11| Design wave height (H) | {{ design_wave_height_m }} | m |12{% if rock_density_kg_m3 is defined %}13| Rock density (ρ_r) | {{ rock_density_kg_m3 }} | kg/m³ |14{% endif %}15{% if water_density_kg_m3 is defined %}16| Water density (ρ_w) | {{ water_density_kg_m3 }} | kg/m³ |17{% endif %}18| Slope angle (α) | {{ slope_angle_deg }} | degrees |19{% if stability_coefficient_kd is defined %}20| Stability coefficient (KD) | {{ stability_coefficient_kd }} | - |21{% endif %}22{% if archetype_description is defined %}23 24### Site Conditions25 26{{ archetype_description }}27{% endif %}28 29{% if tool_available %}30## Available Tool31 32An armor sizing calculation tool is available at `/workspace/{{ meta.name }}_calc.py`. Run it with:33 34```bash35python3 /workspace/{{ meta.name }}_calc.py --help36```37 38You may use this tool to verify your calculations or compute values directly.39{% endif %}40 41## Required42 43Calculate the following:44 451. Specific gravity of the armor rock Sr = ρ_r / ρ_w462. Median armor unit weight W in tonnes473. Nominal armor diameter Dn50 in metres48 49## Applicable Standards50 51- USACE Coastal Engineering Manual (CEM)52- CIRIA C683 Rock Manual53 54## Constraints55 56- No internet access is available. Work from engineering knowledge and the provided tool.57- Use Hudson's equation:58  - W = (ρ_r × H³) / (KD × (Sr − 1)³ × cot(α))59  - where W is in kg, ρ_r is in kg/m³, H is in metres60  - Sr = ρ_r / ρ_w (specific gravity of rock)61  - cot(α) = cos(α) / sin(α) where α is the slope angle from horizontal62- Convert weight to tonnes: W (tonnes) = W (kg) / 100063- Nominal diameter: Dn50 = (W / ρ_r)^(1/3) where W is in kg and ρ_r is in kg/m³64 65## Output Format66 67Show your step-by-step working in Markdown. At the end of your solution, include a JSON block with your final answers in exactly this format:68 69```json70{71  "specific_gravity_sr": <numeric_value>,72  "armor_weight_tonnes": <numeric_value>,73  "nominal_diameter_m": <numeric_value>74}75```76 77Write your complete solution to `/workspace/output.md`.78

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.

Rough quarrystone random

rough_quarrystone_random

Rough angular quarrystone placed randomly on trunk section

queensland-outer-reefnsw-coastal-headlandwa-exposed-coast

Parameter ranges

rock_density_kg_m3: 2500 – 2700
water_density_kg_m3: 1020 – 1030
stability_coefficient_kd: 3 – 4

Rough quarrystone special

rough_quarrystone_special

Rough angular quarrystone with special placement on trunk

sydney-harbour-breakwatermelbourne-port-revetment

Parameter ranges

rock_density_kg_m3: 2500 – 2700
water_density_kg_m3: 1020 – 1030
stability_coefficient_kd: 5 – 6.5

Basalt armor random

basalt_armor_random

Dense basalt armor stone placed randomly

victoria-basalt-coastnorth-qld-volcanic

Parameter ranges

rock_density_kg_m3: 2800 – 3000
water_density_kg_m3: 1020 – 1030
stability_coefficient_kd: 3.5 – 4.5

Freshwater quarrystone

freshwater_quarrystone

Quarrystone armor for freshwater dam or lake revetment

murray-river-weirsnowy-hydro-damwivenhoe-dam

Parameter ranges

rock_density_kg_m3: 2500 – 2700
water_density_kg_m3: 1000 – 1005
stability_coefficient_kd: 3 – 4

Concrete unit random

concrete_unit_random

Concrete armor units (cubes) placed randomly

darwin-harbour-breakwatertownsville-port-expansion

Parameter ranges

rock_density_kg_m3: 2300 – 2400
water_density_kg_m3: 1020 – 1030
stability_coefficient_kd: 6 – 7.5

Example task

queensland-outer-reef-rough-quarrystone-random-preview — hard difficulty, some inputs hidden.

Rough angular quarrystone placed randomly on trunk section. queensland-outer-reef. Required outputs: specific_gravity_sr, armor_weight_tonnes, nominal_diameter_m

The model sees

Scenario context and visible inputs.

design_wave_height_m: 0.5 to 8 m
slope_angle_deg: 18 to 45 degrees

Executable tool: hudson-armor-sizing_calc.py

The model must infer

Inputs withheld at this difficulty.

Stability coefficient kd
stability_coefficient_kd
Water density
water_density_kg_m3
Rock density
rock_density_kg_m3

Stand-in text in the prompt

The armor is {{ archetype.description }} ({{ archetype.site_context }})

The model must produce

The scored JSON answer schema.

{
  "specific_gravity_sr": <number>,
  "armor_weight_tonnes": <number>,
  "nominal_diameter_m": <number>
}

specific_gravity_sr · scored within ±3%
armor_weight_tonnes · scored within ±5%
nominal_diameter_m · scored within ±5%

Hudson Armor Sizing

How this task is generated

Template

Scenario

Difficulty tier

Task prompt

Parameters

Inputs

Scored outputs

Specific gravity sr

Armor weight tonnes

Nominal diameter

Difficulty

easy

medium

hard

Task bundle

Scenario archetypes

Rough quarrystone random

Rough quarrystone special

Basalt armor random

Freshwater quarrystone

Concrete unit random

Example task

The model sees

The model must infer

The model must produce