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

Roadway Spread

Determines the width of water spread across a roadway pavement and curb flow depth using the HEC-22 Manning's equation for triangular gutter sections: T = (Q*n / (K_u * Sx^(5/3) * S_L^(1/2)))^(3/8). Used for inlet spacing design and pavement drainage adequacy checks to ensure roadway safety during design storms.

both: The model must reason numerically unaided.

Standards

HEC-22

Tags

civildrainagegutterhydraulicsinlet-spacingroadwayspread

How this task is generated

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

  1. 01

    Template

    The reusable contract shown on this page.

  2. 02

    Scenario

    An archetype and site context are sampled.

  3. 03

    Difficulty tier

    Inputs may be hidden at harder tiers.

  4. 04

    Task prompt

    The model responds with the declared outputs.

Parameters

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

Inputs

4 inputs

Always given

Included directly in every task prompt.

3

  • Gutter flow

    gutter_flow_m3_s

    Design gutter flow rate Q

    0.001 – 0.2 m³/s

  • Cross slope pct

    cross_slope_pct

    Roadway cross-slope Sx (percentage)

    1 – 6 %

  • Longitudinal slope pct

    longitudinal_slope_pct

    Longitudinal road gradient S_L (percentage)

    0.3 – 10 %

Derived from scenario

Sampled from the scenario and inferable from its description.

1

  • Mannings n

    mannings_n

    Manning's roughness coefficient n for the pavement surface

    Derived from the archetype scenario. Hidden at hard difficulty.

    0.011 – 0.02

Scored outputs

2 outputs

Spread width

spread_width_m

Width of water spread on the roadway T (m)

Scores if within ±3% of the reference value.

Curb depth

curb_depth_m

Flow depth at the curb face d (m)

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

Small urban road, all parameters given, straightforward spread calculation

medium

All inputs given

Arterial or highway with higher flows, all parameters given

hard

Some inputs hidden

Manning's n hidden, agent must infer roughness from road surface description

Hidden inputs

  • Mannings nmannings_n

Prompt replacement text

The road is {{ archetype.description }} located at {{ 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

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 civil engineer specializing in roadway drainage and stormwater inlet design.2 3## Problem4 5Calculate the width of water spread on a roadway gutter and the flow depth at the curb using the HEC-22 Manning's equation for a triangular gutter cross-section.6 7## Given8 9| Parameter | Value | Unit |10|-----------|-------|------|11| Gutter flow (Q) | {{ gutter_flow_m3_s }} | m³/s |12| Roadway cross-slope (Sx) | {{ cross_slope_pct }} | % |13| Longitudinal slope (S_L) | {{ longitudinal_slope_pct }} | % |14{% if mannings_n is defined %}15| Manning's roughness (n) | {{ mannings_n }} | - |16{% endif %}17{% if archetype_description is defined %}18 19### Road Conditions20 21{{ archetype_description }}22{% endif %}23 24{% if tool_available %}25## Available Tool26 27A roadway spread calculation tool is available at `/workspace/{{ meta.name }}_calc.py`. Run it with:28 29```bash30python3 /workspace/{{ meta.name }}_calc.py --help31```32 33You may use this tool to verify your calculations or compute values directly.34{% endif %}35 36## Required37 38Calculate the following:39 401. Spread width T (m) — the width of water spread from the curb face across the roadway412. Flow depth at curb d (m) — the depth of flow at the curb face42 43## Applicable Standards44 45- HEC-22: Urban Drainage Design Manual (FHWA)46 47## Constraints48 49- No internet access is available. Work from engineering knowledge and the provided tool.50- Use Manning's equation for a triangular gutter cross-section (SI units):51 - **Flow equation:** Q = (K_u / n) × Sx^(5/3) × S_L^(1/2) × T^(8/3)52 - where K_u = 0.376 (SI), Sx = cross-slope (m/m), S_L = longitudinal slope (m/m), T = spread (m)53- Solve for spread width:54 - **T** = (Q × n / (K_u × Sx^(5/3) × S_L^(1/2)))^(3/8)55- Flow depth at curb:56 - **d** = T × Sx57- Convert slopes from percentage to m/m before computation (divide by 100).58 59## Output Format60 61Show 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:62 63```json64{65 "spread_width_m": <numeric_value>,66 "curb_depth_m": <numeric_value>67}68```69 70Write your complete solution to `/workspace/output.md`.71

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.

Urban local road

urban_local_road

Urban local road with steep cross-slope and smooth asphalt pavement

sydney-suburban-streetmelbourne-residential-roadbrisbane-local-access
Parameter ranges
gutter_flow_m3_s
0.005 – 0.04
cross_slope_pct
2.5 – 4
longitudinal_slope_pct
0.5 – 3
mannings_n
0.013 – 0.016

Suburban collector

suburban_collector

Suburban collector road with moderate cross-slope and aged asphalt surface

perth-suburban-collectoradelaide-ring-routecanberra-distributor-road
Parameter ranges
gutter_flow_m3_s
0.01 – 0.08
cross_slope_pct
2 – 3
longitudinal_slope_pct
0.5 – 5
mannings_n
0.014 – 0.018

Arterial road

arterial_road

Major arterial road with standard cross-slope and concrete gutter channel

sydney-arterial-corridormelbourne-main-roadgold-coast-boulevard
Parameter ranges
gutter_flow_m3_s
0.02 – 0.12
cross_slope_pct
1.5 – 2.5
longitudinal_slope_pct
0.5 – 6
mannings_n
0.012 – 0.016

Highway shoulder

highway_shoulder

Highway shoulder with shallow cross-slope and textured asphalt surface

bruce-highway-shoulderhume-motorway-vergepacific-highway-shoulder
Parameter ranges
gutter_flow_m3_s
0.03 – 0.2
cross_slope_pct
1 – 2
longitudinal_slope_pct
0.3 – 8
mannings_n
0.014 – 0.02

Example task

sydney-suburban-street-urban-local-road-preview — hard difficulty, some inputs hidden.

Urban local road with steep cross-slope and smooth asphalt pavement. sydney-suburban-street. Required outputs: spread_width_m, curb_depth_m

The model sees

Scenario context and visible inputs.

gutter_flow_m3_s
0.005 to 0.04 m³/s
cross_slope_pct
2.5 to 4 %
longitudinal_slope_pct
0.5 to 3 %

Executable tool: roadway-spread_calc.py

The model must infer

Inputs withheld at this difficulty.

  • Mannings n

    mannings_n

Stand-in text in the prompt

The road is {{ archetype.description }} located at {{ archetype.site_context }}

The model must produce

The scored JSON answer schema.

{
  "spread_width_m": <number>,
  "curb_depth_m": <number>
}
  • spread_width_m · scored within ±3%
  • curb_depth_m · scored within ±3%