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

Culvert Capacity

Determines the headwater depth for circular culverts under both inlet control and outlet control conditions per the FHWA HDS-5 methodology, then identifies the controlling condition. Inlet control uses regression-based unsubmerged/submerged equations while outlet control applies an energy balance with entrance, friction, and exit losses. Used in road drainage design to verify that headwater elevations remain within acceptable limits.

both: The model must reason numerically unaided.

Standards

ARRHDS-5

Tags

civilculvertdrainagehydraulicsinlet-controloutlet-control

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

7 inputs

Always given

Included directly in every task prompt.

5

  • Culvert diameter

    culvert_diameter_m

    Internal culvert diameter D

    0.3 – 3 m

  • Culvert length

    culvert_length_m

    Culvert barrel length L

    5 – 100 m

  • Culvert slope m per m

    culvert_slope_m_per_m

    Culvert barrel slope S

    0.001 – 0.1 m/m

  • Design flow

    design_flow_m3_s

    Design discharge Q through the culvert

    0.1 – 30 m³/s

  • Tailwater depth

    tailwater_depth_m

    Tailwater depth above outlet invert TW

    0 – 5 m

Derived from scenario

Sampled from the scenario and inferable from its description.

1

  • Culvert configuration

    culvert_configuration

    Culvert material and inlet type combination

    Derived from the archetype scenario.

    concrete_square_edge_headwallconcrete_groove_end_headwallconcrete_groove_end_projectingcmp_headwallcmp_miteredcmp_projecting

Optional

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

1

  • Invert elevation m

    invert_elevation_m

    Inlet invert elevation

    Derived from the archetype scenario. Optional input. Hidden at hard difficulty.

    10 – 200 m AHD

Scored outputs

4 outputs

Inlet control hw

inlet_control_hw_m

Headwater depth above inlet invert under inlet control (m)

Scores if within ±5% of the reference value.

Outlet control hw

outlet_control_hw_m

Headwater depth above inlet invert under outlet control (m)

Scores if within ±5% of the reference value.

Controlling condition

controlling_condition

Controlling condition: 1.0 = inlet control, 2.0 = outlet control

Scores if within ±1% of the reference value.

Headwater elevation

headwater_elevation_m

Headwater elevation at controlling condition (m AHD)

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

Concrete culvert with headwall, all parameters given, moderate flow

Culvert configuration restricted to: concrete_square_edge_headwall, concrete_groove_end_headwall

medium

All inputs given

Any material and inlet type, all parameters given, wider flow range

hard

Some inputs hidden

Invert elevation hidden, agent must infer from site context

Hidden inputs

  • Invert elevationinvert_elevation_m

Prompt replacement text

The culvert is 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 hydraulic design and culvert analysis.2 3## Problem4 5Determine the headwater depth under inlet control and outlet control for a circular culvert, and identify the controlling condition using HDS-5 methodology.6 7## Given8 9| Parameter | Value | Unit |10|-----------|-------|------|11| Culvert diameter (D) | {{ culvert_diameter_m }} | m |12| Culvert length (L) | {{ culvert_length_m }} | m |13| Culvert slope (S) | {{ culvert_slope_m_per_m }} | m/m |14| Design flow (Q) | {{ design_flow_m3_s }} | m³/s |15{% if culvert_configuration is defined %}16| Culvert configuration | {{ culvert_configuration }} | - |17{% endif %}18| Tailwater depth (TW) | {{ tailwater_depth_m }} | m |19{% if invert_elevation_m is defined %}20| Inlet invert elevation | {{ invert_elevation_m }} | m AHD |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 32A culvert capacity 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. Headwater depth above inlet invert under inlet control (m)462. Headwater depth above inlet invert under outlet control (m)473. Controlling condition (1.0 = inlet control, 2.0 = outlet control)484. Headwater elevation at the controlling condition (m AHD)49 50## Applicable Standards51 52- HDS-5: Hydraulic Design of Highway Culverts (FHWA)53- ARR: Australian Rainfall and Runoff54 55## Constraints56 57- No internet access is available. Work from engineering knowledge and the provided tool.58- Use HDS-5 methodology for circular culverts in SI units.59 60### Inlet Control (HDS-5)61 62Compute the flow intensity parameter: `Q / (A * D^0.5)` where A = full cross-sectional area of the barrel.63 64**Unsubmerged** (Q/(A*D^0.5) <= 3.5), Form 1:65 66`HW/D = Hc/D + K * (Q/(A*D^0.5))^M + slope_sign * S`67 68where Hc is the specific head at critical depth (dc + Vc^2/(2g)).69 70**Submerged** (Q/(A*D^0.5) >= 4.0):71 72`HW/D = c * (Q/(A*D^0.5))^2 + Y + slope_sign * S`73 74**Transition** (3.5 < Q/(A*D^0.5) < 4.0): linearly interpolate between unsubmerged and submerged values.75 76Regression coefficients (K, M, c, Y) and slope_sign depend on culvert configuration:77 78| Configuration | K | M | c | Y | slope_sign |79|--------------|------|------|--------|------|------------|80| concrete_square_edge_headwall | 0.0098 | 2.0 | 0.0398 | 0.67 | -0.5 |81| concrete_groove_end_headwall | 0.0078 | 2.0 | 0.0292 | 0.74 | -0.5 |82| concrete_groove_end_projecting | 0.0045 | 2.0 | 0.0317 | 0.69 | -0.5 |83| cmp_headwall | 0.0078 | 2.0 | 0.0379 | 0.69 | -0.5 |84| cmp_mitered | 0.0210 | 1.33 | 0.0463 | 0.75 | +0.7 |85| cmp_projecting | 0.0340 | 1.50 | 0.0553 | 0.54 | -0.5 |86 87### Outlet Control (HDS-5)88 89Assuming full-flow conditions through the barrel:90 91`HW = H + ho - L * S`92 93where total head loss H = He + Hf + Ho:94 95- **Entrance loss:** He = ke * V^2/(2g)96- **Friction loss:** Hf = (19.63 * n^2 * L) / R^(4/3) * V^2/(2g)97- **Exit loss:** Ho = 1.0 * V^2/(2g)98 99For full circular pipe: R = D/4, A = pi*D^2/4.100 101Outlet depth: ho = max(TW, (dc + D)/2)102 103where dc is critical depth, found by solving Q^2*T/(g*A^3) = 1 for the circular cross-section.104 105Entrance loss coefficients (ke) and Manning's n by configuration:106 107| Configuration | ke | Manning's n |108|--------------|------|-------------|109| concrete_square_edge_headwall | 0.5 | 0.013 |110| concrete_groove_end_headwall | 0.2 | 0.013 |111| concrete_groove_end_projecting | 0.2 | 0.013 |112| cmp_headwall | 0.5 | 0.024 |113| cmp_mitered | 0.7 | 0.024 |114| cmp_projecting | 0.9 | 0.024 |115 116### Controlling Condition117 118The controlling condition is whichever produces the higher headwater depth. Report 1.0 for inlet control, 2.0 for outlet control.119 120### Headwater Elevation121 122`Headwater elevation = Inlet invert elevation + Controlling headwater depth`123 124## Output Format125 126Show 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:127 128```json129{130 "inlet_control_hw_m": <numeric_value>,131 "outlet_control_hw_m": <numeric_value>,132 "controlling_condition": <numeric_value>,133 "headwater_elevation_m": <numeric_value>134}135```136 137Write your complete solution to `/workspace/output.md`.138

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 culvert

urban_culvert

Urban road culvert crossing in a developed catchment

sydney-road-crossingbrisbane-suburban-culvertmelbourne-trunk-drainage
Parameter ranges
culvert_diameter_m
0.6 – 1.8
culvert_length_m
10 – 50
design_flow_m3_s
0.5 – 8
tailwater_depth_m
0 – 2
invert_elevation_m
20 – 80

Highway culvert

highway_culvert

Highway culvert crossing with moderate to high design flow

perth-highway-crossingpacific-highway-upgrade
Parameter ranges
culvert_diameter_m
0.9 – 2.4
culvert_length_m
15 – 60
design_flow_m3_s
2 – 15
tailwater_depth_m
0 – 3
invert_elevation_m
30 – 150

Rural crossing

rural_crossing

Rural creek or farm track culvert crossing

adelaide-rural-accesshobart-farm-crossinggippsland-farm-track
Parameter ranges
culvert_diameter_m
0.3 – 1.5
culvert_length_m
5 – 30
design_flow_m3_s
0.1 – 4
tailwater_depth_m
0 – 1.5
invert_elevation_m
30 – 120

Hillside crossing

hillside_crossing

Steep terrain culvert crossing with significant grade

toowoomba-hillside-roadblue-mountains-crossing
Parameter ranges
culvert_diameter_m
0.6 – 1.8
culvert_length_m
10 – 40
culvert_slope_m_per_m
0.02 – 0.1
design_flow_m3_s
0.3 – 6
tailwater_depth_m
0 – 2
invert_elevation_m
40 – 180

Tropical crossing

tropical_crossing

Tropical region culvert crossing with high rainfall intensity

darwin-rural-roadcairns-forestry-access
Parameter ranges
culvert_diameter_m
0.9 – 2.4
culvert_length_m
10 – 60
design_flow_m3_s
2 – 12
tailwater_depth_m
0.5 – 2.5
invert_elevation_m
10 – 60

Example task

sydney-road-crossing-urban-culvert-preview — hard difficulty, some inputs hidden.

Urban road culvert crossing in a developed catchment. sydney-road-crossing. Required outputs: inlet_control_hw_m, outlet_control_hw_m, controlling_condition, headwater_elevation_m

The model sees

Scenario context and visible inputs.

culvert_diameter_m
0.6 to 1.8 m
culvert_length_m
10 to 50 m
culvert_slope_m_per_m
0.001 to 0.1 m/m
design_flow_m3_s
0.5 to 8 m³/s
culvert_configuration
concrete_square_edge_headwall
tailwater_depth_m
0 to 2 m

Executable tool: culvert-capacity_calc.py

The model must infer

Inputs withheld at this difficulty.

  • Invert elevation

    invert_elevation_m

Stand-in text in the prompt

The culvert is located at {{ archetype.site_context }}

The model must produce

The scored JSON answer schema.

{
  "inlet_control_hw_m": <number>,
  "outlet_control_hw_m": <number>,
  "controlling_condition": <number>,
  "headwater_elevation_m": <number>
}
  • inlet_control_hw_m · scored within ±5%
  • outlet_control_hw_m · scored within ±5%
  • controlling_condition · scored within ±1%
  • headwater_elevation_m · scored within ±5%