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

civilwith-tool

Exit Gradient

Computes the exit hydraulic gradient at a dam or levee downstream toe using i_exit = delta_h / L_seepage, and the critical gradient for piping initiation from i_cr = (G_s - 1) / (1 + e), per USACE EM 1110-2-1901. Derives the factor of safety against piping and the saturated and buoyant unit weights of the foundation soil. Used in dam safety and geotechnical seepage analysis.

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

Standards

FEMA P-1032 USACE EM 1110-2-1901

Tags

civil dams gradient hydraulics piping seepage

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.

2

Head difference
head_difference_m
Head difference across the structure (upstream pool minus tailwater level)
0.5 – 40 m
Seepage path length
seepage_path_length_m
Total seepage path length through the foundation from upstream to downstream toe
5 – 300 m

Derived from scenario

Sampled from the scenario and inferable from its description.

3

Specific gravity
specific_gravity
Specific gravity of foundation soil solids G_s
Derived from the archetype scenario. Hidden at hard difficulty.
2.55 – 2.8
Void ratio
void_ratio
Void ratio of the foundation soil e
Derived from the archetype scenario. Hidden at hard difficulty.
0.25 – 1.1
Foundation soil type
foundation_soil_type
Foundation soil classification
Derived from the archetype scenario. Hidden at hard difficulty.
clean_sandsilty_sandsandy_siltclayey_siltsilty_clay

Scored outputs

5 outputs

Exit gradient

exit_gradient

Exit gradient at the downstream toe i_exit (dimensionless)

Scores if within ±3% of the reference value.

Critical gradient

critical_gradient

Critical hydraulic gradient for piping initiation i_cr (dimensionless)

Scores if within ±3% of the reference value.

Factor of safety

factor_of_safety

Factor of safety against piping FoS = i_cr / i_exit (dimensionless)

Scores if within ±3% of the reference value.

Saturated unit weight kn m3

saturated_unit_weight_kn_m3

Saturated unit weight of foundation soil gamma_sat (kN/m3)

Scores if within ±3% of the reference value.

Buoyant unit weight kn m3

buoyant_unit_weight_kn_m3

Buoyant (submerged) unit weight of foundation soil gamma_b (kN/m3)

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

Simple earth dam scenario, all parameters given including soil properties

Foundation soil type restricted to: clean_sand

medium

All inputs given

All parameters given, wider range of structure types and soil conditions

hard

Some inputs hidden

Specific gravity, void ratio, and soil type hidden; agent infers from site context

Hidden inputs

Specific gravityspecific_gravity
Void ratiovoid_ratio
Foundation soil typefoundation_soil_type

Prompt replacement text

The structure 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
exit-gradient_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 civil/dams engineer specializing in seepage analysis and dam safety.2 3## Problem4 5Calculate the exit gradient at the downstream toe of a hydraulic structure and determine the factor of safety against piping failure.6 7## Given8 9| Parameter | Value | Unit |10|-----------|-------|------|11| Head difference (delta_h) | {{ head_difference_m }} | m |12| Seepage path length (L) | {{ seepage_path_length_m }} | m |13{% if specific_gravity is defined %}14| Specific gravity of soil solids (G_s) | {{ specific_gravity }} | - |15{% endif %}16{% if void_ratio is defined %}17| Void ratio (e) | {{ void_ratio }} | - |18{% endif %}19{% if foundation_soil_type is defined %}20| Foundation soil type | {{ foundation_soil_type }} | - |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 exit gradient calculation tool is available at `/workspace/exit-gradient_calc.py`. Run it with:33 34```bash35python3 /workspace/exit-gradient_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. Exit gradient at the downstream toe i_exit (dimensionless)462. Critical hydraulic gradient for piping initiation i_cr (dimensionless)473. Factor of safety against piping FoS (dimensionless)484. Saturated unit weight of foundation soil gamma_sat (kN/m3)495. Buoyant unit weight of foundation soil gamma_b (kN/m3)50 51## Applicable Standards52 53- USACE EM 1110-2-1901 — Seepage Analysis and Control for Dams54- FEMA P-1032 — Dam Safety: Evaluation of Seepage55 56## Constraints57 58- No internet access is available. Work from engineering knowledge and the provided tool.59- Use the direct gradient approach for exit gradient:60  - **i_exit = delta_h / L_seepage**61  - Where delta_h is the head difference across the structure and L_seepage is the total seepage path length62- Use the critical gradient formula for piping initiation:63  - **i_cr = (G_s - 1) / (1 + e)**64  - Where G_s is the specific gravity of soil solids and e is the void ratio65- Factor of safety against piping:66  - **FoS = i_cr / i_exit**67  - USACE requires FoS >= 3 to 5 for dams; FoS >= 1.5 for temporary works68- Saturated unit weight:69  - **gamma_sat = (G_s + e) / (1 + e) * gamma_w**70- Buoyant (submerged) unit weight:71  - **gamma_b = gamma_sat - gamma_w = (G_s - 1) / (1 + e) * gamma_w**72- Use gamma_w = 9.81 kN/m373- Typical specific gravity values: clean sand 2.65, silty sand 2.66, sandy silt 2.67, clayey silt 2.70, silty clay 2.7274- Typical void ratio ranges: clean sand 0.55-0.75, silty sand 0.45-0.65, sandy silt 0.40-0.60, clayey silt 0.35-0.55, silty clay 0.30-0.5075 76## Output Format77 78Show 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:79 80```json81{82  "exit_gradient": <numeric_value>,83  "critical_gradient": <numeric_value>,84  "factor_of_safety": <numeric_value>,85  "saturated_unit_weight_kn_m3": <numeric_value>,86  "buoyant_unit_weight_kn_m3": <numeric_value>87}88```89 90Write your complete solution to `/workspace/output.md`.91

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.

Earth dam sand

earth_dam_sand

Earth embankment dam on clean sand foundation with moderate head

darling-downs-farm-damhunter-valley-irrigation-dam

Parameter ranges

head_difference_m: 3 – 15
seepage_path_length_m: 30 – 120
specific_gravity: 2.63 – 2.67
void_ratio: 0.55 – 0.75
foundation_soil_type: clean_sand

Concrete gravity dam

concrete_gravity_dam

Concrete gravity dam on silty sand foundation with high head

snowy-mountains-hydro-damtasmania-power-dam

Parameter ranges

head_difference_m: 10 – 35
seepage_path_length_m: 50 – 200
specific_gravity: 2.64 – 2.68
void_ratio: 0.45 – 0.65
foundation_soil_type: silty_sand

Levee alluvial

levee_alluvial

Levee on alluvial soil foundation with low to moderate head

murray-river-leveefitzroy-river-flood-levee

Parameter ranges

head_difference_m: 1.5 – 8
seepage_path_length_m: 15 – 80
specific_gravity: 2.65 – 2.72
void_ratio: 0.5 – 0.8
foundation_soil_type: sandy_silt, silty_sand

Sheet pile cofferdam

sheet_pile_cofferdam

Sheet pile cofferdam on sandy foundation with low head

sydney-harbour-cofferdambrisbane-river-cofferdam

Parameter ranges

head_difference_m: 0.5 – 5
seepage_path_length_m: 5 – 30
specific_gravity: 2.63 – 2.67
void_ratio: 0.55 – 0.8
foundation_soil_type: clean_sand, silty_sand

Example task

snowy-mountains-hydro-dam-concrete-gravity-dam-preview — hard difficulty, some inputs hidden.

Concrete gravity dam on silty sand foundation with high head. snowy-mountains-hydro-dam. Required outputs: exit_gradient, critical_gradient, factor_of_safety, saturated_unit_weight_kn_m3, buoyant_unit_weight_kn_m3

The model sees

Scenario context and visible inputs.

head_difference_m: 10 to 35 m
seepage_path_length_m: 50 to 200 m

Executable tool: exit-gradient_calc.py

The model must infer

Inputs withheld at this difficulty.

Specific gravity
specific_gravity
Void ratio
void_ratio
Foundation soil type
foundation_soil_type

Stand-in text in the prompt

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

The model must produce

The scored JSON answer schema.

{
  "exit_gradient": <number>,
  "critical_gradient": <number>,
  "factor_of_safety": <number>,
  "saturated_unit_weight_kn_m3": <number>,
  "buoyant_unit_weight_kn_m3": <number>
}

exit_gradient · scored within ±3%
critical_gradient · scored within ±3%
factor_of_safety · scored within ±3%
saturated_unit_weight_kn_m3 · scored within ±3%
buoyant_unit_weight_kn_m3 · scored within ±3%