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

Lateral Earth Pressure

Calculates active and passive earth pressure coefficients, base pressures, and total lateral forces on retaining walls using either Rankine or Coulomb theory. Supports inclined backfill, wall friction, cohesive soils, and uniform surcharge loading, computing the pressure distribution, total force per unit wall length, and the point of application for structural design of retaining structures.

both: The model must reason numerically unaided.

Standards

Coulomb (1776)Rankine (1857)

Tags

deterministicearth-pressuregeotechnicalretaining-wall

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

8 inputs

Always given

Included directly in every task prompt.

2

  • Wall height

    wall_height_m

    Retaining wall height H

    1.5 – 12 m

  • Theory

    theory

    Earth pressure theory to apply

    rankinecoulomb

Derived from scenario

Sampled from the scenario and inferable from its description.

3

  • Friction angle deg

    friction_angle_deg

    Effective friction angle φ'

    Derived from the archetype scenario. Hidden at hard difficulty.

    0 – 45 degrees

  • Cohesion

    cohesion_kpa

    Effective cohesion c'

    Derived from the archetype scenario. Hidden at hard difficulty.

    0 – 100 kPa

  • Unit weight

    unit_weight_kn_m3

    Soil unit weight γ

    Derived from the archetype scenario. Hidden at hard difficulty.

    14 – 22 kN/m³

Optional

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

3

  • Backfill slope deg

    backfill_slope_deg

    Backfill slope angle β above horizontal

    Optional input.

    0 – 30 degrees

  • Wall friction angle deg

    wall_friction_angle_deg

    Wall friction angle δ (Coulomb theory)

    Optional input.

    0 – 30 degrees

  • Surcharge

    surcharge_kpa

    Uniform surcharge on backfill surface q

    Optional input.

    0 – 50 kPa

Scored outputs

7 outputs

Ka

ka

Active earth pressure coefficient Ka

Scores if within ±3% of the reference value.

Kp

kp

Passive earth pressure coefficient Kp

Scores if within ±3% of the reference value.

Active pressure at base

active_pressure_at_base_kpa

Active pressure at base of wall σ_a (kPa)

Scores if within ±3% of the reference value.

Passive pressure at base

passive_pressure_at_base_kpa

Passive pressure at base of wall σ_p (kPa)

Scores if within ±3% of the reference value.

Total active force kn

total_active_force_kn_m

Total active force per unit wall length Pa (kN/m)

Scores if within ±3% of the reference value.

Total passive force kn

total_passive_force_kn_m

Total passive force per unit wall length Pp (kN/m)

Scores if within ±3% of the reference value.

Active force application point

active_force_application_point_m

Active force point of application above base (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

Rankine theory, horizontal backfill, cohesionless soil, no surcharge

Theory restricted to: rankine

Backfill slope deg restricted to: 0

Wall friction angle deg restricted to: 0

Surcharge restricted to: 0

medium

All inputs given

Rankine with inclined backfill or cohesive soil, surcharge may be present

Theory restricted to: rankine

Wall friction angle deg restricted to: 0

hard

Some inputs hidden

Coulomb theory with wall friction, some soil parameters hidden

Hidden inputs

  • Cohesioncohesion_kpa
  • Friction angle degfriction_angle_deg
  • Unit weight kn m3unit_weight_kn_m3

Prompt replacement text

The retained soil is {{ archetype.description }} ({{ archetype.site_context }})

Theory restricted to: coulomb

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 geotechnical engineer specializing in retaining wall design.2 3## Problem4 5Calculate the active and passive lateral earth pressure coefficients and forces acting on a retaining wall using {{ theory | capitalize }} theory.6 7## Given8 9| Parameter | Value | Unit |10|-----------|-------|------|11| Wall height (H) | {{ wall_height_m }} | m |12{% if friction_angle_deg is defined %}13| Effective friction angle (φ') | {{ friction_angle_deg }} | degrees |14{% endif %}15{% if cohesion_kpa is defined %}16| Effective cohesion (c') | {{ cohesion_kpa }} | kPa |17{% endif %}18{% if unit_weight_kn_m3 is defined %}19| Soil unit weight (γ) | {{ unit_weight_kn_m3 }} | kN/m³ |20{% endif %}21{% if backfill_slope_deg is defined %}22| Backfill slope angle (β) | {{ backfill_slope_deg }} | degrees |23{% endif %}24{% if wall_friction_angle_deg is defined %}25| Wall friction angle (δ) | {{ wall_friction_angle_deg }} | degrees |26{% endif %}27{% if surcharge_kpa is defined %}28| Uniform surcharge (q) | {{ surcharge_kpa }} | kPa |29{% endif %}30| Theory | {{ theory }} | - |31{% if archetype_description is defined %}32 33### Site Conditions34 35{{ archetype_description }}36{% endif %}37 38{% if tool_available %}39## Available Tool40 41A lateral earth pressure calculation tool is available at `/workspace/{{ meta.name }}_calc.py`. Run it with:42 43```bash44python3 /workspace/{{ meta.name }}_calc.py --help45```46 47You may use this tool to verify your calculations or compute values directly.48{% endif %}49 50## Required51 52Calculate the following:53 541. Active earth pressure coefficient Ka552. Passive earth pressure coefficient Kp563. Active pressure at the base of the wall σ_a (kPa)574. Passive pressure at the base of the wall σ_p (kPa)585. Total active force per unit wall length Pa (kN/m)596. Total passive force per unit wall length Pp (kN/m)607. Point of application of the active force above the base (m)61 62## Applicable Standards63 64- Rankine, W.J.M. (1857) — On the Stability of Loose Earth65- Coulomb, C.A. (1776) — Essai sur une application des règles de maximis et minimis66 67## Constraints68 69- No internet access is available. Work from engineering knowledge and the provided tool.70- Use the specified theory ({{ theory }}) for calculating earth pressure coefficients.71- **Rankine theory** (horizontal backfill):72 - Ka = tan²(45° − φ'/2)73 - Kp = tan²(45° + φ'/2)74- **Rankine theory** (inclined backfill with slope β):75 - Ka = cosβ × (cosβ − √(cos²β − cos²φ')) / (cosβ + √(cos²β − cos²φ'))76 - Kp = cosβ × (cosβ + √(cos²β − cos²φ')) / (cosβ − √(cos²β − cos²φ'))77- **Coulomb theory** (vertical wall, wall friction δ, backfill slope β):78 - Ka = cos²φ' / [cosδ × (1 + √(sin(φ'+δ)×sin(φ'−β) / (cosδ × cosβ)))²]79 - Kp = cos²φ' / [cosδ × (1 − √(sin(φ'−δ)×sin(φ'+β) / (cosδ × cosβ)))²]80- **Active pressure at depth z:** σ_a = Ka × γ × z + Ka × q − 2c'√Ka81- **Passive pressure at depth z:** σ_p = Kp × γ × z + Kp × q + 2c'√Kp82- **Total active force:** Pa = 0.5 × Ka × γ × H² + Ka × q × H − 2c'√Ka × H83- **Total passive force:** Pp = 0.5 × Kp × γ × H² + Kp × q × H + 2c'√Kp × H84- If total active force is negative (cohesion dominates), report Pa = 085- Point of application is computed from the moment equilibrium of the pressure components86- For φ' = 0 (purely cohesive soil): Ka = Kp = 1.087 88## Output Format89 90Show 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:91 92```json93{94 "ka": <numeric_value>,95 "kp": <numeric_value>,96 "active_pressure_at_base_kpa": <numeric_value>,97 "passive_pressure_at_base_kpa": <numeric_value>,98 "total_active_force_kn_m": <numeric_value>,99 "total_passive_force_kn_m": <numeric_value>,100 "active_force_application_point_m": <numeric_value>101}102```103 104Write your complete solution to `/workspace/output.md`.105

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.

Loose sand

loose_sand

Loose sand backfill

perth-coastalhunter-valley-alluvial
Parameter ranges
friction_angle_deg
28 – 32
cohesion_kpa
0
unit_weight_kn_m3
15 – 17

Medium dense sand

medium_dense_sand

Medium dense sand backfill

sydney-harbourbrisbane-river
Parameter ranges
friction_angle_deg
32 – 36
cohesion_kpa
0
unit_weight_kn_m3
17 – 19

Dense sand gravel

dense_sand_gravel

Dense sand and gravel backfill

cairns-coraladelaide-quarry
Parameter ranges
friction_angle_deg
36 – 42
cohesion_kpa
0
unit_weight_kn_m3
19 – 21

Stiff clay

stiff_clay

Stiff clay backfill

melbourne-basaltsydney-hawkesbury
Parameter ranges
friction_angle_deg
18 – 25
cohesion_kpa
20 – 60
unit_weight_kn_m3
18 – 21

Soft clay

soft_clay

Soft normally consolidated clay

darwin-estuarinebrisbane-alluvial
Parameter ranges
friction_angle_deg
10 – 18
cohesion_kpa
5 – 20
unit_weight_kn_m3
15 – 17

Example task

sydney-harbour-medium-dense-sand-preview — hard difficulty, some inputs hidden.

Medium dense sand backfill. sydney-harbour. Required outputs: ka, kp, active_pressure_at_base_kpa, passive_pressure_at_base_kpa, total_active_force_kn_m, total_passive_force_kn_m

The model sees

Scenario context and visible inputs.

wall_height_m
1.5 to 12 m
backfill_slope_deg
0 degrees
wall_friction_angle_deg
0 degrees
surcharge_kpa
0 kPa
theory
coulomb

Executable tool: lateral-earth-pressure_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 retained soil is {{ archetype.description }} ({{ archetype.site_context }})

The model must produce

The scored JSON answer schema.

{
  "ka": <number>,
  "kp": <number>,
  "active_pressure_at_base_kpa": <number>,
  "passive_pressure_at_base_kpa": <number>,
  "total_active_force_kn_m": <number>,
  "total_passive_force_kn_m": <number>,
  "active_force_application_point_m": <number>
}
  • ka · scored within ±3%
  • kp · scored within ±3%
  • active_pressure_at_base_kpa · scored within ±3%
  • passive_pressure_at_base_kpa · scored within ±3%
  • total_active_force_kn_m · scored within ±3%
  • total_passive_force_kn_m · scored within ±3%
  • active_force_application_point_m · scored within ±5%