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

Retaining Wall Stability

Evaluates the external stability of a rectangular gravity retaining wall against three failure modes: sliding along the base, overturning about the toe, and bearing capacity failure of the foundation soil. Active earth pressure is computed using Rankine theory for horizontal backfill, and bearing capacity uses Terzaghi strip footing factors. Outputs include factors of safety, eccentricity, and maximum base pressure per AS 4678 and Eurocode 7.

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

Standards

AS 4678Eurocode 7

Tags

bearing-capacitycivilgeotechnicalgravity-walloverturningretaining-wallslidingstability

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

11 inputs

Always given

Included directly in every task prompt.

3

  • Wall height

    wall_height_m

    Total height of the gravity retaining wall H

    2 – 6 m

  • Base width

    base_width_m

    Width of the wall base B (typically 0.5H to 0.7H)

    2 – 4.5 m

  • Wall thickness

    wall_thickness_m

    Thickness of the wall stem at the top t

    0.4 – 1.5 m

Derived from scenario

Sampled from the scenario and inferable from its description.

4

  • Concrete unit weight

    concrete_unit_weight_kn_m3

    Unit weight of the wall material (concrete or masonry) gamma_c

    Derived from the archetype scenario.

    22 – 25 kN/m3

  • Backfill friction angle deg

    backfill_friction_angle_deg

    Effective friction angle of the backfill soil phi'

    Derived from the archetype scenario. Hidden at hard difficulty.

    20 – 40 degrees

  • Backfill unit weight

    backfill_unit_weight_kn_m3

    Total unit weight of the backfill soil gamma_s

    Derived from the archetype scenario. Hidden at hard difficulty.

    16 – 21 kN/m3

  • Foundation friction angle deg

    foundation_friction_angle_deg

    Effective friction angle of the foundation soil phi_f

    Derived from the archetype scenario. Hidden at hard difficulty.

    20 – 42 degrees

Optional

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

4

  • Backfill cohesion

    backfill_cohesion_kpa

    Effective cohesion of the backfill soil c'

    Derived from the archetype scenario. Optional input.

    0 – 20 kPa

  • Surcharge

    surcharge_kpa

    Uniform surcharge pressure on the backfill surface q

    Optional input.

    0 – 25 kPa

  • Foundation cohesion

    foundation_cohesion_kpa

    Effective cohesion of the foundation soil c_f

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

    0 – 50 kPa

  • Base friction ratio

    base_friction_ratio

    Ratio of base interface friction to foundation soil friction (typically 2/3)

    Optional input.

    0.5 – 1

Scored outputs

6 outputs

Ka

ka

Rankine active earth pressure coefficient Ka (dimensionless)

Scores if within ±3% of the reference value.

Fos sliding

fos_sliding

Factor of safety against sliding along the base (dimensionless)

Scores if within ±5% of the reference value.

Fos overturning

fos_overturning

Factor of safety against overturning about the toe (dimensionless)

Scores if within ±5% of the reference value.

Fos bearing

fos_bearing

Factor of safety against bearing capacity failure (dimensionless)

Scores if within ±5% of the reference value.

Eccentricity

eccentricity_m

Eccentricity of the resultant force from the base centre e (m)

Scores if within ±5% of the reference value.

Max base pressure

max_base_pressure_kpa

Maximum base contact pressure under the footing q_max (kPa)

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

Cohesionless backfill, no surcharge, all parameters given — simplest three-check variant

Backfill cohesion restricted to: 0

Surcharge restricted to: 0

Foundation cohesion restricted to: 0

medium

All inputs given

Surcharge and cohesion may be present, all parameters given — full formula set

hard

Some inputs hidden

Soil properties hidden, agent must infer from site context and soil description

Hidden inputs

  • Backfill friction angle degbackfill_friction_angle_deg
  • Backfill unit weight kn m3backfill_unit_weight_kn_m3
  • Foundation friction angle degfoundation_friction_angle_deg
  • Foundation cohesionfoundation_cohesion_kpa

Prompt replacement text

The backfill 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
  • retaining-wall-stability_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 geotechnical engineer specializing in retaining wall design and stability analysis per Australian and European standards.2 3## Problem4 5Check the external stability of a rectangular gravity retaining wall against sliding, overturning, and bearing capacity failure. The wall retains a horizontal backfill and is founded at ground level on the foundation soil.6 7## Given8 9| Parameter | Value | Unit |10|-----------|-------|------|11| Wall height (H) | {{ wall_height_m }} | m |12| Base width (B) | {{ base_width_m }} | m |13| Wall stem thickness (t) | {{ wall_thickness_m }} | m |14{% if concrete_unit_weight_kn_m3 is defined %}15| Concrete unit weight (gamma_c) | {{ concrete_unit_weight_kn_m3 }} | kN/m3 |16{% endif %}17{% if backfill_friction_angle_deg is defined %}18| Backfill friction angle (phi') | {{ backfill_friction_angle_deg }} | degrees |19{% endif %}20{% if backfill_unit_weight_kn_m3 is defined %}21| Backfill unit weight (gamma_s) | {{ backfill_unit_weight_kn_m3 }} | kN/m3 |22{% endif %}23{% if backfill_cohesion_kpa is defined %}24| Backfill cohesion (c') | {{ backfill_cohesion_kpa }} | kPa |25{% endif %}26{% if surcharge_kpa is defined %}27| Uniform surcharge (q) | {{ surcharge_kpa }} | kPa |28{% endif %}29{% if foundation_friction_angle_deg is defined %}30| Foundation friction angle (phi_f) | {{ foundation_friction_angle_deg }} | degrees |31{% endif %}32{% if foundation_cohesion_kpa is defined %}33| Foundation cohesion (c_f) | {{ foundation_cohesion_kpa }} | kPa |34{% endif %}35{% if base_friction_ratio is defined %}36| Base friction ratio (delta / phi_f) | {{ base_friction_ratio }} | - |37{% endif %}38{% if archetype_description is defined %}39 40### Site Conditions41 42{{ archetype_description }}43{% endif %}44 45{% if tool_available %}46## Available Tool47 48A retaining wall stability calculation tool is available at `/workspace/{{ meta.name }}_calc.py`. Run it with:49 50```bash51python3 /workspace/{{ meta.name }}_calc.py --help52```53 54You may use this tool to verify your calculations or compute values directly.55{% endif %}56 57## Required58 59Calculate the following:60 611. Active earth pressure coefficient Ka622. Factor of safety against sliding along the base633. Factor of safety against overturning about the toe644. Factor of safety against bearing capacity failure655. Eccentricity of the resultant force from the base centre e (m)666. Maximum base contact pressure q_max (kPa)67 68## Wall Configuration69 70The wall is a rectangular gravity wall. The stem (thickness t) is positioned at the **front** (toe side) of the base. Backfill soil of depth H sits on the heel portion (B - t) of the base behind the stem. The toe is at the front of the base.71 72## Applicable Standards73 74- AS 4678 — Earth Retaining Structures75- Eurocode 7 — Geotechnical Design76 77## Constraints78 79- No internet access is available. Work from engineering knowledge and the provided tool.80- Use **Rankine theory** for active earth pressure (horizontal backfill):81 - Ka = tan^2(45 - phi'/2)82- **Active pressure at depth z:** sigma_a = Ka * gamma_s * z + Ka * q - 2c' * sqrt(Ka)83 - If total active force is negative (cohesion dominates), use Pa = 084- **Sliding check:**85 - Resisting force = V * tan(delta) + c_b * B86 - delta = base_friction_ratio * phi_f (interface friction angle in radians)87 - c_b = base_friction_ratio * c_f (base adhesion)88 - FoS_sliding = Resisting force / Horizontal active force89- **Overturning check:**90 - Stabilising moments about the toe: wall weight, soil on heel, surcharge on heel91 - Overturning moments about the toe: active earth pressure components92 - FoS_overturning = Stabilising moment / Overturning moment93- **Bearing check:**94 - Eccentricity e = B/2 - x_resultant, where x_resultant = M_net / V_total95 - Maximum base pressure: q_max = V/B * (1 + 6e/B) for e <= B/696 - If e > B/6: q_max = V / (3 * x_resultant)97 - Ultimate bearing capacity (Terzaghi strip footing at surface): q_ult = c_f * Nc + 0.5 * gamma_s * B' * Ngamma98 - Use effective width B' = B - 2|e| for eccentric loading99 - Bearing capacity factors: Nq = e^(2*(3pi/4 - phi_f/2)*tan(phi_f)) / (2*cos^2(45 + phi_f/2)), Nc = (Nq-1)/tan(phi_f), Ngamma = 2*(Nq+1)*tan(phi_f)100 - For phi_f = 0: Nc = 5.14, Nq = 1.0, Ngamma = 0101 - FoS_bearing = q_ult / q_max102- Use gamma_w = 9.81 kN/m3 if needed103- Report FoS = 99.99 where the driving force or moment is zero104 105## Output Format106 107Show 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:108 109```json110{111 "ka": <numeric_value>,112 "fos_sliding": <numeric_value>,113 "fos_overturning": <numeric_value>,114 "fos_bearing": <numeric_value>,115 "eccentricity_m": <numeric_value>,116 "max_base_pressure_kpa": <numeric_value>117}118```119 120Write your complete solution to `/workspace/output.md`.121

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.

Granular backfill sandy foundation

granular_backfill_sandy_foundation

Clean granular backfill behind a mass concrete wall on medium dense sand

sydney-harbour-seawallgold-coast-canal-retaining
Parameter ranges
concrete_unit_weight_kn_m3
23 – 24
backfill_friction_angle_deg
30 – 35
backfill_unit_weight_kn_m3
17 – 19
backfill_cohesion_kpa
0
foundation_friction_angle_deg
30 – 36
foundation_cohesion_kpa
0 – 5

Gravel backfill stiff clay foundation

gravel_backfill_stiff_clay_foundation

Compacted gravel backfill behind a gravity wall on stiff clay foundation

melbourne-basalt-clay-sitecanberra-substation-terrace
Parameter ranges
concrete_unit_weight_kn_m3
23 – 24
backfill_friction_angle_deg
34 – 40
backfill_unit_weight_kn_m3
19 – 21
backfill_cohesion_kpa
0
foundation_friction_angle_deg
22 – 28
foundation_cohesion_kpa
20 – 40

Silty sand backfill weathered rock

silty_sand_backfill_weathered_rock

Silty sand backfill behind a concrete gravity wall on weathered rock

brisbane-hillside-retainingcairns-port-access-wall
Parameter ranges
concrete_unit_weight_kn_m3
23 – 25
backfill_friction_angle_deg
26 – 32
backfill_unit_weight_kn_m3
17 – 19
backfill_cohesion_kpa
2 – 8
foundation_friction_angle_deg
35 – 42
foundation_cohesion_kpa
10 – 30

Cohesive backfill sandy foundation

cohesive_backfill_sandy_foundation

Cohesive fill behind a masonry gravity wall on sandy foundation

adelaide-hills-road-wallperth-coastal-terrace
Parameter ranges
concrete_unit_weight_kn_m3
22 – 23
backfill_friction_angle_deg
20 – 28
backfill_unit_weight_kn_m3
17 – 20
backfill_cohesion_kpa
5 – 15
foundation_friction_angle_deg
28 – 34
foundation_cohesion_kpa
0 – 5

Dense sand backfill firm clay

dense_sand_backfill_firm_clay

Dense sand backfill behind a concrete wall on firm clay

darwin-stormwater-channel-walltownsville-wharf-retaining
Parameter ranges
concrete_unit_weight_kn_m3
23 – 24
backfill_friction_angle_deg
32 – 38
backfill_unit_weight_kn_m3
18 – 20
backfill_cohesion_kpa
0
foundation_friction_angle_deg
24 – 30
foundation_cohesion_kpa
10 – 25

Example task

melbourne-basalt-clay-site-gravel-backfill-stiff-clay-foundation-preview — hard difficulty, some inputs hidden.

Compacted gravel backfill behind a gravity wall on stiff clay foundation. melbourne-basalt-clay-site. Required outputs: ka, fos_sliding, fos_overturning, fos_bearing, eccentricity_m, max_base_pressure_kpa

The model sees

Scenario context and visible inputs.

wall_height_m
2 to 6 m
base_width_m
2 to 4.5 m
wall_thickness_m
0.4 to 1.5 m
concrete_unit_weight_kn_m3
23 to 24 kN/m3
backfill_cohesion_kpa
0 to 0 kPa
surcharge_kpa
0 kPa
base_friction_ratio
0.67

Executable tool: retaining-wall-stability_calc.py

The model must infer

Inputs withheld at this difficulty.

  • Backfill friction angle deg

    backfill_friction_angle_deg

  • Foundation cohesion

    foundation_cohesion_kpa

  • Foundation friction angle deg

    foundation_friction_angle_deg

  • Backfill unit weight kn m3

    backfill_unit_weight_kn_m3

Stand-in text in the prompt

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

The model must produce

The scored JSON answer schema.

{
  "ka": <number>,
  "fos_sliding": <number>,
  "fos_overturning": <number>,
  "fos_bearing": <number>,
  "eccentricity_m": <number>,
  "max_base_pressure_kpa": <number>
}
  • ka · scored within ±3%
  • fos_sliding · scored within ±5%
  • fos_overturning · scored within ±5%
  • fos_bearing · scored within ±5%
  • eccentricity_m · scored within ±5%
  • max_base_pressure_kpa · scored within ±5%