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groundwith-tool

Wall Overturning

Evaluates overturning stability of cantilever retaining walls by computing the factor of safety as the ratio of resisting to overturning moments about the wall toe. Uses Rankine active earth pressure (Ka) to determine lateral forces from backfill and surcharge, and sums stabilising moments from the self-weight of the stem, base slab, and backfill soil per AS 4678 and Eurocode 7.

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

Standards

AS 4678Eurocode 7

Tags

geotechnicaloverturningretaining-wallstability

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

9 inputs

Always given

Included directly in every task prompt.

5

  • Wall height

    wall_height_m

    Height of the wall stem above the base slab

    2 – 10 m

  • Base width

    base_width_m

    Total width of the base slab

    1.5 – 8 m

  • Stem thickness

    stem_thickness_m

    Thickness of the wall stem

    0.2 – 1 m

  • Base thickness

    base_thickness_m

    Thickness of the base slab

    0.3 – 1.2 m

  • Concrete unit weight

    concrete_unit_weight_kn_m3

    Unit weight of the reinforced concrete

    23 – 25 kN/m³

Derived from scenario

Sampled from the scenario and inferable from its description.

2

  • Backfill friction angle deg

    backfill_friction_angle_deg

    Effective friction angle of the backfill soil

    Derived from the archetype scenario. Hidden at hard difficulty.

    20 – 45 degrees

  • Backfill unit weight

    backfill_unit_weight_kn_m3

    Unit weight of the backfill soil

    Derived from the archetype scenario. Hidden at hard difficulty.

    15 – 22 kN/m³

Optional

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

2

  • Surcharge

    surcharge_kpa

    Uniform surcharge load on the backfill surface

    Optional input.

    0 – 30 kPa

  • Water table depth

    water_table_depth_m

    Depth to water table from the top of the wall

    Optional input.

    0 – 20 m

Scored outputs

5 outputs

Ka

ka

Rankine active earth pressure coefficient Ka

Scores if within ±3% of the reference value.

Active force kn

active_force_kn_m

Total active force per metre of wall Pa (kN/m)

Scores if within ±5% of the reference value.

Overturning moment knm

overturning_moment_knm_m

Overturning moment about the toe Mo (kNm/m)

Scores if within ±5% of the reference value.

Resisting moment knm

resisting_moment_knm_m

Resisting moment about the toe Mr (kNm/m)

Scores if within ±5% of the reference value.

Factor of safety overturning

factor_of_safety_overturning

Factor of safety against overturning FoS

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

All parameters given, no surcharge, no water table

Surcharge restricted to: 0

Water table restricted to: False

medium

All inputs given

All parameters given, surcharge and water table present

Water table restricted to: True

hard

Some inputs hidden

Soil parameters hidden, surcharge and water table present

Hidden inputs

  • Backfill friction angle degbackfill_friction_angle_deg
  • Backfill unit weight kn m3backfill_unit_weight_kn_m3

Prompt replacement text

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

Water table restricted to: True

Task bundle

The exact instruction and parameter contract used to generate this task, pinned to the published library source.

/workspace

  • instruction.md
  • wall-overturning_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.2 3## Problem4 5Check the stability of a cantilever retaining wall against overturning about the toe using Rankine active earth pressure theory.6 7## Given8 9| Parameter | Value | Unit |10|-----------|-------|------|11| Wall stem height (H) | {{ wall_height_m }} | m |12| Base slab width (B) | {{ base_width_m }} | m |13| Stem thickness (t_stem) | {{ stem_thickness_m }} | m |14| Base slab thickness (t_base) | {{ base_thickness_m }} | m |15{% if backfill_friction_angle_deg is defined %}16| Backfill friction angle (φ') | {{ backfill_friction_angle_deg }} | degrees |17{% endif %}18{% if backfill_unit_weight_kn_m3 is defined %}19| Backfill unit weight (γ_s) | {{ backfill_unit_weight_kn_m3 }} | kN/m³ |20{% endif %}21| Concrete unit weight (γ_c) | {{ concrete_unit_weight_kn_m3 }} | kN/m³ |22{% if surcharge_kpa is defined %}23| Surcharge load (q) | {{ surcharge_kpa }} | kPa |24{% endif %}25{% if water_table_depth_m is defined %}26| Water table depth from wall top | {{ water_table_depth_m }} | m |27{% endif %}28{% if archetype_description is defined %}29 30### Site Conditions31 32{{ archetype_description }}33{% endif %}34 35{% if tool_available %}36## Available Tool37 38A retaining wall overturning calculation tool is available at `/workspace/wall-overturning_calc.py`. Run it with:39 40```bash41python3 /workspace/wall-overturning_calc.py --help42```43 44You may use this tool to verify your calculations or compute values directly.45{% endif %}46 47## Required48 49Calculate the following:50 511. Rankine active earth pressure coefficient Ka522. Total active force per metre of wall Pa (kN/m)533. Overturning moment about the toe Mo (kNm/m)544. Resisting moment about the toe Mr (kNm/m)555. Factor of safety against overturning FoS56 57## Applicable Standards58 59- AS 4678 — Earth-retaining structures60- Eurocode 7 — Geotechnical design61 62## Constraints63 64- No internet access is available. Work from engineering knowledge and the provided tool.65- Use Rankine active earth pressure theory:66 - **Active coefficient:** Ka = (1 - sin φ') / (1 + sin φ')67 - **Active force (triangular):** Pa = 0.5 × Ka × γ_s × H_total²68 - where H_total = wall stem height + base slab thickness69- The active force resultant acts at H_total / 3 from the base.70- If a surcharge q is present, the additional lateral force is Ka × q × H_total, acting at H_total / 2.71- If the water table is within the wall height, add hydrostatic pressure: P_w = 0.5 × γ_w × h_w² (γ_w = 9.81 kN/m³, h_w = submerged height).72- Wall geometry (cantilever L-wall from toe to heel):73 - Toe length = B / 374 - Stem sits on the base starting at the toe length75 - Heel length = B - toe length - stem thickness76- Resisting moment about the toe includes:77 - Base slab self-weight (acting at B/2 from toe)78 - Stem self-weight (acting at toe_length + t_stem/2 from toe)79 - Backfill soil on the heel (acting at toe_length + t_stem + heel/2 from toe)80 - Vertical surcharge on the heel (if applicable)81- **Factor of safety against overturning:** FoS = Mr / Mo (minimum acceptable FoS = 2.0)82 83## Output Format84 85Show 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:86 87```json88{89 "ka": <numeric_value>,90 "active_force_kn_m": <numeric_value>,91 "overturning_moment_knm_m": <numeric_value>,92 "resisting_moment_knm_m": <numeric_value>,93 "factor_of_safety_overturning": <numeric_value>94}95```96 97Write your complete solution to `/workspace/output.md`.98

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 granular fill

loose_granular_fill

Loose granular fill

brisbane-alluvialdarwin-reclaimed
Parameter ranges
backfill_friction_angle_deg
25 – 30
backfill_unit_weight_kn_m3
16 – 18

Medium dense sand

medium_dense_sand

Medium dense sand backfill

perth-coastalhunter-valley-alluvial
Parameter ranges
backfill_friction_angle_deg
30 – 36
backfill_unit_weight_kn_m3
17 – 19

Dense gravel

dense_gravel

Dense compacted gravel

sydney-hawkesburymelbourne-basalt
Parameter ranges
backfill_friction_angle_deg
35 – 42
backfill_unit_weight_kn_m3
19 – 22

Stiff clay fill

stiff_clay_fill

Stiff clay fill

adelaide-stiffcanberra-residual
Parameter ranges
backfill_friction_angle_deg
20 – 28
backfill_unit_weight_kn_m3
17 – 20

Example task

brisbane-alluvial-loose-granular-fill-preview — hard difficulty, some inputs hidden.

Loose granular fill. brisbane-alluvial. Required outputs: ka, active_force_kn_m, overturning_moment_knm_m, resisting_moment_knm_m, factor_of_safety_overturning

The model sees

Scenario context and visible inputs.

wall_height_m
2 to 10 m
base_width_m
1.5 to 8 m
stem_thickness_m
0.2 to 1 m
base_thickness_m
0.3 to 1.2 m
concrete_unit_weight_kn_m3
23 to 25 kN/m³
surcharge_kpa
0 kPa
water_table_depth_m
20 m

Executable tool: wall-overturning_calc.py

The model must infer

Inputs withheld at this difficulty.

  • Backfill friction angle deg

    backfill_friction_angle_deg

  • Backfill unit weight kn m3

    backfill_unit_weight_kn_m3

Stand-in text in the prompt

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

The model must produce

The scored JSON answer schema.

{
  "ka": <number>,
  "active_force_kn_m": <number>,
  "overturning_moment_knm_m": <number>,
  "resisting_moment_knm_m": <number>,
  "factor_of_safety_overturning": <number>
}
  • ka · scored within ±3%
  • active_force_kn_m · scored within ±5%
  • overturning_moment_knm_m · scored within ±5%
  • resisting_moment_knm_m · scored within ±5%
  • factor_of_safety_overturning · scored within ±5%