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groundwith-tool

Immediate Settlement

Calculates the elastic (immediate) settlement of shallow foundations using the Boussinesq equation Si = q*B*(1-nu^2)/E * If, where the influence factor If depends on footing shape and L/B ratio per Bowles (1996) Table 5-6. Supports square, rectangular, and circular footings with flexible or rigid foundation corrections for settlement prediction in granular and stiff cohesive soils.

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

Standards

Boussinesq elastic theoryBowles (1996)

Tags

deterministicelasticgeotechnicalimmediatesettlement

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

  • Applied pressure

    applied_pressure_kpa

    Net applied foundation pressure q

    25 – 500 kPa

  • Footing width

    footing_width_m

    Footing width B (shorter dimension)

    0.5 – 10 m

  • Footing length

    footing_length_m

    Footing length L (longer dimension, L >= B)

    0.5 – 30 m

  • Footing shape

    footing_shape

    Footing shape

    squarerectangularcircular

  • Foundation rigidity

    foundation_rigidity

    Foundation rigidity

    flexiblerigid

Derived from scenario

Sampled from the scenario and inferable from its description.

2

  • Elastic modulus

    elastic_modulus_mpa

    Soil elastic modulus E

    Derived from the archetype scenario. Hidden at hard difficulty.

    2 – 200 MPa

  • Poisson ratio

    poisson_ratio

    Soil Poisson's ratio nu

    Derived from the archetype scenario. Hidden at hard difficulty.

    0.15 – 0.49

Scored outputs

2 outputs

Influence factor

influence_factor

Settlement influence factor I_f

Scores if within ±5% of the reference value.

Settlement

settlement_mm

Immediate elastic settlement Si (mm)

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

Square flexible footing, all parameters given

Footing shape restricted to: square

Foundation rigidity restricted to: flexible

medium

All inputs given

Any shape and rigidity, all parameters given

Footing shape restricted to: square, rectangular, circular

Foundation rigidity restricted to: flexible, rigid

hard

Some inputs hidden

Soil properties hidden, agent must estimate E and nu from site description

Hidden inputs

  • Elastic modulus mpaelastic_modulus_mpa
  • Poisson ratiopoisson_ratio

Prompt replacement text

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

Footing shape restricted to: square, rectangular, circular

Foundation rigidity restricted to: flexible, rigid

Task bundle

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

/workspace

  • instruction.md
  • immediate-settlement_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 foundation settlement analysis.2 3## Task4 5Calculate the elastic (immediate) settlement of a shallow foundation using **Boussinesq elastic theory** with shape-dependent influence factors.6 7## Given Parameters8 9| Parameter | Value | Unit |10|-----------|-------|------|11| Applied pressure (q) | {{ applied_pressure_kpa }} | kPa |12| Footing width (B) | {{ footing_width_m }} | m |13| Footing length (L) | {{ footing_length_m }} | m |14{% if elastic_modulus_mpa is defined %}| Elastic modulus (E) | {{ elastic_modulus_mpa }} | MPa |15{% endif %}{% if poisson_ratio is defined %}| Poisson's ratio (ν) | {{ poisson_ratio }} | - |16{% endif %}| Footing shape | {{ footing_shape }} | - |17| Foundation rigidity | {{ foundation_rigidity }} | - |18 19{% if archetype_description is defined %}20### Site Conditions21 22{{ archetype_description }}23{% endif %}24 25## Method26 27Use the **elastic settlement equation**:28 29**S_i = q × B × (1 − ν²) / E × I_f**30 31where:32- q = net applied pressure (kPa)33- B = footing width (shorter dimension, m)34- ν = Poisson's ratio35- E = elastic modulus (convert to kPa: 1 MPa = 1000 kPa)36- I_f = influence factor (depends on shape and rigidity)37 38### Influence Factors39 40For flexible rectangular footings at the centre (Bowles, 1996):41 42| L/B | I_f |43|-----|-----|44| 1.0 | 1.12 |45| 1.5 | 1.36 |46| 2.0 | 1.53 |47| 3.0 | 1.78 |48| 5.0 | 2.10 |49| 10.0 | 2.54 |50 51Interpolate linearly for intermediate L/B values.52 53For circular footings (flexible centre): I_f = 1.0054 55For rigid foundations: multiply the flexible I_f by 0.8056 57## Constraints58 59- No internet access is available.60- Use the exact equation and influence factor table specified above.61- B is always the shorter dimension (B ≤ L).62- Convert elastic modulus from MPa to kPa before calculation.63- Report settlement in millimetres (mm).64 65{% if tool_available %}66## Available Tool67 68A calculation tool is available at `/workspace/{{ meta.name }}_calc.py`. Run it with:69 70```bash71python3 /workspace/{{ meta.name }}_calc.py --help72```73 74You may use this tool to verify your calculations or compute values directly.75{% endif %}76 77## Required78 79Calculate:80 811. Influence factor I_f (accounting for shape and rigidity)822. Immediate settlement S_i (mm)83 84## Output Format85 86Show your step-by-step working in Markdown. At the end of your solution, include a JSON block with your final answers in exactly this format:87 88```json89{90 "influence_factor": <value>,91 "settlement_mm": <value>92}93```94 95Write your complete solution to `/workspace/output.md`.96

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 to medium sand

perth-coastalgold-coast-sand
Parameter ranges
elastic_modulus_mpa
10 – 30
poisson_ratio
0.25 – 0.35

Dense sand

dense_sand

Dense sand and gravel

hunter-valley-alluvialnewcastle-fill
Parameter ranges
elastic_modulus_mpa
40 – 80
poisson_ratio
0.3 – 0.4

Stiff clay

stiff_clay

Stiff overconsolidated clay

sydney-hawkesburymelbourne-basaltadelaide-stiff
Parameter ranges
elastic_modulus_mpa
15 – 50
poisson_ratio
0.35 – 0.45

Soft clay

soft_clay

Soft normally consolidated clay

brisbane-alluvialdarwin-estuarine
Parameter ranges
elastic_modulus_mpa
2 – 10
poisson_ratio
0.4 – 0.48

Example task

perth-coastal-loose-sand-preview — hard difficulty, some inputs hidden.

Loose to medium sand. perth-coastal. Required outputs: influence_factor, settlement_mm

The model sees

Scenario context and visible inputs.

applied_pressure_kpa
25 to 500 kPa
footing_width_m
0.5 to 10 m
footing_length_m
0.5 to 30 m
footing_shape
square
foundation_rigidity
flexible

Executable tool: immediate-settlement_calc.py

The model must infer

Inputs withheld at this difficulty.

  • Elastic modulus mpa

    elastic_modulus_mpa

  • Poisson ratio

    poisson_ratio

Stand-in text in the prompt

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

The model must produce

The scored JSON answer schema.

{
  "influence_factor": <number>,
  "settlement_mm": <number>
}
  • influence_factor · scored within ±5%
  • settlement_mm · scored within ±3%