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groundwith-tool

Consolidation Settlement

Estimates primary consolidation settlement of clay layers under applied loading using Terzaghi's one-dimensional theory. Handles normally consolidated, overconsolidated, and transitional cases via the compression index (Cc) and recompression index (Cr) on the e-log-p curve, with settlement governed by Sc = CcH/(1+e0) * log10(sigma_vf/sigma_v0) and its variants.

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

Standards

Terzaghi 1D consolidation theory

Tags

clayconsolidationdeterministicgeotechnicalsettlement

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.

4

  • Clay thickness

    clay_thickness_m

    Clay layer thickness H

    1 – 20 m

  • Preconsolidation pressure

    preconsolidation_pressure_kpa

    Preconsolidation pressure sigma'p

    30 – 500 kPa

  • Initial effective stress

    initial_effective_stress_kpa

    Initial effective overburden stress sigma'v0

    20 – 300 kPa

  • Final effective stress

    final_effective_stress_kpa

    Final effective stress after loading sigma'vf

    50 – 600 kPa

Derived from scenario

Sampled from the scenario and inferable from its description.

3

  • Compression index cc

    compression_index_cc

    Compression index Cc

    Derived from the archetype scenario. Hidden at hard difficulty.

    0.1 – 1.5

  • Recompression index cr

    recompression_index_cr

    Recompression index Cr

    Derived from the archetype scenario. Hidden at hard difficulty.

    0.01 – 0.15

  • Initial void ratio e0

    initial_void_ratio_e0

    Initial void ratio e0

    Derived from the archetype scenario. Hidden at hard difficulty.

    0.5 – 3

Scored outputs

2 outputs

Ocr

ocr

Overconsolidation ratio OCR

Scores if within ±3% of the reference value.

Settlement

settlement_mm

Primary consolidation settlement Sc (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

NC clay, all parameters given, single-case settlement

medium

All inputs given

OC clay, all parameters given, two-case settlement possible

hard

Some inputs hidden

Soil properties hidden, agent must determine Cc, Cr, e0 from site description

Hidden inputs

  • Compression index cccompression_index_cc
  • Recompression index crrecompression_index_cr
  • Initial void ratio e0initial_void_ratio_e0

Prompt replacement text

The clay layer 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
  • consolidation-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 primary consolidation settlement of a clay layer using **Terzaghi's one-dimensional consolidation theory**.6 7## Given Parameters8 9| Parameter | Value | Unit |10|-----------|-------|------|11| Clay layer thickness (H) | {{ clay_thickness_m }} | m |12{% if compression_index_cc is defined %}| Compression index (Cc) | {{ compression_index_cc }} | - |13{% endif %}{% if recompression_index_cr is defined %}| Recompression index (Cr) | {{ recompression_index_cr }} | - |14{% endif %}{% if initial_void_ratio_e0 is defined %}| Initial void ratio (e₀) | {{ initial_void_ratio_e0 }} | - |15{% endif %}| Preconsolidation pressure (σ'p) | {{ preconsolidation_pressure_kpa }} | kPa |16| Initial effective stress (σ'v0) | {{ initial_effective_stress_kpa }} | kPa |17| Final effective stress (σ'vf) | {{ final_effective_stress_kpa }} | kPa |18 19{% if archetype_description is defined %}20### Site Conditions21 22{{ archetype_description }}23{% endif %}24 25## Method26 27Use **Terzaghi's 1D consolidation settlement** equations. First determine the overconsolidation ratio:28 29**OCR = σ'p / σ'v0**30 31Then calculate settlement based on the stress state:32 33### Case 1: Normally Consolidated (OCR ≤ 1)34 35**S_c = (Cc × H) / (1 + e₀) × log₁₀(σ'vf / σ'v0)**36 37### Case 2: Overconsolidated, remains OC (σ'vf ≤ σ'p)38 39**S_c = (Cr × H) / (1 + e₀) × log₁₀(σ'vf / σ'v0)**40 41### Case 3: Overconsolidated, becomes NC (σ'vf > σ'p)42 43**S_c = (Cr × H) / (1 + e₀) × log₁₀(σ'p / σ'v0) + (Cc × H) / (1 + e₀) × log₁₀(σ'vf / σ'p)**44 45## Constraints46 47- No internet access is available.48- Use the exact equations specified above.49- Use base-10 logarithm (log₁₀).50- Report settlement in millimetres (mm).51- Determine which case applies based on OCR and the relationship between σ'vf and σ'p.52 53{% if tool_available %}54## Available Tool55 56A calculation tool is available at `/workspace/{{ meta.name }}_calc.py`. Run it with:57 58```bash59python3 /workspace/{{ meta.name }}_calc.py --help60```61 62You may use this tool to verify your calculations or compute values directly.63{% endif %}64 65## Required66 67Calculate:68 691. Overconsolidation ratio (OCR)702. Primary consolidation settlement S_c (mm)71 72## Output Format73 74Show 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:75 76```json77{78 "ocr": <value>,79 "settlement_mm": <value>80}81```82 83Write your complete solution to `/workspace/output.md`.84

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.

Soft nc clay

soft_nc_clay

Soft normally consolidated marine clay

brisbane-alluvialdarwin-estuarinegladstone-marine
Parameter ranges
compression_index_cc
0.4 – 0.8
recompression_index_cr
0.04 – 0.08
initial_void_ratio_e0
1.2 – 2.5

Medium oc clay

medium_oc_clay

Medium overconsolidated clay

sydney-hawkesburymelbourne-brightonadelaide-stiff
Parameter ranges
compression_index_cc
0.2 – 0.4
recompression_index_cr
0.02 – 0.04
initial_void_ratio_e0
0.7 – 1.2

Stiff oc clay

stiff_oc_clay

Stiff heavily overconsolidated clay

melbourne-basaltcanberra-stiffperth-spearwood
Parameter ranges
compression_index_cc
0.1 – 0.25
recompression_index_cr
0.01 – 0.03
initial_void_ratio_e0
0.5 – 0.8

Example task

brisbane-alluvial-soft-nc-clay-preview — hard difficulty, some inputs hidden.

Soft normally consolidated marine clay. brisbane-alluvial. Required outputs: ocr, settlement_mm

The model sees

Scenario context and visible inputs.

clay_thickness_m
1 to 20 m
preconsolidation_pressure_kpa
30 to 500 kPa
initial_effective_stress_kpa
20 to 300 kPa
final_effective_stress_kpa
50 to 600 kPa

Executable tool: consolidation-settlement_calc.py

The model must infer

Inputs withheld at this difficulty.

  • Compression index cc

    compression_index_cc

  • Recompression index cr

    recompression_index_cr

  • Initial void ratio e0

    initial_void_ratio_e0

Stand-in text in the prompt

The clay layer is {{ archetype.description }} ({{ archetype.site_context }})

The model must produce

The scored JSON answer schema.

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