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groundwith-tool

Cpt Parameter Derivation

Derives geotechnical design parameters from cone penetration test (CPTu) data using the Robertson (1990) classification framework. Computes corrected cone resistance qt, normalized parameters Qt and Fr, soil behavior type index Ic, and estimates undrained shear strength (via Nkt) for clay-like soils or friction angle for sand-like soils based on the Ic = 2.6 boundary.

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

Standards

Lunne et al. (1997)Robertson (1990)Robertson and Campanella (1983)

Tags

cptdeterministicgeotechnicalsoil-classification

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

  • Qc

    qc_mpa

    Measured cone resistance

    0.2 – 40 MPa

  • Fs

    fs_kpa

    Measured sleeve friction

    1 – 500 kPa

  • U2

    u2_kpa

    Measured pore water pressure at cone shoulder

    -50 – 1500 kPa

  • Depth

    depth_m

    Test depth below ground surface

    1 – 40 m

Derived from scenario

Sampled from the scenario and inferable from its description.

1

  • Total unit weight

    total_unit_weight_kn_m3

    Total unit weight of soil

    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.

2

  • Water table depth

    water_table_depth_m

    Depth to water table below ground surface

    Optional input.

    0 – 50 m

  • Net area ratio

    net_area_ratio

    Net area ratio of the cone (a)

    Optional input. Hidden at hard difficulty.

    0.55 – 0.85

Scored outputs

7 outputs

Qt mpa

qt_mpa

Corrected cone resistance qt (MPa)

Scores if within ±3% of the reference value.

Friction ratio pct

friction_ratio_pct

Friction ratio Rf (%)

Scores if within ±5% of the reference value.

Qt norm

qt_norm

Normalized cone resistance Qt

Scores if within ±5% of the reference value.

Fr norm

fr_norm

Normalized friction ratio Fr (%)

Scores if within ±5% of the reference value.

Ic

ic

Soil behavior type index Ic (Robertson 1990)

Scores if within ±5% of the reference value.

Su

su_kpa

Estimated undrained shear strength Su (kPa), 0 if sand-like

Scores if within ±5% of the reference value.

Phi deg

phi_deg

Estimated friction angle phi' (degrees), 0 if clay-like

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, soft clay or medium sand archetypes

medium

All inputs given

All parameters given, any soil archetype

hard

Some inputs hidden

Unit weight and net area ratio hidden, agent infers from context

Hidden inputs

  • Total unit weight kn m3total_unit_weight_kn_m3
  • Net area rationet_area_ratio

Prompt replacement text

The CPTu test was performed at a {{ archetype.site_context }} site in {{ archetype.description | lower }} conditions.

Task bundle

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

/workspace

  • instruction.md
  • cpt-parameter-derivation_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 in-situ testing and soil characterization.2 3## Problem4 5Derive soil parameters from Cone Penetration Test (CPT) data using Robertson (1990) normalized classification and standard correlations for strength parameters.6 7## Given8 9| Parameter | Value | Unit |10|-----------|-------|------|11| Cone resistance (qc) | {{ qc_mpa }} | MPa |12| Sleeve friction (fs) | {{ fs_kpa }} | kPa |13| Pore water pressure (u2) | {{ u2_kpa }} | kPa |14| Test depth | {{ depth_m }} | m |15{% if total_unit_weight_kn_m3 is defined %}16| Total unit weight (γ) | {{ total_unit_weight_kn_m3 }} | kN/m³ |17{% endif %}18{% if water_table_depth_m is defined %}19| Water table depth | {{ water_table_depth_m }} | m |20{% endif %}21{% if net_area_ratio is defined %}22| Net area ratio (a) | {{ net_area_ratio }} | - |23{% endif %}24{% if archetype_description is defined %}25 26### Site Conditions27 28{{ archetype_description }}29{% endif %}30 31{% if tool_available %}32## Available Tool33 34A CPT parameter derivation tool is available at `/workspace/cpt-parameter-derivation_calc.py`. Run it with:35 36```bash37python3 /workspace/cpt-parameter-derivation_calc.py --help38```39 40You may use this tool to verify your calculations or compute values directly.41{% endif %}42 43## Required44 45Calculate the following parameters from the CPT data:46 471. Corrected cone resistance qt (MPa): qt = qc + u2·(1 - a) / 1000482. Friction ratio Rf (%): Rf = fs / qt × 100, where qt is in kPa493. Total overburden stress σv0 = γ × depth, and effective overburden stress σ'v0 accounting for water table504. Normalized cone resistance Qt = (qt - σv0) / σ'v0, where qt and stresses are in kPa515. Normalized friction ratio Fr (%) = fs / (qt - σv0) × 100526. Soil behavior type index Ic = √[(3.47 - log₁₀(Qt))² + (log₁₀(Fr) + 1.22)²]537. If Ic > 2.6 (clay-like): undrained shear strength Su = (qt - σv0) / Nkt where Nkt = 14548. If Ic ≤ 2.6 (sand-like): friction angle φ' = 17.6 + 11.0 × log₁₀(Qt) (Robertson & Campanella 1983)55 56## Applicable Standards57 58- Robertson, P.K. (1990) — Soil classification using the cone penetration test59- Lunne, T., Robertson, P.K. and Powell, J.J.M. (1997) — Cone Penetration Testing in Geotechnical Practice60- Robertson, P.K. and Campanella, R.G. (1983) — Interpretation of cone penetration tests61 62## Constraints63 64- No internet access is available. Work from engineering knowledge and the provided tool.65- Use γ_w = 9.81 kN/m³ for pore water pressure calculations.66- Use atmospheric pressure Pa = 100 kPa as the reference for normalization.67- The corrected cone resistance accounts for the unequal end area effect: qt = qc + u2·(1 - a) / 1000, where u2 is in kPa and qc is in MPa.68- For the Ic boundary: Ic > 2.6 indicates clay-like behavior (report Su, set φ' = 0); Ic ≤ 2.6 indicates sand-like behavior (report φ', set Su = 0).69- Use Nkt = 14 for undrained shear strength estimation.70- Clamp Qt to a minimum of 1.0 and Fr to a minimum of 0.1 before computing log values.71 72## Output Format73 74Show 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:75 76```json77{78 "qt_mpa": <numeric_value>,79 "friction_ratio_pct": <numeric_value>,80 "qt_norm": <numeric_value>,81 "fr_norm": <numeric_value>,82 "ic": <numeric_value>,83 "su_kpa": <numeric_value>,84 "phi_deg": <numeric_value>85}86```87 88Write your complete solution to `/workspace/output.md`.89

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 clay

soft_clay

Soft normally consolidated clay with high pore pressure

brisbane-alluvialdarwin-estuarinecairns-coastal
Parameter ranges
qc_mpa
0.2 – 1.5
fs_kpa
5 – 30
u2_kpa
100 – 800
depth_m
3 – 15
total_unit_weight_kn_m3
15 – 17.5
water_table_depth_m
0 – 2
net_area_ratio
0.7 – 0.85

Stiff clay

stiff_clay

Stiff overconsolidated clay

sydney-shalemelbourne-basaltadelaide-stiff
Parameter ranges
qc_mpa
1.5 – 5
fs_kpa
30 – 150
u2_kpa
50 – 500
depth_m
3 – 20
total_unit_weight_kn_m3
17 – 20
water_table_depth_m
1 – 5
net_area_ratio
0.7 – 0.85

Medium sand

medium_sand

Medium dense clean sand

perth-coastalgold-coast-dunenewcastle-sand
Parameter ranges
qc_mpa
5 – 20
fs_kpa
20 – 100
u2_kpa
-20 – 50
depth_m
2 – 20
total_unit_weight_kn_m3
17 – 20
water_table_depth_m
1 – 10
net_area_ratio
0.75 – 0.85

Dense sand

dense_sand

Dense to very dense sand or gravel

hunter-valley-alluvialperth-limestonesydney-hawkesbury
Parameter ranges
qc_mpa
15 – 40
fs_kpa
50 – 300
u2_kpa
-50 – 20
depth_m
5 – 30
total_unit_weight_kn_m3
18 – 22
water_table_depth_m
2 – 15
net_area_ratio
0.75 – 0.85

Example task

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

Soft normally consolidated clay with high pore pressure. brisbane-alluvial. Required outputs: qt_mpa, friction_ratio_pct, qt_norm, fr_norm, ic, su_kpa

The model sees

Scenario context and visible inputs.

qc_mpa
0.2 to 1.5 MPa
fs_kpa
5 to 30 kPa
u2_kpa
100 to 800 kPa
depth_m
3 to 15 m
water_table_depth_m
0 to 2 m

Executable tool: cpt-parameter-derivation_calc.py

The model must infer

Inputs withheld at this difficulty.

  • Total unit weight kn m3

    total_unit_weight_kn_m3

  • Net area ratio

    net_area_ratio

Stand-in text in the prompt

The CPTu test was performed at a {{ archetype.site_context }} site in {{ archetype.description | lower }} conditions.

The model must produce

The scored JSON answer schema.

{
  "qt_mpa": <number>,
  "friction_ratio_pct": <number>,
  "qt_norm": <number>,
  "fr_norm": <number>,
  "ic": <number>,
  "su_kpa": <number>,
  "phi_deg": <number>
}
  • qt_mpa · scored within ±3%
  • friction_ratio_pct · scored within ±5%
  • qt_norm · scored within ±5%
  • fr_norm · scored within ±5%
  • ic · scored within ±5%
  • su_kpa · scored within ±5%
  • phi_deg · scored within ±5%