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Terzaghi Bearing Capacity

Calculates ultimate and allowable bearing capacity of shallow foundations using Terzaghi's (1943) classical equation: qu = c*Nc*sc + q*Nq + 0.5*gamma*B*sg*Ngamma, with shape factors for strip, square, and circular footings. Includes water table correction for overburden and effective unit weight, and bearing capacity factors Nc, Nq from analytical expressions with Ngamma interpolated from standard tables.

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

Standards

Terzaghi (1943)

Tags

bearing-capacitydeterministicgeotechnical

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

8 inputs

Always given

Included directly in every task prompt.

4

  • Footing width

    footing_width_m

    Footing width B

    0.5 – 10 m

  • Embedment depth

    embedment_depth_m

    Foundation embedment depth Df

    0.3 – 5 m

  • Footing shape

    footing_shape

    Footing shape

    stripsquarecircular

  • Factor of safety

    factor_of_safety

    Factor of safety for allowable capacity

    2 – 4

Derived from scenario

Sampled from the scenario and inferable from its description.

3

  • Cohesion

    cohesion_kpa

    Effective cohesion c'

    Derived from the archetype scenario. Hidden at hard difficulty.

    0 – 150 kPa

  • Friction angle deg

    friction_angle_deg

    Effective friction angle phi'

    Derived from the archetype scenario. Hidden at hard difficulty.

    0 – 50 degrees

  • Unit weight

    unit_weight_kn_m3

    Soil unit weight gamma

    Derived from the archetype scenario. Hidden at hard difficulty.

    14 – 23 kN/m³

Optional

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

1

  • Water table depth

    water_table_depth_m

    Depth to water table from ground surface

    Optional input.

    0 – 100 m

Scored outputs

5 outputs

Nc

nc

Bearing capacity factor Nc

Scores if within ±3% of the reference value.

Nq

nq

Bearing capacity factor Nq

Scores if within ±3% of the reference value.

Ngamma

ngamma

Bearing capacity factor Ngamma

Scores if within ±5% of the reference value.

Ultimate bearing capacity

ultimate_bearing_capacity_kpa

Ultimate bearing capacity qu (kPa)

Scores if within ±3% of the reference value.

Allowable bearing capacity

allowable_bearing_capacity_kpa

Allowable bearing capacity qa (kPa)

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

All parameters given, strip footing, no water table

Footing shape restricted to: strip

Water table restricted to: False

medium

All inputs given

All parameters given, any footing shape, water table present

Footing shape restricted to: strip, square, circular

Water table restricted to: True

hard

Some inputs hidden

Some soil parameters hidden, water table present

Hidden inputs

  • Cohesioncohesion_kpa
  • Friction angle degfriction_angle_deg
  • Unit weight kn m3unit_weight_kn_m3

Prompt replacement text

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

Footing shape restricted to: square, circular

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
  • terzaghi-bearing-capacity_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 design.2 3## Problem4 5Calculate the ultimate and allowable bearing capacity of a shallow foundation using Terzaghi's 1943 bearing capacity equation.6 7## Given8 9| Parameter | Value | Unit |10|-----------|-------|------|11| Footing shape | {{ footing_shape }} | - |12| Footing width (B) | {{ footing_width_m }} | m |13| Embedment depth (Df) | {{ embedment_depth_m }} | m |14{% if cohesion_kpa is defined %}15| Effective cohesion (c') | {{ cohesion_kpa }} | kPa |16{% endif %}17{% if friction_angle_deg is defined %}18| Effective friction angle (φ') | {{ friction_angle_deg }} | degrees |19{% endif %}20{% if unit_weight_kn_m3 is defined %}21| Soil unit weight (γ) | {{ unit_weight_kn_m3 }} | kN/m³ |22{% endif %}23{% if water_table_depth_m is defined %}24| Water table depth | {{ water_table_depth_m }} | m |25{% endif %}26| Factor of safety | {{ factor_of_safety }} | - |27{% if archetype_description is defined %}28 29### Site Conditions30 31{{ archetype_description }}32{% endif %}33 34{% if tool_available %}35## Available Tool36 37A bearing capacity calculation tool is available at `/workspace/bearing_capacity_calc.py`. Run it with:38 39```bash40python3 /workspace/bearing_capacity_calc.py --help41```42 43You may use this tool to verify your calculations or compute values directly.44{% endif %}45 46## Required47 48Calculate the following:49 501. Bearing capacity factor Nc512. Bearing capacity factor Nq523. Bearing capacity factor Nγ534. Ultimate bearing capacity qu (kPa)545. Allowable bearing capacity qa (kPa)55 56## Applicable Standards57 58- Terzaghi, K. (1943) — Theoretical Soil Mechanics, John Wiley & Sons59 60## Constraints61 62- No internet access is available. Work from engineering knowledge and the provided tool.63- Use Terzaghi's original bearing capacity equation:64 - **Strip footing:** qu = c'·Nc + q·Nq + 0.5·γ·B·Nγ65 - **Square footing:** qu = 1.3·c'·Nc + q·Nq + 0.4·γ·B·Nγ66 - **Circular footing:** qu = 1.3·c'·Nc + q·Nq + 0.3·γ·B·Nγ67- Overburden pressure q = γ·Df68- Apply water table corrections when the water table is within the influence zone (above Df + B):69 - Use γ_w = 9.81 kN/m³70 - Adjust overburden pressure and effective unit weight based on water table position71- Allowable bearing capacity qa = qu / FoS72- For φ' = 0 (undrained clay): Nc = 5.7, Nq = 1.0, Nγ = 0.073 74## Output Format75 76Show 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:77 78```json79{80 "nc": <numeric_value>,81 "nq": <numeric_value>,82 "ngamma": <numeric_value>,83 "ultimate_bearing_capacity_kpa": <numeric_value>,84 "allowable_bearing_capacity_kpa": <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 nc clay

soft_nc_clay

Soft normally consolidated clay

brisbane-alluvialdarwin-estuarine
Parameter ranges
cohesion_kpa
5 – 15
friction_angle_deg
0 – 5
unit_weight_kn_m3
15 – 17

Medium dense sand

medium_dense_sand

Medium dense sand

perth-coastalhunter-valley-alluvial
Parameter ranges
cohesion_kpa
0
friction_angle_deg
32 – 36
unit_weight_kn_m3
17 – 19

Stiff oc clay

stiff_oc_clay

Stiff overconsolidated clay

sydney-hawkesburyadelaide-stiffmelbourne-basalt
Parameter ranges
cohesion_kpa
50 – 150
friction_angle_deg
5 – 15
unit_weight_kn_m3
18 – 21

Dense sand

dense_sand

Dense sand

perth-coastalcairns-coral
Parameter ranges
cohesion_kpa
0
friction_angle_deg
36 – 42
unit_weight_kn_m3
19 – 21

Example task

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

Soft normally consolidated clay. brisbane-alluvial. Required outputs: nc, nq, ngamma, ultimate_bearing_capacity_kpa, allowable_bearing_capacity_kpa

The model sees

Scenario context and visible inputs.

footing_width_m
0.5 to 10 m
embedment_depth_m
0.3 to 5 m
footing_shape
square
water_table_depth_m
0 to 100 m
factor_of_safety
3

Executable tool: terzaghi-bearing-capacity_calc.py

The model must infer

Inputs withheld at this difficulty.

  • Unit weight kn m3

    unit_weight_kn_m3

  • Cohesion

    cohesion_kpa

  • Friction angle deg

    friction_angle_deg

Stand-in text in the prompt

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

The model must produce

The scored JSON answer schema.

{
  "nc": <number>,
  "nq": <number>,
  "ngamma": <number>,
  "ultimate_bearing_capacity_kpa": <number>,
  "allowable_bearing_capacity_kpa": <number>
}
  • nc · scored within ±3%
  • nq · scored within ±3%
  • ngamma · scored within ±5%
  • ultimate_bearing_capacity_kpa · scored within ±3%
  • allowable_bearing_capacity_kpa · scored within ±3%