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groundwith-tool

Meyerhof Bearing Capacity

Computes ultimate and allowable bearing capacity of shallow foundations using Meyerhof's (1963) general bearing capacity equation: qu = c*Nc*sc*dc*ic + q*Nq*sq*dq*iq + 0.5*gamma*B*Ngamma*sgamma*dgamma*igamma. Applies shape, depth, and inclination correction factors for strip, rectangular, square, and circular footings under vertical or inclined loading conditions.

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

Standards

Meyerhof (1963)

How this task is generated

One template produces many comparable benchmark tasks while keeping the scoring contract fixed.

01
Template
The reusable contract shown on this page.
02
Scenario
An archetype and site context are sampled.
03
Difficulty tier
Inputs may be hidden at harder tiers.
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.

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
Embedment depth
embedment_depth_m
Foundation embedment depth Df
0.3 – 5 m
Footing shape
footing_shape
Footing shape
striprectangularsquarecircular
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.

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.

Load inclination deg
load_inclination_deg
Load inclination angle from vertical
Optional input.
0 – 20 degrees

Scored outputs

14 outputs

Nc

Bearing capacity factor Nc

Scores if within ±3% of the reference value.

Nq

Bearing capacity factor Nq

Scores if within ±3% of the reference value.

Ngamma

ngamma

Bearing capacity factor Ngamma

Scores if within ±3% of the reference value.

Sc

Shape factor sc

Scores if within ±3% of the reference value.

Sq

Shape factor sq

Scores if within ±3% of the reference value.

Sgamma

sgamma

Shape factor sgamma

Scores if within ±3% of the reference value.

Dc

Depth factor dc

Scores if within ±3% of the reference value.

Dq

Depth factor dq

Scores if within ±3% of the reference value.

Dgamma

dgamma

Depth factor dgamma

Scores if within ±3% of the reference value.

Ic

Inclination factor ic

Scores if within ±3% of the reference value.

Iq

Inclination factor iq

Scores if within ±3% of the reference value.

Igamma

igamma

Inclination factor igamma

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

Vertical load, square footing, all parameters given

Footing shape restricted to: square

medium

All inputs given

Vertical or inclined load, any shape, all parameters given

Footing shape restricted to: strip, rectangular, square, circular

hard

Some inputs hidden

Some soil parameters hidden, inclined loading

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: rectangular, square, circular

Task bundle

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

/workspace

instruction.md
meyerhof-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 shallow foundation design.2 3## Task4 5Calculate the ultimate and allowable bearing capacity of a shallow foundation using **Meyerhof's (1963) general bearing capacity equation** with shape, depth, and inclination factors.6 7## Given Parameters8 9| Parameter | Value | Unit |10|-----------|-------|------|11{% if cohesion_kpa is defined %}| Effective cohesion (c') | {{ cohesion_kpa }} | kPa |12{% endif %}{% if friction_angle_deg is defined %}| Effective friction angle (φ') | {{ friction_angle_deg }} | degrees |13{% endif %}{% if unit_weight_kn_m3 is defined %}| Soil unit weight (γ) | {{ unit_weight_kn_m3 }} | kN/m³ |14{% endif %}| Footing width (B) | {{ footing_width_m }} | m |15| Footing length (L) | {{ footing_length_m }} | m |16| Embedment depth (Df) | {{ embedment_depth_m }} | m |17| Footing shape | {{ footing_shape }} | - |18{% if load_inclination_deg is defined and load_inclination_deg|float > 0 %}| Load inclination (θ) | {{ load_inclination_deg }} | degrees from vertical |19{% endif %}| Factor of safety | {{ factor_of_safety }} | - |20 21{% if archetype_description is defined %}22### Site Conditions23 24{{ archetype_description }}25{% endif %}26 27## Method28 29Use the **Meyerhof (1963)** general bearing capacity equation:30 31**q_u = c' × N_c × s_c × d_c × i_c + q × N_q × s_q × d_q × i_q + 0.5 × γ × B × N_γ × s_γ × d_γ × i_γ**32 33where q = γ × D_f (overburden pressure).34 35### Bearing Capacity Factors36 37- N_q = e^(π tan φ) × tan²(45 + φ/2)38- N_c = (N_q − 1) × cot φ  (N_c = 5.14 when φ = 0)39- N_γ = (N_q − 1) × tan(1.4φ)40 41### Shape Factors (K_p = tan²(45 + φ/2))42 43- s_c = 1 + 0.2 × K_p × (B/L)44- s_q = s_γ = 1 + 0.1 × K_p × (B/L) for φ > 10°; otherwise s_q = s_γ = 145 46### Depth Factors47 48- d_c = 1 + 0.2 × √K_p × (D_f/B)49- d_q = d_γ = 1 + 0.1 × √K_p × (D_f/B) for φ > 10°; otherwise d_q = d_γ = 150 51### Inclination Factors52 53- i_c = i_q = (1 − θ/90)²54- i_γ = (1 − θ/φ)² for φ > 0; otherwise i_γ = 055 56For vertical loads (θ = 0): all inclination factors equal 1.57 58## Constraints59 60- No internet access is available.61- Use Meyerhof (1963) equations exactly as specified above.62- B is always the shorter dimension (B ≤ L).63- For strip footings, use B/L ≈ 0 (the L dimension is effectively infinite, so shape factors reduce accordingly — for practical purposes, the footing_length_m value is provided but B/L will be small).64- γ_w = 9.81 kN/m³ (if needed for water table corrections).65 66{% if tool_available %}67## Available Tool68 69A calculation tool is available at `/workspace/{{ meta.name }}_calc.py`. Run it with:70 71```bash72python3 /workspace/{{ meta.name }}_calc.py --help73```74 75You may use this tool to verify your calculations or compute values directly.76{% endif %}77 78## Required79 80Calculate all of the following:81 821. Bearing capacity factors: N_c, N_q, N_γ832. Shape factors: s_c, s_q, s_γ843. Depth factors: d_c, d_q, d_γ854. Inclination factors: i_c, i_q, i_γ865. Ultimate bearing capacity q_u (kPa)876. Allowable bearing capacity q_a = q_u / FoS (kPa)88 89## Output Format90 91Show 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:92 93```json94{95  "nc": <value>,96  "nq": <value>,97  "ngamma": <value>,98  "sc": <value>,99  "sq": <value>,100  "sgamma": <value>,101  "dc": <value>,102  "dq": <value>,103  "dgamma": <value>,104  "ic": <value>,105  "iq": <value>,106  "igamma": <value>,107  "ultimate_bearing_capacity_kpa": <value>,108  "allowable_bearing_capacity_kpa": <value>109}110```111 112Write your complete solution to `/workspace/output.md`.113

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: 28 – 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 gravel

dense_sand_gravel

Dense sand and gravel

cairns-coralnewcastle-fill

Parameter ranges

cohesion_kpa: 0
friction_angle_deg: 36 – 45
unit_weight_kn_m3: 19 – 22

Example task

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

Soft normally consolidated clay. brisbane-alluvial. Required outputs: nc, nq, ngamma, sc, sq, sgamma

The model sees

Scenario context and visible inputs.

footing_width_m: 0.5 to 10 m
footing_length_m: 0.5 to 30 m
embedment_depth_m: 0.3 to 5 m
footing_shape: rectangular
load_inclination_deg: 0 degrees
factor_of_safety: 3

Executable tool: meyerhof-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>,
  "sc": <number>,
  "sq": <number>,
  "sgamma": <number>,
  "dc": <number>,
  "dq": <number>,
  "dgamma": <number>,
  "ic": <number>,
  "iq": <number>,
  "igamma": <number>,
  "ultimate_bearing_capacity_kpa": <number>,
  "allowable_bearing_capacity_kpa": <number>
}

nc · scored within ±3%
nq · scored within ±3%
ngamma · scored within ±3%
sc · scored within ±3%
sq · scored within ±3%
sgamma · scored within ±3%
dc · scored within ±3%
dq · scored within ±3%
dgamma · scored within ±3%
ic · scored within ±3%
iq · scored within ±3%
igamma · scored within ±5%
ultimate_bearing_capacity_kpa · scored within ±3%
allowable_bearing_capacity_kpa · scored within ±3%

Meyerhof Bearing Capacity

How this task is generated

Template

Scenario

Difficulty tier

Task prompt

Parameters

Inputs

Scored outputs

Nc

Nq

Ngamma

Sc

Sq

Sgamma

Dc

Dq

Dgamma

Ic

Iq

Igamma

Ultimate bearing capacity

Allowable bearing capacity

Difficulty

easy

medium

hard

Task bundle

Scenario archetypes

Soft nc clay

Medium dense sand

Stiff oc clay

Dense sand gravel

Example task

The model sees

The model must infer

The model must produce