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groundwith-tool

Infinite Slope

Computes the factor of safety against shallow planar failure on long uniform slopes using the infinite slope equation with Mohr-Coulomb shear strength. Accounts for pore water pressure from a water table parallel to the slope surface, balancing the driving shear stress (gamma*z*sin(beta)*cos(beta)) against the resisting cohesion and frictional strength along the failure plane.

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

Standards

Standard geotechnical texts

Tags

deterministicgeotechnicalslope-stability

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

6 inputs

Always given

Included directly in every task prompt.

2

  • Slope angle deg

    slope_angle_deg

    Slope angle beta

    5 – 45 degrees

  • Failure depth

    failure_depth_m

    Depth to failure surface z

    0.5 – 10 m

Derived from scenario

Sampled from the scenario and inferable from its description.

3

  • Friction angle deg

    friction_angle_deg

    Effective friction angle phi'

    Derived from the archetype scenario. Hidden at hard difficulty.

    0 – 45 degrees

  • Cohesion

    cohesion_kpa

    Effective cohesion c'

    Derived from the archetype scenario. Hidden at hard difficulty.

    0 – 150 kPa

  • 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

4 outputs

Pore pressure

pore_pressure_kpa

Pore water pressure at failure surface u (kPa)

Scores if within ±3% of the reference value.

Driving stress

driving_stress_kpa

Driving shear stress (kPa)

Scores if within ±3% of the reference value.

Resisting stress

resisting_stress_kpa

Resisting shear stress (kPa)

Scores if within ±3% of the reference value.

Factor of safety

factor_of_safety

Factor of safety FoS

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

Dry cohesionless slope — simplest formula

Cohesion restricted to: 0

Water table restricted to: False

medium

All inputs given

Dry slope with cohesion — adds c' term

Water table restricted to: False

hard

Some inputs hidden

Water table present, soil parameters hidden

Hidden inputs

  • Cohesioncohesion_kpa
  • Friction angle degfriction_angle_deg
  • Unit weight kn m3unit_weight_kn_m3

Prompt replacement text

The slope soil 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
  • infinite-slope_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 slope stability.2 3## Problem4 5Calculate the factor of safety against shallow slope failure using the infinite slope method.6 7## Given8 9| Parameter | Value | Unit |10|-----------|-------|------|11| Slope angle (β) | {{ slope_angle_deg }} | degrees |12{% if friction_angle_deg is defined %}13| Effective friction angle (φ') | {{ friction_angle_deg }} | degrees |14{% endif %}15{% if cohesion_kpa is defined %}16| Effective cohesion (c') | {{ cohesion_kpa }} | kPa |17{% endif %}18{% if unit_weight_kn_m3 is defined %}19| Soil unit weight (γ) | {{ unit_weight_kn_m3 }} | kN/m³ |20{% endif %}21| Depth to failure surface (z) | {{ failure_depth_m }} | m |22{% if water_table_depth_m is defined %}23| Water table depth (zw) | {{ water_table_depth_m }} | m |24{% endif %}25{% if archetype_description is defined %}26 27### Site Conditions28 29{{ archetype_description }}30{% endif %}31 32{% if tool_available %}33## Available Tool34 35A slope stability calculation tool is available at `/workspace/infinite_slope_calc.py`. Run it with:36 37```bash38python3 /workspace/infinite_slope_calc.py --help39```40 41You may use this tool to verify your calculations or compute values directly.42{% endif %}43 44## Required45 46Calculate the following:47 481. Pore water pressure at the failure surface u (kPa)492. Driving shear stress along the failure plane (kPa)503. Resisting shear stress along the failure plane (kPa)514. Factor of safety FoS52 53## Applicable Standards54 55- Standard geotechnical textbook infinite slope analysis56 57## Constraints58 59- No internet access is available. Work from engineering knowledge and the provided tool.60- Use the infinite slope equation:61 - Driving stress: τ_d = γ·z·sin(β)·cos(β)62 - Normal effective stress: σ'_n = γ·z·cos²(β) - u63 - Resisting stress: τ_r = c' + σ'_n·tan(φ')64 - FoS = τ_r / τ_d65- Pore pressure (seepage parallel to slope): u = γ_w·(z - zw)·cos²(β) when zw < z, otherwise u = 066- Use γ_w = 9.81 kN/m³67 68## Output Format69 70Show 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:71 72```json73{74 "pore_pressure_kpa": <numeric_value>,75 "driving_stress_kpa": <numeric_value>,76 "resisting_stress_kpa": <numeric_value>,77 "factor_of_safety": <numeric_value>78}79```80 81Write your complete solution to `/workspace/output.md`.82

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

Firm clay

firm_clay

Firm clay

brisbane-alluvialmelbourne-basalt
Parameter ranges
cohesion_kpa
20 – 50
friction_angle_deg
2 – 8
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

Loose sand

loose_sand

Loose sand

hunter-valley-alluvial
Parameter ranges
cohesion_kpa
0
friction_angle_deg
28 – 32
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

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

Silty sand

silty_sand

Silty sand

hunter-valley-alluvial
Parameter ranges
cohesion_kpa
0 – 5
friction_angle_deg
28 – 34
unit_weight_kn_m3
17 – 19

Residual weathered rock

residual_weathered_rock

Residual/weathered rock

sydney-hawkesbury
Parameter ranges
cohesion_kpa
10 – 30
friction_angle_deg
30 – 40
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: pore_pressure_kpa, driving_stress_kpa, resisting_stress_kpa, factor_of_safety

The model sees

Scenario context and visible inputs.

slope_angle_deg
5 to 45 degrees
failure_depth_m
0.5 to 10 m
water_table_depth_m
0 to 100 m

Executable tool: infinite-slope_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 slope soil is {{ archetype.description }} ({{ archetype.site_context }})

The model must produce

The scored JSON answer schema.

{
  "pore_pressure_kpa": <number>,
  "driving_stress_kpa": <number>,
  "resisting_stress_kpa": <number>,
  "factor_of_safety": <number>
}
  • pore_pressure_kpa · scored within ±3%
  • driving_stress_kpa · scored within ±3%
  • resisting_stress_kpa · scored within ±3%
  • factor_of_safety · scored within ±3%