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civilwith-tool

Lateral Earth Pressure

Calculates active and passive earth pressure coefficients and resultant forces on retaining walls using Rankine theory per AS 4678. Handles two-zone pressure distribution when a water table is present, computing effective earth pressure above and below the water table plus hydrostatic thrust. Outputs include Ka, Kp, active and passive forces, overturning moment, and water force per unit wall length for stability assessment.

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

Standards

AS 4678Rankine (1857)

Tags

civilearth-pressuregeotechnicalrankineretaining-wallwater-table

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.

2

  • Wall height

    wall_height_m

    Retaining wall height H

    1 – 12 m

  • Water table depth

    water_table_depth_m

    Depth from ground surface to the water table behind the wall (equal to wall height means no water)

    0 – 12 m

Derived from scenario

Sampled from the scenario and inferable from its description.

2

  • Friction angle deg

    friction_angle_deg

    Effective friction angle of backfill soil phi'

    Derived from the archetype scenario. Hidden at hard difficulty.

    15 – 45 degrees

  • Unit weight

    unit_weight_kn_m3

    Total (bulk) unit weight of backfill soil gamma

    Derived from the archetype scenario. Hidden at hard difficulty.

    15 – 22 kN/m3

Optional

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

3

  • Cohesion

    cohesion_kpa

    Effective cohesion of backfill soil c'

    Derived from the archetype scenario. Optional input.

    0 – 50 kPa

  • Surcharge

    surcharge_kpa

    Uniform surcharge pressure on the backfill surface q

    Optional input.

    0 – 30 kPa

  • Backfill slope deg

    backfill_slope_deg

    Backfill slope angle beta above horizontal

    Optional input.

    0 – 25 degrees

Scored outputs

6 outputs

Ka

ka

Active earth pressure coefficient Ka (dimensionless)

Scores if within ±3% of the reference value.

Kp

kp

Passive earth pressure coefficient Kp (dimensionless)

Scores if within ±3% of the reference value.

Active force

active_force_kn_per_m

Total active earth pressure force per unit wall length Pa (kN/m)

Scores if within ±3% of the reference value.

Passive force

passive_force_kn_per_m

Total passive earth pressure force per unit wall length Pp (kN/m)

Scores if within ±3% of the reference value.

Active moment knm per

active_moment_knm_per_m

Active overturning moment about the wall base Ma (kNm/m)

Scores if within ±3% of the reference value.

Water force

water_force_kn_per_m

Hydrostatic water force per unit wall length Pw (kN/m)

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

Cohesionless sand, no water table, no surcharge, horizontal backfill

Cohesion restricted to: 0

Surcharge restricted to: 0

Backfill slope deg restricted to: 0

medium

All inputs given

Surcharge and cohesion may be present, horizontal or sloping backfill, no water

hard

Some inputs hidden

Water table present, some soil parameters hidden; agent infers from site context

Hidden inputs

  • Friction angle degfriction_angle_deg
  • Unit weight kn m3unit_weight_kn_m3

Prompt replacement text

The retained 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
  • lateral-earth-pressure_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 retaining wall design and earth pressure analysis per Australian standards.2 3## Problem4 5Calculate the active and passive lateral earth pressure coefficients and forces acting on a retaining wall using Rankine theory. Determine the resultant forces, overturning moment, and hydrostatic water force where applicable.6 7## Given8 9| Parameter | Value | Unit |10|-----------|-------|------|11| Wall height (H) | {{ wall_height_m }} | m |12{% if friction_angle_deg is defined %}13| Effective friction angle (phi') | {{ 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 (gamma) | {{ unit_weight_kn_m3 }} | kN/m3 |20{% endif %}21{% if surcharge_kpa is defined %}22| Uniform surcharge (q) | {{ surcharge_kpa }} | kPa |23{% endif %}24{% if water_table_depth_m is defined %}25| Water table depth below ground surface | {{ water_table_depth_m }} | m |26{% endif %}27{% if backfill_slope_deg is defined %}28| Backfill slope angle (beta) | {{ backfill_slope_deg }} | degrees |29{% endif %}30{% if archetype_description is defined %}31 32### Site Conditions33 34{{ archetype_description }}35{% endif %}36 37{% if tool_available %}38## Available Tool39 40A lateral earth pressure calculation tool is available at `/workspace/{{ meta.name }}_calc.py`. Run it with:41 42```bash43python3 /workspace/{{ meta.name }}_calc.py --help44```45 46You may use this tool to verify your calculations or compute values directly.47{% endif %}48 49## Required50 51Calculate the following:52 531. Active earth pressure coefficient Ka542. Passive earth pressure coefficient Kp553. Total active earth pressure force per unit wall length Pa (kN/m)564. Total passive earth pressure force per unit wall length Pp (kN/m)575. Active overturning moment about the wall base Ma (kNm/m)586. Hydrostatic water force per unit wall length Pw (kN/m)59 60## Applicable Standards61 62- AS 4678 — Earth Retaining Structures63- Rankine, W.J.M. (1857) — On the Stability of Loose Earth64 65## Constraints66 67- No internet access is available. Work from engineering knowledge and the provided tool.68- Use **Rankine theory** for earth pressure coefficients:69 - Horizontal backfill: Ka = tan^2(45 - phi'/2), Kp = tan^2(45 + phi'/2)70 - Inclined backfill (slope beta): Ka = cos(beta) * (cos(beta) - sqrt(cos^2(beta) - cos^2(phi'))) / (cos(beta) + sqrt(cos^2(beta) - cos^2(phi')))71- **Active pressure at depth z:** sigma_a = Ka * gamma * z + Ka * q - 2c' * sqrt(Ka)72- **Passive pressure at depth z:** sigma_p = Kp * gamma * z + Kp * q + 2c' * sqrt(Kp)73- **Water table handling:**74 - Above the water table: use total (bulk) unit weight gamma75 - Below the water table: use effective (buoyant) unit weight gamma' = gamma - gamma_w76 - Hydrostatic water pressure acts independently: Pw = 0.5 * gamma_w * h_sub^2 (where h_sub = wall height below water table)77 - Water pressure is NOT multiplied by Ka; it acts equally in all directions (Pascal's law)78- **Total active force:** sum of effective earth pressure components over full wall height79- **Overturning moment:** sum of each active force component multiplied by its lever arm from the base, plus water force moment80- If total active force is negative (cohesion dominates), report Pa = 0 and Ma = 081- If no water table is specified or water table is at full wall height, report Pw = 082- Use gamma_w = 9.81 kN/m383- For phi' = 0 (purely cohesive soil): Ka = Kp = 1.084 85## Output Format86 87Show 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:88 89```json90{91 "ka": <numeric_value>,92 "kp": <numeric_value>,93 "active_force_kn_per_m": <numeric_value>,94 "passive_force_kn_per_m": <numeric_value>,95 "active_moment_knm_per_m": <numeric_value>,96 "water_force_kn_per_m": <numeric_value>97}98```99 100Write your complete solution to `/workspace/output.md`.101

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.

Loose sand dry

loose_sand_dry

Loose sand backfill, no water table

perth-coastal-retaining-wallgold-coast-canal-wall
Parameter ranges
friction_angle_deg
28 – 32
cohesion_kpa
0
unit_weight_kn_m3
16 – 18
water_table_depth_m
12

Medium dense sand dry

medium_dense_sand_dry

Medium dense sand backfill, no water table

sydney-harbour-foreshore-wallbrisbane-river-terrace
Parameter ranges
friction_angle_deg
32 – 36
cohesion_kpa
0
unit_weight_kn_m3
18 – 20
water_table_depth_m
12

Dense gravel fill

dense_gravel_fill

Dense gravel fill behind a cantilever wall

adelaide-quarry-haul-roadcairns-port-wharf-wall
Parameter ranges
friction_angle_deg
36 – 42
cohesion_kpa
0
unit_weight_kn_m3
19 – 21
water_table_depth_m
12

Silty sand with water

silty_sand_with_water

Silty sand backfill with elevated water table

darwin-stormwater-channel-walltownsville-coastal-revetment
Parameter ranges
friction_angle_deg
28 – 34
cohesion_kpa
0 – 5
unit_weight_kn_m3
18 – 20
water_table_depth_m
1 – 4

Stiff clay fill

stiff_clay_fill

Stiff clay backfill behind a gravity wall

melbourne-basalt-clay-wallcanberra-substation-retaining
Parameter ranges
friction_angle_deg
20 – 28
cohesion_kpa
10 – 40
unit_weight_kn_m3
18 – 21
water_table_depth_m
12

Example task

darwin-stormwater-channel-wall-silty-sand-with-water-preview — hard difficulty, some inputs hidden.

Silty sand backfill with elevated water table. darwin-stormwater-channel-wall. Required outputs: ka, kp, active_force_kn_per_m, passive_force_kn_per_m, active_moment_knm_per_m, water_force_kn_per_m

The model sees

Scenario context and visible inputs.

wall_height_m
1 to 12 m
cohesion_kpa
0 to 5 kPa
surcharge_kpa
0 kPa
water_table_depth_m
1 to 4 m
backfill_slope_deg
0 degrees

Executable tool: lateral-earth-pressure_calc.py

The model must infer

Inputs withheld at this difficulty.

  • Unit weight kn m3

    unit_weight_kn_m3

  • Friction angle deg

    friction_angle_deg

Stand-in text in the prompt

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

The model must produce

The scored JSON answer schema.

{
  "ka": <number>,
  "kp": <number>,
  "active_force_kn_per_m": <number>,
  "passive_force_kn_per_m": <number>,
  "active_moment_knm_per_m": <number>,
  "water_force_kn_per_m": <number>
}
  • ka · scored within ±3%
  • kp · scored within ±3%
  • active_force_kn_per_m · scored within ±3%
  • passive_force_kn_per_m · scored within ±3%
  • active_moment_knm_per_m · scored within ±3%
  • water_force_kn_per_m · scored within ±3%