LIVEdataset aec-bench@releasetasks 552models 18disciplines 5last submission … · built …

groundwith-tool

Wall Bearing

Checks bearing pressure adequacy beneath a retaining wall base by computing the eccentricity of the resultant vertical load and applying Meyerhof's effective width method (B' = B - 2e). Compares the maximum bearing pressure on the reduced contact area against the allowable bearing capacity, using Meyerhof bearing capacity factors with depth corrections per AS 4678.

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

Standards

AS 4678 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

8 inputs

Always given

Included directly in every task prompt.

Base width
base_width_m
Base width of the retaining wall footing B
1 – 6 m
Total vertical load kn per m
total_vertical_load_kn_per_m
Total vertical load on wall base per metre run V
20 – 500 kN/m
Net moment knm per m
net_moment_knm_per_m
Net moment about base toe per metre run M
10 – 800 kN.m/m
Allowable bearing capacity
allowable_bearing_capacity_kpa
Allowable bearing capacity of the foundation soil q_all
50 – 600 kPa

Derived from scenario

Sampled from the scenario and inferable from its description.

Soil cohesion
soil_cohesion_kpa
Foundation soil effective cohesion c'
Derived from the archetype scenario. Hidden at hard difficulty.
0 – 150 kPa
Soil friction angle deg
soil_friction_angle_deg
Foundation soil effective friction angle phi'
Derived from the archetype scenario. Hidden at hard difficulty.
0 – 50 degrees
Soil unit weight
soil_unit_weight_kn_m3
Foundation 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.

Embedment depth
embedment_depth_m
Embedment depth of wall base below ground surface Df
Optional input.
0.3 – 3 m

Scored outputs

5 outputs

Eccentricity

eccentricity_m

Eccentricity of resultant from base centre e (m)

Scores if within ±3% of the reference value.

Effective width

effective_width_m

Meyerhof effective base width B' (m)

Scores if within ±3% of the reference value.

Max bearing pressure

max_bearing_pressure_kpa

Maximum bearing pressure q_max (kPa)

Scores if within ±3% of the reference value.

Ultimate bearing capacity

ultimate_bearing_capacity_kpa

Ultimate bearing capacity q_ult (kPa)

Scores if within ±5% of the reference value.

Factor of safety

factor_of_safety

Factor of safety against bearing failure 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

All parameters given, stiff soil, low eccentricity expected

medium

All inputs given

All parameters given, any soil type including soft clay

hard

Some inputs hidden

Soil parameters hidden, agent must infer from site description

Hidden inputs

Soil cohesionsoil_cohesion_kpa
Soil friction angle degsoil_friction_angle_deg
Soil unit weight kn m3soil_unit_weight_kn_m3

Prompt replacement text

The foundation 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
wall-bearing_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.2 3## Problem4 5Check the bearing pressure under a retaining wall base, accounting for eccentricity of the resultant vertical load using Meyerhof's effective width method.6 7## Given8 9| Parameter | Value | Unit |10|-----------|-------|------|11| Base width (B) | {{ base_width_m }} | m |12| Total vertical load (V) | {{ total_vertical_load_kn_per_m }} | kN/m |13| Net moment about toe (M) | {{ net_moment_knm_per_m }} | kN.m/m |14{% if soil_cohesion_kpa is defined %}15| Foundation soil cohesion (c') | {{ soil_cohesion_kpa }} | kPa |16{% endif %}17{% if soil_friction_angle_deg is defined %}18| Foundation soil friction angle (phi') | {{ soil_friction_angle_deg }} | degrees |19{% endif %}20{% if soil_unit_weight_kn_m3 is defined %}21| Foundation soil unit weight (gamma) | {{ soil_unit_weight_kn_m3 }} | kN/m³ |22{% endif %}23{% if embedment_depth_m is defined %}24| Embedment depth (Df) | {{ embedment_depth_m }} | m |25{% endif %}26| Allowable bearing capacity (q_all) | {{ allowable_bearing_capacity_kpa }} | kPa |27{% if archetype_description is defined %}28 29### Site Conditions30 31{{ archetype_description }}32{% endif %}33 34## Method35 36Use the following procedure to check bearing pressure under the wall base:37 38### Step 1 — Eccentricity39 40Calculate the eccentricity of the resultant from the base centre:41 42**e = B/2 - M/V**43 44where M is the net moment about the toe and V is the total vertical load.45 46### Step 2 — Effective Base Width (Meyerhof)47 48**B' = B - 2e**49 50This reduces the base width to account for the eccentric loading.51 52### Step 3 — Maximum Bearing Pressure53 54**q_max = V / B'**55 56This is the maximum bearing pressure on the effective footing area (strip footing per metre run).57 58### Step 4 — Ultimate Bearing Capacity59 60Calculate the ultimate bearing capacity using Meyerhof's equation for a strip footing on the effective width:61 62**q_ult = c' x Nc x dc + q x Nq x dq + 0.5 x gamma x B' x Ngamma x dgamma**63 64where q = gamma x Df (overburden pressure).65 66#### Bearing Capacity Factors (Meyerhof)67 68- N_q = exp(pi x tan(phi)) x tan^2(45 + phi/2)69- N_c = (N_q - 1) x cot(phi)  [N_c = 5.14 when phi = 0]70- N_gamma = (N_q - 1) x tan(1.4 x phi)71 72#### Depth Factors (K_p = tan^2(45 + phi/2))73 74- d_c = 1 + 0.2 x sqrt(K_p) x (Df/B')75- d_q = d_gamma = 1 + 0.1 x sqrt(K_p) x (Df/B') for phi > 10 degrees; otherwise d_q = d_gamma = 176 77### Step 5 — Factor of Safety78 79**FoS = q_all / q_max**80 81## Constraints82 83- No internet access is available. Work from engineering knowledge and the provided tool.84- Use Meyerhof's effective width method (B' = B - 2e) to handle eccentric loading.85- The wall base acts as a strip footing (shape factors = 1.0, inclination factors = 1.0).86- Use the Meyerhof bearing capacity factors and depth factors as specified above.87- For phi = 0 (undrained clay): Nc = 5.14, Nq = 1.0, Ngamma = 0.0.88- gamma_w = 9.81 kN/m³ (if needed).89 90{% if tool_available %}91## Available Tool92 93A calculation tool is available at `/workspace/{{ meta.name }}_calc.py`. Run it with:94 95```bash96python3 /workspace/{{ meta.name }}_calc.py --help97```98 99You may use this tool to verify your calculations or compute values directly.100{% endif %}101 102## Required103 104Calculate the following:105 1061. Eccentricity of the resultant e (m)1072. Effective base width B' (m)1083. Maximum bearing pressure q_max (kPa)1094. Ultimate bearing capacity q_ult (kPa)1105. Factor of safety against bearing failure FoS111 112## Output Format113 114Show 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:115 116```json117{118  "eccentricity_m": <numeric_value>,119  "effective_width_m": <numeric_value>,120  "max_bearing_pressure_kpa": <numeric_value>,121  "ultimate_bearing_capacity_kpa": <numeric_value>,122  "factor_of_safety": <numeric_value>123}124```125 126Write your complete solution to `/workspace/output.md`.127

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

soil_cohesion_kpa: 5 – 15
soil_friction_angle_deg: 0 – 5
soil_unit_weight_kn_m3: 15 – 17

Medium dense sand

medium_dense_sand

Medium dense sand

perth-coastalhunter-valley-alluvial

Parameter ranges

soil_cohesion_kpa: 0
soil_friction_angle_deg: 32 – 36
soil_unit_weight_kn_m3: 17 – 19

Stiff oc clay

stiff_oc_clay

Stiff overconsolidated clay

sydney-hawkesburyadelaide-stiffmelbourne-basalt

Parameter ranges

soil_cohesion_kpa: 50 – 150
soil_friction_angle_deg: 5 – 15
soil_unit_weight_kn_m3: 18 – 21

Dense sand

dense_sand

Dense sand

perth-coastalcairns-coral

Parameter ranges

soil_cohesion_kpa: 0
soil_friction_angle_deg: 36 – 42
soil_unit_weight_kn_m3: 19 – 21

Firm clay

firm_clay

Firm clay

brisbane-alluvialmelbourne-basalt

Parameter ranges

soil_cohesion_kpa: 20 – 50
soil_friction_angle_deg: 2 – 8
soil_unit_weight_kn_m3: 17 – 19

Example task

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

Soft normally consolidated clay. brisbane-alluvial. Required outputs: eccentricity_m, effective_width_m, max_bearing_pressure_kpa, ultimate_bearing_capacity_kpa, factor_of_safety

The model sees

Scenario context and visible inputs.

base_width_m: 1 to 6 m
total_vertical_load_kn_per_m: 20 to 500 kN/m
net_moment_knm_per_m: 10 to 800 kN.m/m
embedment_depth_m: 0.5 m
allowable_bearing_capacity_kpa: 200 kPa

Executable tool: wall-bearing_calc.py

The model must infer

Inputs withheld at this difficulty.

Soil unit weight kn m3
soil_unit_weight_kn_m3
Soil friction angle deg
soil_friction_angle_deg
Soil cohesion
soil_cohesion_kpa

Stand-in text in the prompt

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

The model must produce

The scored JSON answer schema.

{
  "eccentricity_m": <number>,
  "effective_width_m": <number>,
  "max_bearing_pressure_kpa": <number>,
  "ultimate_bearing_capacity_kpa": <number>,
  "factor_of_safety": <number>
}

eccentricity_m · scored within ±3%
effective_width_m · scored within ±3%
max_bearing_pressure_kpa · scored within ±3%
ultimate_bearing_capacity_kpa · scored within ±5%
factor_of_safety · scored within ±3%

Wall Bearing

How this task is generated

Template

Scenario

Difficulty tier

Task prompt

Parameters

Inputs

Scored outputs

Eccentricity

Effective width

Max bearing pressure

Ultimate bearing capacity

Factor of safety

Difficulty

easy

medium

hard

Task bundle

Scenario archetypes

Soft nc clay

Medium dense sand

Stiff oc clay

Dense sand

Firm clay

Example task

The model sees

The model must infer

The model must produce