Retaining Wall — Rankine Active/Passive Earth Pressure mechanism

Model scope

Core Rankine coefficient formulas and the self-weight resultant formula are correct under the stated simplified cohesionless assumptions. The specification declares a surcharge input and outputs resultant location but supplies neither the surcharge formula nor the location calculation, so the instrument cannot be verified as fully specified. The honest-label limitation is appropriate but should also mention the wall/backfill assumptions and that passive pressure requires movement for mobilization.

• Ka=tan²(45−φ/2) and Kp=tan²(45+φ/2) are standard Rankine coefficients only for a vertical wall, level backfill, smooth wall face with wall friction δ=0, and appropriate drained cohesionless soil conditions.
• P=½KγH² is the resultant from soil self-weight only. It does not include the declared surcharge input.
• The surcharge contribution is unspecified. Under the usual uniform-surcharge extension, pressure is Kq throughout the wall height and resultant surcharge force is KqH, but this formula is absent from the specification.
• The claimed active/passive pressure outputs are ambiguous: pressure should be identified as a depth-dependent distribution p(z)=Kγz, with base pressure KγH, rather than a single unspecified pressure.
• Resultant location is not given by the formula. For soil self-weight alone it is H/3 above the base; with surcharge it shifts and requires a moment calculation.
• Passive earth pressure is not generally fully mobilized without sufficient wall movement; the label should state that the result is the theoretical Rankine passive value, not necessarily the design resistance.

Units and conventions

• φ is an angle in degrees in the displayed trigonometric formulas; the implementation must convert degrees to radians if using standard JavaScript trigonometric functions.
• γ is unit weight, such as kN/m³ or lb/ft³; H must use the corresponding length unit.
• P is force per unit wall length, such as kN/m or lb/ft, because the wall length into the page is implicitly one unit.
• Pressure is force per area, such as kPa or lb/ft².
• If surcharge q is used, it must be a uniform vertical surcharge in pressure units compatible with γH, such as kPa or lb/ft².
• The test vectors use the conventional uniform-surcharge extension p_q=Kq, P_q=KqH only where explicitly noted.

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "phi_deg": 30,
    "gamma_kN_per_m3": 18,
    "H_m": 6,
    "surcharge_kPa": 0
  },
  "expected_outputs": {
    "Ka": 0.3333333333,
    "Kp": 3,
    "active_base_pressure_kPa": 36,
    "passive_base_pressure_kPa": 324,
    "active_resultant_kN_per_m": 108,
    "passive_resultant_kN_per_m": 972,
    "active_location_m_above_base": 2,
    "passive_location_m_above_base": 2
  },
  "working": "φ/2=15°. Ka=tan²(45°−15°)=tan²30°=(1/√3)²=1/3. Kp=tan²(45°+15°)=tan²60°=3. Active base pressure=KaγH=(1/3)(18)(6)=36 kPa. Passive base pressure=KpγH=(3)(18)(6)=324 kPa. Active resultant=½KaγH²=½(1/3)(18)(6²)=½(1/3)(18)(36)=108 kN/m. Passive resultant=½(3)(18)(36)=972 kN/m. Each soil-pressure diagram is triangular, so location=H/3=6/3=2 m above the base."
}

Failure boundary

BREAK_CLAIMED · SELF_FLAGGED

The phi=90 degree input causes tan(90 degrees) to divide by zero, making Kp, passive pressure, and passive resultant undefined. The branch-switch vector also exposes arithmetic consistency requirements: the correct passive base pressure for phi=30 degrees, gamma=18 kN/m^3, and H=6 m is 324 kPa, and the correct passive resultant is 972 kN/m.

Other records

Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

• VERIFIED_LEDGER.json
• evidence-tranche5/tranche5-results.json
• BOUNDARY_HAZARD_CATALOG.json