Slope Stability — Infinite Slope Method mechanism

Model scope

The stated formula is a valid simplified infinite-slope factor-of-safety equation under the listed assumptions. The specification cannot receive PASS until gamma_w, the exact definitions of z and m, and the effective-stress meaning of c and phi are made explicit. The honest label is directionally correct but should also state the homogeneous-soil, planar-failure, steady-groundwater, and effective-stress assumptions.

• The formula is standard only when z is the vertical depth above the failure plane and m is the ratio of saturated vertical depth to total vertical depth, with 0 <= m <= 1; neither definition is specified.
• The formula uses gamma_w, but gamma_w is missing from the declared inputs. The specification must state that gamma_w is fixed at approximately 9.81 kN/m^3 or add it as an input.
• c and phi must be effective-stress parameters c' and phi' for the pore-pressure correction to be physically consistent; this is not stated.

Units and conventions

• beta and phi are angles in degrees in the user interface and must be converted to radians before JavaScript trigonometric functions are called.
• c and gamma*z must use consistent stress units, such as c in kPa and gamma in kN/m^3 with z in m.
• gamma and gamma_w must use the same unit system, such as kN/m^3.
• z is assumed to be vertical soil depth, not depth measured normal to the slope.
• m is assumed dimensionless and represents the saturated vertical-depth ratio above the failure plane.
• The standard water unit weight gamma_w = 9.81 kN/m^3 is used in the numerical examples.

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "beta_deg": 45,
    "phi_deg": 45,
    "c_kPa": 10,
    "gamma_kN_per_m3": 18,
    "gamma_w_kN_per_m3": 9.81,
    "z_m": 2,
    "m": 0.5
  },
  "expected_outputs": {
    "FS": 1.28305556
  },
  "working": "Convert angles: beta = 45 degrees, phi = 45 degrees; sin(beta) = 0.70710678, cos(beta) = 0.70710678, cos^2(beta) = 0.5, tan(phi) = 1. Effective unit weight term = gamma - gamma_w*m = 18 - 9.81*0.5 = 13.095 kN/m^3. Numerator = c + (gamma - gamma_w*m)*z*cos^2(beta)*tan(phi) = 10 + 13.095*2*0.5*1 = 23.095 kPa. Denominator = gamma*z*sin(beta)*cos(beta) = 18*2*0.70710678*0.70710678 = 18 kPa. FS = 23.095/18 = 1.28305556."
}

Failure boundary

BREAK_CLAIMED · SELF_FLAGGED

The formula is undefined at phi=90° because tan(phi) requires division by cos(phi)=0; an implementation that returns a numeric FS instead of rejecting the input is broken. A second hazard is the undocumented interpretation of signed beta, which can produce a misleading negative factor of safety.

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