Use this geological calculation for a transparent first-pass interpretation of measured rock, soil, fluid, well, stratigraphic, isotopic, geophysical, or seismic data under an explicitly selected model.

beta

Slope angle beta in degrees.

phi'

Effective friction angle phi' in degrees.

c' (kPa)

Effective cohesion c' in kilopascals.

gamma (kN/m³)

Bulk unit weight gamma in kN/m³.

z (m)

Vertical depth to the failure plane in metres.

ru

Pore water pressure ratio ru = u / (gamma * z).

Factor of safety of an infinite slope with a planar failure plane parallel to the slope at depth z: FS = (c' + gamma*z*cos^2(beta)*(1-ru)*tan(phi')) / (gamma*z*sin(beta)*cos(beta)). The tool evaluates the supplied inputs together and returns the named outputs below; it does not infer omitted operating conditions or change the units shown.^[1]

FS

Factor of safety against plane sliding.

• Geotechnical correlations and idealized failure models depend on stratigraphy, sampling disturbance, drainage, stress history, groundwater, density, anisotropy, scale, construction sequence, and laboratory or field method. Site-specific design requires investigation and code factors.
• Use finite inputs in the displayed units and preserve more precision than the final presentation requires. Independently verify safety-critical, financial, compliance, or production decisions.

Compare independent measurements and models, retain units and analytical metadata, propagate uncertainty, and validate interpretations against logs, cores, maps, laboratory data, or field observations.

• Slope Stability Factor Of Safety Bishop Calculator

  Bishop simplified method of slices with uniform slice width and pore pressure ratio ru: FS solves FS = sum[(c'b + W(1-ru)tan(phi'))/m_alpha] / sum[W sin(alpha)] with m_alpha = cos(alpha) + tan(phi')sin(alpha)/FS.

• Bearing Capacity Terzaghi Calculator

  Ultimate bearing capacity of a shallow strip footing qu = c*Nc + q*Nq + 0.5*gamma*B*Ngamma. Factors: Nq = exp(pi*tan(phi))*tan^2(45 + phi/2), Nc = (Nq - 1)*cot(phi), Ngamma = 2*(Nq + 1)*tan(phi) (Vesic convention for Ngamma; Terzaghi's original third factor differs). Base equation without shape or depth corrections. c and q in kPa, gamma in kN/m3, B in m.

• Bearing Capacity Vesic Calculator

  Ultimate bearing capacity with Vesic (1973) shape and depth factors: qu = c*Nc*sc*dc + q*sq*dq + 0.5*gamma*B*Ngamma*sGamma, dGamma = 1. Factors Nq = exp(pi*tan(phi))*tan^2(45 + phi/2), Nc = (Nq - 1)*cot(phi), Ngamma = 2*(Nq + 1)*tan(phi) (Vesic convention). Shape factors sc = 1 + (B/L)*(Nq/Nc), sq = 1 + (B/L)*tan(phi), sGamma = 1 - 0.4*B/L; depth factors dq = 1 + 2*tan(phi)*(1 - sin(phi))^2*Df/B and dc = dq - (1 - dq)/(Nc*tan(phi)). c and q in kPa, gamma in kN/m3, lengths in m.