Calculate the stress increase in soil from an applied pressure and influence factor (Δσ = qI), or solve for the influence factor or the applied pressure.

Dimensionless factor read from a chart or table for your load shape and depth, e.g. Newmark or Fadum charts.

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Influence Factors – Overview

The calculator solves the pressure relation Δσ = qI and its two inverses. The following geotechnical formulas provide reference context only. Point-load stress, bearing-capacity corrections and settlement are separate models and are not calculated by this widget.

Vertical Stress Influence Factor (Boussinesq/Newmark)

For an elastic homogeneous isotropic half-space, the following reference relations describe vertical stress from a point load or beneath the center of a uniformly loaded circle. Geometry must be used to obtain the appropriate coefficient separately.

Point Load

σz = (Q / z2) Iz
Iz = (3 / (2π)) [1 + (r / z)2]−5/2

Variables:

  • Q is the point load (force)
  • z is the depth below the load
  • r is the radial distance from the load’s axis
  • Iz is the dimensionless influence factor

Uniform Circular Area

σz = q Iz
Iz = 1 − [1 + (a / z)2]−3/2

Variables:

  • q is the uniform surface pressure
  • a is the radius of the loaded area
  • z is the depth below the center of the area
  • Iz is the dimensionless influence factor

Bearing-Capacity Influence Factors

The following general bearing-capacity expression is reference material. Its shape, depth and inclination corrections require a specified compatible method; this calculator does not select those corrections or compute ultimate bearing capacity.

qult = c Nc sc dc ic
+ q Nq sq dq iq
+ ½ γ B Nγ sγ dγ iγ

Bearing-capacity factors (for φ > 0):

Nq = eπ tan φ tan2(45° + φ / 2)
Nc = (Nq − 1) / tan φ
Nγ = 2 (Nq + 1) tan φ

Variables:

  • c is cohesion
  • φ is friction angle
  • γ is unit weight
  • q = γ Df is overburden at foundation level
  • B is footing width (use B/L for rectangles in shape factors)
  • s•, d•, i• are shape, depth, and inclination influence factors
  • qult is ultimate bearing capacity

Notes: The displayed Nγ expression matches FHWA GEC6 Equation 5-8. Shape, depth and inclination corrections are not supplied or automatically constrained here. Do not mix correction sets or infer design acceptance from an entered factor.

Settlement Influence Factor

The following elastic-settlement expression is reference material only. Its settlement coefficient is method-specific and is not interchangeable with the vertical-stress coefficient in the widget; settlement is not computed here.

Si = (qn Beff / Es) (1 − ν2) Is

Variables:

  • Si is immediate settlement
  • qn is net foundation pressure
  • Beff is effective footing width (often min(B,L) for rectangles)
  • Es is soil elastic modulus
  • ν is Poisson’s ratio
  • Is is the settlement influence factor (varies with shape/rigidity)

How to Use the Calculator

  1. Select Induced stress, Influence factor or Applied pressure from the solve menu.
  2. Enter the two known values. Pressure and stress units may differ; the factor must be dimensionless.
  3. Select Calculate to solve the selected value. The last successful result is saved in this browser; changed inputs mark it as needing recalculation.

Scope: The widget performs entered-coefficient pressure arithmetic. The reference soil models have additional assumptions, including elastic half-space idealizations for stress and settlement. Soil layering, groundwater, time effects, factor selection and safe foundation design require separate assessment.