Calculate geotechnical influence factors for vertical stress, bearing capacity, and immediate settlement from load, footing, soil, and depth inputs.

Influence Factor Calculator
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Influence Factors – Overview

This calculator provides three geotechnical influence-factor modes: (1) vertical stress beneath surface loads, (2) bearing-capacity influence factors (shape, depth, inclination), and (3) immediate settlement influence factor. Each tab below corresponds to a different formula set and output.

Vertical Stress Influence Factor (Boussinesq/Newmark)

Use this mode to compute the vertical stress at depth z due to a point load or a uniformly loaded circular area. Results are returned as an influence factor \(I_z\) and the vertical stress \(\sigma_z\).

Point Load

σz = Q Iz where Iz = (3 z³) / (2π (r² + z²)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
  • \(I_z\) is the dimensionless influence factor

Uniform Circular Area

σz = q Iz where 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
  • \(I_z\) is the dimensionless influence factor

Bearing-Capacity Influence Factors

This mode returns shape (\(s\)), depth (\(d\)), and inclination (\(i\)) influence factors along with bearing-capacity factors \(N_c, N_q, N_\gamma\), then computes ultimate bearing capacity \(q_{ult}\).

qᵤₗₜ = c Nc sc dc ic + q Nq sq dq iq + (1) / (2) γ B N_γ s_γ d_γ i_γ

Bearing-capacity factors (for \(\phi > 0\)):

Nq = eπ tanφ tan²(45^° + (φ) / (2)), Nc = (Nq - 1) / (tanφ), N_γ = 2 (Nq + 1) tanφ

Variables:

  • \(c\) is cohesion
  • \(\phi\) is friction angle
  • \(\gamma\) is unit weight
  • \(q = \gamma D_f\) is overburden at foundation level
  • \(B\) is footing width (use \(B/L\) for rectangles in shape factors)
  • \(s_\bullet, d_\bullet, i_\bullet\) are shape, depth, and inclination influence factors
  • \(q_{ult}\) is ultimate bearing capacity

Notes: The calculator applies common Meyerhof/Vesic-style corrections for shape, depth, and inclination and constrains values to typical ranges to avoid non-physical results.

Settlement Influence Factor

This mode computes immediate (elastic) settlement using an influence factor \(I_s\), footing size, net pressure, soil modulus, and Poisson’s ratio.

Sᵢ = (qₙ Beff) / (Eₛ) (1 - nu²) Iₛ

Variables:

  • \(S_i\) is immediate settlement
  • \(q_n\) is net foundation pressure
  • \(B_{\mathrm{eff}}\) is effective footing width (often \(\min(B,L)\) for rectangles)
  • \(E_s\) is soil elastic modulus
  • \(\nu\) is Poisson’s ratio
  • \(I_s\) is the settlement influence factor (varies with shape/rigidity)

How to Use the Calculator

  1. Select the tab that matches your problem (Vertical Stress, Bearing Capacity, or Settlement).
  2. Enter the required inputs shown on that tab.
  3. Click Calculate to view the influence factor(s) and results. Results persist on reload.

Assumptions: Elastic, homogeneous, isotropic soil for stress/settlement; conventional shallow-foundation theory for bearing capacity; no groundwater or time-dependent effects unless incorporated via inputs.