GEO-03

Vesić bearing capacity

Vesić rigidity-based bearing with compressibility factors.

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Bearing capacityVesić 1973API RP 2GEO

Governing equation

q_u = c N_c \zeta_c + q N_q \zeta_q + \tfrac12 \gamma B N_\gamma \zeta_\gamma

where

c: Cohesion (kPa)
q: Surcharge γDf (kPa)
\gamma: Unit weight (kN/m³)
B: Width (m)
N_c: Factor Nc (—)
N_q: Factor Nq (—)
N_\gamma: Factor Nγ (—)
\zeta_c: Modifier ζc (—)
\zeta_q: Modifier ζq (—)
\zeta_\gamma: Modifier ζγ (—)
q_u: Ultimate bearing (kPa)

Lecture brief

Historical brief

Soil mechanics became a quantitative laboratory after Karl von Terzaghi’s 1925–1943 work on effective stress, consolidation and bearing. These sheets still size shallow foundations, retaining walls, piles and drainage in SI. This sheet (GEO-03 — Vesić bearing capacity) is the form associated with Vesić 1973 · API RP 2GEO. Working symbols: $c$ , $q$ , $\gamma$ , $B$ , $N_c$ , $N_q$ , $N_\gamma$ , $\zeta_c$ , $\zeta_q$ , $\zeta_\gamma$ $\rightarrow$ $q_u$ . Vesić related the plastic zone to a rigidity index Ir = G / (c + σ tan φ) and reduced Nγ for compressible soils.

Purpose

Purpose: compute

q_u

from

c

q

\gamma

B

N_c

N_q

N_\gamma

\zeta_c

\zeta_q

\zeta_\gamma

in Geotechnical engineering via

q_u = c N_c \zeta_c + q N_q \zeta_q + \tfrac12 \gamma B N_\gamma \zeta_\gamma

Vesić rigidity-based bearing with compressibility factors. Use it when a real geotechnical engineering question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

c = 15.000\,\mathrm{kPa}

q = 30.000\,\mathrm{kPa}

\gamma = 18.000\,\mathrm{kN/m^{3}}

B = 3.000\,\mathrm{m}

N_c = 25.000\,\mathrm{—}

N_q = 12.000\,\mathrm{—}

N_\gamma = 10.000\,\mathrm{—}

\zeta_c = 1.100\,\mathrm{—}

\zeta_q = 1.100\,\mathrm{—}

\zeta_\gamma = 0.850\,\mathrm{—}

, the governing relation

q_u = c N_c \zeta_c + q N_q \zeta_q + \tfrac12 \gamma B N_\gamma \zeta_\gamma

yields

q_u = 1038.000\,\mathrm{kPa}

. Enter bearing factors already including rigidity reduction, or set them from charts. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Cohesion c15 kPaSurcharge γDf q30 kPaUnit weight \gamma18 kN/m³Width B3 mFactor Nc N_c25 —Factor Nq N_q12 —Factor Nγ N_\gamma10 —Modifier ζc \zeta_c1.1 —Modifier ζq \zeta_q1.1 —Modifier ζγ \zeta_\gamma0.85 —

Outputs

Ultimate bearing q_u1038.000 kPa

Reading speed

Watch on YouTube

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Narration of this film

Enter bearing factors already including rigidity reduction, or set them from charts.

Vesić related the plastic zone to a rigidity index Ir = G / (c + σ tan φ) and reduced Nγ for compressible soils.

Reading speed

Watch on YouTube