GEO-13

Terzaghi bearing capacity

q_ult = c Nc + γ D_f Nq + 0.5 γ B Nγ. The three-term strip foundation.

Reading speed

BearingTerzaghi 1943

Governing equation

q_{ult}=c N_c+\gamma D_f N_q+\tfrac12\gamma B N_\gamma

where

c': Cohesion (kPa)
N_c: Nc factor (—)
N_q: Nq factor (—)
N_\gamma: Nγ factor (—)
\gamma: Unit weight (kN/m³)
D_f: Embedment (m)
B: Width (m)
q_{ult}: 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-13 — Terzaghi bearing capacity) is the form associated with Terzaghi 1943. Working symbols: $c'$ , $N_c$ , $N_q$ , $N_\gamma$ , $\gamma$ , $D_f$ , $B$ $\rightarrow$ $q_{ult}$ . Prandtl's wedge plus overburden and self-weight. Nc, Nq, Nγ grow with φ′.

Purpose

Purpose: compute

q_{ult}

from

c'

N_c

N_q

N_\gamma

\gamma

D_f

B

in Geotechnical engineering via

q_{ult}=c N_c+\gamma D_f N_q+\tfrac12\gamma B N_\gamma

q_ult = c Nc + γ D_f Nq + 0.5 γ B Nγ. The three-term strip foundation. 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' = 10.000\,\mathrm{kPa}

N_c = 30.000\,\mathrm{—}

N_q = 18.000\,\mathrm{—}

N_\gamma = 15.000\,\mathrm{—}

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

D_f = 1.500\,\mathrm{m}

B = 2.000\,\mathrm{m}

, the governing relation

q_{ult}=c N_c+\gamma D_f N_q+\tfrac12\gamma B N_\gamma

yields

q_{ult} = 1056.0\,\mathrm{kPa}

. A strip footing, a plastic wedge, three capacity bars. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Cohesion c'10 kPaNc factor N_c30 —Nq factor N_q18 —Nγ factor N_\gamma15 —Unit weight \gamma18 kN/m³Embedment D_f1.5 mWidth B2 m

Outputs

Ultimate bearing q_{ult}1056.0 kPa

Reading speed

Watch on YouTube

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Narration of this film

A strip footing, a plastic wedge, three capacity bars.

Prandtl's wedge plus overburden and self-weight. Nc, Nq, Nγ grow with φ′.

Reading speed

Watch on YouTube