GEO-01

Terzaghi ultimate bearing

Ultimate bearing of a shallow strip footing on c–φ soil.

Reading speed

Bearing capacityTerzaghi 1943Eurocode 7

Governing equation

q_u = c N_c + \gamma D_f N_q + \tfrac12 \gamma B N_\gamma

where

c: Cohesion (kPa)
\gamma: Unit weight (kN/m³)
D_f: Embedment (m)
B: Width (m)
N_c: Factor Nc (—)
N_q: Factor Nq (—)
N_\gamma: Factor Nγ (—)
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-01 — Terzaghi ultimate bearing) is the form associated with Terzaghi 1943 · Eurocode 7. Working symbols: $c$ , $\gamma$ , $D_f$ , $B$ , $N_c$ , $N_q$ , $N_\gamma$ $\rightarrow$ $q_u$ . Terzaghi superposed cohesion, surcharge and self-weight plastic zones with bearing factors Nc, Nq and Nγ derived from Prandtl-type mechanisms.

Purpose

Purpose: compute

q_u

from

c

\gamma

D_f

B

N_c

N_q

N_\gamma

in Geotechnical engineering via

q_u = c N_c + \gamma D_f N_q + \tfrac12 \gamma B N_\gamma

Ultimate bearing of a shallow strip footing on c–φ soil. 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 = 25.000\,\mathrm{kPa}

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

D_f = 1.500\,\mathrm{m}

B = 2.000\,\mathrm{m}

N_c = 17.700\,\mathrm{—}

N_q = 7.400\,\mathrm{—}

N_\gamma = 5.000\,\mathrm{—}

, the governing relation

q_u = c N_c + \gamma D_f N_q + \tfrac12 \gamma B N_\gamma

yields

q_u = 732.300\,\mathrm{kPa}

. Strip footing; enter chart Nc, Nq, Nγ. No shape or inclination factors. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Cohesion c25 kPaUnit weight \gamma18 kN/m³Embedment D_f1.5 mWidth B2 mFactor Nc N_c17.7 —Factor Nq N_q7.4 —Factor Nγ N_\gamma5 —

Outputs

Ultimate bearing q_u732.300 kPa

Reading speed

Watch on YouTube

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Narration of this film

Strip footing; enter chart Nc, Nq, Nγ. No shape or inclination factors.

Terzaghi superposed cohesion, surcharge and self-weight plastic zones with bearing factors Nc, Nq and Nγ derived from Prandtl-type mechanisms.

Reading speed

Watch on YouTube