GEO-02

Meyerhof bearing with shape

Meyerhof extends Terzaghi with shape, depth and inclination factors.

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Bearing capacityMeyerhof 1963CFEM

Governing equation

q_u = c N_c s_c + \gamma D_f N_q s_q + \tfrac12 \gamma B N_\gamma s_\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 (—)
s_c: Shape sc (—)
s_q: Shape sq (—)
s_\gamma: Shape sγ (—)
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-02 — Meyerhof bearing with shape) is the form associated with Meyerhof 1963 · CFEM. Working symbols: $c$ , $\gamma$ , $D_f$ , $B$ , $N_c$ , $N_q$ , $N_\gamma$ , $s_c$ , $s_q$ , $s_\gamma$ $\rightarrow$ $q_u$ . Meyerhof's mechanism allows a log-spiral that reaches the ground surface; empirical sc, sq, sγ correct from strip to rectangle.

Purpose

Purpose: compute

q_u

from

c

\gamma

D_f

B

N_c

N_q

N_\gamma

s_c

s_q

s_\gamma

in Geotechnical engineering via

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

Meyerhof extends Terzaghi with shape, depth and inclination 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 = 20.000\,\mathrm{kPa}

\gamma = 19.000\,\mathrm{kN/m^{3}}

D_f = 1.200\,\mathrm{m}

B = 2.500\,\mathrm{m}

N_c = 20.000\,\mathrm{—}

N_q = 10.000\,\mathrm{—}

N_\gamma = 8.000\,\mathrm{—}

s_c = 1.200\,\mathrm{—}

s_q = 1.150\,\mathrm{—}

s_\gamma = 0.900\,\mathrm{—}

, the governing relation

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

yields

q_u = 913.200\,\mathrm{kPa}

. Vertical concentric load. Enter Nc, Nq, Nγ and shape factors. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Cohesion c20 kPaUnit weight \gamma19 kN/m³Embedment D_f1.2 mWidth B2.5 mFactor Nc N_c20 —Factor Nq N_q10 —Factor Nγ N_\gamma8 —Shape sc s_c1.2 —Shape sq s_q1.15 —Shape sγ s_\gamma0.9 —

Outputs

Ultimate bearing q_u913.200 kPa

Reading speed

Watch on YouTube

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Narration of this film

Vertical concentric load. Enter Nc, Nq, Nγ and shape factors.

Meyerhof's mechanism allows a log-spiral that reaches the ground surface; empirical sc, sq, sγ correct from strip to rectangle.

Reading speed

Watch on YouTube