GEO-23

Skempton undrained bearing

Nc = 5.14 (1+0.2 B/L)(1+0.2 Df/B) ≤ 9. qu = cu Nc + γ Df.

Reading speed

BearingSkempton 1951

Governing equation

N_c=5.14\,(1+0.2 B/L)(1+0.2 D_f/B)\le 9

where

c_u: Undrained strength (kPa)
B: Width (m)
L: Length (m)
D_f: Embedment (m)
\gamma: Unit weight (kN/m³)
N_c: Skempton Nc (—)
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-23 — Skempton undrained bearing) is the form associated with Skempton 1951. Working symbols: $c_u$ , $B$ , $L$ , $D_f$ , $\gamma$ $\rightarrow$ $N_c$ , $q_u$ . φu = 0 Prandtl value 5.14, raised by shape and embedment, capped at 9 for a deep square.

Purpose

Purpose: compute

N_c

q_u

from

c_u

B

L

D_f

\gamma

in Geotechnical engineering via

N_c=5.14\,(1+0.2 B/L)(1+0.2 D_f/B)\le 9

Nc = 5.14 (1+0.2 B/L)(1+0.2 Df/B) ≤ 9. qu = cu Nc + γ Df. 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_u = 40.000\,\mathrm{kPa}

B = 2.000\,\mathrm{m}

L = 2.000\,\mathrm{m}

D_f = 1.500\,\mathrm{m}

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

, the governing relation

N_c=5.14\,(1+0.2 B/L)(1+0.2 D_f/B)\le 9

yields

N_c = 7.09\,\mathrm{—}

q_u = 310.7\,\mathrm{kPa}

. A clay foundation, a plastic bulb, an Nc bar that saturates with depth. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Undrained strength c_u40 kPaWidth B2 mLength L2 mEmbedment D_f1.5 mUnit weight \gamma18 kN/m³

Outputs

Skempton Nc N_c7.09 —
Ultimate bearing q_u310.7 kPa

Reading speed

Watch on YouTube

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Narration of this film

A clay foundation, a plastic bulb, an Nc bar that saturates with depth.

φu = 0 Prandtl value 5.14, raised by shape and embedment, capped at 9 for a deep square.

Reading speed

Watch on YouTube