GEO-27

Pile β effective-stress friction

Qs = β σ′v As with β = K tan δ. Sand and drained clay.

Reading speed

PilesBurland β

Governing equation

Q_s=\beta\sigma'_v A_s,\quad \beta=K\tan\delta

where

K: Earth-pressure K (—)
\delta: Interface friction (°)
\sigma'_v: Mean effective overburden (kPa)
D: Diameter (m)
L: Embedded length (m)
\beta: β factor (—)
Q_s: Shaft resistance (kN)

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-27 — Pile β effective-stress friction) is the form associated with Burland β. Working symbols: $K$ , $\delta$ , $\sigma'_v$ , $D$ , $L$ $\rightarrow$ $\beta$ , $Q_s$ . Effective radial stress K σ′v times interface tan δ. K often (1−sin φ′) to Kp/3.

Purpose

Purpose: compute

\beta

Q_s

from

K

\delta

\sigma'_v

D

L

in Geotechnical engineering via

Q_s=\beta\sigma'_v A_s,\quad \beta=K\tan\delta

Qs = β σ′v As with β = K tan δ. Sand and drained clay. 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

K = 0.500\,\mathrm{—}

\delta = 24.000\,\mathrm{^{\circ}}

\sigma'_v = 120.000\,\mathrm{kPa}

D = 0.500\,\mathrm{m}

L = 15.000\,\mathrm{m}

, the governing relation

Q_s=\beta\sigma'_v A_s,\quad \beta=K\tan\delta

yields

\beta = 0.223\,\mathrm{—}

Q_s = 629.4\,\mathrm{kN}

. A pile in sand, an effective overburden, a β arrow. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Earth-pressure K K0.5 —Interface friction \delta24 °Mean effective overburden \sigma'_v120 kPaDiameter D0.5 mEmbedded length L15 m

Outputs

β factor \beta0.223 —
Shaft resistance Q_s629.4 kN

Reading speed

Watch on YouTube

Free library

Full library

Free PDF / open book

YouTube channels

00:0 / 00:08

Narration of this film

A pile in sand, an effective overburden, a β arrow.

Effective radial stress K σ′v times interface tan δ. K often (1−sin φ′) to Kp/3.

Reading speed

Watch on YouTube