GEO-28

Janbu constrained-modulus settlement

M = m pa (σ′/pa)^a, s = Δσ′ H / M. Nonlinear constrained modulus.

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SettlementJanbu

Governing equation

M=m\,p_a(\sigma'/p_a)^a,\quad s=\Delta\sigma' H/M

where

m: Modulus number (—)
a: Stress exponent (—)
\sigma': Effective stress (kPa)
\Delta\sigma': Stress increment (kPa)
H: Layer thickness (m)
M: Constrained modulus (kPa)
s: Settlement (mm)

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-28 — Janbu constrained-modulus settlement) is the form associated with Janbu. Working symbols: $m$ , $a$ , $\sigma'$ , $\Delta\sigma'$ , $H$ $\rightarrow$ $M$ , $s$ . Janbu's modulus number m and stress exponent a collapse oedometer curves onto a power law.

Purpose

Purpose: compute

M

s

from

m

a

\sigma'

\Delta\sigma'

H

in Geotechnical engineering via

M=m\,p_a(\sigma'/p_a)^a,\quad s=\Delta\sigma' H/M

M = m pa (σ′/pa)^a, s = Δσ′ H / M. Nonlinear constrained modulus. 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

m = 80.000\,\mathrm{—}

a = 0.500\,\mathrm{—}

\sigma' = 100.000\,\mathrm{kPa}

\Delta\sigma' = 40.000\,\mathrm{kPa}

H = 4.000\,\mathrm{m}

, the governing relation

M=m\,p_a(\sigma'/p_a)^a,\quad s=\Delta\sigma' H/M

yields

M = 8000\,\mathrm{kPa}

s = 20.0\,\mathrm{mm}

. A clay layer, a stress increment, a Janbu spring. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Modulus number m80 —Stress exponent a0.5 —Effective stress \sigma'100 kPaStress increment \Delta\sigma'40 kPaLayer thickness H4 m

Outputs

Constrained modulus M8000 kPa
Settlement s20.0 mm

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Narration of this film

A clay layer, a stress increment, a Janbu spring.

Janbu's modulus number m and stress exponent a collapse oedometer curves onto a power law.

Reading speed

Watch on YouTube