GEO-37

Vesic rigidity index Ir

Ir = G / (c + σ′ tan φ′). Rigid if Ir > I_r,crit, otherwise a compressibility correction.

Reading speed

BearingVesic Ir

Governing equation

I_r=\dfrac{G}{c+\sigma'\tan\varphi'}

where

G: Shear modulus (MPa)
c': Cohesion (kPa)
\sigma': Mean effective (kPa)
\varphi': Friction angle (°)
I_r: Rigidity index (—)

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-37 — Vesic rigidity index Ir) is the form associated with Vesic Ir. Working symbols: $G$ , $c'$ , $\sigma'$ , $\varphi'$ $\rightarrow$ $I_r$ . Vesic compared the elastic stiffness to the strength on the failure envelope. Soft soils need ξc, ξq, ξγ < 1.

Purpose

Purpose: compute

I_r

from

G

c'

\sigma'

\varphi'

in Geotechnical engineering via

I_r=\dfrac{G}{c+\sigma'\tan\varphi'}

Ir = G / (c + σ′ tan φ′). Rigid if Ir > I_r,crit, otherwise a compressibility correction. 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

G = 12.000\,\mathrm{MPa}

c' = 10.000\,\mathrm{kPa}

\sigma' = 80.000\,\mathrm{kPa}

\varphi' = 28.000\,\mathrm{^{\circ}}

, the governing relation

I_r=\dfrac{G}{c+\sigma'\tan\varphi'}

yields

I_r = 228.4\,\mathrm{—}

. A shear modulus, a strength, a dimensionless rigidity. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Shear modulus G12 MPaCohesion c'10 kPaMean effective \sigma'80 kPaFriction angle \varphi'28 °

Outputs

Rigidity index I_r228.4 —

Reading speed

Watch on YouTube

Free library

Full library

Free PDF / open book

YouTube channels

00:0 / 00:08

Narration of this film

A shear modulus, a strength, a dimensionless rigidity.

Vesic compared the elastic stiffness to the strength on the failure envelope. Soft soils need ξc, ξq, ξγ < 1.

Reading speed

Watch on YouTube