Effective stress

An introduction to effective stress

Krishna Kumar, kks32@cam.ac.uk

University of Nottingham, UK
8th March 2018

Objectives

Stresses in soil
Terzaghi’s principle of effective stress
Effective stresses - soil strength

Everyone is a geotechnical engineer!

Stresses in solid

Visualising stresses using a photoelastic material

Stresses in soil

A: Highly stressed region at particle contact

$$\sigma' = 1GPa $$

B: Low stress region on particle

$$\sigma' \approx 200 kPa$$

C: Void

$$\sigma' = ?$$

Stresses in soil

Average stress over a small region of say 10x10x10 grains, where solid (skeleton), and fluid (voids) co-exist at each "point".

Effective stress model

Total normal stress: $\sigma = F / A$

for equilibrium in the direction normal to XX

$$F = \sum N' + \mathit{u} A$$

$$F / A = \sum N' / A + \mathit{u}$$

i.e.,

$$\sigma =\sigma ' + \mathit{u}$$

Terzaghi's principle of effective stress (1923)

$$\sigma = \sigma' + u $$ Total stress = Effective stress + pore pressure

Visualising effective stresses in soil

source: simple shear in granular materials
https://www.youtube.com/watch?v=Z6rvdkI4T8I

Effective stresses in a sandcastle

Curved meniscii give negative pore-pressure, Total Stress is zero Effective Stress positive.

Strength of soil

Shear resistance of a soil is a function of effective stresses

If we look at soil at a micro-scale, there is usually nothing physically gluing the particles together, the particles are free to slide over each other under the actions of the stresses applied to them. Soil gets its strength from friction and interlocking between soil particles. If we look at two planes of spherical particles, as shown in figure, it can be seen that in order to shear along the slip-plane, we mobilise strength from sliding between particles (friction) and we must provide enough force to make the particles in the upper layer rise up over those in the lower layer (interlocking). Both of these forces are influenced by the stresses acting on the particles (effective stress), but not by the stresses acting within the fluid (pore pressure). The integral of the pore pressures acting on the curved surface of the particle will give an upwards force equal to the buoyancy of the particle and hence only the buoyant unit weight of the particles will lead to an increase in effective stress with depth. Pore pressure can, however, play a role in the strength of soils in that it can influence the value of the effective stress. If we consider the stress state on the surface of a sandcastle, then in the direction perpendicular to the surface there is no applied total stress. Fluid within the pores of the damp soil tends to concentrate at the particle contacts, as shown in Fig.3. The curved menisci on these small droplets of water cause the water to have a negative (gauge) pore-pressure. From Terzaghi’s formula, this then causes the effective stress to be positive and hence enough strength to be available for the sandcastle to stand. If extra water is added to the pores by the incoming tide, the pores fill, the menisci disappear and the fluid pressure returns to zero. The strength of the soil falls, the slopes become unstable and the sandcastle collapses.

Why do dogs dig shallow pits?

Summary

Effective stress represents the stresses carried by soil grains
The remainder of the stress is carried by the pore fluid
Effective stress, not total stress is what governs the behaviour of soils strength and stiffness
Capillary suction can influence soil's effective stresses
Effective stress increases with depth