The rate of flow in impervious soils is very slow and compression occurs gradually. The pore water pressure decreases as water escapes from the soil network. The dissipation of pore water pressure transfers the load to the soil skeleton in the form of inter-granular pressure, which is successful in causing compressive deformation of the soil mass. As a consequence, inter-granular pressure is referred to as effective stress concept.
Applied or absolute stress refers to the externally applied strain. The soil network undergoes compression only after it shares the external load, in the form of effective stress. Efficient stress equation is a time-dependent relationship.
Note : Notation σ’ is used for effective stress
Effective Stress Concept Explained
Consider a wavy surface Y – Y that passes through the points of contact without cutting through the particles in a saturated soil. The stress level at the contact points is so high that the points of contact yield or crush, resulting in small contact areas.
As a result, the natural and tangential forces at the contact points are dispersed around the contact areas. When the wavy surface is projected on a horizontal (or vertical) plane, the total area A is made up of the contact area, Am, and the water area, Aw, which add up to form the vertical portion V. The contact area Am is very small in comparison to the total cross-section A, as can be seen.
As shown in the figure horizontal plane in as saturated soil can be calculates as :
Here,
σ = total stress or avg. applied stress
N = total force carried by particles at contact
Aw = area of plane passing through water
A = total projected area (Am+Aw)
u = pore water pressure (= Uw, for saturated soil)
But the contact area is very small, hence
In general σ’= N/A is stress carried by particles at contact and is known as effective stress. It is stress calculated on the basis of total area A and not on the contact area Am.
The applied or total stress, σ is known from the external loading and pore water pressure can be actually measured or determined.
Effective Stress (σ’) is computed as :
Karl Terzaghi was the first to propose this effective stress definition. In soil mechanics, this is a critical concept. Effective stresses affect a number of properties, including volume change, shearing strength, permeability and compressibility.
To summarise, the efficient stress theory is as follows :
- Total stress minus pore pressure equals effective stress.
- The shearing strength of soil is regulated by effective stress.
- Soil volume shift is governed by effective stress.
Importance of Effective Stress Principle
In Geo-technical problems, the definition of effective stress is extremely important. Stress applied to soils cannot create instantaneous strains as it does in steel or concrete.
When an external load is applied to a saturated soil, pore pressure is produced, which is then dissipated and converted into inter-granular or effective pressure with a specific time lag. The rate of dissipation is determined by the soil type.
Pore pressure issues are more extreme in clayey soils than they are in sandy soils.
Shock loading and vibration can cause pore pressure to build in sandy soils, resulting in liquefaction problems. Under impact loading, liquefaction refers to the transformation of a saturated fine sand or silt into a fluid mass due to the loss of particle contacts.
Efficient stress affects shear strength and volume changes in soils. There will be no improvement in volume if total stress and pore pressure rose at the same rate (Δσ = Δu).
Increased effective stress, on the other hand, allows soil particles to compact more densely. As a consequence, efficient stresses must be used in stability assessments and settlement computations.
In the production of effective stress, the rate of shearing is a significant factor.
Earth system failures are normally gradual, taking months or even years to occur. Pore pressures may not play a significant role in such circumstances. Base loading on a soft clay, on the other hand, causes pore pressure and low drainage.