Principle of Effective Stress Study Notes for Civil Engineering

The article contains fundamental notes on "Principle of Effective Stress" topic of "Soil Mechanics & Foundation Engineering" subject. Also useful for the preparation of various upcoming exams like GATE Civil Engineering(CE) 2018/ IES/ BARC/ ISRO/ VIZAG/ DMRC/ SSC-JE 2017/State Engineering Services exams and other important upcoming competitive exams.

Principle of Effective Stress

Stresses in the Ground

Total Stress

When a load is applied to soil, it is carried by the solid grains and the water in the pores. The total vertical stress acting at a point below the ground surface is due to the weight of everything that lies above, including soil, water, and surface loading. Total stress thus increases with depth and with unit weight.

Vertical total stress at depth z, σ_v = γ.Z

Below a water body, the total stress is the sum of the weight of the soil up to the surface and the weight of water above this. σ_v = γ.Z + γ_w.Z_w

_{The total stress may also be denoted by} σ_z_{or just σ. It varies with changes in water level and with excavation.}

2. Pore Water Pressure

The pressure of water in the pores of the soil is called pore water pressure (u). The magnitude of pore water pressure depends on:

the depth below the water table.
the conditions of seepage flow.

Under hydrostatic conditions, no water flow takes place, and the pore pressure at a given point is given by
u = γ_w.h

where h = depth below water table or overlying water surface

It is convenient to think of pore water pressure as the pressure exerted by a column of water in an imaginary standpipe inserted at the given point.

The natural level of groundwater is called the water table or the phreatic surface. Under conditions of no seepage flow, the water table is horizontal. The magnitude of the pore water pressure at the water table is zero. Below the water table, pore water pressures are positive.

Principle of Effective Stress

The principle of effective stress was enunciated by Karl Terzaghi in the year 1936. This principle is valid only for saturated soils, and consists of two parts:

1. At any point in a soil mass, the effective stress (represented by or s' ) is related to total stress (s) and pore water pressure (u) as

= σ - u

Both the total stress and pore water pressure can be measured at any point.

2. All measurable effects of a change of stress, such as compression and a change of shearing resistance, are exclusively due to changes in effective stress.

Compression =
Shear Strength =

In a saturated soil system, as the voids are completely filled with water, the pore water pressure acts equally in all directions.
The effective stress is not the exact contact stress between particles but the distribution of load carried by the soil particles over the area considered. It cannot be measured and can only be computed.
If the total stress is increased due to additional load applied to the soil, the pore water pressure initially increases to counteract the additional stress. This increase in pressure within the pores might cause water to drain out of the soil mass, and the load is transferred to the solid grains. This will lead to the increase of effective stress.

Effective Stress in Unsaturated Zone

Above the water table, when the soil is saturated, pore pressure will be negative (less than atmospheric). The height above the water table to which the soil is saturated is called the capillary rise, and this depends on the grain size and the size of pores. In coarse soils, the capillary rise is very small.

Between the top of the saturated zone and the ground surface, the soil is partially saturated, with a consequent reduction in unit weight. The pore pressure in a partially saturated soil consists of two components:
Pore water pressure = u_w
Pore air pressure = u_a

Effective Stress Under Hydrodynamic Conditions

There is a change in pore water pressure in conditions of seepage flow within the ground. Consider seepage occurring between two points P and Q. The potential driving the water flow is the hydraulic gradient between the two points, which is equal to the head drop per unit length. In steady state seepage, the gradient remains constant.

Hydraulic gradient from P to Q, i = dh/ds
As water percolates through soil, it exerts a drag on soil particles it comes in contact with. Depending on the flow direction, either downward of upward, the drag either increases or decreases inter-particle contact forces.
A downward flow increases effective stress.
In contrast, an upward flow opposes the force of gravity and can even cause to counteract completely the contact forces. In such a situation, effective stress is reduced to zero and the soil behaves like a very viscous liquid. Such a state is known as quick sand condition. In nature, this condition is usually observed in coarse silt or fine sand subject to artesian conditions.

At the bottom of the soil column,

During quick sand condition, the effective stress is reduced to zero.

where i_cr = critical hydraulic gradient

This shows that when water flows upward under a hydraulic gradient of about 1, it completely neutralizes the force on account of the weight of particles, and thus leaves the particles suspended in water.

Importance of Effective Stress

At any point within the soil mass, the magnitudes of both total stress and pore water pressure are dependent on the groundwater position. With a shift in the water table due to seasonal fluctuations, there is a resulting change in the distribution in pore water pressure with depth.
Changes in water level below ground result in changes in effective stresses below the water table. A rise increases the pore water pressure at all elevations thus causing a decrease in effective stress. In contrast, a fall in the water table produces an increase in the effective stress.
Changes in water level above ground do not cause changes in effective stresses in the ground below. A rise above ground surface increases both the total stress and the pore water pressure by the same amount, and consequently, effective stress is not altered.

In some analyses, it is better to work with the changes of quantity, rather than in absolute quantities. The effective stress expression then becomes:

Ds´ = Ds - Du

If both total stress and pore water pressure change by the same amount, the effective stress remains constant.

*****

Next Topic - Darcy's Law and 1D-Permeability

For detailed schedule of GATE Civil Engineering(CE) 2018 Champion Study Plan, Click here

GATE Civil Engineering(CE) 2018 Champion Study Plan

To help you with your preparation for GATE 2018 Exam, gradeup has launched 2018 GATE Online Test Series based on the latest pattern and level of GATE exam with in-built virtual calculator.

Details about 2018 GATE Online Test Series

GATE 2018 Civil Engineering Syllabus, Download PDF!

Thanks,
Team gradeup

" Download Gradeup, Best GATE exam app for Preparation"