6.1 Introduction • Soil is a multi phase system (consisting of solids and voids filled with air and water) • To perform any kind of analysis - we must understand stress distribution where the

effective stress principle is probably the most important concept in geotechnical engineering. • The compressibility and shearing resistance of a soil depend to a great extent on the

effective stress.

Chapter Six In Situ Stresses

6.2 Stresses in Saturated Soil without Seepage

The total stress due to an applied vertical load on the soil mass is equal to:

σv = σ’v + u σ’v: effective stress or the stress carried by the soil grains σv: total stress u: pore water pressure

6.2.1 The Pore Water Pressure

6.2.2 the total stress

The total stress at the elevation of point A (in the following figure) can be obtained from the saturated unit weight of the soil and the unit weight of water above it. Thus,

6.2.3 The Effective Stress

To calculate the effective stress: 1. Draw soil profile

2. Calculate total stress 3. Calculate pore water pressure 4. Deduce effective stress

Checking the values at B

σ ′ =σ − u • σv(B) = H1 γw +H2γsat

• u = (H1+H2) γw

Thus, σ'v(B) = H1 γw +H2γsat -(H1+H2) γw = H2(γsat – γw)= H2γ’

Example A soil profile is shown in the following figure, calculate the total stress, pore water pressure, and effective stress at points A, B and C

6.3 Relationship between Horizontal and Vertical Stress The horizontal stress component can be expressed as :

σ’h= Κο . σ’v Where Ko is the coefficient of lateral earth pressure at rest Ko is constant for the same soil layer and unit weight.

6.4 Stresses due to Flow 1- Stresses in Saturated Soil with Upward Seepage

Checking the values at C:

Note that h/H2 is the hydraulic gradient i caused by the flow, thus

Decrease of stresses due to upward seepage

If the rate of seepage and thereby the hydraulic gradient gradually are increased, a limiting condition will be reached, at which point:

Under such a situation, soil stability is lost. This situation generally is referred to as boiling, or a quick condition.

In general For upward flow in granular soils:

If i > ic, the effective stresses is negative. i.e., no inter-granular contact & thus failure.

Checking the values at C

Increase of stresses due to downward seepage

The hydraulic gradient is : i = h/H2

2- Stresses in Saturated Soil with downward Seepage

6.5 Capillary Rise in Soils Water may rise above ground water table due to surface tension known as capillary

action

In soils, the pores in the soil mass can be considered as capillary tubes.

the height of capillary rise is inversely proportional to the diameter of the capillary tube (i.e. the voids in the soils)

Since the voids in soils are about the same size as the size of the particles, capillary rise will be bigger for fine‐grained soils (that is clay)

The pressure at any point in the Capillary tube above the free water surface will be negative with respect to atmospheric pressure, and the magnitude may be given

by hcγw

If Capillary zone is fully saturated, the pore water pressure at any point in the capillary zone is negative and equal to u = ‐hγw (h being the height of the point above the water table.)

If Capillary zone is partially saturated, the pore water pressure at any point in the

capillary zone is also negative and equal to (S being the degree of saturation in percent)

Effective Stress in Capillary zone is large because the pore water pressure is negative.

However, in design, the negative pore water pressure in the capillary zone is neglected (taken to be zero), and the effective stress is taken equal to the total stress

Example

A soil profile is shown in the Figure below. Given: H1 = 6 ft, H2 = 3 ft, H3 = 6 ft. Plot the variation of σ, u, and σ’ with depth.