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# Lecture 4 - EFFECTIVE STRESS Notes | EduRev

## : Lecture 4 - EFFECTIVE STRESS Notes | EduRev

``` Page 1

Dept. of Civil Engg. Indian Institute of Technology, Kanpur                                                                                        1
Module 1
Lecture 4
Soil Aggregate -4
Topics
1.6  EFFECTIVE STRESS
1.6.1   Effective Stress Concept in Saturated Soils
1.6.2   Critical Hydraulic Gradient and Boiling

1.6  EFFECTIVE STRESS
1.6.1 Effective Stress Concept in Saturated Soils
Terzaghi (1925, 1936) was the first to suggest the principle of effective stress. According to this, the total
vertical stress   at a point O in a soil mass as shown in Figure 1.28a can be given by

(1.56)

Figure 1.28 Effective-stress concepts. (a) Section. (b) Section at the level of O. (c) forces
carried by soil solids at their place of contact
Page 2

Dept. of Civil Engg. Indian Institute of Technology, Kanpur                                                                                        1
Module 1
Lecture 4
Soil Aggregate -4
Topics
1.6  EFFECTIVE STRESS
1.6.1   Effective Stress Concept in Saturated Soils
1.6.2   Critical Hydraulic Gradient and Boiling

1.6  EFFECTIVE STRESS
1.6.1 Effective Stress Concept in Saturated Soils
Terzaghi (1925, 1936) was the first to suggest the principle of effective stress. According to this, the total
vertical stress   at a point O in a soil mass as shown in Figure 1.28a can be given by

(1.56)

Figure 1.28 Effective-stress concepts. (a) Section. (b) Section at the level of O. (c) forces
carried by soil solids at their place of contact
Dept. of Civil Engg. Indian Institute of Technology, Kanpur                                                                                        2
The total vertical stress   consists of two parts. One part is carried by water and is continuous and acts with
equal intensity in all directions. This is the pore water pressure or neutral stress u. from Figure 1.28a,

(1.57)
The other part is the stress carried by the soil structure and is called the effective stress   . Thus

(1.58)
Combining eqs. (1.56) to (1.58).

(1.59)
Where    is the submerged unit weight of soil

.
For dry soils,

In general, if the normal total stresses at a point in a soil mass are

as shown in Figure 1.29,
the effective stresses can be given as follows:

Where

are the effective stresses and   is the pore water pressure,

.
The principle of effective stress [eq. (1.58)] is one of the most important findings in sol mechanics. The
present developments on compressibility of soils, shear strength, and lateral earth pressure on retaining
structures are all based on the effective stress concept.
The term effective stress is sometimes used interchangeably with the term inter-granular stress by soils and
foundation engineers. Although the terms are approximately the same, there is some difference. In order to

Figure 1.29 Normal total stresses in a soil mass
Page 3

Dept. of Civil Engg. Indian Institute of Technology, Kanpur                                                                                        1
Module 1
Lecture 4
Soil Aggregate -4
Topics
1.6  EFFECTIVE STRESS
1.6.1   Effective Stress Concept in Saturated Soils
1.6.2   Critical Hydraulic Gradient and Boiling

1.6  EFFECTIVE STRESS
1.6.1 Effective Stress Concept in Saturated Soils
Terzaghi (1925, 1936) was the first to suggest the principle of effective stress. According to this, the total
vertical stress   at a point O in a soil mass as shown in Figure 1.28a can be given by

(1.56)

Figure 1.28 Effective-stress concepts. (a) Section. (b) Section at the level of O. (c) forces
carried by soil solids at their place of contact
Dept. of Civil Engg. Indian Institute of Technology, Kanpur                                                                                        2
The total vertical stress   consists of two parts. One part is carried by water and is continuous and acts with
equal intensity in all directions. This is the pore water pressure or neutral stress u. from Figure 1.28a,

(1.57)
The other part is the stress carried by the soil structure and is called the effective stress   . Thus

(1.58)
Combining eqs. (1.56) to (1.58).

(1.59)
Where    is the submerged unit weight of soil

.
For dry soils,

In general, if the normal total stresses at a point in a soil mass are

as shown in Figure 1.29,
the effective stresses can be given as follows:

Where

are the effective stresses and   is the pore water pressure,

.
The principle of effective stress [eq. (1.58)] is one of the most important findings in sol mechanics. The
present developments on compressibility of soils, shear strength, and lateral earth pressure on retaining
structures are all based on the effective stress concept.
The term effective stress is sometimes used interchangeably with the term inter-granular stress by soils and
foundation engineers. Although the terms are approximately the same, there is some difference. In order to

Figure 1.29 Normal total stresses in a soil mass
Dept. of Civil Engg. Indian Institute of Technology, Kanpur                                                                                        3

visualize the difference, first refer to Figure 1.28. The total vertical force F at the level of O in Figure 1.28a
is the sum of the following forces:
1. The force carried by soil solids at their point of contact,

. This can be seen by considering a wavy
surface XX which passes through the point O and the points of contact of the solid particles.

are the resultant forces acting at the points of contact of the soil solids. So,

Where

are the vertical components of the forces

2. The force carried by water,

Where

3. The electrical attractive force between the solid particles at the level of

4. The electrical repulsive force between the solid particles at the level of

.
Thus, the total vertical force is

Or

Where   is the total stress at the level of O, and so

Where

Hence

(1.60)
The value of a in the above equation is very small in the working stress range. We can thus approximate eq.
(1.60) as

(1.61)
For granular soils, silts, and clays of low plasticity, the magnitudes of A’ and R’ are small; so for all practical
purposes, the intergranular stress becomes
Page 4

Dept. of Civil Engg. Indian Institute of Technology, Kanpur                                                                                        1
Module 1
Lecture 4
Soil Aggregate -4
Topics
1.6  EFFECTIVE STRESS
1.6.1   Effective Stress Concept in Saturated Soils
1.6.2   Critical Hydraulic Gradient and Boiling

1.6  EFFECTIVE STRESS
1.6.1 Effective Stress Concept in Saturated Soils
Terzaghi (1925, 1936) was the first to suggest the principle of effective stress. According to this, the total
vertical stress   at a point O in a soil mass as shown in Figure 1.28a can be given by

(1.56)

Figure 1.28 Effective-stress concepts. (a) Section. (b) Section at the level of O. (c) forces
carried by soil solids at their place of contact
Dept. of Civil Engg. Indian Institute of Technology, Kanpur                                                                                        2
The total vertical stress   consists of two parts. One part is carried by water and is continuous and acts with
equal intensity in all directions. This is the pore water pressure or neutral stress u. from Figure 1.28a,

(1.57)
The other part is the stress carried by the soil structure and is called the effective stress   . Thus

(1.58)
Combining eqs. (1.56) to (1.58).

(1.59)
Where    is the submerged unit weight of soil

.
For dry soils,

In general, if the normal total stresses at a point in a soil mass are

as shown in Figure 1.29,
the effective stresses can be given as follows:

Where

are the effective stresses and   is the pore water pressure,

.
The principle of effective stress [eq. (1.58)] is one of the most important findings in sol mechanics. The
present developments on compressibility of soils, shear strength, and lateral earth pressure on retaining
structures are all based on the effective stress concept.
The term effective stress is sometimes used interchangeably with the term inter-granular stress by soils and
foundation engineers. Although the terms are approximately the same, there is some difference. In order to

Figure 1.29 Normal total stresses in a soil mass
Dept. of Civil Engg. Indian Institute of Technology, Kanpur                                                                                        3

visualize the difference, first refer to Figure 1.28. The total vertical force F at the level of O in Figure 1.28a
is the sum of the following forces:
1. The force carried by soil solids at their point of contact,

. This can be seen by considering a wavy
surface XX which passes through the point O and the points of contact of the solid particles.

are the resultant forces acting at the points of contact of the soil solids. So,

Where

are the vertical components of the forces

2. The force carried by water,

Where

3. The electrical attractive force between the solid particles at the level of

4. The electrical repulsive force between the solid particles at the level of

.
Thus, the total vertical force is

Or

Where   is the total stress at the level of O, and so

Where

Hence

(1.60)
The value of a in the above equation is very small in the working stress range. We can thus approximate eq.
(1.60) as

(1.61)
For granular soils, silts, and clays of low plasticity, the magnitudes of A’ and R’ are small; so for all practical
purposes, the intergranular stress becomes
Dept. of Civil Engg. Indian Institute of Technology, Kanpur                                                                                        4

(1.62)
For this case, eqs. (1.58) and (1.62) are similar and

. However, if A’- R’ is large,

. Such
situations can be encountered in highly plastic, dispersed clays.

1.6.2  Critical Hydraulic Gradient and Boiling

Consider a condition where there is an upward flow of water through a soil layer, as shown in Figure 1.30a.
The total stress at a point O is

(1.63)
Where

is the saturated unit weight of soil. The pore water pressure at O is

(1.64)
And the effective stress at O is

(1.65)
If the flow rate of water through the soil is continuously increased, the value of x will increase and will reach
a condition where

. This condition is generally referred to as boiling. Since the effective stress in the
soil is zero, the soil will not be stable. Thus

Figure 1.30  Critical hydraulic gradient and boiling
Page 5

Dept. of Civil Engg. Indian Institute of Technology, Kanpur                                                                                        1
Module 1
Lecture 4
Soil Aggregate -4
Topics
1.6  EFFECTIVE STRESS
1.6.1   Effective Stress Concept in Saturated Soils
1.6.2   Critical Hydraulic Gradient and Boiling

1.6  EFFECTIVE STRESS
1.6.1 Effective Stress Concept in Saturated Soils
Terzaghi (1925, 1936) was the first to suggest the principle of effective stress. According to this, the total
vertical stress   at a point O in a soil mass as shown in Figure 1.28a can be given by

(1.56)

Figure 1.28 Effective-stress concepts. (a) Section. (b) Section at the level of O. (c) forces
carried by soil solids at their place of contact
Dept. of Civil Engg. Indian Institute of Technology, Kanpur                                                                                        2
The total vertical stress   consists of two parts. One part is carried by water and is continuous and acts with
equal intensity in all directions. This is the pore water pressure or neutral stress u. from Figure 1.28a,

(1.57)
The other part is the stress carried by the soil structure and is called the effective stress   . Thus

(1.58)
Combining eqs. (1.56) to (1.58).

(1.59)
Where    is the submerged unit weight of soil

.
For dry soils,

In general, if the normal total stresses at a point in a soil mass are

as shown in Figure 1.29,
the effective stresses can be given as follows:

Where

are the effective stresses and   is the pore water pressure,

.
The principle of effective stress [eq. (1.58)] is one of the most important findings in sol mechanics. The
present developments on compressibility of soils, shear strength, and lateral earth pressure on retaining
structures are all based on the effective stress concept.
The term effective stress is sometimes used interchangeably with the term inter-granular stress by soils and
foundation engineers. Although the terms are approximately the same, there is some difference. In order to

Figure 1.29 Normal total stresses in a soil mass
Dept. of Civil Engg. Indian Institute of Technology, Kanpur                                                                                        3

visualize the difference, first refer to Figure 1.28. The total vertical force F at the level of O in Figure 1.28a
is the sum of the following forces:
1. The force carried by soil solids at their point of contact,

. This can be seen by considering a wavy
surface XX which passes through the point O and the points of contact of the solid particles.

are the resultant forces acting at the points of contact of the soil solids. So,

Where

are the vertical components of the forces

2. The force carried by water,

Where

3. The electrical attractive force between the solid particles at the level of

4. The electrical repulsive force between the solid particles at the level of

.
Thus, the total vertical force is

Or

Where   is the total stress at the level of O, and so

Where

Hence

(1.60)
The value of a in the above equation is very small in the working stress range. We can thus approximate eq.
(1.60) as

(1.61)
For granular soils, silts, and clays of low plasticity, the magnitudes of A’ and R’ are small; so for all practical
purposes, the intergranular stress becomes
Dept. of Civil Engg. Indian Institute of Technology, Kanpur                                                                                        4

(1.62)
For this case, eqs. (1.58) and (1.62) are similar and

. However, if A’- R’ is large,

. Such
situations can be encountered in highly plastic, dispersed clays.

1.6.2  Critical Hydraulic Gradient and Boiling

Consider a condition where there is an upward flow of water through a soil layer, as shown in Figure 1.30a.
The total stress at a point O is

(1.63)
Where

is the saturated unit weight of soil. The pore water pressure at O is

(1.64)
And the effective stress at O is

(1.65)
If the flow rate of water through the soil is continuously increased, the value of x will increase and will reach
a condition where

. This condition is generally referred to as boiling. Since the effective stress in the
soil is zero, the soil will not be stable. Thus

Figure 1.30  Critical hydraulic gradient and boiling
Dept. of Civil Engg. Indian Institute of Technology, Kanpur                                                                                        5

Or

(1.66)
Where