Lecture 4 - EFFECTIVE STRESS Notes | EduRev

: Lecture 4 - EFFECTIVE STRESS Notes | EduRev

 Page 1


NPTEL- Advanced Geotechnical Engineering   
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


NPTEL- Advanced Geotechnical Engineering   
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 
NPTEL- Advanced Geotechnical Engineering   
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


NPTEL- Advanced Geotechnical Engineering   
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 
NPTEL- Advanced Geotechnical Engineering   
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 
NPTEL- Advanced Geotechnical Engineering   
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


NPTEL- Advanced Geotechnical Engineering   
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 
NPTEL- Advanced Geotechnical Engineering   
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 
NPTEL- Advanced Geotechnical Engineering   
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 
NPTEL- Advanced Geotechnical Engineering   
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


NPTEL- Advanced Geotechnical Engineering   
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 
NPTEL- Advanced Geotechnical Engineering   
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 
NPTEL- Advanced Geotechnical Engineering   
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 
NPTEL- Advanced Geotechnical Engineering   
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 
NPTEL- Advanced Geotechnical Engineering   
Dept. of Civil Engg. Indian Institute of Technology, Kanpur                                                                                        5  
 
Or  
  
 
 
 
 
 
  
 
 
           (1.66) 
Where  
  
 is the critical hydraulic gradient. 
 
 
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