ch1 soil mechanics

Addis Ababa University, Faculty of Technology, Department of Civil Engineering normal stress, the shear stress is increased from zero to the maximum blocks to slide along their contact area. area. When

t  f   ,

forcing the two

s n =0, the shear stress has to be mobilized to a

maximum value of c  to  to make the sliding possible. If the fricti on angle between blocks A blocks A and B is

f  then for the values of s >0, t  has to be increased to overcome the resistance to sliding s ´ tan f  caused by friction (Coulomb s frictional law). Consequently, the summation of c  and   and shear stress needed to slide the two blocks on the plane of s ´ tan f represents the maximum shear  

contact (slip or failure failu re plane). In a real soil, if a predetermined sliding plane is forced to occur, occur, the soil below and the soil above the failure plane will not act as ri gid bodies but will deform, causing a volume change around the sliding and forming a shear band  (Fig.  (Fig. 1.3b).

Figure 1.3: 1.3: (a) Mechanical concept of sliding. (b) Soil deformation deformation and a shear band.

In a coordinate system with

s n   plotted

as abscissa and

t

  as ordinate, Eq. (1.9) is

represented by the line shown in Fig. (1.4a). This equation was originally written in terms of total stress and was only partially successful in predicting the shear strength of real soils. Coulomb s failure criterion was subsequently redefined as:

t  f   = c ' + s n' tan f '  

(1.10)

Figure 1.4: 1.4: Coulomb s failure criteria: (a) total stress (b) effective stress.

where and

f'

t  f  

is the shear strength,

sn

 is  is the effective normal normal stress, c    is  is the effective cohesion,

 

the effective angle of internal friction of the soil. In both the total and effective effective stress

conditions, the shear stress is solely taken by the soil particles, since the liquid in the voids



Soil Mechanics II: Lecture Note

5

Instructor: Dr. Hadush Seged