Module 2 : Theory of Earth Pressure and Bearing Capacity
Lecture 8 : Development of Bearing Capacity Theory [ Section 8.1: Terzaghi's & Meyerhof's Bearing Capacity Theory ]
Consider a footing of width B and depth D f loaded with Q and resting on a soil of unit weight . The failure of the zones is divided into three zones as shown below. The zone1 represents an active Rankine zone, and the zones 3 are passive zones. The boundaries of the active Rankine zone rise at an angle of , and those of the passive zones at with the horizontal. The zones 2 are known as zones of radial shear, because the lines that constitute one set in the shear pattern in these zones radiate from the outer edge of the base of the footing. Since the base of the footing is rough, the soil located between it and the two surfaces of sliding remains in a state of equilibrium and acts as if it formed part of the footing. The surfaces ad and bd rise at to the horizontal. At the instant of failure, the pressure on each of the surfaces ad and bd is equal to the resultant of the passive earth pressure and the cohesion force . Since slip occurs along these faces, the resultant earth pressure acts at angle to the normal on each face and as a consequence in a vertical direction. If the weight of the soil adb is disregarded, the equilibrium of the footing requires that
---------- (1)
The passive pressure required to produce a slip on def can be divided into two parts, and . The force represents the resistance due to weight of the mass adef. The point of application of is located at the lower third point of ad. The force acts at the midpoint of contact surface ad. The value of the bearing capacity may be calculated as :
. The failure of the zones is divided into three zones as shown below. The zone1 represents an active Rankine zone, and the zones 3 are passive zones. The boundaries of the active Rankine zone rise at an angle of 
, and those of the passive zones at 
with the horizontal. The zones 2 are known as zones of radial shear, because the lines that constitute one set in the shear pattern in these zones radiate from the outer edge of the base of the footing. Since the base of the footing is rough, the soil located between it and the two surfaces of sliding remains in a state of equilibrium and acts as if it formed part of the footing. The surfaces ad and bd rise at 
to the horizontal. At the instant of failure, the pressure on each of the surfaces ad and bd is equal to the resultant of the passive earth pressure 
and the cohesion force 
. Since slip occurs along these faces, the resultant earth pressure acts at angle 
to the normal on each face and as a consequence in a vertical direction. If the weight of the soil adb is disregarded, the equilibrium of the footing requires that 
and 
. The force 
represents the resistance due to weight of the mass adef. The point of application of 
is located at the lower third point of ad. The force 
acts at the midpoint of contact surface ad.
