DHARM

466 GEOTECHNICAL ENGINEERING

2c/ NÖ f g.zc

s (^3) c s 3
A D
H
G
F f
III
IV
K
O¢ O
f
(45° – /2)
f
(45° – /2)
f
(90° – )f
E
J s 1 s
B
Mohr’s circle
for cohesionless
soil ( )II
Mohr’s circle for cohesive soil ( )
envelope for cohesionless ( ) soil
I
f
(45° + /2)
f C
(45° – /2)
f
Envelope for cohesive (c-f) soil
t
c
Fig. 13.14 Mohr’s circles of stress for active for a cohesionless soil and for a cohesive soil
Pav is the lateral pressure on the imaginary vertical face through the heel of the wall,
acting at H/3 above the base. The weight of the soil wedge is W, acting through its centroid.
The vector sum of these is the total thrust Pa on the back of the wall.
13.6.8Active Earth Pressure of Cohesive Soil
A cohesive soil is partially self-supporting and it will, therefore, exert a smaller pressure on a
retaining wall than a cohesionless soil with the same angle of friction and density.
The Mohr’s circle of stress for a cohesionless soil and for a cohesive soil for an element at
a depth z for the active case are superimposed and shown in Fig. 13.14.
From the geometry of Fig. 13.14,
The difference between σ 3 and σ (^3) c = AD = EF =
CE
cos( 45 °−φ/ ) 2
But, CE
CG
CE
c
= and also,
CE
CG

°−
°+

°− °−
°−
sin( )
sin( / )
sin( /)cos( /)
cos( / )
90
45 2
2
45 2 45 2
45 2
φ
φ
φφ
φ
∴ CE = 2c sin (45° – φ/2)
Substituting, (σ 3 – σ (^3) c) =
245 2
45 2
csin( / )
cos( / )
°−
°−
φ
φ = 2c tan (45° – φ/2)
σ (^3) c= σ 3 – 2c tan (45° – φ/2)
But, σ 3 for a cohesionless soil = γ.z. tan^2 (45° – φ/2)
∴ σ (^3) c = γ. z tan^2 (45° – φ/2) – 2c tan (45° – φ/2) ...(Eq. 13.21)