Environmental Engineering Reference
In-Depth Information
Figure 12.38 Active and passive earth pressure states for soil with matric suction.
Figure 12.39 Mohr circle construction for active earth pressure case.
The following trigonometric relation can be used to sim-
plify Eq. 12.35:
Terzaghi and Peck (1967) used the variable N φ to desig-
nate the above trigonometric relation:
1
tan 2 45
φ
2
1
N φ =
cos φ
sin φ
(12.39)
sin φ =
(12.36)
1
+
1
+
sin φ
The active pressure σ h
u a for an element of soil at any
Equation 12.36 can now be written as:
depth can be written as
2 c 1
1
N φ
1
N φ
sin φ
u a ) 1
sin φ
σ h
u a =
v
u a )
2 c
(12.40)
σ h
u a =
v
sin φ
. (12.37)
1
+
1
+
sin φ
The above equation can also be rewritten by taking into
account the individual components of cohesion:
The trigonometric function appearing in Eq. 12.37 can
be written in terms of the angle of the slip planes from a
vertical plane:
1
N φ
1
N φ
2 c
σ h
u a =
v
u a )
tan 2 45
sin φ
φ
1
1
 
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