THE THEORY OF CONJUGATE PRESSURES.
Hence, substituting in (14), and cancelling
p' cos a - x/cos2 a— cos2p
1 cos a + x/cos2 a - cos2 p
165
(15)
Now, as the stresses are inclined to one another at the angle a, the
inteusity of the vertical pressures in the case of earthwork will be equal to
the weight of a unit column multiplied by cos a.
q' = wh cos a.
The mean intensity, therefore, is
, wh
q^-^ cos a
and the total pressure
_wh~
y=— cos a.
Accordingly,
pcos a cos “- ^cos2 a—cos2p
2 cos a+ x/cos2 a - cos2 <p
(16)
It will be seen that when the surface of the ground is horizontal a=0,
cos a = 1, and
^ wh^ I - sin p
2 ' 1 + sin p’
as previously demonstrated.
For a surface sloping upwards at the angle of repose, a = <p and
T wh2
I—^— cos p. ....
■ (17)
According to Professor Rankine, the line of action of the resultant
force is always parallel to the surface of the ground.
theory, due to Dr. Scheffler, détermines the
direction of the earth thrust as inclined to
the horizontal at a constant angle, identical
with the angle of repose. In this way,
although the total amount of the thrust is
greater by Scheffler’s hypothesis (being as EG
to E F, fig. 88), yet, except in one instance,
the overturning effect is less, owing to the
nearer approach of the line of thrust to the
vertical. The one exception is the case in
which the surface of the ground has an in-
clination p to the horizontal, and then the
two theories lead to the same result.
Another modification, due to Professor
A modification of the
Reilly, takes into consideration the batter, or inclination to the vertical,