IÔ2
DOCK ENGINEERING.
with the sides M O and M L equal. With centre M and radius
MN = ^-^ describe the arc N0 N Nj N2 cutting M L in N. Join N O,
which thus becomes the measure of the résultant intensity r.
The angle 0 being variable, the angle H M L = 20 will also vary, and
with it the angle MON, which is the obliquity of the direction of the
resultant in reference to O M, the normal to the plane, A 0. The locus of
the point N is the semicircumference N0N N2. The angle M OjN attains
its maximum value, manifestly, when the direction of r is a tangent to
the curve—i.e., when the point N coincides with Nr When this is the
case the angle M N O is a right angle, and the angle MON becomes
.,MN . .^q - p
sin = sin ;
OM q^p
q-p
Write sinp=^-^,
« 1 - sinø
Whence — = ,---; —-• .... (12)
q 1 + sinp • 7
In applying this theory to earth pressure, it is to be noted that the angle
MON represents the limiting angle consistent with equilibrium ; in
other words, the angle of repose (p). Equation (12) then determines the
minimum intensity, p, of horizontal pressure necessary to maintain the
stability of a mass of earth, the measure of whose vertical pressure intensity
is q.
In the case of a retaining wall, the earthwork behind which does not
rise above a horizontal surface level with the coping, q is equal to the weight
of a unit column of earth of height, h —i.e.,
q =wh.
The mean intensity is
wh
?i=T