301 
1912-13.] Plane Strain in a Wedge. 
(12) It has been recently shown* that the voids in various building- 
stones and cements form a considerable percentage of the total volume 
in many cases. In view of this it has been thought desirable to consider 
the effect of porosity on the stresses in a masonry dam. To deal with 
the question in any form it will be necessary to make some assumption 
as to the pressure of the water in the pores. It will be assumed in what 
follows that this pressure falls off uniformly along any plane x = constant, 
from full water pressure at front face to zero at free face, the axis of 
x being taken in the central plane of the dam. 
A point of importance in dealing with the question is that of the 
relation between volume porosity and sectional porosity. By sectional 
porosity is meant the ratio which the area of air-space cut through in 
any section bears to the total area of the section. Under certain 
circumstances volume porosity and sectional porosity are equal, but in 
what follows only sectional porosity will be used. It will be assumed 
that the pores are so small as to cause no disturbance of stress at their 
boundaries. 
Let p = pressure of water in the pores, 
m = area of solid per unit of area of any section, 
m = area of pores ; 
then m + m = unity. 
The above assumption as to p gives 
p = Pr sin (a + 0)/sin 2a = wr sin (a + 0) , say, 
where P r = pressure of water on face 0 = a, 
or 
P = pg cos (a-P), 
where ~p — density of water. 
If 0, 00, and rp denote the actual stresses in the elastic material of 
the dam (not the stresses exerted across unit area of any section at the 
point), then the stress equations of equilibrium are 
0 _ 10-2 rr- 
0r roO r 
00 
0 
dr 
rO + 
1 0 -V 
- -^ 7 , 00 + 
r o0^ 
-—wsm(a + 0) + — cos (3 — 0) = 0 , 
m y 'm 
- m w cos (a + 0) + -- sin (3 — 0) = 0 . 
m ' 7 m 
If we make the same assumption as in equations (22), then 
A = B' = — wr sin (a + 0) - L gr cos (B-0). 
Di m 
* Messrs Baldwin-Wiseman and Griffith, Proc. Ind. Civil Eng., vol. clxxix. p. 306. 
