74 Tl NNKI.INc; 



and without endangering the fall of the roof or the caving of 

 tlu- sides by removing too great a portion of the timbers at one 

 time. 



Thickness of Lining Masonry. It is obvious, of course, that 

 the masonry lining must !>r thick enough to support the press- 

 ure of the earth which it sustains ; but, as it is impossible to 

 estimate these pressures at all accurately, it is diiticult to say 

 definitely just what thickness is required in any individual case. 

 Kniikine gives the following formulas for determining the 

 depths of keystone required in different soils : 

 For firm soils, 



d = V/0.12 -, 



T S 



and for soft spils, 



/ r 2 

 d = V/0.48-, 



T S 



where d = the depth of the crown in feet, r = the rise of the 

 arch in feet, and * = the span of the arch in feet. Other 

 writers, among them Professor Curioni, attempt to give rational 

 methods for calculating the thickness of tunnel lining ; but they 

 are all open to objection because of the amount of hypothesis 

 required concerning pressures which are of necessity indetermi- 

 nate. Therefore, to avoid tedious and uncertain calculations, 

 the engineer adopts dimensions which experience has proven to 

 be ample under similar conditions in the past. Thus we have 

 all gradations in thickness, from hard-rock tunnels requiring 

 no lining, and tunnels through rocks which simply require a 

 thin shell to protect them from the atmosphere, to soft-ground 

 tunnels where a masoniy lining 3 ft. or more in thickness is 

 employed. Table II. shows the thickness of masonry lining 

 used in tunnels through soft soils of various kinds. 



The thickness of the masonry lining is seldom uniform at 

 all points, as is indicated by Table II. Figs. 46 and 47 show 

 common methods of varying the thickness of lining at different 

 points, and are self-explanatory. 



