DETEKMINlNii THK ( KNTEU LINK 17 



upper part forming the roof arch is usually a semi-circle or 

 semi-oval, while the lower part, comprising the side walls 

 and invert or floor, varies greatly in outline. Sometiiiit/s tin- 

 side walls are vertical and the invert is omitted, us shown by 

 Fig. 9; and sometimes the side walls are inclined, with their 

 bottoms hraced apart by the invert, as shown by Fig. 10. In 

 more treacherous soils the side walls are curved, and are con- 

 nected by small curved sections to the invert, as shown by Fig. 



Fi 9 9 Fig. 10. Fig.ll. 



Fios. 9 to 11. Typical Sectional Profiles for Tunnel. 



11. In the last example the side walls are commonly called 

 skewbacks, and the lower part of the section is a polycentric 

 figure like the upper part, but dissimilar in form. 



In a tunnel section whose profile is composed entirely of 

 arcs the following conditions are essential : The centers of the 

 springer arcs Cra and Ea', Fig. 8, must be located on the line 

 GrE\ the center of the roof arc bDb' must be located on the 

 axis HD ; the total number of centers must be an odd number; 

 the radii of the succeeding arcs from Cr toward D and E toward 

 I) must decrease in length, and finally the sum of the angles 

 subtended by the several arcs must equal 180. 



Dimensions of Section. The dimensions to be given to the 

 cross-section of a tunnel depend upon the purpose for whirli it 

 is to l)e used. Whatever the purpose of the tunnel, the follow- 

 ing three points have to be considered in determining the size 

 of its cross-section : (1) The size of clear opening required ; (2) 

 the thickness of lining masonry necessary; and (3) the decrease 

 in the clear opening from the deformation of the lining. 



Railway tunnels may be built either to accommodate one or 



