DETERMINING THE CENTER LINE 15 



Doubling the value of $ and making the angle ABC = 2<, 

 the line BC will be fixed and the point C located by taking 

 AB = BC. On BO the ordinates are laid off to locate the curve. 

 Prolong CB so that CD = CB. Then the portion of the curve 

 CE is symmetrical with CE, and the ordinates used to locate 

 EC may lie employed to locate CF, by laying them off in the 

 reverse order. 



FORM AND DIMENSIONS OF CROSS-SECTION. 



In deciding upon the sectional profile of a tunnel two factors 

 have to be taken into consideration: (1) The form of section 

 best suited to the conditions, and (2) the interior dimensions of 

 this section. 



Form of Section. The form of the sectional profile of a tun- 

 nel should be such that the lining is of the l>est form to i 

 the pressures exerted by the unsupported walls of the tunnel 

 excavation, and these vary with the character of the material 

 penetrated. These pressures are both vertical and lateral in 

 direction ; the. roof, deprived of support by the excavation, tends 

 to fall, and the, opposite sides for the same reason tend to slide 

 inward along a plane more or less inclined, depending upon the 

 friction and cohesion of the material. In some rocks the co- 

 hesion is so great that they will stand vertically, while it may 

 be very small in loose earth which slides along a plane whose 

 inclination is directly projiortioiial to the cohesion. 



From the theory of resistance of profiles we know that the 

 resistance of a line to exterior normal forces is directly propor- 

 tional to its decree of curvature, and consequently inversely 

 proportional to the radius of the curve. Hence the sectional 

 profile of a tunnel excavated through hard rock, when- there 

 are no lateral pressures owing to the great cohesion of the ma- 

 terial, and having to resist only the vertical pressure, should 

 le designed to offer the greatest resistance at its highest point, 

 and the curve must, therefore, he sharjier there, and may de- 

 crease toward the base. In <|uicksaml, mud, or other material 



