16 



TUNNELING 



practically without cohesion, the pressures will all be normal 

 to the line of the profile, and a circular section is the one best 

 suited to resist them. These theoretical considerations have 

 been proved correct by actual experience, and they may be 

 employed to determine in a general way the form of section to 

 be adopted. Applying them to very hard rock, they give us 

 a section with an arched roof and vertical side walls. In softer 

 materials they give us an elliptical section with its major axis 

 vertical, and in very soft quicksands and mud they give us the 

 circular section. These three forms of cross-section and their 

 modifications are the ones commonly employed for tunnels. 

 An important exception to this general practice, however, is 

 met with in some of the underground city rapid-transit rail- 

 ways built of late years, where a rectangular or box section is 

 employed. These tunnels are usually of small depth, so that 

 the vertical pressures are comparatively light, and the bending 

 strains, which they exert upon the flat roof, are provided for by 

 employing steel girders to form the roof lining. 



From what has been said it will be seen that it is impossible 

 to establish a standard sectional profile to suit all conditions. 

 The best one for the majority of conditions, and the one most 

 commonly employed, is a polycentric figure in which the num- 

 ber of centers and the 

 length of the radii are 

 fixed by the engineer to 

 meet the particular con- 

 ditions which exist. In 

 a general way this form 

 of center may be con- 

 sidered as composed of 

 two parts symmetrical 

 in respect to the vertical 

 axis. Fig. 8 shows such 

 a profile, in which DH is the vertical axis. The section is 

 unsymmetrical in respect to the horizontal axis GrE. The 



FIG. 8. Diagram of Polycentric Sectional Profile. 



