Ali Nazem - School of Mining Engineering, College of Engineering, University of Tehran, Tehran, Iran
Mohammad-Forough Hossaini - School of Mining Engineering, College of Engineering, University of Tehran, Tehran, Iran
hosein Rahami - School of Engineering Science, College of Science, University of Tehran, Tehran, Iran
Rouhollah Bolghonabadi - School of Mining Engineering, College of Engineering, University of Tehran, Tehran, Iran

Elastic solutions applicable to single underground openings usually suffer from geometry related simplification. Most tunnel shapes possess two axes of symmetry while a wide range of geometries used in tunneling practice involve only one symmetry axis. D-shape or horse-shoe shape tunnels and others with arched roof and floor are examples of the later category (one symmetry axis). In the present paper, with the use of conformal mapping, two methods were developed to determine the appropriate mapping functions on which an analytical elastic solution for a tunnel with one vertical axis of symmetry is based. These conformal mapping functions turn complicated geometries into a unit circle for the sake of simplification. These two approaches were introduced into a computer program used for an arbitrary tunnel cross section. Results showed that the second approach has more accuracy and is able to produce any shape, since it uses a nonlinear structure in its constitutive equations. Besides, the values for different coefficients have been presented for a variety of tunnel geometry curvature, as well as acceptable variation for the coefficients to represent tunnels with conventional shapes.

arched roof tunnel, conformal mapping, theory of elasticity, tunnel cross section, underground opening