Analytical Solutions for the Construction of Deeply Buried Circular Tunnels with Two Liners in Rheological Rock

The construction of underground tunnels is a time-dependent process. The states of stress and strain in the ground vary with time due to the construction process. Stress and strain variations are heavily dependent on the rheological behavior of the hosting rock mass. In this paper, analytical closed-form solutions are developed for the excavation of a circular tunnel supported by the construction of two elastic liners in a viscoelastic surrounding rock under a hydrostatic stress field. In the solutions, the stiffness and installation times of the liners are accounted for. To simulate realistically the process of tunnel excavation, a time-dependent excavation process is considered in the development of the solutions, assuming that the radius of the tunnel grows from zero until its final value according to a time-dependent function to be specified by the designers. The integral equations for the supporting pressures between rock and first liner are derived according to the boundary conditions for linear viscoelastic rocks (unified model). Then, explicit analytical expressions are obtained by considering either the Maxwell or the Boltzmann viscoelastic model for the rheology of the rock mass. Applications of the obtained solutions are illustrated using two examples, where the response in terms of displacements and stresses caused by various combinations of excavation rate, first and second liner installation times, and the rheological properties of the rock is illustrated.

[1]  Shucai Li,et al.  A complex variable solution for stress and displacement field around a lined circular tunnel at great depth , 2009 .

[2]  A. Guenot,et al.  An analytical solution for time-dependent displacements in a circular tunnel , 1987 .

[3]  M. Gurtin,et al.  On the linear theory of viscoelasticity , 1962 .

[4]  G. Anagnostou,et al.  The Applicability of the Ground Response Curve to Tunnelling Problems that Violate Rotational Symmetry , 2011, Rock Mechanics and Rock Engineering.

[5]  Paul F. Gnirk,et al.  The Deformational Behavior Of A Circular Mine Shaft Situated In A Viscoelastic Medium Under Hydrostatic Stress , 1964 .

[6]  D. P. Mason,et al.  Support to rock excavations provided by sprayed liners , 2008 .

[7]  Mohammed Tayib Akrawi.  Stress analysis in viscoelastic bodies under sinusoidal loads , 1964 .

[8]  Isam Shahrour,et al.  Numerical analysis of the interaction between twin-tunnels: Influence of the relative position and construction procedure , 2008 .

[9]  R. Christensen.  Theory of viscoelasticity : an introduction , 1971 .

[10]  En-Jui Lee,et al.  Stress analysis in visco-elastic bodies , 1955 .

[11]  Colin B. Brown,et al.  Flexible Culverts Under High Fills , 1968 .

[12]  Ahmad Fahimifar,et al.  Analytical solution for the excavation of circular tunnels in a visco-elastic Burger’s material under hydrostatic stress field , 2010 .

[13]  C. Fairhurst,et al.  The elasto-plastic response of underground excavations in rock masses that satisfy the Hoek-Brown failure criterion , 1999 .

[14]  E. T. Brown,et al.  Rock Mechanics: For Underground Mining , 1985 .

[15]  Klaus Thoeni,et al.  Nonlinear analysis of NATM tunnel construction with the boundary element method , 2012 .

[16]  A. Jeffrey,et al.  Integral equations: A short course , 1976 .

[17]  Guriĭ Nikolaevich Savin,et al.  Stress concentration around holes , 1961 .

[18]  G. Nie,et al.  Analytical expressions for stress and displacement fields in viscoelastic axisymmetric plane problem involving time-dependent boundary regions , 2010 .

[19]  D. P. Mason,et al.  Support provided to rock excavations by a system of two liners , 2009 .

[20]  Yang Zhifa,et al.  Back-analysis of viscoelastic displacements in a soft rock road tunnel , 2001 .

[21]  A. I. Sofianos,et al.  Supported Axisymmetric Tunnels Within Linear Viscoelastic Burgers Rocks , 2011 .

[22]  Vyacheslav E. Naumov,et al.  Mechanics of Growing Deformable Solids: A Review , 1994 .

[23]  Xia-Ting Feng,et al.  Identification of visco-elastic models for rocks using genetic programming coupled with the modified particle swarm optimization algorithm , 2006 .

[24]  H. Einstein,et al.  SIMPLIFIED ANALYSIS FOR TUNNEL SUPPORTS , 1979 .