Analytical solution for deep rectangular structures subjected to far-field shear stresses

Underground structures located in seismic areas have to support the static loads transferred from the surrounding ground under normal working conditions, as well as the loads imposed by any seismic event. Typically underground structures have cross section dimensions much smaller than the wave length of ground peak velocities, in which case inertial forces can be neglected and the structure can be designed using a pseudo-static analysis, where the seismic-induced loads or deformations can be approximated by a far-field shear stress or strain. Current close-form solutions for deep rectangular structures subjected to a far-field shear stress are approximations that do not consider all the relevant variables. An analytical solution is presented in this paper for deep rectangular structures with a far-field shear stress. Complex variable theory and conformal mapping have been used to develop the solution, which is applicable to deep rectangular structures in a homogeneous, isotropic, elastic medium. The solution shows that the deformations of the structure depend on the relative stiffness between the structure and the surrounding ground, and on the shape of the structure. The analytical solution has been verified by comparing its predictions with results from a finite element method and from previously published data.

[1]  Arnold Verruijt,et al.  A COMPLEX VARIABLE SOLUTION FOR A DEFORMING CIRCULAR TUNNEL IN AN ELASTIC HALF-PLANE , 1997 .

[2]  A J Hendron,et al.  STATE OF THE ART OF SOFT-GROUND TUNNELING , 1972 .

[3]  G. E. Exadaktylos,et al.  A closed-form elastic solution for stresses and displacements around tunnels , 2002 .

[4]  Raymond D. Mindlin,et al.  Stress Distribution around a Tunnel , 1940 .

[5]  P. Theocaris.  Peculiarities of the artificial crack , 1991 .

[6]  Joseph Penzien,et al.  Seismically induced racking of tunnel linings , 2000 .

[7]  C. M. St John,et al.  Aseismic design of underground structures , 1987 .

[8]  Antonio Bobet,et al.  EFFECT OF PORE WATER PRESSURE ON TUNNEL SUPPORT DURING STATIC AND SEISMIC LOADING , 2003 .

[9]  Hasan Gerçek.  An elastic solution for stresses around tunnels with conventional shapes , 1997 .

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

[11]  Pantelis Liolios,et al.  A semi-analytical elastic stress–displacement solution for notched circular openings in rocks , 2003 .

[12]  P. Theocaris,et al.  From the rectangular hole to the ideal crack , 1989 .

[13]  Terry R. Howard.  Seismic Design of Embankments and Caverns , 1983 .

[14]  Hongbin Huo.  Seismic design and analysis of rectangular underground structures , 2005 .

[15]  S. Timoshenko,et al.  Theory of elasticity , 1975 .

[16]  R. D. Mindlin.  Stress Distribution Around a Hole Near the Edge of a Plate under Tension , 1989 .

[17]  Joseph Penzien,et al.  Stresses in linings of bored tunnels , 1998 .

[18]  Birger Schmidt,et al.  SEISMIC DESIGN AND ANALYSIS OF UNDERGROUND STRUCTURES , 2001 .

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

[20]  J. W. Brown,et al.  Complex Variables and Applications , 1985 .

[21]  Arnold Verruijt,et al.  A complex variable solution for a deforming buoyant tunnel in a heavy elastic half-plane , 2002 .

[22]  Alfred J. Hendron,et al.  Dynamic and Static Design Considerations for Underground Chambers , 1983 .

[23]  Arnold Verruijt,et al.  DEFORMATIONS OF AN ELASTIC HALF PLANE WITH A CIRCULAR CAVITY , 1998 .

[24]  M. D. Motok,et al.  Stress concentration on the contour of a plate opening of an arbitrary corner radius of curvature , 1997 .

[25]  N. Muskhelishvili.  Some basic problems of the mathematical theory of elasticity , 1953 .

[26]  I. S. Sokolnikoff.  Mathematical theory of elasticity , 1946 .