On Analytic Solutions of Elastic Net Displacements around a Circular Tunnel
Authors
Abstract:
Displacements around a tunnel, occurring as a result of excavation, consist of the elastic and plastic parts. In this paper, we discuss the elastic part of displacements as a result of excavation, called net displacement. In general, the previous analytical solutions presented for determining the displacements around a circular tunnel in an elastic medium do not give the net displacements directly. The well-known Kirsch solution is the most widely used method for determining the induced stresses and net displacements around a circular opening in a biaxially-loaded plate of homogeneous, isotropic, continuous, linearly elastic material. However, the complete solution for obtaining the net displacements has not been presented or highlighted in the available literature. Using the linear elasticity, this paper reviews and presents three different analytical methods for determining the net displacements directly as well as induced stresses around a circular tunnel. The three solution methods are the Lame' method, airy stress function method, and complex variable method. The tunnel is assumed to be situated in an elastic, continuum, and isotropic medium in the plane strain condition. The solutions are presented for both the hydrostatic and non-hydrostatic in situ stresses in the 2D biaxial loading condition along with an internal pressure. Loading and unloading in tunneling occurring as a result of excavation and stress differences between the induced and initial ones are considered to evaluate the net displacements directly. Finally, some examples are given to demonstrate the complete solution and show the difference between the net elastic displacements as a result of excavation and total elastic displacements that are not real.
similar resources
Thermo-Elastic Analysis of Non-Uniform Functionally Graded Circular Plate Resting on a Gradient Elastic Foundation
Present paper is devoted to stress and deformation analyses of heated variable thickness functionally graded (FG) circular plate with clamped supported, embedded on a gradient elastic foundation and subjected to non-uniform transverse load. The plate is coupled by an elastic medium which is simulated as a Winkler- Pasternak foundation with gradient coefficients in the radial and circumferential...
full textFlow Visualization Around a Non - Circular Tube
The flow behavior around a cam shaped tube in cross flow has been investigated experimentally using flow visualization and pressure distribution measurement. The range of attack angle and Reynolds number based on an equivalent circular diameter are within 0 ≤ α ≤ 360˚ and 2 x 104 < Reeq < 3.4 x 104, respectively. The pressure drag features are clarified in relation to the flow behavior around t...
full textNonlinear Buckling of Circular Nano Plates on Elastic Foundation
The following article investigates nonlinear symmetric buckling of moderately thick circular Nano plates with an orthotropic property under uniform radial compressive in-plane mechanical load. Taking into account Eringen nonlocal elasticity theory, principle of virtual work, first order shear deformation plate theory (FSDT) and nonlinear Von-Karman strains, the governing equations are obtained ...
full textthermo-elastic analysis of non-uniform functionally graded circular plate resting on a gradient elastic foundation
present paper is devoted to stress and deformation analyses of heated variable thickness functionally graded (fg) circular plate with clamped supported, embedded on a gradient elastic foundation and subjected to non-uniform transverse load. the plate is coupled by an elastic medium which is simulated as a winkler- pasternak foundation with gradient coefficients in the radial and circumferential...
full textThe radial disc structure around a magnetic neutron star: analytic and semi-analytic solutions
The radial structure of a thin accretion disc is calculated in the presence of a central dipole magnetic field aligned with the rotation axis. The problem is treated using a modified expression for the turbulent magnetic diffusion, which allows the angular momentum equation to be integrated analytically. The governing algebraic equations are solved iteratively between 1 and 10 4 stellar radii. ...
full textMy Resources
Journal title
volume 11 issue 2
pages 419- 432
publication date 2020-04-01
By following a journal you will be notified via email when a new issue of this journal is published.
Hosted on Doprax cloud platform doprax.com
copyright © 2015-2023