the ground reaction curve (grc) is a vital component of the convergence-confinement method, which possesses many applications in the underground space designs. it defines a relation between the tunnel wall deformations and the ground pressure acting on the tunnel walls. generally, grc includes descending and ascending branches. according to many researchers, the descending branch trend for the ...

The design of underground spaces is mainly carried out using empirical, analytical, and numerical methods. The convergence confinement method (CCM) is an analytical technique that is widely utilized in analyzing the stability of underground spaces. However, the main challenge in the stability analysis is the selection of an accurate constitutive model for rock mass, and particularly, its post-f...

we present a collocation method to obtain the approximate solutionof troesch's problem which arises in the confinement of a plasmacolumn by radiation pressure and applied physics. by using thechristov rational functions and collocation points, this methodtransforms troesch's problem into a system of nonlinear algebraicequations. the rate of convergence is shown to be exponential. then...

We present a collocation method to obtain the approximate solution of Troesch's problem which arises in the confinement of a plasma column by radiation pressure and applied physics. By using the Christov rational functions and collocation points, this method transforms Troesch's problem into a system of nonlinear algebraic equations. The rate of convergence is shown to be exponential. The numer...

Dimensionless coefficient () in convergence confinement method shows the relaxation of stress in the wall of the tunnel at different excavation movements. This factor is considered a constant number in previous studies and tunnel geometric characteristics (such as depth, cross-section shape, radius, soil material, etc.) are not included in its determination; however, ignoring these effects can...

this paper addresses the problem of quantifying the mechanical contribution of rockbolts installed systematically around tunnels (regularly spaced around the tunnel) excavated in rock masses. assuming that the mechanical contribution of grouted rockbolts is that of increasing internal pressure within a broken rock mass, a new procedure for computation of ground response curves for a circular tu...

A saddle point variational (SPV ) method was applied to the Dirac equation as an example of a fully relativistic equation with both negative and positive energy solutions. The effect of the negative energy states was mitigated by maximizing the energy with respect to a relevant parameter while at the same time minimizing it with respect to another parameter in the wave function. The Cornell pot...