• Geomechanics and Engineering
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• v.22 no.6
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• pp.509-518
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• 2020

Multi-layered primary linings have been proved to be highly effective for tunneling in severe squeezing grounds. But there still has not existed well-established design method for it. Basically, there are two main critical problems in this method, including determinations of allowable deformation and distribution of support stiffness. In order to address such problems, an attempt to investigate the mechanical response of a circular tunnel with double primary linings is performed in this paper. Analytical solutions in closed form for stresses and displacements around tunnels are derived. In addition, the effectiveness and reliability of theoretical formulas provided are well validated by using the numerical method. Finally, based on the analytical solutions, a parametric investigation on the effects of allowable deformation and distribution of support stiffness on tunnel performance is conducted. Results show that the rock pressure and displacement are significantly affected by these two design parameters. It can be found that rock pressure decreases as either allowable deformation increases or stiffness of the first primary lining decreases, but rock displacement shows an opposite trend. This paper can provide a useful guidance for the design of multi-layered primary linings.

• Geomechanics and Engineering
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• v.15 no.3
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• pp.889-898
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• 2018

Backfilling of mine stopes with waste rocks or tailings is commonly done to enhance ground stability. It is also an alternative for mining wastes disposal. A successful application of underground backfilling requires an accurate evaluation of the stress distribution in stopes. Over the years, various analytical solutions have been proposed to assess these stresses. Most of them were based on the arching theory, considering uniform stresses across horizontal layer elements. The vertical and horizontal stresses in vertical stopes are principal stresses only along the vertical center line, but not close to the walls where there is rotation of the principal stresses. A few solutions use arc layer elements that follow the iso-contours of the minor principal stresses, based on numerical solutions. In this paper, a modified analytical solution is developed for the stresses in vertical backfilled stopes, considering a circular arc distribution. The proposed solution is calibrated with a few numerical modeling results and then validated by additional numerical simulations under different conditions.

• Geomechanics and Engineering
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• v.30 no.4
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• pp.363-372
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• 2022

One of the most frequent issues in tunnel excavation is the collapse of rock blocks and the dropping of rock fragments from the tunnel face. The tunnel face can be reinforced using a number of techniques. One of the most popular and affordable solutions is the use of face longitudinal dowels, which has benefits including high strength, flexibility, and ease of cutting. In order to examine the reinforced face, this work shows the longitudinal deformation profile and ground response curve for a tunnel face. This approach is based on assumptions made during the analysis phase of problem solving. By knowing the tunnel face response and dowel behavior, the interaction of two elements can be solved. The rock element equation derived from the rock bolt method is combined with the dowel differential equation to solve the reinforced ground response curve (GRC). With a straightforward and accurate analytical equation, the new differential equation produces the reinforced displacement of the tunnel face at each stage of excavation. With simple equations and a less involved computational process, this approach offers quick and accurate solutions. The FLAC3D simulation has been compared with the suggested analytical approach. A logical error is apparent from the discrepancies between the two solutions. Each component of the equation's effect has also been described.

• Coupled systems mechanics
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• v.11 no.2
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• pp.151-166
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• 2022

Peltier cells have low efficiency, but they are becoming attractive alternatives for affordable and environmentally clean cooling. In this line, the current article develops closed-form and semianalytical solutions to improve the temperature distribution of Bi₂Te₃ thermoelements. From the distribution, the main objective of the current work-the optimal electric intensity to maximize cooling-is inferred. The general one-dimensional differential coupled equation is integrated for linear and quadratic geometry of thermoelements, under temperature constant properties. For a general shape, a piece-wise solution based on heat flux continuity among virtual layers gives accurate analytical solutions. For variable properties, another piece-wise solution is developed but solved iteratively. Taking advantage of the formulae, the optimal intensity is directly derived with a minimal computational cost; its value will be of utility for more advanced designs. Finally, a parametric study including straight, two linear, barrel, hourglass and vase geometries is presented, drawing conclusions on how the shape of the thermoelement affects the coupled phenomena. A specially developed coupled and non-linear finite element research code is run taking into account all the materials of the cell and using symmetries and repetitions. These accurate results are used to validate the analytical ones.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.27 no.3
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• pp.159-167
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• 2015

In this paper, the errors found in the existed analytical solutions described the mechanism of residual pore-water pressure accumulation were examined and a new analytical was proposed. The new analytical solution was derived by using a Fourier series expansion and separation of variables was verified by comparison with the existed both analytical and numerical solutions and experimental result. The new analytical solution is very simple that there is no need for numerical integration for deep soil thickness. In addition, the solutions of the residual pore-water pressure for finite, deep, and shallow soil thickness reveled that it is possible to approach from finite to shallow soil thickness, but not possible to deep soil thickness because there was discontinues zone between finite and deep soil thickness.

• Earthquakes and Structures
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• v.24 no.1
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• pp.65-79
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• 2023

A simplified analytical solution for seismic response of tunnel cross section in horizontally layered ground subjected to oblique incidence of SH wave is deduced in this paper. The proposed analytical solution consists of two main steps: free-field response in layered field and tunnel response. The free field responses of the layered ground are obtained by one-dimensional finite element method in time domain. The tunnel lining is treated as a thick-wall cylinder to calculate the tunnel response, which subject to free field stress. The analytical solutions are verified by comparing with the dynamic numerical results of two-dimensional ground-lining interaction analysis under earthquake in some common situations, which have a good agreement. Then, the appropriate range of the proposed analytical solution is analyzed, considering the height of the layered ground, the wavelength and incident angle of SH wave. Finally, by using the analytical solutions, the effects of the ground material, burial depth of the tunnel, and lining thickness and the slippage effect at the ground-lining interface on the seismic response of tunnels are investigated. The proposed solution could serve as a useful tool for seismic analysis and design of tunnels in layered ground.

• Proceedings of the KSME Conference
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• 2000.11a
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• pp.458-463
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• 2000

The mechanical structures generally have discontinuous parts such as the cracks, notches and holes owing to various reasons. In this paper, in order to analyze effectively these singularity problems using the finite element method, a mixed analysis method which an analytical solution and finite element solutions are simultaneously used is newly proposed. As the analytical solution is used in the singularity region and the finite element solutions are used in the remaining regions except this singular zone, this analysis method reasonably provides for the numerical solution of a singularity problem. Through various numerical examples, it is shown that the proposed analysis method is very convenient and gives comparatively accurate solution.

• Structural Engineering and Mechanics
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• v.43 no.2
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• pp.211-223
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• 2012

This paper deals with large deformation post-buckling of a linear-elastic and hygrothermal beam with axially nonmovable pinned-pinned ends and subjected to a significant increase in swelling by an alternative method. Analytical approximate solutions for the geometrically nonlinear problem are presented. The solution for the limiting case of a string is also obtained. By coupling of the well-known Maclaurin series expansion and orthogonal Chebyshev polynomials, the governing differential equation with sinusoidal nonlinearity can be reduced to form a cubic-nonlinear equation, and supplementary condition with cosinoidal nonlinearity can also be simplified to be a polynomial integral equation. Analytical approximations to the resulting boundary condition problem are established by combining the Newton's method with the method of harmonic balance. Two approximate formulae for load along axis, potential strain for free hygrothermal expansion and periodic solution are established for small as well as large angle of rotation at the end of the beam. Illustrative examples are selected and compared to "reference" solution obtained by the shooting method to substantiate the accuracy and correctness of the approximate analytical approach.

• Journal of Korean Society for Atmospheric Environment
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• v.15 no.E
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• pp.65-71
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• 1999

The log-normal size distribution theories developed recently for aerosol coagulation are reviewed. The analytical solutiosn to Brownian coagulation developed recently for various particle size regimes are reviewed. In order to describe the evolution of the size distribution of a coagulating aerosol over the entire size range, the analytical solutions developed individually for the free-molecule regime, the transition regime, the nearcontinuum regime, and the continuum regime have been combined. The work described here represents the first analytical solution to the aerosol coagulation problem covering the entire particle size range.

• Structural Engineering and Mechanics
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• v.36 no.6
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• pp.669-678
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• 2010

In general means, the stress concentration problem of elastic plate with a rectangular hole can be investigated by numerical methods, and only approximative results are derived. This paper deduces an analytical study of the stress concentration due to a rectangular hole in an elastic plate under bending loads. Base on classical elasticity theory and FEM applying the U-transformation technique, the uncoupled governing equations with 3-DOF are established, and the analytical displacement solutions of the finite element equations are derived in series form or double integral form. Therefore, the stress concentration factor can then be discussed easily and conveniently. For the plate subjected to unidirectional bending loads, the non-conforming plate bending element with four nodes and 12-DOF is taken as examples to demonstrate the application of the proposed method. The inner force distribution is obtained. The solutions are adequate for the condition when the hole is far away from the edges and the thin plate subjected to any transverse loadings.