• Geomechanics and Engineering
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• 제8권5호
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• pp.741-756
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• 2015

The prediction of impending collapse of deep tunnel is one of the most difficult problems. Collapse mechanism of deep tunnel in layered soils is derived using a new curved failure mechanism within the framework of upper bound theorem, and effects of seepage forces are considered. Nonlinear failure criterion is adopted in the present analysis, and the possible collapse shape of deep tunnel in the layered soils is discussed in this paper. In the layered soils, the internal energy dissipations along velocity discontinuity are calculated, and the external work rates are produced by weight, seepage forces and supporting pressure. With upper bound theorem of limit analysis, two different curve functions are proposed for the two different soil stratums. The specific shape of collapse surface is discussed, using the proposed curve functions. Effects of nonlinear coefficient, initial cohesion, pore water pressure and unit weight on potential collapse are analyzed. According to the numerical results, with the nonlinear coefficient increase, the shape of collapse block will increase. With initial cohesion of the upper soil increase, the shape of failure block will be flat, and with the lower soil improving, the size of collapsing will be large. Furthermore, the shape of collapsing will decrease with the unit weight decrease.

• Geomechanics and Engineering
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• 제14권6호
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• pp.571-580
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• 2018

The failure mechanism of tunnel roof is investigated with upper bound theorem of limit analysis. The stochastic settlement and nonlinear failure criterion are considered in the present analysis. For the collapse of tunnel roof, the surface settlement is estimated by the simplified stochastic medium theory. The failure curve expressions of collapse blocks in homogeneous and in layered soils are derived, and the effects of material parameters on the potential range of failure mechanisms are discussed. The results show that the material parameters of initial cohesion, nonlinear coefficient and unit weight have significant influences on the potential range of collapse block in homogeneous media. The proportion of collapse block increases as the initial cohesion increases, while decreases as the nonlinear coefficient and the unit weight increase. The ground surface settlement increases with the tunnel radius increasing, while the possible collapse proportion decreases with increase of the tunnel radius. In layered stratum, the study is investigated to analyze the effects of material parameters of different layered media on the proportion of possible collapse block.

• Geomechanics and Engineering
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• 제10권1호
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• pp.21-35
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• 2016

Employing non-associated flow rule and Power-Law failure criterion, the failure mechanisms of tunnel roof in homogeneous and layered soils are studied in present analysis. From the viewpoint of energy, limit analysis upper bound theorem and variation principle are introduced to study the influence of dilatancy on the collapse mechanism of rectangular tunnel considering effects of supporting force and seepage force. Through calculation, the collapsing curve expressions of rectangular tunnel which are excavated in homogeneous soil and layered soils respectively are derived. The accuracy of this work is verified by comparing with the existing research results. The collapsing surface shapes with different dilatancy coefficients are draw out and the influence of dilatancy coefficient on possible collapsing range is analyzed. The results show that, in homogeneous soil, the potential collapsing range decreases with the decrease of the dilatancy coefficient. In layered soils, the total height and the width on the layered position of possible collapsing block increase and the width of the falling block on tunnel roof decrease when only the upper soil's dilatancy coefficient decrease. When only the lower soil's dilatancy coefficient decrease or both layers' dilatancy coefficients decrease, the range of the potential collapsing block reduces.

• 터널과지하공간
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• 제26권6호
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• pp.475-483
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• 2016

지하공동 굴착현장에서 관찰되는 절리분포 양상에 대한 자료를 기반으로 굴착과정에서 형성될 수 있는 사면체 블록의 형상, 규모 및 붕락 가능성을 절리 영속성을 고려하여 예측하는 수치해석 기법을 개발하였다. 절리 영속성 분석결과를 이용하여 절리면의 확장성에 따른 개착면에서의 표출정도 및 블록형성 가능성 해석을 수행하는 기능을 고안하여 기존에 개발된 결정론적 3차원 블록해석모델에 접목시켰다. 개선된 수치해석모델의 신뢰성을 고찰하기 위하여 실제 블록 붕락이 발생된 굴착현장에 대한 해석을 수행하였다. 조사된 절리분포 양상에 의거하여 대표 방향성을 설정하고 잠재적 블록 형성을 분석하여 붕락된 블록 형상에 부합된 해석 결과를 도출하였으며, 이에 근거하여 굴착과정에서의 붕락 진행 미캐니즘을 블록형상을 고려하여 고찰하였다.

• Geomechanics and Engineering
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• 제13권3호
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• pp.505-515
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• 2017

Based on the collapse characteristics of a shallow rectangular cavity, a three-dimensional failure mechanism which can be used to study the collapsing region of the rock mass above a shallow cavity roof is constructed. Considering the effects of surcharge pressure and surface bolt on the collapsing block, the external rate of works produced by surcharge pressure and surface bolt are included in the energy dissipation calculation. Using variational approach, an analytic expression of surface equation for the collapsing block, which can be used to study the collapsing region of the rock mass above a shallow cavity roof, is derived in the framework of upper bound theorem. Based on the analytic expression of surface equation, the shape of the collapsing block for shallow cavity is drawn. Moreover, the changing law of the collapsing region for different parameters indicates that the collapsing region of rock mass decreases with the increase of the density of surface bolt. This conclusion can provide reference for practicing geotechnical engineers to achieve an optimal design of supporting structure for a shallow cavity.

• Geomechanics and Engineering
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• 제13권2호
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• pp.217-235
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• 2017

The stability prediction of shallow buried tunnels is one of the most difficult tasks in civil engineering. The aim of this work is to predict the state of collapse in shallow tunnel in layered soils by employing non-associated flow rule and nonlinear failure criterion within the framework of upper bound theorem. Particular emphasis is first given to consider the effects of dilation on the collapse mechanism of shallow tunnel. Furthermore, the seepage forces and surface settlement are considered to analyze the influence of different dilation coefficients on the collapse shape. Two different curve functions which describe two different soil layers are obtained by virtual work equations under the variational principle. The distinct characteristics of falling blocks up and down the water level are discussed in the present work. According to the numerical results, the potential collapse range decreases with the increase of the dilation coefficient. In layered soils, both of the single layer's dilation coefficient and two layers' dilation coefficients increase, the range of the potential collapse block reduces.

• Structural Engineering and Mechanics
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• 제10권2호
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• pp.181-195
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• 2000

A two-step procedure for the application of non linear constrained programming to the limit analysis of rigid brick-block systems with no-tension and frictional interface is implemented and applied to various masonry structures. In the first step, a linear problem of programming, obtained by applying the upper bound theorem of limit analysis to systems of blocks interacting through no-tension and dilatant interfaces, is solved. The solution of this linear program is then employed as initial guess for a non linear and non convex problem of programming, obtained applying both the 'mechanism' and the 'equilibrium' approaches to the same block system with no-tension and frictional interfaces. The optimiser used is based on the sequential quadratic programming. The gradients of the constraints required are provided directly in symbolic form. In this way the program easily converges to the optimal solution even for systems with many degrees of freedom. Various numerical analyses showed that the procedure allows a reliable investigation of the ultimate behaviour of jointed structures, such as stone masonry structures, under statical load conditions.

• Bulletin of the Korean Chemical Society
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• 제20권9호
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• pp.1045-1048
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• 1999

Electronic structures calculated based upon the extended Huckel tight-binding method for Ba1-xKxBiO3 with x = 0, 0.04, and 0.4 are reported. It is noticed that the commensurate ordering of Bi 3+ and Bi 5+ is responsible for the insulating and semiconducting behavior in BaBiO3 and Ba0.96K0.04BiO4. The band gaps of 3.2 eV and 1.4 eV for the former and the latter compounds, respectively, are consistent with the experimental results. Doping in Bi 6s-block band up to x = 0.4 causes the collapse of the ordering of Bi 3+ and Bi 5+, thereby resulting in the superconductivity in the Ba0.6K0.4BiO3 compound. Strikingly, the character of oxygen contributes to the conducting mechanism than that of the bismuth. This is quite different from the cuprate superconductors in which the character of copper dominates that of oxygen.