Analysis of excavations in jointed rock of infinite extent

Sofianos, A.I.; Watson, J. O.

doi:10.1002/nag.1610100203

Cited by 5 publications

(9 citation statements)

References 4 publications

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“…In the second approach, the initial clamping forces are calculated using BEM with the presence of a joint element. The results of the second approach have more similarity to those of the numerical solution 3, 25. In the second approach, it is inevitable to use a numerical solution, which has the ability to simulate the presence of a joint in order to get a reliable clamping force as input for the analytical solutions.…”

Section: The Crawford–bray Model For Symmetric Blocksmentioning

confidence: 88%

“…Two different approaches calculating initial clamping forces were compared by Sofianos 3, 25. In the first approach, the initial clamping forces were estimated using an elastic solution.…”

Section: The Crawford–bray Model For Symmetric Blocksmentioning

confidence: 99%

“…Using BEM together with a simulation of the joint element obstructs the basic purpose of an analytical solution. It is also understood that the model uncertainty of analytical solutions depends on the joint stiffness ratio of discontinuities 3, 25. The influences of other important key parameters were not discussed in the research mentioned.…”

Section: The Crawford–bray Model For Symmetric Blocksmentioning

confidence: 99%

“…Ignoring the vertical stress field is another source that may give an overestimation of the initial clamping force. Previous research 3, 6, 25 addressed the uncertainties of the Crawford–Bray analytical solution, but no detailed investigation has been carried out to quantify the model uncertainty in the presence of vertical in situ stress and for different conditions of joint stiffness and other key parameters. The objective of this paper is to cover this gap.…”

Section: The Crawford–bray Model For Symmetric Blocksmentioning

confidence: 99%

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Investigation of model uncertainty for block stability analysis

Bagheri

Stille

2011

Num Anal Meth Geomechanics

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SUMMARYThe application of probabilistic design, such as FORM, is expanding rapidly in the design of geotechnical structures. The analytical solution proposed by Crawford and Bray for analyzing block stability can be used as a performance function to carry out probabilistic design. The solution benefits from considering both clamping forces and joint stiffness. However, imperfect assumptions and simplifications in the solution generate model uncertainties. The amount of model uncertainty must be considered in order to assess a reliable design. The purpose of this paper is to identify when the analytical solution is applicable and quantify the model uncertainty of the solution. The amount of model uncertainty for the analytical solution has been assessed for different conditions. The results show that at a shallow depth with a low value of in situ stress ratio (horizontal stress/vertical stress), the analytical solution predicts that the block is stable whereas DEM shows that the block is unstable. The results of the analyses indicate that in cases with low stress ratio, cases with high anisotropy of joint stiffness or the case of a semiapical angle close to the friction angle, the accuracy of the analytical solution is low. Neglecting key parameters, such as the absolute value of joint shear and normal stiffness, vertical in situ stress and its influence on joint relaxation generate model uncertainty in the analytical solution. The analyses show that by having more information about the key parameters, the model uncertainty factor could be identified more precisely.

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Section: The Crawford–bray Model For Symmetric Blocksmentioning

confidence: 88%

“…Two different approaches calculating initial clamping forces were compared by Sofianos 3, 25. In the first approach, the initial clamping forces were estimated using an elastic solution.…”

Section: The Crawford–bray Model For Symmetric Blocksmentioning

confidence: 99%

Section: The Crawford–bray Model For Symmetric Blocksmentioning

confidence: 99%

Section: The Crawford–bray Model For Symmetric Blocksmentioning

confidence: 99%

See 2 more Smart Citations

Investigation of model uncertainty for block stability analysis

Bagheri

Stille

2011

Num Anal Meth Geomechanics

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“…A comparison of results using the numerical discrete method and Crawford–Bray's analytical solution showed a significant difference in calculated block stability. One explanation could be that clamping forces in a discontinuous medium are generally lower due to stress relaxation of joints than those calculated using continuous mechanics .…”

Section: Introductionmentioning

confidence: 97%

A new analytical solution based on joint relaxation for analyzing symmetrical block stability

Bagheri

Stille

2011

Num Anal Meth Geomechanics

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SUMMARYThe magnitude of clamping forces has a significant influence on the estimated ultimate pullout force of a block. The Crawford-Bray equation, which is fundamental in considering clamping forces, is only a function of horizontal stress and block height. Further research to incorporate the influence of induced stress in block stability analysis was considered, but all the previous analytical solutions for analyzing block stability assume a continuum medium to estimate clamping forces and do not allow joint deformations to occur before block movement due to gravity. Assuming a continuous medium to estimate clamping forces leads to an overestimation of block stability and therefore unsafe design. In this paper, an attempt has been made to deepen the understanding of the block failure mechanism and correct the estimated magnitude of clamping forces in a discontinuous medium. A conceptual model is proposed based on the loading-unloading of the block from an in-situ state to failure. Based on this model, an analytical solution has been developed that calculates clamping forces in a discontinuous medium. The validity and model uncertainty of the solution were checked for different conditions. The new analytical solution is both precise and accurate and can be used as a design tool to estimate block stability. Copyright © 2011 John Wiley & Sons, Ltd. Block failure is not just one of the most common failure modes in tunnels but is also very complex. Various design tools such as kinematic analysis, analytical solutions and numerical discrete methods are available to analyze block stability. Analytical solutions are particularly important since they provide a conceptual description of the complex failure mechanism as well as a basis for understanding the interaction between factors governing block stability. Analytical solutions can also be used to generate the performance function for probabilistic analysis.Calculation of block stability based on ignoring clamping forces produces an uneconomical design [1]. On the other hand, an overestimation of clamping forces leads to an unsafe design. The precise estimation of clamping forces is thus a critical issue. The analytical solutions for estimating clamping forces available today [2][3][4][5][6][7][8][9][10][11] are based on continuum mechanics and may overestimate the clamping forces. A comparison of results using the numerical discrete method and CrawfordBray's analytical solution [12] showed a significant difference in calculated block stability. One explanation could be that clamping forces in a discontinuous medium are generally lower due to stress relaxation of joints than those calculated using continuous mechanics [12,13].Crawford and Bray [2] assumed constant clamping forces when in reality clamping forces change from the initial state, due to excavation and block movements. Using a model that is closer to reality

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Evaluation of the leading band coefficients of the boundary integral system of equations

Sofianos¹

1987

Commun. appl. numer. methods

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Analysis of excavations in jointed rock of infinite extent

Cited by 5 publications

References 4 publications

Investigation of model uncertainty for block stability analysis

Investigation of model uncertainty for block stability analysis

A new analytical solution based on joint relaxation for analyzing symmetrical block stability

Evaluation of the leading band coefficients of the boundary integral system of equations

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