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Block stability analysis using deterministic and probabilistic methods
KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering, Soil and Rock Mechanics.
2011 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis presents a discussion of design tools for analysing block stability around a tunnel. First, it was determined that joint length and field stress have a significant influence on estimating block stability. The results of calculations using methods based on kinematic limit equilibrium (KLE) were compared with the results of filtered DFN-DEM, which are closer to reality. The comparison shows that none of the KLE approaches– conventional, limited joint length, limited joint length with stress and probabilistic KLE – could provide results similar to DFN-DEM. This is due to KLE’s unrealistic assumptions in estimating either volume or clamping forces.

A simple mechanism for estimating clamping forces such as continuum mechanics or the solution proposed by Crawford-Bray leads to an overestimation of clamping forces, and thus unsafe design. The results of such approaches were compared to those of DEM, and it was determined that these simple mechanisms ignore a key stage of relaxation of clamping forces due to joint existence. The amount of relaxation is a function of many parameters, such as stiffness of the joint and surrounding rock, the joint friction angle and the block half-apical angle.

Based on a conceptual model, the key stage was considered in a new analytical solution for symmetric blocks, and the amount of joint relaxation was quantified. The results of the new analytical solution compared to those of DEM and the model uncertainty of the new solution were quantified.

Further numerical investigations based on local and regional stress models were performed to study initial clamping forces. Numerical analyses reveal that local stresses, which are a product of regional stress and joint stiffness, govern block stability. Models with a block assembly show that the clamping forces in a block assembly are equal to the clamping forces in a regional stress model. Therefore, considering a single block in massive rock results in lower clamping forces and thus safer design compared to a block assembly in the same condition of in-situ stress and properties.

Furthermore, a sensitivity analysis was conducted to determine which is  the most important parameter by assessing sensitivity factors and studying the applicability of the partial coefficient method for designing block stability.

It was determined that the governing parameter is the dispersion of the half-apical angle. For a dip angle with a high dispersion, partial factors become very large and the design value for clamping forces is close to zero. This suggests that in cases with a high dispersion of the half-apical angle, the clamping forces could be ignored in a stability analysis, unlike in cases with a lower dispersion. The costs of gathering more information about the joint dip angle could be compared to the costs of overdesign. The use of partial factors is uncertain, at least without dividing the problem into sub-classes. The application of partial factors is possible in some circumstances but not always, and a FORM analysis is preferable.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology , 2011. , xiv, 72 p.
Series
Trita-JOB PHD, ISSN 1650-9501 ; 1016
Keyword [en]
Block stability analysis, Model uncertainty, Joint relaxation, Partial factor, Sensitivity analysis
National Category
Geotechnical Engineering
Identifiers
URN: urn:nbn:se:kth:diva-49447OAI: oai:DiVA.org:kth-49447DiVA: diva2:459693
Public defence
2011-12-14, D3, Lindstedtsvägen 5, Entreplan, KTH, Stockholm, 10:00 (English)
Opponent
Supervisors
Note
QC 20111201Available from: 2011-12-01 Created: 2011-11-28 Last updated: 2012-03-22Bibliographically approved
List of papers
1. Design consideration of large caverns by using advanced drilling equipment
Open this publication in new window or tab >>Design consideration of large caverns by using advanced drilling equipment
2007 (English)In: Felsbau, ISSN 0174-6979, Vol. 25, no 5, 131-136 p.Article in journal (Refereed) Published
National Category
Civil Engineering
Identifiers
urn:nbn:se:kth:diva-25091 (URN)2-s2.0-35448996070 (Scopus ID)
Note

QC 20101008

Available from: 2010-10-08 Created: 2010-10-08 Last updated: 2016-05-11Bibliographically approved
2. Investigation of model uncertainty for block stability analysis
Open this publication in new window or tab >>Investigation of model uncertainty for block stability analysis
2011 (English)In: International journal for numerical and analytical methods in geomechanics (Print), ISSN 0363-9061, E-ISSN 1096-9853, Vol. 35, no 7, 824-836 p.Article in journal (Refereed) Published
Abstract [en]

The 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.

Keyword
block stability, analytical solution, model uncertainty
National Category
Materials Engineering
Identifiers
urn:nbn:se:kth:diva-33465 (URN)10.1002/nag.926 (DOI)000289677900005 ()2-s2.0-79954524258 (Scopus ID)
Note
QC 20110523Available from: 2011-05-23 Created: 2011-05-09 Last updated: 2017-12-11Bibliographically approved
3. A new analytical solution based on joint relaxation for analyzing symmetrical block stability
Open this publication in new window or tab >>A new analytical solution based on joint relaxation for analyzing symmetrical block stability
2013 (English)In: International Journal for Numerical and analytical in geomechanics,, ISSN 0363-9061, Vol. 37, no 8, 771-786 p.Article in journal (Refereed) Published
Abstract [en]

The 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.

Keyword
block stability, joint relaxation, analytical solution, DEM, model uncertainty
National Category
Earth and Related Environmental Sciences
Identifiers
urn:nbn:se:kth:diva-50062 (URN)10.1002/nag.1119 (DOI)000318950400001 ()2-s2.0-84877924947 (Scopus ID)
Note

Updated from "Epubl" to "Published" QC 20130625

Available from: 2011-12-01 Created: 2011-12-01 Last updated: 2013-06-25Bibliographically approved
4. Application of partial factors to block stability analysis
Open this publication in new window or tab >>Application of partial factors to block stability analysis
(English)In: Georisk: Assessment and Management of Risk for Engineered Systems and Geohazards, ISSN 1749-9518, E-ISSN 1749-9526Article in journal (Other academic) Submitted
National Category
Earth and Related Environmental Sciences
Identifiers
urn:nbn:se:kth:diva-50067 (URN)
Note
QS 2011Available from: 2011-12-01 Created: 2011-12-01 Last updated: 2017-12-08Bibliographically approved
5. Some aspects on model uncertainty in the calculation of block stability using Kinematics Limit Equilibrium
Open this publication in new window or tab >>Some aspects on model uncertainty in the calculation of block stability using Kinematics Limit Equilibrium
2008 (English)In: 42nd U.S. Rock Mechanics - 2nd U.S.-Canada Rock Mechanics Symposium, American Rock Mechanics Association , 2008Conference paper, Published paper (Refereed)
Abstract [en]

Kinematics Limit Equilibrium (KLE) is one of the most commonly used approaches for evaluating block stability around underground openings. Model uncertainty in using (probabilistic) KLE has been assessed by comparing block stability results with the results of the Discrete Fracture Network-Distinct Element Method (DFN-DEM) approach. The KLE analysis has been performed based on Monte Carlo random generation for fracture orientations and lengths (probabilistic KLE). The results show that the probabilistic KLE underestimates the unstable block volume. The calculated mean value of unstable block volumes using probabilistic KLE is much smaller than DFN-DEM simulation results, which provide a closer representation of reality.

Place, publisher, year, edition, pages
American Rock Mechanics Association, 2008
Keyword
DEM Simulation, Discrete fracture network, Distinct element methods, Fracture orientations, Limit equilibrium, Mean values, Model uncertainties, MONTE CARLO, Random generation, Stability results, Underground opening
National Category
Civil Engineering
Identifiers
urn:nbn:se:kth:diva-25094 (URN)2-s2.0-69549129644 (Scopus ID)
Conference
42nd U.S. Rock Mechanics - 2nd U.S.-Canada Rock Mechanics Symposium 2008; San Francisco, CA; 29 June 2008 through 2 July 2008
Note
QC 20101008Available from: 2010-10-08 Created: 2010-10-08 Last updated: 2012-03-22Bibliographically approved

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