The key‐group method

Bafghi, A R Yarahmadi; Verdel, Thierry

doi:10.1002/nag.283

Cited by 36 publications

(10 citation statements)

References 6 publications

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“…In the current study, the failure modes in the blocks can be divided into translational modes and rotational modes. Translational modes include free falling or uplifting, single plane sliding, and double plane sliding [17,24,29,32,33]. The safety factor of the key block can be calculated as the following according to the KBT [13]:…”

Section: Methodology For Probabilistic Blocksmentioning

confidence: 99%

“…Later, Lin and Fairhurst [15], and Mauldon and Goodman [16] theoretically solved the rotation problems of blocks in stability analysis and continuously developed the vector analysis method. Yarahmadi-Bafghi and Verdel [17] extended KBT to a key-group method, which considered not only individual key blocks but also groups of collapsible blocks and explained how to identify the key groups. Continuously, Noroozi et al [18] performed a rock slope stability analysis using the key-group method under 2D and 3D conditions, and the outcomes of the 3D analysis were in good agreement with reality and the results of 2D analysis.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Jointed Surrounding Rock Mass Stability Analysis on an Underground Cavern in a Hydropower Station Based on the Extended Key Block Theory

Jia

Lian

et al. 2017

Energies

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Abstract:The jointed surrounding rock mass stability is of utmost importance to integral stability during the construction and long-term safety operation of the underground caverns in hydropower stations. The key blocks play a significant role in the integral stability of the jointed surrounding rock mass, therefore it is critical to determine the location, size, and failure mode of random key blocks. This paper proposes an improved method combining the traditional key block theory (KBT) and the force transfer algorithm to accurately calculate the safety factors of probabilistic key blocks in the surrounding rock mass. The force transfer algorithm can consider the interactions between the internal blocks. After the probabilistic characteristics of the joint fissures are obtained, the stereographic projection method is employed to determine the locations of dangerous joints. Then the vector analysis method is used to search the random blocks, determine the sliding directions of random blocks, and calculate the block sizes and safety factors near the free surface of the underground cavern, which can be used to comprehensively evaluate the surrounding rock mass stability. The above numerical results have provided powerful guidance for developing a reinforcement system for the surrounding rock mass.

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Section: Methodology For Probabilistic Blocksmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Jointed Surrounding Rock Mass Stability Analysis on an Underground Cavern in a Hydropower Station Based on the Extended Key Block Theory

Jia

Lian

et al. 2017

Energies

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“…A procedure has been also established for implementing key‐group analysis based on the main steps of the key‐block analysis (i.e. steps 1–2 below), followed by a specific key‐group analysis (steps 3–5): Identify the key blocks using the vector method. Remove the unstable single key blocks when the safety factor computed from a limit equilibrium analysis is less than a given limit, and return to step one until there is no more unstable key blocks. Identify the neighbor's common to one or several remaining single and stable key blocks (those that were not removed in the previous steps). Construct all possible groups with the remaining single key blocks and each of the previously identified neighbors. Perform a stability analysis of the groups (limit equilibrium method) and remove the unstable groups or only keep the stable group having the minimum safety factor. Iterate using the new geometry (from step 1) until there are no more blocks capable of being combined .…”

Section: Review On the Key‐group Methodsmentioning

confidence: 99%

“…In reality, however, groups of ‘stable’ blocks, when considered as a whole, may in some instances prove to be unstable. Yarahmadi and Verdel proposed the ‘key‐group method’, which combines groups of collapsible blocks into an iterative and progressive analysis of the stability of discontinuous rock slopes . This method is all intrinsically deterministic.…”

Section: Introductionmentioning

confidence: 99%

3D key‐group method for slope stability analysis

Noroozi

Jalali

Yarahmadibafghi

2011

Num Anal Meth Geomechanics

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Because of the simplicity and the speed of execution, methods used in static stability analyses have yet remained relevant. The key-block method, which is the most famous of them, is used for the stability analysis of fractured rock masses. The KBM method is just based on finding key blocks, and if no such blocks are found to be unstable, it is concluded that the whole of the rock mass is stable. Literally, though groups of 'stable' blocks are taken together into account, in some cases, it may prove to be unstable. An iterative and progressive stability analysis of the discontinuous rock slopes can be performed using the keygroup method, in which groups of collapsible blocks are combined. This method is literally a twodimensional (2D) limit equilibrium approach. Because of the normally conservational results of 2D analysis, a three-dimensional (3D) analysis seems to be necessary.In this paper, the 2D key-group method is developed into three dimensions so that a more literal analysis of a fractured rock mass can be performed. Using Mathematica software, a computer program was prepared to implement the proposed methodology on a real case. Then, in order to assess the proposed 3D procedure, its implementation results are compared with the outcomes of the 2D key-group method. Finally, tectonic block No.2 of Choghart open pit mine was investigated as a case study using the proposed 3D methodology. Results of the comparison revealed that the outcomes of the 3D analysis of this block conform to the reality and the results of 2D analysis.

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“…Mauldon and Goodman (1996) examined the kinematic and kinetic constraints on block rotations and developed an analytical model for the study of rotational failure in jointed rock. Yarahmadi-Bafghi and Verdel (2003) proposed the "key-group method" that considers not only individual key blocks but also groups of collapsible blocks, and Noroozi et al (2012) developed the key-group method for three-dimensional space. Tonon (2007) presented an incremental-iterative algorithm for analyzing the general failure modes of rock blocks D r a f t taking into account large block displacements and rotations.…”

Section: Introductionmentioning

confidence: 99%

Analysis of removability and stability of rock blocks by considering the rock bridge effect

Zheng

Xia

2016

Can. Geotech. J.

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In traditional block theory, the removability and stability of rock blocks are analyzed independently; that is, the stability of a removable block is analyzed in detail, and nonremovable blocks are regarded as stable. However, in practical situations, nonremovable blocks may pose more danger than removable blocks. This paper presents a unified method for analyzing the removability and stability of rock blocks. In this method, the cracking of rock bridges is considered and nonremovable blocks are not assumed to be stable. First, possible cracking rock bridges are identified by extending finite-sized fractures and comparing the boundary surfaces of the resulting blocks with those of the original blocks. Then, the sliding direction associated with each possible moving block is determined by solving an optimization problem. The normal force acting on each sliding surface is determined, and the resisting force on each rock bridge is calculated and integrated into the total resisting force when calculating the safety factor of a possible moving block. Procedures to determine all possible moving blocks are introduced, and the possible moving block with the minimum safety factor is regarded as the actual moving block. The corresponding minimum safety factor is defined as the actual safety factor of the block. The proposed method is verified by considering a few examples. The results show that nonremovable blocks may be unstable if the cracking of rock bridges is considered.

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The key‐group method

Cited by 36 publications

References 6 publications

Jointed Surrounding Rock Mass Stability Analysis on an Underground Cavern in a Hydropower Station Based on the Extended Key Block Theory

Jointed Surrounding Rock Mass Stability Analysis on an Underground Cavern in a Hydropower Station Based on the Extended Key Block Theory

3D key‐group method for slope stability analysis

Analysis of removability and stability of rock blocks by considering the rock bridge effect

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