Key Block Theory Research Articles

A knowledge-data dually driven paradigm for accurate identification of key blocks in complex rock slopes

Accurate identification and effective support of key blocks are crucial for ensuring the stability and safety of rock slopes. The number of structural planes and rock blocks were reduced in previous studies. This impairs the ability to characterize complex rock slopes accurately and inhibits the identification of key blocks. In this paper, a knowledge-data dually driven paradigm for accurate identification of key blocks in complex rock slopes is proposed. Our basic idea is to integrate key block theory into data-driven models based on finely characterizing structural features to identify key blocks in complex rock slopes accurately. The proposed novel paradigm consists of (1) representing rock slopes as graph-structured data based on complex systems theory, (2) identifying key nodes in the graph-structured data using graph deep learning, and (3) mapping the key nodes of graph-structured data to corresponding key blocks in the rock slope. Verification experiments and real-case applications are conducted by the proposed method. The verification results demonstrate excellent model performance, strong generalization capability, and effective classification results. Moreover, the real case application is conducted on the northern slope of the Yanqianshan Iron Mine. The results show that the proposed method can accurately identify key blocks in complex rock slopes, which can provide a decision-making basis and rational recommendations for effective support and instability prevention of rock slopes, thereby ensuring the stability of rock engineering and the safety of life and property.

An open-source MATLAB toolbox for 3D block cutting and 3D mesh cutting in geotechnical engineering

This study presents a simple approach and its associated MATLAB toolbox for 3D block cutting and mesh cutting. The approach is suitable for the meshes of numerical methods including the Key Block Theory (KBT), the Discontinuous Deformation Analysis (DDA), the Numerical Manifold Method (NMM), and the cut Finite Element Method (Cut-FEM). The strategy is based on calculations on convex bodies. It uses two different forms of representation: the geometric representation which includes vertices and faces, and the algebraic representation which consists of inequalities. The cutting was implemented on the algebraic representation, and the resulting inequalities were converted into a geometric representation. The above strategy turned out to be robust and straightforward to execute, at the cost of a general body being regarded as a combination of convex bodies. The efficiency guarantee was considered through pre-checking algorithms. The source code was provided, as well as some simple examples.

Rock mass substitute geometry theory (SGT) and 3D centroid sliding pyramid (CSP) method

Discontinuous analysis methods are typically used for the stability analysis of fractured rock masses with multiple sets of joints. Among various discontinuous methods, the key block theory (KBT) requires less data input, has a higher computational efficiency, and is suitable for wide-ranging engineering applications. Classical discontinuous numerical methods typically require complete boundary information for rock block units. However, current information-gathering methods can only capture information on rock surfaces. The proposed rock mass substitute geometry theory (SGT) overcomes this limitation by using local geometric information to equivalently represent the original geometric body simplifying subsequent analyses. A 3D centroid sliding pyramid (CSP) method is introduced for motion state analysis of a rock block that uses only the collinear faces of a block’s free surfaces. A comparison of CSP with KBT proves that CSP not only addresses the issue of collecting only surface information of rock masses but it significantly minimizes the computation scale. Additionally, a 3D discontinuous analysis program was developed, encompassing the entire process of rock mass information gathering, 3D discontinuous modeling, and 3D CSP analysis. The effectiveness and efficiency of the method were validated using stochastically generated models, while its practical engineering applicability was demonstrated at an engineering site.

Engineering geological characteristics and failure mechanics of Jure rock avalanche, Nepal

IntroductionThe rock avalanches are a frequent and disruptive phenomenon in the Himalayas and other mountain chains. To minimize future losses, it is essential to investigate the engineering geological causative factors and mechanism of these mass wasting events.Study areaThe present work is aimed at assessing the failure mechanism of the disastrous 2014 Jure rock avalanche along Araniko Highway, Northern Nepal. The event had blocked the Sunkoshi River and blocked an economically significant route to China.Geotechnical properties and analysisInitially, rockmass characterization and intact strength attribute were determined for the site to classify the failure zone. The parameters measured and obtained from the field and laboratory were integrated into the analytical models to obtain a conclusive interpretation of the failure mechanism. Structural, kinematic, and key block theory analyses have been carried out for decipher the evolution of the failure zone.Results and discussionRock mass was found to be of fair quality, however, the structural instabilities and the presence of water has led to a progressive failure. Movement of the key block and subsequent sliding of wedges and foot failure appears to be a possible failure mechanism.ConclusionThe present research explores the contributory engineering geological aspects of the Jure rock avalanche. The investigation results can be used to tackle similar large scale rock avalanches in similar geological terrains and thus minimizing the losses.

Application of the deterministic block theory to the slope stability design of an open-pit mine in Morocco

Purpose. Discontinuities in rock masses are natural fractures that delimit various block shapes and sizes, which can fall, slide or topple from the excavation and collapse under their own weight inducing probably severe damage. Thus, it is essential to carry out a block analysis before beginning any surface or underground excavation project. This paper proposes a methodology based on key block theory analysis to select the suitable slope of different discontinuous rock masses of an open-pit mine in Morocco. Methods. At first, the main discontinuities of each bench are determined and projected onto a stereonet with a maximum dip angle of the excavation plane. Then, it is possible to identify the removable blocks by using the theorem of removability according to block theory. After that, a limit equilibrium analysis is performed to determine the failure mode and the friction angle required to stabilize the blocks. When the selected dip angle of the slope plane is found to be unsuitable, it is changed and reduced by one degree, and the same approach is repeated until the maximum safe slope dip angle is obtained. Findings. The results of the proposed methodology based on key block theory analysis have shown that the maximum safe slope angles of the studied benches are in the range of 63-73°. When compared to the slope angles used in the mine, which are between 58-78°, the results of this study are close to in-situ conditions. Originality. In this research, the maximum safe slope angle of fractured rock masses was optimized by eliminating slope angles inducing unstable blocks (key blocks) and by using the stereographic projection method of key block theory. Practical implications. Using this methodology, stability of rock slopes in civil or mining-engineering projects can be designed or assessed when geotechnical data are very limited.

Stability analysis of fractured rock masses based on an extended key block theory considering the forces between blocks and block rotation

Key block theory is a widely used method in rock engineering for analyzing the stability of fractured rock masses. However, the traditional theory does not consider the forces between blocks and block rotation very well, its results may differ from real conditions. Therefore, we proposed an extended key block theory by considering the forces between blocks and block rotation. The forces between blocks were calculated by a displacement constraint method of the rigid body based on 3DEC platform. In the analysis of block rotation, block rotatability was analyzed by a geometric condition and mechanical condition. Net moments and rotational safety factors of movable blocks were calculated to judge whether the block rotates. Considering block rotation along an edge and block translation, block failure modes can be divided into free falling, single-plane sliding, double-plane sliding, edge rotation, and sliding rotation. We created a 3DEC-KBM program that incorporates the extended method into the 3DEC platform. This method not only obtains more accurate forces between blocks but also has more efficiency compared with the direct application of 3DEC. The correctness of this method was verified by the 3DEC results of a single-block slope model, and it was adopted to analyze the stability of a fractured rock slope and fractured rock masses surrounding an underground cavern. The research results showed the following: (1) The forces between blocks often decrease block stability, but also improve the stability of some blocks; (2) The forces between blocks is easier to make the blocks rotation comparing with the case only considering the gravity effect, because of the changing position and direction of the resultant force acting on a block; (3) Compared with the traditional key block theory, the extended method has higher accuracy and it is necessary to consider the blocks’ rotation when taking the forces between blocks into account.

Anchorage design analysis and field monitoring of large key blocks in high and steep rock slope

One of the main failure modes of rock slope is the instability of the key block formed by cutting combination of structural planes. In view of the block stability and control problem caused by the combination of structural planes in the high and steep rock slope in Southwest China, the key block theory method and on-site monitoring method are used to study the stability of the key block after the excavation of the slope, the optimization of the design parameters of anchor cable support, and the deformation characteristics and change laws of the slope with the construction process are analyzed. The research results show that the large block formed by the discontinuity layer and layer fracture of the slope reaches 26000 m3, sliding along the structural plane on both sides, with low safety factor. The safety monitoring data show that the block is stable after the reinforcement with anchor cable.

A General Block Stability Analysis Algorithm for Arbitrary Block Shapes

In rock engineering, block theory is a fundamental theory that aims to analyze the finiteness, removability, and mechanical stability of convex blocks under different engineering conditions. In practice, the possible combinations of the fractures and joint sets that may generate key blocks can be identified by stereographic projection graphs of block theory. However, classic key block theory does not provide solutions for nonconvex blocks, which are very common in civil projects, such as those with underground edges, corners, and portals. To enhance the availability of block theory, a general algorithm that can analyze the removability and stability of blocks of arbitrary shapes is proposed in this paper. In the proposed algorithm, the joint pyramid for blocks of arbitrary shapes can be computed, and the faces of the blocks are grouped according to their normal vectors such that parallel or nonadjacent sliding faces with the same normal vector can be immediately identified when the sliding mode is determined. With this algorithm, blocks of arbitrary shapes can be analyzed, and users do not need to have experience interpreting graphs of block theory to take advantage of its accuracy and effectiveness. The proposed algorithm was verified by several benchmarking examples, and it was further applied to investigate the stability of the left bank rock slope of a dam. The results showed that the proposed algorithm is correct, effective, and feasible for use in the design and support of excavation in complex rock masses.

Stability Analysis and Reliability Evaluation in Cataclastic Loose Rock Mass Blocks

Cataclastic rock masses with multiple failure modes and mechanisms are critical geological problems in the construction of rock slopes. Cataclastic rock masses are widely distributed in slopes of a hydropower project located on Lancang River, which is located in Tibet, China. In this study, the potentially unstable block of the slope is divided into key block and secondary key block based on the key block theory, and the system reliability evaluation theory is introduced. The method for quantitatively analyzing the rock mass stability of cataclastic slopes with sliding failure is established. Then, the spatial distribution of cataclastic rock masses and discontinuities in several rock slopes of a hydropower project are determined using traditional geological surveying and 3D laser scanning. At last, combining the BATE 2.0 software and the stereographic projection of the vector, the proposed method is applied to the study area. The results show that the main failure mode of the studied slope is wedge failure, and the system reliability is 1.69. With the increase in the instability probability of the key block, the increase in the instability probability of the system block is obvious, which reflects the controlling effect of the key block on the stability of the system block. The calculated system instability probability is slightly larger than the key block instability probability.

Analysis of Roof Deformation Mechanism and Control Measures with Roof Cutting and Pressure Releasing in Gob‐Side Entry Retaining

The mechanical model of the basic roof fracture structure is established on the basis of key block theory to study the roof breaking mechanism of gob‐side entry retaining under roof cutting and pressure relief, and the analytical formula of roof support resistance is derived when the key block of the basic roof is stable. The influence of roof cutting angle and cutting height on roof support resistance is also analyzed. Determining the cutting seam parameters of the retained roadway roof is necessary to identify the support resistance of the roadway roof due to the correlation between the roof cutting parameters and the support resistance. Taking the II 632 haulage drift of the Hengyuan coal mine as the engineering background, FLAC3D numerical simulation is used in this paper to analyze the influence of different roof cutting angles and cutting heights on the surrounding rock structure evolution of retained roadways. Results show that the roof cutting angle and cutting height respond to the support resistance of the retained roadway roof, and the support resistance required by the roof increases with the roof cutting angle and cutting height. This condition ensures that the side roof of the gob can be cut off smoothly, and the support resistance required by the roof of retained roadways is within a reasonable range. Through theoretical and numerical simulation analysis, the reasonable roof cutting height of II 632 haulage drift is 8 m and the roof cutting angle is 15°. The theoretical analysis and numerical simulation results reveal that the required support resistance to maintain the stability of the roadway roof is 0.38 MPa. The supporting scheme of the roof of the II 632 haulage drift in the Hengyuan coal mine is then designed. Finally, the field industrial test is used for verification. The borehole imaging results show that the overall line of the retained roadway roof is small based on the description of field monitoring results. The deformation of the surrounding rock surface of the retained roadway is less than 100 mm, and the roadway is 40 m from the lagging working face. The deformation rate of surrounding rock decreases with the increase in distance from the working face. The integrity of the retained roadway roof is good, and the deformation of the surrounding rock is effectively controlled.

Stability of a rock mass using the key block theory: a case study

In underground mines, excavating disturb the initial equilibrium state of the rock mass, and therefore require selection of a support in order to control the movement of rocks, avoid landslide and work safely. Thus, the progress of mining operations in the ST2 mineralization, in the eastern zone of the Bouazzer mine, is disrupted because of stability problems. On the basis of field observations and analyzes of core drill, the geological and structural study, carried out in this area, has shown the existence of three types of facies: altered and cracked diorite, cobaltiferous mineralization which is in contact with serpentinites. In fact, the empirical methods such as Barton, Bieniawski and the recommendations of the AFTES have qualified the rock mass as poor, furthermore they proposed as kind of supports: steel arches, shotcrete and rock-bolts. Numerical simulation by the finite element method proved to be very complex due to existence of several types of discontinuities (faults, shistosities and joints).These discontinuities are natural fractures that delimit various shapes and sizes of wedges, which can become detached from the roof or siding of the excavation and collapse under their own weight. Although the empirical methods cited above provide supports for each facies, however, this support is expensive and difficult to implement in practice because it must cover the entire surface of the excavation and thus not allowing to detect stable blocks that do not require a support. For this it was essential to carry out an analysis of wedges to better locate unstable blocks. The treatment of fracturing data has highlighted the presence of five sets of discontinuities of which three sets are principals and the other two are minor joints. Then, while taking into account the geometrical, mechanical data of the discontinuities as well as the geometrical data of the excavation, we were able to detect the shape and the size of the unstable blocks and the sets of discontinuities delimiting them and which favor their sliding and tilting. Thus, we calculated the number of anchor bolts needed to stabilize these blocks in order to ensure an acceptable safety factor. This study shows clearly how a wedge analysis of the rock mass can guide and optimize the support work.

Tunnel stability assessment by 3D DDA-key block analysis

The key block theory is often the first analysis carried out in assessing potential instability caused by tunneling through jointed rock masses. This study suggests that it is beneficial to include it as the first step for a detailed design analysis by discrete numerical modeling, such as 3D DDA. The procedure is illustrated with an example which is simplified but is general and contains both primary and secondary key blocks. The agreement of the identified key blocks from 3D DDA and the key block theory provides credence for the DDA study, while the DDA, in turn, gives insights on how the failure of the unstable blocks evolves and complements the key block analysis.

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

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.

Stability of undercut space in fragment orebody based on key block theory

Undercut is one kind of important spaces to place the mining blocks in the mass underground mining. This structure is also used as a compensation space during blasting. In the process of underground mining in the fragment orebody, it is important and critical to analyze the stability and blockage of the three-dimensional wedges created around the undercut space. The wedge stability is mainly controlled by factors including geometry (i.e., the size, shape and spatial location of the wedge and undercut), the strength (shear and tensile) of the discontinuities that created the wedge, and the stress distribution within the rock mass. The Unwedge software was used to conduct the orthogonal simulation tests (three factors and five levels) that considered different cross sections, trends, and plunges of the undercut space. The results demonstrate that the control value of the safety factor of wedge is set to be 1.2. The optimal parameters are determined in the undercut space, such as the blasting fragmentation, orientation of the fluid flow, and the equipment gradeability; the wedge stability can be evaluated in the light of the block images and continuous falling; the stability of the key block meets the needs of the undercut space, the parameters gained are reasonable and optimal. Cross section is 27°, trend is from 315° to 325° (it is 320° at in-suit test) and plunge is 5°.

Stability analysis of statically indeterminate blocks in key block theory and application to rock slope in Jinping-I Hydropower Station

Using the movability analysis in block theory, one can easily determine all movable blocks. However, only for a movable block with no more than two structural surfaces, called the statically determinate block, can the factor of safety be determined by the static analysis, which limits more extensive application of key block theory. In order to analyze general movable blocks with multiple structural planes, an optimization model for solving the safety factor of blocks is built in this paper. In the model, the safety factor as well as the normal stress on the slip surface is taken as independent variables; and the objective function is specified as the safety factor alone. The statically admissible conditions include the system of equilibrium equations, non-negativity of both normal stress on the slip surface and thrust inside the block. Since the objective function is linear and the constraint functions are polynomials of no more than degree-2, it is weak in nonlinearity and can be solved by those conventional optimization techniques, and disadvantages of the conventional block theory are overcome. After some typical examples are tested, the stability of the left bank rock slope of Jinping-I Hydropower Station is conducted in detail, and the stability evolution due to excavation is systematically studied by this method.

Study on calculation of rock pressure for ultra-shallow tunnel in poor surrounding rock and its tunneling procedure

A computational method of rock pressure applied to an ultra-shallow tunnel is presented by key block theory, and its mathematical formula is proposed according to a mechanical tunnel model with super-shallow depth. Theoretical analysis shows that the tunnel is subject to asymmetric rock pressure due to oblique topography. The rock pressure applied to the tunnel crown and sidewall is closely related to the surrounding rock bulk density, tunnel size, depth and angle of oblique ground slope. The rock pressure applied to the tunnel crown is much greater than that to the sidewalls, and the load applied to the left sidewall is also greater than that to the right sidewall. Meanwhile, the safety of the lining for an ultra-shallow tunnel in strata with inclined surface is affected by rock pressure and tunnel support parameters. Steel pipe grouting from ground surface is used to consolidate the unfavorable surrounding rock before tunnel excavation, and the reinforcing scope is proposed according to the analysis of the asymmetric load induced by tunnel excavation in weak rock with inclined ground surface. The tunneling procedure of bench cut method with pipe roof protection is still discussed and carried out in this paper according to the special geological condition. The method and tunneling procedure have been successfully utilized to design and drive a real expressway tunnel. The practice in building the super-shallow tunnel has proved the feasibility of the calculation method and tunneling procedure presented in this paper.

Key block theory application for rock slope stability analysis in the foundations of medieval castles in Slovakia

Abstract This research investigates the stability of rock slopes in the foundations of selected medieval castles in Slovakia. In the first phase, static analysis of the 45 selected medieval castle rock slopes was performed, where more than 12,000 potentially unstable blocks were analyzed and the factor of safety in static condition was calculated using the key block theory implemented in the Kbslope module of PTworkshop software. Based on results of the static stability analysis, a pseudo-static analysis was performed adopting the seismic acceleration in accordance with Slovak Technical Standards – Seismic actions on structures. This was implemented by calculating the vectors of horizontal force acting upon shear failure in the direction of the slope face with a zero vertical component. When non-finite and tapered blocks were ignored, the results proved that 14% of the 12,217 blocks investigated under static conditions could be considered unstable. This number increased to 23% under pseudo-static conditions, when seismic acceleration was implemented in the stability calculations. A detailed stability assessment of the Gymes Castle located in western Slovakia was carried out with delineation of blocks prone to rock sliding and proper stabilization methods, based on joint sets orientation measurements performed on the 3D point cloud generated by laser scanner.

Polyhedral modelling of underground excavations

Abstract The use of key-block theory for the analysis of blocky rock mass structures in mining and civil engineering is well established. Such methods have traditionally been used to analyse the stability of rock blocks at free surfaces only. These methods have also been limited to the analysis of relatively few discontinuities, usually assumed to be infinitely persistent. Development of more advanced algorithms has removed these limitations and allowed the development of a modeller capable of handling multiple curved, finite persistent discontinuities. We discuss this modeller and its capability of predicting the existence of polyhedra with unlimited facets and morphologies. This paper describes the use of this polyhedral modeller for the study of the stability of an underground excavation and offers significant advantages over the algorithm recently reported by Menendez-Diaz et al. (2009) [3] which is restricted to the analysis of pentahedral blocks formed by four discontinuity sets.

Support design of river crossing tunnel using keyblock concept and its validation by monitoring of the countermeasure by digital photogrammetry

Mountainous sites are increasingly selected for such infrastructure developments as highway or waste disposal plant projects, and the number of works carried out in/on rock masses has increased accordingly. Because rock masses have long been involved in civil works, several good analytical methods have been developed for the evaluation of rock behaviors. However, no effective technique is in place that can perfectly forecast and precisely control the behavior of a group of rock masses that have countless cracks and fragile discontinuities. This paper reports on a research that aimed to develop an integrated technology for controlling civil works in/on discontinuous rock masses, which covers processes from survey, analysis to measurement and combines a block analysis-based design technique with a rock behavior monitoring technique using digital photogrammetry. The block theory is one of the analytical methods capable of dealing with the behavior of discontinuities, which is essentially a 3D phenomenon, while the digital photogrammetry technique allows mapping measurement targets on 3D coordinates. Combining these techniques would allow controlling discontinuities from survey to construction processes. Here, these techniques are put into practice in an actual tunneling work, which proved that combining the 3D design concept with the keyblock analysis, as well as the observation method with digital photogrammetry, was very effective and essential for the evaluation of complex geological conditions. Suzuka Tunnel was first bored by 5 m in diameter TBM and was enlarged to about 250 m2. The tunnel of 17 m diameter was designed to pass through under Sosorogawa River and the crown of the tunnel is less than 15 m below the bottom of the river. The tunnel excavation may cause rock mass instability in the area and the change of groundwater flow condition could lead to flooding. If any action was not taken, collapse of the tunnel would give considerable impact to the river flow that is important for agriculture in the local society. Using discontinuity data from TBM wall, we detected some unstable blocks by Keyblock theory. And we designed rockbolts to protect removable blocks. And we planed 3D monitoring method to verify effectiveness of the counter-measure. We developed digital photogrammetry system to observe tunnel displacement. The displacement, size and orientation of the rock masses were three dimensionally monitored with this system. A change shown in Figure was detected when the cutting face was approaching the fault (white line), and a discontinuous rock behavior was observed. (A) Reprinted with permission from Elsevier. For the covering abstract see ITRD E124500.

Stability analysis of block in the surrounding rock mass of a large underground excavation

Keyblock has been received a lot of attention in underground engineering because it loses its stability first after excavation. Block theory originally proposed by Shi could not build the geometric characteristics of keyblock and explain how to determine the precise locations of keyblock. Therefore, the Unwedge program based on keyblock theory could not predict complicated polyhedral block except tetrahedral block and determine its precise location. In this paper, the stability of keyblock of a large underground excavation is analyzed in detail. First, the Unwedge program (Ver.2.35) is used to identify possible keyblocks and some limitations are discussed. Then many kinds of geometric models of polyhedral keyblock are built, a new computer program is developed to search keyblocks and determine their precise locations, comprehensively considering the action of gravity and dynamic loadings. Finally, the results of two methods are compared and the differences are analyzed.