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Block theory has been widely used in analyzing the stability of rock blocks during engineering activities in jointed rock masses due to its simplicity and computational efficiency. This paper extended the traditional block theory to tunnels constructed using tunnel boring machine (TBM) by incorporating the disc cutter-block interaction mechanism. The rock blocks were divided into front, corner and rear blocks according to their spatial positions with respect to the cutterhead. The interaction between different blocks and the disc cutters mounted on the cutterhead were examined by estimating the forces exerted by disc cutters on the blocks relative to the location of the blocks in the face, direction of movement of the discs, and the depth of penetration. The estimated forces were then used in a subsequent analysis to calculate factor of safety for individual blocks and probability of blocks dislodging from its location. Two new evaluation parameters, e A and e η , were proposed to account for the probability of block instability. e A is the ratio of exposed area of unstable blocks to the face area and quantifies the size of unstable blocks relative to the face, and e η is the ratio of cutterhead rotation angles making a block unstable to the total rotation angles in a revolution which reflects the possibility of encountering an unstable block during a single round of revolution. This paper discussed the implementation of the idea of using fundamental concepts of block theory to determine block stability at the face and related analysis for assessment of face stability. The proposed method was used in evaluation of the stability conditions for a water-conveyance tunnel in western China that is currently under construction using a hard rock TBM.

Analyzing the stability of rock blocks is important in rock engineering. Most block analysis methods assume the blocks are formed by planar fractures whereas the stability of blocks formed by curved fractures are rarely investigated. However, large fractures observed in field are often curved. This paper presents a method for analyzing the stability of blocks formed by both planar and curved fractures. The blocks are represented as assemblages of element-blocks with possible cracked rock bridges. First, the triangle meshes representing the curved boundaries of blocks are simplified using an edge-collapsing-based method. Then, possible cracking rock bridges are determined by extending fracture facets and comparing the boundary surfaces in the new block system with those in the original one. The connection relation of the element-blocks are used to determine possible moving blocks, and the resisting force on rock bridges are considered when calculating the safety factor of each possible moving block. Finally, the possible moving block with the minimum safety factor is regarded as the actual moving block and the associated minimum safety factor is defined as the actual safety factor of the block. Several analytical examples are given to validate the proposed method and the results show that blocks formed by curved fractures may be unstable if the cracking of rock bridges is considered.

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.

Several failure modes may occur around underground excavations, one of the most common being block failure. The size distribution and occurrence probabilities of unstable blocks depend on discontinuity parameters such as size, shape, intensity, and orientation. The knowledge about the size and the number of blocks provides critical information to optimize site characterization and design procedures, or at least to accomplish this more efficiently. In this work we introduce a new attribute, Circular Variance, to measure the degree of dispersion of the fracture poles in angular domain based on borehole data. In our study the final objective is to present a predictive model of the mean rate of the formation of unstable rock blocks and their uncertainty. To fulfill this goal, we introduce a hybrid approach based on the combination of probabilistic discrete fracture network modeling, rock block failure instability analysis and supervised vector machine concepts. The present research studies the impact of P32, circular variance, and mean radius of the fractures on the mean generation rate of unstable blocks in a tunnel at El Teniente mine, Chile. A two and three factors supervised Poisson regression models are compared against each other for the prediction of the mean generation rate of unstable blocks. The results showed a good agreement between the real number of unstable blocks and the estimated ones with supervised Poisson regression models.

Valid modeling and identification of rock blocks are the keys to analyzing rock-mass stability. Based on the Monte Carlo method and 2D Poisson point process, an enhanced polygonal discrete fracture network (DFN) model is proposed firstly. The equal area conversion algorithm and subarea simulation method are used to control fracture size and to determine fracture shape, respectively. Then, coupling the polygonal DFN model with the large-scale geological model, a refined rock mass structure model for identifying rock blocks is established. Subsequently, the spatial representations of polygonal fracture planes, complex geological surfaces and free surfaces are presented. And the major characteristics and the refined modeling method of complex rock blocks and block-groups are analyzed. Finally, a modified and precise topology-based identification method of rock blocks and block-groups is put forward. The application in the underground powerhouse of a hydropower station indicates that the proposed approach and scheme are very efficient and can identify arbitrary-shaped rock blocks. The identified rock blocks and block-groups contain geometric information, geological information as well as physical and mechanical information. This research contributes to further study on the stability analysis of rock blocks and block-groups and rock mass seepage.

Preventing the fresh air from reaching the fire seat by sealing the portals or placing obstructions is a promising approach to put out a fire in long tunnels. A series of fire tests using methanol fuel with nominal heat release rates of 5.6 kW and 11.2 kW were carried out in a 1/20 reduced-scale model tunnel with the sizes of 20.8 m long, 0.45 m wide and 0.23 m high to explore the impact of blockage in tunnel on the effectiveness of fire-fighting. Blocks of two configurations were considered, i.e., one is down-standing blocks and the other is upward blocks. The blockage ratio was fixed at 65% and two blocks were symmetrically positioned at varying distances. With down-standing blocks at 8 m, 6 m and 4 m, the self-extinction times reduces by approximately 11%, 34% and 47% respectively for a 5.6 kW fire and by 20%, 30% and 42% respectively for an 11.2 kW fire. The shorter the distance of the blocks to the fire seat, the quicker the time to self-extinct. The reduction in self-extinction time with blocks at 10 m is insignificant. A similar result was obtained for upward blocks at varying distances. Comparably, the down-standing block makes the fires extinct more quickly than its counterpart. The presence of blocks significantly promotes the mixing of smoke layer and accelerates the descent rate of smoke layer, which results in highly vitiated supplying air approaching fire seat thus a reduction in the time to self-extinct.

Mechanical behavior of a jointed rock mass with non-persistent joints located adjacent to a free surface on the wall of an excavation was simulated under without and with support stress on the free surface using approximately 0.5 m cubical synthetic jointed rock blocks having 9 non-persistent joints of length 0.5 m, width 0.1 m and a certain orientation arranged in an en echelon and a symmetrical pattern using PFC3D software package. The joint orientation was changed from one block to another to study the effect of joint orientation on strength, deformability and failure modes of the jointed blocks. First the micro-mechanical parameters of the PFC3D model were calibrated using the macro mechanical properties of the synthetic intact standard cylindrical specimens and macro mechanical properties of a limited number of physical experiments performed on synthetic jointed rock blocks of approximately 0.5 m cubes. Under no support stress, the synthetic jointed rock blocks exhibited the same three failure modes: (a) intact rock failure, (b) step-path failure and (c) planar failure under both physical experiments and numerical simulations for different orientations. The jointed blocks which failed under intact rock failure mode and planar or step-path failure mode produced high and low jointed block strengths, respectively. Three phases of convergence of free surface were discovered. The joint orientation and support stress played important roles on convergence magnitude. The average increment of jointed block strength turned out to be about 10, 7.9 and 6.6 times the support stress when support stresses of 0.06 MPa, 0.20 MPa and 0.40 MPa were applied, respectively. The modeling results offer some guideline in support design for underground excavations.

Two modifications are made to enable the use of the discontinuous deformation analysis (DDA) method to investigate the sequential construction of an underground cavern complex. One modification is the “block birth and death” approach. With the aid of a boundary block searching algorithm, this approach excavates the blocks in any closed domain step by step and is verified by a DDA example. The other modification is an updating algorithm of the rock bolt called the dull-reactivating method. In this new algorithm, the coordinates of the ending endpoints of the dull rock bolts are regularly updated and the corresponding rock bolts in the sequential reinforcement region are reactivated. The initial geostress field and the sequential construction of the underground cavern complex of the Dagangshan hydropower station in Southwest China are simulated with the modified DDA method. Valuable results are obtained by analysing the displacement, stress and rock bolt force. In the construction processes, the blocks around each cavern form a bearing capacity system to prevent the block deformation, and the rock bolts jointly support the stress release as a system. At the sidewalls of the main machine building and the downstream side wall of the tail surge chamber, the blocks cut by joints with a high dip angle suffer a strong stress release, and the tension forces of the several rock bolts are so large that they should be noticed, which provides a basis for the construction guidance of the project.

The orientation, trace length, spacing, and location of probabilistic discontinuities in rock masses are randomly developed. Thus, the shape, size, and location of blocks cut off by these probabilistic discontinuities are accordingly stochastic. It is difficult, or even impossible, to determine the volume and location of the blocks using the block theory proposed by Goodman and Shi (1985) . Stochastic block analysis (SBA) is capable of identifying three-dimensional (3-D) stochastic blocks from a randomly developed discontinuity network (discrete fracture network). However, in practice, 3-D blocks are not identified well in simulated fracture networks and so the use of SBA is seldom encountered. In this paper, the procedures involved in stochastic block identification are first outlined. The concept and calculation of overlaying area and ratio are then introduced. Then, the stochastic block identification results are used to explore the statistical distribution of the block size and overlaying ratio. Subsequently, the laws governing development of the stochastic blocks were elucidated. The results show that the block size has a negative exponential distribution and the overlaying ratio follows a Γ distribution. The overlaying ratio increases as the trace length to spacing ratio increases. We further outline, for the first time, approaches to determine block support measures by analyzing the characteristics of the statistical distributions of the stochastic blocks. Block support issues relating to a practical underground plant were also studied. The lengths and anchor forces and spacings of the rock bolts were quantitatively determined according to the results of a statistical analysis of the stochastic blocks. Statistical analysis of stochastic blocks is of great significance in understanding the development characteristics of the stochastic blocks and in quantitatively determining block support measures.

An extended key block method for rock mass stability analysis is proposed by considering the force effect of key blocks in later batches to the first batch which is exposed at rock mass surfaces. Through a realistic numerical representation of a three-dimensional rock mass, different batches of key blocks are searched by means of a progressive failure process. A force transfer algorithm is developed to consider the interactions of the key blocks in different batches. The calculated sliding forces in the first batch which consider the later batches’ effect will lead to a better design of rock supports. After selection of a reinforcement scheme, the stability of the reinforced rock mass is re-assessed. Those larger instable blocks formed by inside blocks with anchored surface blocks are checked out. It is found that the two-step check of a reinforcement scheme, i.e. (1) safety check of the bolted individual blocks; (2) safety check of the bolted block groups is more effective. Results show that the proposed rock support design method is more realistic and rational for the reinforcement of blocky rock mass.

It has been gaining credence over the past several decades that the spatial characteristics of rock joints exert detrimental effect on the stability of tunnel structures. The deterministic joint spatial distribution around the tunnel was defined by digital photogrammetry technique, which statistically provides the basis for performing Monte-Carlo simulation of stochastic joints that are hidden inside the surrounding rock. The blocks generated by the intersection between structural planes and excavation surfaces were analyzed based on the block theory and limit equilibrium. The keyblocks were identified and the corresponding factors of safety were determined. All these analysis procedures were codified into the computer program GeoSMA-3D (Geotechnical Structure and Model Analysis). The developed software satisfied the fast analysis requirements of joint plane simulation, spatial block modelling, keyblock identification and failure process illustration. The case study was performed with reference to Dabeigou Tunnel on Duolun Second-class Highway in Duolun Town, Nei Mongol, China. Failure process illustration would be useful to facilitate the practical engineers to understand the basic mechanism and select the strengthening strategies.

The occurrence of geologic planes is a major feature of rock mass. In underground excavation, the intersection of geologic planes and excavation surfaces generates blocks. A new methodology for block identification is presented. This methodology employs finite element (FE) modeling technique to identify blocks so it is different from the traditional topology-based block identification algorithms. As complex spatial excavation surfaces are precisely simulated by FE model, this methodology can identify blocks considering complex profile and layout of underground caverns. By considering the finiteness of geologic planes, convex and concave blocks can be both identified. As is defined on FE model, the identified block system can be visualized directly by employing FE graphic system. As a result, there is no need to specially develop graphic system for block visualization. A case study is done on a large scale hydropower underground cavern complex. The block identification results prove the effectiveness of the proposed methodology. The results are further compared with the observation data derived from in situ investigation. The comparison indicates that the proposed block identification methodology is reliable. Therefore, it provides a new approach for block analysis.

Geometrical modeling of rock joints in 3D space determines the geometrical parameters of joints such as orientation, frequency, size, shape and location. Joint size and volumetric frequency among the parameters are very difficult to obtain because a complete joint plane within rock mass cannot be observed directly. In this study, a recent technique developed by the author was used to estimate the joint size and volumetric frequency. The developed technique uses the least square method to estimate the joint diameter distribution, whose by-product is the volumetric frequency. This technique was applied to a cut slope close to a rail-road tunnel under design and the removability of rock blocks formed by circular joints simulated by statistical estimation was analysed. The volume, height, perimetric length and occurrence probabilities of rock blocks around a tunnel were calculated. The block analysis result was compared with that of a commercial program, UDEC (Universal Distinct Element Code). (A) This paper was presented at Safety in the underground space - Proceedings of the ITA-AITES 2006 World Tunnel Congress and the 32nd ITA General Assembly, Seoul, Korea, 22-27 April 2006. For the covering abstract see ITRD E129148. “Reprinted with permission from Elsevier”.

We present, in this paper, a set of computer codes for the studies of rock block instability during the boring of a tunnel with the aim of a better safety during works. The first code is for data acquisition, which is the determination of the discontinuity families extracted by image analysis of front end. The second code, using the rock mass model obtained above, determines and draws all the instable blocks for a portion of tunnel, allowing statistic representation of block problems inside the tunnel. This code is based on the Warburton algorithm with some improvements. The third one, is an evaluation of the number of bolts or anchors corresponding to a given safety level. (A) This paper was presented at Safety in the underground space - Proceedings of the ITA-AITES 2006 World Tunnel Congress and the 32nd ITA General Assembly, Seoul, Korea, 22-27 April 2006. For the covering abstract see ITRD E129148. "Reprinted with permission from Elsevier".

Discontinuities within the rock mass can divide the rock into blocks with different sizes and shapes based on the geometrical parameters and pattern of existing joints. The volume of blocks created by cross-cutting of joints has a key role in underground works and selecting the proper supporting system. In this paper the possible shapes which a block can take as a result of the cross-cutting of the joints, as well as the general principles existing in block volume calculation methods are described, and a new method which concerns an especial focus on dip angel, strike, spacing and density of joints is proposed. By this method the block volume calculation is performed more accurately. The software used in this study is AutoCAD. This method proved an acceptable result on a case study performed on a part of horseshoe tunnel of Marvdasht railway having 8 (m) length and 5.35 (m) diameter. This tunnel has been drilled within limestone rock using blasting method. (A) This paper was presented at Safety in the underground space - Proceedings of the ITA-AITES 2006 World Tunnel Congress and the 32nd ITA General Assembly, Seoul, Korea, 22-27 April 2006. For the covering abstract see ITRD E129148. "Reprinted with permission from Elsevier".