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Spatial characterization of joint planes and stability analysis of tunnel blocks
Abstract
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.
... Wang et al. [10] used the Monte Carlo method to generate stochastic structural planes, based on which movable blocks were analyzed using the block theory and limit equilibrium. Sun et al. [11] used the Monte Carlo method to develop a 3D stochastic network model of the structural plane with a Baecher disk model based on the SfM photogrammetric method. ...
... Numerous studies have focused on extracting geometric features of structural planes. For example, Wang et al. [10] employed a three-dimensional image reconstruction technique to conduct topological identification of joints and obtained information on deterministic structural planes. Guo et al. [42] proposed a semi-automatically extraction method of rock mass structural plane information based on three-dimensional point clouds. ...
... The focus of this paper is to address the limitation of traditional method in generating structural planes, i.e., the inability of traditional methods to take into account parameter correlations. The traditional method regards the structured plane as the Baecher model and focuses on six parameters of the structural plane, including dip direction, dip, trace length, and center coordinates of the disc when generating the structural plane [10,47]. These structural planes are distributed stochastically in a certain size of 3D space. ...
The stochastic structural plane of a rock mass is the key factor controlling the stability of rock mass. Obtaining the distribution of stochastic structural planes within a rock mass is crucial for analyzing rock mass stability and supporting rock slopes effectively. The conventional Monte Carlo method generates each parameter of stochastic structural planes separately without considering the correlation between the parameters. To address the above problem, this study novelly uses the denoising diffusion probabilistic model (DDPM) to generate stochastic structural planes. DDPM belongs to the deep generative model, which can generate stochastic structural planes without assuming the probability distribution of stochastic structural planes in advance. It takes structural plane parameters as an integral input into the model and can automatically capture the correlations between structural plane parameters during generation. This idea has been used for stochastic structural plane generation of the Oernlia slope in the eastern part of Straumsvatnet Lake, Nordland County, north-central Norway. The accuracy was verified by descriptive statistics (i.e., histogram, box plot, cumulative distribution curve), similarity measures (i.e., mean square error, KL divergence, JS divergence, Wasserstein distance, Euclidean distance), error analysis, and the linear regression plot. Moreover, the linear regression plots between the dip direction and the dip angle verified that DDPM can effectively and automatically capture the correlation between parameters.
... For these three failure modes, the focus was on the state of slope blocks during the failure process. The contribution of control-type joint surfaces was determined using the limit equilibrium theory, with a stability coefficient Fs=1 at the limit equilibrium, which quantified their effects on the stability of slope blocks (Sengani et al. 2021;Wang et al. 2013). Considering the actual situation of the joint surfaces separating the blocks from the slopes, the role of cohesion of joint surface was not considered in the calculations. ...
... The anti-sliding force FR along the sliding surface and stability coefficient Fs is (Wang et al. 2013): ...
... Then the stability coefficient Fs can be obtained (Wang et al. 2013 ...
The instability of slope blocks occurred frequently along traffic corridor in Southeastern Tibet (TCST), which was primarily controlled by the rock mass structures. A rapid method evaluating the control effects of rock mass structures was proposed through field statistics of the slopes and rock mass structures along TCST, which combined the stereographic projection method, modified M-JCS model, and limit equilibrium theory. The instabilities of slope blocks along TCST were then evaluated rapidly, and the different control factors of instability were analyzed. Results showed that the probabilities of toppling (5.31%), planar (16.15%), and wedge (35.37%) failure of slope blocks along TCST increased sequentially. These instability modes were respectively controlled by the anti-dip joint, the joint parallel to slope surface with a dip angle smaller than the slope angle (single-joint), and two groups of joints inclined out of the slope (double-joints). Regarding the control effects on slope block instability, the stabilization ability of double-joints (72.7%), anti-dip joint (67.4%), and single-joint (57.6%) decreased sequentially, resulting in different probabilities of slope block instability. Additionally, nearby regional faults significantly influenced the joints, leading to spatial heterogeneity and segmental clustering in the stabilization ability provided by joints to the slope blocks. Consequently, the stability of slope blocks gradually weakened as they approached the fault zones. This paper can provide guidance and assistance for investigating the development characteristics of rock mass structures and the stability of slope blocks.
... Rafiee and Vinches (2008) combined geological statistical analysis and conventional methods to model the threedimensional structure of rock masses. Wang et al. (2013) reproduced the position and shape of the joints around the tunnel based on the Monte Carlo method and achieved the identification of key blocks based on the limit equilibrium theory. Salvini et al. (2017) successfully used the data from UAV image photointerpretation to study the geological structure of the rock mass and built a three-dimensional DFN model of its fracture system. ...
... Moreover, there are some studies focusing on generating stochastic structural planes to try to further indentify key blocks in rock masses (Wang et al. 2013. This is also the objective of our research work in this paper. ...
... In this paper, we consider the structured plane as the Baecher model and focus on six parameters of structural planes including inclination, dip angle, trace length, and the center coordinates of the disc when generating the structured plane. These parameters have been shown to be reasonable in previous studies (Wang et al. 2013;Han et al. 2016), and we choose to perform structural plane generation based on them. And the results in this paper also prove the reasonableness. ...
... Similarly, Zhang et al. [51] extracted the discontinuity trace information using trace feature point; the total processing time was <2 min. Meanwhile, commercial software and opensource programs, such as Rockscan [30], GeoSMA-3D [63], CAE Sirovision [28] and Discontinuity Set Extractor (DSE) [32], have been gradually developed and applied in the acquisition and interpretation of tunnel face data,. However, the interpretation of images in some software packages may experience a long time as the generation of a high density point cloud is computationally expensive [32]. ...
... Li et al. [37] conducted research on the automatic extraction of the discontinuity orientation, spacing, trace, roughness, and aperture, which were used to calculate RMR and GSI. The other application of the extracted discontinuity information is to analyze the stability of the surrounding rock mass of the tunnel [28,33,34,63], which accounts for 13% of the subsequent analysis, as shown in Fig. 7 (b). Huang et al. [28] used the coordinates and orientations of joints to generate a 3D discrete model and investigate the stability of the surrounding rock of the tunnel; their study results could guide the installation of tunnel supports. ...
... The integrated system can support the high-precision design of tunnels in construction. Similarly, Wang et al. [63] performed a 3D stability analysis of tunnel blocks using the discontinuity information and the analysis results provided a guidance for the adjustment of support parameters. ...
During the rock tunnel construction, one of the critical aspects lies on the support design to secure the construction safety. Due to the extreme complex underground geological and geotechnical condition, the support design needs to be dynamic and ideally should consider all related data and information comprehensively and timely. Different Internet of things (IoT) and other related information technologies (IT) have been widely applied during tunnel construction to collect a large amount of monitoring data, which in turn demands real time or just-in-time (JIT) data processing for decision making. To understand the state-of-the-art IoT-based dynamic tunnel support design, a comprehensive review is conducted from the perspectives of real time or just-in-time data acquisition, data interpretation and data aggregation. For different types of technologies, their time consumptions, technology strengths and drawbacks were thoroughly analyzed in a full and seamless “data acquisition-interpretation-aggregation” workflow linking to the dynamic tunnel support optimum design. As a result of the review, three primary research gaps are identified, i.e., the high time consumption of data interpretation, dilemmas of conventional and AI-supported aggregation methods, and long retrieval time for similar design cases. Focusing on these three gaps, three key concepts, namely, time consumption, accuracy, and degree of automation, are proposed as key indicators for the tunnel support design. A conceptual framework, just-in-time tunnel support design is further proposed, where the most appropriate and efficient methods can be conceptually integrated and lead towards technical implementation. This review contributes to the comprehensive understanding of timely dynamic tunnel support design and provides future insights of promoting JIT tunnel support optimum design.
... Based on the block theory and modern computer technique, a three-dimensional numerical software GeoSMA-3D is developed for identifying key blocks [15,48,49]. The main procedures include three dimension discontinuities network simulation, analysis of intersecting lines between discontinuities and surfaces, analysis of primary loops, loops location analysis, isolated loops deleting, relative loop analysis, closed block identification, and key block determination [48,49]. ...
... Based on the block theory and modern computer technique, a three-dimensional numerical software GeoSMA-3D is developed for identifying key blocks [15,48,49]. The main procedures include three dimension discontinuities network simulation, analysis of intersecting lines between discontinuities and surfaces, analysis of primary loops, loops location analysis, isolated loops deleting, relative loop analysis, closed block identification, and key block determination [48,49]. The block search module in GeoSMA-3D was used to determine the key blocks based on the classical block theory. ...
... Combining the information of joints derived from ShapeMetriX3D with the block search module in the GeoSMA-3D software, the judgment of block stability and the visualization of key blocks can be achieved. The block search module in GeoSMA-3D can provide the visualization of key blocks, as well as quantitative information such as the safety factor, volume, and sliding surface of key blocks [15,48,49]. The key blocks determined in the original procedure were under static loading. ...
Shear strength deterioration of rock joints and its induced instability of key blocks subjected to dynamic disturbance constitute the mechanism of many geological disasters such as rockburst, landslide, and rockfall. In this study, the influence of dynamic disturbance on rock joints was quantified in the form of stress, of which model was established by quasistatic method. The dynamic shear strength of rock joints was analyzed theoretically following the Coulomb-Navier criterion and further investigated experimentally by split Hopkinson pressure bar (SHPB) tests with impact velocities of 4.850 m/s, 8.722 m/s, 12.784 m/s, and 16.935 m/s. The effect of engineering disturbance on shear strength of rock joints was measured, and a degradation coefficient was used to describe it quantitatively. Considering the degradation of dynamic shear strength of rock joints and its influence on block stability, the method for determining key blocks under dynamic disturbance was given. Implementing this method into the program of Geotechnical Structure and Model Analysis-3D (GeoSMA-3D) developed by the authors’ team, the visualization of key blocks was achieved. From theoretical analysis and experimental investigation, it was figured out that the shear strength of rock joints is degraded under dynamic disturbance. The degradation of friction angle becomes more sensitive than that of cohesion. Additionally, numerical results show that the number of key blocks was increased with the increasing impact velocities.
... Key blocks are finally identified and visualized. The developed software package has been successfully applied to different projects comparing to field measurements, such as rock slopes (Wang and Ni 2014) and tunnels (Wang et al. 2013b). In this study, determination of key blocks is an initial step for slope stability analysis. ...
... The generated blocky system from GeoSMA-3D will be implemented in a discontinuous deformation analysis (DDA) code for further investigation, which corresponds to an advanced discretization process. In the following, the discretization of blocky system from GeoSMA-3D will be introduced briefly, and further details of the software can be found elsewhere (Wang et al. 2011, 2013b, Wang and Ni 2014. ...
... These geometric features finally form polyhedrons or blocks. The following criteria are used in GeoSMA-3D to determine whether a set of structural planes can form a block, and further details of DFN model simulation can be found elsewhere (Wang et al. 2011, 2013b, Wang and Ni 2014. ...
Rock is a heterogeneous material, which introduces complexity in the analysis of rock slopes, since both the existing discontinuities within the rock mass and the intact rock contribute to the degradation of strength. Rock failure is often catastrophic due to the brittle nature of the material, involving the sliding along structural planes and the fracturing of rock bridge. This paper proposes an advanced discretization method of rock mass based on block theory. An in-house software, GeoSMA-3D, has been developed to generate the discrete fracture network (DFN) model, considering both measured and artificial joints. Measured joints are obtained from the photogrammetry analysis on the excavation face. Statistical tools then facilitate to derive artificial joints within the rock mass. Key blocks are searched to provide guidance on potential reinforcement measures. The discretized blocky system is subsequently implemented into a discontinuous deformation analysis (DDA) code. Strength reduction technique is employed to analyze the stability of the slope, where the factor of safety can be obtained once excessive deformation of slope profile is observed. The combined analysis approach also provides the failure mode, which can be used to guide the choice of strengthening strategy if needed. Finally, an illustrated example is presented for the analysis of a rock slope of 20 m height inclined at 60° using combined GeoSMA-3D and DDA calculation.
... The most commonly used method for generating stochastic structural planes is the Monte Carlo method (Hatzor, 1993;Kulatilake et al., 1993;Meyer & Einstein, 2002;Wang et al., 2013;Warburton, 1985). The method is based on the principles of probabilistic and statistical theories, calculating the mean and variance of each geometric parameter of the structural plane. ...
... The most commonly used method for generating stochastic structural planes is the Monte Carlo method (Hatzor, 1993;Kulatilake et al., 1993;Meyer & Einstein, 2002;Wang et al., 2013;Warburton, 1985). On the basis of principles of probabilistic and statistical theories, this method calculates the mean and variance of each geometric parameter of the structural plane. ...
Tunnels stand as indispensable pillars of transportation infrastructure, assuming a central and transformative role in fostering the sustainable evolution of urban. The excavation process of tunnels presents a spectrum of geological challenges, encompassing the potential for instability and collapse. Ensuring the stability of the tunnel is a top priority in tunnel construction. The destabilization leading to collapse in certain tunnels is intricately connected to the structural planes of the rock mass. Accurately obtaining the distribution of structural planes within the rock mass is the necessary basis for maintaining the stability of the tunnel. The conventional Monte Carlo method generates each parameter of stochastic structural planes separately without considering the correlations between the parameters. To address this limitation, we propose a stochastic structural plane generation method based on deep generative model (DGM). The model takes the measured factual structural plane data as input, and the neural network realizes the generation of structural plane data with automatic learning of the distribution law of structural planes and the correlations between each parameters without assuming the probability distribution of stochastic structural planes in advance. This method has been used for stochastic structural plane generation of the rock mass in the Yuelongmen Tunnel located in Mianyang city, Sichuan province. The validation results show that the proposed DGM-based method automatically captures the correlation between structural plane parameters while ensuring the greater accuracy of the generated structural planes.
... The surrounding rock stability and mechanical behavior of the roadway or tunnel construction have been widely studied. Some researchers carried out model tests to study the mechanical behavior of a circular tunnel with homogeneous strata [10,11] and analyzed the failure characteristics and strain field of the tunnel surrounding rock [12][13][14][15][16]. Precast cracks or faults have also been explored by a large volume of existing research [17][18][19]. ...
... To better observe the deformation around the The surrounding rock stability and mechanical behavior of the roadway or tunnel construction have been widely studied. Some researchers carried out model tests to study the mechanical behavior of a circular tunnel with homogeneous strata [10,11] and analyzed the failure characteristics and strain field of the tunnel surrounding rock [12][13][14][15][16]. Precast cracks or faults have also been explored by a large volume of existing research [17][18][19]. ...
Ore bodies incubating within fault zones are a common phenomenon in geological strata and pose a huge challenge for underground mining. To effectively exploit mineral resources, the layout of the mining roadway and the interaction between the roadway and geological fault must be considered. In this paper, a bonding fracture was formed on granite samples to simulate a closed fault, under which a circular hole was fabricated to simulate the roadway of the gold mine. We performed a biaxial compression test at a true-triaxial electrohydraulic servo testing system for granite samples with a combined fracture-hole structure. It is worth noting that the fracture inclination β and relative distance between fracture and hole L were taken into account. The digital image correlation (DIC) technique was used to observe the displacement and strain field evolution around the fracture-hole structure. Our results demonstrate that (1) the strength of the granite sample decreases with increasing bonding fracture dip angle β, and the displacement drops between the hanging wall and foot wall raised in both the horizontal and vertical displacement directions. Macroscopic cracks become dense, and the failure degree becomes severe around simulated fault areas. (2) With the increase in the distance L, the strength of the granite sample increases, the influence of the hole on the slip of the fracture plane is weakened, and the discontinuity of displacement becomes less obvious. (3) The maximum principal strain field quantitatively reveals the details of the crack initiation, propagation, and coalescence around the fracture-hole structure, and displacement nucleation is observed in the vertical displacement field.
... Class IV discontinuities are widely accommodated inside rock masses; these discontinuities significantly affect the physical and mechanical properties of the rock mass, and their geometric parameters always follow a specified probabilistic distribution. Hence, Class IV discontinuities are usually generated randomly, and they are defined as "stochastic discontinuities" in modelling endeavours (Wang et al., 2013). The orientation data 3 https://www.springer.com/journal/12303 ...
... The spatial distributions of these large-scale discontinuities are remarkably different from those of stochastic discontinuities, and they lack a specified probabilistic distribution function. Hence, they are usually defined as "deterministic" discontinuities (Wang et al., 2013). A deterministic discontinuity can be regarded as an infinite plane, that is, the diameter of the discontinuity model is + (the disc model is chosen as the discontinuity model here). ...
Traditional methods used to demarcate homogeneous structural domains are mainly concerned with small-scale discontinuities; this approach can be regarded as a process for evaluating the degree of homogeneity among stochastic discontinuities from one site to another. This process forms the basis for determining the distribution of stochastic discontinuities within a homogeneous structural domain; however, it neglects large-scale discontinuities. In this study, the statistically homogeneous structural domains within a large-scale jointed rock mass were meticulously demarcated in three dimensions, which was performed in four steps. 1) A three-dimensional discontinuity network model was constructed containing both deterministic and stochastic discontinuities. 2) The model was subsequently discretized into a large number of cubic grids, and the MBi values of all the grids were calculated. 3) Using the K-means algorithm, the structural domain boundaries within the tested rock mass were meticulously demarcated, and a composited model consisting of homogeneous structural domains was constructed. 4) Each homogeneous structural domain was separately visualized. This demarcation method can consider large-scale discontinuities and improve the identification sensitivity in a large-scale jointed rock mass with a high accuracy. Moreover, the separate presentation of structural domains directly reflects the morphological properties unique to each structural domain.
... Using this library can not only improve the efficiency, but also greatly increase the robustness and scalability of the program and provide the benefit of an interface for the 3D visualization platform. Goodman and Shi (1985) put forward that there are primarily two kinds of failure models of the block system: a single-side sliding model, and a double-sided sliding model, which are theoretical foundations of the GeoSMA-3D software mentioned below (Wang and Ni 2014;Wang et al. 2013Wang et al. , 2017. Figure 7a shows the single-side sliding model. After obtaining the dip direction α and dip angle β of the structural plane, the cosine of the inclination θ is calculated from the spatial geometry (shown in Eqs. 1, and 2) and then calculate the gravity of the rock mass G is calculated; in accordance with the principle of the limit equilibrium, the safety factor F s can be determined by the ratio of the anti-sliding force and sliding force (Eq. ...
... To address the block identification problem, a geotechnical structure and model analysis-3D (GeoSMA-3D) system are developed to investigate the stability of jointed rock (Wang and Ni 2014;Wang et al. 2013Wang et al. , 2017. Based on block theory and the limit equilibrium criterion, the rock structural characteristics (nonlinear, inhomogeneous, and anisotropic) can be reproduced. ...
High-steep slope information collection and multistep rocky slope stability analysis play an important role in slope engineering. However, traditional on-site investigations suffer from terrain restrictions and data omissions. This paper presents a block identification method based on UAV (unnamed aerial vehicle) photogrammetry and its computer implementation. An SfM (structure from motion) method is introduced and a 3D reconstruction software-PhotoScan was used to build the DEM (digital elevation model) of the rock mass for real-time monitoring. Then, an RANSAC (random sample consensus) shape detection algorithm was used to search the structural planes in the point cloud model. A computer program GeoSMA-3D (geotechnical structure and model analysis-3D) has been developed to implement engineering applications and a case study was carried out which confirmed the efficiency of the method in dealing with complex surface modeling and multistep rocky slope stability analysis.
... They calculated risk potential besides static and quasi-static analysis of the site. Wang et al. [16] combined Monte Carlo technique with key block method to analyze the stability of a tunnel blocks. ...
... Finally, the weighted safety factor of unstable groups and blocks for different stages of the analysis is calculated based on their related volume using Eq. (16). ...
Slope stability analysis of jointed rocks has been the focus of many studies. The presence of joints and discontinuities in rock environments intensifies instability along with the development of block movements. Many analytical and numerical methods have been proposed and applied to analyze the stability of jointed rock slopes. Computation complexity, incapability of presenting a reliable safety factor to be used for developing a proper design operation and improper analysis speed are the known challenges of these methods. This paper has developed the analytical well-known Key Group Method (KGM) to Toppling-Free fall-Sliding Key Group (TFS_KGM) version. For this, toppling and free fall failure are added to the existing method in order to better analyze of jointed rock slopes. In this method, unstable key blocks participate in creating groups which may rotate or free fall besides sliding. The new TFS_KGM computes stability conditions and final safety factors based on the most unstable sliding, rotating and free fall movements with consideration of in situ stresses. Results of using this method in jointed rock slopes and the comparison with DEM numerical, KBM and KGM analytical methods show that the method is very effective particular when the geometrical conditions of the jointed rocks make the toppling and free fall failures potentially possible. The method demonstrates a simple computation method along with a proper analysis speed. It also provides accurate design safety factors and much more optimized critical failure areas than previous methods.
... It intersects with the tunnel trend at a large angle and contains numerous steep and compressive structural planes. As per the intersection between the tunnel trend and structural plane, the surrounding rock seriously threatens the stability of the tunnel face (Wang et al. 2013). ...
The Maoxian Tunnel in Sichuan, China has experienced significant deformation and supporting failure in the surrounding phyllite rock. To address this problem, on-site engineering geological investigation and testing methods were deployed in the present study to examine the characteristics and mechanism of deformation in the tunnel. Scanning electron microscopy, rock hydraulic tests, and uniaxial compressive tests were used to investigate the hydraulic and mechanical properties of the surrounding rock, and to examine the mechanisms underlying the significant deformation. The results suggest that the large deformation in Maoxian Tunnel is a result of shear expansion and progressive failure of the soft rock under high stress. To enhance the integrity and self-sustaining ability of the rock mass, it is necessary to promptly construct support structures and reinforce the surrounding rock.
... Earlier in-situ block identification can only be conducted in the field by using some simple tools, which are time-consuming, human-bias, sometimes hazardous, and limited by inaccessible terrain Kong et al., 2021). With the rapid evolution and wide range application of modern computer technology, some scholars focused on developing unstable block searching algorithms by integrating key block theory with the threedimensional (3D) discrete fracture network (DFN) simulation technique (Chen et al., 2003;Zhang et al., 2010;Wang et al., 2013;Wang and Ni, 2014;Zhang et al., 2020). These algorithms have been successfully applied in large scale underground cavern complexes. ...
A R T I C L E I N F O Keywords: Block automatic extraction Dangerous rock block Block geometric characterization Block stability analysis In-situ block Discontinuity trace map A B S T R A C T Using a rock slope surface model generated from unmanned aerial vehicle (UAV) digital photogrammetry, this study develops a new semi-automatic dangerous rock blocks extraction approach. It consists of four steps: (1) three dimensional trace map extraction and projection; (2) convex polygon searching using a depth-first search algorithm and a sign consistency test; (3) true block formation analysis based on the geometric topology; and (4) block removability, failure mode and stability analyses using the edge vector, active resultant vector and limit equilibrium method, respectively. Compared with existing block identification methods, the proposed approach considers the contribution of line-type discontinuities on block formation and integrates geometric and mechanical modelling processes in one program. This approach is suitable for rockfall sources quantitative assessment. The locations, geometric parameters, and stability results of all identified blocks can be automatically obtained, and these could provide a reference for rockfall hazard assessment. The proposed approach is applied to a railway bridge case in China, and the corresponding rockfall hazard is evaluated. At the end of this paper, the joint sets related to block formation, uncertainties of block shapes, and discontinuity size effect are discussed.
... In the computational model, there is a significant dispersion for tunnel damage depth at joint spacing from 0.25 m to 1.0 m, as shown in Fig. 17c.In general, a smaller spacing of joints implies more numbers of joints and thus is detrimental to the tunnel stability (Barton 2013;Wang et al. 2013). But on another side, more joints will absorb more blast wave energies and reduce the blast-induced surrounding rock damage (Lanari and Fakhimi 2015). ...
Drill and blast method is an accepted technique of tunnel excavation but it often causes over-break or even threatens the stability of the surrounding rock. Moreover, the rock mass mostly contains different forms of discontinuities and so more severe damage may develop under the blasting loads. In this paper, numerical modeling on the damage of jointed tunnel excavation subject to blast shock was carried out with three-dimension Distinct Element Code (3DEC). The blast-induced damage zones (BIDZ) including failure zones and open zones are as evaluation indicators. The effects of joint geometrical and mechanical properties, tunnel depth and advance length on damage depth were evaluated. The influence extent of these factors was also compared by arithmetic mean of maximum damage depth and its standard deviation. Lastly, the results are contrasted with an existing empirical formula. It is found that increasing advance length has a more obvious effect on tunnel damage comparing with other factors, and failure zones begin to develop when the advance length exceeds 2 m in the model. If the joint inclination angle increases above 60°, the tunnel is prone to instability and the failure rocks is mainly found at the tunnel roof. For all joint strike angles, there is a clear damage zones in the surrounding rock, and failure zones are mainly located at the sidewall. The damage depth is highly dispersive within 1 m of the joint spacing. This research provides an insightful understanding of damage magnitude of jointed rock mass during tunnel excavation with blasting.
... Currently, many researchers are conducting research on the identification and classification of discontinuities [9], but little attention has been given to discontinuity traces. However, discontinuity traces play an important role in evaluations of the quality of rock masses [3,7,10] and stability analyses of rock masses [11,12]. This study considered how to extract discontinuity traces quickly and accurately. ...
The spatial characteristics of discontinuity traces play an important role in evaluations of the quality of rock masses. Most researchers have extracted discontinuity traces through the gray attributes of two-dimensional (2D) photo images or the geometric attributes of three-dimensional (3D) point clouds, while few researchers have paid attention to other important attributes of the original 3D point clouds, that is, the color attributes. By analyzing the color changes in a 3D point cloud, discontinuity traces in the smooth areas of a rock surface can be extracted, which cannot be obtained from the geometric attributes of the 3D point cloud. At the same time, a necessary filtering step has been designed to identify redundant shadow traces caused by sunlight on the rocks' surface , and a multiscale spatial local binary pattern (MS-LBP) algorithm was proposed to eliminate the influence of shadows. Next, the geometric attributes of the 3D point cloud were fused to extract the potential discontinuity trace points on the rocks' surface. For cases in which the potential dis-continuity trace points are too scattered, a local line normalization thinning algorithm was proposed to refine the potential discontinuity trace points. Finally, an algorithm for establishing a two-way connection between a local vector buffer algorithm and a connectivity judgment algorithm was used to connect the discontinuity trace points to obtain the discontinuity traces of the rock mass's surface. In addition, three datasets were used to compare the results extracted by existing methods. The results showed that the proposed method can extract the discontinuity traces of rock masses with higher accuracy, thereby providing data support for evaluations of the quality of rock masses and stability analyses.
... To reduce the storage space of block data, Boon et al. (2015) proposed a single data structure consisting only of the faces. Block identification is a basic research, which can be combined with the discrete fracture networks and probability theory; distribution forecast of blocks (Wang et al., 2013;Zheng et al., 2017) and quality evaluation of rock mass (Palmstrom, 2005;Ni et al., 2017) can be carried out. Zhang et al. (2019) used this method to identify blocks and then evaluate face stability under disc cutters loading of TBM. ...
The traditional cutting algorithm has a clear concept and is easy to implement, but it cannot consider the finiteness of the discontinuities. Based on the traditional cutting algorithm, an accurate identification method of blocks is proposed, which can identify blocks formed by finite discontinuities and excavation surface. A visual program for identifying blocks and stability analysis is developed by using Microsoft Foundation Class and OpenGL, and then it is applied to tunnel engineering. The shape and the number of the key blocks identified by this method are not limited and consistent with actual engineering. In the case that the size of the discontinuities cannot be accurately obtained, the influence of the size change of the dominant discontinuities on the key block is discussed, which will make up the lack of parameters. The number and volume of the key blocks are large when discontinuities are assumed to be infinite, and the calculation results are conservative. However, the volume and location of the blocks have great reference value and guiding significance for practical engineering.
... The discontinuous surface inside the rock mass controls the deformation and strength of the rock mass under loading. In general, discontinuities have a significant impact on stability of rock engineering, such as the stability of deep underground tunnels (Wang et al., 2013), the safety of underground nuclear waste storage (Read, 2004) and the stability of rock slopes (Zhao et al., 2020). Therefore, a thorough understanding of the microcracking behavior and mechanical properties of rocks is essential for the evaluation of the stability of rock engineering. ...
A linear parallel bond model combined with Weibull distribution to take into account the mechanical heterogeneity of brittle rocks is used to investigate the cracking behavior, acoustic emission (AE) characteristics and full-field stress evolution of rocks containing three parallel pre-existing flaws under uniaxial compression. The intact model is calibrated to the macro mechanical properties of rocks obtained from laboratory tests. The numerical results indicate that the presence of three parallel pre-existing flaws weakens the mechanical properties of rocks. As the flaw inclination increases, uniaxial compression strength shows a trend of first decreasing and then increasing, and the elastic modulus and Poisson's ratio are roughly increasing. The displacement localization zones chronologically formed around pre-existing flaws can interact with each other, and the damage or fracture processes of pre-cracked samples are complicated. And the tensile stress in x direction concentrates around pre-existing flaws. As the flaw inclination increases, the tensile stress concentration area at the end of the pre-existing flaws in the x direction also changes, at the same time, the area of the tensile stress concentration area in the y direction gradually decreases. And AE events with high fracture intensity are located in the macroscopic shear zone or split zone.
... Moreover, numerical simulations, such as the discontinuous deformation analysis method (DDA), numerical manifold method (NMM) and discrete element method (DEM), can well calculate the deformation and stress condition of discontinuous media. Among them, professional software such as Unwedge and General Block can also search and recognize the key blocks, and many researchers have performed many useful studies on model reconstruction and identification of complex blocks (González-Palacio et al. 2005;Wang et al. 2013;Zhang et al. 2014Zhang et al. , 2017Assali et al. 2016;Fu et al. 2016;Li et al. 2017;Liu et al. 2017;Boldini et al. 2018). However, each model has a different spatial distribution for joints despite having identical probability distributions. ...
Jointed network simulations tend to be more random in nature due to the uncertainty of rock mass structures. In this paper, a series of jointed network models can be established in batches using Monte Carlo simulation (MSC) and loop iteration. Taking the joints, tunnel profile and their intersections as the edges E and vertices V of graph G, the jointed network model can serve as an unweighted undigraph. Then, the breadth-first search is introduced to search the closed paths around the tunnel profile, such as the potential key blocks. With batch simulation of network models, the spatial distribution characteristics and probability distribution rules of blocks can be automatically analysed during the search process. For comparison, the Laohushan tunnel of the Jinan Belt Expressway in China has been analysed using the breadth-first search, discontinuous deformation analysis method and procedure of “Finding the Key Blocks-Unrolled Tunnel Joint Trace Maps”. Each simulation starts from the same probabilistic model of geometrical parameters of joints but develops differently with different outcomes. The spatial distribution rule of potential key blocks simulated by the aforementioned batch jointed network models is essentially identical to the actual rockfall during tunnel excavation.
... The structural analysis technique is also known as limit equilibrium analysis. The structural analysis in underground excavations is an important task that makes use of some forces acting between the weight of the rockmass and the reaction forces acting upon the face of excavation to determine the stability of the structure (Wang et al. 2013). Martin (2012) further reported this approach as an analysis that describes the condition of the ground and the stability of the surrounding rock during excavation. ...
Historically, the idea of designing and installing rockbolts in rockmasses can be traced back to the construction of the Snowy Mountain hydroelectric scheme in Australia, which was completed in 1974. The use of rockbolts as a ground support system has been widely applied to enhance the stability of structures in mining and to resist the movement of keyblocks in underground excavations. The strength of a rockbolt as a rock support tool lies in its ability to improve the tensile and shear strength needed to maintain the load-bearing capacity of a rockmass. Currently, rockbolts are extensively used as reinforcement methods in mining and civil engineering projects to support deforming rockmasses in coal and hard rock mining, tunnelling and underground openings. The performance of a rockbolt depends on the design parameters such as load-bearing capacity of the bolt, strength of the bolt, bolt diameter, length of the bolt and bolt spacing. This study provides a detailed review of the various applications of rockbolts in mining operations. In addition, the integration of smart sensors in rockbolts to enhance monitoring of displacement measurements, stresses, subsidence of pillars and ground pressure on structures are discussed in this paper. The use of smart rockbolt devices, which has improved the monitoring and evaluation of critical parameters in rockbolts such as the axial force, corrosion occurrence, grout quality and resin delamination, are also discussed. This review shows that with the numerous applications of rockbolts in mining, especially in underground excavations and tunneling engineering, rockbolts can be used as supports in rocks with different geological conditions. Nevertheless, this paper highlights that there are still some areas that need improvement in rockbolting technology.
... It should be emphasized that both the strength and stability should be considered in the study of tunnel support systems because all steel structures have the potential of buckling failure, especially slender steel frames. Damage to the support system caused by buckling is a common occurrence and may threaten construction safety and progress [25][26][27][28][29]. Stability research has primarily focused on the following three aspects: (1) buckling of buried pipes due to ground explosion, foundation excavation, or collapsed rock [30][31][32]; (2) buckling of tunnel lining under an uneven load or hydrostatic pressure [33][34][35][36][37][38][39]; (3) buckling of steel-concrete composite structures (concrete-filled steel tubes (CFST) and steel-concrete-steel (SCS) sandwich structures) under compression [40,41]. ...
The steel frame is the main bearing structure that ensures the safety of tunnel construction. Structural damage due to instability is a common occurrence and cannot be ignored. The instability mechanism of the traditional steel arch was analyzed, and an innovative steel frame type called the π-type steel-concrete composite support (π-type SCCS) was proposed to improve the bearing capacity and structural stability. First, the constitutive and interface relations of concrete-filled steel tubes were verified. Then, the buckling model of the π-type SCCS was established by considering the effect of geometric and material nonlinearity. The characteristic parameters of the steel frame were comprehensively analyzed regarding the instability mode, internal force development, and stress variation and were optimized under different construction states. In addition, the influence of different parameters on the structure stability was clarified, including the design of the steel frame and the grouting reinforcement. Finally, the influence of the wall thickness and geometric imperfections on the stability of the π-type SCCS during local buckling was investigated. The results can provide a theoretical basis and references for highly stable tunnel support design
... Fracman [6], Siromodel [7] and 3DEC [8] are examples of commercial software packages that can construct DFN, generate rock block systems and perform block stability analysis. In addition to commercial codes, research-oriented programs capable of generating 3D block systems from DFN data are also mentioned in the rock mechanics literature: BLOCKS [9], Block Generation Language [10], MSB Code [11], DC Code [12], RESOBLOK [13], GeoSMA-3D [14], GeneralBlock [15], 3D Block Generation Program [16], Rock Block Cutting program [17] and General Block [18] are examples of programs developed by the academia. Nonetheless, all these codes have two disadvantages: they do not provide for a block shape and size analysis based on Kalenchuk et al. [19] sound approach and they are either commercial (proprietary) or restricted to certain research groups. ...
In this paper, a Python library named UnBlocks-gen is presented for the generation and analysis of 3D rock block systems. The library provides the tools for the construction of Discrete Fracture Networks; the generation of rock blocks based on the constructed DFN; and the analysis of blocks’ geometrical characteristics, such as shape and size. An illustrative example is presented based on the Brazilian Monte Seco tunnel. It shows the library capabilities in dealing with complex Discrete Fracture Networks as well as performing excavation through a selected region of the block system. The library shall be valuable to research that attempts to understand the relations between rock masses’ geometrical characteristics and behavior during engineering works.
... Chen et al. [24,25] and Wu [26] evaluated and analyzed the treatment effect of tunnel collapse section by combined numerical simulation with on-site monitoring. Close range photography and remote sensing technology provide the possibility of structural surface measurement in tunnel monitoring [27][28][29][30]. Zuo et al. [31] analyzed the factors influencing collapse and the instability mode of surrounding rock for tunnels crossing the fault zone with water rich soft rock and proposed joint treatment measures for inside and outside the tunnel. ...
Collapse is one of the most dangerous geological disasters in tunnel construction, and it is an urgent engineering problem which needs to be solved. Taking the collapse of the top of an actual tunnel face as an example, through field investigation and theoretical calculation methods, the mechanism of tunnel collapse was studied, and the treatment and evaluation of the collapse area were proposed based on field monitoring data. The results show that the extrusion and bulging deformation on the palm surface and the tensile fracture in the top inclined stratum led to the shear slip of the block along the structural surface and the local collapse of the surrounding rock. Based on the block theory, the potential unstable block at the top of the tunnel was successfully identified, and the treatment method of ‘protecting before filling and then digging’ was proposed. The comprehensive treatment measures of advance bolts, steel arch support, collapse backfill, and step excavation were adopted, with on-site monitoring followed up step by step. Based on the analysis of surrounding rock deformation and stress characteristics, in this paper we demonstrate that the treatment effects of the collapse area are good, and ensure the safety and smooth progress of construction. The proposed treatment method achieved the expected goal and was shown to be able to provide successful treatment for similar collapse cases of tunnel engineering.
... Due to the existence of joint planes, the spatial characterization is usually observed in surrounding rocks, which cannot be simply described by analytical solutions. To solve this problem, the block theory was introduced to characterize the blocky stratified rock mass (Wang et al. 2013;Huang et al. 2020). However, such a practice is not suitable for shallow buried tunnels which are always subject to complex geological conditions (Huang and Song 2013;Eshraghi and Zare 2015). ...
A new procedure is presented in this paper to assess the tunnel face stability in anisotropic and nonhomogeneous soils. The three-dimensional (3D) rotational failure mechanism proposed by Subrin and Wong (2002) is used to include the anisotropic and nonhomogeneous soil parameters into the computational model. Regarding previous findings, the cohesion of soils is modeled as varying with direction to account for the anisotropy and linearly increasing with depth for the nonhomogeneity. A more complex case with two-layer soils is considered where sudden changes of cohesion, nonhomogeneous coefficient, and unit weight at the interface are assumed. A degraded program and a numerical simulation with FLAC 3D are performed to validate the proposed methodology. The critical support pressures are calculated using the proposed approach to show the influences of the involved parameters on tunnel face stability. Sixteen combinations of different parameters are specially chosen to investigate their influences on the shape of the failure block. According to the numerical results, the 3D profiles of failure mechanisms are plotted to give a visual description of face failure.
... Therefore, it is of great significance for geological engineers to accurately determine discontinuity parameters to understand the characteristics of fractured rock masses, which are relevant to many geological engineering activities such as mining engineering, slope engineering, hydraulic engineering, and nuclear wastes disposal engineering (Vöge et al., 2013;Zhang et al., 2017;Zhou et al., 2018Zhou et al., , 2019Li et al., 2018;Tuckey and Stead, 2016). Usually, geologists have sought to understand the properties of rock mass based on field data collected from borehole logging, outcrop mapping, or tunnel faces with limited exposures Menegoni et al., 2019;Feng et al., 2018;Wang et al., 2013;Buyer et al., 2020), and using numerical simulation methods (Rabczuk et al., 2007;Rabczuk and Belytschko, 2004). Remarkably, because of the specific geomorphological conditions, outcrops of the Xinchang underground research laboratory (URL) site (the area-specific URL) have a large number of natural discontinuities, which can provide abundant data for the study of fractured rock mass properties. ...
The geological parameters of rock discontinuities are of great significance for the evaluation of high-level radioactive waste repository and underground research laboratory (URL) site characteristics. To provide sufficient basis for the construction of the Xinchang URL site, this paper presents a comprehensive set of methods for acquisition of discontinuity parameters. In this set of methods, a high precision three-dimensional point cloud model of an outcrop with real geographic information is established based on close-range photogrammetry technology, from which not only planar discontinuities but also linear discontinuities can be identified and extracted by a semi-automatic method. A new fast-fuzzy clustering method is proposed to cluster discontinuity sets. The statistics method based on topographic window projection is improved to increase the rationality of estimating the geometric characteristics of fracture traces. As a preliminary validation, the results of this case study reveal that these methods have good applicability in acquiring discontinuity parameters, which is also conducive to the establishment of a deterministic-stochastic discrete fracture network (DSDFN) model to further analyze the properties of fractured rock mass. In addition, it is preliminarily found that some outcrops different locations have structures with similar geological features to a certain extent; moreover, the fractures exposed on the outcrop surface have distribution characteristics similar to those in the granite body obtained by drilling. Above all, the presented multidisciplinary methods could provide an alternative and practical approach for low-cost and accurate acquisition of discontinuity parameters, and thus, to study the properties of fractured rock mass effectively.
... A GeoSMA-3D system was used to analyze the stability of rock mass. Geotechnical Structure and Model Analysis system (GeoSMA-3D) was developed by our research team to investigate the stability of jointed rocks (Wang et al. 2013). Based on the block theory and limit equilibrium criterion, the rock structural characteristics (nonlinear, inhomogeneous and anisotropy) can be reproduced within the framework of GeoSMA-3D program. ...
Rock cliff faces are mostly avoided in rock engineering research, especially where the scale of the slope exceeds the scale of fracturing present in the rock mass. The research to understand the rock cliff face joints plays an important role in slope engineering. This paper presents a rock block identification method based on unnamed aerial vehicle photogrammetry and its computer implementation of Cliff face rock, Fort Munro Pakistan. An advance bundle adjustment method was used to build the real three-dimensional (3D) surface model of the rock mass. Later, random sample consensus algorithm was used to search the structural planes in cloud point model. A computer program, geotechnical structure and model analysis (GeoSMA-3D) was developed to solve the engineering problems and to verify the example. The program confirmed the efficiency of the theory in dealing with complex surface modelling and cliff face rocky slope stability analysis. The approach presented can be applied as a general guiding design principle for cliff face rock slope.
... Investigation shows that these joints mostly belong to incipient discontinuities, minor faults, bedding planes, etc. Because the quantity is relatively small, these large-scale joints can be defined as 'deterministic joints' [19]. It is possible to define the diameter of a large-scale joint as infinite (note that the disc-joint model is used for creating a joint network). ...
In rock engineering projects, professionals assess the overall rock mass qualities using a sole value. However, the true qualities of partial rock masses are incompatible with such a value. To address this problem, the idea of regionally classifying rock mass qualities is proposed and the associated procedure presented. To achieve this goal, the probabilistic and deterministic joints within the study area were determined, and a three-dimensional joint network model was created. Then, the three-dimensional joint network model was discretized into interlocking subdomains, and the modified blockiness index (MBi) was used to finely identify the homogeneous structural regions, together with the k-means algorithm and the sum of squared errors (SSE). A synthetic model comprising homogeneous structural regions was developed and validated with respect to the extracted cross-sections. Next, an improved rock mass rating system (RMRmbi) was introduced, and the viability of RMRmbi was supported through a significant amount of theoretical cases and several real cases. Finally, visualization of regional RMRmbi classification results was performed. Results show that: (i) the homogeneous structural regions are finely demarcated in three dimensions, and (ii) the proposed idea can overcome the problem of rock mass quality classification using the conventional approach often leading to ‘overgeneralization’.
... However, recent advances in photogrammetry and laser measurement techniques have greatly improved our capabilities to characterize rock masses, both at the surface (see e.g., Gigli and Casagli, 2011) and underground. For instance, Wang et al. (2013) employ classical photogrammetry to https://doi.org/10.1016/j.tust.2018.09.026 obtain the discontinuity sets needed to analyze the stability of blocks using block-theory and limit equilibrium; and Zhu et al. (2016) also employ classical photogrammetry to identify discontinuity sets and to conduct a discontinuous deformation analysis (DDA) of block stability. Similarly, Fekete et al. (2010) use a laser scanner to compare the excavation surface and the final contour of the tunnel lining (hence allowing them to compute the thickness of shotcrete installed), and to develop a discontinuity model of the rock mass in which the tunnel is constructed. ...
A new methodology to identify discontinuity sets at the tunnel face based on the Structure from Motion (SfM) photogrammetric technique is proposed. The work focuses on the performance of this technique when employed to characterize the ground mass under real tunneling conditions, illustrating its possibilities and analyzing several aspects that affect the quality of the obtained results. By means of a set of overlapping photographs from the tunnel face, SfM constructs a 3D point cloud model, from which discontinuities are identified using a discontinuity set extractor software. To orientate and scale the digital model, an easy-to-use “portable orientation template” specifically developed for this work, is employed. The proposed methodology is applied to two real tunnels under construction in Northern Spain. Its results are compared with those obtained with a traditional analysis based on manual compass measurements. Results show that the SfM methodology provides an adequate characterization of the structure of the rock mass, identifying the same number of discontinuity sets as the compass measurements approach and with differences in orientation that are within the uncertainty range associated to manual measurements. Only one sub-horizontal set presented higher orientation differences, but this is mainly due to the presence of shotcrete at the face. In addition to the advantages of a “distant” measurement technique—e.g., health and safety advantages, capability to characterize unreachable areas, etc.— as well as to the advantage of its reduced cost, the proposed SfM methodology and its associated tools allow one to represent planes associated to each discontinuity set back into the original 3D digital point model, and to perform detailed analyses that clarify and improve the obtained results. Finally, an analysis about the minimum number of photographs needed to adequately characterize the tunnel face is conducted, with results showing that around 15 good quality photographs are enough for tunnel faces with excavated areas of about 50 m².
... In this paper, we address the DFN method. In recent years, many DFN models based on the Poisson process have been used to analyze the local stability of rock slopes, tunnels and caverns (Ivanova et al. 2014;Wang et al. 2013;Zhang 2015;Zhang et al. 2014;Zhang and Lei 2013). There are six main types of fracture network models. ...
Based on a 3D model of a discrete fracture network (DFN) in a rock mass, an improved projective method for computing the 3D mechanical connectivity rate was proposed. The Monte Carlo simulation method, 2D Poisson process and 3D geological modeling technique were integrated into a polyhedral DFN modeling approach, and the simulation results were verified by numerical tests and graphical inspection. Next, the traditional projective approach for calculating the rock mass connectivity rate was improved using the 3D DFN models by (1) using the polyhedral model to replace the Baecher disk model; (2) taking the real cross section of the rock mass, rather than a part of the cross section, as the test plane; and (3) dynamically searching the joint connectivity rates using different dip directions and dip angles at different elevations to calculate the maximum, minimum and average values of the joint connectivity at each elevation. In a case study, the improved method and traditional method were used to compute the mechanical connectivity rate of the slope of a dam abutment. The results of the two methods were further used to compute the cohesive force of the rock masses. Finally, a comparison showed that the cohesive force derived from the traditional method had a higher error, whereas the cohesive force derived from the improved method was consistent with the suggested values. According to the comparison, the effectivity and validity of the improved method were verified indirectly.
... However, the rock mass structure models for block identification are mostly geometric models. Wang et al. (2013) adopted Monte-Carlo method to reproduce the location and shape of joints around a tunnel in the joint modeling process. Based on the quantified relationship between total unstable block volume and fracture spacing (Starzec and Tsang, 2002) and the bootstrapping technique (Rogers et al., 2006), Elmo et al. (2014) developed a full-scale DFN model including fracture orientation, size and intensity from all available geotechnical data. ...
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.
... Large-scale visible fracture traces (e.g., faults/ dykes) can be mapped (Umili et al. 2013) or monitored using non-contact approach (Firpo et al. 2011) to classify the rock mass. Stochastic fractures (e.g., joints) are then generated to form a 3D blocky system (Wang and Ni 2014;Wang et al. 2011Wang et al. , 2013bZhang and Lei 2013). Numerical tests on blocky systems calculate the REV size and the equivalent mechanical properties subsequently, where the mechanical parameters of joint aperture and roughness can be considered explicitly (Chalhoub and Pouya 2008;Kulatilake 1985;Pouya and Ghoreychi 2001;Xu and Dowd 2010). ...
Estimation of representative elementary volume (REV) is significant to analyze fractured rock mass in the framework of continuum mechanics. Engineers can therefore simplify the analysis by using an equivalent rock block with an average property, and the influence of fractures can be neglected in finite element modelling. The indicators to determine the REV size based on the joint geometrical parameters include the volumetric fracture intensity (P32) and the fracture tensor, but this type of calculation generally provides a lower bound evaluation. A novel conceptual framework of damage coefficient is introduced in this paper to consider the mechanical properties of fractures, such as joint aperture and roughness. A parametric study has been performed to establish the correlation between the proposed dimensionless damage coefficient and the traditional derived P32 value. The effectiveness of the developed method is demonstrated by a case study, where a larger mechanical REV size is indeed calculated based on the damage coefficient.
The research team’s developed GeoSMA-3D (three-dimensional geotechnical structure and model analysis) program was used to enable the visualization analysis of tunnel engineering by determining information about the key blocks and the deterministic fracture surfaces in Diaoyutai Tunnel in Liaoning Province, China. The seepage characteristics of rough fractures with varied intersecting angles were investigated under excavation disturbance, and the effective permeability of the surrounding rock blocks was estimated. Three-dimensional morphology scanning and a point cloud splicing algorithm were used to characterize the geometric properties of the rough fractures quantitatively. The numerical model of rough fractures with varied intersecting angles was investigated via COMSOL Multiphysics software. Besides this, the seepage characteristics (as flow velocity distribution and the water pressure evolution) in the rough fractures were simulated and analyzed. The simulation results assisted in understanding the evolution of seepage characteristics in rough fractures with varied intersecting angles under different stresses. In this study, for rock matrix, the anti-analysis technique was employed to import the kriging method into MATLAB based on the surface permeability of the rock blocks. Furthermore, the cuboid model developed by COMSOL™ and MATLAB was used to characterize the internal permeability of the rock blocks to obtain the effective permeability by using the obtained permeability spatial distribution. In this context, the total flow through the nonuniform area was estimated and the geometric mean was proposed as an appropriate measure. Moreover, the developed program provides a nondestructive method to estimate the effective permeability of large rock samples under excavation disturbance.
This study proposes a new measurement system based on Structure from Motion (SfM) photogrammetry to evaluate tunnel face. The main goal is to determine the tunnel face discontinuity pattern and orientation for the tunnel face stability evaluation. A 3D point cloud model is generated from overlapping images of the tunnel face 3D polystyrene model using SfM photogrammetry. The discontinuities pattern and orientation are determined using facet extraction of KD-tree plugin in CloudCompare. The same set of overlapping images were analyzed in four different quality setting; (low, medium, high, ultra-high) with different set of point cloud number which control the accuracy of the discontinuity's measurement. In this study, high quality setting shows the consistent measurement of the discontinuities pattern and orientation in comparison to the real 3D polystyrene tunnel face model. Validation of the pattern results from CloudCompare were carried out using JudGeo. The cluster analysis shows two sets of discontinuity with mean dip and dip direction of 82°/164° and 84°/307° respectively. Both orientations were verified manually with a geological compass. The high-quality point cloud and manual compass measurement of the orientation highlight the similarity of the concentration for both discontinuities set for the replica tunnel face. This evaluation of tunnel face proposed method has the advantages of evaluating inaccessible areas and avoiding professional bias.
In rock tunnels, the intersection of discontinuities and excavation surfaces tends to generate rock blocks, resulting in disasters. The block generation approach is an important study. The element-assembling approach has advantages in terms of robustness and fine characterization; however, the computational speed is a bottleneck, and efficient subdivision of the rock mass is also urgently needed. In this paper, a fast mesh model for subdividing a tunnel-surrounding rock is proposed using a polyhedron-slicing algorithm, which has obvious advantages in terms of ease of implementation and low requirements for element quality. For the mesh model, a block-generation approach based on an element-assembling idea is presented, and it highlights three innovative measures for improving the computational speed: designing of a new polyhedron data structure for a fast polyhedron-slicing algorithm, the construction and maintenance of the connections between elements, and the use of a composite detection approach for the contact between a discontinuity and an element. The applicability and accuracy of the proposed approach for complex blocks are verified by two cases. Compared with traditional methods, the three measures can improve the computational speed by 45%∼55%, 25%∼35%, and 15% respectively. Combining them can improve the computational speed by about 90%, indicating that the effect is noticeable. Meanwhile, it has a limitation that a fast mesh model with excavation section is only suitable for tunnels, which can be solved by improving the slicing algorithm in the subsequent work.
Digital photogrammetry is becoming an important tool for remote data acquisition. The use of digital outcrop models (DOMs) for fracture analysis has grown in the field of geosciences. Structure-from-Motion- Multi-view Stereo (SfM-MVS) is a recent technique that allows the creation of DOMs in a simple and inexpensive way. To direct an in-depth study of the application of SfM-MVS in the investigation of fractured media, the thesis sought to answer which parameters related to these systems can be obtained through the 3D models generated by SfM-MVS, and which factors have an influence on the data accuracy. Models of different outcrops (igneous, sedimentary and metamorphic rocks) were generated using sets of images at different scales, captured by different cameras and platforms. The models were analyzed using three approaches: to measure fracture properties; qualitative analysis of the factors that influence its quality and the derived data; and investigation of the quality levels offered by Agisoft Metashape. As a result, a list of best practices for fieldwork for the construction of an DOM was produced. It was
concluded that the RPA is the most flexible platform available for different topographies, as it allows flight planning or manual piloting, while offering a good cost-benefit. In fracture analysis, algorithms that calculate orientation, spacing and persistence are easily implemented. These three parameters depend on the ability to identify fractures in the generated 3D model. This, in turn, is influenced by the spatial resolution and the presence of deformations in the model. For roughness, the difficulty of quantification lies in the efficient conversion of the Joint Roughness Coefficient (JRC) to three-dimensional space. In investigating the options offered by the Metashape program, the analyzed data suggest the accuracy-quality pairs high-high and highest-high as the best costbenefit ones, the first being the safest for application in field conditions. The results obtained point to the existence of a tripod, composed of three highly correlated elements: scope, time and
cost. Changing one of them without impacting the others will sacrifice the final quality of the model, and consequently of the analysis. Another important result was the development of the multiplatform application SurvAid, an image survey planning tool; and the open software CAPI, dedicated to the structural analysis of DOMs. In conclusion, SfM-MVS proved to be a powerful technique for generating MDAs, which can be used in fracture analysis. Still, it should be seen as a complementary tool to field work.
Geological discontinuities govern the strength and deformation of rock mass and play an important role in the stability of geotechnical excavations, such as tunnels, caverns, slopes, and mines. In this paper, the failure mechanism of a tunnel in the vicinity of a fault zone is investigated by physical model tests with dimensions of 3 m × 2.4 m × 0.4 m, in which the non-contact Digital Image Correlation (DIC) technique is employed to provide full-field displacement measurements. Results show that the fault zone near the tunnel shoulder has a significant influence on the stability of the surrounding rock, in terms of strain localization and failure initiation. With the increase of surcharge loading, cracks initiate at the two sidewalls, following by the initiation of cracks at the left shoulder and the crown. Cracks propagate to the fault zone eventually, leading to asymmetrical collapse. The stress loosening zone (SLZ) in the surrounding rock after tunnel excavation is significantly influenced by the fault zone near the left shoulder of the tunnel, showing the occurrence of stress redistribution. It is recommended to implement reinforcement in the rock mass between the tunnel and the fault to improve the stability.
SfM method has been deployed to investigate structural planes of rock mass in tunnel to meet the need of rapid and digital construction. 3D surface model of tunnel rock mass has been reconstructed rapidly, effectively, and accurately. And then the characteristic parameters of structural planes are obtained. Based on this method, probabilistic model of the dip, dip angle, trace length, and spacing of structural planes has been determined and significance test of F value is carried out. A 3D stochastic network model of structural plane with Baecher disk model is established based on Monte Carlo method. Through sectioning of the structural plane network model, the two-dimensional profile of trace distribution has been generated and compared with that of actual excavated structural plane. The maximum difference ratio is 19.1%, which shows that this method can identify the structural plane and obtain the characteristic parameter accurately and rapidly. The results show that the stochastic network model of structural planes generated is highly reliable.
Direct contact measurements for rock mass discontinuities are generally difficult to perform, time consuming, biased, and often dangerous. This paper presents an automatic characterization method for rock mass discontinuities that uses 3D point clouds, which can be obtained through non-contact measuring techniques such as photogrammetry and Light Detection and Ranging (LiDAR). In this method, five discontinuity parameters, namely, the orientation, trace, spacing, roughness, and aperture, are extracted automatically. The overall methodology is as follows: (1) orientation is determined by using an improved K-means clustering method; (2) trace segments are detected by using the Normal Tensor Voting Theory, and four post-processing techniques are employed to compute the trace length; (3) spacing is calculated by plotting virtual normal scan lines on the projected traces; (4) roughness is evaluated by the correlation between the Joint Roughness Coefficient (JRC) and the root mean square of the discontinuity surface profile; and (5) aperture is obtained by computing the average minimum width based on sub-pixel edge detection. The proposed method was applied to a drill-and-blast rock tunnel, where the extracted discontinuity parameters were used to calculate the Rock Mass Rating (RMR) value and Geological Strength Index (GSI) of the rock mass. The application results showed that photogrammetry was more objective and efficient for acquiring rock mass discontinuity information, and that it could be used as a potential alternative to the traditional discontinuity mapping method.
The identification of structural plane connectivity is an application problem in rock mass engineering. Theoretically, information of exposed rock mass and its internal borehole is of great significance to predict network of unexcavated rock structural plane, especially in tunnel engineering. In this paper, parameters of structural planes have been obtained through borehole imaging in advance drilling borehole of tunnel face. Furthermore, a geometric discrimination method for the multiple structural plane based on the included angle has been proposed. And then, spatial distribution of the large scale structural plane in the unexcavated rock mass has been recognized by effective assistant techniques. To verify this method, the binocular photogrammetry method has been adopted to investigate the parameters of structural planes during excavation, and then the structural plane model of tunnel face has been constructed. The tunnel face mapping has been compared with that of section of the predicted model. The results showed that included angle identification method based on three boreholes is highly reliable and can be used to accurately construct the deterministic structural plane network in front of the tunnel face.
The estimation of the shield face support pressure is essential for the stability of the shield excavation face. The face support pressure of the earth pressure balance (EPB) shield tunneling machine is mainly composed of the support pressure of the cutterhead and the earth chamber pressure. To ensure the requirements of safe construction, the theoretical face support pressure is one of the most significant references for the earth chamber pressure setting. This paper analyzed the in situ monitoring data of the shield earth chamber pressure from a shield tunneling project of the Xi'an Metro Line 4 in full-section coarse sand. A nonlinear stepwise increase in the earth chamber pressure from the top to the bottom of the tunnel face was obtained. The fluctuation range of the earth chamber pressure gradually increased with an increase in the cover depth. Meanwhile, several types of silo-wedge models were established according to different assumptions proposed by previous studies and this paper. The rationality of their calculations and the applicability of related assumptions were discussed based on practical engineering and new working conditions.
In a tunnel, instabilities in the surrounding rock mostly occur within the sidewalls and crown. After acquiring the rock mass structure, a combination of laboratory experiments, numerical simulations, and in situ monitoring data can permit a more reasonable stability analysis of the surrounding rock and engineering support design to ensure a safer engineering project. To overcome the shortcomings (e.g., inefficiency, high labor costs, and safety risks) of traditional methods for mapping the rock mass structures of the sidewalls and crowns of tunnels, this study proposes a safe, rapid, and efficient method that can acquire a 3D digital elevation model (DEM) of the sidewalls and crown of a tunnel and the corresponding rock mass structures by using digital photogrammetry (DP). The proposed method was then tested in an engineering tunnel. Error analysis of check points and discontinuity orientations showed that the errors were within a reasonable range. The method was further applied to traffic tunnel #1 of the China Jinping Underground Laboratory Phase II (CJPL-II), and the spatial coordinates and orientations of the joints were obtained. A 3D quasi-deterministic discrete model was subsequently established by converting the coordinates and orientations of the joints from a geological coordinate system to a local coordinate system in discrete element software. The quasi-deterministic model was then used to confirm that the joint persistence has an important influence on the stability of the surrounding rock of a tunnel and, thus, affects the support installation. Finally, the joint persistence value was determined by the size of the onsite unstable block. The results of this study provide a reference for the design, construction, and support of similar deep-buried jointed hard rock tunnels.
The frequent microseismicity affects the stability and reliability of surrounding rock and the safety of supporting structures in deep mining tunnels. The limit state equations of rock blocks under microseismic loads were developed to indicate the stability conditions and sliding characteristics. The scarce field data result in the uncertainty of the physico-mechanical parameters of tunnel surrounding rock. According to the insufficient statistical information for the rockmass, a method of the interval non-probabilistic reliability was proposed to analyze the stability of surrounding jointed rockmass. The method considered both microseismic loads and the uncertainty of rockmass parameters. The solving approach of interval non-probabilistic reliability was optimized, and it can be available when the field data is scarce. To verify the proposed method, the interval non-probabilistic reliability was used to evaluate the stability of the mining tunnel rockmass in the Yongshaba mine (China). The calculated interval non-probabilistic reliability was compared with the safety factor and random reliability. Results show that the interval non-probabilistic reliability model is in agreement with practical situations. It is proved that the proposed method of interval non-probabilistic reliability, considering both the uncertainty of the rockmass parameters and the microseismic loads, is a beneficial complement to the traditional analysis methods of safety factor and random reliability.
Considering the uncertainty and complexity of the influencing factors, the present study focused on the multi-level and multi-index evaluation system for analyzing rock slope stability. Quantitative analysis of the influence degree of the evaluation index on the rock slope stability was carried out by extension theory. The most significant factors affecting rock slope stability and the corresponding evaluation index were obtained. Further, the study presents a concept about the instability characterization coefficient of the key block, which is an important factor controlling slope stability. With this coefficient implemented into the search module of key blocks in the program Geotechnical Structure and Model Analysis-3D (GeoSMA-3D), developed by the corresponding author’s team, a further determination and visualization of key blocks were achieved. However, in many previous studies, there was no good correlation between the theoretical key blocks and the actual rock slope engineering, which led to derailment between theoretical analysis and practical engineering. Hence, this paper proposed the characterization safety factor of rock slope stability that combined the instability characterization coefficient with the weight of key blocks. The influence degree of each key block on rock slope stability was determined by the size of the instability characterization coefficient of key blocks. The weight of each key block on the slope stability was determined by combining this coefficient with the analytic hierarchy process (AHP). The key block information was applied to characterize the rock slope stability. The present study proposed a convenient and feasible evaluation method regarding rock slope stability. For the specific rock slope engineering, the significance of each evaluation index was determined and the most significant index was obtained. The determination and visualization of key blocks and the judgment of the slope stability were investigated, which verified the applicability and feasibility of this evaluation method.
This paper presents the design optimization for the Xianglushan tungsten mine using the room and pillar mining technique. The influence of pillar height, pillar length, pillar width, room length and room width on the stability of room and pillars was examined through analyses using the orthogonal experimental design method. The pillar and room sizes were identified as the most critical factors. The types of rock masses in the Xianglushan tungsten mine were identified in terms of rock mass classification and the mechanical parameters of those rock masses were assessed. A numerical model was developed in the continuum-based finite-element program 3D-σ to simulate the excavation process. Given fixed mining and pillar heights, the maximum room width and minimum pillar width were calculated. A separate calculation was also conducted to assess the stable excavation span using the stability graph method. The results obtained from numerical parametric study and empiricalbased analysis are consistent. A comprehensive field monitoring programme is introduced, including the data from acoustic emissions, stresses and displacements. The measured responses of pillars and roof rock demonstrate that the proposed design optimization is effective.
During the construction of horizontal jet grouting, the high pressurized fluids (water or grout) are injected into the soil, and it may induce expansion to the ground, which will cause significant movements of the surrounding ground. Simplified analysis of the construction process of installation of horizontal jet grout columns is perform, based on Verruijt's solution for calculating the deformation by expansion of a circular cavity with uniform radial stress in a half space, and a method for predicting ground displacements caused by installing single horizontal jet grout column is proposed in this paper. The variation of stress state due to installation of horizontal jet grout columns is investigated, and the equation for determining the stress at the interface of the plastic and the elastic zones is established. Considering the common jetting parameters and the mechanical parameters of the surrounding soil, an empirical equation is proposed for determining the radius of plastic zone based on the principle of energy. Comparison between the calculated values and field data shows that the proposed method yields a reasonable prediction.
Based on the random weighted method, the mechanical parameter heterogeneity of each units of the rock mass unit model is achieved. To study the heterogeneous rock mass unit model, the rock bridge transfixion mechanism is analyzed in terms of five main factors: dip angle, rock bridge angle, length, width and end spacing of cracks. Then, a rock bridge transfixion coefficient formula of the surface rock mass under static load is proposed by orthogonal experiment and data fitting, while the existing transfixion coefficient is modified. By adopting the theory proposed above, identification of spatial location of the key block and stability analysis are made using the GeoSMA-3D system in a tunneling project.
Stress and deformation response of tunnels is significantly affect by presence of joints or weak planes. In this study, stress and deformation around underground opening in jointed rocks is investigated with help of universal distinct element code (UDEC). Initial verification of the analysis is carried out with the help of analytical solution on the elastic stress distribution of circular opening with weak planes. In this paper, the deformation response of the tunnel under different joint inclination and under different confining conditions have been analysed. A comparative study of deformation response for a single joint and a joint set has also been taken into consideration.
Statistical description of rock mass properties is essential for two reasons: (1) Analyses in rock engineering require statistical descriptions to take the distributive character of properties into account, and (2) Field sampling requires statistical descriptions to develop sampling plans and to draw inferences from data. For both purposes, it is essential to know appropriate distributions of rock mass properties. Based on the evaluation of a large number of joint data and taking previous work into account, it was determined that the best fitting distribution for joint ″length″ is lognormal and for joint spacing exponential. Based on these conclusions, a model was developed for inferring joint set parameters and for estimating the intensity of jointing (joint surface area per volume) from outcropt data.
Within a certain domain of rock mass, identification of all blocks cut by three-dimensional finite random or fixed discontinuities is a critical basic problem in jointed rock mass researches. Based on general method of spatial block topological identification with stochastic discontinuities cutting, the block identification of slope and cavern rock the different characteristics of simply connected loops and multiple connected loops, how to identify the different block types uniformly is discussed. This paper develops an efficient numerical approach to predict deterministic size effects in structures made of quasi-brittle materials using the GeoSMA-3D([1-3]) method. Three jointed rock structures were modelled to validate the approach. Based on these, with classic block theory combined, the technique of block progressive failure analysis of slope/cavern is achieved. Finally, cases of slopes and caverns are studied. The main analysis procedures are given, including 3D discontinuities network simulation, analysis of intersecting lines between discontinuities and surfaces. The process of solving intersecting lines between discontinuities and surfaces of slope/cavern is discussed emphatically. The predicted size effect is in good agreement with site observed data. (C) 2011 Published by Elsevier Ltd. Selection and peer-review under responsibility of ICM11
Engineering Classification of Rock Masses for the Design of Tunnel Support An analysis of some 200 tunnel case records has revealed a useful correlation between the amount and type of permanent support and the rock mass qualityQ, with respect to tunnel stability. The numerical value ofQ ranges from 0.001 (for exceptionally poor quality squeezing-ground) up to 1000 (for exceptionally good quality rock which is practically unjointed). The rock mass qualityQ is a function of six parameters, each of which has a rating of importance, which can be estimated from surface mapping and can be updated during subsequent excavation. The six parameters are as follows; theRQD index, the number of joint sets, the roughness of the weakest joints, the degree of alteration or filling along the weakest joints, and two further parameters which account for the rock load and water inflow. In combination these parameters represent the rock block-size, the interblock shear strength, and the active stress. The proposed classification is illustrated by means of field examples and selected case records. Detailed analysis of the rock mass quality and corresponding support practice has shown that suitable permanent support can be estimated for the whole spectrum of rock qualities. This estimate is based on the rock mass quality Q, the support pressure, and the dimensions and purpose of the excavation. The support pressure appears to be a function ofQ, the joint roughness, and the number of joint sets. The latter two determine the dilatency and the degree of freedom of the rock mass. Detailed recommendations for support measures include various combinations of shotcrete, bolting, and cast concrete arches together with the appropriate bolt spacings and lengths, and the requisite thickness of shotcrete or concrete. The boundary between self supporting tunnels and those requiring some form of permanent support can be determined from the rock mass qualityQ.
A classification based on properties of rock materials and rock masses, termed the Geomechanics Classification, is proposed. The geological parameters are specified and the functional features of the Geomechanics Classification is demonstrated by applying it to the selection of primary support in tunnel design. The proposed classification system is based on a detailed study of all existing major rock classifications.
Rock slopes stability has been one of the fundamental issues facing geotechnical engineering researchers. Due to the pre-existing joints, the intactness of the rock is weakened. The mechanical characteristics are changed correspondingly along with joint-induced stress redistribution within the rock mass if the sliding limit at the joint or part of it is exceeded. In this study, spatial block topological identification techniques are applied to distinguish all blocks cut by 3D finite random or fixed discontinuities. Based on the available photographic information of rock slopes, the sliding forces and the corresponding factor of safety are evaluated through limit equilibrium conditions by the classic block theory. The rock slope stability analysis software, GeoSMA-3D (Geotechnical Structure and Model Analysis), satisfying the requirements of spatial block modeling, joint plane simulation, key block identification and analysis and sliding process display, was developed. The application of such a software on the analysis of a rock slope, which is located near the inlet of Daiyuling No. 1 tunnel on the Zhuanghe–Gaizhou highway networks, was performed. The assessed results were compared with the monitored data to validate the effectiveness of such software.
An algebraic algorithm has been developed for predicting the formation of three-dimensional tetrahedral blocks on the excavation surfaces based on the orientations and locations of discontinuity planes obtained from DOM drilling operation. Traces of discontinuity planes on the excavation surface have been predicted by adopting the algebraic projection technique and the persistence of discontinuity has been considered to determine the extent of trace on the projecting plane. Formation of potential tetrahedral blocks has been algebraically discerned by utilizing the plane equations of discontinuities. Three-dimensional geometry of each individual block is precisely defined and stability of each block subject to the body weight is estimated by considering both the kinematic behavior and the mechanical properties of block forming discontinuity planes. Practical applicability of block model is illustrated by performing the block analysis for the underground tunnel excavation.
The first large-span tunnel in the northern area of Liaoning province is scheduled to be completed in 2003. This tunnel is 460 m in length, 21.242 m in width and 15.52m in height. However, The stability of large-span tunnel is affected by faults or joints located nearby. Hence, a better understanding of the mechanics of influence, especially regarding the risk assessment of faults is required. At the department of geotechnical engineering, the influence of faults on the stability of underground openings has been investigated using numerical methods. In this paper, especially the displacement behavior for different locations of a fault around the large-span opening is discussed. The deformation of the fault after the excavation is also briefly presented. It is hope that this case study will shed some light on future projects of similar nature, and a good reference in the design and construction of similar tunnel engineering projects.
Described is a limit analysis of keyblock stability which yields bounds on the ranges of stability and instability, and their region of overlap, potential instability. The mathematical problem of finding these limits is carried out by using linear programming. The resulting stability measure is mapped on to a gray scale and plotted on a grid representing all possible keyblocks around a tunnel. A parametric study of the effects of joint orientation and initial stress ratio on block stability is presented.
The probabilistic block theory which was suggested by Hatzor and Goodman (1992) was applied to an telecommunication tunnel by taking into consideration the individual joints obtained from face mapping during tunnel construction. Using the actual unrolled joint trace that was developed in the Banpo telecommunication tunnel during tunnelling, a statistical analysis of observed discontinuity data was performed. The deterministic analysis and probabilistic keyblock concept were applied and their results were compared with the observed failure modes. The result obtained from the deterministic analysis resulted in a large difference compared with the observed failure pattern; the analysis method which considers the joint combination probability gave more similar results to the observed data than the deterministic analysis. Furthemore, individual keyblock analysis was performed by means of the newly developed program. While the positions of the keyblocks were predicted properly by the individual keyblock analysis, the predicted sizes of the keyblocks were found to be different from the observed data. It was acknowledged from the individual keyblock analysis that most keyblocks are composed of steeply inclined joints in the crown or in the side wall fo a tunnel. But, in the fault-zone, any method based upon the block theory could not predict the failure pattern properly. It can be concluded that the continuous careful investigations of geological conditions were very important in tunnelling through a rock mass that experiences mainly structure-induced failures.
During underground excavation many surrounding rock failures have close relationship with joints. The stability study on tunnel in jointed rock mass is of importance to rock engineering, especially tunneling and underground space development. In this paper, a numerical code called RFPA was used to study the influence of different dip angle of layered joints and the lateral pressure coefficient on the stability of tunnel in jointed rock mass. Numerical analysis indicated that both the dip angle of joints and the lateral pressure coefficient have significant impacts on the failure mode and displacement characters of tunnel. The progressive failure processes of tunnel in jointed rock mass were presented and the mechanisms were discussed. The applicable condition of geographical method by Goodman is also discussed. These results offer a guideline in support design.
This paper presents a study the non-pyramidal key blocks of the rock mass. After a review of the Key Blocks Method (KBM), the study focuses on the analysis of key blocks formed by three and four discontinuity planes in underground excavations. The concept of non-pyramidal key blocks is described and their generation from a geometric operation called dislocation, thus determining the pentahedral key blocks that may be formed. To do so, the software program ASTUR (Analysis of the Support of Tunnels in Rock) was used, which develops a ubiquitous approach and allows the analysis of both pyramidal and non-pyramidal tetrahedral and pentahedral blocks.From this analysis, it is possible to ascertain the behavior of the block stability as a function of the trend and plunge of the tunnel axis. Isoplethograms have been used to illustrate how the block assembly might affect the design of an excavation.It may be concluded from the study that it is necessary to analyze the non-pyramidal key blocks with four discontinuity planes, since these may generate blocks with a large volume and a much lower safety factor than that obtained by blocks with three planes. In this respect, the ASTUR software improves on existing programs in the analysis of instability in ubiquitous rock mass. The results obtained were applied to the design of an access tunnel in an underground marble mine situated in the south east of Spain.
A three-dimensional statistical joint modeling technique was used to analyze the stability of rock blocks around a tunnel. The rock blocks generated from the joints and the tunnel were analyzed for their volume, height, perimeter, safety factor, and probability of occurrence. All these procedures were programmed into the computer program blocstab. The characteristics of rock block occurrence due to the variation of joint persistence (diameter), orientation and volumetric frequency were investigated. The rock block stability around a storage cavern of liquefied petroleum gas in Korea was analyzed as a case study. Here, the joints were assumed to follow the Baecher disk model for their shape and location, and their orientations were modeled by the Fisher distribution. The joint diameter distribution was estimated by using the window sampling method recently developed by Song and Lee.
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.
Key block methods based on ubiquitous approaches have been widely used over the past 30 years to perform rapid analyses of rock mass stability. Although these methods have meant a great step forward, they only consider pyramidal key blocks.This paper provides a new geometrical method for identifying both pyramidal and non-pyramidal key blocks in discontinuous rock masses for tunnel excavation. Using a ubiquitous approach, the non-pyramidal key blocks are determined by geometrical dislocation in relation to the advance in the direction of the tunnel axis. The blocks are parameterized with the advance and the block with the maximum volume is calculated.We point out that non-pyramidal pentahedral blocks larger than the pyramidal tetrahedral may be found depending on discontinuity planes. These pentahedral blocks will never be obtained by truncation of a tetrahedral block.The concepts introduced in this study have been implemented in the ASTUR computer program. Using this program, we select the orientation in which a tunnel must be excavated so as to generate the minimum number of large volume key blocks.We conclude that identification of pyramidal and non-pyramidal key block are necessary when studying tunnel stability. It is not enough to analyze pyramidal blocks as is proposed in most of the ubiquitous approaches used nowadays.
Beginning with the original work of Shi [Discontinuous deformation analysis: a new numerical method for the statics and dynamics of block systems. Ph.D. thesis, University of California, Berkeley (1988)], called the Discontinuous Deformation Analysis (DDA) method, a number of extensions to the method have been explored. The extensions consist of improving the contact algorithm, adding block fracturing and sub-blocking capabilities. Contacts between blocks have been modeled using an Augmented Lagrangian Method instead of the penalty method originally proposed by Shi. This allows block-to-block contacts to be enforced more precisely and block contact forces to be determined more accurately. A sub-blocking capability has been developed, whereby blocks are discretized into sub-blocks. The continuity of the sub-block contacts is preserved and the variation of stresses in each large block can be determined. The sub-blocking capability is done using a consistent formulation in which the same methodology is used for the sub-blocks as the original large blocks. This is different from other discrete block methods that imbed finite difference zones or finite elements inside larger blocks. Finally, two block fracturing algorithms have been implemented in the DDA method. Using a three-parameter (cohesion, friction, tensile strength) Mohr-Coulomb criterion, one algorithm allows intact rocks to be broken into smaller blocks. Fracturing can be in shear or tension. The second algorithm allows fractures to propagate in the sub-blocks either in Mode I (tensile fracturing) or Mode II (shear fracturing). All three extensions have been implemented into the original DDA program of Shi. With the three extensions, the DDA method is more applicable to a greater range of rock mechanics problems and other engineering problems involving blocky systems. Examples of application of the method, for plane stress condition, are presented with regard to rock fall, slope stability and underground excavation problems.
A methodology for the analysis of jointed rock data is described. The situation where a body of rock is divided into distinct blocks by families of roughly parallel fracture surfaces (joints) is considered. During the excavation of a tunnel through such rock, some of the blocks come into contact with the excavation face and may form so-called keyblocks. We address the problems of estimating the number of keyblocks per square metre of an excavation face, evaluating the distribution of keyblock volumes and estimating the probability that a suspected keyblock, part of which is observed as a closed polygon on an excavation face, may form a complete keyblock. Monte-Carlo methods and simulation are used.
A computational is derived to analyse the stability of a single three-dimensional rock block. It is assumed that the block is rigid and that it is located in an otherwise fixed body of rock and bounded by a combination of flat discontinuities and excavation surfaces. In common with most other solutions for three-dimensional blocks, possible block movements are assumed to be limited to translation only, and rotation is excluded.The block geometries that can be handled by the new procedure are more complex and realistic than those in existing solutions. To start with, the block can be an arbitrary polyhedron with various re-entrant surface features, such as notches and cavities. In addition, any number of its faces may be free and exposed at excavation surfaces.The computational procedure is based on a vector analysis of the block's stability. Part of the computation tests the geometrical configuration of the fixed faces initially in contact with the block to find whether they permit it to move. If so, the procedure can determine the nature and direction of the attempted movement and can usually calculate a factor of safety indicating the likelihood that such movement will be prevented by friction.A method is also outlined for calculating areas of block faces, together with the block's volume and centre of mass. These quantities are relevant to a few of the parameters in the stability analysis.
In this paper, a numerical approach to modeling progressive failure leading to collapse in rock and associated seismicity is reported. In the first part, a newly developed numerical code, RFPAZ° (Rock Failure Process Analysis), is introduced. The program allows modeling of the observed evolution of damage and associated seismic events due to progressive failure leading to collapse in brittle rock. There are three features distinguishing the approach from conventional numerical methods such as FEM: (1) by introducing heterogeneity of rock parameters into the model, RFPAZ° can simulate non-linear behavior in rock using a linear method, (2) by introducing elastic modulus reduction for failed elements, RFPA2D can process discontinuum mechanics problems by a continuum mechanics method; and (3) by recording the event-rate of failed elements, the seismicities associated with the progressive failure in rock can be simulated. In the second part of the paper, the applications of RFPA2D in simulating geological process and in solving mining design problems are illustrated. Numerical simulation of a fault initiation process indicates that some of the important phenomena, such as coalescence of microfracture, the nucleation and growth of crack clusters, fault initiation and development, elastic rebound, dilatation, uplift and seismic behavior, etc. can be simulated with this numerical code. The simulation of progressive failure leading to collapse in underground openings demonstrates the capacity of this code in solving mining design problems.
This work on rock mechanics points toward the practical applications of interest to tunnelers, miners, and foundation engineers. It is about the ''geometric facts of intersecting discontinuities penetrating a three-dimensional solid.'' Familiarity with matrix notation and vector operations required.
Probabilistic prediction of key block occurrences
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Study of Mechanical Behaviors in the Contraction Process of Road Tunnel
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