Joint Trace Research Articles

Artificial intelligence-aided semi-automatic joint trace detection from textured three-dimensional models of rock mass

It is of great importance to obtain precise trace data, as traces are frequently the sole visible and measurable parameter in most outcrops. The manual recognition and detection of traces on high-resolution three-dimensional (3D) models are relatively straightforward but time-consuming. One potential solution to enhance this process is to use machine learning algorithms to detect the 3D traces. In this study, a unique pixel-wise texture mapper algorithm generates a dense point cloud representation of an outcrop with the precise resolution of the original textured three-dimensional (3D) model. A virtual digital image rendering was then employed to capture virtual images of selected regions. This technique helps to overcome limitations caused by the surface morphology of the rock mass, such as restricted access, lighting conditions, and shading effects. After AI-powered trace detection on two-dimensional (2D) images, a 3D data structuring technique was applied to the selected trace pixels. In the 3D data structuring, the trace data were structured through 2D thinning, 3D reprojection, clustering, segmentation, and segment linking. Finally, the linked segments were exported as 3D polylines, with each polyline in the output corresponding to a trace. The efficacy of the proposed method was assessed using a 3D model of a real-world case study, which was used to compare the results of artificial intelligence (AI)-aided and human intelligence trace detection. Rosette diagrams, which visualize the distribution of trace orientations, confirmed the high similarity between the automatically and manually generated trace maps. In conclusion, the proposed semi-automatic method was easy to use, fast, and accurate in detecting the dominant jointing system of the rock mass.

Three-dimensional finite element simulation and reconstruction of jointed rock masses for bench blasting

During the numerical simulation of blasting in jointed rock masses, the accuracy of joint geometric parameters is one of the key factors affecting the numerical results. To facilitate the numerical simulation, most of the previous studies on blasting in jointed rock masses were conducted on regular jointed rocks, which is not conducive to fully revealing the dynamic responses and blast-induced damage characteristics of jointed rock mass. In this study, scanline sampling and borehole sampling were employed to obtain the surface and internal joint structures of the rock bench. To represent the joint geometry, a reconstruction technique for three-dimensional (3D) jointed rock masses in LS-DYNA was proposed utilizing MATLAB code. In the process, the elements on joint surfaces were identified and assigned mechanical parameters of joints to construct the 3D jointed rock model, where the geometrical properties of generated joints obey the statistical distribution obtained from the scanline survey. Taking an open-pit limestone mine as an example, a statistical analysis of the 3D distribution of joints was carried out and used to construct a 3D jointed rock numerical model for bench blasting. Comparisons between the bench slope extracted from the numerical model and the actual joint trace mapping from a rock exposure are performed, and the similarity between the two contour plots of joint orientations reaches 91.6 %. For comparison tests, the bench blasting was simulated by an intact rock model and the jointed rock model. The results indicate that the dynamic responses and blast-induced damage characteristics of jointed rocks are significantly affected by the geometry of joints. Compared with the intact rock model, the presence of joints causes stress concentration and local strengthening of rock damage between adjacent joints, which results in a 30.5 % increase in the damage volume. Furthermore, a field blasting test was conducted to analyze the accuracy of the jointed rock model. The results show that the fragment size distributions obtained from the jointed rock numerical model and the filed test are generally consistent, and the error between them in the proportion of rock fragments with a size of 0 ∼ 100 mm is only 12.8 %. These findings indicate that the proposed reconstruction method of the jointed rock model is considerably robust for characterizing the joint geometry of in situ rock masses and simulating the bench blasting in jointed rock masses.

A novel moisture damage detection method for asphalt pavement from GPR signal with CWT and CNN

To locate the moisture damage area in asphalt pavement, an automatic detection method by leveraging the state-of-the-art deep learning approach and continuous wavelet transform (CWT) method from high frequency GPR signal was presented. A numeric simulation and a laboratory experiment were employed to analyze the response of GPR signal in moisture damage area. GPR signals were transferred to time-frequency domain by using a CWT method, before comparing CWT results among normal pavement, moisture and bridge joints. Moisture damage datasets, including 8215 traces of moisture damages, 8215 traces of normal pavement and 7643 traces of bridge joints, were extracted from GPR field survey of bridge pavement with 2.3 GHz antenna. The maximum and mean values of CWT results were obtained from the dataset and used to normalize the CWT dataset. Typical classification models, including Resnet50, ResNet18, ShuffleNet, EfficientNet, NasNetmobile and DenseNet, were trained and compared on the CWT dataset. The result indicates that the CWT features among normal pavement, moisture damage and bridge joints have significant differences. Moreover, the energy distribution in the CWT image can represent the moisture damage depth and width information, proving that the CWT method is effective for extracting moisture damage features from GPR signal. The overall performance of ResNet50 model is best with high accuracy and high efficiency in moisture detection compared to other models. Experimental results proved the promising performance of our approach in detecting moisture damage in asphalt pavement, and this method could also be used for subsurface target detection in other GPR application.

Numerical Investigation for the Effect of Joint Persistence on Rock Slope Stability Using a Lattice Spring-Based Synthetic Rock Mass Model

This study underscores the profound influence of rock joints, both persistent and non-persistent with rock bridges, on the stability and behavior of rock masses—a critical consideration for sustainable engineering and natural structures, especially in rock slope stability. Leveraging the lattice spring-based synthetic rock mass (LS-SRM) modeling approach, this research aims to understand the impact of persistent and non-persistent joint parameters on rock slope stability. The Slope Model, a Synthetic Rock Mass (SRM) approach-based code, is used to investigate the joint parameters such as dip angle, spacing, rock bridge length, and trace overlapping. The results show that the mobilizing zones in slopes with non-persistent joints were smaller and shallower compared to slopes with fully persistent joints. The joint dip angle was found to heavily influence the failure mode in rock slopes with non-coplanar rock bridges. Shallow joint dip angles led to tensile failures, whereas steeper joint dip angles resulted in shear-tensile failures. Slopes with wider joint spacings exhibited deeper failure zones and a higher factor of safety, while longer rock bridge lengths enhanced slope stability and led to lower failure zones. The overlapping of joint traces has no apparent impact on slope stability and failure mechanism. This comprehensive analysis contributes valuable insights into sustainable rock engineering practices and the design of resilient structures in natural environments.

An Anonymous Authentication Scheme with Selective Linkability and Threshold Traceability

In order to protect the user's privacy identity, authentication requires anonymous authentication. Anonymous authentication is divided into unconditional anonymous authentication and traceable anonymous authentication. Unconditional anonymous authentication can verify that the user belongs to an anonymous set, but the user's true identity cannot be obtained. However, in some applications, it is necessary to trace the true identity of the user. Therefore, a traceable anonymous authentication scheme is proposed. In order to prevent random tracing, the proposed scheme uses threshold joint tracing. When the identity of the authenticator needs to be traced, the threshold number of members can jointly trace the identity of the authenticator. In some special network applications such as anonymous electronic voting, in order to prevent repeated authentications and repeated elections, it is necessary to verify whether the two authentication signatures are signed by the same user without revealing the true identity of the user. Therefore, the proposed anonymous authentication scheme should have selective linkability. In order to achieve linkable authentication, the linkable tag is embedded by linkable ring signature. Compared with similar schemes through the simulation experiments, the implementation time of the proposed scheme is slightly better than other schemes.

Scanline intersection similarity: A similarity metric for joint trace maps

Although various automatic joint trace survey methods have been proposed, it has been difficult to evaluate their accuracy. This difficulty lies in the lack of comprehensive metrics for expressing the similarity between the automatically derived trace maps and those derived manually. In this study, a novel metric is proposed to express the similarity between joint trace maps using a single numerical value. The proposed metric, scanline intersection similarity (SIS), expresses trace map similarity by evaluating the similarity between trace-scanline intersections on many orthogonal scanline pairs. The expressiveness of SIS was tested on multiple synthetic trace map pairs, and the results confirmed that SIS comprehensively reflects trace map similarity in terms of trace frequency, trace orientation, and the spatial distribution of traces. Comparisons with conventional metrics used in computer vision, namely, intersection over union (IoU) and boundary F1 (BF) scores, revealed that SIS expresses trace map similarity more accurately. IoU and BF scores led to misleading conclusions because of their evaluation of trace map similarity using the areal overlap of traces. To further demonstrate the applicability of SIS, the accuracy of deep-learning-based trace detection using U-Net (University of Freiburg, Germany) and DeepLabV3+ (Google, USA) was evaluated and compared using SIS.

Potential applications of deep learning in automatic rock joint trace mapping in a rock mass

In blasted rock slopes and underground openings, rock joints are visible in different forms. Rock joints are often exposed as planes confining rock blocks and visible as traces on a well-blasted, smooth rock mass surface. A realistic rock joint model should include both visual forms of joints in a rock mass: i.e., both joint traces and joint planes. Imaged-based 2D semantic segmentation using deep learning via the Convolutional Neural Network (CNN) has shown promising results in extracting joint traces in a rock mass. In 3D analysis, research studies using deep learning have demonstrated outperforming results in automatically extracting joint planes from an unstructured 3D point cloud compared to state-of-the-art methods. We discuss a pilot study using 3D true colour point cloud and their source and derived 2D images in this paper. In the study, we aim to implement and compare various CNN-based networks found in the literature for automatic extraction of joint traces from laser scanning and photogrammetry data. Extracted joint traces can then be clustered and connected to potential joint planes as joint objects in a discrete joint model. This can contribute to a more accurate estimation of rock joint persistence. The goal of the study is to compare the efficiency and accuracy between using 2D images and 3D point cloud as input data. Data are collected from two infrastructure projects with blasted rock slopes and tunnels in Norway.

Digital image processing-based automatic detection algorithm of cross joint trace and its application in mining roadway excavation practice

This paper proposes a digital image processing-based detection algorithm for cross joint traces of coal roadway heading face. Initially, the acquired images were preprocessed, i.e., adaptive correction was conducted for non-uniform illumination images based on the 2D gamma function. The edge detection algorithm was then applied to extract the edges of the structural plane, followed by the filtration of the non-structural plane noises. Moreover, the Hough transform algorithm was applied to extract the linear edges; finally, the edges were locally connected in accordance with the angle and distance criteria. The experimental results show that this algorithm can be used to reduce the noise caused by non-uniform illumination and avoid the mutual interference of multi-scale edges, so as to effectively extract the traces of the cross joint. Furthermore, Q-system and rock mass rating (RMR ) , were applied to conduct a quantitative evaluation on the stand-up time of unsupported roof in the four test images. The Q-system quality scores are 26.7, 43.3, 3.1, and 6.7, and the RMR quality scores are 56.84, 58.73, 48.42, and 51.42, respectively. The stand-up time of unsupported roofs with a span of 4.6 m are 30, 36, 7.7 and 14 d, respectively.

Study on size effect of jointed rock mass and influencing factors of the REV size based on the SRM method

Based on the Yaojiayu tunnel of Binlai Expressway, the size effect of jointed rock mass and influencing factors of the representative elementary volume (REV) were studied. The point cloud image of jointed rock mass near the tunnel face was collected by 3D laser scanning technology. Through the Geology Plane software independently developed by Shandong University, the structural plane data were processed and obtained. According to the structural plane data, the discrete fracture network (DFN) was established. Based on the laboratory test results of rock samples in the tunnel site, the particles were embedded into DFN to construct the synthetic rock mass (SRM). The size effect and REV of the jointed rock mass were studied based on the uniaxial compressive strength (UCS) and Young's modulus obtained by uniaxial compression test simulations. It is concluded that the REV size of the jointed rock mass is 7 m × 7 m × 14 m, which provides the criterion and calculation parameters for simulating tunnel excavation in jointed rock mass by the continuous deformation calculation method. In order to study the influence of joint geometric parameters (trace length, spacing, and dip angle) on REV size, different multi-scale SRM models were established by changing the parameters of structural planes. It is observed that within a certain size range, the REV size is negatively correlated with the joint trace length and dip angle, while positively correlated with the joint spacing. And the size of REV is gradually stable with the increase of geometric parameters of joints. Based on the influence law of joint geometry parameters on REV, the REV size range of different engineering can be estimated approximately.

Semi-automatic calculation of joint trace length from digital images based on deep learning and data structuring techniques

A new semi-automated method is proposed in this study that detects joint traces from digital images and calculates the length distribution through three-dimensional data structuring. The method comprises detecting the pixels corresponding to the joint trace in digital images and calculating the length distribution through three-dimensional data structuring of the pixels detected as the joint trace. Semantic segmentation based on deep learning techniques is applied to the detection of joint trace pixels to overcome the limitations of rule-based image processing techniques. For training a deep learning network, various rock joint images were sampled and labeled, following which the data sets for training, validation, and testing were prepared through classification and augmentation. Using the prepared datasets, the performance of the classifiers based on widely used semantic segmentation networks, namely U-Net (University of Freiburg, Germany) network and DeepLabV3+ (Google, USA) network, was compared. The classifier based on the DeepLabV3+ network was ultimately selected and applied. The trained classifier successfully detected pixels corresponding to the joint trace in images of both flat and uneven rock surfaces, indicating that the deep learning technique could be applied effectively to joint trace detection from digital images. Further, a data structuring technique is proposed to calculate the joint trace length using pixelwise data detected through the trained classifier. This technique uses point cloud data obtained by photogrammetry, and comprises two-dimensional thinning and segmentation, three-dimensional projection, segmentation, and segment linking. The entire proposed method, from detecting the joint trace pixels to three-dimensional data structuring, was verified by applying it to both simple flat and uneven rock surface models.

ESTIMATION OF ROCK JOINT TRACE LENGTH USING SUPPORT VECTOR MACHINE (SVM)

Jointed rock masses modeling needs the geometrical parameters of joints such as orientation, spacing, trace length, shape, and location. The rock joint trace length is one of the most critical design parameters in rock engineering and geotechnics. It controls the stability of the rock slope and tunnels in jointed rock masses by affecting rock mass strength. This parameter is usually determined through a joint survey in the field. Among the parameters, trace length is challenging because a complete joint plane within rock mass cannot be observed directly. The development of predictive models to determine rock joint length seems to be essential in rock engineering. This research made an effort to introduce a support vector machine (SVM) model to estimate rock joint trace length. The SVM is an advanced intelligence method used to solve the problem characterized by a small sample, non-linearity, and high dimension with a good generalization performance. In this study, three data sets from the sedimentary, igneous, and metamorphic rocks were organized, which location of joints on the scanline, aperture, spacing, orientation (D/DD), roughness, Schmidt rebound of the joint’s wall, type of termination, trace lengths in both sides of the scanline and joint sets were measured. The results of SVM prediction demonstrate that predicted and measured results are in good agreement. The SVM model-based results were compared with those obtained from field surveys. The proposed SVM model-based model was very efficient in predicting rock joint trace length values. The actual trace length could be estimated; thus, the expensive, difficult, time-consuming, and destructive joint surveys related to obscured joints could be avoided.

Trace elements and plasma metabolomics in a general population from Spain: The Hortega Study

BACKGROUND AND AIM: Limited studies have evaluated the joint influence of trace elements on metabolic pathways. We analyzed the association of 12 trace elements with 54 plasma metabolites in 1144 participants from the Hortega Study, a population-based sample from Spain. METHODS: Urine antimony (Sb), arsenic (As), As adjusted by arsenobetaine (Asb), barium (Ba), cadmium (Cd), chromium (Cr), cobalt (Co), molybdenum (Mo) and vanadium (V); and plasma copper (Cu), selenium (Se) and zinc (Zn) were measured with ICP-MS and AAS, respectively. Serum metabolomic profiles, including lipoprotein subclasses, were assessed by NMR-spectrometry. We jointly correlated metabolites by principal component (PC) analysis. Bayesian Kernel Machine Regression (BKMR) allowed to evaluate the influence of trace element mixtures on metabolomic profiles. RESULTS:The geometric means of trace element exposure biomarker levels were, 0.07, 68.69, 6.53, 62.03, 0.37, 3.55, 0.25, 26.09 and 2.08 μg/g for urine Sb, As, As adjusted by Asb, Ba, Cd, Cr, Co, Mo and V, and 93.88, 83.73 and 77.13 μg/L, for plasma Cu, Se and Zn. Cu was inversely associated with metabolic principal component (mPC) 1 (reflecting increasing non-essential and essential branch-chained aminoacids and bacterial co-metabolism versus decreasing VLDL lipoproteins subclasses); Se and Zn were inversely associated with mPC 2 (reflecting increasing essential aromatic aminoacids and bacterial co-metabolism); The corresponding associations for mPC 3 (reflecting increasing LDL lipoprotein subclasses) were positive for plasma Cu, Se and Zn and inverse for urine Co. Plasma Zn was inversely associated with mPC 4 (reflecting increasing HDL lipoprotein subclasses). These associations remained after multiple-trace element adjustment. BKMR to assess joint trace element exposure was confirmatory. CONCLUSIONS:Excessive exposure to Co, Cu, Se, and Zn was associated with metabolite profiles traditionally linked to cardiometabolic risk and bacterial co-metabolism. While our findings should be confirmed in other studies, interventions to prevent uncontrolled exposure to these trace elements may be needed. KEYWORDS: Microbiome, Mixtures, Metabolomics, Biomarkers of exposure

Neutrosophic Function for Assessing the Scale Effect of the Rock Joint Surface Roughness

A new investigation method is proposed for recording large-sized joint profiles and making statistical analyses of the joint roughness coefficient (JRC) values of the 10–300 cm sized profiles. The mechanical hand profilograph is used for joint roughness measurement due to its advantage of easy operation and high accuracy in recording joint traces. Based on the proposed method, it provides sufficient samples from various positions on the large joint profile, which allows the statistical evaluation of JRC values. A neutrosophic number (NN) is employed for revealing determinate and/or indeterminate information as it consists of determinate and indeterminate parts. Due to the uncertainty of JRC in the real world, NN is chosen to represent the JRC value, which is not only random but also a fuzzy indefinite parameter. The neutrosophic function is used to analyze and express the scale effect of joint surface roughness, and its derivative is used to describe the changing trend of the scale effect. The results show that the JRC value of the joint profile is related to the scale and has a negative effect on the surface roughness of the rock joint. The indeterminate information about the scale effect on joint roughness is described by the neutrosophic functions, and the derivative indicated that the JRC values of small samples are more sensitive than those of large-sized examples. When the length of the sample exceeds the stationarity limit of 80 cm, the roughness appears to be almost scale independent.

Unsupervised Hyperspectral Band Selection With Multigraph Integrated Embedding and Robust Self-Contained Regression

Band selection is an effective means to alleviate the curse of dimensionality in hyperspectral data. Many methods select a compact and low redundant band subset, which is inadequate as it may degrade the classification performance. Instead, more emphasis shall be put on selecting representative bands. In this article, we propose a robust unsupervised band selection method to address this issue. Our method reveals bandwise representativeness based on the comprehensive interband neighborhood structure. It incorporates an interband neighborhood graph into a sparse self-contained regression model in order to provide a reasonable measure for bandwise representativeness. The derived coefficient matrix not only uncovers bandwise importance values but also is coherent to the generalized interband local neighborhood structure. For constructing the interband neighboring structural graph, an integrated multigraph model is employed to achieve better generalization performance. It combines the benefit of multiple graphs but is insusceptible to the defects of a single one. To enhance the reliability of this model, a joint trace minimum and nonnegative constraint is imposed on the coefficient matrix. Accordingly, a multigraph integrated embedding and robust self-contained regression model (MGRSR) is formulated. In addition, an iterative update algorithm is developed to solve the problem. Comparative experiments on three hyperspectral data sets illustrate that MGRSR is robust to various data and has superior performance compared with several state-of-the-art methods.

A state-of-the-art review of automated extraction of rock mass discontinuity characteristics using three-dimensional surface models

In the last two decades, significant research has been conducted in the field of automated extraction of rock mass discontinuity characteristics from three-dimensional (3D) models. This provides several methodologies for acquiring discontinuity measurements from 3D models, such as point clouds generated using laser scanning or photogrammetry. However, even with numerous automated and semi-automated methods presented in the literature, there is not one single method that can automatically characterize discontinuities accurately in a minimum of time. In this paper, we critically review all the existing methods proposed in the literature for the extraction of discontinuity characteristics such as joint sets and orientations, persistence, joint spacing, roughness and block size using point clouds, digital elevation maps, or meshes. As a result of this review, we identify the strengths and drawbacks of each method used for extracting those characteristics. We found that the approaches based on voxels and region growing are superior in extracting joint planes from 3D point clouds. Normal tensor voting with trace growth algorithm is a robust method for measuring joint trace length from 3D meshes. Spacing is estimated by calculating the perpendicular distance between joint planes. Several independent roughness indices are presented to quantify roughness from 3D surface models, but there is a need to incorporate these indices into automated methodologies. There is a lack of efficient algorithms for direct computation of block size from 3D rock mass surface models. • Review of automatic and semi-automatic methods for discontinuity characterization. • Focused on joint sets, orientation, persistence, spacing, roughness and block size. • Strengths and limitations of methods are discussed from a practical perspective. • Computation time, number of parameters, accuracy, and robustness are discussed. • Region growing was found fast and accurate for joint detection from LiDAR data.

Identification of structural domains considering the combined effect of multiple joint characteristics

A structural domain represents a volume of rock masses with similar mechanical and hydrological properties. This paper presents a new multivariate method, built upon the classical statistical method, for identifying structural domains by considering a combined effect of multiple joint characteristics. First, joints are placed into corresponding cells according to a comprehensive categorization of joint characteristics. Second, based on the frequencies of joints in each cell, a contingency table analysis and appropriate χ 2 test are used to identify structural domains. In this method, the joint frequency in each cell is determined not only by joint orientation but also by joint trace length and aperture. A group of simulated joint populations is used to check the validity of the proposed method. Seven joint populations with a total of 731 joints collected in Southeast Dalian Port, China are evaluated using the proposed method. Calculations show that the differences in both distribution forms and sequences of joint characteristics produce apparently different identification results. A combined effect of multiple joint characteristics is found to play an important role in the identification of structural domains. Reliable results for the multivariate method are obtained, given the objective of analysis and practical application.

Image‐based discontinuity identification

AbstractKnowledge about the joint network is important in rock engineering. It controls the stability and strength of blocky rock masses. Thus, the joint network is mapped in more or less detail, regarding the specifications. To do so, different methods have evolved over the years. One of these methods is digital mapping, based on the visual and spatial appearance of the distinct joints. This mapping usually is done by an experienced geologist. However, the trend in digital mapping is towards a supervised but mainly autonomous identification of discontinuities. One aspect of this automated process is the recognition of joints in digital outcrop images by their optical attributes. This contribution presents a density based joint plane detection. By the combination of a vector based joint plane detection and a pixel based joint trace detection, not only joints, but also the foliation in the investigated tunnel face could be extracted very accurately. The approach represents the current state of research and further improvements are to be expected.

A homomorphic encrypted reversible information hiding scheme for integrity authentication and piracy tracing

Reversible information hiding plays an important roles in the field of privacy protection. In this paper, a new reversible information hiding scheme is proposed which supports the direct operation in homomorphic encrypted domain. The proposed “Joint Hiding and Tracing, JHT” tactics and the “3 Level Integrity Authentication Scheme” devote to piracy tracing and integrity authentication. To enhance security, the Paillier homomorphic encryption and Arnold technology are employed. Furthermore, we present the dual region division tactics including Data/Signature region division and Texture/Smooth region division. Data/Signature region division is to circumvent conflicts, and Texture/Smooth region division is fit well with the human visual characteristics. Besides, neighboring quadratic optimization approach is presented to eliminate the smooth/texture isolated islands in the texture/smooth regions. In addition, Extended Integer Transform and position image are developed to achieve reversibility and circumvent overflow/underflow problems. Experimental results confirm the efficient of the proposed scheme, and demonstrate it not only realizes privacy protection, integrity authentication and piracy tracing, but also holds the characteristics of higher security, larger capacity and better restoration quality.

Vision and spectroscopic sensing for joint tracing in narrow gap laser butt welding

The automated laser beam butt welding process is sensitive to positioning the laser beam with respect to the joint because a small offset may result in detrimental lack of sidewall fusion. This problem is even more pronounced in case of narrow gap butt welding, where most of the commercial automatic joint tracing systems fail to detect the exact position and size of the gap. In this work, a dual vision and spectroscopic sensing approach is proposed to trace narrow gap butt joints during laser welding. The system consists of a camera with suitable illumination and matched optical filters and a fast miniature spectrometer. An image processing algorithm of the camera recordings has been developed in order to estimate the laser spot position relative to the joint position. The spectral emissions from the laser induced plasma plume have been acquired by the spectrometer, and based on the measurements of the intensities of selected lines of the spectrum, the electron temperature signal has been calculated and correlated to variations of process conditions. The individual performances of these two systems have been experimentally investigated and evaluated offline by data from several welding experiments, where artificial abrupt as well as gradual deviations of the laser beam out of the joint were produced. Results indicate that a combination of the information provided by the vision and spectroscopic systems is beneficial for development of a hybrid sensing system for joint tracing.

Statistical analysis of scale effect on equivalent elastic modulus of jointed rock masses

The study of scale effects plays an important role in the evaluation of mechanical properties of rock masses. There have been many studies on this topic; however, few have been able to effectively analyze relationships between size and deformation properties analytically. This paper presents an investigation of scale effects on deformation properties of jointed rock masses by using analytical and statistical methods. First, the analytical formula for E eq (equivalent elastic modulus) of jointed rock with a parallel joint set was derived. This derivation is related to a geometrical parameter ρ’, defined as joint trace length per unit area. Second, model of a half-space rock with a parallel joint set was constructed and subsequently sampled to specimens with different locations and lengths. The expectation and standard deviation of the ρ’ of rock samples were derived to statistically describe scale effect of ρ’. Then, the scale effect of 1/E eq (equivalent elastic compliance) was analyzed. The investigation shows that expectation of 1/E eq is a constant with varying size and standard deviation of 1/E eq decreases and periodically fluctuates with increasing size. The applicability of the conclusions was discussed, and some extended studies on stochastic jointed rock masses were made. Finally, representative elementary volumes of the rock model were determined according to the analytical solutions.