Crack Line Research Articles

Eddy current quantitative evaluation of high-speed railway contact wire cracks based on neural network

PurposeThe purpose of this study is to study the quantitative evaluation method of contact wire cracks by analyzing the changing law of eddy current signal characteristics under different cracks of contact wire of high-speed railway so as to provide a new way of thinking and method for the detection of contact wire injuries of high-speed railway.Design/methodology/approachBased on the principle of eddy current detection and the specification parameters of high-speed railway contact wires in China, a finite element model for eddy current testing of contact wires was established to explore the variation patterns of crack signal characteristics in numerical simulation. A crack detection system based on eddy current detection was built, and eddy current detection voltage data was obtained for cracks of different depths and widths. By analyzing the variation law of eddy current signals, characteristic parameters were obtained and a quantitative evaluation model for crack width and depth was established based on the back propagation (BP) neural network.FindingsNumerical simulation and experimental detection of eddy current signal change rule is basically consistent, based on the law of the selected characteristics of the parameters in the BP neural network crack quantitative evaluation model also has a certain degree of effectiveness and reliability. BP neural network training results show that the classification accuracy for different widths and depths of the classification is 100 and 85.71%, respectively, and can be effectively realized on the high-speed railway contact line cracks of the quantitative evaluation classification.Originality/valueThis study establishes a new type of high-speed railway contact wire crack detection and identification method, which provides a new technical means for high-speed railway contact wire injury detection. The study of eddy current characteristic law and quantitative evaluation model for different cracks in contact line has important academic value and practical significance, and it has certain guiding significance for the detection technology of contact line in high-speed railway.

Experimental study on internal damage mechanisms and performance state perception of tunnel linings under different loading paths

The state of tunnel lining structures plays a crucial role in determining safety and service quality throughout their serving life. Therefore, establishing a quantitative method for evaluating the bearing capacity of linings is crucial. Understanding the process and status of crack propagation is key to ensuring structural safety. The three-dimensional development of lining damage cracks is closely related to structural safety. Unveiling the spatial growth of these cracks and the evolution of structural performance is vital for an accurate assessment of lining safety. Key factors in crack propagation, along with non-destructive detection methods, serve as primary approaches for evaluating the safety condition. This paper explores the evolution law and evaluation model of the bearing capacity of plain concrete linings under different loading paths. The distribution of structural stiffness changes significantly under different boundary settings. Therefore, full-scale loading tests of lining components were conducted, designing two types of linings: one intact and the other with initial defects, to simulate the failure of plain concrete linings under diverse loading conditions. The results show that: (1) The damage development of linings exhibits clear staged evolution characteristics; (2) The spatial development of lining cracks can be divided into three stages; (3) There are significant differences in ultrasonic parameters at different stages. Consequently, a method for evaluating the local bearing capacity state of linings based on the coupling of crack characteristics and ultrasonic parameters is proposed; (4) This method is also applicable to linings with initial damage, where damage evolution follows similar stages. The findings provide theoretical guidance for predicting and preventing crack propagation in operational tunnel linings.

A highly efficient tunnel lining crack detection model based on Mini-Unet

The accurate detection of tunnel lining cracks and prompt identification of their primary causes are critical for maintaining tunnel availability. The advancement of deep learning, particularly in the domain of convolutional neural network (CNN) for image segmentation, has made tunnel lining crack detection more feasible. However, the CNN-based technique for tunnel lining crack detection commonly prioritizes increasing algorithmic complexity to enhance detection accuracy, posing a challenge in balancing the accuracy of detection and the efficiency of the algorithm. Motivated by the superior performance of Unet in image segmentation, this paper proposes a lightweight tunnel lining crack detection model named Mini-Unet, which refined the Unet architecture and utilized depthwise separable convolutions (DSConv) to replace some standard convolution layers. In the optimization of the proposed model parameters, applying a hybrid loss function that integrated dice loss and cross-entropy loss effectively tackled the imbalance between crack and background categories. Several models were set up to contrast with Mini-Unet and the experimental results were analyzed. Mini-Unet achieves a mean intersection over union (MIoU) of 60.76%, a mean precision of 84.18%, and a frame per second (FPS) of 5.635, respectively. Mini-Unet outperforms several mainstream models, enabling rapid detection while maintaining identified accuracy and facilitating the practical application of AI power for real-time tunnel lining crack detection.

Microbial-Induced Calcium Carbonate Precipitation and Basalt Fiber Cloth Reinforcement Used for Sustainable Repair of Tunnel Lining Cracks

The increasing problem of urban traffic congestion has led to the extensive use of underground tunnels. However, tunnel lining cracks pose a major threat to the integrity and safety of the structure. Although the traditional repair method is effective, it often requires higher construction technology and higher cost, and may cause damage to the concrete structure. In this study, microbial-induced calcium carbonate precipitation (MICP) was combined with basalt fiber cloth to repair and reinforce tunnel lining cracks. Bacillus pasteurii was used to optimize the microbial mineralization process, and the effectiveness of the method on cracks with different widths was evaluated using a water seepage test. In addition, the mechanical properties of the reinforced tunnel lining were tested. The microbial mineralization process effectively repaired cracks with widths of 1 mm, 2 mm, and 3 mm. The use of unidirectional basalt fiber cloth increased the bearing capacity of the strengthened member by 12.5%. The combined reinforcement method also enhances the deflection performance and alleviates the influence of water seepage on the bonding performance. This innovative and sustainable approach not only provides an effective solution for the repair of tunnel lining cracks, but also contributes to the broader field of eco-friendly building materials. This study highlights the potential of using this combination approach to improve the durability and performance of underground infrastructure.

High-Precision Defect Detection in Solar Cells Using YOLOv10 Deep Learning Model

This study presents an advanced defect detection approach for solar cells using the YOLOv10 deep learning model. Leveraging a comprehensive dataset of 10,500 solar cell images annotated with 12 distinct defect types, our model integrates Compact Inverted Blocks (CIBs) and Partial Self-Attention (PSA) modules to enhance feature extraction and classification accuracy. Training on the Viking cluster with state-of-the-art GPUs, our model achieved remarkable results, including a mean Average Precision (mAP@0.5) of 98.5%. Detailed analysis of the model’s performance revealed exceptional precision and recall rates for most defect classes, notably achieving 100% accuracy in detecting black core, corner, fragment, scratch, and short circuit defects. Even for challenging defect types such as a thick line and star crack, the model maintained high performance, with accuracies of 94% and 96%, respectively. The Recall–Confidence and Precision–Recall curves further demonstrate the model’s robustness and reliability across varying confidence thresholds. This research not only advances the state of automated defect detection in photovoltaic manufacturing but also underscores the potential of YOLOv10 for real-time applications. Our findings suggest significant implications for improving the quality control process in solar cell production. Although the model demonstrates high accuracy across most defect types, certain subtle defects, such as thick lines and star cracks, remain challenging, indicating potential areas for further optimization in future work.

Mechanical behaviour of double lining with outer segmental lining and inner fibre reinforced concrete lining under internal water pressure

Double lining with outer segmental lining and inner reinforced concrete lining is extensively used for water conveyance tunnel with internal water pressure. In order to improve the performance of the double lining, the steel rebar and fibre reinforced concrete (R/FRC) is designed for inner lining to enhance the tensile strength of reinforced concrete (RC). Full-scale tests were conducted to compare the mechanical behaviour of double lining with inner RC and R/FRC linings. The test results showed that both types of lining failed in four stages: elastic stage, inner lining cracking stage, crack stabilization and segmental joint damage stage, and failure stage. The cracks firstly occurred in the inner lining near the segmental joints and then propagated to the whole inner lining ring. Finally, the crack width and segmental joint opening successively exceeded the thresholds, and the double lining failed until the breaking of segmental joints. Compared with inner RC lining, R/FRC lining had better performance in terms of the initial cracking load, cracking-control ability, post-cracking stiffness, service limit capacity of inner lining and waterproof capacity of segmental lining. The improvement ratios were 36.3%, 50.3%, 46.3%, 37.2% and 31.1%, respectively. The influences of fibre volume fraction, fibre aspect ratio, and reinforcement ratio of steel rebar on the mechanical performance of R/FRC lining were also investigated based on a previously proposed analytical model. The parametric analysis demonstrated that higher fibre volume fraction and fibre aspect ratio can result in more significant increase of mechanical performance of R/FRC lining. The steel fibres were found to have more significant effects on the post-cracking behaviour of the lining than same amounts of reinforcing bars. Finally, an optimized function was proposed to fulfil a balance of lining performance and economy. The experimental and analytical results indicated that R/FRC lining can substitute RC lining and perform higher mechanical performance in water conveyance tunnels.

Failure analysis and deformation characteristics of shield tunnel obliquely crossing ground fissure under earthquake

In order to study the deformation law and failure characteristics of shield tunnel obliquely crossing ground fissure under earthquake action, taking the shield tunnel of Xi ’an Metro Line 8 crossing f3 ground fissure as the engineering background, the 1: 20 shaking table model test method was used to analyze the strain of shield tunnel, the contact pressure with surrounding rock soil, the dislocation of segment and the axial force of bolt in detail, and the seismic damage mechanism and failure characteristics of shield tunnel obliquely crossing ground fissure were obtained. The test results show that under the action of earthquake, the shield tunnel has complex three-dimensional deformation characteristics, among which the vertical deformation is the most obvious. The deformation is mainly concentrated in the location of the ground fissure. The tensile strain and contact pressure of the hanging wall of the tunnel segment are greater than the strain value and contact pressure of the footwall. Because the vertical deformation of the tunnel is the largest, the bolts at the vault and the arch bottom are most obviously pulled. Excavation after the test, it can be seen that the tunnel appeared the phenomenon of ring joint opening, lining cracking and other damage. Under the action of the earthquake, the shield tunnel across the ground fissure is mainly subjected to tensile failure. The failure area is within 10 m from the ground fissure in the hanging wall and footwall, and the total length is 20 m. The closer to the ground fissure, the more serious the damage. The research results provide a scientific and reasonable reference for the subsequent construction and disaster prevention and mitigation design of Xi ’an Metro.

Characteristics of deformation and defect of shield tunnel in coastal structured soil in China

Shield tunnel is a type of linear underground structure assembled by lining segments, characterized with long joint, weak stiffness, and strict deformation control requirement. The situation of the long-term deformation and defect of the shield tunnel in soft ground in coastal area of China is severe, mainly attributed to the tunneling-induced ground consolidation, frozen cross passage, groundwater pumping, cyclic train load, and nearby construction. Shield tunnel is buried in ground, and the above factors could result in underlying ground settlement, overlying ground loading/unloading, and at-side ground unloading. As a result, the tunnel could suffer from different types of structural deformation and defect. Based upon the aforementioned different reasons, this study investigates the characteristics of the tunnel deformation and defect corresponding to the different types of ground stress change and deformation. It is found that tunneling-induced ground consolidation, frozen cross passage, groundwater pumping, and cyclic train load mainly contribute to the longitudinal differential settlement but negligible transverse convergence, associated with water leakages at circumferential joints. In comparison, surface surcharge and at-side unloading not only cause significant longitudinal differential deformation but also increase transverse lining internal forces, resulting in water leakages at circumferential joints, longitudinal lining concrete cracks and water leakages. Finally, nearby construction could strongly disturb the ground and cause the generation of excess pore-water pressure, making the shield tunnel deformation develops continuously after the nearby construction is completed.

Sprain energy consequences for damage localization and fracture mechanics

The 2023 smooth Lagrangian Crack-Band Model (slCBM), inspired by the 2020 invention of the gap test, prevented spurious damage localization during fracture growth by introducing the second gradient of the displacement field vector, named the "sprain," as the localization limiter. The key idea was that, in the finite element implementation, the displacement vector and its gradient should be treated as independent fields with the lowest ([Formula: see text]) continuity, constrained by a second-order Lagrange multiplier tensor. Coupled with a realistic constitutive law for triaxial softening damage, such as microplane model M7, the known limitations of the classical Crack Band Model were eliminated. Here, we show that the slCBM closely reproduces the size effect revealed by the gap test at various crack-parallel stresses. To describe it, we present an approximate corrective formula, although a strong loading-path dependence limits its applicability. Except for the rare case of zero crack-parallel stresses, the fracture predictions of the line crack models (linear elastic fracture mechanics, phase-field, extended finite element method (XFEM), cohesive crack models) can be as much as 100% in error. We argue that the localization limiter concept must be extended by including the resistance to material rotation gradients. We also show that, without this resistance, the existing strain-gradient damage theories may predict a wrong fracture pattern and have, for Mode II and III fractures, a load capacity error as much as 55%. Finally, we argue that the crack-parallel stress effect must occur in all materials, ranging from concrete to atomistically sharp cracks in crystals.

Wave scattering in a cracked exponentially graded magnetoelectroelastic half‐plane

AbstractAn exponentially graded with respect to depth magnetoelectroelastic (MEE) half‐plane containing two line or curvilinear cracks under time‐harmonic SH wave is studied. The defined mechanical problem is described by boundary integral equations (BIEs) along the cracks boundaries. The computational tool based on the non‐hypersingular traction boundary integral equation method (BIEM) is developed, verified and inserted in numerical simulations. It is based on the analytically derived Green's function and free‐field wave motion solution for exponentially graded MEE half‐plane. The dependence of the generalized stress intensity factors (SIFs) on the material gradient parameters, on the dynamic load characteristics, on the cracks position and their shape, on the dynamic interaction between cracks and between them and half‐plane boundary is numerically analyzed.

Using fractal voids to understand Mode I compressive fracture in brittle materials – A two-dimensional analysis

Unlike cases of direct or indirect tensile loading, analysis of Mode I fracture in cases of compressive loading must necessarily consider two-dimensional flaw geometries. The consequent analytical complications have resulted in little theoretical evolution towards understanding Mode I fracture in compressive loading. Researchers have recently observed that the linear elastic (LE) stress fields surrounding two-dimensional flaws in compression appear to have indicative value regarding Mode I fracture, but no rational framework has yet been proposed for their interpretation. Herein it is demonstrated that by idealizing void surfaces as fractal, and using what will be called the “small flaw assumption,” LE stress fields can be interpreted to obtain significant insight regarding brittle Mode I compressive fracture. Using fractal voids, a rational and consistent explanation for the satisfaction of the stress and energy criteria at the surface of two-dimensional flaws is presented. The discussion resolves many typical theoretical issues in the literature in a manner consistent with fundamental Griffith theory, and accounts for size and shape effects. The framework further enables the computationally efficient prediction of peak KI values associated with the propagation of line cracks from two-dimensional flaws from a brittle medium subject to macroscopic uniaxial compression via LE stress fields.

Physical and mechanical response of large-diameter shield tunnel lining structure under non-uniform fire: A full-scale fire test-based study

When a fire occurs in an underground shield tunnel, it can result in substantial property damage and cause permanent harm to the tunnel lining structure. This is especially true for large-diameter shield tunnels that have numerous segments and joints, and are exposed to specific fire conditions in certain areas. This paper constructs a full-scale shield tunnel fire test platform and conducts a non-uniform fire test using the lining system of a three-ring large-diameter shield tunnel with an inner diameter of 10.5 m. Based on the tests, the temperature field distribution, high-temperature bursting, cracking phenomena, and deformation under fire conditions are observed. Furthermore, the post-fire damage forms of tunnel lining structures are obtained through the post-fire ultimate loading test, and the corresponding mechanism is explained. The test results illustrate that the radial and circumferential distribution of internal temperature within the tunnel lining, as well as the radial temperature gradient distribution on the inner surface of the lining, have non-uniform distribution characteristics. As a result, the macroscopic phenomena of lining concrete bursting and crack development during the fire test mainly occur near the fire source, where the temperature rise gradient is the highest. In addition, the lining structure has a deformation characteristic of local outward expansion and cannot recover after the fire load is removed. The ultimate form of damage after the fire is dominated by crush damage from the inside out of the lining joints in the fire-exposed area. The above results serve as a foundation for future tunnel fire safety design and evaluation.

An Experimental Study on the Performance of Materials for Repairing Cracks in Tunnel Linings under Erosive Environments

Addressing the current lining cracking problem in coastal tunnels, this paper independently introduces a novel type of repair material for tunnel lining cracks—the composite repair material consisting of waterborne epoxy resin and ultrafine cement (referred to as EC composite repair material). Through indoor testing, we have analyzed the change rule of the mass change rate, compressive strength, flexural strength, and chloride ion concentration of the repair material samples in erosive environments, with the dosage of each component in the EC composite repair material being varied. We have also investigated the working performance, mechanical properties, and microstructure of the repair material. The results of this study show that when the proportion of each component of ultrafine cement, waterborne epoxy resin, waterborne epoxy curing agent, waterborne polyurethane, defoamer, and water is 100:50:50:2.5:0.5:30, the performance of the EC composite repair material in a chloride ion-rich environment is optimal in all aspects. When the mixing ratio of each component of the EC composite repair material is as stated above, the repair material exhibits the best performance in a chloride ion erosion environment. With this ratio of components in the EC composite repair material, the fluidity, setting time, compressive strength, flexural strength, and bond strength of the repair material in a chloride ion erosion environment can meet the requirements of relevant specifications, and it is highly effective in repairing tunnel lining cracks. The polymeric film formed by the reaction between the waterborne epoxy resin emulsion and the curing agent fills the pores between the hydration products, resulting in a densely packed internal structure of EC composite repair material with enhanced erosion resistance, making it very suitable for repairing cracks in tunnel linings in erosive environments.

Intelligent segmentation and quantification of tunnel lining cracks via computer vision

Aiming to automatically, precisely, and rapidly detect tunnel lining cracks from images and extract geometric information for structural condition assessment, this study proposes a novel tunnel lining crack segmentation network (TCSegNet) and establishes a framework for calculating key geometric parameters of cracks. A tunnel lining crack segmentation dataset is first built by conducting on-site inspections of metro tunnels and collecting open-sourced tunnel images. Afterward, the TCSegNet, conforming to the encoder–decoder architectural paradigm, is designed to separate cracks from lining images pixel-to-pixel. An improved ConvNeXt and developed efficient atrous spatial pyramid pooling module constitute the encoder. The skip connections, upsampling modules, and tailored segmentation head form the decoder. Upon the segmentation results of TCSegNet, a computing framework integrating multiple digital image processing techniques is proposed to obtain the length, average width, and maximum width of cracks. The experimental results show that the TCSegNet achieves leading results among several dominant models, with 70.78% mean intersection over union (mIoU) and 57.43% F1score. Furthermore, the TCSegNet has 32.01 million parameters, requires 55.13 billion floating point operations, and gets 107.28 frames per second, proving that it has low time and space complexities and implements real-time segmentation. Also, the rationality and effectiveness of TCSegNet in alleviating the crack disjoint problem and preserving crack edge details are verified through comparative experiments. In addition, the TCSegNet achieves 71.99%, 70.45%, and 70.23% mIoU in high-resolution image segmentation, robustness, and generalization tests, respectively, demonstrating that it is competent for detecting high-resolution lining images, has a solid resistance to illumination variations, and can be well generalized to other tunnel lining image datasets. Finally, the applicability of the crack quantification framework is validated by practical application examples. The developed approaches in this study provide pixel-level segmentation results and detailed measurements of concrete lining cracks to assess tunnel structural safety status.

Evaluation method of tunnel cracking disease under biased pressure based on enhanced image fractal features

This paper focuses on the tunnel cracking disease under biased pressure. Through model tests on three lining conditions, the study investigates the expansion process of surface cracks on the lining under biased pressure. Proposing an improved method for calculating fractal characteristics of lining crack disease based on box counting dimension. Quantifying crack disease through digital image processing to obtain two parameters: total width and fractal dimension. Discussed the relationship between quantification parameters of surface crack disease in linings and the service performance of the lining. 29 groups of crack disease quantization parameters obtained by model test were selected to establish the disease sample space, and the spatial data were automatically learned and grouped based on clustering method. Finally, a new diagnostic Index of Tunnel Lining Defect Index-Crack & Dimension (TLDI-C&D) and its disease classification criteria for the whole lining ring are proposed. The results indicate that under the biased pressure, regardless of the presence of pre-existing defects, the biased pressure region is the most severely diseased area in terms of cracking. Compared to the intact lining, the initial cracking loads for arch crown defects and arch waist defects are advanced by 33.1 % and 73.0 %, respectively. After the apparent cracks in the lining are fully formed, pre-existing defects no longer affect the speed and distribution of crack propagation.The larger the fractal dimension, the more complex the morphology of the corresponding crack disease. Under the same image area, the ratio of crack quantity to width has a greater impact on the fractal dimension. There is a corresponding relationship between quantification parameters of crack disease and the bearing performance of the lining structure, making them indicators for measuring the load-bearing capacity of the lining. The most reasonable grading level for lining crack disease under the biased pressure is four levels. The diagnostic index for tunnel lining cracks, TLDI-C&D is 1.0～2.2 (level I), 2.2～3.2 (level II), 3.2～4.3 (level III), and 4.3～5.5 (level IV). On-site measurements have proven the accuracy of this crack disease diagnostic evaluation method.

Fracture resistance of ultratranslucent multilayered zirconia veneers with different facial thicknesses.

To assess the fracture resistance of computer-aided design and computer-aided manufacturing (CAD/CAM) ultratranslucent multilayered zirconia (5Y-YZP) veneers with varying facial thickness. Sixty translucent zirconia veneers were designed and milled using a chairside CAD/CAM system for maxillary central incisors. The butt joint incisal veneer tooth preparations consisted of 1.00 mm incisal reduction, 0.40 mm chamfer margin, and three different facial reductions; 0.50, 0.75, and 1 mm, respectively. The ceramic veneers were cemented to printed resin dies and subjected to thermal cycling. Subsequently, the restorations were loaded with compressive loading force, and fracture occurrences were recorded. Scanning electron microscope (SEM) images of the fractured specimens were captured. The fracture resistance varied among the veneers with different facial thicknesses. Ultratranslucent zirconia veneers with a facial thickness of 1.00 mm exhibited the highest fracture resistance values (742.15 N), followed by those with 0.75 mm facial thickness (673 N). Minimally invasive veneers with 0.50 mm thickness displayed similar fracture resistance as thicker veneers with 0.75 mm. However, veneers with 1.00 mm thickness displayed the highest values. SEM fracture patterns for 0.50 and 0.75 mm display similar and fewer crack lines than 1.00 mm veneers. RESEARCH HIGHLIGHTS: Minimally invasive zirconia veneers exhibit similar fracture resistance to thicker veneers.

Enhancing tunnel crack detection with linear seam using mixed stride convolution and attention mechanism

Cracks in tunnel lining structures constitute a common and serious problem that jeopardizes the safety of traffic and the durability of the tunnel. The similarity between lining seams and cracks in terms of strength and morphological characteristics renders the detection of cracks in tunnel lining structures challenging. To address this issue, a new deep learning-based method for crack detection in tunnel lining structures is proposed. First, an improved attention mechanism is introduced for the morphological features of lining seams, which not only aggregates global spatial information but also features along two dimensions, height and width, to mine more long-distance feature information. Furthermore, a mixed strip convolution module leveraging four different directions of strip convolution is proposed. This module captures remote contextual information from various angles to avoid interference from background pixels. To evaluate the proposed approach, the two modules are integrated into a U-shaped network, and experiments are conducted on Tunnel200, a tunnel lining crack dataset, as well as the publicly available crack datasets Crack500 and DeepCrack. The results show that the approach outperforms existing methods and achieves superior performance on these datasets.

Identifying the dominant influencing factors of secondary lining cracking risk in an operating mountain tunnel

PurposeA risk-based method is proposed to identify the dominant influencing factors of secondary lining cracking in an operating mountain tunnel with weak surrounding rock.Design/methodology/approachBased on the inspection data from a mountain tunnel in Southwest China, a lognormal proportional hazard model is established to describe the statistical distribution of secondary lining cracks. Then, the model parameters are obtained by using the Bayesian regression method, and the importance of influencing factors can be sorted based on the absolute values of the parameters.FindingsThe results show that the order of importance of the influencing factors of secondary lining cracks is as follows: location of the crack on the tunnel profile, rock mass grade of the surrounding rock, time to completion of the secondary lining, and void behind the secondary lining. Accordingly, the location of the crack on the tunnel profile and rock mass grade of the surrounding rock are the two most important influencing factors of secondary lining cracks in the investigated mountain tunnel, and appropriate maintenance measures should be focused on these two aspects.Originality/valueThis study provides a general and effective reference for identifying the dominant influencing factors of secondary lining cracks to guide the targeted maintenance in mountain tunnels.

Physical model test and application of 3D printing rock-like specimens to laminated rock tunnels

Weak structural plane deformation is responsible for the non-uniform large deformation disasters in layered rock tunnels, resulting in steel arch distortion and secondary lining cracking. In this study, a servo biaxial testing system was employed to conduct physical modeling tests on layered rock tunnels with bedding planes of varying dip angles. The influence of structural anisotropy in layered rocks on the micro displacement and strain field of surrounding rocks was analyzed using digital image correlation (DIC) technology. The spatiotemporal evolution of non-uniform deformation of surrounding rocks was investigated, and numerical simulation was performed to verify the experimental results. The findings indicate that the displacement and strain field of the surrounding layered rocks are all maximized at the horizontal bedding planes and decrease linearly with the increasing dip angle. The failure of the layered surrounding rock with different dip angles occurs and extends along the bedding planes. Compressive strain failure occurs after excavation under high horizontal stress. This study provides significant theoretical support for the analysis, prediction, and control of non-uniform deformation of tunnel surrounding rocks.

Nonlinear Vibration of Cracked Porous FG-GPL RC Cylindrical Panels Using a Phase-Field Crack Model

This study is concerned with the nonlinear free vibration of a cracked functionally graded porous cylindrical panel reinforced with graphene platelets by introducing a phase-field crack model. Conventional crack modeling by separating the grid nodes lying on the crack line is not only painstaking but also suffers from numerical instability. To overcome this problem, the internal crack is modeled by adopting the phase-field formulation and a virtual geometry rotation. The nonlinear numerical method is developed based on the first-order shear deformation theory incorporated with the von Kármán geometry nonlinearity in the framework of the 2-D extended natural element method, a recently introduced mesh-free method. The crack-induced singular field is represented by adopting the crack-tip singular functions, and the troublesome numerical locking is restrained by combining the MITC3+ shell concept and the shear stabilization factor. The curved shell surface is mapped to a 2-D rectangular NEM grid to avoid difficulty in defining the interpolation functions. The developed numerical method is verified through a comparison with the reference solutions, and the large-amplitude free vibration of porous cracked functionally graded grapheme platelet-reinforced cylindrical panels is profoundly examined by changing the major parameters.