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Keywords = FPZ length

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19 pages, 67535 KiB  
Article
Investigation of the Layered Effect on the Tensile Fracture Characteristics of Sandstone Using Intact and Pre-Cracked Brazilian Disk Specimens
by Yuchen Zhong, Qi Hao, Huini Liu, Xiling Liu, Lichang Wang and Qin Xie
Appl. Sci. 2025, 15(4), 2149; https://doi.org/10.3390/app15042149 - 18 Feb 2025
Viewed by 526
Abstract
To investigate the stratification effect on rock splitting and Mode I fracture characteristics, standard Brazilian splitting disk specimens and straight-crack disk specimens were subjected to splitting loading tests, and a high-speed camera system and acoustic emission (AE) system were used to study the [...] Read more.
To investigate the stratification effect on rock splitting and Mode I fracture characteristics, standard Brazilian splitting disk specimens and straight-crack disk specimens were subjected to splitting loading tests, and a high-speed camera system and acoustic emission (AE) system were used to study the rocks’ mechanical properties, fracture parameters, and AE characteristics. The results demonstrate the following: (1) The tensile strength and fracture toughness of the layered rock exhibit significant stratification effects, gradually decreasing with the increase in the number of layers and the layer angle. (2) The different angles of the stratification planes lead to the diversity of failure modes in the disk specimens. (3) The S-value and the cumulative AE count curve of specimens without prefabricated cracks show two types of pattern during loading: fluctuating increase mode, and “gentle–steep” increase mode. (4) Layered rock specimens exhibit a low ratio of rise time to voltage amplitude (RA) value and high average frequency (AF) characteristics during fracture, and the shear failure mainly occurs during the stable propagation phase after the initiation of macroscopic cracks. (5) The fracture process zone (FPZ)’s length at the peak point of the specimens decreases exponentially with the increase in the number of layers, but this reduction does not go on indefinitely, and there exists a minimum value. Within the range of 0° to 60°, the FPZ length decreases linearly with increasing stratification angle. Full article
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26 pages, 6267 KiB  
Review
A Review of the Hydraulic Fracturing in Ductile Reservoirs: Theory, Simulation, and Experiment
by Dawei Zhu, Guofeng Han, Honglan Zou, Mingyue Cui, Chong Liang and Fei Yao
Processes 2022, 10(10), 2022; https://doi.org/10.3390/pr10102022 - 7 Oct 2022
Cited by 9 | Viewed by 3743
Abstract
The bottom-hole pressure of hydraulic fracturing in ductile reservoirs is much higher than that of the hydraulic fracturing simulation, and the fracture toughness inferred from the field data is 1–3 orders of magnitude higher than that measured in the laboratory. The rock apparent [...] Read more.
The bottom-hole pressure of hydraulic fracturing in ductile reservoirs is much higher than that of the hydraulic fracturing simulation, and the fracture toughness inferred from the field data is 1–3 orders of magnitude higher than that measured in the laboratory. The rock apparent fracture toughness increases with the increase in the confining pressure. Excluding the influence of the fluid viscosity and the fluid lag on the apparent fracture toughness, the fracture process zone (FPZ) at the fracture tip can explain the orders of magnitude of difference in the apparent fracture toughness between the laboratory and the field. The fracture tip is passivated by plastic deformation, forming a wide and short hydraulic fracture. However, the size of the FPZ obtained in the laboratory is in the order of centimeters to decimeters, while an FPZ of 10 m magnitude is speculated in the field. The FPZ size is affected by the rock property, grain size, pore fluid, temperature, loading rate, and loading configuration. It is found that the FPZ has a size effect that tends to disappear when the rock specimen size reaches the scale of meters. However, this cannot fully explain the experience of hydraulic fracturing practice. The hydraulic fracturing behavior is also affected by the relation between the fracture toughness and the fracture length. The fracture behavior of type II and mixed type for the ductile rock is poorly understood. At present, the apparent fracture toughness model and the cohesive zone model (CZM) are the most suitable criteria for the fracture propagation in ductile reservoirs, but they cannot fully characterize the influence of the rock plastic deformation on the hydraulic fracturing. The elastic-plastic constitutive model needs to be used to characterize the stress–strain behavior in the hydraulic fracturing simulation, and the fracture propagation criteria suitable for ductile reservoirs also need to be developed. Full article
(This article belongs to the Special Issue Advances in Numerical Modeling for Deep Water Geo-Environment)
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25 pages, 7165 KiB  
Article
Experimental Study on the Effect of Bedding on the Fracture Process Zone of Shale
by Tiewu Tang, Xiaoshan Shi, Xiaojing Zhu and Liyun Li
Energies 2022, 15(17), 6359; https://doi.org/10.3390/en15176359 - 31 Aug 2022
Cited by 4 | Viewed by 1685
Abstract
The conventional fracture in shale hydraulic fracturing belongs to the type-I fracture, and the size of the fracture process zone (FPZ) is an important index to measure the fracability of rock mass. This index is also one of the feasible entry points to [...] Read more.
The conventional fracture in shale hydraulic fracturing belongs to the type-I fracture, and the size of the fracture process zone (FPZ) is an important index to measure the fracability of rock mass. This index is also one of the feasible entry points to study the complexity of the fracture network. In order to visually observe the type-I FPZ at the tip of shale fractures, and to study the relationship between the mechanical properties, the shape and size of the FPZ, and the bedding structure, Notched Semi-Circular Bend (NSCB) tests were conducted with three typical fracture direction-bedding orientations (splitter, arrester, divider). The digital image correlation (DIC) method was used to realize the intuitive observation of the real fracture process and the FPZ near the fracture tip. The test found that the FPZ of shale is narrow and long as a whole and is “flame-like”. The height-to-length ratio of the FPZ at the fracture tip determines whether bending and deflection happen between the new fracture and the prefabricated cracks when the fracture occurs. Most of the specimens often appear in the FPZ with a beaded high shear strain zone before the fracture, which is caused by the oblique communication of micro-cracks in the FPZ before the fracture. The appearance of a beaded zone of high shear strain indicates that macroscopic fracture is imminent. The research results can be used for the design of disaster early warning and prevention programs. Full article
(This article belongs to the Special Issue Fracture Mechanics and Energy Geo-Structures)
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24 pages, 10679 KiB  
Article
Fracture Behavior and Digital Image Analysis of GFRP Reinforced Concrete Notched Beams
by Mohammod Minhajur Rahman, Xudong Zhao, Tommaso D’Antino, Francesco Focacci and Christian Carloni
Materials 2022, 15(17), 5981; https://doi.org/10.3390/ma15175981 - 30 Aug 2022
Cited by 7 | Viewed by 2292
Abstract
This study presents three-point bending fracture tests on glass fiber-reinforced polymer (GFRP) reinforced concrete notched beams. Few studies have been conducted to date to understand the fracture behavior of this type of specimens. The specimens have nominal depth, width, and length equal to [...] Read more.
This study presents three-point bending fracture tests on glass fiber-reinforced polymer (GFRP) reinforced concrete notched beams. Few studies have been conducted to date to understand the fracture behavior of this type of specimens. The specimens have nominal depth, width, and length equal to 150 mm, 150 mm, and 550 mm. Plain concrete notched beams with the same dimensions are cast from the same batch of concrete to compare the responses with GFRP reinforced concrete notched beams. The notch of the plain concrete specimens is either saw cut or cast. These two notch fabrication methods are compared based on the load responses. The peak load, crack mouth opening displacement (CMOD), GFRP bar slip at two ends, and load point displacement are used to discuss the results of the fracture tests. In addition, digital image analysis is performed to identify the fracture process zone (FPZ) and the location of the neutral axis, which are used to determine the force in the GFRP bar via cross-sectional analysis. Finally, the GFRP bar force versus slip responses are compared with those from the pull-out tests performed on the same bar to show that the bond of the bar in the pull-out tests represents an upper bound limit compared to the behavior in bending. Full article
(This article belongs to the Special Issue Bond Behavior of Externally Bonded and Internal Reinforcement)
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20 pages, 7585 KiB  
Article
A Numerical Method for Applying Cohesive Stress on Fracture Process Zone in Concrete Using Nonlinear Spring Element
by Zhuheng Li
Materials 2022, 15(3), 1251; https://doi.org/10.3390/ma15031251 - 8 Feb 2022
Cited by 9 | Viewed by 2291
Abstract
Aiming at the numerical simulation of the entire crack propagation process in concrete, a numerical method is proposed, in which cohesive stress on the fracture process zone (FPZ) is simulated and applied by a nonlinear spring element. Using displacement control, the cohesive stress [...] Read more.
Aiming at the numerical simulation of the entire crack propagation process in concrete, a numerical method is proposed, in which cohesive stress on the fracture process zone (FPZ) is simulated and applied by a nonlinear spring element. Using displacement control, the cohesive stress values on the FPZ are obtained from solving a system of nonlinear equations through an iterative process. According to a crack propagation criterion based on initial fracture toughness, the approach adds the spring elements to finite element analysis when simulating mode I crack propagation in standard three-point bending notched concrete beams with different strengths, initial crack ratios (a0/D), and depths (D). The simulated load versus displacement (P-Delta) curves are performed to recalculate the fracture energy and verify the accuracy of cohesion in the proposed method. The simulated load versus crack mouth opening displacement (P-CMOD) curves are consistent with the previous experimental results. Subsequently, the variations of the FPZ length and the crack extension resistance (KR) curves are studied according to the proposed iterative approach. Compared with the existing methods using a noniterative process, the iterative approach generates a larger maximum FPZ length and KR curve where the FPZ length is mainly determined by the fracture energy, tensile strength, and geometry shape of the beam, and the KR curve is primarily determined by the fracture energy and FPZ length. The significant differences in numerical results indicate that the applying cohesion is essential in numerical simulation. It is reasonable to conclude that the proposed nonlinear spring element is more applicable and practical in the numerical simulation of the concrete mode I crack propagation process by improving the accuracy of the cohesion applied on the FPZ. Full article
(This article belongs to the Special Issue Material Science in Transportation and Construction Engineering)
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14 pages, 5247 KiB  
Article
Determining the Fracture Process Zone Length and Mode I Stress Intensity Factor in Concrete Structures via Mechanoluminescent Technology
by Seong-Kyum Kim, Ho Geun Shin, Suman Timilsina and Ji Sik Kim
Sensors 2020, 20(5), 1257; https://doi.org/10.3390/s20051257 - 25 Feb 2020
Cited by 9 | Viewed by 4229
Abstract
The mechanoluminescent (ML) technology that is being developed as a new and substitutive technology for structural health monitoring systems (SHMS) comprises stress/strain sensing micro-/nanoparticles embedded in a suitable binder, digital imaging system, and digital image processing techniques. The potential of ML technology to [...] Read more.
The mechanoluminescent (ML) technology that is being developed as a new and substitutive technology for structural health monitoring systems (SHMS) comprises stress/strain sensing micro-/nanoparticles embedded in a suitable binder, digital imaging system, and digital image processing techniques. The potential of ML technology to reveal the fracture process zone (FPZ) that is commonly found in structural materials like concrete and to calculate the stress intensity factor (SIF) of concrete, which are crucial for SHMS, has never been done before. Therefore, the potential of ML technology to measure the length of the FPZ and to calculate the SIF has been demonstrated in this work by considering a single-edge notched bend (SENB) test of the concrete structures. The image segmentation approach based on the histogram of an ML image as well the skeletonization of an ML image have been introduced in this work to facilitate the measurement of the length of ML pattern, crack, and FPZ. The results show ML technology has the potential to determine fracture toughness, to visualize FPZ and cracks, and to measure their lengths in structural material like concrete, which makes it applicable to structural health monitoring systems (SHMS) to characterize the structural integrity of structures. Full article
(This article belongs to the Special Issue Smart Structures and Materials for Sensor Applications)
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13 pages, 6273 KiB  
Technical Note
Crack Propagation and Fracture Process Zone (FPZ) of Wood in the Longitudinal Direction Determined Using Digital Image Correlation (DIC) Technique
by Ying Yu, Weihang Zeng, Wen Liu, He Zhang and Xiaohong Wang
Remote Sens. 2019, 11(13), 1562; https://doi.org/10.3390/rs11131562 - 2 Jul 2019
Cited by 35 | Viewed by 5176
Abstract
As a state-of-the-art method, the digital image correlation (DIC) technique is used to capture the fracture properties of wood along the longitudinal direction, such as the crack propagation, the strain field, and the fracture process zone (FPZ). Single-edge notched (SEN) specimens made of [...] Read more.
As a state-of-the-art method, the digital image correlation (DIC) technique is used to capture the fracture properties of wood along the longitudinal direction, such as the crack propagation, the strain field, and the fracture process zone (FPZ). Single-edge notched (SEN) specimens made of Douglas fir (Pseudotsuga menziesii) from Canada with different notch-to-depth ratios are tested by three-point-bending (3-p-b) experiment. The crack mouth opening displacements (CMOD) measured by the clip gauge and DIC technique agree well with each other, verifying the applicability of the DIC technique. Then, the quasi-brittle fracture process of wood is analyzed by combing the load-CMOD curve and the strain field in front of the preformed crack. Additionally, the equivalent elastic crack length is calculated using the linear superposition hypothesis. The comparison between the FPZ evolution and the equivalent elastic crack shows that specimens with higher notch-to-depth ratios have better cohesive effect and higher cracking resistance. Full article
(This article belongs to the Special Issue Vision-Based Sensing in Engineering Structures)
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12 pages, 4350 KiB  
Article
Experimental Study on the Fracture Process Zone Characteristics in Concrete Utilizing DIC and AE Methods
by Shuhong Dai, Xiaoli Liu and Kumar Nawnit
Appl. Sci. 2019, 9(7), 1346; https://doi.org/10.3390/app9071346 - 30 Mar 2019
Cited by 56 | Viewed by 5111
Abstract
The present work focuses on investigating the characteristics of the fracture process zone (FPZ) in concrete. The Single-edge notched (SEN) concrete beams under three-points bending are employed for conducting mode I fracture propagation. The displacement fields on the specimen surface and the internal [...] Read more.
The present work focuses on investigating the characteristics of the fracture process zone (FPZ) in concrete. The Single-edge notched (SEN) concrete beams under three-points bending are employed for conducting mode I fracture propagation. The displacement fields on the specimen surface and the internal AE signal of specimen are obtained simultaneously in real time by digital image correlation (DIC) and acoustic emission (AE) techniques. The experimental and analytical results indicated that the crack tip position, the crack extension length and the stress intensity factors (SIF) are obtained dynamically and quantitatively by DIC technique, and the length of FPZ is identified, respectively, by DIC and AE techniques in the crack extension process. The distribution of internal AE events is consistent with that of FPZ identified from surface deformation of specimens. Full article
(This article belongs to the Special Issue Advances in Digital Image Correlation (DIC))
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14 pages, 5984 KiB  
Article
Influence of Water–Oil Saturation on the Fracture Process Zone: A Modified Dugdale–Barenblatt Model
by Yuanxun Nie, Guangqing Zhang, Yuekun Xing and Shiyuan Li
Energies 2018, 11(11), 2882; https://doi.org/10.3390/en11112882 - 24 Oct 2018
Cited by 14 | Viewed by 2902
Abstract
The wetting and nonwetting fluid saturations in porous reservoirs always change during long-term injection and production. The fracture process zone (FPZ) is a prominent feature in the rock fracture process. If the FPZ properties are influenced by pore fluids, the process of hydraulic [...] Read more.
The wetting and nonwetting fluid saturations in porous reservoirs always change during long-term injection and production. The fracture process zone (FPZ) is a prominent feature in the rock fracture process. If the FPZ properties are influenced by pore fluids, the process of hydraulic fracturing will change greatly. The existing models do not consider the role of pore fluid when characterizing the FPZ. In this paper, a modified Dugdale–Barenblatt (D–B) model with capillary pressure is proposed. The model reflects the fact that the FPZ length decreases nonlinearly with the increase in capillary pressure, and it reveals the mechanism of capillary pressure on the equivalent fracture cohesion in the FPZ, which affects the FPZ length. Three-point bending tests were carried out on sandstone under various fluid saturations through digital image correlation (DIC), acoustic emission (AE), and scanning electron microscope (SEM). It was found that the FPZ length of the water–oil-saturated samples was 30–50% smaller than that of water-saturated/oil-saturated samples due to the capillary pressure effect, and the modified D–B model was well consistent with the experiments. The AE behaviors of different saturated samples were not the same: The cumulative AE signals changed abruptly at 90% of the peak load for the water–oil-saturated samples and at 50% of the peak load for water-saturated samples. This demonstrated that the effect of capillary pressure was more obvious than the weakening effect of microstructural damages. The significant influence of capillary pressure on FPZ requires continuous recognition in hydraulic fracturing design. Full article
(This article belongs to the Section L: Energy Sources)
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