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Model development activities are increasing in pavement research and engineering applications. At the same time, there is ambiguity and a lack of consistency with regard to checking and quantifying credibility and suitability for the intended application. Specifically, usage of the terms Verification and Validation (V&V) is seen to vary across contributions. In this context, this paper was motivated by the desire to provide a best-practice reference that underlines the significance of the V&V terms, clarifies their definition, and promotes a more unified usage. Accordingly, the objective was to offer examples that introduce the V&V jargon, demonstrate basic V&V concepts and processes, and highlight certain fine points. A total of five distinct models were introduced and discussed: (1) load-related responses in asphalt pavements, (2) load-related responses in concrete pavements, (3) crack initiation and propagation in asphalt concrete, (4) linear viscoelasticity of asphalt concrete, and (5) water flow through asphalt concrete pores. A general conclusion from this work is that successful V&V efforts are closely linked to a clear definition of the intended usage, i.e., the specific reality of interest being targeted by the model. It is also concluded that documenting V&V efforts is integral to any computational model development. Doing so communicates to potential users the region of confidence for the model alongside the expected differences with the reality of interest. [ABSTRACT FROM AUTHOR]

Research on single faults like tooth root cracks and bearing outer ring failures is well-established. However, existing studies often replace the actual crack propagation path with a simplified linear crack model, neglecting the variation in stress intensity factors. They do not account for the coupling effect between gear teeth when calculating gear mesh stiffness. In practice, gearbox failures are predominantly compound failures involving both gears and bearings. This paper simulates the actual crack propagation path based on Workbench, introduces a dual-tooth meshing zone method to address the tooth-to-tooth coupling effect, and establishes a dynamic model of a system with compound faults of tooth root cracks and bearing outer ring defects. The dynamic response of the system under different levels of deterioration is then investigated. The findings indicate that the crack propagation path exhibits a concave shape, with the curvature of the path increasing as the crack deteriorates. The time-varying mesh stiffness calculated by considering tooth-to-tooth coupling effects aligns more closely with the finite element results. By analyzing the evolution patterns of the impact components and sidebands during the deterioration process, the dynamic evolution trends of the coupling phenomenon between tooth root cracks and bearing outer ring faults are clarified. [ABSTRACT FROM AUTHOR]

A reasonable crack driving force is the key to preventing compression cracks and eliminating unrealistic crack propagation in phase field fracture analysis. Thus, examining the roles of volumetric strain energy (VSE) and deviatoric strain energy (DSE) in influencing crack propagation is necessary. This paper presents a comprehensive analysis of the following four different approaches to energy decomposition‐driven crack propagation: the positive volumetric strain energy method (VSEM), deviatoric strain energy method (DSEM), volumetric‐deviatoric strain energy method (VDSEM), and no decomposition method (NM). All of the strain energy is involved in the development of the crack propagation. The following four examples are investigated: two benchmark single‐side notched examples, a complex crack containing a hole example, and a crack coalescence in an asymmetric double notch example. The VSEM's numerical findings align with literature and experimental observations, confirming that positive VSE rather than DSE promotes crack propagation. Highlights: 1)This paper suggests a strategy for phase field fracture with positive volumetric strain energy driven crack growth.2)The experimental results are in excellent agreement with the numerical results of the current model.3)The model is to be traced back to the minimum strain energy density criterion.4)The model helps capture and understand the fracture features of brittle materials. [ABSTRACT FROM AUTHOR]

The high-cycle bending fatigue experiment is one of the most important necessary steps in guiding the crankshaft manufacturing process, especially for high-power engines. In this paper, an accelerated method was proposed to shorten the time period of this experiment. First, the loading period was quickened through the prediction of the residual fatigue life based on the unscented Kalman filtering algorithm approach and the crack growth speed. Then, the accuracy of the predictions was improved obviously based on the modified training section based on the theory of fracture mechanics. Finally, the fatigue limit load analysis result was proposed based on the predicted fatigue life and the modified SAFL (statistical analysis for the fatigue limit) method. The main conclusion proposed from this paper is that compared with the conventional training sections, the modified training sections based on the theory of fracture mechanics can obviously improve the accuracy of the remaining fatigue life prediction results, which makes this approach more suitable for the application. In addition, compared with the system's inherent natural frequency, the fatigue crack can save the experiment time more effectively and thus is superior to the former factor as the failure criterion parameter. [ABSTRACT FROM AUTHOR]

The mechanical properties of fractured rock have always been a focal point in the rock mechanics field. Based on previous research, this paper proposes improvements to the SPH method and applies it to the study of crack propagation in fractured rocks. By conducting uniaxial compression tests and simulating crack propagation on various specimens with different crack shapes, the characteristics of crack propagation were obtained. The comparison between the simulated results in this study and existing experimental and numerical simulation results confirms the validity of the SPH method employed in this paper. The present study utilizes the proposed methodology to analyze the influence of the crack angle, width, and orientation on crack propagation. The SPH method employed in this study effectively demonstrates the expansion process of fractured rock under uniaxial compression, providing valuable insights for the engineering applications of SPH. [ABSTRACT FROM AUTHOR]

The joints and fissures in a natural rock mass can affect the mechanical properties of the rock mass, the propagation of a blasting stress wave, and the blasting effect of the smooth surface of roadways. In the process of roadway drilling and blasting, there will inevitably be some joints between the two blast holes. Taking the joint angle as the starting point, this paper studies the rule of rock explosion crack propagation and stress variation when there are joints with different angles between two blast holes and analyzes the influence of joints on rock mechanical properties and blasting effects. The numerical simulation method and the software ANSYS/LS-DYNA are used to establish 7 rock mass models with various joint angles. When there is no joint between two holes and joints of 15°, 30°, 45°, 60°, 75°, and 90°, the propagation of explosive cracks and stress variations in the rock mass are discussed. The results show that the joints at different angles have obvious guiding and blocking effects on the propagation of explosive cracks, and as joint angles increase, the guiding effect becomes more apparent and the blocking effect becomes weaker. The effective stress of the rock mass will vary depending on the angles of the joints between the hole and the joint. As the joint angle increases, the joint's influence on the reflection and superposition of stress waves gradually weakens, and the peak value of the effective stress of the rock mass gradually decreases. The peak effective stress of the rock mass on the blasting side of the joint is similarly impacted by the superposition of stress waves, and the extreme value may be seen at the critical node of each change curve. The explosive crack will break through at the critical location because the maximal effective stress of the rock mass is distributed in a "W" form on the blasting side of the joint. [ABSTRACT FROM AUTHOR]

This paper introduces the development of a dynamic seepage network method (DSN) within a two-dimensional discontinuous deformation analysis (2D-DDA) framework. The primary goal is to identify actual fractures and seepage spaces, establish a seepage network, and automatically compute hydraulic water pressure within blocky systems. In addition, a new coupled dynamic hydromechanical model (DDA–DSN) is proposed to investigate seepage behavior in time-varying fractured rock masses. The DSN method tracks fracture propagation between blocks during seepage flow, while the DDA component characterizes the translation, rotation, and deformation of arbitrarily formed blocks. The paper covers fundamental theories, the determination of neighboring non-contact block pairs, the creation of seepage networks, hydraulic pressure calculations, and the integration of DDA and DSN in detail. Furthermore, the validity of the coupled DDA–DSN hydromechanical model is confirmed by comparing numerical results with experimental measurements. These results highlight the model's effectiveness in capturing fluid flow behavior within fractured rock masses, emphasizing the exceptional capabilities of DSN in identifying seepage spaces, constructing seepage networks, and automatically computing hydraulic pressure. Overall, this proposed model holds significant promise for addressing engineering challenges related to seepage flow behavior inner the rock masses. Highlights: Developed a new algorithm for identifying the real fractures, forming the seepage pathways, and calculating the hydraulic water pressure on blocks automatically in 2D-DDA. Proposed a new coupled DDA–DSN model to investigate the seepage behavior in time-varying fractured rock mass systems. Checked validity of the DDA–DSN model by contrasting several numerical findings with experimental measurements. [ABSTRACT FROM AUTHOR]

Shale gas is an important supplement to the supply of natural gas resources and plays an important role on the world's energy stage. The efficient implementation of hydraulic fracturing is the key issue in the exploration and exploitation of shale gas. The existence of bedding structure results in a distinct anisotropy of shale rock formation. The anisotropic behaviors of shale rock have important impacts on wellbore stability, hydraulic fracture propagation, and the formation of complex fracture networks. This paper briefly reviews previous work on the anisotropic mechanical properties of shale rock and their relation to hydraulic fracturing in shale reservoirs. In this paper, the research status of work addressing the lithological characteristics of shale rock is summarized first, particularly work considering the mineral constituent, which determines its physical and mechanical behavior in essence. Then the anisotropic physical and mechanical properties of shale specimens, including ultrasonic anisotropy, mechanical behavior under uniaxial and triaxial compression tests, and tensile property under the Brazilian test, are summarized, and the state of the literature on fracture toughness anisotropy is discussed. The concerns of anisotropic mechanical behavior under laboratory tests are emphasized in this paper, particularly the evaluation of shale brittleness based on mechanical characteristics, which is discussed in detail. Finally, further concerns such as the effects of bedding plane on hydraulic fracturing failure strength, crack propagation, and failure pattern are also drawn out. This review study will provide a better understanding of current research findings on the anisotropic mechanical properties of shale rock, which can provide insight into the shale anisotropy related to the fracture propagation of hydraulic fracturing in shale reservoirs. [ABSTRACT FROM AUTHOR]

The microscopic parameters in the numerical method have an important influence on the results and computational efficiency of the models. The existing calibration methods of microscopic parameters in the finite-discrete element method (FDEM) are based on two-dimensional (2D) FDEM model, and there is a lack of calibration methods for microscopic parameters suitable for three-dimensional (3D) FDEM model. Therefore, this paper proposes a fast and convenient calibration method for the microscopic parameters of the 3D FDEM model. First, a tangential contact force calculation algorithm based on the total normal force is proposed and verified by the slider model. Subsequently, assuming that the penalty parameter of the solid element is equal to the penalty parameter of the joint element, the relationship between the normal penalty parameter and the tangential penalty parameter, and the relationship between the normal penalty parameter and the Young's modulus are studied using several numerical models. Moreover, the tensile strength and crack propagation path of the Brazilian disc model under different fracture energy parameter combinations are studied, and the fracture energy parameters are calibrated. Then, the triaxial compression model under different confining pressures is used to calibrate the cohesion c and the internal friction angle φ. In addition, the effects of loading rate, mesh size and time step on the model strength and calculation time are considered, respectively. Finally, the numerical simulation of dynamic Brazilian splitting test is carried out to verify the reliability of the parameter calibration method proposed in this paper. Although the calibration method of microscopic parameters is not unique, the microscopic parameter calibration method has important reference significance and is conducive to the application of 3D FDEM model. Highlights: A tangential contact force calculation algorithm based on the total normal contact force is proposed and verified by the slider model. The tangential penalty parameter in the 3D FDEM model needs to be greater than the normal penalty parameter, and the threshold of the normal penalty parameter is 50 times Young 's modulus. The tensile strength of the Brazilian disc model always begins to converge when the fracture energy GII is equal to 10GI, and the crack propagation path is along the central diameter direction. [ABSTRACT FROM AUTHOR]

A novel procedure has emerged in recent years within oilfields - namely, the utilization of a hybrid fracturing method employing pre-CO2 injection along with sand-carry slick water. In this paper, based on the real logging data of shale oil reservoirs in the second member of Cangdong Sag, Huanghua Depression, combined with the GOHFER, a coupled 3-D hydraulic fracture propagation model is proposed. This research delves into an examination of how engineering factors exert their influence on the process of fracture propagation. The quantitative analysis is conducted encompassing critical fracture parameters such as half-length, height, and width, and self-defined fracture seepage area and fracture front fractal dimension. The research findings indicate that as injection displacement increases, the fracture shape undergoes a transformation from being "long, low, and wide" to becoming "short, high, and narrow". [ABSTRACT FROM AUTHOR]

This paper proposed three new fracturing methods, slick water with an integrated variable viscosity fracturing, supercritical CO2 shock fracturing and pulse hydraulic fracturing. To verify the efficacy of the new methods, we conducted laboratory true-triaxial fracturing experiments by using outcrops collected from the Lower Shihezi formation, Ordos Basin. The results indicate that supercritical CO2 shock fracturing is observed to have the lowest breakdown pressure compared with other methods. [ABSTRACT FROM AUTHOR]

Tight sandstone has a tight structure and low natural production capacity, usually requiring the use of fracturing technology to achieve industrial production. Supercritical CO2 fracturing has attracted much attention due to its clean and efficient properties. In this paper, using the principles of damage mechanics, the crack propagation law during supercritical CO2 fracturing was studied by using numerical methods. The influence of different factors on the fracture propagation patterns is analyzed. Results indicate that supercritical CO2 fracturing can form complex fracture distribution patterns. This mode is divided into three different stages: slow fracture propagation, rapid fracture propagation, and rigid fracture propagation. In addition, highly heterogeneous formations generate more secondary fractures but limit their expansion. [ABSTRACT FROM AUTHOR]

This paper shows a new low-cost technology for the measurement of crack propagation in quasi-fragile materials based on a stereo pair of cameras and LED light spots. The two cameras record the displacement experienced by a series of LED white lights. For each frame, the X, Y and Z 3D coordinates of all the centroids of the LED points are obtained. From this information, it is possible to determine the variation of the distance between any two of them. In this case, 2 strips of 12 LED lights each were arranged in such a way that the points of both strips coincided in pairs in height. The algorithm made it possible to monitor the increase in distance that occurred between each pair of lights at the same height. The paper shows the mathematical basis of this technological solution. A test has been carried out by installing this system in a concrete cube 150 mm side and subjected to a wedge-splitting test. The results show that it is possible to monitor the crack propagation (position of the crack front) during the test and to know the crack width too. At present, the accuracy of this technique is only limited by the camera resolution and the computer processing capability. [ABSTRACT FROM AUTHOR]

Mixed mode fracture is a widely studied topic, while the coupling effects of mixed mode cracking are unclear. In this paper, elastic fracture behaviors and the coupling effects of the mixed mode cracks are studied in detail based on the finite element method, experimental study and linear elastic fracture mechanics. Results show that there always exist II-III coupling effects at the crack tips of mixed mode cracks, which have many effects on the crack tip field and crack propagation behavior. It is found that a mode II component at the tip of a mixed mode crack is the main reason for crack deflection, while the mode III components show no effect. For any mixed mode crack, mode II components at the crack tip can be divided as that by mode II loading which causes plane crack propagation, and by the coupling effect which causes spatial crack propagation. On this basis, a new fracture criterion suitable for any mixed mode crack is proposed, combined with the coupling effect and the linear elastic superposition principle. The research in this paper provides a solution to the problem of an II-III coupling effect in mixed mode fracture research and further promotes the development of fracture mechanics. [ABSTRACT FROM AUTHOR]

With the development of economy, conventional oil and gas resources can no longer meet people's needs. Looking for additional oil resources has become one of the problems that must be solved at present. In recent years, the maturity of oil shale in-situ mining technology has made oil shale come into people's view again after two centuries. Oil shale is rich in reserves and has broad prospects for development, but the efficiency of oil shale in-situ mining is not high at present. Therefore, it is necessary to carry out hydraulic fracturing and fracture making transformation to increase the overheated area of oil shale. This can increase oil and gas transmission channels and solve the problem of low heating efficiency. Hydraulic fracturing fracturing treatment of oil shale to achieve short-term production increase is of great significance to ease the contradiction between energy supply and demand and promote healthy economic development. In this paper, ABAQUS software is used to study the initiation and propagation of water fracturing fractures in horizontal wells of oil shale. The main research contents and results are as follows: Analyze the fracture initiation and propagation of oil shale horizontal wells. Based on the two-dimensional fracture model of oil shale horizontal wells, the simulation of complex fracture network formed by the intersection of hydraulic fractures and natural fractures is carried out by embedding Cohesive. It is concluded that the distribution of the width of the complex seam mesh is very different. It is in the shape of "wide in the middle and narrow around". The seam length increases in a "ladder" way. This paper mainly studies the initiation and propagation of hydraulic fracturing fractures in horizontal wells of oil shale through theoretical analysis and numerical simulation. It is hoped that it can provide some reference for oil shale in-situ mining in the future. [ABSTRACT FROM AUTHOR]

Soil–rock mixture is a common geo-material found in natural deposit slopes and various constructions, such as tunnels, hydropower stations, and subgrades. The complex mechanical characteristics of soil–rock mixture arise from its multi-phase compositions and cooperative interactions. This paper investigated the mechanical properties of soil–rock mixture, focusing on the influence of rock content, and soil–rock interface strength was discussed. Specimens with varying rock contents were subjected to uniaxial compression tests. The results indicated that rock content, as a key structural parameter, significantly controls the crack propagation trends. As rock content increases, the initial structure of the soil matrix is damaged, leading to the formation of a weak-strength soil–rock interface. The failure mode transitions from longitudinal cracking to multiple shear fractures. To analyze the strength of the soil–rock interface from a mesoscopic perspective, simulations of soil–rock mixture specimens with irregular rock blocks were conducted using the particle discrete element method (PDEM). At the meso-scale, the specimen with 30% rock content exhibited a complex particle displacement distribution, with differences in the direction and magnitude of displacement between soil and rock particles being critical to the failure modes of the specimen. As the soil–rock interface strength increased from 0.1 to 0.9, the distribution of force chains within the specimen shifted from a centralized to a more uniform distribution, and the thickness of force chains became increasingly uniform. The strength responses of the soil–rock mixture under uniaxial compression condition were discussed, revealing that the uniaxial compression strength (UCS) of soil–rock mixture decreases exponentially with increasing rock content. An estimation formula was developed to characterize the UCS of soil–rock mixture in relation to rock content and interface strength. The findings from both the experiments and simulations can provide valuable insights for evaluating the stability of deposit slopes and other constructions involving soil–rock mixture. [ABSTRACT FROM AUTHOR]

Numerical modeling of hydraulic fracturing is complicated when a fracture reaches a stress barrier. For high barriers, it may require changing the computational scheme. In view of the strong influence of stress barriers on the final footprint and opening of a hydraulic fracture, for decades, their modeling has been the subject of special investigations. Actually, classical models of propagation within a pay layer with impenetrable boundaries referred to the case of extremely high-stress contrast in neighbor layers. Further improvements tended to account for the fracture growth in these layers by including stress contrasts as input parameters of a model. This tendency resulted in the suggestion and successive enhancements of pseudo-three-dimensional models. All of them have used stress intensity factors (SIFs) to characterize the combined resistance caused by stress contrasts, material strength, and fluid viscosity. Specifically, the SIFs served to formulate the conditions that control the front penetration into a neighbor layer. This key concept presents the background of our research. Despite examples of modeling propagation through barriers, there is no general theory clarifying when and why conventional schemes may become inefficient and how to overcome computational difficulties. This paper presents the theory and practical recommendations following it. We start with the definition of the barrier intensity, which exposes that the barrier strength may change from zero for contrast-free propagation to infinity for channelized propagation. The analysis reveals two types of computational difficulties caused by spatial discretization as follows: (i) general, arising for fine grids and aggravated by a barrier, and (ii) specific, caused entirely by a strong barrier. The asymptotic approach, which avoids spatial discretization, is suggested. It is illustrated by solving benchmark problems for barriers of arbitrary intensity. The analysis distinguishes three typical stages of the fracture penetration into a barrier and provides theoretical values of the Nolte–Smith slope parameter and arrest time as functions of the barrier intensity. Special analysis establishes the accuracy and bounds of the asymptotic approach. It appears that the approach provides physically significant and accurate results for fracture penetration into high, intermediate, and even weak stress barriers. On this basis, simple practical recommendations are given for modeling hydraulic fractures in rocks with stress barriers. The recommendations may be promptly implemented in any program using spatial discretization to model fracture propagation. [ABSTRACT FROM AUTHOR]

The establishment of a more realistic CO2 fracturing model serves to elucidate the intricate mechanisms underlying CO2 fracturing transformation. Additionally, it furnishes a foundational framework for devising comprehensive fracturing construction plans. However, current research has neglected to consider the influence of CO2 on rock properties during CO2 fracturing, resulting in an inability to precisely replicate the alterations in the reservoir post-CO2 injection into the formation. This disparity from the actual conditions poses a substantial limitation to the application and advancement of CO2 fracturing technology. This work integrates variations in the physical parameters of rocks after complete contact and reaction with CO2 into the numerical model of crack propagation. This comprehensive approach fully acknowledges the impact of pre-CO2 exposure on the mechanical parameters of reservoir rocks. Consequently, it authentically restores the reservoir state following CO2 injection, ensuring a more accurate representation of the post-fracturing conditions. In comparison with conventional numerical simulation methods, the approach outlined in this paper yields a reduction in the error associated with predicting fracturing pressure by 9.8%. [ABSTRACT FROM AUTHOR]

Hydraulic fracturing is the predominant technology for the development of unconventional resources, and understanding multi-fracture propagation behavior is the foundation for hydraulic fracturing optimization. To deeply understand multi-fracture propagation behavior in natural formations, this paper proposes a numerical simulation which considers the fluid-solid coupling process based on the displacement discontinuity method and the finite volume method. The simulation indicates that high stress difference and low approach angle are the main factors limiting the stimulated volume, while low stress difference and high approach angle are beneficial for creating modification zones. In addition, the natural fracture density also has a great effect on fracture propagation. With increasing natural fracture density, the stimulated volume also increases greatly, which plays a significant role in enhancing the SRA. These findings are critical in comprehending the impact of geological parameters on deep fractured shale reservoirs. [ABSTRACT FROM AUTHOR]

Hydraulic fracturing technology is vital for the efficient extraction of oil and gas from low-permeability tight sandstone reservoirs.Taking the central Bohai oilfield in China as an example, these fields are typically composed of thinly interbedded tight sandstone, characterized by low permeability and significant lithological heterogeneity between layers. Fractures may either be confined, limiting vertical growth and reducing production, or overextend into water-bearing zones, causing contamination and compromising reservoir integrity. Therefore, predicting vertical fracture propagation during field fracturing operations is critical for efficient resource extraction.However, there is still a lack of comprehensive understanding of the mechanisms governing vertical fracture growth offshore.This paper applies numerical simulations based on the finite element method to elucidate the interlayer fracture propagation behavior in low-permeability tight sandstone reservoirs. A fracture propagation model for thin interlayered tight sandstone formations is constructed, and the effects of various factors on hydraulic fracture propagation are systematically analyzed, including geological factors such as interlayer stress contrast, thickness, and differences in elastic modulus, as well as operational parameters including fracturing fluid viscosity and injection rate. This study clarifies the cross-layer propagation patterns of hydraulic fractures under the influence of multiple factors and yields a comprehensive prediction chart for fracture propagation thickness under the combination of complex factors. The results of this research can provide theoretical support for the design of reservoir stimulation operations in low-permeability tight sandstone oilfields. [ABSTRACT FROM AUTHOR]

The life of compressor impeller is very short under extreme working conditions, so it is necessary to explore the life extension method and mechanism. Since the crack initiation location cannot be accurately predicted in advance, the hole drilling strategy of prefabricated hole will determine the remaining life of impeller after cracks appear. This article presents a strategy of prefabricated hole to extend the fatigue crack propagation life (FCPL) of compressor impeller. The stress distribution of impeller during operation is simulated by finite element method, and the crack initiation location is determined. The Forman-Newman-de Koning model is used to investigate the effects of hole drilling strategy and rotational speed on FCPL, and the three-dimensional crack propagation process is simulated. In addition, this paper investigates the main phenomena and influencing mechanism for the extension of FCPL due to prefabricated hole. It is found that the prefabricated hole can attract the crack propagation path, and make the crack pass through the hole more easily. At this time, the crack propagation driving force will decrease sharply, and the crack propagation rate will decrease accordingly, thus extends the FCPL. Even if it cannot pass through the hole, the optimal hole drilling strategy can extend life by 104.23%. The life extension effect of prefabricated hole increases with the increase of speed. The design in this paper can reduce the economic cost to a great extent, and provides a new idea for the life extension problem of complex models. [ABSTRACT FROM AUTHOR]

High temperatures during a fire can lead to the evaporation of moisture and the degradation of hydration products within concrete, consequently compromising its mechanical properties. This paper thoroughly investigates the effect of fire-induced high temperatures on the residual load-bearing capacity of concrete structures, with a focus on prestressed concrete T-beams. By conducting constant temperature tests and residual load-bearing capacity tests, complemented by finite element modeling, this study examines the degradation of mechanical properties in prestressed concrete T-beams due to fire exposure and its impact on post-fire residual load-bearing capacity. Additionally, an equivalent concrete compressive strength method was employed to propose a calculation method for concrete material degradation under high temperatures and a corresponding concrete strength reduction factor. Simplified calculations were also performed for the high-temperature damage to reinforcement and prestressed tendons, leading to the derivation of a simplified formula for the residual load-bearing capacity of post-fire prestressed concrete T-beams. The results indicate that in prestressed concrete T-beams exposed to fire, an increase in holding time results in more severe damage modes, accelerated crack propagation, and wider crack widths during bending failure. Under the same load, a longer holding time corresponds to a more pronounced reduction in deflection. At holding times of 60 min, 120 min, and 180 min, the prestress losses were 48.17%, 85.16%, and 93.26%, respectively. The cracking load decreased by 15%, 27%, and 42%, while the residual load-bearing capacity decreased by 11%, 21%, and 28%. Comparison with experimental data demonstrates that both the finite element model and the simplified calculation formula exhibit high accuracy, offering a reliable reference for the performance evaluation of post-fire prestressed concrete T-beams. [ABSTRACT FROM AUTHOR]

[Objective] Unconventional oil and gas reservoirs are characterized by poor physical properties and complex stress conditions. Hydraulic fracturing is essential for improving the efficiency of exploring and developing these resources. Traditional indoor hydraulic fracturing experiments typically simulate crack propagation under a single stress state, failing to capture the crack morphology under the complex stresses of actual formations and natural fracture disturbances. [Methods] In this paper, a full-diameter core hydraulic fracturing ultrasonic testing device with independent axial stress loading has been developed. This experimental device includes multiple sets of independent pressure systems and acoustic emission data acquisition systems, allowing it to simulate various complex stress conditions found in real formations. It detects rock failure characteristics through acoustic emissions and records the response during fracture initiation and propagation in real time. Experiments focused on natural fracture stability and hydraulic fracturing under complex stress conditions were carried out on cores with natural frequencies at angles of 30°, 45°, and 60° using the instrument. Custom-designed rock samples were used to explore fracture propagation laws under varying conditions, offering a new method for simulating reservoir hydraulic fracturing effects under complex stress. [Results] The experimental results indicate the following: (1) The amplitude of acoustic emission signals is positively correlated with crack formation characteristics. A sudden increase in acoustic emission signals demonstrates the pressure point where cracks begin to destabilize; (2) Cores with 45° natural fractures exhibit the least stability. Fracture occurs at a pressure of 14.1 MPa, with prominent acoustic emission characteristics. By contrast, 30° and 60° natural fractures mainly result in shear and partial tensile fractures after instability; (3) Induced stress interference causes the fracture path to shift as hydraulic fractures approach. With increasing natural fracture angles, fracture offset becomes more obvious, leading to two major acoustic emission signal events. [Conclusions] The full-diameter core hydraulic fracturing ultrasonic detection device, equipped with independently controlled axial stress loading, addresses the challenges of predicting hydraulic fracturing effects under complex formation conditions. By combining artificial core samples with stress differential control, the device offers new insights into artificial fracture propagation mechanisms and acoustic emission fracture monitoring technologies. By utilizing artificial rock sample preparation, an axial stress loading system, a water pressure loading system, and an acoustic emission data acquisition system, it is possible to conduct fracture propagation experiments under various complex stress conditions. At the same time, according to the characteristics of the experimental device, the experimental design of other reservoir reconstruction challenges can be carried out. The device can also be upgraded and optimized. This setup effectively clarifies the hydraulic fracturing effects in actual reservoirs with complex stress, providing a foundation for reservoir stimulation strategies. [ABSTRACT FROM AUTHOR]

The mechanical and electrical deterioration of chromium (Cr) thin films sputtered onto polyethylene terephthalate (PET) substrates under tensile strain was studied. Understanding mechanical and electrical stability due to imposed strain is particularly important for device reliability, as the demand for flexible electronic devices increases. Cr thin films, widely spread across the field of electronic and sensor applications, face crack propagation with electrical degradation with tensile stress that can seriously compromise the performance. Accordingly, this study offers new findings on how Cr film thickness might influence crack formation and electrical resistance differently and also the general guidelines for flexible electronic component design with respect to long-term durability. Electrical resistances were measured while mechanically stretching 100- and 200 nm thin sheets. The study focused on crack development and propagation mechanisms in both film thicknesses and their effects on percentage change in electrical resistance (PCER). Scanning electronic microscopy (SEM) was used to characterize surface morphology and observe cracks as the strain rose. Early crack formation in 100 nm Cr films led to rapid PCER increases due to quick crack propagation and fast electrical degradation. Thicker 200 nm films, however, showed a more gradual PCER rise with fewer but deeper cracks, indicating a regulated strain response. Unlike the sharp PCER spike in 100 nm films, 200 nm samples were more variable, with three out of four showing a slight PCER decrease at the end, hinting at partial crack repair or conductive realignment before full failure. These results underscore the role of layer thickness in managing crack propagation and electrical stability, relevant for flexible electronics and strain sensors. This paper is aligned with the ninth goal of the United Nations Sustainable Development Goals, specifically Target 9.5: Enhance Research and Upgrade Industrial Technologies. [ABSTRACT FROM AUTHOR]

Numerical simulations play a key role in the optimization of fracturing operation designs for unconventional reservoirs. Because of the presence of numerous natural discontinuities and pores, the rock masses of reservoirs can be regarded as fractured porous media. In this paper, a fully coupled discontinuous deformation analysis model is newly developed to simulate the hydromechanical processes in fractured and porous media. The coupling of fracture seepage, pore seepage, and fracture network propagation is realized under the framework of DDA. The developed model is verified with several examples. Then, the developed DDA model is applied to simulate the hydraulic fracturing processes in fractured porous rock masses, and the effects of rock mass permeability on fracturing are investigated. Our findings suggest that high rock permeability may inhibit the stimulation of fracture networks, while increasing the viscosity of fracturing fluids can enhance the fracturing efficiency. This study provides a valuable numerical tool for simulating hydromechanical processes in fractured and porous media and can be used to analyze various geo-mechanical problems related to fluid interactions. [ABSTRACT FROM AUTHOR]

To address the environmental and formation damage caused by traditional hydraulic fracturing in coalbed methane and shale gas extraction, supercritical CO2 (SC-CO2) fracturing technology has emerged as an effective alternative due to its low viscosity, high diffusivity, and waterless nature. This paper reviews recent advancements in experiments and numerical simulations to explore the mechanisms of fracture initiation and propagation in this technology, with a focus on analyzing fracture initiation pressure, propagation patterns, and influencing factors. The findings show that SC-CO2 fracturing can generate complex fracture networks at lower initiation pressures, with stress conditions, temperature, and natural fractures significantly impacting fracture initiation and propagation. Additionally, the paper highlights existing limitations in accurately simulating CO2 flow, phase transitions, and its interactions with natural fractures, offering optimization suggestions and future perspectives. [ABSTRACT FROM AUTHOR]

This paper presents a detailed analytical approach for the bending analysis of reinforced concrete beams, integrating both structural mechanics principles and Eurocode 2 provisions. The general analytical expressions derived for the curvature were applied for the transverse displacement analysis of a simply supported reinforced concrete beam under four-point loading, focusing on key limit states: the initiation of cracking, the yielding of tensile reinforcement and the compressive failure of concrete. The displacement's results were validated through experimental testing, showing a high degree of accuracy in the elastic and crack propagation phases. Deviations in the yielding phase were attributed to the conservative material assumptions within the Eurocode 2 framework, though the analytical model remained reliable overall. To streamline the computational process for more complex structures, a simplified model utilising a non-linear rotational spring was further developed. This model effectively captures the influence of cracking with significantly reduced computational effort, making it suitable for serviceability limit state analyses in complex loading scenarios, such as seismic impacts. The results demonstrate that combining detailed analytical methods with this simplified model provides an efficient and practical solution for the analysis of reinforced concrete beams, balancing precision with computational efficiency. [ABSTRACT FROM AUTHOR]

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In order to prevent structural damage or high repair costs caused by concrete crack propagation, the use of microbial-induced CaCO3 precipitation to repair concrete cracks has been a hot topic in recent years. However, due to environmental constraints such as oxygen concentration, the width and depth of repaired cracks are seriously insufficient, which affects the further development of microbial self-healing agents. In this paper, a ternary microbial self-healing agent composed of different proportions of Bacillus pasteurii, Saccharomyces cerevisiae, and Bacillus mucilaginosus was designed, and its crack repair ability was evaluated. When the mixing ratio was 7:1:2, the cell concentration was the highest, the precipitation amount of CaCO3 was the highest, and the crystallinity of calcite crystal was the highest. Compared to the single microorganism, the mortar specimens with ternary microorganisms had the largest repair area (up to 100%) and the deepest repair depth (CaCO3 presents at 9–12 mm from the crack surface). This is because when the concrete breaks, all three microorganisms are activated by water, O2, and CO2. Saccharomyces cerevisiae and Bacillus mucilaginosus accelerated the growth of Bacillus pasteurii and more mineralized products; CaCO3 was rapidly formed and quickly filled on the crack surface. When CaCO3 seals the surface of the crack, the internal Saccharomyces cerevisiae and Bacillus mucilaginosus continue to play a role. Bacillus mucilaginosus can accelerate the dissolution of CO2 produced by the anaerobic fermentation of Saccharomyces cerevisiae and the hydrolysis of CO32−, thereby improving the repair of the crack depth direction. [ABSTRACT FROM AUTHOR]

In this paper, the influence of Cr element on the mechanical properties of welded joints of gas-shielded solid wire used in oil and gas long-distance pipelines was studied by means of tensile test, impact test, and hardness test, and the microstructure and crack propagation path of weld were characterized by means of an optical microscope, scanning electron microscope, and electron backscattering diffraction. The results show that with the addition of Cr, the strength and toughness of the weld are significantly improved, in which the tensile strength is increased from 607 MPa to 656 MPa, and the impact toughness is increased from 126.37 J to 223.79 J. The proportion of the ferrite side plate in the weld structure is reduced by about 20%, and the effective grain size of acicular ferrite is reduced by about 15%. The reason is that the addition of the Cr element improves the hardenability of the weld structure, inhibits the formation of the ferrite side plate, and promotes the effective refinement of acicular ferrite, which increases the proportion of high-angle grain boundaries in the weld, effectively hindering the crack propagation, improves the crack propagation work, and thus improves the strength and toughness of the weld. [ABSTRACT FROM AUTHOR]

This paper introduces a comprehensive computational framework, comprising a finite deformation crystal inelasticity constitutive model and phase field model, for modeling crack growth in superelastic nitinol polycrystalline microstructures. The crystal inelasticity model represents crystal stretching and lattice rotation from elastic mechanisms, as well as local inelastic deformation due to austenite-martensite phase transformation. The phase field formulation decomposes the Helmholtz free energy density into stored elastic energy, phase transformation energy, and crack surface energy components. The elastic energy accounts for tension-compression asymmetry with the formation of the crack through a spectral decomposition. Kinetic Monte Carlo simulations generate equilibrium area fractions of different surface orientations, which serve as weights for the surface energy. An adaptive wavelet-enhanced hierarchical finite element (FE) model is introduced to alleviate high computational overhead in phase field crack simulations. Simulations with the coupled inelasticity phase field model are conducted under various loading conditions including Mode-I tension, a quasi-static Kalthoff experiment, and cyclic loading of polycrystalline microstructures. Crack propagation is effectively predicted by this model, providing valuable insights into the material mechanical behavior with growing cracks. [ABSTRACT FROM AUTHOR]

At present, in the process of volume fracturing for a tight reservoir, employing the spiral perforation method to induce the fracture propagation direction would always obtain an unsatisfactory effect, which causes the deflection and tortuosity of hydraulic fractures. Therefore, researchers presented the fixed-plane perforation method for enhancing the effect on volume fracturing. In this paper, the three-dimensional discrete lattice method is used to study the initiation and propagation law of horizontal well fixed-plane perforation in unconventional reservoirs under two different stress states. The results show that it is more suitable to use fixed-plane perforation for reducing the initiation pressure. When employing the fixed-plane perforation method, fracture always initiates in the perforation plane, presents as an irregular fan-shaped failure surface, and then propagates along the wellbore. The initiation pressure is highly correlated to the phasing angle between adjacent perforations under different conditions, and the rate of increase in the initiation pressure decreases by around 1.59~6.38% when the phasing angle reaches 30°. The fracturing pressure is inversely correlated with the diameter and tunnel length of the perforations and the horizontal stress difference. When the diameter increases to 17 mm, the tunnel length increases to 25 cm or the horizontal stress difference reaches 8 MPa. These results reveal an insignificant effect of the above parameters on the initiation pressure. [ABSTRACT FROM AUTHOR]

With the increasing demand for the performance and design refinement of steel structures (including houses, bridges, and infrastructure), many structures have adopted ultimate bearing capacity in service. The design service lives of steel building structures are generally more than 50 years, and most of them contain bolted connections, which suffer from extreme conditions such as fire (high temperature) during service. When the structure contains defects or cracks and bolt holes, it is easy to produce stress concentration at the defect location, which leads to crack nucleation and crack propagation, reduces the bearing capacity of the structure, and causes the collapse of the structure and causes disasters. In the process of structural damage and crack propagation, the traditional method has some disadvantages, such as stress singularity, the mesh needing to be redivided, and the crack being restricted to mesh; however, the integral method of peridynamics (PD) can completely avoid these problems. Therefore, in this paper, the constitutive equation of PD in high temperature is derived according to the variation law of steel material properties when changed by temperature increase and peridynamics parameters; the damage and crack expansion characteristics of Q345 steel specimens with bolt holes and a central double-crack at 20 °C, 200 °C, 400 °C, and 600 °C were analyzed to clarify the structural damage and failure mechanism. This study is helpful for providing theoretical support for the design of high-temperature steel structures, improving the stability of the structure, and ensuring the bearing capacity of the structure and the safety of people's lives and property. [ABSTRACT FROM AUTHOR]

This paper discusses the possible early crack detectability performances of low contact ratio (LCR) and high contact ratio (HCR) spur gears. CAD models of the LCR and HCR gears are created using the rack cutter type tool. Static bending stress analyses are performed to define the starting point of the cracks and crack propagation analyses are conducted to define the realistic crack paths. Using the healthy and cracked gear geometries, the single tooth stiffness (STS) and the time-varying mesh stiffness (TVMS) of the LCR and HCR gears are calculated numerically. A six degrees of freedom dynamic model of the single-stage gear system is proposed. Dynamic force variation of the LCR and HCR gears are calculated by using the dynamic model. Statistical failure indicators, which are kurtosis, RMS, crest factor, mean, standard deviation, and variance, are used for the determination of the crack in the early stage. The results show that all statistical indicators increase with the increase in the crack length. The statistical indicators increase more for LCR gears than for HCR gears. Although HCR gears have many advantages over LCR gears, it has been determined that their crack detection capacity is lower than that of LCR gears. [ABSTRACT FROM AUTHOR]

This paper presents an approach to evaluate the failure of arbitrarily inclined interfaces using FE models with structured spatial discretization, providing accurate prediction of crack propagation along paths known a priori that are not constrained to the element boundaries. The combination of algorithms for the generation of structured discretization of representative polycrystalline microstructures with novel cohesive element formulations allow modelling the failure of complex topologies along rasterised boundaries, with noticeably higher computational efficiency and comparable accuracy. Two formulations of raster cohesive elements are presented, adopting either elastic-brittle or Tvergaard–Hutchinson traction separation laws. The formulations proposed are first validated comparing the failure of the interface within bi-crystal structures discretised using hexahedral elements either within a structured mesh (i.e. with rasterised boundaries) or an unstructured mesh (i.e. with planar boundary). Subsequently, the effectiveness of the formulations is demonstrated comparing the inter-granular crack propagation within complex polycrystalline microstructures. The behaviour of the novel cohesive element formulation in structured meshes consisting of regular hexahedral elements is in excellent agreement with the deformation and failure of classic cohesive element formulations placed along the planar boundaries of unstructured meshes consisting of tetrahedral elements. The higher computational cost of the raster cohesive elements is more than compensated by the increase in computational efficiency of structured meshes when compared to unstructured meshes, leading to a reduction of the simulation time of up to over 200 times for the simulations presented in the paper, thus allowing the simulation of large domains. [ABSTRACT FROM AUTHOR]

The modeling of the concrete matrix serves as a foundation for mesoscale analysis of concrete, which provides a crucial avenue for investigating the crack propagation and strength characteristics of concrete. However, the primary prerequisite for conducting such analyses is the generation of aggregate models. By combining the advantages of Voronoi diagrams and the random walk algorithm (RWA), a Voronoi–random walk algorithm is proposed in this paper. The algorithm overcomes the limitations of traditional methods, including constraints on aggregate volume fraction, low computational efficiency, and insufficient randomness in aggregate distribution. The meso-structure of a concrete block was modeled by the proposed method, and then its failure behavior under uniaxial compression was simulated using the finite element method. The numerical results agreed well with the experimental observations, indicating the effectiveness and accuracy of the proposed approach. [ABSTRACT FROM AUTHOR]

The application of nanomaterials as modifiers in the field of asphalt is increasingly widespread, and this paper aims to systematically review research on the impact of nanomaterials on asphalt viscosity. The results find that nanomaterials tend to increase asphalt's viscosity, enhancing its resistance to high-temperature rutting and low-temperature cracking. Zero-dimension nanomaterials firmly adhere to the asphalt surface, augmenting non-bonding interactions through van der Waals forces and engaging in chemical reactions to form a spatial network structure. One-dimensional nanomaterials interact with non-polar asphalt molecules, forming bonds between tube walls, thereby enhancing adhesion, stability, and resistance to cyclic loading. Meanwhile, these bundled materials act as reinforcement to transmit stress, preventing or delaying crack propagation. Two-dimensional nanomaterials, such as graphene and graphene oxide, participate in chemical interactions, forming hydrogen bonds and aromatic deposits with asphalt molecules, affecting asphalt's surface roughness and aggregate movement, which exhibit strong adsorption capacity and increase the viscosity of asphalt. Polymers reduce thermal movement and compact asphalt structures, absorbing light components and promoting the formation of a cross-linked network, thus enhancing high-temperature deformation resistance. However, challenges such as poor compatibility and dispersion, high production costs, and environmental and health concerns currently hinder the widespread application of nanomaterial-modified asphalt. Consequently, addressing these issues through comprehensive economic and ecological evaluations is crucial before large-scale practical implementation. [ABSTRACT FROM AUTHOR]

Determination of the cracking behavior during crack propagation helps to better understand damage and fracture processes in brittle rocks. The paper studies the cracking behavior of rocks on three scales: macro-deformation (or macro-cracking), internal micro-fracture, and surface crack coalescence. Under uniaxial compression, the cracking behavior of two types of sandstone specimens having single flaws was experimentally and systematically investigated. Acoustic emission (AE) and three-dimensional digital image correlation (3D-DIC) techniques were utilized to continuously monitor the acoustic shock signals generated by micro-fracture events inside the specimen and the specimen surface cracking process. The experimental results show that at the crack initiation stage, many micro-tensile fractures within the rock are initiated and coalesced, and small strain localized zones (SLZs) appear on the specimen surface. In the crack propagation stage, micro-fractures coalesce into macro-fractures that propagate in tensile mode to form surface cracks, which finally break in tension or slide against each other in shear mode. The formation of SLZs is related to the dip angle of pre-existing flaws, which determines the direction and mode of crack propagation. In conclusion, the strong acoustic-optical evidence accompanying different cracking behaviors is discussed in detail. From both acoustic and optical perspectives, it reveals and explains how flaws and material properties affect the strength and cracking mechanisms of brittle rocks. The study aids comprehension of the potential relation between internal micro-fracture and surface cracking in the process of engineering rock mass failure. [ABSTRACT FROM AUTHOR]

Cement-stabilized macadam is a type of heterogeneous and discontinuous material. To study the mesomechanical behavior of cement-stabilized macadam particles, a discrete-element model of cement-stabilized macadam is constructed according to the random distribution theory and certain porosity and gradation. The constitutive relations of contact between particles may be linear contact, linear bonding, and linear parallel bonding. The stress–strain, crack propagation, particle velocity, stress transfer, and force chain distribution of cement-stabilized macadam were analyzed after comparing the results of simulated uniaxial compression with laboratory tests. The results of uniaxial compression calculations for cement-stabilized macadam were in good agreement with the experimental data. At the beginning of loading, the upper/lower particles moved toward the middle; at the peak loading stage, the particle movement was mainly in the vertical direction; and at the final of loading, the particles mainly moved to the sides. With the increase in loading, the contact force between particles became larger and larger. At the loading peak, the contact force between particles reached the maximum value, and the normal and tangential contact forces of particles were not evenly distributed. Microcracks at each stage were mainly vertical cracks, most of which were located at 70–110°. In this paper, the uniaxial compression test of cement-stabilized macadam was dynamically simulated using discrete-element theory, and the mesoscopic structure and dynamic variation process of parameters were analyzed. It provides references for the study of damage of heterogeneous and discontinuous quasi-brittle materials. [ABSTRACT FROM AUTHOR]

Wind turbine blades bear the maximum cyclic load and varying self-weights in turbulent wind environments, which accelerate the propagation of cracks that ultimately progress from minor faults, resulting in blade failure and significant maintenance and shutdown costs. To address this issue, this paper proposes an adaptive control strategy for the blade's useful life. The control system is divided into the inner control loop and the outer control loop. The outer loop is based on the Paris crack propagation model combined with a particle filtering algorithm and calculates the degradation of the blade life under the crack threshold conditions provided by the operation and maintenance strategy to determine the parameter settings of the inner-loop load-shedding controller. The control strategy we propose can balance the load-shedding capability of the controller with the fatigue load of the pitch actuator while considering the predefined remaining useful blade life in the operation and maintenance strategy, avoiding unplanned downtime and reducing maintenance costs. [ABSTRACT FROM AUTHOR]

This paper investigates the three-dimensional crack propagation and damage evolution process of metallic column shells under internal explosive loading. The calibration of four typical failure parameters for 40CrMnSiB steel was conducted through experiments and subsequently applied to simulations. The numerical simulation results employing the four failure criteria were compared with the differences and similarities observed in freeze-recovery tests and ultra-high-speed tests. This analysis addressed the critical issue of determining failure criteria for the fracture of a metal shell under internal explosive loads. Building upon this foundation, the damage parameter Dc, linked to the cumulative crack density, was defined based on the evolution characteristics of a substantial number of cracks. The relationship between the damage parameter and crack velocity over time was established, and the influence of the internal central pressure on the damage parameter and crack velocity was investigated. Variations in the fracture modes were found under different failure criteria, with the principal strain failure criterion proving to be the most effective for simulating 3D crack propagation in a pure shear fracture mode. Through statistical analysis of the shell penetration fracture radius data, it was determined that the fracture radius remained essentially constant during the crack evolution process and could be considered a constant. The propagation velocity of axial cracks ranged between 5300 m/s and 12600 m/s, surpassing the Rayleigh wave velocity of the shell material and decreasing linearly with time. The increase in shell damage exhibited an initial rapid phase, followed by deceleration, demonstrating accelerated damage during the propagation stage of the blast wave and decelerated damage after the arrival of the rarefaction wave. This study provides an effective approach for investigating crack propagation and damage evolution. The derived crack propagation and damage evolution law serves as a valuable reference for the development of crack velocity theory and the construction of shell damage evolution modes. [ABSTRACT FROM AUTHOR]