Analytical solution for the effective elastic properties of rocks with the tilted penny-shaped cracks in the transversely isotropic background

Seismic prediction of cracks is of great significance in many disciplines,for which the rock physics model is indispensable.However,up to now,multitudinous analytical models focus primarily on the cracked rock with the isotropic background,while the explicit model for the cracked rock with the anisotropic background is rarely investigated in spite of such case being often encountered in the earth.Hence,we first studied dependences of the crack opening displacement tensors on the crack dip angle in the coordinate systems formed by symmetry planes of the crack and the background anisotropy,respectively,by forty groups of numerical experiments.Based on the conclusion from the experiments,the analytical solution was derived for the effective elastic properties of the rock with the inclined penny-shaped cracks in the transversely isotropic background.Further,we comprehensively analyzed,according to the developed model,effects of the crack dip angle,background anisotropy,filling fluid and crack density on the effective elastic properties of the cracked rock.The analysis results indicate that the dip angle and background anisotropy can significantly either enhance or weaken the anisotropy degrees of the P-and SH-wave velocities,whereas they have relatively small effects on the SV-wave velocity anisotropy.Moreover,the filling fluid can increase the stiffness coefficients related to the compressional modulus by reducing crack compliance parameters,while its effects on shear coefficients depend on the crack dip angle.The increasing crack density reduces velocities of the dry rock,and decreasing rates of the velocities are affected by the crack dip angle.By comparing with exact numerical results and experimental data,it was demonstrated that the proposed model can achieve high-precision estimations of stiffness coefficients.Moreover,the assumption of the weakly anisotropic background results in the consistency between the proposed model and Hudson's published theory for the orthorhombic rock.

Effect of carbon material and surfactant on ink property and resulting surface cracks of fuel-cell microporous layers

Ensuring the consistency of electrode structure in proton-exchange-membrane fuel cells is highly desired yet challenging because of wide-existing and unguided cracks in the microporous layer(MPL). The first thing is to evaluate the homogeneity of MPL with cracks quantitatively. This paper proposes the homogeneity index of a full-scale MPL with an area of 50 cm~2, which is yet to be reported in the literature to our knowledge. Besides, the effects of the carbon material and surfactant on the ink and resulting MPL structure have been studied. The ink with a high network development degree produces an MPL with low crack density, but the ink with high PDI produces an MPL with low crack homogeneity. The polarity of the surfactant and the non-polarity of polytetrafluoroethylene(PTFE) are not mutually soluble,resulting in the heterogeneous PTFE distribution. The findings of this study provide guidelines for MPL fabrication.

A phase-field model for simulating the propagation behavior of mixed-mode cracks during the hydraulic fracturing process in fractured reservoirs

A novel phase-field model for the propagation of mixed-mode hydraulic fractures,characterized by the formation of mixed-mode fractures due to the interactions between fluids and solids,is proposed.In this model,the driving force for the phase field consists of both tensile and shear components,with the fluid contribution primarily manifesting in the tension driving force.The displacement and pressure are solved simultaneously by an implicit method.The numerical solution's iterative format is established by the finite element discretization and Newton-Raphson(NR)iterative methods.The correctness of the model is verified through the uniaxial compression physical experiments on fluid-pressurized rocks,and the limitations of the hydraulic fracture expansion phase-field model,which only considers mode I fractures,are revealed.In addition,the influence of matrix mode II fracture toughness value,natural fracture mode II toughness value,and fracturing fluid injection rate on the hydraulic fracture propagation in porous media with natural fractures is studied.

Experimental study of the damage characteristics of rocks containing non-penetrating cracks under cyclic loading

The damage evolution process of non-penetrating cracks often causes some unexpected engineering disasters.Gypsum specimens containing non-penetrating crack(s)are used to study the damage evolution and characteristics under cyclic loading.The results show that under cyclic loading,the relationship between the number of non-penetrating crack(s)and the characteristic parameters(cyclic number,peak stress,peak strain,failure stress,and failure strain)of the pre-cracked specimens can be represented by a decreasing linear function.The damage evolution equation is fitted by calibrating the accumulative plastic strain for each cycle,and the damage constitutive equation is proposed by the concept of effective stress.Additionally,non-penetrating cracks are more likely to cause uneven stress distribution,damage accumulation,and local failure of specimen.The local failure can change the stress distribution and relieve the inhibition of non-penetrating crack extension and eventually cause a dramatic destruction of the specimen.Therefore,the evolution process caused by non-penetrating cracks can be regarded as one of the important reasons for inducing rockburst.These results are expected to improve the understanding of the process of spalling formation and rockburst and can be used to analyze the stability of rocks or rock structures.

Evaluation of the injection and plugging ability of a novel epoxy resin in cement cracks

Sustained casing pressure(SCP)is a crucial issue in the oil and gas production lifecycle.Epoxy resins,exhibiting exceptional compressive strength,ductility,and shear bonding strength,have the potential to form reliable barriers.The injectivity and sealing capacity of the epoxy resin is crucial parameters for the success of shallow remediation operations.This study aimed to develop and assess a novel solid-free resin sealant as an alternative to Portland cement for mitigating fluid leakage.The investigation evaluated the viscosity,compressive strength,and brittleness index of the epoxy resin sealant,as well as its tangential and normal shear strengths in conjunction with casing steel.The flow characteristics and sealing abilities of conventional cement and epoxy resin were comparatively analyzed in cracks.The results showed that the application of a viscosity reducer facilitated control over the curing time of the epoxy resin,ranging from 1.5 to 6 h,and reduced the initial viscosity from 865.53 to 118.71 m Pa,s.The mechanical properties of the epoxy resin initially increased with a rise in curing agent content before experiencing a minor decrease.The epoxy resin containing 30%curing agent exhibited optimal mechanical properties.After a 14-day curing period,the epoxy resin's compressive strength reached81.37 MPa,2.12 times higher than that of cement,whereas the elastic modulus of cement was 2.99 times greater than that of the epoxy resin.The brittleness index of epoxy resin is only 3.42,demonstrating high flexibility and toughness.The tangential and normal shear strengths of the epoxy resin exceeded those of cement by 3.17 and 2.82 times,respectively.In a 0.5 mm-wide crack,the injection pressure of the epoxy resin remained below 0.075 MPa,indicating superior injection and flow capabilities.Conversely,the injection pressure of cement surged dramatically to 2.61 MPa within 5 min.The breakthrough pressure of0.5 PV epoxy resin reached 7.53 MPa,decreasing the crack's permeability to 0.02 D,a mere 9.49%of the permeability observed following cement plugging.Upon sealing a 2 mm-wide crack using epoxy resin,the maximum breakthrough pressure attained 5.47 MPa,3.48 times of cement.These results suggest that epoxy resin sealant can be employed safely and effectively to seal cracks in the cement.

Effect of drying cracks on swelling and self-healing of bentonite-sand blocks used as engineered barriers for radioactive waste disposal

Experiments were conducted to evaluate the healing of drying cracks in air-dried bentonite-sand blocks after hydration and swelling in groundwater,providing justifications to simplify the protection of blocks prior to installation in a high-level radioactive waste repository.Synthetic groundwater was prepared to represent the geochemistry of Beishan groundwater,and was used to hydrate the blocks during the swelling pressure and swelling strain measurements,as Beishan is the most promising site for China's repository.Healing of the surface cracks was recorded by photography,and healing of the internal cracks was visualized by CT images and hydraulic conductivity of air-dried blocks.The results indicate that the maximum swelling pressure and swelling strain are primarily affected by the geochemistry of Beishan groundwater,but not affected by the drying cracks.The maximum swelling pressure and swelling strain of air-dried blocks are comparable to or even higher than the pressure and strain of fresh blocks.The maximum swelling pressure measured in strong(i.e.high ion strength)Beishan groundwater was 44%of the pressure measured in deionized(DI)water,and the maximum swelling strain was reduced to 23%of the strain measured in DI water.Nevertheless,the remained swelling of the blocks hydrated in strong Beishan groundwater was sufficient to heal the surface and internal drying cracks,as demonstrated by the pictures of surface cracks and CT images.The hydraulic conductivity of the air-dried block permeated with strong groundwater was comparable(3.7×higher)to the hydraulic conductivity of the fresh block,indicating the self-healing of drying cracks after hydration and swelling in groundwater.A simplified method of protecting the block with plastic wraps before installation is recommended,since the remained swelling of the block hydrated in Beishan groundwater is sufficient to heal the drying cracks.

Elimination of cracks in stainless steel casings via 3D printed sand molds with an internal topology structure

The important supporting component in a gas turbine is the casing,which has the characteristics of large size,complex structure,and thin wall.In the context of existing 3DP sand casting processes,casting crack defects are prone to occur.This leads to an increase in the scrap rate of casings,causing significant resource wastage.Additionally,the presence of cracks poses a significant safety hazard after the casings are put into service.The generation of different types of crack defects in stainless steel casings is closely related to casting stress and the high-temperature concession of the sand mold.Therefore,the types and causes of cracks in stainless steel casing products,based on their structural characteristics,were systematically analyzed.Various sand molds with different internal topology designs were printed using the 3DP technology to investigate the impact of sand mold structures on high-temperature concession.The optimal sand mold structure was used to cast casings,and the crack suppression effect was verified by analyzing its eddy current testing results.The experimental results indicate that the skeleton structure has an excellent effect on suppressing cracks in the casing.This research holds important theoretical and engineering significance in improving the quality of casing castings and reducing production costs.

Intelligent extraction of road cracks based on vehicle laser point cloud and panoramic sequence images

In light of the limited efficacy of conventional methods for identifying pavement cracks and the absence of comprehensive depth and location data in two-dimensional photographs,this study presents an intelligent strategy for extracting road cracks.This methodology involves the integration of laser point cloud data obtained from a vehicle-mounted system and a panoramic sequence of images.The study employs a vehicle-mounted LiDAR measurement system to acquire laser point cloud and panoramic sequence image data simultaneously.A convolutional neural network is utilized to extract cracks from the panoramic sequence image.The extracted sequence image is then aligned with the laser point cloud,enabling the assignment of RGB information to the vehicle-mounted three dimensional(3D)point cloud and location information to the two dimensional(2D)panoramic image.Additionally,a threshold value is set based on the crack elevation change to extract the aligned roadway point cloud.The three-dimensional data pertaining to the cracks can be acquired.The experimental findings demonstrate that the use of convolutional neural networks has yielded noteworthy outcomes in the extraction of road cracks.The utilization of point cloud and image alignment techniques enables the extraction of precise location data pertaining to road cracks.This approach exhibits superior accuracy when compared to conventional methods.Moreover,it facilitates rapid and accurate identification and localization of road cracks,thereby playing a crucial role in ensuring road maintenance and traffic safety.Consequently,this technique finds extensive application in the domains of intelligent transportation and urbanization development.The technology exhibits significant promise for use in the domains of intelligent transportation and city development.

A hybrid attention deep learning network for refined segmentation of cracks from shield tunnel lining images

This research developed a hybrid position-channel network (named PCNet) through incorporating newly designed channel and position attention modules into U-Net to alleviate the crack discontinuity problem in channel and spatial dimensions. In PCNet, the U-Net is used as a baseline to extract informative spatial and channel-wise features from shield tunnel lining crack images. A channel and a position attention module are designed and embedded after each convolution layer of U-Net to model the feature interdependencies in channel and spatial dimensions. These attention modules can make the U-Net adaptively integrate local crack features with their global dependencies. Experiments were conducted utilizing the dataset based on the images from Shanghai metro shield tunnels. The results validate the effectiveness of the designed channel and position attention modules, since they can individually increase balanced accuracy (BA) by 11.25% and 12.95%, intersection over union (IoU) by 10.79% and 11.83%, and F1 score by 9.96% and 10.63%, respectively. In comparison with the state-of-the-art models (i.e. LinkNet, PSPNet, U-Net, PANet, and Mask R–CNN) on the testing dataset, the proposed PCNet outperforms others with an improvement of BA, IoU, and F1 score owing to the implementation of the channel and position attention modules. These evaluation metrics indicate that the proposed PCNet presents refined crack segmentation with improved performance and is a practicable approach to segment shield tunnel lining cracks in field practice.

Deep Learning Method to Detect the Road Cracks and Potholes for Smart Cities

The increasing global population at a rapid pace makes road trafficdense;managing such massive traffic is challenging. In developing countrieslike Pakistan, road traffic accidents (RTA) have the highest mortality percentageamong other Asian countries. The main reasons for RTAs are roadcracks and potholes. Understanding the need for an automated system forthe detection of cracks and potholes, this study proposes a decision supportsystem (DSS) for an autonomous road information system for smart citydevelopment with the use of deep learning. The proposed DSS works in layerswhere initially the image of roads is captured and coordinates attached to theimage with the help of global positioning system (GPS), communicated tothe decision layer to find about the cracks and potholes in the roads, andeventually, that information is passed to the road management informationsystem, which gives information to drivers and the maintenance department.For the decision layer, we projected a CNN-based model for pothole crackdetection (PCD). Aimed at training, a K-fold cross-validation strategy wasused where the value of K was set to 10. The training of PCD was completedwith a self-collected dataset consisting of 6000 images from Pakistani roads.The proposed PCD achieved 98% of precision, 97% recall, and accuracy whiletesting on unseen images. The results produced by our model are higher thanthe existing model in terms of performance and computational cost, whichproves its significance.

Pavement Cracks Coupled With Shadows:A New Shadow-Crack Dataset and A Shadow-Removal-Oriented Crack Detection Approach

Automatic pavement crack detection is a critical task for maintaining the pavement stability and driving safety.The task is challenging because the shadows on the pavement may have similar intensity with the crack,which interfere with the crack detection performance.Till to the present,there still lacks efficient algorithm models and training datasets to deal with the interference brought by the shadows.To fill in the gap,we made several contributions as follows.First,we proposed a new pavement shadow and crack dataset,which contains a variety of shadow and pavement pixel size combinations.It also covers all common cracks(linear cracks and network cracks),placing higher demands on crack detection methods.Second,we designed a two-step shadow-removal-oriented crack detection approach:SROCD,which improves the performance of the algorithm by first removing the shadow and then detecting it.In addition to shadows,the method can cope with other noise disturbances.Third,we explored the mechanism of how shadows affect crack detection.Based on this mechanism,we propose a data augmentation method based on the difference in brightness values,which can adapt to brightness changes caused by seasonal and weather changes.Finally,we introduced a residual feature augmentation algorithm to detect small cracks that can predict sudden disasters,and the algorithm improves the performance of the model overall.We compare our method with the state-of-the-art methods on existing pavement crack datasets and the shadow-crack dataset,and the experimental results demonstrate the superiority of our method.

Recent research progress in the mechanism and suppression of fusion welding-induced liquation cracking of nickel based superalloys

Nickel-based superalloys are extensively used in the crucial hot-section components of industrial gas turbines,aeronautics,and astronautics because of their excellent mechanical properties and corrosion resistance at high temperatures.Fusion welding serves as an effective means for joining and repairing these alloys;however,fusion welding-induced liquation cracking has been a challenging issue.This paper comprehensively reviewed recent liquation cracking,discussing the formation mechanisms,cracking criteria,and remedies.In recent investigations,regulating material composition,changing the preweld heat treatment of the base metal,optimizing the welding process parameters,and applying auxiliary control methods are effective strategies for mitigating cracks.To promote the application of nickel-based superalloys,further research on the combination impact of multiple elements on cracking prevention and specific quantitative criteria for liquation cracking is necessary.

Peridynamic Study on Fracture Mode and Crack Propagation Path of a Plate with Multiple Cracks Subjected to Uniaxial Tension

How to simulate fracture mode and crack propagation path in a plate with multiple cracks is an attractive but difficult issue in fracture mechanics.Peridynamics is a recently developed nonlocal continuum formulation that can spontaneously predict the crack nucleation,branch and propagation in materials and structures through a meshfree discrete technique.In this paper,the peridynamic motion equation with boundary traction is improved by simplifying the boundary transfer functions.We calculate the critical cracking load and the fracture angles of the plate with multiple cracks under uniaxial tension.The results are consistent with those predicted by classical fracture mechanics.The fracture mode and crack propagation path are also determined.The calculation shows that the brittle fracture process of the plate with multiple cracks can be conveniently and correctly simulated by the peridynamic motion equation with boundary conditions.

Study on oxygen transport and titanium oxidation in coating cracks under parallel gas flow based on LBM modelling

The oxygen transportation from surrounding air to coating cracks is an important factor in the oxidation and ignition of titanium alloy. In this work, the oxygen transport and surface oxidation of titanium in inclined cracks of coating under parallel airflow are studied with the lattice Boltzmann method(LBM).A boundary scheme of LBM about surface reaction is developed. The conversion factors are utilized to build the relationship between the physical scale and the lattice scale. The reliability of the LBM model is validated by the finite element method(FEM). The results show that the convective mass transport driven by the surrounding airflow and the vortex structure formed inside the crack are the two significant factors that influence the oxygen transport in cracks. The convective mass transfer plays a major role in oxygen transport when the inclination angle of the crack is small. For the cases with a large inclination angle, the oxygen transfer from the top to the bottom of the crack is mainly controlled by mass diffusion mechanism. The oxygen concentration in inclined cracks is generally less than that in vertical cracks, and oxidation and ignition of the substrate titanium might be more likely to occur in relatively vertical cracks.

Semi-analytical solution for internal forces of tunnel lining with multiple longitudinal cracks

Longitudinal cracks on the tunnel lining significantly influence the performance of tunnels in operation.In this study,we propose a semi-analytical method that provides a simple and effective way to calculate the internal forces of tunnel linings with multiple cracks.The semi-analytical solution is obtained using structural analysis considering the flexural rigidity for the cracked longitudinal section of the tunnel lining.Then the proposed solution is verified numerically.Using the proposed method,the influences of the crack depth and the number of cracks on the bending moment and modified crack tip stress are investigated.With the increase in crack depth,the bending moment of lining scetion adjacent to the crack decreases,while the bending moment of lining scetion far away from the crack increases slightly.The more the number of cracks in a tunnel lining,the easier the new cracks initiated.

Seismic dynamic stability of double-slider rock slopes containing tension cracks

Earthquakes have significant impact on rock slopes,thus studying the seismic stability of double-slider rock slopes containing tension cracks is crucial.We proposed an analysis method on the seismic dynamic slope stability.This method utilizes discrete Fourier transform to decompose real earthquake waves into a combination of harmonic waves.These waves are then used in conjunction with the pseudo-dynamic method and safety factor calculation formula to compute the safety factor.This approach accurately captures the influence of seismic time history characteristics on the dynamic stability of double-slider rock slopes containing tension cracks.The minimum safety factor in the obtained time history curves of the safety factor reflects the most unfavorable state of the slopes under seismic effects.Quantitative analysis is conducted using six sets of actual earthquake ground motion data obtained from the Pacific Earthquake Engineering Research Center’s NGAWest2 ground-shaking record database.The conclusions are as follows:(1)There is an inverse correlation between the average seismic acceleration amplitude and the minimum safety factor.Conversely,the seismic acceleration amplitude standard deviation shows a positive correlation with the minimum safety factor.The global sensitivity of geometric parameters in the slope model is higher than other influencing factors.(2)The proposed dynamic stability analysis method can capture the dynamic characteristics of earthquakes,emphasizing the minimum safety factor of the slope in the seismic time history as a stability indicator.In contrast,the pseudo-static method may yield unsafe results.(3)A safety factor expression considering hydrostatic pressure is proposed.A negative correlation was observed between the height of the water level line and the minimum safety factor.

Numerical Modelling of Drying Induced Cracks in Wood Discs Using the Extended Finite Element Method

Drying crack is a common phenomenon occurring during moisture discharge from wood,reducing efficient wood utilization.Drying crack is primarily caused by drying stress,and the reasonable methods for determining drying stress are sparse.In this study,the initiation and propagation of cracks during wood discs drying were simulated using the extended finite element method(XFEM).The distribution of drying stress and displacement was analyzed at different crack conditions based on the simulation results.This study aimed to solve the problem of the limitation of drying stress testing methods and provide a new idea for the study of wood drying stress.The numerical simulation results are found in good agreement with the experimental results,thus corroborating the feasibility of XFEM in modeling drying crack of wood discs.The stress concentration was observed at the crack tip region,while a minor stress was presented in the region of crack passing through,indicating that the crack formation process was also a process of releasing drying stress.Further,more energy was required to form double cracks in comparison with the single crack mode.

Correlation analysis of longitudinal cracks and vertical deformation within asphalt pavement of cold regions

The asphalt pavement longitudinal crack is a common distress in cold regions,resulting from uneven deformation of the subgrade.Analysis of the correlation law between uneven deformation and crack distress is of positive significance for understanding the mechanism of crack initiation,and putting forward treatment measures.In view of the complexity of longitudinal crack inducement and road surface deformation,the grey relational method was used to analyze this relationship.Through long-term monitoring of the vertical deformation data of typical road sections,the vertical deformation law of the pavement surface and its deformation characteristics under the action of temperature field are analyzed.Parameters such as vertical relative deformation,vertical relative deformation rate and vertical differential deformation VDSr were constructed to describe vertical deformation characteristics.Typical distribution characteristics of longitudinal fractures and their length and distribution characteristics are also described.The grey correlation analysis theory was utilized to analyze the relationship between deformation characteristics of sections,cross sections and monitoring points and longitudinal crack characteristics(length and location).The analysis reveals a linear positive correlation or a high correlation between several indicators.This study can provide a deeper understanding of the occurrence and development mechanism of longitudinal cracks in asphalt pavement of cold areas,and give references for the research of road engineering structure,materials and distress prevention.

A Dugdale-Barenblatt model for elliptical orifice problem with asymmetric cracks in one-dimensional orthorhombic quasicrystals

By means of Muskhelishvili’s method and the technique of generalized conformal mapping,the physical plane problems are transformed into regular mathematical problems in quasicrystals(QCs).The analytical solution to an elliptical orifice problem with asymmetric cracks in one-dimensional(1D)orthorhombic QCs is obtained.By using the Dugdale-Barenblatt model,the plastic simulation at the crack tip of the elliptical orifice with asymmetric cracks in 1D orthorhombic QCs is performed.Finally,the size of the atomic cohesive force zone is determined precisely,and the size of the atomic cohesive force zone around the crack tip of an elliptical orifice with a single crack or two symmetric cracks is obtained.

Characterization of alpine meadow surface crack and its correlation with root-soil properties

Quantifying surface cracks in alpine meadows is a prerequisite and a key aspect in the study of grassland crack development.Crack characterization indices are crucial for the quantitative characterization of complex cracks,serving as vital factors in assessing the degree of cracking and the development morphology.So far,research on evaluating the degree of grassland degradation through crack characterization indices is rare,especially the quantitative analysis of the development of surface cracks in alpine meadows is relatively scarce.Therefore,based on the phenomenon of surface cracking during the degradation of alpine meadows in some regions of the Qinghai-Tibet Plateau,we selected the alpine meadow in the Huangcheng Mongolian Township,Menyuan Hui Autonomous County,Qinghai Province,China as the study area,used unmanned aerial vehicle(UAV)sensing technology to acquire low-altitude images of alpine meadow surface cracks at different degrees of degradation(light,medium,and heavy degradation),and analyzed the representative metrics characterizing the degree of crack development by interpreting the crack length,length density,branch angle,and burrow(rat hole)distribution density and combining them with in situ crack width and depth measurements.Finally,the correlations between the crack characterization indices and the soil and root parameters of sample plots at different degrees of degradation in the study area were analyzed using the grey relation analysis.The results revealed that with the increase of degradation,the physical and chemical properties of soil and the mechanical properties of root-soil composite changed significantly,the vegetation coverage reduced,and the root system aggregated in the surface layer of alpine meadow.As the degree of degradation increased,the fracture morphology developed from"linear"to"dendritic",and eventually to a complex and irregular"polygonal"pattern.The crack length,width,depth,and length density were identified as the crack characterization indices via analysis of variance.The results of grey relation analysis also revealed that the crack length,width,depth,and length density were all highly correlated with root length density,and as the degradation of alpine meadows intensified,the underground biomass increased dramatically,forming a dense layer of grass felt,which has a significant impact on the formation and expansion of cracks.