Simulation of Corrosion-Induced Cracking of Reinforced Concrete Based on Fracture Phase Field Method

Accurate simulation of the cracking process caused by rust expansion of reinforced concrete(RC)structures plays an intuitive role in revealing the corrosion-induced failure mechanism.Considering the quasi-brittle fracture of concrete,the fracture phase field driven by the compressive-shear term is constructed and added to the traditional brittle fracture phase field model.The rationality of the proposed model is verified by a mixed fracture example under a shear displacement load.Then,the extended fracture phase model is applied to simulate the corrosion-induced cracking process of RC.The cracking patterns caused by non-uniform corrosion expansion are discussed for RC specimens with homogeneous macroscopically or heterogeneous with different polygonal aggregate distributions at the mesoscopic scale.Then,the effects of the protective layer on the crack propagation trajectory and cracking resistance are investigated,illustrating that the cracking angle and cracking resistance increase with the increase of the protective layer thickness,consistent with the experimental observation.Finally,the corrosion-induced cracking process of concrete specimens with large and small spacing rebars is simulated,and the interaction of multiple corrosion cracking is easily influenced by the reinforcement spacing,which increases with the decrease of the steel bar interval.These conclusions play an important role in the design of engineering anti-corrosion measures.The fracture phase field model can provide strong support for the life assessment of RC structures.

Numerical simulation of spatial distributions of mining-induced stress and fracture fields for three coal mining layouts

In this study, the spatial distributions of stress and fracture fields for three typical underground coal mining layouts, Le, non-pillar mining （NM）, top-coal caving mining （TCM） and protective coal-seam mining （PCM）, are modeled using discrete element software UDEC, The numerical results show that different mining layouts can lead to different mining-induced stress fields, resulting in diverse fracture fields, For the PCM, the mining influenced area in front of the mining faces is the largest, and the stress concentration factor in front of the mining faces is the lowest, The spatial shapes of the mining-induced fracture fields under NM, TCM and PCM differ, and they are characterized by trapezoidal, triangular and tower shapes, respectively, The fractal dimensions of mining-induced fractures of the three mining layouts decrease in the order of PCM, TCM and NM, It is also shown that the PCM can result in a better gas control effect in coal mines with high outburst potential, The numerical results are expected to provide a basis for understanding of mining-induced gas seepage fields and provide a reference for high- efficiency coal mining,

Effect of dynamic loading orientation on fracture properties of surrounding rocks in twin tunnels

For expedited transportation,vehicular tunnels are often designed as two adjacent tunnels,which frequently experience dynamic stress waves from various orientations during blasting excavation.To analyze the impact of dynamic loading orientation on the stability of the twin-tunnel,a split Hopkinson pressure bar(SHPB)apparatus was used to conduct a dynamic test on the twin-tunnel specimens.The two tunnels were rotated around the specimen’s center to consider the effect of dynamic loading orientation.LS-DYNA software was used for numerical simulation to reveal the failure properties and stress wave propagation law of the twin-tunnel specimens.The findings indicate that,for a twin-tunnel exposed to a dynamic load from different orientations,the crack initiation position appears most often at the tunnel corner,tunnel spandrel,and tunnel floor.As the impact direction is created by a certain angle(30°,45°,60°,120°,135°,and 150°),the fractures are produced in the middle of the line between the left tunnel corner and the right tunnel spandrel.As the impact loading angle(a)is 90°,the tunnel sustains minimal damage,and only tensile fractures form in the surrounding rocks.The orientation of the impact load could change the stress distribution in the twin-tunnel,and major fractures are more likely to form in areas where the tensile stress is concentrated.

Tensile Fractures and in situ Stress Measurement Data Constraints on Cretaceous-Present Tectonic Stress Field Evolution of the Tanlu Fault Zone in Shandong Province,North China Craton

Tectonic stress fields are the key drivers of tectonic events and the evolution of regional structures.The tectonic stress field evolution of the Tanlu fault zone in Shandong Province,located in the east of the North China Craton(NCC),may have preserved records of the NCC’s tectonic history.Borehole television survey and hydraulic fracturing were conducted to analyze the paleo and present tectonic stress fields.Three groups of tensile fractures were identified via borehole television,their azimuths being NNW-SSE,NW-SE and NE-SW,representing multiple stages of tectonic events.Hydraulic fracturing data indicates that the study region is experiencing NEE-SWW-oriented compression and nearly-N-Soriented extension,in accordance with strike-slip and compression.Since the Cretaceous,the orientation of the extensional stress has evolved counterclockwise and sequentially from nearly-NW-SE-oriented to NE-SW-oriented and even nearly N-S-oriented,the stress state having transitioned from strike-slip-extension to strike-slip-compression,in association with the rotating and oblique subduction of the Pacific Plate beneath the NCC,with the participation of the Indian Plate.

Numerical simulation of gas migration into mining-induced fracture network in the goaf

Gas extraction practice has been proven for the clear majority of coal mines in China to be unfavorable using drill holes in the coal seam. Rather, mining-induced fractures in the goaf should be utilized for gas extraction. To study gas migration in mining-induced fractures, one mining face of 10 th Mine in Pingdingshan Coalmine Group in Henan, China, has been selected as the case study for this work. By establishing the mathematical model of gas migration under the influence of coal seam mining, discrete element software UDEC and Multiphysics software COMSOL are employed to model gas migration in mining-induced fractures above the goaf. The results show that as the working face advances, the goaf overburden gradually forms a mining-induced fracture network in the shape of a trapezoid, the size of which increases with the distance of coal face advance. Compared with gas migration in the overburden matrix, the gas flow in the fracture network due to mining is far greater. The largest mining-induced fracture is located at the upper end of the trapezoidal zone, which results in the largest gas flux in the network. When drilling for gas extraction in a mining-induced fracture field, the gas concentration is reduced in the whole region during the process of gas drainage, and the rate of gas concentration drops faster in the fractured zone. It is shown that with gas drainage, the gas flow velocity in the mininginduced fracture network is faster.

Grouting theories and technologies for the reinforcement of fractured rocks surrounding deep roadways

Grouting is an effective method to improve the integrity and stability of fractured rocks that surround deep roadways.After years of research and practice,various theories and a complete set of grouting technologies for deep roadways with fractured rocks have been developed and are widely applied in Chinese coal mining production.This paper systematically summarizes and analyzes the research results concerning the theory,design,materials,processes,and equipment for the grouting and reinforcement of fractured rocks surrounding deep roadways.Specifically,in terms of grouting methods,pregrouting,groutingwhile-excavation,and postgrouting methods are explored;in terms of grouting theory,backfill grouting,compaction grouting,infiltration grouting,and fracture grouting theories are studied.In addition,this paper also studies grouting borehole arrangement,water-cement ratio,grouting pressure,grouting volume,grout diffusion radius,and other grouting parameters and their determination methods.On this basis,this paper explores the physical and mechanical properties of organic and organic-inorganic composite grouting materials,and assess grouting reinforcement quality testing methods and instruments.Taken as the field cases,the application of pregrouting in front of heading faces,groutingwhile-excavation,and postgrouting in the Kouzidong coal mine are then introduced,and the effects of the grouting reinforcements are evaluated.This paper proposes a development direction for grouting technology based on problems existing in the grouting reinforcement of fractured rocks surrounding deep roadways.

Simulation of Paleotectonic Stress Fields and Distribution Prediction of Tectonic Fractures at the Hudi Coal Mine, Qinshui Basin

Study on tectonic fractures based on the inversion of tectonic stress fields is an effective method. In this study, a geological model was set up based on geological data from the Hudi Coal Mine, Qinshui Basin, a mechanical model was established under the condition of rock mechanics and geostress, and the finite element method was used to simulate the paleotectonic stress field. Based on the Griffith and Mohr-Coulomb criterion, the distribution of tectonic fractures in the Shanxi Formation during the Indosinian, Yanshanian, and Himalayan period can be predicted with the index of comprehensive rupture rate. The results show that the acting force of the Pacific Plate and the India Plate to the North China Plate formed the direction of principal stress is N-S, NW - SE, and NE - SW, respectively, in different periods in the study area. Changes in the direction and strength of the acting force led to the regional gradients of tectonic stress magnitude, which resulted in an asymmetrical distribution state of the stress conditions in different periods. It is suggested that the low-stress areas are mainly located in the fault zones and extend along the direction of the fault zones. Furthermore, the high-stress areas are located in the junction of fold belts and the binding site of multiple folds. The development of tectonic fractures was affected by the distribution of stress intensity and the tectonic position of folds and faults, which resulted in some developed areas with level I and II. There are obvious differences in the development of tectonic fractures in the fold and fault zones and the anticline and syncline structure at the same fold zones. The tectonic fractures of the Shanxi Formation during the Himalayan period are more developed than those during the Indosinian and Yanshanian period due to the superposition of the late tectonic movement to the early tectonic movement and the differences in the magnitude and direction of stress intensity.

The Relationship between Fractures and Tectonic Stress Field in the Extra Low-Permeability Sandstone Reservoir at the South of Western Sichuan Depression

The formation and distribution of fractures are controlled by paleotectonic stress field, and their preservative status and effects on development are dominated by the modern stress field. Since Triassic, it has experienced four tectonic movements and developed four sets of tectonic fractures in the extra low-permeability sandstone reservoir at the south of western Sichuan depression. The strikes of fractures are in the S-N, NE-SW, E-W, and NW-SE directions respectively. At the end of Triassic, under the horizontal compression tectonic stress field, for which the maximum principal stress direction was NW.SE, the fractures were well developed near the S-N faults and at the end of NE-SW faults, because of their stress concentration. At the end of Cretaceous, in the horizontal compression stress fields of the NE-SW direction, the stress was obviously lower near the NE-SW faults, thus, fractures mainly developed near the S-N faults. At the end of Neogene-Early Pleistocene, under the horizontal compression tectonic stress fields of E-W direction, stress concentrated near the NE-SW faults and fractures developed at these places, especially at the end of the NE-SE faults, the cross positions of NE-SW, and S-N faults. Therefore, fractures developed mostly near S-N faults and NE-SW faults. At the cross positions of the above two sets of faults, the degree of development of the fractures was the highest. Under the modern stress field of the NW-SE direction, the NW-SE fractures were mainly the seepage ones with tensional state, the best connectivity, the widest aperture, the highest permeability, and the minimum opening pressure.

Effect of hydraulic fracturing induced stress field on weak surface activation during unconventional reservoir development

Unconventional reservoirs usually contain many weak surfaces such as faults,laminae and natural fractures,and effective activation and utilization of these weak surfaces in reservoirs can significantly improve the extraction effect.In hydraulic fracturing,when the artificial fracture approaches the natural fracture,the natural fracture would be influenced by both the original in-situ stress field and the hydraulic fracturing-induced stress field.In this paper,the hydraulic fracturing-induced stress field is calculated based on the relative position of hydraulic fracture and natural fracture,the original in-situ stress,the net pressure inside the hydraulic fracture and the pore pressure of the formation.Furthermore,the stability model of the natural fracture is established by combining the Mohr-Coulomb rupture criterion,and extensive parametric studies are conducted to explore the impact of each parameter on the stability of the natural fracture.The validity of the proposed model is verified by comparing with the reservoir characteristics and fracturing process of the X-well 150e155 formation in the Songliao Basin.It is found that the stress field induced by the hydraulic fracture inhibits the activation of the natural fracture after the artificial fracture crossed the natural fracture.Therefore,for similar reservoirs as X-well 150e155,it is suggested to connect natural fractures with hydraulic fractures first and then activate natural fractures which can effectively utilize the natural fractures and form a complex fracture network.

Characteristics of evolution of mining-induced stress field in the longwall panel:insights from physical modeling

The evolution of mining-induced stress field in longwall panel is closely related to the fracture field and the breaking characteristics of strata.Few laboratory experiments have been conducted to investigate the stress field.This study investigated its evolution by constructing a large-scale physical model according to the in situ conditions of the longwall panel.Theoretical analysis was used to reveal the mechanism of stress distribution in the overburden.The modelling results showed that:(1)The major principal stress field is arch-shaped,and the strata overlying both the solid zones and gob constitute a series of coordinated load-bearing structures.The stress increasing zone is like a macro stress arch.High stress is especially concentrated on both shoulders of the arch-shaped structure.The stress concentration of the solid zone in front of the gob is higher than the rear solid zone.(2)The characteristics of the vertical stress field in different regions are significantly different.Stress decreases in the zone above the gob and increases in solid zones on both sides of it.The mechanical analysis show that for a given stratum,the trajectories of principal stress are arch-shaped or inverselyarched,referred to as the‘‘principal stress arch’’,irrespective of its initial breaking or periodic breaking,and determines the fracture morphology.That is,the trajectories of tensile principal stress are inversely arched before the first breaking of the strata,and cause the breaking lines to resemble an inverted funnel.In case of periodic breaking,the breaking line forms an obtuse angle with the advancing direction of the panel.Good agreement was obtained between the results of physical modeling and the theoretical analysis.

Characteristics of electromagnetic vector field generated from rock fracturing

Rock fracturing is often accompanied by electromagnetic phenomenon.As a vector field,in addition to the intensity that is widely concerned,the generated electromagnetic field also has obvious direction-ality.To this end,a set of electromagnetic antennas capable of simultaneous three-axis measurement is used to monitor the electromagnetic vector field generated from rock fracturing based on Brazilian tests.The signal amplitude on each axis can represent the magnitude of actual magnetic flux density component on the three axes.The intensity and directional characteristics of electromagnetic signals received at different positions are studied using vector synthesis.The directionality of electromagnetic radiation measured using a three-axis electromagnetic antenna shows that the direction of the magnetic flux intensity generated by rock fracturing tends to be parallel to the crack surface,and the measured signal intensity is greater in a direction closer to the crack surface.

Development characteristics and quantitative prediction of reservoir fractures in the Chaoyanggou oil field

The Chaoyanggou oil field is a fractured low-permeability reservoir, where the distribution of oil and gas is controlled by the distribution and development of fractures.Based on outcrop, drilling core, thin section and log data, the development characteristics of fractures in this area are described.On this basis, the degree of fracture development was predicted by quantitative analysis of fracture strength and numerical simulation.The result shows that four groups of structural fractures, i.e., in near NS, and EW directions and in due NW and NE directions, were developed in the reservoir, with the nearly NS and EW fractures dominant, which are the along bedding decollement fractures formed by compressive folding action, while low angle shear fractures are related to thrusts.These fractures are mainly formed in the reversed tectonic stage at the end of the Mingshui formation during the Cretaceous period.The degree of fracture development is controlled by such factors as lithology, stratum thickness, faults, folds and depth.The fractures are developed with a clear zonation and are best developed in the northern zone, moderately developed towards the south and poorly developed in the middle zone.These prediction results are in good agreement with interpretation results from logs.

Effects of Magnetic Field on Fracture of Al-Li Alloy Containing Ce rium

The effects of magnetic field on fracture feature and microstructure of Al-Li a lloys containing Ce were investigated. Experiment results show that the fracture features and the microstructures are changed with the magnetic field. The fract ure surface of the alloys is mainly quasi-cleavage without applying magnetic fi eld. With a magnetic field, the fracture of quasi-cleavage changes to more second ary cracks and less quasi-cleavage plates on fracture surface. Grains become thinner and uniform with applying magnetic field. The influence of magnetic f ield on atom diffusion was discussed.

Simulation of size effects by a phase field model for fracture

In phase field fracture models the value of the order parameter distin- guishes between broken and undamaged material. At crack faces the order param- eter interpolates smoothly between these two states of the material, which can be regarded as phases. The crack evolution follows implicitly from the time inte- gration of an evolution equation of the order parameter, which is coupled to the mechanical field equations. Among other phenomena phase field fracture mod- els are able to reproduce crack nucleation in initially sound materials. For a 1D setting it has been shown that crack nucleation is triggered by the loss of stability of the unfractured, spatially homogeneous solution, and that the stability point depends on the size of the considered structure. This work numerically investi- gates to which extend size effects are reproduced by the 2D phase field model. Exemplarily, a finite element study of the hole size effect is performed and the simulation results are compared to exnerimental data.

Evolution of the deformation field and earthquake fracture precursors of strike-slip faults

Seismic hazard analysis is gaining increased attention in the present era because of the catastrophic effects of earthquakes.Scientists always have as a goal to develop new techniques that will help forecast earthquakes before their reoccurrence. In this research,we have performed a shear failure experiment on rock samples with prefabricated cracks to simulate the process of plate movement that forms strike-slip faults. We studied the evolution law of the deformation field to simulate the shear failure experiment, and these results gave us a comprehensive understanding of the elaborate strain distribution law and its formation process with which to identify actual fault zones. We performed uniaxial compression tests on marble slabs with prefabricated double shear cracks to study the distribution and evolution of the deformation field during shear failure. Analysis of the strain field at different loading stages showed that with an increase in the load, the shear strain field initially changed to a disordered-style distribution. Further, the strain field was partially concentrated and finally completely concentrated near the crack and then distributed in the shape of a strip along the crack. We also computed coefficients of variation(CVs) for the physical quantities u, v, and exy, which varied with the load. The CV curves were found to correspond to the different loading stages. We found that at the uniform deformation stage, the CV value was small and changed slowly,whereas at the later nonuniform deformation stage, the CV value increased sharply and changed abruptly. Therefore, the precursor to a rock sample breakdown can be predicted by observing the variation characteristics of CV statistics. The correlation we found between our experimental and theoretical results revealed that our crack evolution and sample deformation results showed good coupling with seismic distribution characteristics near the San Andreas Fault.

Interaction among fractures and stress field computation of fracture systems

The interaction problem among fractures under the action of compressional stress is studied in this paper by using the finite element method and boundary element method respectively.The mechanical criteria which differentiate between the independent fractures and fracture systems and their computation methods are presented in this paper.The proportional conditions between length and spacing of fractures that exist interaction for several kinds of fracture groups of different geometric arrangement are given.The effect of interaction among fractures on the displacement field,stress field and strain energy distribution are computed.The relations between the fracture system of conjugate array and conjugate earthquakes are also discussed in this paper.

Research on evolution of mining pressure field and fracture field and gas emission features

The relation betweenmining pressure field-fracture field and gas emission of working face is analyzed,and the concept that there is a stress point (or strain point) among permeability of coal is presented.It is believed that the mutation of coal permeability caused by the sudden loading or unloading of working face roof as periodic weighting occurs is the main reason that a lot of gas pour into the working face.Based on the above concept,the relation is established among abutment pressure during periodic weighting,permeability of coal seam and gas emission,and relation graph is drawn.Then the loading and unloading features of coal at the moment of fracture and non-fracture of main roof are revealed.And finally it is presented that the process of sudden loading or unloading as periodic weighting occurs plays an important role in rupture propagation of coal,analytical movement of gas and gas emission.

Mining-induced movement properties and fissure time-space evolution law in overlying strata

Mining-induced fracture zone will be produced in the overlying strata after the coal was mined.In this article,the mining-induced deformation of overlying strata and the time-space evolution law of fissure were studied by the methods of physical simulation and field measurement.The results show that bed separation fissure and vertical fissure will appear in the overlying strata above mining face,which form the wedge-shaped fissure zone.The open degree of fissure depends on the size of uncoordinated deformation between neighbor layers,and the absolute strata sinking controls both the width of bed separation zone and the open degree of vertical breakage fissure.At last,the calculating formula was deducted based on theoretical analysis.

Deformation characteristics and reinforcement technology for entry subjected to mining-induced stresses

The entry at Zhangcun coal mine in Lu＇an coal mining area in Shanxi Province suffered from severe mining-induced stresses with the heading face driven oppositely to an adjacent working face. In this paper, the characteristics of deformation and failure of the entry were investigated in terms of the tempo-spatial relations between heading and working faces through field study and numerical modeling. The three-dimensional （3D） finite difference models were built to investigate stresses, displacements and damages in the surrounding rocks of the entry and the working face. The field study includes selection of reinforcing methods and materials, design parameters, and determination of cable prestress. The monitoring data of entry deformation and stress along the cables during every stage were presented. The state of the reinforced entry was evaluated based on the monitoring data. The results demonstrate that before the heading face of the entry crosses the adjacent working face, the influence of advanced abutment pressure caused by adjacent working face upon the entry is not significant. After they cross each other, however, the lateral abutment pressure will have an evident impact on the entry. The displacement rate of the entry will be greatly increased and reaches a certain value within a certain distance between the heading face and the working face. Then, it will increase again with the presence of secondary mining-induced pressure on the entry when the present working face advances. The fully-grouted cable with short length, high strength and high prestress is an effective way to reinforce the entry suffering from severe mining-induced stresses, which greatly reduces the displacement and failure possibility of the entry. Finally, the principles and recommendations for reinforcing design of entries suffering from severe mining-induced stresses were proposed according to field study, numerical modeling and experiences from other coal mines. Problems encountered in field study and suggestions for reinforcement were also discussed.

DAMAGE AND FRACTURE EVALUATION OF GRANULAR COMPOSITE MATERIALS BY DIGITAL IMAGE CORRELATION METHOD

This paper presents the applications of digital image correlation technique to the mesoscopic damage and fracture study of some granular based composite materials including steel- fiber reinforced concrete,sandstone and crystal-polymer composite.The deformation fields of the composite materials resulted from stress localization were obtained by the correlation computation of the surface images with loading steps and thus the related damage prediction and fracture parameters were evaluated.The correlation searching could be performed either directly based on the gray levels of the digital images or from the wavelet transform(WT)coefficients of the transform spectrum.The latter was developed by the authors and showed higher resolution and sensitivity to the singularity detection. Because the displacement components came from the rough surfaces of the composite materials without any coats of gratings or fringes of optical interferometry,both surface profiles and the deformation fields of the composites were visualized which was helpful to compare each other to analyze the damage of those heterogeneous materials.