Quantitative characterization of the brittleness of deep shales by integrating mineral content,elastic parameters,in situ stress conditions and logging analysis

Deep shale reservoirs(3500–4500 m)exhibit significantly different stress states than moderately deep shale reservoirs(2000–3500 m).As a result,the brittleness response mechanisms of deep shales are also different.It is urgent to investigate methods to evaluate the brittleness of deep shales to meet the increasingly urgent needs of deep shale gas development.In this paper,the quotient of Young’s modulus divided by Poisson’s ratio based on triaxial compression tests under in situ stress conditions is taken as SSBV(Static Standard Brittleness Value).A new and pragmatic technique is developed to determine the static brittleness index that considers elastic parameters,the mineral content,and the in situ stress conditions(BIEMS).The coefficient of determination between BIEMS and SSBV reaches 0.555 for experimental data and 0.805 for field data.This coefficient is higher than that of other brittleness indices when compared to SSBV.BIEMS can offer detailed insights into shale brittleness under various conditions,including different mineral compositions,depths,and stress states.This technique can provide a solid data-based foundation for the selection of‘sweet spots’for single-well engineering and the comparison of the brittleness of shale gas production layers in different areas.

Fourth-order phase-field modeling for brittle fracture in piezoelectric materials

Failure analyses of piezoelectric structures and devices are of engineering and scientific significance.In this paper,a fourth-order phase-field fracture model for piezoelectric solids is developed based on the Hamilton principle.Three typical electric boundary conditions are involved in the present model to characterize the fracture behaviors in various physical situations.A staggered algorithm is used to simulate the crack propagation.The polynomial splines over hierarchical T-meshes(PHT-splines)are adopted as the basis function,which owns the C1continuity.Systematic numerical simulations are performed to study the influence of the electric boundary conditions and the applied electric field on the fracture behaviors of piezoelectric materials.The electric boundary conditions may influence crack paths and fracture loads significantly.The present research may be helpful for the reliability evaluation of the piezoelectric structure in the future applications.

Particle Discontinuous Deformation Analysis of Static and Dynamic Crack Propagation in Brittle Material

Crack propagation in brittle material is not only crucial for structural safety evaluation,but also has a wideranging impact on material design,damage assessment,resource extraction,and scientific research.A thorough investigation into the behavior of crack propagation contributes to a better understanding and control of the properties of brittle materials,thereby enhancing the reliability and safety of both materials and structures.As an implicit discrete elementmethod,the Discontinuous Deformation Analysis(DDA)has gained significant attention for its developments and applications in recent years.Among these developments,the particle DDA equipped with the bonded particle model is a powerful tool for predicting the whole process of material from continuity to failure.The primary objective of this research is to develop and utilize the particle DDAtomodel and understand the complex behavior of cracks in brittle materials under both static and dynamic loadings.The particle DDA is applied to several classical crack propagation problems,including the crack branching,compact tensile test,Kalthoff impact experiment,and tensile test of a rectangular plate with a hole.The evolutions of cracks under various stress or geometrical conditions are carefully investigated.The simulated results are compared with the experiments and other numerical results.It is found that the crack propagation patterns,including crack branching and the formation of secondary cracks,can be well reproduced.The results show that the particle DDA is a qualified method for crack propagation problems,providing valuable insights into the fracture mechanism of brittle materials.

A statistical damage-based constitutive model for shearing of rock joints in brittle drop mode

Some rock joints exhibit significant brittleness,characterized by a sharp decrease in shear stress upon reaching the peak strength.However,existing models often fail to accurately represent this behavior and are encumbered by numerous parameters lacking clear mechanical significance.This study presents a new statistical damage constitutive model rooted in both damage mechanics and statistics,containing only three model parameters.The proposed model encompasses all stages of joint shearing,including the compaction stage,linear stage,plastic yielding stage,drop stage,strain softening stage,and residual strength stage.To derive the analytical expression of the constitutive model,three boundary conditions are introduced.Experimental data from both natural and artificial rock joints is utilized to validate the model,resulting in average absolute relative errors ranging from 3%to 8%.Moreover,a comparative analysis with established models illustrates that the proposed model captures stress drop and post-peak strain softening more effectively,with model parameters possessing clearer mechanical interpretations.Furthermore,parameter analysis is conducted to investigate the impacts of model parameters on the curves and unveil the relationship between these parameters and the mechanical properties of rock joints.Importantly,the proposed model is straightforward in form,and all model parameters can be obtained from direct shear tests,thus facilitating the utilization in numerical simulations.

Systematic prediction of the gas content, fractures, and brittleness in fractured shale reservoirs with TTI medium

The main objective is to optimize the development of shale gas-rich areas by predicting seismic sweet spot parameters in shale reservoirs. We systematically assessed the fracture development, fracture gas content, and rock brittleness in fractured gas-bearing shale reservoirs. To better characterize gas-bearing shale reservoirs with tilted fractures, we optimized the petrophysical modeling based on the equivalent medium theory. Based on the advantages of shale petrophysical modeling, we not only considered the brittle mineral fraction but also the combined effect of shale porosity, gas saturation, and total organic carbon(TOC) when optimizing the brittleness index. Due to fractures generally functioning as essential channels for fluid storage and movement, fracture density and fracture fluid identification factors are critical geophysical parameters for fractured reservoir prediction. We defined a new fracture gas indication factor(GFI) to detect fracture-effective gas content. A new linear PP-wave reflection coefficient equation for a tilted transversely isotropic(TTI) medium was rederived, realizing the direct prediction of anisotropic fracture parameters and the isotropic elasticity parameters from offset vector tile(OVT)-domain seismic data. Synthetic seismic data experiments demonstrated that the inversion algorithm based on the L_P quasinorm sparsity constraint and the split-component inversion strategy exhibits high stability and noise resistance. Finally, we applied our new prediction method to evaluate fractured gas-bearing shale reservoirs in the Sichuan Basin of China, demonstrating its effectiveness.

A microscopic approach to brittle creep and time-dependent fracturing of rocks based on stress corrosion model

A brittle creep and time-dependent fracturing process model of rock is established by incorporating the stress corrosion model into discrete element method to analyze the creep behavior and microcrack evolution in brittle rocks at a micro-scale level.Experimental validation of the model is performed,followed by numerical simu-lations to investigate the creep properties and microcrack evolution in rocks under single-stage loading,multi-stage loading,and confining pressure,at various constant stress levels.The results demonstrate that as the stress level increases in single-stage creep simulations,the time-to-failure progressively decreases.The growth of microcracks during uniaxial creep occurs in three stages,with tensile microcracks being predominant and the spatial distribution of microcracks becoming more dispersed at higher stress levels.In multi-stage loadingunloading simulations,microcracks continue to form during the unloading stage,indicating cumulative damage resulting from increased axial stress.Additionally,the creep behaviour of rocks under confining pressure is not solely determined by the magnitude of the confining pressure,but is also influenced by the magnitude of the axial stress.The findings contribute to a better understanding of rock deformation and failure processes under different loading conditions,and they can be valuable for applications in rock mechanics and rock engineering.

Advances in peridynamics modeling of deformation and fracturing of brittle geomaterials

Peridynamics(PD)is an emerging method that establishes a theoretical framework based on non-local theory to describe material mechanical behavior with spatial integral equations.It gives a unified expression of the me-dium including state transformation and characterization in different scales.It is showing great potential for evaluating the complicated mechanical behaviors of brittle solids.In the past two decades,peridynamics has been showing its great potential and advantages in modeling crackings of brittle materials although there are many challenges.The present paper summarizes firstly the theoretical framework and advantages of peridy-namics for modeling fracturing.It introduces then the theoretical improvements to address challenges of peri-dynamics in modeling brittle solid crackings including the release of Poisson ratio limit,different fracture criteria,contact-friction models,coupled constitutive models,and computing accuracy.Afterward,the extension of peridynamics is introduced to the coupled modeling with the other methods such as finite element method,phase field method,and particle-like method before its applications in static and dynamic cracking as well as those under impacts.Meanwhile,some contents that require further exploration are briefly summarized.Finally,the blind spots and future development of peridynamics are analyzed and discussed for the deformation and fracturing modeling of brittle geomaterials.

Analysis of the Application Effect of Structured Healthcare Education in Brittle Diabetic Patients

Objective:To explore the application effect of structured healthcare education in patients with brittle diabetes mellitus.Methods:188 brittle diabetic patients admitted to our hospital from May 2021 to December 2023 were selected as the study subjects,and were divided into the control group(n=94)and the observation group(n=94)according to the random number table method.The control group used conventional nursing intervention and the observation group used structured healthcare education.The general information,glycemic indexes,self-efficacy,compliance,and nursing satisfaction of patients in the two groups were observed.Results:There was no statistical significance in the basic information of the two groups of patients(P>0.05);after the intervention,the fasting plasma glucose,2-hour postprandial blood glucose,and HbA1c of the patients in the observation group were lower than those of the control group(P<0.001);after the intervention,the self-efficacy scores of the patients in the two groups increased,and the scores of the observation group were significantly higher than those of the control group(P<0.001);the total adherence rate of the patients in the observation group(90/95.75%)was significantly higher than that of the control group(80/90.10%)(χ^(2)=6.144,P<0.05);and the total satisfaction rate of patients in the observation group(92/97.87%)was significantly higher than that of the control group(78/82.98%)(χ^(2)=12.042,P<0.05).Conclusion:In patients with brittle diabetes mellitus,structured healthcare education can effectively control patients’blood glucose levels,improve patients’self-efficacy and adherence,and enhance patient satisfaction.

An improved method to calculate the rock brittleness index PEECR based on linear energy storage law

The peak elastic strain energy consumption ratio(PEECR)is a rock brittleness index proposed by Gong and Wang.In the present study,based on the linear energy storage law of rock under triaxial compression,a new method was proposed to calculate the PEECR.The PEECR uses a simplified method to calculate the peak elastic strain energy.To solve this problem accurately,triaxial cyclic loading-unloading compression tests were carried out on shale.Strain energy parameters were calculated from the test curves.The results show that there is a linear relationship between the elastic strain energy and input strain energy,indicating that the linear energy storage law in rock is applicable to triaxial compression state.The universality of the linear energy storage law of rock under triaxial compression is also verified by the data in the published literature.Then,the peak elastic strain energy can be accurately determined using the linear energy storage law,and the PEECR is improved based on this.Finally,the PEECR and the improved PEECR were compared using the triaxial cyclic loading-unloading compression tests on three rocks(shale,red sandstone and granite),and the improved PEECR was compared with 11 existing energy-based brittleness indexes.The results show that the improved PEECR can further reflect the rock brittleness more accurately.

Anomalous yield and intermediate temperature brittleness behaviors of directionally solidified nickel-based superalloy

A nickel-based superalloy with good corrosion resistance was fabricated by directional solidification, and its microstructure and tensile properties at elevated temperatures were investigated. Microstructure observations reveal that the γ＇ precipitates are arrayed in the y matrix regularly with some MC, Ni5Hf and M3B2 particles distributed along the grain boundary. The tensile tests exhibit that the tensile properties depend on temperature significantly and demonstrate obvious anomalous yield and intermediate-temperature brittleness （ITB） behavior. Below 650℃, the yield strength decreases slightly but the ultimate tensile strength almost has no change. When the temperature is between 650 ℃ and 750 ℃, the yield and ultimate tensile strengths rise rapidly, and after then they both decrease gradually with temperature increasing further. The elongation has its minimum value at about 700 ℃. The TEM examination exhibits that sharing of the γ＇ by dislocation is almost the main deformation mechanism at low temperatures, but the γ＇ by-pass dominates the deformation at high temperatures. The transition temperature from shearing to by-pass should be around 800 ℃. The anomalous yield and intermediate-temperature brittleness behaviors should be attributed to the high content of γ＇. In addition, the carbides and eutectic structure also contribute some to the ITB behaviors of the alloy.

Thermal-hydro-mechanical coupling stress intensity factor of brittle rock

A new calculation formula of THM coupling stress intensity factor was derived by the boundary collocation method, in which an additional constant stress function was successfully introduced for the cracked specimen with hydraulic pressure applied on its crack surface. Based on the newly derived formula, THM coupling fracture modes （including tensile, shear and mixed fracture mode） can be predicted by a new fracture criterion of stress intensity factor ratio, where the maximum axial load was measured by self-designed THM coupling fracture test. SEM analyses of THM coupling fractured surface indicate that the higher the temperature and hydraulic pressure are and the lower the confining pressure is, the more easily the intergranular （tension） fracture occurs. The transgranular （shear） fracture occurs in the opposite case while the mixed-mode fracture occurs in the middle case. The tested THM coupling fracture mechanisms are in good agreement with the predicted THM coupling fracture modes, which can verify correction of the newly-derived THM coupling stress intensity factor formula.

Evaluation of Urban Village Renovation System in Xi’an City of China Based on Brittleness Analysis

Renovation system of urban villages in Xi'an City was evaluated. Influence factors of urban village renovation were analyzed on the basis of brittleness theory, and an evaluation index system established through multi-level inconsistency decomposing. By incorporating the catastrophe theory with fuzzy mathematical theory, the mathematic model was created, and catastrophe membership function was obtained as well as evaluation results. Policies for the renovation of urban villages and new direction of the renovation were interpreted. The application case proved that catastrophe progression method was objective and effective and it could provide new concepts for the evaluation and adjustment of urban village renovation. Moreover, application of brittleness theory in the research on urban village renovation is of great instruction and reference value for the present urban construction.

APPLICATION OF DIAMOND TWIST DRILL FOR DRILLING HARD-BRITTLE MATERIALS

A new conception, which combines the advantages of both twist drill and diamond grit, is proposed to develop a new tool for drilling hard brittle materials. The manufacturing process of the drill is introduced, and drilling experiments are carried out by using of the drill developed. As a result, not only it can drill holes with a high efficiency, but also a good quality of hole inlet and outlet can be obtained for such materials as glasses, marble, granite, Al 2O 3, etc. The prospect in practical application of the technique developed is also discussed.

Brittleness index and seismic rock physics model for anisotropic tight-oil sandstone reservoirs

Brittleness analysis becomes important when looking for sweet spots in tightoil sandstone reservoirs. Hence, appropriate indices are required as accurate brittleness evaluation criteria. We construct a seismic rock physics model for tight-oil sandstone reservoirs with vertical fractures. Because of the complexities in lithology and pore structure and the anisotropic characteristics of tight-oil sandstone reservoirs, the proposed model is based on the solid components, pore connectivity, pore type, and fractures to better describe the sandstone reservoir microstructure. Using the model, we analyze the brittleness sensitivity of the elastic parameters in an anisotropic medium and establish a new brittleness index. We show the applicability of the proposed brittleness index for tight-oil sandstone reservoirs by considering the brittleness sensitivity, the rock physics response characteristics, and cross-plots. Compared with conventional brittleness indexes, the new brittleness index has high brittleness sensitivity and it is the highest in oil-bearing brittle zones with relatively high porosity. The results also suggest that the new brittleness index is much more sensitive to elastic properties variations, and thus can presumably better predict the brittleness characteristics of sweet spots in tight-oil sandstone reservoirs.

Burial depth interval of the shale brittle–ductile transition zone and its implications in shale gas exploration and production

Brittleness and ductility of shale are closely related to shale gas exploration and production. How to predict brittleness and ductility of shale is one of the key issues in the study of shale gas preservation and hydraulic fracturing treatments. The magnitude of shale brittleness was often determined by brittle mineral content(for example, quartz and feldspars) in shale gas exploration.However, the shale brittleness is also controlled by burial depth. Shale brittle/ductile properties such as brittle, semibrittle and ductile can mutually transform with burial depth variation. We established a work flow of determining the burial depth interval of brittle–ductile transition zone for a given shale. Two boundaries were employed to divide the burial depth interval of shale brittle/ductile properties. One is the bottom boundary of the brittle zone(BZ), and the other is the top boundary of the ductile zone(DZ). The brittle–ductile transition zone(BDTZ) is between them.The bottom boundary of BZ was determined by the overconsolidation ratio(OCR) threshold value combined with pre-consolidation stress which the shale experienced over geological time. The top boundary of DZ was determined based on the critical confining pressure of brittle–ductile transition. The OCR threshold value and the critical confining pressure were obtained from uniaxial strain andtriaxial compression tests. The BZ, DZ and BDTZ of the Lower Silurian Longmaxi shale in some representative shale gas exploration wells in eastern Sichuan and western Hubei areas were determined according to the above work flow. The results show that the BZ varies with the maximum burial depth and the DZ varies with the density of the overlying rocks except for the critical confining pressure.Moreover, the BDTZ determined by the above work flow is probably the best burial depth interval for marine shale gas exploration and production in Southern China. Shale located in the BDTZ is semi-brittle and is not prone to be severely naturally fractured but likely to respond well to hydraulic fracturing. The depth interval of BDTZ determined by our work flow could be a valuable parameter of shale gas estimation in geology and engineering.

Construction of a novel brittleness index equation and analysis of anisotropic brittleness characteristics for unconventional shale formations

The brittleness prediction of shale formations is of interest to researchers nowadays.Conventional methods of brittleness prediction are usually based on isotropic models while shale is anisotropic.In order to obtain a better prediction of shale brittleness,our study firstly proposed a novel brittleness index equation based on the Voigt–Reuss–Hill average,which combines two classical isotropic methods.The proposed method introduces upper and lower brittleness bounds,which take the uncertainty of brittleness prediction into consideration.In addition,this method can give us acceptable predictions by using limited input values.Secondly,an anisotropic rock physics model was constructed.Two parameters were introduced into our model,which can be used to simulate the lamination of clay minerals and the dip angle of formation.In addition,rock physics templates have been built to analyze the sensitivity of brittleness parameters.Finally,the effects of kerogen,pore structure,clay lamination and shale formation dip have been investigated in terms of anisotropy.The prediction shows that the vertical/horizontal Young’s modulus is always below one while the vertical/horizontal Poisson’s ratio(PR)can be either greater or less than 1.Our study finds different degrees of shale lamination may be the explanation for the random distribution of Vani(the ratio of vertical PR to horizontal PR).

Rotary ultrasonic-assisted milling of brittle materials

In order to improve the machining efficiency of ultrasonic milling,the easiest and most effective approach was started with the improvement of tool design.The main objective of this research was to utilize rotary ultrasonic machining (RUM's) effectiveness in removing brittle materials to extend the applications of this independent,innovative manufacturing method (self-driving rotary ultrasonic machining),and to experimentally investigate its milling application on brittle materials.The designed tool was used in the conjunction with previously established RUM machine tools,and glass was selected as workpiece for experiments.The interrelationship between feed rate and depth of cut was discussed.By measuring the surface roughness of workpiece,the overall efficacy of utilizing RUM for milling was evaluated and presented.Ultrasonic assisted milling results in the reduction of milling resistance,which leads to a greater process rate.

Discrete element modeling on the crack evolution behavior of brittle sandstone containing three fissures under uniaxial compression

Based on experimental restilts of brittle, intact sandstone under uniaxial compression, the micro-parameters were firstly confirmed by adopting particle flow code （PFC2D）. Then, the validation of the simulated models were cross checked with the experimental results of brittle sandstone containing three parallel fissures under uniaxial compression. The simulated results agreed very well with the experimental results, including the peak strength, peak axial strain, and ultimate failure mode. Using the same micro- parameters, the numerical models containing a new geometry of three fissures are constructed to investigate the fissure angle on the fracture mechanical behavior of brittle sandstone under uniaxial compression. The strength and deformation parameters of brittle sandstone containing new three fissures are dependent to the fissure angle. With the increase of the fis- sure angle, the elastic modulus, the crack damage threshold, and the peak strength of brittle sandstone containing three fissures firstly increase and secondly decrease. But the peak axial strain is nonlinearly related to the fissure angle. In the entire process of deformation, the crack initiation and propagation behavior of brittle sandstone containing three fissures under uniaxial compression are investigated with respect to the fissure angle. Six different crack coalescence modes are identified for brittle sandstone containing three fissures under uniaxial compression. The influence of the fissure angle on the length of crack propagation and crack coalescence stress is evaluated. These investigated conclusions are very important for ensuring the stability and safety of rock engineering with intermittent structures.

Pre-stack basis pursuit seismic inversion for brittleness of shale

Brittleness of rock plays a significant role in exploration and development of shale gas reservoirs. Young＇s modulus and Poisson＇s ratio are the key param- eters for evaluating the rock brittleness in shale gas exploration because their combination relationship can quantitatively characterize the rock brittleness. The high- value anomaly of Young＇s modulus and the low-value anomaly of Poisson＇s ratio represent high brittleness of shale. The technique of pre-stack amplitude variation with angle inversion allows geoscientists to estimate Young＇s modulus and Poisson＇s ratio from seismic data. A model constrained basis pursuit inversion method is proposed for stably estimating Young＇s modulus and Poisson＇s ratio. Test results of synthetic gather data show that Young＇s modulus and Poisson＇s ratio can be estimated reasonably. With the novel method, the inverted Young＇s modulus and Poisson＇s ratio of real field data focus the layer boundaries better, which is helpful for us to evaluate the brittleness of shale gas reservoirs. The results of brittleness evaluation show a good agreement with the results of well interpretation.

A NEW DAMAGE MODEL FOR MICROCRACK-WEAKENED BRITTLE SOLIDS

In the present paper, a micromechanically based damage model for microcrack-weakened solids is developed. The concept of the domain of microcrack growth (DMG) is defined and used to describe the damage state and the anisotropic properties of brittle materials. After choosing an appropriate fracture criterion of microcrack, we obtain the analytical expression of DMG under a monotonically in- creasing proportional plane stress. Under a complex loading path, the evolution equation of DMG and the overall effective compliance tensor of damaged materials are given.