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.

Characterization and evaluation of brittleness of deep bedded sandstone from the perspective of the whole life-cycle evolution process

The quantitative determination and evaluation of rock brittleness are crucial for the estimation of excavation efficiency and the improvement of hydraulic fracturing efficiency.Therefore,a“three-stage”triaxial loading and unloading stress path is designed and proposed.Subsequently,six brittleness indices are selected.In addition,the evolution characteristics of the six brittleness indices selected are characterized based on the bedding effect and the effect of confining pressure.Then,the entropy weight method(EWM)is introduced to assign weight to the six brittleness indices,and the comprehensive brittleness index Bcis defined and evaluated.Next,the new brittleness classification standard is determined,and the brittleness differences between the two stress paths are quantified.Finally,compared with the previous evaluation methods,the rationality of the proposed comprehensive brittleness index Bcis also verified.These results indicate that the proposed brittleness index Bccan reflect the brittle characteristics of deep bedded sandstone from the perspective of the whole life-cycle evolution process.Accordingly,the method proposed seems to offer reliable evaluations of the brittleness of deep bedded sandstone in deep engineering practices,although further validation is necessary.

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.

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.

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).

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.

GRAIN BOUNDARY SEGREGATION AND INTERGRANULAR BRITTLENESS IN HIGH STRENGTH ALUMINIUM ALLOY

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Rock brittleness indices and their applications to different fields of rock engineering:A review

Brittleness is an important parameter controlling the mechanical behavior and failure characteristics of rocks under loading and unloading conditions,such as fracability,cutability,drillability and rockburst proneness.As such,it is of high practical value to correctly evaluate rock brittleness.However,the definition and measurement method of rock brittleness have been very diverse and not yet been standardized.In this paper,the definitions of rock brittleness are firstly reviewed,and several representative definitions of rock brittleness are identified and briefly discussed.The development and role of rock brittleness in different fields of rock engineering are also studied.Eighty brittleness indices publicly available in rock mechanics literature are compiled,and the measurement method,applicability and limitations of some indices are discussed.The results show that(1)the large number of brittleness indices and brittleness definitions is attributed to the different foci on the rock behavior when it breaks;(2)indices developed in one field usually are not directly applicable to other fields;and(3)the term“brittleness”is sometimes misused,and many empirically-obtained brittleness indices,which lack theoretical basis,fail to truly reflect rock brittleness.On the basis of this review,three measurement methods are identified,i.e.(1)elastic deformation before fracture,(2)shape of post-peak stressestrain curves,and(3)methods based on fracture mechanics theory,which have the potential to be further refined and unified to become the standard measurement methods of rock brittleness.It is highly beneficial for the rock mechanics community to develop a robust definition of rock brittleness.This study will undoubtedly provide a comprehensive timely reference for selecting an appropriate brittleness index for their applications,and will also pave the way for the development of a standard definition and measurement method of rock brittleness in the long term.

The construction of shale rock physics model and brittleness prediction for high-porosity shale gas-bearing reservoir

Due to the huge differences between the unconventional shale and conventional sand reservoirs in many aspects such as the types and the characteristics of minerals,matrix pores and fluids,the construction of shale rock physics model is significant for the exploration and development of shale reservoirs.To make a better characterization of shale gas-bearing reservoirs,we first propose a new but more suitable rock physics model to characterize the reservoirs.We then use a well A to demonstrate the feasibility and reliability of the proposed rock physics model of shale gas-bearing reservoirs.Moreover,we propose a new brittleness indicator for the high-porosity and organic-rich shale gas-bearing reservoirs.Based on the parameter analysis using the constructed rock physics model,we finally compare the new brittleness indicator with the commonly used Young’s modulus in the content of quartz and organic matter,the matrix porosity,and the types of filled fluids.We also propose a new shale brittleness index by integrating the proposed new brittleness indicator and the Poisson’s ratio.Tests on real data sets demonstrate that the new brittleness indicator and index are more sensitive than the commonly used Young’s modulus and brittleness index for the high-porosity and high-brittleness shale gas-bearing reservoirs.

Brittleness research on complex system based on brittle link entropy

As the scale of complex system is growing larger and larger, interferences from internal and outer system can result in the collapse of one subsystem in a complex system. They will not only make one subsystem collapse but also influence the other subsystems. Moreover, the whole complex system can collapse consequently. The mechanism of collapse of complex system is due to the brittleness of complex system that is presented and argued as the basic characteristic in this paper. It is the brittleness link entropy between subsystems that leads to the collapse of whole system. Effective ways that can be adopted to reduce the brittleness entropy can see the successful control of brittleness.

Coupling Analysis of Disaster Bearing Capacity of Urban Lifeline System Based on Brittleness Entropy

Urban or regional disaster bearing capacity mainly depends on the disaster bearing capacity of lifeline systems. In the analysis of disaster bearing capacity evaluation of lifeline system, we should not only investigate the complexity, balance and reliability of network characteristics, but also consider the relation between each subsystem. A new brittleness entropy of city disaster vulnerability associated coupling analysis method is proposed based on the brittleness of complex system theory. Correlation characteristics are reflected and evaluated in the brittle link entropy and the whole lifeline system, and then the vulnerability of city lifeline system can be quantified in flood scenarios. As a result of the coupling analysis and calculation, power system has the greatest effect among other subsystems. Because the key factors and influence of water supply system are uncertainties, the water supply system work or supply should be restored first after the disaster. The results show that the method can provide the basis for the optimization of system management, and control the repair work after disaster and coordination between subsystems.

Research on basic characteristics of complex system brittleness

Tbe goal of this paper is to research one new characteristic of complex system. Brittleness, which is one new characteritic of complex system, is presented in this paper. The linguistic and qualitative descriptions of complex system are also given in this paper.Otherwise, the qualitative description of complex system is presented at first. On the basis of analyzing the existing brittleness problems, linguistic description and mathematic description of brittleness are given as well. Three kinds of phenomena to judge brittleness of complex system are also given, based on catastrophe theory. Basic characteristics of brittleness are given on the basis of its mathematic description. Two critical point sets are defined by using catastrophe theory. The definition of brittleness and its related theory can serve the control of complex system, and provide theoretical basis for the design and control of complex system.

Brittleness characteristics of tight oil siltstones

岩石易碎物直接影响水库断裂，它的评估为建立是必要的在水库改过以前折断条件。动态、静态的易碎物数据在 Songliao 盆从 Qingshankou 形成的 siltstones 被收集。易碎塑料的转变基于压力紧张关系被调查。结果建议静态的有弹性的参数计算的易碎物索引否定地与压力落下系数和定义为规范的幼仔模量和泊松比率的一般水准的易碎物索引 B 2, 被相关，强烈与压力落下被相关。易碎物索引 B 2, 幼仔模量，和泊松比率与易碎的矿物质内容相关；也就是说石英，碳酸盐，和黄铁矿。我们也基于索引 B 2 调查了在毛孔液体和孔和动态易碎的特征之间的关联。毛孔液体增加岩石和还原剂易碎物的粘性；而且与增加孔，岩石易碎物减少。浸透气体的 siltstone 易碎物索引在浸透油或浸透水的 siltstone 比那高；在浸透油、浸透水的 siltstone 的易碎物索引的差别是很小的。由比较岩石力学和超声的实验，我们比从超声的实验获得了的发现从岩石力学实验获得的易碎物索引小；不过，两个都与象他们的差别一样增加孔减少。没有影响他们，超声的波浪通过岩石标本宣传，而岩石力学实验是破坏的并且导致 microcracking 和孔增加；因而，低孔的岩石的易碎物被内部 microcrack 系统的形成影响。

Brittleness index predictions from Lower Barnett Shale well-log data applying an optimized data matching algorithm at various sampling densities

The capability of accurately predicting mineralogical brittleness index (BI) from basic suites of well logs is desirable as it provides a useful indicator of the fracability of tight formations.Measuring mineralogical components in rocks is expensive and time consuming.However,the basic well log curves are not well correlated with BI so correlation-based,machine-learning methods are not able to derive highly accurate BI predictions using such data.A correlation-free,optimized data-matching algorithm is configured to predict BI on a supervised basis from well log and core data available from two published wells in the Lower Barnett Shale Formation (Texas).This transparent open box (TOB) algorithm matches data records by calculating the sum of squared errors between their variables and selecting the best matches as those with the minimum squared errors.It then applies optimizers to adjust weights applied to individual variable errors to minimize the root mean square error (RMSE)between calculated and predicted (BI).The prediction accuracy achieved by TOB using just five well logs (Gr,ρb,Ns,Rs,Dt) to predict BI is dependent on the density of data records sampled.At a sampling density of about one sample per 0.5 ft BI is predicted with RMSE~0.056 and R^(2)~0.790.At a sampling density of about one sample per0.1 ft BI is predicted with RMSE~0.008 and R^(2)~0.995.Adding a stratigraphic height index as an additional (sixth)input variable method improves BI prediction accuracy to RMSE~0.003 and R^(2)~0.999 for the two wells with only 1 record in 10,000 yielding a BI prediction error of>±0.1.The model has the potential to be applied in an unsupervised basis to predict BI from basic well log data in surrounding wells lacking mineralogical measurements but with similar lithofacies and burial histories.The method could also be extended to predict elastic rock properties in and seismic attributes from wells and seismic data to improve the precision of brittleness index and fracability mapping spatially.

Effect of RE on the Brittleness of Electrolytic Boronization Coating

The electrolytic coatings of boron and RE-boron on medium carbon steel are carried out in molten salt mix- tures respectively.The brittleness of both coatings has been measured by using sound-emission with the method of three point bending.Results show that the brittleness of electrolytic boronization coating can be obviously de- creased by addition of RE elements.Meanwhile,the shape of crack and the solid solubility of RE in boride and α-Fe phase are determined,and the effect of RE on the lattice constant of Fe_2B is discussed.From these experi- ments,the authors explain the cause of the brittleness decreasing of electrolytic boronization coating.

ATOMIC STATES AND BRITTLENESS OF hcp Ti_3Al-ORDERED-TYPE ALLOYS

On the basis of the framework of systematic science of alloys （SSA）, the basic information such as states, volumes, and potential energies of characteristic atoms in hcp Ti-Al system have been determined. The average atomic state of the hcp Ti3Al compound consisting of ψ4^Ti and ψ0^Al atoms is 0.75[Ar] （3dn）^0.573 （3dc）^2.1685 （4sc）^0.972 （4sf）^0.3093 ＋ 0.25[Ne] （3sc）^1.32 （3pc）^1.19 （3sf ＋ 3pf）^0.49. The brittleness of the ordered hcp Ti3Al compound has been discussed considering the fundamental factors, which are atomic states, bond networks, potential energy wave planes, and the ratio xTi/xAl. The existence of more pc and more dc directional electrons in the hcp Ti3Al compound lead to considerable brittleness; From bond networks and potential energy wave planes, the hcp Ti3Al compound has poorer ductility than the pure hcp Ti metal and the pure fcc Al metal; The Al-rich hcp Ti3Al ordered type alloys have poorer ductility than the Ti-rich hcp Ti3Al ordered type alloys.

Cascading failure prevention of complex systems based on brittleness entropy game

A non-cooperative game model based on brittleness entropy is formulated for preventing cascading failure of complex systems.Subsystems of a complex system are mapped to the players of the game.The influence of collapsed subsystems to other subsystems is also taken into account in the definition of payoff function except for their own entropy increase.This influence is named brittleness entropy.Each player has two optional strategies;rational for negative entropy and irrational for negative entropy.The model is designed to identify the players who select an irrational strategy for negative entropy.The players who select the irrational strategy for negative entropy continue to compete for negative entropy after the recovery of ordered state and make other subsystems can' t get enough negative entropy to reduce entropy increase.It leads to cascading failure of the complex system in the end.Genetic algorithm is used to seek the solution of game model,and the simulation result verifies the effectiveness of the proposed model.The model provides a new way to prevent cascading failure of complex systems.

CRITICAL NOTCH(CRACK)SIZE AS A CHARACTERISTIC PARAMETER EVALUATING CRYOGENIC BRITTLENESS IN LOW CARBON STEEL

The effect of notch depth on the cryogenic fracture behavior has been studied using a low car- bon steel.An analysis was made for the fracture features at T_c~*(cryogenic brittleness-char- acteristic temperature)at which the facture load reaehes a valley value.Furthermore,accord- ing to the experimental results and engineering design practice,a concept of critical notch (crack)'size for cryogenic brittleness,a_c,as well as its limit value a_c~*,was put forward and recommended to be a basic characteristic parameter for controlling the brittleness. Mathematical derivation was carried out to give the expression of a_c and a_c~*,the reliability of which was verified by the modeling tests under both static and cyclic loading conditions.

Brittleness Generation Mechanism and Failure Model of High Strength Lightweight Aggregate Concrete

The brittleness generation mechanism of high strength lightweight aggregate con-crete(HSLWAC) was presented, and it was indicated that lightweight aggregate was the vulnerable spot, initiating brittleness. Based on the analysis of the brittleness failure by the load-deflection curve, the brittleness presented by HSLWAC was more prominent compared with ordinary lightweight aggregate concrete of the same strength grade. The model of brittleness failure was also established.