ULTIMATE LOAD-BEARING CAPACITY OF CYLINDER DERIVED FROM AUTOFRETTAGE UNDER IDEAL CONDITION

According to the basic theory on autofrettage and according to the 4th strength theory, several parameters and their relations are studied under ideal condition, including σej/σy, the equivalent stress of total stresses at elastoplastic juncture; σei/σy, the equivalent stress of total stresses at inside surface; σej＇/σy, the equivalent stress of residual stresses at elastoplastic juncture; σei＇/σy, the equivalent stress of residual stresses at inside surface; and p/σy, load-bearing capacity of an autofrettaged cylinder. By theoretical study on relations between the parameters, noticeable results and laws are achieved： to satisfy ｜σei＇｜=σy. the relation between kj and k is, k^2lnkj^2-k^2-kj^2＋2=0, when k→∞, kj = √e = 1.648 72, as based on the 3rd strength theory, where k is the outside/inside radius ratio of a cylinder, kj is the ratio of elastoplastic juncture radius to inside radius of a cylinder; If the plastic region covers the whole wall of a cylinder, for compressive yield not to occur after removing autofrettage pressure, the ultimate k is k=-2.218 46 as based on the 3rd strength theory; With k=2.218 46, a cylinder＇s ultimate load-bearing capacity equals its entire yield pressure, or p/σy=21nk/√3; The maximum and optimum load-bearing capacity of an autofrettaged cylinder is just 2 times the loading which an unautofrettaged cylinder can bear elastically, or p/σy=2（k^2-1）/√3 k^2, and the limit of the load-bearing capacity of an autofrettaged cylinder is also just 2 times that of an unautofrettaged cylinder. The conclusions are the same as based on the 3rd strength theory, but some equations are different from each other.

Effect of Optimum Plastic Depth on Stresses and Load-bearing Capacity of Autofrettaged Cylinder

Autofrettage is an effective measure to even distribution of stresses and raise load-bearing capacity for （ultra-）high pressure apparatus. Currently, the research on autofrettage has focused mostly on specific engineering problems, while general theoretical study is rarely done. To discover the general law contained in autofrettage theory, by the aid of the authors’ previous work and according to the third strength theory, theoretical problems about autofrettage are studied including residual stresses and their equivalent stress, total stresses and their equivalent stress, etc. Because of the equation of optimum depth of plastic zone which is presented in the authors’ previous work, the equations for the residual stresses and their equivalent stress as well as the total stress and their equivalent stress are simplified greatly. Thus the law of distribution of the residual stresses and their equivalent stress as well as the total stress and their equivalent stress and the varying tendency of these stresses are discovered. The relation among various parameters are revealed. The safe and optimum load-bearing conditions for cylinders are obtained. According to the results obtained by theoretical analysis, it is shown that if the two parameters, namely ratio of outside to inside radius, k, and depth of plastic zone, kj, meet the equation of optimum depth of plastic zone, when the pressure contained in an autofrettaged cylinder is lower than two times the initial yield pressure of the unautofrettaged cylinder, the equivalent residual stress and the equivalent total stress at the inside surface as well as the elastic-plastic juncture of a cylinder are lower than yield strength. When an autofrettaged cylinder is subjected to just two times the initial yield pressure of the unautofrettaged cylinder, the equivalent total stress within the whole plastic zone is just identically equal to the yield strength, or it is a constant. The proposed research theoretically depicts the stress state of ultra-）high pressure autofrettaged cylinder more accurately and more reasonably and provides the reference for design of （ultra-）high pressure apparatus.

A comparison study on structure-function relationship of polysaccharides obtained from sea buckthorn berries using different methods:antioxidant and bile acid-binding capacity

In this study,the structural characters,antioxidant activities and bile acid-binding ability of sea buckthorn polysaccharides(HRPs)obtained by the commonly used hot water(HRP-W),pressurized hot water(HRP-H),ultrasonic(HRP-U),acid(HRP-C)and alkali(HRP-A)assisted extraction methods were investigated.The results demonstrated that extraction methods had significant effects on extraction yield,monosaccharide composition,molecular weight,particle size,triple-helical structure,and surface morphology of HRPs except for the major linkage bands.Thermogravimetric analysis showed that HRP-U with filamentous reticular microstructure exhibited better thermal stability.The HRP-A with the lowest molecular weight and highest arabinose content possessed the best antioxidant activities.Moreover,the rheological analysis indicated that HRPs with higher galacturonic acid content and molecular weight showed higher viscosity and stronger crosslinking network(HRP-C,HRP-W and HRP-U),which exhibited stronger bile acid binding capacity.The present findings provide scientific evidence in the preparation technology of sea buckthorn polysaccharides with good antioxidant and bile acid binding capacity which are related to the structure affected by the extraction methods.

Effect of Trimetazidine on Functional Capacity in Patient with Ischaemic Cardiomyopathy (TOFCAPI)

Objective: This study aimed to evaluate the efficacy of trimetazidine on exercise capacity via a six-minute walk test in patients with ischaemic cardiomyopathy and also evaluate the effect of trimetazidine on left ventricular function via echocardiography in the same population. Methods: This prospective observational study, conducted at the National Institute of Cardiovascular Diseases in Dhaka, Bangladesh, enrolled 200 patients with ischaemic cardiomyopathy and a depressed left ventricular ejection fraction (LVEF Results: In this study (n = 200) of ischaemic cardiomyopathy patients, the mean age was 58 years, with 76% of the patients being male. All study subjects received GDMT (Guideline-Directed Medical Therapy) for angina and heart failure. Those who received the modified released form of trimetazidine developed lesions during the 1st and 2nd follow-ups, during which the LVEF, LVIDd, and six-minute walk distance significantly improved (p Conclusion: The findings of the present study demonstrated that the addition of modified-release trimetazidine to GDMT can improve exercise capacity and left ventricular function in patients with ischaemic cardiomyopathy.

Functional Capacity of Patients with Venous Thromboembolic Disease Six to Twelve Months after Treatment

Background: Venous thromboembolism (VTE) is among the leading causes of hospital-related disability-adjusted life years lost. We aimed to determine the prevalence and determinants of functional capacity impairment six to twelve months after an acute VTE event. Methods: This was a cross-sectional study conducted between January and April 2021 in two referral hospitals of Yaoundé, including consenting adult patients admitted to these hospitals six to twelve months ago for VTE. We excluded dead patients and those with any comorbidity or symptoms limiting physical activity. The functional outcome was assessed with the six-minute walk test. Functional capacity impairment was defined as walking distance lower than the expected value. Results: We included 27 cases in this study with a mean age of 53.2 ± 14.4 years. The prevalence of functional capacity impairment was 29.6% (95% CI: 14.8 - 48.1). Factors associated with poor functional outcome were obesity (OR: 59.5;95% CI: 4.6 - 767.2;p - 207.4;p = 0.017), massive PE (OR: 30;95% CI: 2.5 - 354;p = 0.004), and poor adherence to treatment (OR: 30.3;95% CI: 2.5 - 333.3;p = 0.004). Conclusion: Functional capacity impairment is common in the medium-term after VTE and factors associated with this poor outcome are obesity, the severity of the VTE, and poor adherence to treatment.

Effect of speed humps on instantaneous traffic emissions in a microscopic model with limited deceleration capacity

As a common transportation facility, speed humps can control the speed of vehicles on special road sections to reduce traffic risks. At the same time, they also cause instantaneous traffic emissions. Based on the classic instantaneous traffic emission model and the limited deceleration capacity microscopic traffic flow model with slow-to-start rules, this paper has investigated the impact of speed humps on traffic flow and the instantaneous emissions of vehicle pollutants in a single lane situation. The numerical simulation results have shown that speed humps have significant effects on traffic flow and traffic emissions. In a free-flow region, the increase of speed humps leads to the continuous rise of CO_(2), NO_X and PM emissions. Within some density ranges, one finds that these pollutant emissions can evolve into some higher values under some random seeds. Under other random seeds, they can evolve into some lower values. In a wide moving jam region, the emission values of these pollutants sometimes appear as continuous or intermittent phenomenon. Compared to the refined Na Sch model, the present model has lower instantaneous emissions such as CO_(2), NO_X and PM and higher volatile organic components(VOC) emissions. Compared to the limited deceleration capacity model without slow-to-start rules, the present model also has lower instantaneous emissions such as CO_(2), NO_X and PM and higher VOC emissions in a wide moving jam region. These results can also be confirmed or explained by the statistical values of vehicle velocity and acceleration.

Prediction of Damping Capacity Demand in Seismic Base Isolators via Machine Learning

Base isolators used in buildings provide both a good acceleration reduction and structural vibration control structures.The base isolators may lose their damping capacity over time due to environmental or dynamic effects.This deterioration of them requires the determination of the maintenance and repair needs and is important for the long-termisolator life.In this study,an artificial intelligence prediction model has been developed to determine the damage and maintenance-repair requirements of isolators as a result of environmental effects and dynamic factors over time.With the developed model,the required damping capacity of the isolator structure was estimated and compared with the previously placed isolator capacity,and the decrease in the damping property was tried to be determined.For this purpose,a data set was created by collecting the behavior of structures with single degrees of freedom(SDOF),different stiffness,damping ratio and natural period isolated from the foundation under far fault earthquakes.The data is divided into 5 different damping classes varying between 10%and 50%.Machine learning model was trained in damping classes with the data on the structure’s response to random seismic vibrations.As a result of the isolator behavior under randomly selected earthquakes,the recorded motion and structural acceleration of the structure against any seismic vibration were examined,and the decrease in the damping capacity was estimated on a class basis.The performance loss of the isolators,which are separated according to their damping properties,has been tried to be determined,and the reductions in the amounts to be taken into account have been determined by class.In the developed prediction model,using various supervised machine learning classification algorithms,the classification algorithm providing the highest precision for the model has been decided.When the results are examined,it has been determined that the damping of the isolator structure with the machine learning method is predicted successfully at a level exceeding 96%,and it is an effective method in deciding whether there is a decrease in the damping capacity.

Battery pack capacity estimation for electric vehicles based on enhanced machine learning and field data

Accurate capacity estimation is of great importance for the reliable state monitoring,timely maintenance,and second-life utilization of lithium-ion batteries.Despite numerous works on battery capacity estimation using laboratory datasets,most of them are applied to battery cells and lack satisfactory fidelity when extended to real-world electric vehicle(EV)battery packs.The challenges intensify for large-sized EV battery packs,where unpredictable operating profiles and low-quality data acquisition hinder precise capacity estimation.To fill the gap,this study introduces a novel data-driven battery pack capacity estimation method grounded in field data.The proposed approach begins by determining labeled capacity through an innovative combination of the inverse ampere-hour integral,open circuit voltage-based,and resistance-based correction methods.Then,multiple health features are extracted from incremental capacity curves,voltage curves,equivalent circuit model parameters,and operating temperature to thoroughly characterize battery aging behavior.A feature selection procedure is performed to determine the optimal feature set based on the Pearson correlation coefficient.Moreover,a convolutional neural network and bidirectional gated recurrent unit,enhanced by an attention mechanism,are employed to estimate the battery pack capacity in real-world EV applications.Finally,the proposed method is validated with a field dataset from two EVs,covering approximately 35,000 kilometers.The results demonstrate that the proposed method exhibits better estimation performance with an error of less than 1.1%compared to existing methods.This work shows great potential for accurate large-sized EV battery pack capacity estimation based on field data,which provides significant insights into reliable labeled capacity calculation,effective features extraction,and machine learning-enabled health diagnosis.

A comparative study of data-driven battery capacity estimation based on partial charging curves

With its generality and practicality, the combination of partial charging curves and machine learning(ML) for battery capacity estimation has attracted widespread attention. However, a clear classification,fair comparison, and performance rationalization of these methods are lacking, due to the scattered existing studies. To address these issues, we develop 20 capacity estimation methods from three perspectives:charging sequence construction, input forms, and ML models. 22,582 charging curves are generated from 44 cells with different battery chemistry and operating conditions to validate the performance. Through comprehensive and unbiased comparison, the long short-term memory(LSTM) based neural network exhibits the best accuracy and robustness. Across all 6503 tested samples, the mean absolute percentage error(MAPE) for capacity estimation using LSTM is 0.61%, with a maximum error of only 3.94%. Even with the addition of 3 m V voltage noise or the extension of sampling intervals to 60 s, the average MAPE remains below 2%. Furthermore, the charging sequences are provided with physical explanations related to battery degradation to enhance confidence in their application. Recommendations for using other competitive methods are also presented. This work provides valuable insights and guidance for estimating battery capacity based on partial charging curves.

Durable K-ion batteries with 100%capacity retention up to 40,000 cycles

Currently,the major challenge in terms of research on K-ion batteries is to ensure that they possess satisfactory cycle stability and specific capacity,especially in terms of the intrinsically sluggish kinetics induced by the large radius of K+ions.Here,we explore high-performance K-ion half/full batteries with high rate capability,high specific capacity,and extremely durable cycle stability based on carbon nanosheets with tailored N dopants,which can alleviate the change of volume,increase electronic conductivity,and enhance the K+ion adsorption.The as-assembled K-ion half-batteries show an excellent rate capability of 468 mA h g^(−1) at 100 mA g^(−1),which is superior to those of most carbon materials reported to date.Moreover,the as-assembled half-cells have an outstanding life span,running 40,000 cycles over 8 months with a specific capacity retention of 100%at a high current density of 2000 mA g^(−1),and the target full cells deliver a high reversible specific capacity of 146 mA h g^(−1) after 2000 cycles over 2 months,with a specific capacity retention of 113%at a high current density of 500 mA g^(−1),both of which are state of the art in the field of K-ion batteries.This study might provide some insights into and potential avenues for exploration of advanced K-ion batteries with durable stability for practical applications.

Effective Capacity of URLLC over Parallel Fading Channels with Imperfect Channel State Information

This paper investigates the effective capacity of a point-to-point ultra-reliable low latency communication(URLLC)transmission over multiple parallel sub-channels at finite blocklength(FBL)with imperfect channel state information(CSI).Based on reasonable assumptions and approximations,we derive the effective capacity as a function of the pilot length,decoding error probability,transmit power and the sub-channel number.Then we reveal significant impact of the above parameters on the effective capacity.A closed-form lower bound of the effective capacity is derived and an alternating optimization based algorithm is proposed to find the optimal pilot length and decoding error probability.Simulation results validate our theoretical analysis and show that the closedform lower bound is very tight.In addition,through the simulations of the optimized effective capacity,insights for pilot length and decoding error probability optimization are provided to evaluate the optimal parameters in realistic systems.

MOF-derived porous graphitic carbon with optimized plateau capacity and rate capability for high performance lithium-ion capacitors

The development of anode materials with high rate capability and long charge-discharge plateau is the key to improve per-formance of lithium-ion capacitors(LICs).Herein,the porous graphitic carbon(PGC-1300)derived from a new triply interpenetrated co-balt metal-organic framework(Co-MOF)was prepared through the facile and robust carbonization at 1300°C and washing by HCl solu-tion.The as-prepared PGC-1300 featured an optimized graphitization degree and porous framework,which not only contributes to high plateau capacity(105.0 mAh·g^(−1)below 0.2 V at 0.05 A·g^(−1)),but also supplies more convenient pathways for ions and increases the rate capability(128.5 mAh·g^(−1)at 3.2 A·g^(−1)).According to the kinetics analyses,it can be found that diffusion regulated surface induced capa-citive process and Li-ions intercalation process are coexisted for lithium-ion storage.Additionally,LIC PGC-1300//AC constructed with pre-lithiated PGC-1300 anode and activated carbon(AC)cathode exhibited an increased energy density of 102.8 Wh·kg^(−1),a power dens-ity of 6017.1 W·kg^(−1),together with the excellent cyclic stability(91.6%retention after 10000 cycles at 1.0 A·g^(−1)).

Tensile Strain Capacity Prediction of Engineered Cementitious Composites (ECC) Using Soft Computing Techniques

Plain concrete is strong in compression but brittle in tension,having a low tensile strain capacity that can significantly degrade the long-term performance of concrete structures,even when steel reinforcing is present.In order to address these challenges,short polymer fibers are randomly dispersed in a cement-based matrix to forma highly ductile engineered cementitious composite(ECC).Thismaterial exhibits high ductility under tensile forces,with its tensile strain being several hundred times greater than conventional concrete.Since concrete is inherently weak in tension,the tensile strain capacity(TSC)has become one of the most extensively researched properties.As a result,developing a model to predict the TSC of the ECC and to optimize the mixture proportions becomes challenging.Meanwhile,the effort required for laboratory trial batches to determine the TSC is reduced.To achieve the research objectives,five distinct models,artificial neural network(ANN),nonlinear model(NLR),linear relationship model(LR),multi-logistic model(MLR),and M5P-tree model(M5P),are investigated and employed to predict the TSCof ECCmixtures containing fly ash.Data from115 mixtures are gathered and analyzed to develop a new model.The input variables include mixture proportions,fiber length and diameter,and the time required for curing the various mixtures.The model’s effectiveness is evaluated and verified based on statistical parameters such as R2,mean absolute error(MAE),scatter index(SI),root mean squared error(RMSE),and objective function(OBJ)value.Consequently,the ANN model outperforms the others in predicting the TSC of the ECC,with RMSE,MAE,OBJ,SI,and R2 values of 0.42%,0.3%,0.33%,0.135%,and 0.98,respectively.

Exogenous calcium enhances the physiological status and photosynthetic capacity of rose under drought stress

Drought(water shortage)can substantially limit the yield and economic value of rose plants(Rosa spp.).Here,we characterized the effect of exogenous calcium(Ca^(2+))on the antioxidant system and photosynthesis-related properties of rose under polyethylene glycol 6000(PEG6000)-induced drought stress.Chlorophyll levels,as well as leaf and root biomass,were significantly reduced by drought;drought also had a major effect on the enzymatic antioxidant system and increased concentrations of reactive oxygen species.Application of exogenous Ca^(2+)increased the net photosynthetic rate and stomatal conductance of leaves,enhanced water-use efficiency,and increased the length and width of stomata following exposure to drought.Organ-specific physiological responses were observed under different concentrations of Ca^(2+).Application of 5 mmol·L^(-1)Ca^(2+)promoted photosynthesis and antioxidant activity in the leaves,and application of 10 mmol·L^(-1)Ca^(2+)promoted antioxidant activity in the roots.Application of exogenous Ca^(2+)greatly enhanced the phenotype and photosynthetic capacity of potted rose plants following exposure to drought stress.Overall,our findings indicate that the application of exogenous Ca^(2+)enhances the drought resistance of roses by promoting physiological adaptation and that it could be used to aid the cultivation of rose plants.

A hierarchical enhanced data-driven battery pack capacity estimation framework for real-world operating conditions with fewer labeled data

Battery pack capacity estimation under real-world operating conditions is important for battery performance optimization and health management,contributing to the reliability and longevity of batterypowered systems.However,complex operating conditions,coupling cell-to-cell inconsistency,and limited labeled data pose great challenges to accurate and robust battery pack capacity estimation.To address these issues,this paper proposes a hierarchical data-driven framework aimed at enhancing the training of machine learning models with fewer labeled data.Unlike traditional data-driven methods that lack interpretability,the hierarchical data-driven framework unveils the“mechanism”of the black box inside the data-driven framework by splitting the final estimation target into cell-level and pack-level intermediate targets.A generalized feature matrix is devised without requiring all cell voltages,significantly reducing the computational cost and memory resources.The generated intermediate target labels and the corresponding features are hierarchically employed to enhance the training of two machine learning models,effectively alleviating the difficulty of learning the relationship from all features due to fewer labeled data and addressing the dilemma of requiring extensive labeled data for accurate estimation.Using only 10%of degradation data,the proposed framework outperforms the state-of-the-art battery pack capacity estimation methods,achieving mean absolute percentage errors of 0.608%,0.601%,and 1.128%for three battery packs whose degradation load profiles represent real-world operating conditions.Its high accuracy,adaptability,and robustness indicate the potential in different application scenarios,which is promising for reducing laborious and expensive aging experiments at the pack level and facilitating the development of battery technology.

Enhanced reversible hydrogen storage properties of wrinkled graphene microflowers confined LiBH_(4) system with high volumetric hydrogen storage capacity

LiBH_(4)with high hydrogen storage density,is regarded as one of the most promising hydrogen storage materials.Nevertheless,it suffers from high dehydrogenation temperature and poor reversibility for practical use.Nanoconfinement is effective in achieving low dehydrogenation temperature and favorable reversibility.Besides,graphene can serve as supporting materials for LiBH_(4)catalysts and also destabilize LiBH_(4)via interfacial reaction.However,graphene has never been used alone as a frame material for nanoconfining LiBH_(4).In this study,graphene microflowers with large pore volumes were prepared and used as nanoconfinement framework material for LiBH_(4),and the nanoconfinement effect of graphene was revealed.After loading 70 wt%of LiBH_(4) and mechanically compressed at 350 MPa,8.0 wt% of H2 can be released within 100 min at 320C,corresponding to the highest volumetric hydrogen storage density of 94.9 g H2 L^(-1)ever reported.Thanks to the nanoconfinement of graphene,the rate-limiting step of dehydrogenation of nanoconfined LiBH_(4) was changed and its apparent activation energy of the dehydrogenation(107.3 kJ mol^(-1))was 42%lower than that of pure LiBH_(4).Moreover,the formation of the intermediate Li_(2)B_(12)H_(12) was effectively inhibited,and the stable nanoconfined structure enhanced the reversibility of LiBH_(4).This work widens the understanding of graphene's nanoconfinement effect and provides new insights for developing high-density hydrogen storage materials.

Atomic Ni directional-substitution on ZnIn_(2)S_(4) nanosheet to achieve the equilibrium of elevated redox capacity and efficient carrier-kinetics performance in photocatalysis

It is a challenge to coordinate carrier-kinetics performance and the redox capacity of photogenerated charges synchronously at the atomic level for boosting photocatalytic activity.Herein,the atomic Ni was introduced into the lattice of hexagonal ZnIn_(2)S_(4) nanosheets(Ni/ZnIn_(2)S_(4))via directionalsubstituting Zn atom with the facile hydrothermal method.The electronic structure calculations indicate that the introduction of Ni atom effectively extracts more electrons and acts as active site for subsequent reduction reaction.Besides the optimized light absorption range,the elevation of Efand ECBendows Ni/ZnIn_(2)S_(4) photocatalyst with the increased electron concentration and the enhanced reduction ability for surface reaction.Moreover,ultrafast transient absorption spectroscopy,as well as a series of electrochemical tests,demonstrates that Ni/ZnIn_(2)S_(4) possesses 2.15 times longer lifetime of the excited charge carriers and an order of magnitude increase for carrier mobility and separation efficiency compared with pristine ZnIn_(2)S_(4).These efficient kinetics performances of charge carriers and enhanced redox capacity synergistically boost photocatalytic activity,in which a 3-times higher conversion efficiency of nitrobenzene reduction was achieved upon Ni/ZnIn_(2)S_(4).Our study not only provides in-depth insights into the effect of atomic directional-substitution on the kinetic behavior of photogenerated charges,but also opens an avenue to the synchronous optimization of redox capacity and carrier-kinetics performance for efficient solar energy conversion.

Effects of thinning and understory removal on water use efficiency of Pinus massoniana:evidence from photosynthetic capacity and stable carbon isotope analyses

Understanding the relationship between forest management and water use efficiency(WUE)is important for evaluating forest adaptability to climate change.However,the effects of thinning and understory removal on WUE and its key controlling processes are not well understood,which limits our comprehension of the physiological mechanisms of various management practices.In this study,four forest management measures(no thinning:NT;understory removal:UR;light thinning:LT;and heavy thinning:HT)were carried out in Pinus massoniana plantations in a subtropical region of China.Photosynthetic capacity and needle stable carbon isotope composition(δ^(13)C)were measured to assess instantaneous water use efficiency(WUE_(inst))and long-term water use efficiency(WUE_(i)).Multiple regression models and structural equation modelling(SEM)identified the effects of soil properties and physiological performances on WUE_(inst)and WUE_(i).The results show that WUE_(inst)values among the four treatments were insignificant.However,compared with the NT stand(35.8μmol·mol^(-1)),WUE_(i)values significantly increased to 41.7μmol·mol^(-1)in the UR,50.1μmol·mol^(-1)in the LT and 46.6μmol·mol^(-1)in HT treatments,largely explained by photosynthetic capacity and soil water content.Understory removal did not change physiological performance(needle water potential and photosynthetic capacity).Thinning increased the net photosynthetic rate(A_n)but not stomatal conductance(g_s)or predawn needle water potential(ψ_(pd)),implying that the improvement in water use efficiency for thinned stands was largely driven by radiation interception than by soil water availability.In general,thinning may be an appropriate management measure to promote P.massoniana WUE to cope with seasonal droughts under future extreme climates.

Three-dimensional limit variation analysis on the ultimate pullout capacity of the anchor cables based on the Hoek-Brown failure criterion

Only simplified two-dimensional model and a single failure mode are adopted to calculate the ultimate pullout capacity(UPC)of anchor cables in most previous research.This study focuses on a more comprehensive combination failure mode that consists of bond failure of an anchorage body and failure of an anchored rock mass.The three-dimensional ultimate pullout capacity of the anchor cables is calculated based on the Hoek-Brown failure criterion and variation analysis method.The numerical solution for the curvilinear function in fracture plane is obtained based on the finite difference theory,which more accurately reflects the failure state of the anchor cable,as opposed to that being assumed in advance.The results reveal that relying solely on a single failure mode for UPC calculations has limitations,as changes in parameter values not only directly impact the UPC value but also can alter the failure model and thus the calculation method.