Estimating shear strength of high-level pillars supported with cemented backfilling using the HoekeBrown strength criterion

Deep metal mines are often mined using the high-level pillars with subsequent cementation backfilling(HLSCB)mining method.At the design stage,it is therefore important to have a reasonable method for determining the shear strength of the high-level pillars(i.e.cohesion and internal friction angle)when they are supported by cemented backfilling.In this study,a formula was derived for the upper limit of the confining pressure σ3max on a high-level pillar supported by cemented backfilling in a deep metal mine.A new method of estimating the shear strength of such pillars was then proposed based on the Hoek eBrown failure criterion.Our analysis indicates that the horizontal stress σhh acting on the cemented backfill pillar can be simplified by expressing it as a constant value.A reasonable and effective value for σ3max can then be determined.The value of s3max predicted using the proposed method is generally less than 3 MPa.Within this range,the shear strength of the high-level pillar is accurately calculated using the equivalent MohreCoulomb theory.The proposed method can effectively avoid the calculation of inaccurate shear strength values for the high-level pillars when the original HoekeBrown criterion is used in the presence of large confining pressures,i.e.the situation in which the cohesion value is too large and the friction angle is too small can effectively be avoided.The proposed method is applied to a deep metal mine in China that is being excavated using the HLSCB method.The shear strength parameters of the high-level pillars obtained using the proposed method were input in the numerical simulations.The numerical results show that the recommended level heights and sizes of the high-level pillars and rooms in the mine are rational.

Prediction models of burst strength degradation for casing with considerations of both wear and corrosion

Casing wear and casing corrosion are serious problems affecting casing integrity failure in deep and ultra-deep wells.This paper aims to predict the casing burst strength with considerations of both wear and corrosion.Firstly,the crescent wear shape is simplified into three categories according to common mathematical models.Then,based on the mechano-electrochemical(M-E)interaction,the prediction model of corrosion depth is built with worn depth as the initial condition,and the prediction models of burst strength of the worn casing and corroded casing are obtained.Secondly,the accuracy of different prediction models is validated by numerical simulation,and the main influence factors on casing strength are obtained.At last,the theoretical models are applied to an ultra-deep well in Northwest China,and the dangerous well sections caused by wear and corrosion are predicted,and the corrosion rate threshold to ensure the safety of casing is obtained.The results show that the existence of wear defects results in a stress concentration and enhanced M-E interaction on corrosion depth growth.The accuracy of different mathematical models is different:the slot ring model is most accurate for predicting corrosion depth,and the eccentric model is most accurate for predicting the burst strength of corroded casing.The burst strength of the casing will be overestimated by more than one-third if the M-E interaction is neglected,so the coupling effect of wear and corrosion should be sufficiently considered in casing integrity evaluation.

Enhancing the Interaction of Carbon Nanotubes by Metal-Organic Decomposition with Improved Mechanical Strength and Ultra-Broadband EMI Shielding Performance

The remarkable properties of carbon nanotubes(CNTs)have led to promising applications in the field of electromagnetic inter-ference(EMI)shielding.However,for macroscopic CNT assemblies,such as CNT film,achieving high electrical and mechanical properties remains challenging,which heavily depends on the tube-tube interac-tions of CNTs.Herein,we develop a novel strategy based on metal-organic decomposition(MOD)to fabricate a flexible silver-carbon nanotube(Ag-CNT)film.The Ag particles are introduced in situ into the CNT film through annealing of MOD,leading to enhanced tube-tube interactions.As a result,the electrical conductivity of Ag-CNT film is up to 6.82×10^(5) S m^(-1),and the EMI shielding effectiveness of Ag-CNT film with a thickness of~7.8μm exceeds 66 dB in the ultra-broad frequency range(3-40 GHz).The tensile strength and Young’s modulus of Ag-CNT film increase from 30.09±3.14 to 76.06±6.20 MPa(~253%)and from 1.12±0.33 to 8.90±0.97 GPa(~795%),respectively.Moreover,the Ag-CNT film exhibits excellent near-field shield-ing performance,which can effectively block wireless transmission.This innovative approach provides an effective route to further apply macroscopic CNT assemblies to future portable and wearable electronic devices.

DUCTILE CRACK INITIATION AND STEADY-STATE PROPAGATION OF HIGH STRENGTH STRUCTURAL STEEL

The resistance to crack propagation at earlier stage for a high strength structural steel with certain ductility and its correlation to microstructures,stress states,deformation history and strain characteristics have been investigated.The resistance to crack propagation is mainly de- termined by the plastic constrain ahead of the crack tip,the elastic energy and plastic work absorbed in the stress-strain field.These are connected with the state function of triaxial stress.The deformation history and strain characteristic during deformation of material are described by the flow line in which the deformation history and strain characteristic restrain the crack initiation at stage Ⅱ and the crack propagation at stage Ⅲ.The strain hardening rate may sensitively reflect the stress distribution and micro-fracture mechanism in the interi- or of material.

Semi-analytical steady-state response prediction for multi-dimensional quasi-Hamiltonian systems

The majority of nonlinear stochastic systems can be expressed as the quasi-Hamiltonian systems in science and engineering. Moreover, the corresponding Hamiltonian system offers two concepts of integrability and resonance that can fully describe the global relationship among the degrees-of-freedom(DOFs) of the system. In this work, an effective and promising approximate semi-analytical method is proposed for the steady-state response of multi-dimensional quasi-Hamiltonian systems. To be specific, the trial solution of the reduced Fokker–Plank–Kolmogorov(FPK) equation is obtained by using radial basis function(RBF) neural networks. Then, the residual generated by substituting the trial solution into the reduced FPK equation is considered, and a loss function is constructed by combining random sampling technique. The unknown weight coefficients are optimized by minimizing the loss function through the Lagrange multiplier method. Moreover, an efficient sampling strategy is employed to promote the implementation of algorithms. Finally, two numerical examples are studied in detail, and all the semi-analytical solutions are compared with Monte Carlo simulations(MCS) results. The results indicate that the complex nonlinear dynamic features of the system response can be captured through the proposed scheme accurately.

A Posteriori Stabilized Sixth-Order Finite Volume Scheme with Adaptive Stencil Construction:Basics for the 1D Steady-State Hyperbolic Equations

We propose an adaptive stencil construction for high-order accurate finite volume schemes a posteriori stabilized devoted to solve one-dimensional steady-state hyperbolic equations.High accuracy(up to the sixth-order presently)is achieved,thanks to polynomial recon-structions while stability is provided with an a posteriori MOOD method which controls the cell polynomial degree for eliminating non-physical oscillations in the vicinity of dis-continuities.We supplemented this scheme with a stencil construction allowing to reduce even further the numerical dissipation.The stencil is shifted away from troubles(shocks,discontinuities,etc.)leading to less oscillating polynomial reconstructions.Experimented on linear,Burgers',and Euler equations,we demonstrate that the adaptive stencil technique manages to retrieve smooth solutions with optimal order of accuracy but also irregular ones without spurious oscillations.Moreover,we numerically show that the approach allows to reduce the dissipation still maintaining the essentially non-oscillatory behavior.

Assessment of compressive strength of jet grouting by machine learning

Jet grouting is one of the most popular soil improvement techniques,but its design usually involves great uncertainties that can lead to economic cost overruns in construction projects.The high dispersion in the properties of the improved material leads to designers assuming a conservative,arbitrary and unjustified strength,which is even sometimes subjected to the results of the test fields.The present paper presents an approach for prediction of the uniaxial compressive strength(UCS)of jet grouting columns based on the analysis of several machine learning algorithms on a database of 854 results mainly collected from different research papers.The selected machine learning model(extremely randomized trees)relates the soil type and various parameters of the technique to the value of the compressive strength.Despite the complex mechanism that surrounds the jet grouting process,evidenced by the high dispersion and low correlation of the variables studied,the trained model allows to optimally predict the values of compressive strength with a significant improvement with respect to the existing works.Consequently,this work proposes for the first time a reliable and easily applicable approach for estimation of the compressive strength of jet grouting columns.

The influence of resistance exercise training prescription variables on skeletal muscle mass,strength,and physical function in healthy adults:An umbrella review

Purpose:The aim of this umbrella review was to determine the impact of resistance training(RT)and individual RT prescription variables on muscle mass,strength,and physical function in healthy adults.Methods:Following Preferred Reporting Items for Systematic Reviews and Meta-Analyses(PRISMA)guidelines,we systematically searched and screened eligible systematic reviews reporting the effects of differing RT prescription variables on muscle mass(or its proxies),strength,and/or physical function in healthy adults aged>18 years.Results:We identified 44 systematic reviews that met our inclusion criteria.The methodological quality of these reviews was assessed using A Measurement Tool to Assess Systematic Reviews;standardized effectiveness statements were generated.We found that RT was consistently a potent stimulus for increasing skeletal muscle mass(4/4 reviews provide some or sufficient evidence),strength(4/6 reviews provided some or sufficient evidence),and physical function(1/1 review provided some evidence).RT load(6/8 reviews provided some or sufficient evidence),weekly frequency(2/4 reviews provided some or sufficient evidence),volume(3/7 reviews provided some or sufficient evidence),and exercise order(1/1 review provided some evidence)impacted RT-induced increases in muscular strength.We discovered that 2/3 reviews provided some or sufficient evidence that RT volume and contraction velocity influenced skeletal muscle mass,while 4/7 reviews provided insufficient evidence in favor of RT load impacting skeletal muscle mass.There was insufficient evidence to conclude that time of day,periodization,inter-set rest,set configuration,set end point,contraction velocity/time under tension,or exercise order(only pertaining to hypertrophy)influenced skeletal muscle adaptations.A paucity of data limited insights into the impact of RT prescription variables on physical function.Conclusion:Overall,RT increased muscle mass,strength,and physical function compared to no exercise.RT intensity(load)and weekly frequency impacted RT-induced increases in muscular strength but not muscle hypertrophy.RT volume(number of sets)influenced muscular strength and hypertrophy.

Correlation between Combined Urinary Metal Exposure and Grip Strength under Three Statistical Models:A Cross-sectional Study in Rural Guangxi

Objective This study aimed to investigate the potential relationship between urinary metals copper(Cu),arsenic(As),strontium(Sr),barium(Ba),iron(Fe),lead(Pb)and manganese(Mn)and grip strength.Methods We used linear regression models,quantile g-computation and Bayesian kernel machine regression(BKMR)to assess the relationship between metals and grip strength.Results In the multimetal linear regression,Cu(β=−2.119),As(β=−1.318),Sr(β=−2.480),Ba(β=0.781),Fe(β=1.130)and Mn(β=−0.404)were significantly correlated with grip strength(P<0.05).The results of the quantile g-computation showed that the risk of occurrence of grip strength reduction was−1.007(95%confidence interval:−1.362,−0.652;P<0.001)when each quartile of the mixture of the seven metals was increased.Bayesian kernel function regression model analysis showed that mixtures of the seven metals had a negative overall effect on grip strength,with Cu,As and Sr being negatively associated with grip strength levels.In the total population,potential interactions were observed between As and Mn and between Cu and Mn(P_(interactions) of 0.003 and 0.018,respectively).Conclusion In summary,this study suggests that combined exposure to metal mixtures is negatively associated with grip strength.Cu,Sr and As were negatively correlated with grip strength levels,and there were potential interactions between As and Mn and between Cu and Mn.

Muscle strength and non-alcoholic fatty liver disease/metabolicassociated fatty liver disease

This editorial comments on an article published in a recent issue of World Journal of Gastroenterology,entitled“Association of low muscle strength with metabolic dysfunction-associated fatty liver disease:A nationwide study”.We focused on the association between muscle strength and the incidence of non-alcoholic fatty liver disease(NAFLD)and metabolic-associated fatty liver disease(MAFLD),as well as the mechanisms underlying the correlation and related clinical applications.NAFLD,which is now redefined as MAFLD,is one of the most common chronic liver diseases globally with an increasing prevalence and is characterized by malnutrition,which may contribute to decreased muscle strength.Reduction of muscle strength reportedly has a pathogenesis similar to that of NAFLD/MAFLD,including insulin resistance,inflammation,sedentary behavior,as well as insufficient vitamin D.Multiple studies have focused on the relationship between sarcopenia or muscle strength and NAFLD.However,studies investigating the relationship between muscle strength and MAFLD are limited.Owing to the shortage of specific medications for NAFLD/MAFLD treatment,early detection is essential.Furthermore,the relationship between muscle strength and NAFLD/MAFLD suggests that improvements in muscle strength may have an impact on disease prevention and may provide novel insights into treatments including dietary therapy,as well as tailored physical activity.

Improving creep strength of the fine-grained heat-affected zone of novel 9Cr martensitic heat-resistant steel via modified thermo-mechanical treatment

The infamous type Ⅳ failure within the fine-grained heat-affected zone (FGHAZ) in G115 steel weldments seriously threatens the safe operation of ultra-supercritical (USC) power plants.In this work,the traditional thermo-mechanical treatment was modified via the replacement of hot-rolling with cold rolling,i.e.,normalizing,cold rolling,and tempering (NCT),which was developed to improve the creep strength of the FGHAZ in G115 steel weldments.The NCT treatment effectively promoted the dissolution of preformed M_(23)C_(6)particles and relieved the boundary segregation of C and Cr during welding thermal cycling,which accelerated the dispersed reprecipitation of M_(23)C_(6) particles within the fresh reaustenitized grains during post-weld heat treatment.In addition,the precipitation of Cu-rich phases and MX particles was promoted evidently due to the deformation-induced dislocations.As a result,the interacting actions between precipitates,dislocations,and boundaries during creep were reinforced considerably.Following this strategy,the creep rupture life of the FGHAZ in G115 steel weldments can be prolonged by 18.6%,which can further push the application of G115 steel in USC power plants.

Secondary steady-state and time-periodic flows from a basic flow with square array of odd number of vortices

In a magnetohydrodynamic(MHD)driven fluid cell,a plane non-parallel flow in a square domain satisfying a free-slip boundary condition is examined.The energy dissipation of the flow is controlled by the viscosity and linear friction.The latter arises from the influence of the Hartmann bottom boundary layer in a three-dimensional(3D)MHD experiment in a square bottomed cell.The basic flow in this fluid system is a square eddy flow exhibiting a network of N~2 vortices rotating alternately in clockwise and anticlockwise directions.When N is odd,the instability of the flow gives rise to secondary steady-state flows and secondary time-periodic flows,exhibiting similar characteristics to those observed when N=3.For this reason,this study focuses on the instability of the square eddy flow of nine vortices.It is shown that there exist eight bi-critical values corresponding to the existence of eight neutral eigenfunction spaces.Especially,there exist non-real neutral eigenfunctions,which produce secondary time-periodic flows exhibiting vortices merging in an oscillatory manner.This Hopf bifurcation phenomenon has not been observed in earlier investigations.

High-Intensity Interval Training v/s Steady-State Cardio in Rehabilitation of Neurological Patients

Neuropathy is nerve damage that can cause chronic neuropathic pain, which is challenging to cure and has a significant financial burden. Exercise therapies, including High-Intensity Interval Training (HIIT) and steady-state cardio, are being explored as potential treatments for neuropathic pain. This systematic review compares the effectiveness of HIIT and steady-state cardio for improving function in neurological patients. This article provides an overview of the systematic review conducted on the effects of exercise on neuropathic patients, with a focus on high-intensity interval training (HIIT) and steady-state cardio. The authors conducted a comprehensive search of various databases, identified relevant studies based on predetermined inclusion criteria, and used the EPPI automation application to process the data. The final selection of studies was based on validity and relevance, with redundant articles removed. The article reviews four studies that compare high-intensity interval training (HIIT) to moderate-intensity continuous training (MICT) on various health outcomes. The studies found that HIIT can improve aerobic fitness, cerebral blood flow, and brain function in stroke patients;lower diastolic blood pressure more than MICT and improve insulin sensitivity and skeletal muscle mitochondrial content in obese individuals, potentially helping with the prevention and management of type 2 diabetes. In people with multiple sclerosis, acute exercise can decrease the plasma neurofilament light chain while increasing the flow of the kynurenine pathway. The available clinical and preclinical data suggest that further study on high-intensity interval training (HIIT) and its potential to alleviate neuropathic pain is justified. Randomized controlled trials are needed to investigate the type, intensity, frequency, and duration of exercise, which could lead to consensus and specific HIIT-based advice for patients with neuropathies.

Tensile strength and failure behavior of rock-mortar interfaces: Direct and indirect measurements

The tensile strength at the rock-concrete interface is one of the crucial factors controlling the failure mechanisms of structures,such as concrete gravity dams.Despite the critical importance of the failure mechanism and tensile strength of rock-concrete interfaces,understanding of these factors remains very limited.This study investigated the tensile strength and fracturing processes at rock-mortar interfaces subjected to direct and indirect tensile loadings.Digital image correlation(DIC)and acoustic emission(AE)techniques were used to monitor the failure mechanisms of specimens subjected to direct tension and indirect loading(Brazilian tests).The results indicated that the direct tensile strength of the rock-mortar specimens was lower than their indirect tensile strength,with a direct/indirect tensile strength ratio of 65%.DIC strain field data and moment tensor inversions(MTI)of AE events indicated that a significant number of shear microcracks occurred in the specimens subjected to the Brazilian test.The presence of these shear microcracks,which require more energy to break,resulted in a higher tensile strength during the Brazilian tests.In contrast,microcracks were predominantly tensile in specimens subjected to direct tension,leading to a lower tensile strength.Spatiotemporal monitoring of the cracking processes in the rock-mortar interfaces revealed that they show AE precursors before failure under the Brazilian test,whereas they show a minimal number of AE events before failure under direct tension.Due to different microcracking mechanisms,specimens tested under Brazilian tests showed lower roughness with flatter fracture surfaces than those tested under direct tension with jagged and rough fracture surfaces.The results of this study shed light on better understanding the micromechanics of damage in the rock-concrete interfaces for a safer design of engineering structures.

Investigation of anisotropic strength criteria for layered rock mass

Layered rock mass is a type of engineering rock mass with sound mechanical anisotropy,which is generally unfavorable to the stability of underground works.To investigate the strength anisotropy of layered rock,the Mohr-Coulomb and Hoek-Brown criteria are introduced to establish the two transverse isotropic strength criteria based on Jaeger's single weak plane theory and maximum axial strain theory,and parameter determination methods.Furthermore,the sensitivity of strength parameters(K 1,K 2,and K 3)that are used to characterize the anisotropy strength of non-sliding failure involved in the strength criteria and confining pressure are investigated.The results demonstrate that strength parameters K 1 and K 2 affect the strength of layered rock samples at all bedding angles except for the bedding angle of 90°and the angle range that can cause the shear sliding failure along the bedding plane.The strength of samples at any bedding angle decreases with increasing K 1,whereas the opposite is for K 2.Except for bedding angles of 0°and 90°and the bedding angle range that can cause the shear sliding along the bedding plane,K 3 has an impact on the strength of rock samples with other bedding angles that the specimens'strength increases with increase of K 3.In addition,the strength of the rock sample increases as confining pressure rises.Furthermore,the uniaxial and triaxial tests of chlorite schist samples were carried out to verify and evaluate the strength criteria proposed in the paper.It shows that the predicted strength is in good agreement with the experimental results.To test the applicability of the strength criterion,the strength data of several types of rock in the literature are compared.Finally,a comparison is made between the fitting effects of the two strength criteria and other available criteria for layered rocks.

Analysis of mechanical strengths of extreme line casing joint considering geometric, material, and contact nonlinearities

To address the challenges associated with difficult casing running,limited annular space,and poor cementing quality in the completion of ultra-deep wells,the extreme line casing offers an effective solution over conventional casings.However,due to its smaller size,the joint strength of extreme line casing is reduced,which may cause failure when running in the hole.To address this issue,this study focuses on the CST-ZTΦ139.7 mm×7.72 mm extreme line casing and employs the elastic-plastic mechanics to establish a comprehensive analysis of the casing joint,taking into account the influence of geometric and material nonlinearities.A finite element model is developed to analyze the forces and deformations of the extreme line casing joint under axial tension and external collapse load.The model investigates the stress distribution of each thread tooth subjected to various tensile forces and external pressures.Additionally,the tensile strength and crushing strength of the extreme line casing joint are determined through both analytical and experimental approaches.The findings reveal that,under axial tensile load,the bearing surface of each thread tooth experiences uneven stress,with relatively high equivalent stress at the root of each thread tooth.The end thread teeth are valuable spots for failure.It is observed that the critical fracture axial load of thread decreases linearly with the increase of thread tooth sequence.Under external pressure,the circumferential stress is highest at the small end of the external thread,leading to yield deformation.The tensile strength of the joint obtained from the finite element model exhibits a relative error of less than 7%compared to the analytical and experimental values,proving the reliability of the finite element model.The tensile strength of the joint is 3091.9 k N.Moreover,in terms of anti-collapse capability,the joints demonstrate higher resistance to collapse compared to the casing body,which is consistent with the test results where the pipe body experiences collapse and failure while the joints remain intact during the experiment.The failure load of the casing body under external collapse pressure is 87.4 MPa.The present study provides a basic understanding of the mechanical strengths of extreme line casing joint.

Uniaxial Compressive Strength Prediction for Rock Material in Deep Mine Using Boosting-Based Machine Learning Methods and Optimization Algorithms

Traditional laboratory tests for measuring rock uniaxial compressive strength(UCS)are tedious and timeconsuming.There is a pressing need for more effective methods to determine rock UCS,especially in deep mining environments under high in-situ stress.Thus,this study aims to develop an advanced model for predicting the UCS of rockmaterial in deepmining environments by combining three boosting-basedmachine learning methods with four optimization algorithms.For this purpose,the Lead-Zinc mine in Southwest China is considered as the case study.Rock density,P-wave velocity,and point load strength index are used as input variables,and UCS is regarded as the output.Subsequently,twelve hybrid predictive models are obtained.Root mean square error(RMSE),mean absolute error(MAE),coefficient of determination(R2),and the proportion of the mean absolute percentage error less than 20%(A-20)are selected as the evaluation metrics.Experimental results showed that the hybridmodel consisting of the extreme gradient boostingmethod and the artificial bee colony algorithm(XGBoost-ABC)achieved satisfactory results on the training dataset and exhibited the best generalization performance on the testing dataset.The values of R2,A-20,RMSE,and MAE on the training dataset are 0.98,1.0,3.11 MPa,and 2.23MPa,respectively.The highest values of R2 and A-20(0.93 and 0.96),and the smallest RMSE and MAE values of 4.78 MPa and 3.76MPa,are observed on the testing dataset.The proposed hybrid model can be considered a reliable and effective method for predicting rock UCS in deep mines.

Strength criterion for crystalline rocks considering grain size effect and tensile-compressive strength ratio

The macroscopic mechanical properties of rocks are significantly influenced by their microstructure.As a material bonded by mineral grains,the grain morphology of crystalline rock is the primary factor influencing the strength.However,most strength criteria neglect the strength variations caused by different grain characteristics in rocks.Furthermore,the traditional linear criteria tend to overestimate tensile strength and exhibit apex singularity.To address these shortcomings,a piecewise strength criterion that considers the grain size effect has been proposed.A part of an ellipse was employed to construct the envelope of the tensive-shear region on the meridian plane,to accurately reproduce the low tensile-compressive strength ratio.Based on the analysis of experimental data,both linear and exponential modification functions that account for grain size effects were integrated into the proposed criterion.The corresponding finite element algorithm has been implemented.The accuracy and applicability of the proposed criterion were validated by comparing with the experimental data.

A simple atomization approach enables monolayer dispersion of nano graphenes in cementitious composites with excellent strength gains

Carbon nano additives(CNAs)are critical to achieving the unique properties of functionalized composites,however,controlling the dispersion of CNAs in material matrix is always a challenging task.In this study,a simple atomization approach was successfully developed to promote the dispersion efficiency of graphene nanoplatelets(GNPs)in cement composites.This atomization approach can be integrated with the direct,indirect and combined ultrasonic stirrings in a homemade automatic stirring-atomization device.Mechanical and microstructure tests were performed on hardened cement pastes blended with GNPs in different stirring and mixing approaches.Results show that the direct ultrasonic stirrings enabled more homogeneous dispersions of GNP particles with a smaller size for a longer duration.The atomized droplets with the mean size of~100μm largely mitigated GNPs’agglomerations.Monolayer GNPs were observed in the cement matrix with the strength gain by up to 54%,and the total porosity decrease by 21%in 0.3 wt%GNPs dosage.The greatly enhanced dispersion efficiency of GNPs in cement also raised the cement hydration.This work provides an effective and manpower saving technique toward dispersing CNAs in engineering materials with great industrialization prospects.

Retrospective and prospective review of the generalized nonlinear strength theory for geomaterials

Strength theory is the basic theory for calculating and designing the strength of engineering materials in civil,hydraulic,mechanical,aerospace,military,and other engineering disciplines.Therefore,the comprehensive study of the generalized nonlinear strength theory(GNST)of geomaterials has significance for the construction of engineering rock strength.This paper reviews the GNST of geomaterials to demonstrate the research status of nonlinear strength characteristics of geomaterials under complex stress paths.First,it systematically summarizes the research progress of GNST(classical and empirical criteria).Then,the latest research the authors conducted over the past five years on the GNST is introduced,and a generalized three-dimensional(3D)nonlinear Hoek‒Brown(HB)criterion(NGHB criterion)is proposed for practical applications.This criterion can be degenerated into the existing three modified HB criteria and has a better prediction performance.The strength prediction errors for six rocks and two in-situ rock masses are 2.0724%-3.5091%and 1.0144%-3.2321%,respectively.Finally,the development and outlook of the GNST are expounded,and a new topic about the building strength index of rock mass and determining the strength of in-situ engineering rock mass is proposed.The summarization of the GNST provides theoretical traceability and optimization for constructing in-situ engineering rock mass strength.