An Investigation into the Compressive Strength,Permeability and Microstructure of Quartzite-Rock-Sand Mortar

River sand is an essential component used as a fine aggregate in mortar and concrete.Due to unrestrained exploitation,river sand resources are gradually being exhausted.This requires alternative solutions.This study deals with the properties of cement mortar containing different levels of manufactured sand(MS)based on quartzite,used to replace river sand.The river sand was replaced at 20%,40%,60%and 80%with MS(by weight or volume).The mechanical properties,transfer properties,and microstructure were examined and compared to a control group to study the impact of the replacement level.The results indicate that the compressive strength can be improved by increasing such a level.The strength was improved by 35.1%and 45.5%over that of the control mortar at replacement levels of 60%and 80%,respectively.Although there was a weak link between porosity and gas permeability in the mortars with manufactured sand,the gas permeability decreased with growing the replacement level.The microstructure of the MS mortar was denser,and the cement paste had fewer microcracks with increasing the replacement level.

Unconfined compressive strength and failure behaviour of completely weathered granite from a fault zone

Understanding the strength characteristics and deformation behaviour of the tunnel surrounding rock in a fault zone is significant for tunnel stability evaluation.In this study,a series of unconfined compression tests were conducted to investigate the mechanical characteristics and failure behaviour of completely weathered granite(CWG)from a fault zone,considering with height-diameter(h/d)ratio,dry densities(ρd)and moisture contents(ω).Based on the experimental results,a regression mathematical model of unconfined compressive strength(UCS)for CWG was developed using the Multiple Nonlinear Regression method(MNLR).The research results indicated that the UCS of the specimen with a h/d ratio of 0.6 decreased with the increase ofω.When the h/d ratio increased to 1.0,the UCS increasedωwith up to 10.5%and then decreased.Increasingρd is conducive to the improvement of the UCS at anyω.The deformation and rupture process as well as final failure modes of the specimen are controlled by h/d ratio,ρd andω,and the h/d ratio is the dominant factor affecting the final failure mode,followed byωandρd.The specimens with different h/d ratio exhibited completely different fracture mode,i.e.,typical splitting failure(h/d=0.6)and shear failure(h/d=1.0).By comparing the experimental results,this regression model for predicting UCS is accurate and reliable,and the h/d ratio is the dominant factor affecting the UCS of CWG,followed byρd and thenω.These findings provide important references for maintenance of the tunnel crossing other fault fractured zones,especially at low confining pressure or unconfined condition.

Effect of compressive strength on the performance of the NEMO-LIM model in Arctic Sea ice simulation

Satellite records show that the extent and thickness of sea ice in the Arctic Ocean have significantly decreased since the early 1970s.The prediction of sea ice is highly important,but accurate simulation of sea ice variations remains highly challenging.For improving model performance,sensitivity experiments were conducted using the coupled ocean and sea ice model(NEMO-LIM),and the simulation results were compared against satellite observations.Moreover,the contribution ratios of dynamic and thermodynamic processes to sea ice variations were analyzed.The results show that the performance of the model in reconstructing the spatial distribution of Arctic sea ice is highly sensitive to ice strength decay constant(C^(rhg)).By reducing the C^(rhg) constant,the sea ice compressive strength increases,leading to improved simulated sea ice states.The contribution of thermodynamic processes to sea ice melting was reduced due to less deformation and fracture of sea ice with increased compressive strength.Meanwhile,dynamic processes constrained more sea ice to the central Arctic Ocean and contributed to the increases in ice concentration,reducing the simulation bias in the central Arctic Ocean in summer.The root mean square error(RMSE)between modeled and the CryoSat-2/SMOS satellite observed ice thickness was reduced in the compressive strength-enhanced model solution.The ice thickness,especially of multiyear thick ice,was also reduced and matched with the satellite observation better in the freezing season.These provide an essential foundation on exploring the response of the marine ecosystem and biogeochemical cycling to sea ice changes.

Experimental Study on the Compressive Strength of Concrete with Different Wheat Straw Treatment Techniques

The treatment of wheat straw is very difficult,and its utilization rate is very low;accumulation causes air pollution and even fire.To make full use of wheat straw resources,we examined how using different physical and chemical methods to treat the wheat straw which can improve its strength abilities,or enhance the activity of wheat straw ash.In terms of concrete additives,it can reduce the amount of cement used.In this paper,we found that alkali treatment can significantly improve the tensile strength of wheat straw fiber,but polyvinyl alcohol treatment has no obvious effect on the strength of wheat straw fiber after alkali treatment.At the same time,we analyzed the wheat straw fiber microstructure through scanning electron microscopy,and we also studied the wheat straw ash chemical composition after 600℃ high-temperature treatment.Through the compressive strength test,we found that the strength of concrete decreases with increasing of wheat straw fiber and wheat straw powder content,and the compressive strength of concrete with wheat straw ash instead of 5%cement decreases little,and the strength of the concrete also decreases with the increasing of wheat straw ash.Through the macroscopic observation of the failure form of concrete,we found that the failure form of concrete with wheat straw ash is similar to that of common concrete,while the failure degree of concrete with wheat straw fiber and wheat straw powder is weakened.Through the scanning electron microscope test of the concrete,it was found that wheat straw fiber has an effect on the cracking of concrete and the inner compactness of concrete can also be affected by adding wheat straw ash and wheat straw powder.

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 Limestone Powder and Metakaolin Co-Blending on the Hydration Process and Mechanical Properties of Q-Phase Cement

A ternary system comprising Ca_(20)Al_(26)Mg_(3)Si_(3)O_(68)(Q-phase),limestone,and metakaolin is proposed,and its hydration behavior,hydration product phases,microstructure,and mechanical properties are investigated and compared with pure Q-phase cement.The results indicate that the ternary system exhibits exceptional and sustained compressive strength even under a 40℃environment,significantly outperforming pure Q-phase.The mechanism lies in that metakaolin effectively inhibits the transformation of metastable phase.Meanwhile,the interactions among Q-phase,limestone,and metakaolin further enhance the cementitious performance.The ternary system effectively addresses potential issues of strength loss in Q-phase cement application,and as a low-carbon cementitious material system,it holds promising potential applications.

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.

High-Volume Mineral Admixtures Cement: The Effects of Particle Size Distribution

The effects of high-volume slag-fly ash cement with different particle sizes on hydration degree,microstructure and mechanical properties were systematically studied,by means of laser particle size(DLS),X-ray diffraction (XRD),comprehensive thermal analysis (TG-DTA),scanning electron microscopy(SEM) and mechanical properties tests.The results show that suitable particle size distribution of cementitious material has significantly promoting effects on hydration reaction rate and mechanical properties.Compared with slag without further grinding,the slag after ball milling for 4 h has an obvious improvement in reactivity,which also provides a faster hydration rate and higher compressive strength for the cementitious material.When the slag milled for 1 and 4 h is mixed at a mass ratio of 2:1 (i e,slag with D_(50) of 7.4μm and average size of 9.9μm,and slag with D_(50) value of 2.6μm and average size of 5.3μm),and a certain amount of fly ash is added in,the most obvious improvement of compressive strength of cement is achieved.

Failure behavior and strength model of blocky rock mass with and without rockbolts

To better understand the failure behaviours and strength of bolt-reinforced blocky rocks,large scale extensive laboratory experiments are carried out on blocky rock-like specimens with and without rockbolt reinforcement.The results show that both shear failure and tensile failure along joint surfaces are observed but the shear failure is a main controlling factor for the peak strength of the rock mass with and without rockbolts.The rockbolts are necked and shear deformation simultaneously happens in bolt reinforced rock specimens.As the joint dip angle increases,the joint shear failure becomes more dominant.The number of rockbolts has a significant impact on the peak strain and uniaxial compressive strength(UCS),but little influence on the deformation modulus of the rock mass.Using the Winkler beam model to represent the rockbolt behaviours,an analytical model for the prediction of the strength of boltreinforced blocky rocks is proposed.Good agreement between the UCS values predicted by proposed model and obtained from experiments suggest an encouraging performance of the proposed model.In addition,the performance of the proposed model is further assessed using published results in the literature,indicating the proposed model can be used effectively in the prediction of UCS of bolt-reinforced blocky rocks.

Exploring the mechanical behavior and microstructure of compacted loess subjected to dry-wet cycles and chemical contamination

Due to climatic factors and rapid urbanization,the soil in the Loess Plateau,China,experiences the coupled effects of dry-wet cycles and chemical contamination.Understanding the mechanical behavior and corresponding microstructural evolution of contaminated loess subjected to dry-wet cycles is essential to elucidate the soil degradation mechanism.Therefore,direct shear and consolidation tests were performed to investigate the variations in mechanical properties of compacted loess contaminated with acetic acid,sodium hydroxide,and sodium sulfate during dry-wet cycles.The mechanical response mechanisms were investigated using zeta potential,mineral chemical composition,and scanning electron microscopy(SEM)tests.The results indicate that the mechanical deterioration of sodium hydroxidecontaminated loess during dry-wet cycles decreases with increasing contaminant concentration,which is mainly attributed to the thickening of the electrical double layer(EDL)by Nat and the precipitation of calcite,as well as the formation of colloidal flocs induced by OH,thus inhibiting the development of large pores during the dry-wet process.In contrast,the attenuation of mechanical properties of both acetic acid-and sodium sulfate-contaminated loess becomes more severe with increasing contaminant concentration,with the latter being more particularly significant.This is primarily due to the reduction of the EDL thickness and the erosion of cement in the acidic environment,which facilitates the connectivity of pores during dry-wet cycles.Furthermore,the salt expansion generated by the drying process of saline loess further intensifies the structural disturbance.Consequently,the mechanical performance of compacted loess is sensitive to both pollutant type and concentration,exhibiting different response patterns in the dry-wet cycling condition.

Predicting uniaxial compressive strength of tuff after accelerated freeze-thaw testing: Comparative analysis of regression models and artificial neural networks

Ignimbrites have been widely used as building materials in many historical and touristic structures in the Kayseri region of Türkiye. Their diverse colours and textures make them a popular choice for modern construction as well. However, ignimbrites are particularly vulnerable to atmospheric conditions, such as freeze-thaw cycles, due to their high porosity, which is a result of their formation process. When water enters the pores of the ignimbrites, it can freeze during cold weather. As the water freezes and expands, it generates internal stress within the stone, causing micro-cracks to develop. Over time, repeated freeze-thaw (F-T) cycles lead to the growth of these micro-cracks into larger cracks, compromising the structural integrity of the ignimbrites and eventually making them unsuitable for use as building materials. The determination of the long-term F-T performance of ignimbrites can be established after long F-T experimental processes. Determining the long-term F-T performance of ignimbrites typically requires extensive experimental testing over prolonged freeze-thaw cycles. To streamline this process, developing accurate predictive equations becomes crucial. In this study, such equations were formulated using classical regression analyses and artificial neural networks (ANN) based on data obtained from these experiments, allowing for the prediction of the F-T performance of ignimbrites and other similar building stones without the need for lengthy testing. In this study, uniaxial compressive strength, ultrasonic propagation velocity, apparent porosity and mass loss of ignimbrites after long-term F-T were determined. Following the F-T cycles, the disintegration rate was evaluated using decay function approaches, while uniaxial compressive strength (UCS) values were predicted with minimal input parameters through both regression and ANN analyses. The ANN and regression models created for this purpose were first started with a single input value and then developed with two and three combinations. The predictive performance of the models was assessed by comparing them to regression models using the coefficient of determination (R2) as the evaluation criterion. As a result of the study, higher R2 values (0.87) were obtained in models built with artificial neural network. The results of the study indicate that ANN usage can produce results close to experimental outcomes in predicting the long-term F-T performance of ignimbrite samples.

The Performance Evolution Characteristics of Insitu Concrete at the Permafrost Regions

This study aimed to investigate the performance evolution characteristics of concrete under permafrost ambient temperatures and to explore methods to mitigate the thermal perturbation by concrete on the permafrost environment.A program was designed to investigate the properties of various concretes at three curing conditions.The compressive strength development pattern of each group was evaluated and the concrete's performance was characterized by compressive strength damage degree,hydration temperature and SEM analysis in a low temperature environment.The experimental results show that the incorporation of fly ash alone or incombination with other admixtures in concrete under low-temperature curing does not deteriorate its microstructure,and at the same time,it can slow down the hydration rate of cement and significantly reduce the exothermic heat of hydration of concrete.These findings are expected to provide valuable references for the proportioning design of concrete in permafrost environments.

Fluid-Related Performances and Compressive Strength of Clinker-Free Cementitious Backfill Material Based on Phosphate Tailings

Phosphate tailings are usually used as backfill material in order to recycle tailings resources.This study considers the effect of the mix proportions of clinker-free binders on the fluidity,compressive strength and other key performances of cementitious backfill materials based on phosphate tailings.In particular,three solid wastes,phosphogypsum(PG),semi-aqueous phosphogypsum(HPG)and calcium carbide slag(CS),were selected to activate wet ground granulated blast furnace slag(WGGBS)and three different phosphate tailings backfill materials were prepared.Fluidity,rheology,settling ratio,compressive strength,water resistance and ion leaching behavior of backfill materials were determined.According to the results,when either PG or HPG is used as the sole activator,the fluidity properties of the materials are enhanced.Phosphate tailings backfill material activated with PG present the largest fluidity and the lowest yield stress.Furthermore,the backfill material’s compressive strength is considerably increased to 2.9 MPa at 28 days after WGGBS activation using a mix of HPG and CS,all with a settling ratio of only 1.15 percent.Additionally,all the three ratios of binder have obvious solidification effects on heavy metal ions Cu and Zn,and P in phosphate tailings.

STABILITY OF THE RAREFACTION WAVE IN THE SINGULAR LIMIT OF A SHARP INTERFACE PROBLEM FOR THE COMPRESSIBLE NAVIER-STOKES/ALLEN-CAHN SYSTEM

This paper is concerned with the global well-posedness of the solution to the compressible Navier-Stokes/Allen-Cahn system and its sharp interface limit in one-dimensional space.For the perturbations with small energy but possibly large oscillations of rarefaction wave solutions near phase separation,and where the strength of the initial phase field could be arbitrarily large,we prove that the solution of the Cauchy problem exists for all time,and converges to the centered rarefaction wave solution of the corresponding standard two-phase Euler equation as the viscosity and the thickness of the interface tend to zero.The proof is mainly based on a scaling argument and a basic energy method.

Effect of Partial Replacement of Fly Ash by Decoration Waste Powder on the Fresh and Mechanical Properties of Geopolymer Masonry Mortar

This study aims to investigate the feasibility of using decoration waste powder(DWP)as a partial replacement for fly ash(FA)in the preparation of geopolymer masonry mortar,and to examine the effect of different DWP replacement rates(0%-40%)on the fresh and mechanical properties of the mortar.The results showed that each group of geopolymer masonry mortar exhibited excellent water retention performance,with a water retention rate of 100%,which was due to the unique geopolymer mortar system and high viscosity of the alkaline activator solution.Compared to the control group,the flowability of the mortar containing lower contents of DWP(10%and 20%)was higher.However,as the DWP replacement rate further increased,the flowability gradually decreased.The DWP could absorb the free water in the reaction system of geopolymer mortar,thereby limiting the occurrence of geopolymerization reaction.The incorporation of DWP in the mortar resulted in a decrease in compressive strength compared to the mortar without DWP.However,even at a replacement rate of 40%,the compressive strength of the mortar still exceeded 15 MPa,which met the requirements of the masonry mortar.It was feasible to use DWP in the geopolymer masonry mortar.Although the addition of DWP caused some performance loss,it did not affect its usability.

Predicting dynamic compressive strength of frozen-thawed rocks by characteristic impedance and data-driven methods

In cold regions,the dynamic compressive strength(DCS)of rock damaged by freeze-thaw weathering significantly influences the stability of rock engineering.Nevertheless,testing the dynamic strength under freeze-thaw weathering conditions is often both time-consuming and expensive.Therefore,this study considers the effect of characteristic impedance on DCS and aims to quickly determine the DCS of frozen-thawed rocks through the application of machine-learning techniques.Initially,a database of DCS for frozen-thawed rocks,comprising 216 rock specimens,was compiled.Three external load parameters(freeze-thaw cycle number,confining pressure,and impact pressure)and two rock parameters(characteristic impedance and porosity)were selected as input variables,with DCS as the predicted target.This research optimized the kernel scale,penalty factor,and insensitive loss coefficient of the support vector regression(SVR)model using five swarm intelligent optimization algorithms,leading to the development of five hybrid models.In addition,a statistical DCS prediction equation using multiple linear regression techniques was developed.The performance of the prediction models was comprehensively evaluated using two error indexes and two trend indexes.A sensitivity analysis based on the cosine amplitude method has also been conducted.The results demonstrate that the proposed hybrid SVR-based models consistently provided accurate DCS predictions.Among these models,the SVR model optimized with the chameleon swarm algorithm exhibited the best performance,with metrics indicating its effectiveness,including root mean square error(RMSE)﹦3.9675,mean absolute error(MAE)﹦2.9673,coefficient of determination(R^(2))﹦0.98631,and variance accounted for(VAF)﹦98.634.This suggests that the chameleon swarm algorithm yielded the most optimal results for enhancing SVR models.Notably,impact pressure and characteristic impedance emerged as the two most influential parameters in DCS prediction.This research is anticipated to serve as a reliable reference for estimating the DCS of rocks subjected to freeze-thaw weathering.

Influence of Ultra Fine Glass Powder on the Properties and Microstructure of Mortars

This study focuses on the effect of ultrafine waste glass powder on cement strength,gas permeability and pore structure.Varying contents were considered,with particle sizes ranging from 2 to 20μm.Moreover,alkali activation was considered to ameliorate the reactivity and cementitious properties,which were assessed by using scanning electron microscopy(SEM),energy-dispersive X-ray spectroscopy(EDS),and specific surface area pore size distribution analysis.According to the results,without the addition of alkali activators,the performance of glass powder mortar decreases as the amount of glass powder increases,affecting various aspects such as strength and resistance to gas permeability.Only 5%glass powder mortar demonstrated a compressive strength at 60 days higher than that of the control group.However,adding alkali activator(CaO)during hydration ameliorated the hydration environment,increased the alkalinity of the composite system,activated the reactivity of glass powder,and enhanced the interaction of glass powder and pozzolanic reaction.In general,compared to ordinary cement mortar,alkali-activated glass powder mortar produces more hydration products,showcases elevated density,and exhibits improved gas resistance.Furthermore,alkali-activated glass powder mortar demonstrates an improvement in performance across various aspects as the content increases.At a substitution rate of 15%,the glass powder mortar reaches its optimal levels of strength and resistance to gas permeability,with a compressive strength increase ranging from 28.4%to 34%,and a gas permeation rate reduction between 51.8%and 66.7%.

Prediction of Geopolymer Concrete Compressive Strength Using Convolutional Neural Networks

Geopolymer concrete emerges as a promising avenue for sustainable development and offers an effective solution to environmental problems.Its attributes as a non-toxic,low-carbon,and economical substitute for conventional cement concrete,coupled with its elevated compressive strength and reduced shrinkage properties,position it as a pivotal material for diverse applications spanning from architectural structures to transportation infrastructure.In this context,this study sets out the task of using machine learning(ML)algorithms to increase the accuracy and interpretability of predicting the compressive strength of geopolymer concrete in the civil engineering field.To achieve this goal,a new approach using convolutional neural networks(CNNs)has been adopted.This study focuses on creating a comprehensive dataset consisting of compositional and strength parameters of 162 geopolymer concrete mixes,all containing Class F fly ash.The selection of optimal input parameters is guided by two distinct criteria.The first criterion leverages insights garnered from previous research on the influence of individual features on compressive strength.The second criterion scrutinizes the impact of these features within the model’s predictive framework.Key to enhancing the CNN model’s performance is the meticulous determination of the optimal hyperparameters.Through a systematic trial-and-error process,the study ascertains the ideal number of epochs for data division and the optimal value of k for k-fold cross-validation—a technique vital to the model’s robustness.The model’s predictive prowess is rigorously assessed via a suite of performance metrics and comprehensive score analyses.Furthermore,the model’s adaptability is gauged by integrating a secondary dataset into its predictive framework,facilitating a comparative evaluation against conventional prediction methods.To unravel the intricacies of the CNN model’s learning trajectory,a loss plot is deployed to elucidate its learning rate.The study culminates in compelling findings that underscore the CNN model’s accurate prediction of geopolymer concrete compressive strength.To maximize the dataset’s potential,the application of bivariate plots unveils nuanced trends and interactions among variables,fortifying the consistency with earlier research.Evidenced by promising prediction accuracy,the study’s outcomes hold significant promise in guiding the development of innovative geopolymer concrete formulations,thereby reinforcing its role as an eco-conscious and robust construction material.The findings prove that the CNN model accurately estimated geopolymer concrete’s compressive strength.The results show that the prediction accuracy is promising and can be used for the development of new geopolymer concrete mixes.The outcomes not only underscore the significance of leveraging technology for sustainable construction practices but also pave the way for innovation and efficiency in the field of civil engineering.

Effect of intermittent joint distribution on the mechanical and acoustic behavior of rock masses

The mechanical characteristics and acoustic behavior of rock masses are greatly influenced by stochastic joints.In this study,numerical models of rock masses incorporating intermittent joints with different numbers and dip angles were produced using the finite element method(FEM)with the intrinsic cohesive zone model(ICZM).Then,the uniaxial compressive and wave propagation simulations were performed.The results indicate that the joint number and dip angle can affect the mechanical and acoustic properties of the models.The uniaxial compressive strength(UCS)and wave velocity of rock masses decrease monotonically as the joint number increases.However,the wave velocity grows monotonically as the joint dip angle increases.When the joint dip angle is 45°–60°,the UCS of the rock mass is lower than that of other dip angles.The wave velocity parallel to the joints is greater than that perpendicular to the joints.When the dip angle of joints remains unchanged,the UCS and wave velocity are positively related.When the joint dip angle increases,the variation amplitude of the UCS regarding the wave velocity increases.To reveal the effect of the joint distribution on the velocity,a theoretical model was also proposed.According to the theoretical wave velocity,the change in wave velocity of models with various joint numbers and dip angles was consistent with the simulation results.Furthermore,a theoretical indicator(i.e.fabric tensor)was adopted to analyze the variation of the wave velocity and UCS.

Two-dimensional face stability analysis in rock masses governed by the Hoek-Brown strength criterion with a new multi-horn mechanism

The face stability problem is a major concern for tunnels excavated in rock masses governed by the Hoek-Brown strength criterion.To provide an accurate prediction for the theoretical solution of the critical face pressure,this study adopts the piecewise linear method(PLM)to account for the nonlinearity of the strength envelope and proposes a new multi-horn rotational mechanism based on the Hoek-Brown strength criterion and the associative flow rule.The analytical solution of critical support pressure is derived from the energy-work balance equation in the framework of the plastic limit theorem;it is formulated as a multivariable nonlinear optimization problem relying on 2m dependent variables(m is the number of segments).Meanwhile,two classic linearized measures,the generalized tangential technique(GTT)and equivalent Mohr-Coulomb parameters method(EMM),are incorporated into the analysis for comparison.Surprisingly,the parametric study indicates a significant improvement in support pressure by up to 13%compared with the GTT,and as expected,the stability of the tunnel face is greatly influenced by the rock strength parameters.The stress distribution on the rupture surface is calculated to gain an intuitive understanding of the failure at the limit state.Although the limit analysis is incapable of calculating the true stress distribution in rock masses,a rough approximation of the stress vector on the rupture surface is permitted.In the end,sets of normalized face pressure are provided in the form of charts for a quick assessment of face stability in rock masses.