Ground reinforcement is crucial for tunnel construction, especially in soft rock tunnels. Existing analytical models are inadequate for predicting the ground reaction curves (GRCs) for reinforced tunnels in strain-sof...Ground reinforcement is crucial for tunnel construction, especially in soft rock tunnels. Existing analytical models are inadequate for predicting the ground reaction curves (GRCs) for reinforced tunnels in strain-softening (SS) rock masses. This study proposes a novel analytical model to determine the GRCs of SS rock masses, incorporating ground reinforcement and intermediate principal stress (IPS). The SS constitutive model captures the progressive post- peak failure, while the elastic-brittle model simulates reinforced rock masses. Nine combined states are innovatively investigated to analyze plastic zone development in natural and reinforced regions. Each region is analyzed separately, and coupled through boundary conditions at interface. Comparison with three types of existing models indicates that these models overestimate reinforcement effects. The deformation prediction errors of single geological material models may exceed 75%. Furthermore, neglecting softening and residual zones in natural regions could lead to errors over 50%. Considering the IPS can effectively utilize the rock strength to reduce tunnel deformation by at least 30%, thereby saving on reinforcement and support costs. The computational results show a satisfactory agreement with the monitoring data from a model test and two tunnel projects. The proposed model may offer valuable insights into the design and construction of reinforced tunnel engineering.展开更多
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 s...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.展开更多
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...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.展开更多
This study systematically investigated the coupling effects of confiningpressure and strain rate on the dynamic strength of granite through dynamic triaxial compression tests.A dynamic strength criterion was developed...This study systematically investigated the coupling effects of confiningpressure and strain rate on the dynamic strength of granite through dynamic triaxial compression tests.A dynamic strength criterion was developed to incorporate these coupling effects for further analysis.Moreover,the research thoroughly revealed the underlying mechanism by which these coupling effects influencethe rock strength.The results revealed that both confiningpressure and strain rate significantly enhanced the dynamic strength of rock;however,a mutual inhibition effect emerged under their coupling.Specifically,as the confiningpressure increased,the strengthening effect of strain rate gradually diminished.Conversely,increasing the strain rate weakened the strengthening effect of confiningpressure.The proposed strength criterion successfully predicted rock strength under various confiningpressures(0-225 MPa)and strain rates(10^(-6)-600 s^(-1)).It achieved an average prediction error of only 8.3%,which represents a 65%improvement in accuracy compared to models that consider confiningpressure and strain rate effects independently.At the micro-mechanism level,increasing confiningpressure and strain rate promoted crack propagation in a transgranular(TG)mode,thereby enhancing the overall rock strength.However,under the coupling effects,the interference and interaction of TG cracks weakened the overall strengthening effect.This indicated that the competitive interaction between confiningpressure and strain rate during crack propagation constitutes the intrinsic mechanism underlying their mutual inhibitory effect on rock strength.This study provides a more accurate theoretical basis for understanding the dynamic responses of rocks and contributes valuable insights for disaster prevention and control in deep rock engineering projects.展开更多
Room and pillar mining is an underground mining method that utilizes natural pillar support to control rock mass behavior,ensuring mine stability and a safe mine environment.This study specifically documents the influ...Room and pillar mining is an underground mining method that utilizes natural pillar support to control rock mass behavior,ensuring mine stability and a safe mine environment.This study specifically documents the influence of the intermediate principal stress component on the pillar behavior.So far only classical failure criteria ignoring the influence of the intermediate principal stress component were used for underground pillar design.By using an extended Hoek-Brown failure criterion in comparison with the classical Hoek-Brown failure criterion,the influence of the intermediate principal stress component is documented by indicating those areas where the failure criterion is violated.This study demonstrates,that depending on the rock type,the intermediate principal stress component can have a significant effect.Ignoring this influence can lead to uneconomic pillar design and incorrect determination of the factor of safety.展开更多
The generalized Zhang-Zhu(GZZ)strength criterion was proposed as an extension to the Hoek-Brown criterion and the Mogi criterion.The introduction to mean normal stress results in a non-smooth and non-convex yield surf...The generalized Zhang-Zhu(GZZ)strength criterion was proposed as an extension to the Hoek-Brown criterion and the Mogi criterion.The introduction to mean normal stress results in a non-smooth and non-convex yield surface,which presents a challenge for updating plastic stress.Current research primarily focuses on modified smooth GZZ criteria or approximate solutions,which inevitably lead to increased computational costs or inaccuracies.In this paper,an accurate stress updating algorithm is proposed based on the original GZZ criterion.The algorithm operates entirely in the principal stress space,where numerical singularities at the intersection of yield surfaces are avoided by defining four different types of stress updating.This approach simplifies the GZZ criterion compared to its formulation in general stress space.The return mapping is employed to compute the updated stress and consistent stiffness matrix,facilitating calculations using both finite element implicit and explicit algorithms.Finally,the accuracy of the proposed method is validated using rock true triaxial test data and semianalytical solutions for stresses and displacement around a circular opening under the GZZ criterion.展开更多
Biaxial compression tests are performed on 100 mm × 100 mm × 100 mm cubic specimens of plain high-strength highperformance concrete （HSHPC） at seven kinds of stress ratios, σ2：σ3 =0 ： - 1, -0.20 ： - 1...Biaxial compression tests are performed on 100 mm × 100 mm × 100 mm cubic specimens of plain high-strength highperformance concrete （HSHPC） at seven kinds of stress ratios, σ2：σ3 =0 ： - 1, -0.20 ： - 1, -0.30 ： - 1, -0.40 ： - 1, -0.50 ： -1, -0. 75 ： - 1, and - 1.00 ： - 1 after exposure to normal and high temperatures of 20, 200, 300, 400, 500 and 600 ℃, using a large static-dynamic true triaxial machine. Frictionreducing pads are three layers of plastic membranes with glycerine in-between for the compressive loading plane. Failure modes of the specimens are described. The two principally static compressive strengths are measured. The influences of the temperatures and stress ratios on the biaxial strengths of HSHPC after exposure to high temperatures are also analyzed. The experimental results show that the uniaxial compressive strength of plain HSHPC after exposure to high temperatures does not decrease completely with the increase in temperature; the ratios of the biaxial to its uniaxial compressive strengths depend on the stress ratios and brittleness-stiffness of HSHPC after exposure to different high temperatures. The formula of the Kupfer-Gerstle failure criterion modified with the temperature and stress ratio parameters for plain HSHPC is proposed.展开更多
Based on the dynamic loading(1-100 s^(-1)) experiments under different temperatures(223-298 K) and stress states, uniaxial and biaxial strength criterion of a Hydroxyl-terminated polybutadiene(HTPB)based composite sol...Based on the dynamic loading(1-100 s^(-1)) experiments under different temperatures(223-298 K) and stress states, uniaxial and biaxial strength criterion of a Hydroxyl-terminated polybutadiene(HTPB)based composite solid propellant were further investigated. These experiments were conducted through the use of a new uniaxial INSTRON testing machine, different new designed gripping apparatus and samples with different configurations. According to the test results, dynamic uniaxial tensile strength criterion of the propellant was directly constructed with the master curve of the uniaxial maximum tensile stress. Whereas, a new method was proposed to determine the dynamic uniaxial compressive strength of the propellant in this study. Then uniaxial compressive strength criterion of the propellant was constructed based on the related master curve. Moreover, it found that the uniaxial tensilecompressive strength ratio of the propellant is more sensitive to loading temperature under the test conditions. The value of this parameter is about 0.4 at room temperature, and it reduces to 0.2-0.3 at low temperatures. Finally, the theoretical biaxial strength criterion of HTPB propellant under dynamic loading was constructed with the unified strength theory, the uniaxial strength and the typical biaxial tensile strength. In addition, the theoretical limit lines of the principal stress plane for the propellant under dynamic loading at different temperatures were further plotted, and the scope of the limit line increases with decreasing temperature.展开更多
The Hoek-Brown （HB） strength criterion has been widely applied to the estimation of strength of intact rock and rock mass, while evolving ever since. However, negligence of the effect of the intermediate principal s...The Hoek-Brown （HB） strength criterion has been widely applied to the estimation of strength of intact rock and rock mass, while evolving ever since. However, negligence of the effect of the intermediate principal stress still remains in the criterion＇s latest version. At the same time, several three-dimensional （3D） HB strength, which can takes into account the influence of the intermediate principal stress, have already been proposed, among which the 3D HB criterion proposed by Zhang and Zhu seems to be the most reasonable one. However, the Zhang 3D HB criterion may have problems with some stress path close to triaxial extension state because of the non-convexity characteristic of its failure surface. In this paper, a new 3D HB strength criterion is presented based on a generalized form of the HB criterion, which also considers the effect of the intermediate principal stress and inherits all the merits of the original version of the HB criterion. In addition, this new criterion can remedy to some extent the shortcomings observed in the Zhang 3D HB criterion. Polyaxial tests for five different rocks from pub- lished literatures are used for evaluating this new criterion and comparing it with the Zhang 3D HB criterion. The re- sults show that this new criterion may over-predict or under- predict the polyaxial strength of rocks but the errors are rela- tively small, and similar results are also found for the Zhang 3D HB criterion, which one is better depends on the type of the rock under estimation.展开更多
A new unified strength criterion in the principal stress space has been proposed for use with normal strength concrete （NC） and high strength concrete （HSC） in compressioncompression-tension, compression-tension-t...A new unified strength criterion in the principal stress space has been proposed for use with normal strength concrete （NC） and high strength concrete （HSC） in compressioncompression-tension, compression-tension-tension, triaxial tension, and biaxial stress states. The study covers concrete with strengths ranging from 20 to 130 MPa. The conception of damage Poisson＇s ratio is defined and the expression for damage Poisson＇s ratio is determined basically. The failure mechanism of concrete is illustrated, which points out that damage Poisson＇s ratio is the key to determining the failure of concrete. Furthermore, for the concrete under biaxial stress conditions, the unified strength criterion is simplified and a simplified strength criterion in the form of curves is also proposed. The strength criterion is physically meaningful and easy to calculate, which can be applied to analytic solution and numerical solution of concrete structures.展开更多
The failure criterion of rocks is a critical factor involved in reliability design and stability analysis of geotechnical engineering.In order to accurately evaluate the triaxial compressive strength of rocks under di...The failure criterion of rocks is a critical factor involved in reliability design and stability analysis of geotechnical engineering.In order to accurately evaluate the triaxial compressive strength of rocks under different confining pressures,a nonlinear empirical strength criterion based on Mohr-Coulomb criterion was proposed in this paper.Through the analysis of triaxial test strength of 11 types of rock materials,the feasibility and validity of proposed criterion was discussed.For a further verification,six typical strength criteria were selected,and the prediction results of each criterion and test results were statistically analyzed.The comparative comparison results show that the prediction results obtained by applying this new criterion to 97 conventional triaxial compression tests of 11 different rock materials are highly consistent with the experimental data.Statistical analysis was executed to assess the application of the new criterion and other classical criteria in predicting the failure behavior of rock.This proposed empirical criterion provides a new reference and method for the determination of triaxial compressive strength of rock materials.展开更多
Coal seam destabilization inflicts damage to equipment, causes property loss and personnel casualties,and severely threatens mining safety and efficient production. To further understand this destabilization based on ...Coal seam destabilization inflicts damage to equipment, causes property loss and personnel casualties,and severely threatens mining safety and efficient production. To further understand this destabilization based on the basic theory of Lippmann seam destabilization, a mathematical model was introduced for gas pressure distribution by considering intermediate principal stress and support resistance.Subsequently, we established a translation model suitable for the entire roadway coal seam with rocky roof and floor by applying the unified form of yield criterion in the state of plane strain. We also obtained the analytic expressions of coal seam stress distribution on both sides of the roadway and the widths of plastic and disturbance zones. Afterward, we analyzed several typical cases with different material yield criteria, obtained the plastic zone widths of the coal seam under different gas pressures, and assessed the effects of support resistance, roadway size, and coal strength on coal seam destabilization. Results showed that: the results obtained on the basis of Wilson and Mohr–Coulomb criteria are considerably conservative, and the use of Druker–Prager criteria to evaluate the rockburst-induced coal seam destabilization is safer than the use of the two other criteria; coal seam stability is correlated with gas pressure;and high-pressure gas accelerates the coal seam destabilization.展开更多
The Hoek-Brown(HB)strength criterion has been applied widely in a large number of projects around the world.However,this criterion ignores the intermediate principal stress s2.Many evidences have demonstrated that the...The Hoek-Brown(HB)strength criterion has been applied widely in a large number of projects around the world.However,this criterion ignores the intermediate principal stress s2.Many evidences have demonstrated that the rock strength is dependent on s2.Thus it is necessary to extend the HB criterion into a three-dimensional(3D)form.In this study,the effect of s2 on the strength of rocks is identified by reviewing the true triaxial tests of various rock types reported in the literature.A simple 3D strength criterion is developed.The modified criterion is verified by the true triaxial tests of 13 rock types.The results indicate that the modified criterion can achieve a good fit to most of rock types.It can represent a series of criteria as b varies.For comparisons,several existing 3D versions of the HB criterion are selected to predict the strengths of these rock types.It is indicated that the proposed criterion works better than other criteria.A substantial relationship between parameter b and the unconfined compressive strength is established,which guarantees that the proposed criterion can still work well even in the absence of true triaxial test data.展开更多
Based on the upper bound limit analysis theorem and the shear strength reduction technique, the equation for expressing critical limit-equilibrium state was employed to define the safety factor of a given slope and it...Based on the upper bound limit analysis theorem and the shear strength reduction technique, the equation for expressing critical limit-equilibrium state was employed to define the safety factor of a given slope and its corresponding critical failure mechanism by means of the kinematical approach of limit analysis theory. The nonlinear shear strength parameters were treated as variable parameters and a kinematically admissible failure mechanism was considered for calculation schemes. The iterative optimization method was adopted to obtain the safety factors. Case study and comparative analysis show that solutions presented here agree with available predictions when nonlinear criterion reduces to linear criterion, and the validity of present method could be illuminated. From the numerical results, it can also be seen that nonlinear parameter rn, slope foot gradient ,β, height of slope H, slope top gradient a and soil bulk density γ have significant effects on the safety factor of the slope.展开更多
Hoek–Brown(HB)strength criterion can reflect rock’s inherent failure nature,so it is more suitable for analyzing the stability of rock slopes.However,the traditional limit equilibrium methods are at present only sui...Hoek–Brown(HB)strength criterion can reflect rock’s inherent failure nature,so it is more suitable for analyzing the stability of rock slopes.However,the traditional limit equilibrium methods are at present only suitable for analyzing the rock slope stability using the linear equivalent Mohr–Coulomb(EMC)strength parameters instead of the nonlinear HB strength criterion.Therefore,a new method derived to analyze directly the rock slope stability using the nonlinear HB strength criterion for arbitrary curve slip surface was described in the limit equilibrium framework.The current method was established based on certain assumptions concerning the stresses on the slip surface through amending the initial normal stressσ0 obtained without considering the effect of inter-slice forces,and it can satisfy all static equilibrium conditions of the sliding body,so the current method can obtain the reasonable and strict factor of safety(FOS)solutions.Compared with the results of other methods in some examples,the feasibility of the current method was verified.Meanwhile,the parametric analysis shows that the slope angleβhas an important influence on the difference of the results obtained using the nonlinear HB strength criterion and its linear EMC strength parameters.Forβ≤45°,both of the results are similar,showing the traditional limit equilibrium methods using the linear EMC strength parameters and the current method are all suitable to analyze rock slope stability,but forβ>60°,the differences of both the results are obvious,showing the actual slope stability state can not be reflected in the traditional limit equilibrium methods,and then the current method should be used.展开更多
With the increase of mining depth of mineral resources,the rock mass stress state is being more and more complex.The rock mass show different features,namely,with the increase of hydrostatic pressure,rock mass failure...With the increase of mining depth of mineral resources,the rock mass stress state is being more and more complex.The rock mass show different features,namely,with the increase of hydrostatic pressure,rock mass failure mode turns from brittle tension failure to structure ductile failure and its limit strength also increases.The restriction of minimal principal stress on the initiation and development of microcrack and the change of micro-unit stress state by the intermediate principal stress play a decisive role in the increase of rock mass limit strength.Based on the rock mass failure behavior law under complex stress state and the σ2-dependence on the rock mass strength,we proposed a Modified Mohr-Coulomb(M-MC) strength criterion which is smooth and convex.Finally,the M-MC criterion is validated by multiaxial test data of eight kinds of rock mass.We also compared the fitting results with Mohr-Coulomb criterion(MC).It shows that the new criterion fits the test data better than the Mohr-Coulomb criterion.So the M-MC strength criterion well reveals the rock mass bearing behavior and can be widely used in the rock mass strength analysis.The results can provide theoretical foundations for stability analysis and reinforcement design of complex underground engineering.展开更多
In this paper, the Mohr-Coulomb shear strength criterion is modified by mobilising the cohesion and internal friction angle with normal stress, in order to capture the nonlinearity and critical state concept for intac...In this paper, the Mohr-Coulomb shear strength criterion is modified by mobilising the cohesion and internal friction angle with normal stress, in order to capture the nonlinearity and critical state concept for intact rocks reported in the literature. The mathematical expression for the strength is the same as the classical form, but the terms of cohesion and internal friction angle depend on the normal stress now,leading to a nonlinear relationship between the strength and normal stress. It covers both the tension and compression regions with different expressions for cohesion and internal friction angle. The strengths from the two regions join continuously at the transition of zero normal stress. The part in the compression region approximately satisfies the conditions of critical state, where the maximum shear strength is reached. Due to the nonlinearity, the classical simple relationship between the parameters of cohesion, internal friction angle and uniaxial compressive strength from the linear Mohr-Coulomb criterion does not hold anymore. The equation for determining one of the three parameters in terms of the other two is supplied. This equation is nonlinear and thus a nonlinear equation solver is needed. For simplicity, the classical linear relationship is used as a local approximation. The approximate modified Mohr-Coulomb criterion has been implemented in a fracture mechanics based numerical code FRACOD,and an example case of deep tunnel failure is presented to demonstrate the difference between the original and modified Mohr-Coulomb criteria. It is shown that the nonlinear modified Mohr-Coulomb criterion predicts somewhat deeper and more intensive fracturing regions in the surrounding rock mass than the original linear Mohr-Coulomb criterion. A more comprehensive piecewise nonlinear shear strength criterion is also included in Appendix B for those readers who are interested. It covers the tensile, compressive, brittle-ductile behaviour transition and the critical state, and gives smooth transitions.展开更多
Fibre-reinforced polymer(FRP)has the advantages of high strength,light weight,corrosion resistance and convenient construction and is widely used in repairing and strengthening damaged concrete columns.Most of the exi...Fibre-reinforced polymer(FRP)has the advantages of high strength,light weight,corrosion resistance and convenient construction and is widely used in repairing and strengthening damaged concrete columns.Most of the existing strength models were built by regression analysis of experimental data;however,in this article,a new unified strength model is proposed using the Hoek-Brown failure criterion.To study the strength of FRP-confined damaged and undamaged concrete columns,900 test data were collected from the published literature and a large database that contains the cross-sectional shape of each specimen,the damage type,the damage level and the FRP-confined stiffness was established.A new strength model using the Hoek-Brown failure criterion was established and is suitable for both circular and square columns that are undamaged,load-damaged and fire-damaged.Based on the database,most of the existing strength models from the published literature and the model proposed in this paper were evaluated.The evaluation shows that the proposed model can predict the compressive strength for FRP-confined pre-damaged and undamaged concrete columns with good accuracy.展开更多
As known, there is a large number of dentin tubules in dentin. These tubules have varying radii and are shaped into radially parallel pattern. The anisotropy of microstructure of dentin shows that dentin should be tre...As known, there is a large number of dentin tubules in dentin. These tubules have varying radii and are shaped into radially parallel pattern. The anisotropy of microstructure of dentin shows that dentin should be treated as a ma- terial of varying transverse isotropy. In this Part, the elastic stress-strain relations and the quadratic strength criterion are established in the form of having varying transverse isotropy, in the framework of micromechanics to take into account of the effect of the microstructures-dentin tubules. Simplified forms for isotropic and ho- mogeneous cases, as well as the corresponding plane stress form of the stress-strain relations are also given. These theoretical models are very well supported by the experiments shown later in the continued paper (Part Ⅱ).展开更多
In order to study the mechanism of bearing behavior at the tip of a pile embedded in rock, the generalized nonlinear unified strength criterion and slip line principle for resolving the differential equation systems w...In order to study the mechanism of bearing behavior at the tip of a pile embedded in rock, the generalized nonlinear unified strength criterion and slip line principle for resolving the differential equation systems which govern the stress field were applied to derive the ultimate end beating capacity based on some reasonable hypothesis and failure plane model. Both numerical simulation and test results were compared with the theoretic solution. The results show good consistency with each other and verify the validity of the present approach. The depth effect with respective to embedment ratio and other influence factors like geological strength index, intermediate principal stress, overburden factor, and damage on end bearing capacity were discussed in the analytical solution. The results show that the proposed yield criterion can be much better for investigating the ultimate end bearing performance of rock-socketed pile. The end bearing capacity increases with embedment ratio and the increasing degree is influenced intensely by the above parameters. Furthermore, ignoring intermediate stress effect would underestimate the strength properties of the rock material and lead to a very conservative estimation value.展开更多
基金Projects(52208382, 52278387, 51738002) supported by the National Natural Science Foundation of ChinaProject(2022YJS072) supported by the Fundamental Research Funds for the Central Universities,China。
文摘Ground reinforcement is crucial for tunnel construction, especially in soft rock tunnels. Existing analytical models are inadequate for predicting the ground reaction curves (GRCs) for reinforced tunnels in strain-softening (SS) rock masses. This study proposes a novel analytical model to determine the GRCs of SS rock masses, incorporating ground reinforcement and intermediate principal stress (IPS). The SS constitutive model captures the progressive post- peak failure, while the elastic-brittle model simulates reinforced rock masses. Nine combined states are innovatively investigated to analyze plastic zone development in natural and reinforced regions. Each region is analyzed separately, and coupled through boundary conditions at interface. Comparison with three types of existing models indicates that these models overestimate reinforcement effects. The deformation prediction errors of single geological material models may exceed 75%. Furthermore, neglecting softening and residual zones in natural regions could lead to errors over 50%. Considering the IPS can effectively utilize the rock strength to reduce tunnel deformation by at least 30%, thereby saving on reinforcement and support costs. The computational results show a satisfactory agreement with the monitoring data from a model test and two tunnel projects. The proposed model may offer valuable insights into the design and construction of reinforced tunnel engineering.
基金Financial support for this work was provided by the General Program and Youth Fund Program of the National Natural Science Foundation of China(Grant Nos.42377175 and 42002292).
文摘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.
基金Project(2023YFC2907403)supported by the National Key R&D Program of ChinaProject(52074021)supported by the National Natural Science Foundation of China+1 种基金Project(2242045)supported by Beijing Natural Science Foundation,ChinaProject(ZD202216)supported by the Beijing Association of Higher Education,China。
文摘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.
基金financiallysupported by the National Natural Science Foundation of China(Grant No.42577209)the Natural Science Foundation of Jiangsu Province(Grant No.BK20241489)the Open Research Fund of State Key Laboratory of Geomechanics and Geotechnical Engineering,Institute of Rock and Soil Mechanics,Chinese Academy of Sciences(Grant No.SKLGME023009).
文摘This study systematically investigated the coupling effects of confiningpressure and strain rate on the dynamic strength of granite through dynamic triaxial compression tests.A dynamic strength criterion was developed to incorporate these coupling effects for further analysis.Moreover,the research thoroughly revealed the underlying mechanism by which these coupling effects influencethe rock strength.The results revealed that both confiningpressure and strain rate significantly enhanced the dynamic strength of rock;however,a mutual inhibition effect emerged under their coupling.Specifically,as the confiningpressure increased,the strengthening effect of strain rate gradually diminished.Conversely,increasing the strain rate weakened the strengthening effect of confiningpressure.The proposed strength criterion successfully predicted rock strength under various confiningpressures(0-225 MPa)and strain rates(10^(-6)-600 s^(-1)).It achieved an average prediction error of only 8.3%,which represents a 65%improvement in accuracy compared to models that consider confiningpressure and strain rate effects independently.At the micro-mechanism level,increasing confiningpressure and strain rate promoted crack propagation in a transgranular(TG)mode,thereby enhancing the overall rock strength.However,under the coupling effects,the interference and interaction of TG cracks weakened the overall strengthening effect.This indicated that the competitive interaction between confiningpressure and strain rate during crack propagation constitutes the intrinsic mechanism underlying their mutual inhibitory effect on rock strength.This study provides a more accurate theoretical basis for understanding the dynamic responses of rocks and contributes valuable insights for disaster prevention and control in deep rock engineering projects.
文摘Room and pillar mining is an underground mining method that utilizes natural pillar support to control rock mass behavior,ensuring mine stability and a safe mine environment.This study specifically documents the influence of the intermediate principal stress component on the pillar behavior.So far only classical failure criteria ignoring the influence of the intermediate principal stress component were used for underground pillar design.By using an extended Hoek-Brown failure criterion in comparison with the classical Hoek-Brown failure criterion,the influence of the intermediate principal stress component is documented by indicating those areas where the failure criterion is violated.This study demonstrates,that depending on the rock type,the intermediate principal stress component can have a significant effect.Ignoring this influence can lead to uneconomic pillar design and incorrect determination of the factor of safety.
基金the financial support provided by the National Key R&D Program of China(Grant No.2022YFB2302102)the National Natural Science Foundation of China(Grant Nos.42472340 and 42072308).
文摘The generalized Zhang-Zhu(GZZ)strength criterion was proposed as an extension to the Hoek-Brown criterion and the Mogi criterion.The introduction to mean normal stress results in a non-smooth and non-convex yield surface,which presents a challenge for updating plastic stress.Current research primarily focuses on modified smooth GZZ criteria or approximate solutions,which inevitably lead to increased computational costs or inaccuracies.In this paper,an accurate stress updating algorithm is proposed based on the original GZZ criterion.The algorithm operates entirely in the principal stress space,where numerical singularities at the intersection of yield surfaces are avoided by defining four different types of stress updating.This approach simplifies the GZZ criterion compared to its formulation in general stress space.The return mapping is employed to compute the updated stress and consistent stiffness matrix,facilitating calculations using both finite element implicit and explicit algorithms.Finally,the accuracy of the proposed method is validated using rock true triaxial test data and semianalytical solutions for stresses and displacement around a circular opening under the GZZ criterion.
文摘Biaxial compression tests are performed on 100 mm × 100 mm × 100 mm cubic specimens of plain high-strength highperformance concrete （HSHPC） at seven kinds of stress ratios, σ2：σ3 =0 ： - 1, -0.20 ： - 1, -0.30 ： - 1, -0.40 ： - 1, -0.50 ： -1, -0. 75 ： - 1, and - 1.00 ： - 1 after exposure to normal and high temperatures of 20, 200, 300, 400, 500 and 600 ℃, using a large static-dynamic true triaxial machine. Frictionreducing pads are three layers of plastic membranes with glycerine in-between for the compressive loading plane. Failure modes of the specimens are described. The two principally static compressive strengths are measured. The influences of the temperatures and stress ratios on the biaxial strengths of HSHPC after exposure to high temperatures are also analyzed. The experimental results show that the uniaxial compressive strength of plain HSHPC after exposure to high temperatures does not decrease completely with the increase in temperature; the ratios of the biaxial to its uniaxial compressive strengths depend on the stress ratios and brittleness-stiffness of HSHPC after exposure to different high temperatures. The formula of the Kupfer-Gerstle failure criterion modified with the temperature and stress ratio parameters for plain HSHPC is proposed.
基金financial support of the National 973 Program in China (No. 61338)the National Funds in China (Nos.11772352, 61407200203 and 51328050101)
文摘Based on the dynamic loading(1-100 s^(-1)) experiments under different temperatures(223-298 K) and stress states, uniaxial and biaxial strength criterion of a Hydroxyl-terminated polybutadiene(HTPB)based composite solid propellant were further investigated. These experiments were conducted through the use of a new uniaxial INSTRON testing machine, different new designed gripping apparatus and samples with different configurations. According to the test results, dynamic uniaxial tensile strength criterion of the propellant was directly constructed with the master curve of the uniaxial maximum tensile stress. Whereas, a new method was proposed to determine the dynamic uniaxial compressive strength of the propellant in this study. Then uniaxial compressive strength criterion of the propellant was constructed based on the related master curve. Moreover, it found that the uniaxial tensilecompressive strength ratio of the propellant is more sensitive to loading temperature under the test conditions. The value of this parameter is about 0.4 at room temperature, and it reduces to 0.2-0.3 at low temperatures. Finally, the theoretical biaxial strength criterion of HTPB propellant under dynamic loading was constructed with the unified strength theory, the uniaxial strength and the typical biaxial tensile strength. In addition, the theoretical limit lines of the principal stress plane for the propellant under dynamic loading at different temperatures were further plotted, and the scope of the limit line increases with decreasing temperature.
基金supported by Western Transportation Technology Funds of China (200731800038)the Special Fund for Basic Scientific Research of Central Colleges,Chang’an University(CHD2011JC175)
文摘The Hoek-Brown （HB） strength criterion has been widely applied to the estimation of strength of intact rock and rock mass, while evolving ever since. However, negligence of the effect of the intermediate principal stress still remains in the criterion＇s latest version. At the same time, several three-dimensional （3D） HB strength, which can takes into account the influence of the intermediate principal stress, have already been proposed, among which the 3D HB criterion proposed by Zhang and Zhu seems to be the most reasonable one. However, the Zhang 3D HB criterion may have problems with some stress path close to triaxial extension state because of the non-convexity characteristic of its failure surface. In this paper, a new 3D HB strength criterion is presented based on a generalized form of the HB criterion, which also considers the effect of the intermediate principal stress and inherits all the merits of the original version of the HB criterion. In addition, this new criterion can remedy to some extent the shortcomings observed in the Zhang 3D HB criterion. Polyaxial tests for five different rocks from pub- lished literatures are used for evaluating this new criterion and comparing it with the Zhang 3D HB criterion. The re- sults show that this new criterion may over-predict or under- predict the polyaxial strength of rocks but the errors are rela- tively small, and similar results are also found for the Zhang 3D HB criterion, which one is better depends on the type of the rock under estimation.
基金Project supported by the National Natural Science Foundation of China (Nos. 50438020 and 50578162).
文摘A new unified strength criterion in the principal stress space has been proposed for use with normal strength concrete （NC） and high strength concrete （HSC） in compressioncompression-tension, compression-tension-tension, triaxial tension, and biaxial stress states. The study covers concrete with strengths ranging from 20 to 130 MPa. The conception of damage Poisson＇s ratio is defined and the expression for damage Poisson＇s ratio is determined basically. The failure mechanism of concrete is illustrated, which points out that damage Poisson＇s ratio is the key to determining the failure of concrete. Furthermore, for the concrete under biaxial stress conditions, the unified strength criterion is simplified and a simplified strength criterion in the form of curves is also proposed. The strength criterion is physically meaningful and easy to calculate, which can be applied to analytic solution and numerical solution of concrete structures.
基金Project(51774322)supported by the National Natural Science Foundation of ChinaProject(2018JJ2500)supported by Natural Science Foundation of Hunan Province,China+1 种基金Project(2020JGB135)supported by Degree and Postgraduate Education Reform Project of Central South University,ChinaProject(2018zzts209)supported by the Fundamental Research Funds for the Central Universities,China。
文摘The failure criterion of rocks is a critical factor involved in reliability design and stability analysis of geotechnical engineering.In order to accurately evaluate the triaxial compressive strength of rocks under different confining pressures,a nonlinear empirical strength criterion based on Mohr-Coulomb criterion was proposed in this paper.Through the analysis of triaxial test strength of 11 types of rock materials,the feasibility and validity of proposed criterion was discussed.For a further verification,six typical strength criteria were selected,and the prediction results of each criterion and test results were statistically analyzed.The comparative comparison results show that the prediction results obtained by applying this new criterion to 97 conventional triaxial compression tests of 11 different rock materials are highly consistent with the experimental data.Statistical analysis was executed to assess the application of the new criterion and other classical criteria in predicting the failure behavior of rock.This proposed empirical criterion provides a new reference and method for the determination of triaxial compressive strength of rock materials.
基金support of National Natural Science Foundation of China (Nos. 51674158 and 51604168)the Natural Science Foundation of Shandong Provincial (No. ZR2016EEQ18)+2 种基金and the Source Innovation Program (Applied Research Special-Youth Special) of Qingdao (No. 17-1-138-jch)Shandong University of Science and Technology ResearchFund (No. 2015JQJH105)the Taishan Scholar Talent Team Support Plan for Advantaged & Unique Discipline Areas
文摘Coal seam destabilization inflicts damage to equipment, causes property loss and personnel casualties,and severely threatens mining safety and efficient production. To further understand this destabilization based on the basic theory of Lippmann seam destabilization, a mathematical model was introduced for gas pressure distribution by considering intermediate principal stress and support resistance.Subsequently, we established a translation model suitable for the entire roadway coal seam with rocky roof and floor by applying the unified form of yield criterion in the state of plane strain. We also obtained the analytic expressions of coal seam stress distribution on both sides of the roadway and the widths of plastic and disturbance zones. Afterward, we analyzed several typical cases with different material yield criteria, obtained the plastic zone widths of the coal seam under different gas pressures, and assessed the effects of support resistance, roadway size, and coal strength on coal seam destabilization. Results showed that: the results obtained on the basis of Wilson and Mohr–Coulomb criteria are considerably conservative, and the use of Druker–Prager criteria to evaluate the rockburst-induced coal seam destabilization is safer than the use of the two other criteria; coal seam stability is correlated with gas pressure;and high-pressure gas accelerates the coal seam destabilization.
基金This work was supported by the Key Research and Development Programof Shaanxi,China(Grant Nos.2019SF-231and 2020SF-394)the Natural Science Foundation of China(Grant No.41630639).
文摘The Hoek-Brown(HB)strength criterion has been applied widely in a large number of projects around the world.However,this criterion ignores the intermediate principal stress s2.Many evidences have demonstrated that the rock strength is dependent on s2.Thus it is necessary to extend the HB criterion into a three-dimensional(3D)form.In this study,the effect of s2 on the strength of rocks is identified by reviewing the true triaxial tests of various rock types reported in the literature.A simple 3D strength criterion is developed.The modified criterion is verified by the true triaxial tests of 13 rock types.The results indicate that the modified criterion can achieve a good fit to most of rock types.It can represent a series of criteria as b varies.For comparisons,several existing 3D versions of the HB criterion are selected to predict the strengths of these rock types.It is indicated that the proposed criterion works better than other criteria.A substantial relationship between parameter b and the unconfined compressive strength is established,which guarantees that the proposed criterion can still work well even in the absence of true triaxial test data.
基金Project(2006318802111) supported by West Traffic Construction Science and Technology of ChinaProject(2008yb004) supported by Excellent Doctorate Dissertations of Central South University, China Project(2008G032-3) supported by Key Item of Science and Technology Research of Railway Ministry of China
文摘Based on the upper bound limit analysis theorem and the shear strength reduction technique, the equation for expressing critical limit-equilibrium state was employed to define the safety factor of a given slope and its corresponding critical failure mechanism by means of the kinematical approach of limit analysis theory. The nonlinear shear strength parameters were treated as variable parameters and a kinematically admissible failure mechanism was considered for calculation schemes. The iterative optimization method was adopted to obtain the safety factors. Case study and comparative analysis show that solutions presented here agree with available predictions when nonlinear criterion reduces to linear criterion, and the validity of present method could be illuminated. From the numerical results, it can also be seen that nonlinear parameter rn, slope foot gradient ,β, height of slope H, slope top gradient a and soil bulk density γ have significant effects on the safety factor of the slope.
基金Project(2015M580702)supported by China Postdoctoral Science FoundationProject(51608541)supported by the National Natural Science Foundation of ChinaProject(2014122066)supported by the Guizhou Provincial Department of Transportation Foundation,China
文摘Hoek–Brown(HB)strength criterion can reflect rock’s inherent failure nature,so it is more suitable for analyzing the stability of rock slopes.However,the traditional limit equilibrium methods are at present only suitable for analyzing the rock slope stability using the linear equivalent Mohr–Coulomb(EMC)strength parameters instead of the nonlinear HB strength criterion.Therefore,a new method derived to analyze directly the rock slope stability using the nonlinear HB strength criterion for arbitrary curve slip surface was described in the limit equilibrium framework.The current method was established based on certain assumptions concerning the stresses on the slip surface through amending the initial normal stressσ0 obtained without considering the effect of inter-slice forces,and it can satisfy all static equilibrium conditions of the sliding body,so the current method can obtain the reasonable and strict factor of safety(FOS)solutions.Compared with the results of other methods in some examples,the feasibility of the current method was verified.Meanwhile,the parametric analysis shows that the slope angleβhas an important influence on the difference of the results obtained using the nonlinear HB strength criterion and its linear EMC strength parameters.Forβ≤45°,both of the results are similar,showing the traditional limit equilibrium methods using the linear EMC strength parameters and the current method are all suitable to analyze rock slope stability,but forβ>60°,the differences of both the results are obvious,showing the actual slope stability state can not be reflected in the traditional limit equilibrium methods,and then the current method should be used.
基金supported by the National Natural Science Foundation of China (Nos.50774082 and 50804046)
文摘With the increase of mining depth of mineral resources,the rock mass stress state is being more and more complex.The rock mass show different features,namely,with the increase of hydrostatic pressure,rock mass failure mode turns from brittle tension failure to structure ductile failure and its limit strength also increases.The restriction of minimal principal stress on the initiation and development of microcrack and the change of micro-unit stress state by the intermediate principal stress play a decisive role in the increase of rock mass limit strength.Based on the rock mass failure behavior law under complex stress state and the σ2-dependence on the rock mass strength,we proposed a Modified Mohr-Coulomb(M-MC) strength criterion which is smooth and convex.Finally,the M-MC criterion is validated by multiaxial test data of eight kinds of rock mass.We also compared the fitting results with Mohr-Coulomb criterion(MC).It shows that the new criterion fits the test data better than the Mohr-Coulomb criterion.So the M-MC strength criterion well reveals the rock mass bearing behavior and can be widely used in the rock mass strength analysis.The results can provide theoretical foundations for stability analysis and reinforcement design of complex underground engineering.
基金the International Collaboration Project on Coupled Fracture Mechanics Modelling(project team consisting of CSIRO,SDUST,Posiva,KIGAM,KICT,CAS-IRSM,DUT/Mechsoft,SNU,LBNL,ETH,Aalto Uni.,GFZ and TYUT)Taishan Scholar Talent Team Support Plan for Advantaged&Unique Discipline Areas,Shandong Province
文摘In this paper, the Mohr-Coulomb shear strength criterion is modified by mobilising the cohesion and internal friction angle with normal stress, in order to capture the nonlinearity and critical state concept for intact rocks reported in the literature. The mathematical expression for the strength is the same as the classical form, but the terms of cohesion and internal friction angle depend on the normal stress now,leading to a nonlinear relationship between the strength and normal stress. It covers both the tension and compression regions with different expressions for cohesion and internal friction angle. The strengths from the two regions join continuously at the transition of zero normal stress. The part in the compression region approximately satisfies the conditions of critical state, where the maximum shear strength is reached. Due to the nonlinearity, the classical simple relationship between the parameters of cohesion, internal friction angle and uniaxial compressive strength from the linear Mohr-Coulomb criterion does not hold anymore. The equation for determining one of the three parameters in terms of the other two is supplied. This equation is nonlinear and thus a nonlinear equation solver is needed. For simplicity, the classical linear relationship is used as a local approximation. The approximate modified Mohr-Coulomb criterion has been implemented in a fracture mechanics based numerical code FRACOD,and an example case of deep tunnel failure is presented to demonstrate the difference between the original and modified Mohr-Coulomb criteria. It is shown that the nonlinear modified Mohr-Coulomb criterion predicts somewhat deeper and more intensive fracturing regions in the surrounding rock mass than the original linear Mohr-Coulomb criterion. A more comprehensive piecewise nonlinear shear strength criterion is also included in Appendix B for those readers who are interested. It covers the tensile, compressive, brittle-ductile behaviour transition and the critical state, and gives smooth transitions.
基金Project(2017M622540)supported by the China Postdoctoral Science FoundationProject(51808419)supported by the National Natural Science Foundation of China+1 种基金Project(2019CFB217)supported by the National Natural Science Foundation of Hubei Province,ChinaProject(201623)supported by the Science and Technology Project of Wuhan Urban and Rural Construction Committee,China。
文摘Fibre-reinforced polymer(FRP)has the advantages of high strength,light weight,corrosion resistance and convenient construction and is widely used in repairing and strengthening damaged concrete columns.Most of the existing strength models were built by regression analysis of experimental data;however,in this article,a new unified strength model is proposed using the Hoek-Brown failure criterion.To study the strength of FRP-confined damaged and undamaged concrete columns,900 test data were collected from the published literature and a large database that contains the cross-sectional shape of each specimen,the damage type,the damage level and the FRP-confined stiffness was established.A new strength model using the Hoek-Brown failure criterion was established and is suitable for both circular and square columns that are undamaged,load-damaged and fire-damaged.Based on the database,most of the existing strength models from the published literature and the model proposed in this paper were evaluated.The evaluation shows that the proposed model can predict the compressive strength for FRP-confined pre-damaged and undamaged concrete columns with good accuracy.
基金The project supported by the National Natural Science Foundation of China (19525207).
文摘As known, there is a large number of dentin tubules in dentin. These tubules have varying radii and are shaped into radially parallel pattern. The anisotropy of microstructure of dentin shows that dentin should be treated as a ma- terial of varying transverse isotropy. In this Part, the elastic stress-strain relations and the quadratic strength criterion are established in the form of having varying transverse isotropy, in the framework of micromechanics to take into account of the effect of the microstructures-dentin tubules. Simplified forms for isotropic and ho- mogeneous cases, as well as the corresponding plane stress form of the stress-strain relations are also given. These theoretical models are very well supported by the experiments shown later in the continued paper (Part Ⅱ).
基金Project(2007AA11Z134) supported by the National High-tech Research and Development Program of ChinaProject(10JJ4035) supported by Hunan Provincial Natural Science Foundation of ChinaProject(04SK2008) supported by Hunan Provincial Science and Technology Department,China
文摘In order to study the mechanism of bearing behavior at the tip of a pile embedded in rock, the generalized nonlinear unified strength criterion and slip line principle for resolving the differential equation systems which govern the stress field were applied to derive the ultimate end beating capacity based on some reasonable hypothesis and failure plane model. Both numerical simulation and test results were compared with the theoretic solution. The results show good consistency with each other and verify the validity of the present approach. The depth effect with respective to embedment ratio and other influence factors like geological strength index, intermediate principal stress, overburden factor, and damage on end bearing capacity were discussed in the analytical solution. The results show that the proposed yield criterion can be much better for investigating the ultimate end bearing performance of rock-socketed pile. The end bearing capacity increases with embedment ratio and the increasing degree is influenced intensely by the above parameters. Furthermore, ignoring intermediate stress effect would underestimate the strength properties of the rock material and lead to a very conservative estimation value.
