Modeling time-dependent mechanical behavior of hard rock considering excavation-induced damage and complex 3D stress states

To investigate the long-term stability of deep rocks,a three-dimensional(3D)time-dependent model that accounts for excavation-induced damage and complex stress state is developed.This model comprises three main components:a 3D viscoplastic isotropic constitutive relation that considers excavation damage and complex stress state,a quantitative relationship between critical irreversible deformation and complex stress state,and evolution characteristics of strength parameters.The proposed model is implemented in a self-developed numerical code,i.e.CASRock.The reliability of the model is validated through experiments.It is indicated that the time-dependent fracturing potential index(xTFPI)at a given time during the attenuation creep stage shows a negative correlation with the extent of excavationinduced damage.The time-dependent fracturing process of rock demonstrates a distinct interval effect of the intermediate principal stress,thereby highlighting the 3D stress-dependent characteristic of the model.Finally,the influence of excavation-induced damage and intermediate principal stress on the time-dependent fracturing characteristics of the surrounding rocks around the tunnel is discussed.

Microdynamic mechanical properties and fracture evolution mechanism of monzogabbro with a true triaxial multilevel disturbance method

The far-field microdynamic disturbance caused by the excavation of deep mineral resources and underground engineering can induce surrounding rock damage in high-stress conditions and even lead to disasters.However,the mechanical properties and damage/fracture evolution mechanisms of deep rock induced by microdynamic disturbance under three-dimensional stress states are unclear.Therefore,a true triaxial multilevel disturbance test method is proposed,which can completely simulate natural geostress,excavation stress redistribution(such as stress unloading,concentration and rotation),and subsequently the microdynamic disturbance triggering damaged rock failure.Based on a dynamic true triaxial test platform,true triaxial microdynamic disturbance tests under different frequency and amplitudes were carried out on monzogabbro.The results show that increasing amplitude or decreasing frequency diminishes the failure strength of monzogabbro.Deformation modulus gradually decreases during disturbance failure.As frequency and amplitude increase,the degradation rate of deformation modulus decreases slightly,disturbance dissipated energy increases significantly,and disturbance deformation anisotropy strengthens obviously.A damage model has been proposed to quantitatively characterize the disturbance-induced damage evolution at different frequency and amplitude under true triaxial stress.Before disturbance failure,the micro-tensile crack mechanism is dominant,and the micro-shear crack mechanism increases significantly at failure.With the increase of amplitude and frequency,the micro-shear crack mechanism increases.When approaching disturbance failure,the acoustic emission fractal dimension changes from a stable value to local large oscillation,and finally increases sharply to a high value at failure.Finally,the disturbance-induced failure mechanism of surrounding rock in deep engineering is clearly elucidated.

Investigation of anisotropic strength criteria for layered rock mass

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

Mechanical parameter evolutions and deterioration constitutive model for ductile-brittle failure of surrounding rock in high-stress underground engineering

The deep surrounding rock is usually in the true triaxial stress state,and previous constitutive models based on the understanding of uniaxial and conventional triaxial test results have difficulty characterizing the degradation and fracture process of rock ductile–brittle failure under true triaxial stress state.Therefore,this study conducted a series of true triaxial tests to obtain the understanding of the ductile–brittle behaviour of rock,and then combined the test results and the Mogi–Coulomb strength criterion,and proposed calculation methods for the elastic modulus E,cohesion c and internal friction angle u and the evolution functions of E,c and u of rock under true triaxial stresses.With the decreasing of the minimum principal stress r3 or increasing of the intermediate principal stress r2,the marble post-peak stress drop rate gradually increases,the ductility gradually weakens,and the brittleness significantly strengthens.The calculation method and evolution function of rock E,c and u under true triaxial stress were proposed.E decreased at first and then tended to remain stable with the increasing of equivalent plastic strain increment dep.c and u slowly increased at first and then rapidly decreased.With a method of parameter degradation rate to realize post-peak stress drop rate to reflect the ductile–brittle characteristics,a new three-dimensional ductile–brittle deterioration mechanical model(3DBDM)was established.The proposed model can accurately characterize the influence of r2 and r3 on mechanical parameters,the ductile–brittle behaviour of rock under true triaxial stresses,and the asymmetric failure characteristics of surrounding rock after excavation of deep underground engineering.The proposed model can be reduced to elastic–perfectly plastic,elastic–brittle,cohesion weakening friction strengthening(CWFS),Mohr–Coulomb,and Drucker–Prager models.

Mechanism of progressive failure of a slope with a steep joint under the action of freezing and thawing:model test

The stability of slope rock masses is influenced by freeze-thaw cycles in cold region,and the mechanism of stability deterioration is not clear.In order to understand the damage and progressive failure characteristics of rock masses under the action of freezing and thawing,a model test was conducted on slope with steep joint in this study.The temperature,frost heaving pressure and deformation of slope rock mass were monitored in real-time during the test and the progressive failure mode was studied.The experimental results show that the temperature variations of cracking and the rock mass of a slope are different.There are obvious latent heat stages in the temperature-change plot in the crack,but not in the slope rock masses.The frost heaving effect in the fracture is closely related to the constraint conditions,which change with the deformation of the fracture.The frost heaving pressure fluctuates periodically during freezing and continues to decrease during thawing.The surface deformation of the rock mass increases during freezing,and the deformation is restored when it thaws.Freeze-thaw cycling results in residual deformation of the rock mass which cannot be fully restored.Analysis shows that the rock mass at the free side of the steep-dip joint rotates slightly under the frost heaving effect,causing fracture propagation.The fracture propagation pattern is a circular arc at the beginning,then extends to the possible sliding direction of the rock mass.Frost heaving force and fracture water pressure are the key factors for the failure of the slope,which can cause the crack to penetrate the rock mass,and a landslide ensues when the overall anti-sliding resistance of the rock mass is overcome.

Post-liquefaction shearing behaviour of saturated gravelly soils: Experimental study and discrete element simulation

To investigate the post-liquefaction shearing behaviour of saturated gravelly soil,laboratory tests were conducted using a staticedynamic multi-purpose triaxial apparatus.In addition,numerical simulations using the discrete element method(DEM)were performed to preliminarily understand the micromechanism of gravelly soil in monotonic loading after liquefaction.The influences of dry density,initial confining stress and degree of liquefaction on the post-liquefaction shearing behaviour of gravelly soil were discussed,and the evolution of the micro-parameters of the granular system was also analysed.The results show that the stressestrain responses of gravelly soil after liquefaction can be divided into three stages:(1)low strength stage,(2)super-linear strength recovery stage,and(3)sublinear strength recovery stage,which are distinctly different from those of the general saturated gravelly soil without previous cyclic loading.The initial state and prior dynamic stress history have significant influences on the post-liquefaction shearing behaviour of gravelly soil.The DEM simulation revealed that the average coordination number sharply increases,the contact normal shows an obvious orientation distribution,and the destroyed force chain backbones are reconstructed in the monotonic reloading process after liquefaction.The evolution of the micro-parameters of the granular system clearly reflects the interior interaction process and micro-mechanisms in the particles during the three different stages of the macro-mechanical behaviour of gravelly soil.

Characterizing large-scale weak interlayer shear zones using conditional random field theory

The shear behavior of large-scale weak intercalation shear zones(WISZs)often governs the stability of foundations,rock slopes,and underground structures.However,due to their wide distribution,undulating morphology,complex fabrics,and varying degrees of contact states,characterizing the shear behavior of natural and complex large-scale WISZs precisely is challenging.This study proposes an analytical method to address this issue,based on geological fieldwork and relevant experimental results.The analytical method utilizes the random field theory and Kriging interpolation technique to simplify the spatial uncertainties of the structural and fabric features for WISZs into the spatial correlation and variability of their mechanical parameters.The Kriging conditional random field of the friction angle of WISZs is embedded in the discrete element software 3DEC,enabling activation analysis of WISZ C2 in the underground caverns of the Baihetan hydropower station.The results indicate that the activation scope of WISZ C2 induced by the excavation of underground caverns is approximately 0.5e1 times the main powerhouse span,showing local activation.Furthermore,the overall safety factor of WISZ C2 follows a normal distribution with an average value of 3.697.

Upper-Bound Limit Analysis of the Multi-Layer Slope Stability and Failure Mode Based on Generalized Horizontal Slice Method

Multi-layer slopes are widely found in clay residue receiving fields.A generalized horizontal slice method(GHSM)for assessing the stability of multi-layer slopes that considers the energy dissipation between adjacent horizontal slices is presented.In view of the upper-bound limit analysis theory,the energy equation is derived and the ultimate failure mode is generated by comparing the sliding surface passing through the slope toe(mode A)with that below(mode B).In addition,the influence of the number of slices on the stability coefficients in the GHSM is studied and the stable value is obtained.Compared to the original method(Chen’s method),the GHSM can acquire more precise results,which takes into account the energy dissipation in the inner sliding soil mass.Moreover,the GHSM,limit equilibrium method(LEM)and numerical simulation method(NSM)are applied to analyze the stability of a multi-layer slope with different slope angles and the results of the safety factor and failure mode are very close in each case.The ultimate failure modes are shown to be mode B when the slope angle is not more than 28°.It illustrates that the determination of the ultimate sliding surface requires comparison of multiple failure modes,not only mode A.

Unsaturated expansive soil fissure characteristics combined with engineering behaviors

The relationship among the surface fissure ratio, moisture content, seepage coefficient and deformation modulus of field unsaturated expansive soil in Nanning, Guangxi Province, China, was obtained by a direct or indirect method. Digital images of expansive soil of the surface fissure with different moisture contents were analyzed with the binarization statistic method. In addition, the fissure fractal dimension was computed with a self-compiled program. Combined with in situ seepage and loading plate tests, the relationship among the surface fissure ratio, moisture content, seepage coefficient and deformation modulus was initially established. The surface fissure ratio and moisture content show a linear relation, ＂y=-0.019 1x＋1.028 5＂ for rufous expansive soil and ＂y=-0.07 1x＋2.610 5＂ for grey expansive soil. Soil initial seepage coefficient and surface fissure ratio show a power function relation, ＂y=1× 10^-9exp（15.472x）＂ for rufous expansive soil and ＂y=5× 10^-7exp（4.209 6x）＂ for grey expansive soil. Grey expansive soil deformation modulus and surface fissure ratio show a power fimction relation of ＂y=3.935 7exp（0.993 6x）＂. Based on the binarization and fractal dimension methods, the results show that the surface fissure statistics can depict the fissure distribution in the view of two dimensions. And the evolvement behaviors of permeability and the deformation modulus can indirectly describe the developing state of the fissure. The analysis reflects that the engineering behaviors of unsaturated expansive soil are objectively influenced by fissure.

A linearly-independent higher-order extended numerical manifold method and its application to multiple crack growth simulation

The numerical manifold method(NMM)can be viewed as an inherent continuous-discontinuous numerical method,which is based on two cover systems including mathematical and physical covers.Higher-order NMM that adopts higher-order polynomials as its local approximations generally shows higher precision than zero-order NMM whose local approximations are constants.Therefore,higherorder NMM will be an excellent choice for crack propagation problem which requires higher stress accuracy.In addition,it is crucial to improve the stress accuracy around the crack tip for determining the direction of crack growth according to the maximum circumferential stress criterion in fracture mechanics.Thus,some other enriched local approximations are introduced to model the stress singularity at the crack tip.Generally,higher-order NMM,especially first-order NMM wherein local approximations are first-order polynomials,has the linear dependence problems as other partition of unit(PUM)based numerical methods does.To overcome this problem,an extended NMM is developed based on a new local approximation derived from the triangular plate element in the finite element method(FEM),which has no linear dependence issue.Meanwhile,the stresses at the nodes of mathematical mesh(the nodal stresses in FEM)are continuous and the degrees of freedom defined on the physical patches are physically meaningful.Next,the extended NMM is employed to solve multiple crack propagation problems.It shows that the fracture mechanics requirement and mechanical equilibrium can be satisfied by the trial-and-error method and the adjustment of the load multiplier in the process of crack propagation.Four numerical examples are illustrated to verify the feasibility of the proposed extended NMM.The numerical examples indicate that the crack growths simulated by the extended NMM are in good accordance with the reference solutions.Thus the effectiveness and correctness of the developed NMM have been validated.

Effects of liquefaction-induced large lateral ground deformation on pile foundations

The pile-soil system interaction computational model in liquefaction-induced lateral spreading ground was established by the finite difference numerical method.Considering an elastic-plastic subgrade reaction method,numerical methods involving finite difference approach of pile in liquefaction-induced lateral spreading ground were derived and implemented into a finite difference program.Based on the monotonic loading tests on saturated sand after liquefaction,the liquefaction lateral deformation of the site where group piles are located was predicted.The effects of lateral ground deformation after liquefaction on a group of pile foundations were studied using the fmite difference program mentioned above,and the failure mechanism of group piles in liquefaction-induced lateral spreading ground was obtained.The applicability of the program was preliminarily verified.The results show that the bending moments at the interfaces between liquefied and non-liquefied soil layers are larger than those at the pile＇s top when the pile＇s top is embedded.The value of the additional static bending moment is larger than the peak dynamic bending moment during the earthquake,so in the pile foundation design,more than the superstructure＇s dynamics should be considered and the effect of lateral ground deformation on pile foundations cannot be neglected.

Model test of the stability degradation of a prestressed anchored rock slope system in a corrosive environment

The long-term stability of a prestressed anchored slope might be influenced by the durability of the anchorage structure.To understand long-term stability of anchored rock slopes,the research presented herein evaluated the performance evolution of a prestressed anchored bedding slope system in a corrosive environment by model test.The corrosion process in a prestressed anchor bar was monitored in terms of its open-circuit potential(OCP),corrosion current density(CCD),and electrochemical impedance spectroscopy(EIS).The stability of the prestressed anchored slope was evaluated by monitoring changes in anchorage force and displacements.The experimental results show that prestress and oxygen could reduce the corrosion resistance of the anchor bar,and anchor bars in a chloride-rich environment are very susceptible to corrosion.Prestressed tendons in a corrosive environment suffer a loss of anchorage force,the prestress decreases rapidly after locking,and the rate thereof decreases until stabilising;in the later stage,corrosion leads to the reduction of the cross-sectional area of the steel bar which may cause the reduction in anchorage force again.Anchorage force controls the deformation and stability of the anchored slope,the prestress loss caused by later corrosion may lead to an increased rate of displacement and stability degradation of the prestressed anchored rock slope.

An improved specimen preparation method for marine shallow gasbearing sand sediments and its validations

Instabilities of shallow gas-charged seabed are potential geological hazards in ocean engineering.In practice,the conventional field sampling techniques failed to obtain undisturbed gas-bearing sediments from the seabed for laboratory mechanical testing because of sensitive gas exsolution and escape from sediments.However,preparation of representative remoulded gas-charged specimens is a challenging issue,because it is rather difficult to quantitatively control the gas content and obtain uniform distribution of gas bubbles within the specimen.Given the above problems,this work proposes a reliable approach to reconstitute the high-saturation specimen of gas-charged sediments in the laboratory by an improved multifunction integrated triaxial apparatus(MITA).This apparatus is developed based on an advanced stress path triaxial system by introducing a temperature-controlled system and a wavemonitoring system.The temperature-controlled system is used to accurately mimic the in situ environments of sediments in the seabed.The wave-monitoring system is utilized to identify exsolution point of free gas and examine the disturbance of gas to specimens during gas exsolution.The detailed procedure of gassy specimen preparation is introduced.Then,the quality of prepared specimens using our improved apparatus is validated by the high-resolution micro-X-ray computed tomography(mCT)scanning test,from which bubble occurrence and size distribution within the gassy sand specimen can be obtained;and preliminary mechanical tests on gassy sand specimens with various initial saturation degrees are performed.The proposed specimen preparation procedure succeeds in proving the postulated occurrence state of gas bubbles in coarse-grained sediments and accurately controlling the gas content.

Outdoor Aging Performance of HDPE Geogrid

An outdoor aging test base for geosynthetics was established in Wuhan,central China to investigate the long-term aging performance of geosynthetics. Outdoor photo-oxygen aging tests for high density polyethylene(HDPE) geogrid have been carried out in the base. Test results show that in the initial nine months,the tensile strength of geogrid remains unchanged or even gets larger,while the corresponding strain at break decreases slightly,exhibiting hard and brittle trend due to secondary compensatory responses to the ultraviolet(UV) aging: UV provides the required chemical crosslinking energy,resulting in the polymer crosslinking reaction. Tensile strength of the geogrid increases by about 5% in the initial nine months,but decreases after the initial nine months. The long-term research results at the test base could provide first-hand data for researching the aging properties of HDPE geogrid.

Cleaner geopolymer prepared by co-activation of gasification coal fly ash and steel slag:durability properties and economic assessment

Geopolymer is a material with high early strength.However,the insufficient durability properties,such as long-term strength,acid-base resistance,freeze-thaw resistance,leaching toxicity,thermal stability,sulfate resistance and carbonation resistance,restrain its practical application.Herein,a longterm stable geopolymer composite with high final strength(ASK1)was synthesized from shell coal gasification fly ash(SFA)and steel slag(SS).Additionally,a geopolymer composite with high early strength(ASK2)was also synthesized for comparison.The results showed that ASK1 exhibited better performance on freezing-thawing resistance,carbonization resistance and heavy metals stabilization compared to the ASK2 at long-term curing.Raising the curing temperature could accelerate the unconfined compressive strength(UCS)development at initial curing ages of 3 to 7 d.Both ASK1 and ASK2 exhibited excellent acid-base and sulfate corrosion resistance.An increase for UCS was seen under KOH solution and MgSO_(4)solution corrosion for ASK1.All leaching concentrations of heavy metals out of the two geopolymers were below the standard threshold,even after 50 freezingthawing cycles.Both ASK1 and ASK2 geopolymer concrete exhibited higher sustainability and economic efficiency than Portland cement concrete.The result of this study not only provides a suitable way for the utilization of industrial solid waste in civil and environmental engineering,but also opens a new approach to improve the long-term stabilities of the geopolymers.

Compression Characteristic and Creep Behavior of Moraine Soil at Xingkang Bridge,West Sichuan,China

The compression and creep characteristics of moraine soil are important mechanical properties of geomaterials to be analyzed during the construction process of engineering projects.However,related references about these characteristics through large-size in-situ tests have rarely been reported.In this study,in-situ tests of particle size distribution,compression deformation,and compression creep were conducted at the Xingkang Bridge,West Sichuan,China.The results show that the uniformity coefficient of moraine soil ranges from 12.1 to 183.3,and gradation coefficient ranges from 0.4 to 2.8.The total compression deformations of moraine samples during the conventional compression deformation test are 4.70,4.07,and 0.47 mm,and their residual deformations are 2.81,2.45,and 0.22 mm,respectively.The deformation modulus ranges from 127.3 to 676.4 MPa,and elastic modulus ranges from 316.3 to 765.7 MPa.During compression creep tests,moraine soil enters the steady creep stage after 3.8 h of loading pressure at 445 k Pa,and it keeps steady after 14 h of loading pressure at 900 k Pa.The Burgers model and generalized Kelvin model predict the deformation well in transient,deceleration and steady creep stages.Results provide a valuable reference for the analysis of the compression deformation and creep behavior of moraine soil during engineering construction and management.

Model Test Study on Response of Weathered Rock Slope to Rainfall Infiltration under Different Conditions

Weathered rock(especially granite)slopes are prone to failure under the action of rainfall,making it necessary to study the response of weathered rock slope to rainfall infiltration for landslide prevention.In this study,a series of model tests of weathered rock slope under different conditions were conducted.The matric suction,volumetric water content,earth pressure and deformation of slope were monitored in real time during rainfall.The response of the slope to rainfall infiltration,failure process and failure mode of slope under different conditions were analyzed,and the early warning criterion for the failure of weathered rock slope caused by rainfall was studied.The results show that the slope deformation evolution process under rainfall condition was closely related to the dissipation of matric suction.When the distribution of the matrix suction(or water content)of slope met the condition that the resistance to sliding of the slip-mass was overcome,the displacement increased sharply and landslide occurred.Three factors including rainfall process,lithologic condition and excavation condition significantly affect the response of weathered rock slope to rainfall.It can be found from the test results under different conditions that compared with intermittent rainfall condition,the rainfall intensity and infiltration depth were smaller when the slope entering accelerated deformation stage under the condition of incremental rainfall.The accumulated rainfall when weathered clastic landslide occurring was greater than that of weathered granite,which results in greater disaster risk.The excavation angle and moisture distribution of a slope were the main factors affecting the stability of a slope.In addition,the evolution processes and critical displacement velocities of slopes were studied by combining the deformation curves and matrix suction curves,which can be used as reference for early warning of rainfall-induced weathered rock landslide.

Effect of confining pressure on rock breaking by high-pressure waterjet-assisted TBM

High-pressure waterjet-assisted tunnel boring machine(WTBM)is an efficient method for improving the tunneling performance of a tunnel boring machine(TBM)and reducing the wear of its disc cutters in hard rock with high geostresses.Confining pressure directly affects the efficiency of rock breaking and the configuration of the disc cutters.In this study,we evaluated the effect of confining pressure on WTBM rock breaking by developing a self-designed and manufactured experimental system,including confining pressure loading,TBM disc-cutter penetration,and high-pressure waterjet.The macro fracture,acoustic emission(AE),peak normal force drop,and specific energy(SE)were analyzed for four different confining pressures(10,20,30,and 35 MPa).The results showed that the cutting depth of the waterjet increased linearly as the waterjet pressure increased and decreased with the gradual increase in the nozzle moving speed.The expansion and development of cracks formed rock debris,and the size of the rock fragments decreased with an increase in confining pressure.When the waterjet pressure was 280 MPa,the nozzle moving velocity was 800 mm/min and the kerf space was 75 mm,which indicated that the confining pressure,which was 23.16 MPa,minimized the cutting SE under this condition.However,regardless of the confining pressure,the maximum normal force of WTBM was less than that of a TBM,whereas the SE of WTBM was less than that of complete TBM cutting mode(CTCM).The average force drop and average drop rate of SE were approximately 25%,and 80%,respectively.The results of this study can inspire the design and mechanism of a TBM assisted by a high-pressure waterjet.

Deformation Forecasting of Huangtupo Riverside Landslide in the Case of Frequent Microseisms

Ever since the impoundment of Three Gorges Reservoir（TGR）, the seismicity in head region of TGR has increased significantly. Coupled with wide fluctuation of water level each year, it becomes more important to study the deformation forecasting of landslides beside TGR. As a famous active landslide beside TGR, Huangtupo riverside landslide is selected for a case study. Based on long term water level fluctuation and seismic monitoring, three typical adverse conditions are determined. With the established 3D numerical landslide model, seepage-dynamic coupling calculation is conducted under the seismic intensity of V degree. Results are as follows： 1. the dynamic water pressure formed by water level fluctuation will intensify the deformation of landslide; 2. under seismic load, the dynamic hysteresis is significant in defective geological bodies, such as weak layer and slip zone soil, because of much higher damping ratios, the seismic accelerate would be amplified in these elements; 3. microseisms are not intense enough to cause the landslide instability suddenly, but long term deformation accumulation effect of landslide should be paid more attention; 4. in numerical simulation, the factors of unbalance force and excess pore pressure also can be used in forecasting deformation tendency of landslide.

Hardening-Softening Constitutive Model of Hard Brittle Rocks Considering Dilatant Effects and Safety Evaluation Index

The damage and even failure of hard brittle rocks has been the most important challenge facing the safety of construction of deep engineering works,so the key to solving this problem is the recognition of the strength characteristics and description of the mechanical behavior of hard brittle rocks.Therefore,in view of this problem,in this study,we first analyzed the strength and mechanical response characteristics revealed in tests of,and site excavation in,hard brittle rocks.Second,by analyzing rock-strength envelopes on meridional and deviatoric planes,the generalized polyaxial strain energy(GPSE)strength criterion was applied.This allows description of the effects of the minimum principal stress,intermediate principal stress,hydrostatic pressure,and Lode’s angle of stress on the strength of hard rocks.By establishing evolutionary relationships of strength parameters and dilation parameters with plastic volumetric strain in rock failure,we established an elasto-plastic mechanical constitutive model for hard brittle rocks based on the GPSE criterion.In addition,through use of the failure approach index theory and the dilatancy safety factor,an evaluation index for degree of damage considering dilatant effects of rocks was proposed.Finally,the constitutive model established in this study and the proposed evaluation index were integrated into the numerical simulation method to simulate triaxial tests on rocks and numerical simulation of deformation and fracture of the rocks surrounding the deep-buried auxiliary tunnels in China’s Jinping II Hydropower Station.In this way,the reasonableness of the model and the index was verified.The strength theory and the constitutive model established in this research are applicable to the analysis of high-stress deformation and fracture of hard brittle rock masses,which supports the theoretical work related to deep engineering operations.