Numerical analysis on the factors affecting post-peak characteristics of coal under uniaxial compression

The post-peak characteristics of coal serve as a direct reflection of its failure process and are essential parameters for evaluating brittleness and bursting liability.Understanding the significant factors that influence post-peak characteristics can offer valuable insights for the prevention of coal bursts.In this study,the Synthetic Rock Mass method is employed to establish a numerical model,and the factors affecting coal post-peak characteristics are analyzed from four perspectives:coal matrix mechanical parameters,structural weak surface properties,height-to-width ratio,and loading rate.The research identifies four significant influencing factors:deformation modulus,density of discrete fracture networks,height-to-width ratio,and loading rate.The response and sensitivity of post-peak characteristics to single-factor and multi-factor interactions are assessed.The result suggested that feasible prevention and control measures for coal bursts can be formulated through four approaches:weakening the mechanical properties of coal pillars,increasing the number of structural weak surfaces in coal pillars,reducing the width of coal pillars,and optimizing mining and excavation speed.The efficacy of measures aimed at weakening the mechanical properties of coal is successfully demonstrated through a case study on coal burst prevention using large-diameter borehole drilling.

A post-peak dilatancy model for soft rock and its application in deep tunnel excavation

The dilation angle is the most commonly used parameter to study nonlinear post-peak dilatancy(PPD)behavior and simulate surrounding rock deformation;however,simplified or constant dilatancy models are often used in numerical calculations owing to their simple mathematical forms.This study developed a PPD model for rocks(rock masses)based on the Alejanoe-Alonso(A-A)dilatancy model.The developed model comprehensively reflects the influences of confining pressure(σ_(3))and plastic shear strain(γ^(p)),with the advantages of a simple mathematical form,while requiring fewer parameters and demonstrating a clear physical significance.The overall fitting accuracy of the PPD model for 11 different rocks was found to be higher than that of the A-A model,particularly for Witwatersrand quartzite and jointed granite.The applicability and reliability of the PPD model to jointed granites and different scaled Moura coals were also investigated,and the model was found to be more suitable for the soft and large-scale rocks,e.g.deep rock mass.The PPD model was also successfully applied in studying the mechanical response of a circular tunnel excavated in strain-softening rock mass,and the developed semi-analytical solution was compared and verified with existing analytical solutions.The sensitivities of the rock dilatancy to γ^(p) and σ_(3) showed significant spatial variabilities along the radial direction of the surrounding rock,and the dilation angle did not exhibit a monotonical increasing or decreasing law from the elasticeplastic boundary to the tunnel wall,thereby presenting the σ3-or γ^(p)-dominated differential effects of rock dilatancy.Tunnel deformation parabolically or exponentially increased with increasing in situ stress(buried depth).The developed PPD model is promising to conduct refined numerical and analytical analyses for deep tunneling,which produces extensive plastic deformation and exhibits significant nonlinear post-peak behavior.

Experimental study of post-peak behavior of bimrocks with high rock block proportions

Design and construction of engineering structures in geomaterials with block-in-matrix texture(referred as bimrock) such as conglomerates,breccias and agglomerates are challenging tasks for engineers.When dealing with these materials in important structures such as open pits with high walls and pillars of deep underground mines,understanding the complete stress-strain behavior,including post-peak region,is a formidable yet crucial engineering practice.To study the post-peak behavior of bimrocks,artificial specimens were fabricated with a mixture of rock blocks and a cementing agent.All the experiments were conducted under uniaxial compression using a servo-control testing machine.The results show that the specimens with the highest block proportion(around 90% by mass) showed a small decrease in stress with strain increment in the post-peak region.The specimens with lower block proportions were characterized by an approximately steep fall in stress and following to residual stress.Based on the study,it is inferred that all the artificial specimens undergo post-failure deformation and the type of post behavior depends on rock block proportions.

Mechanical behavior of sandstone during post-peak cyclic loading and unloading under hydromechanical coupling

This paper investigates mechanical behaviours of sandstone during post-peak cyclic loading and unloading subjected to hydromechanical coupling effect, confirming the peak and residual strengths reduction laws of sandstone with water pressure, and revealing the influence of water pressure on the upper limit stress and deformation characteristics of sandstone during post-peak cyclic loading and unloading.Regarding the rock strength, the experimental study confirms that the peak strength σ_(p) and residual strength σ_(r) decrease as water pressure P increases. Especially, the normalized strength parameters σ_(p)/σ_(pk) and σ_(r)/σ_(re) was negatively and linearly correlated with the P/σ_(3). Moreover, the Hoek-Brown strength criterion can be applied to describe the relationship between effective peak strength and effective confining stress. During post-peak cyclic loading and unloading, both the upper limit stress σ_(p(i)) and crack damage threshold stress σ_(cd(i)) of each cycle tend to decrease with the increasing cycle number. A hysteresis loop exists among the loading and unloading stress–strain curves, indicating the unloading deformation modulus E_(unload) is larger than the loading deformation modulus E_(load). Based on experimental results,a post-peak strength prediction model related to water pressure and plastic shear strain is established.

Load-bearing characteristics and energy evolution of fractured rock masses after granite and sandstone grouting

Experiments on grouting-reinforced rock mass specimens with different particle sizes and features were carried out in this study to examine the effects of grouting reinforcement on the load-bearing characteristics of fractured rock mass.The strength and deformation features of grouting-reinforced rock mass were analyzed under different loading manners;the energy evolution mechanism of grouting-reinforced rock mass specimens with different particle sizes and features was investigated;the energy dissipation ratio and post-peak stress decreasing rate were employed to evaluate the bearing stability of grouting-reinforced rock mass.The results show that the strength and ductility of granite-reinforced rock mass(GRM)under biaxial loading are higher than that of sandstone-reinforced rock mass(SRM)under uniaxial loading.Besides,the energy evolution characteristics of grouting-reinforced rock mass under uniaxial and biaxial loading mainly could be divided into early,middle,and late stages.In the early stage,total,elastic,and dissipation energies were quite small with flatter curves;in the middle stage,elastic energy increased rapidly,whereas dissipation energy increased slowly;in the late stage,dissipation energy increased sharply.The energy dissipation ratio was used to represent the pre-peak plastic deformation.Under uniaxial loading,this ratio increased as the particle size increased and the pre-peak plastic deformation of grouting-reinforced rock mass became larger;under biaxial loading,it dropped as the particle size increased,and the pre-peak plastic deformation of grouting-reinforced rock mass became smaller.The post-peak stress decline rate A_(v) was used to assess the post-peak bearing performance of grouting-reinforced rock mass.Under uniaxial loading,parameter A_(v) exhibited reduction as the particle size kept increasing,and the ability of post-peak of grouting-reinforced rock mass to allow deformation development was greater,and the bearing capacity was greater;under biaxial loading,A_(v) increased with the particle size,and the ability of post-peak of grouting-reinforced rock mass to allow deformation development was low and the bearing capacity was reduced.The findings are considered instrumental in improving the stability of the roadway-surrounding rock by granite and sandstone grouting.

On the calibration of a shear stress criterion for rock joints to represent the full stress-strain profile

Conventional numerical solutions developed to describe the geomechanical behavior of rock interfaces subjected to differential load emphasize peak and residual shear strengths.The detailed analysis of preand post-peak shear stress-displacement behavior is central to various time-dependent and dynamic rock mechanic problems such as rockbursts and structural instabilities in highly stressed conditions.The complete stress-displacement surface(CSDS)model was developed to describe analytically the pre-and post-peak behavior of rock interfaces under differential loads.Original formulations of the CSDS model required extensive curve-fitting iterations which limited its practical applicability and transparent integration into engineering tools.The present work proposes modifications to the CSDS model aimed at developing a comprehensive and modern calibration protocol to describe the complete shear stressdisplacement behavior of rock interfaces under differential loads.The proposed update to the CSDS model incorporates the concept of mobilized shear strength to enhance the post-peak formulations.Barton’s concepts of joint roughness coefficient(JRC)and joint compressive strength(JCS)are incorporated to facilitate empirical estimations for peak shear stress and normal closure relations.Triaxial/uniaxial compression test and direct shear test results are used to validate the updated model and exemplify the proposed calibration method.The results illustrate that the revised model successfully predicts the post-peak and complete axial stressestrain and shear stressedisplacement curves for rock joints.

Mechanical properties and energy mechanism of saturated sandstones

The effects of saturation on post-peak mechanical properties and energy features are main focal points for sandstones. To obtain these important attributes, post-peak cyclic loading and unloading tests were conducted on sandstone rock samples under natural and saturated states using the RMT-150B rock mechanics testing system. After successful processing of these tests, comparisons of stress-strain, strength, deformation, damage, and degradation of mechanical properties, wave velocity, and energy features of sandstone were conducted between natural and saturated states. The results show that saturation has evident weakening effects on uniaxial cyclic loading and unloading strength and elastic modulus of post-peak fracture sandstone. With the increase of post-peak loading and unloading period, the increases in amplitude of peak axial, lateral, and volumetric strains are all enhanced at approximately constant speed under the natural state. The increase in amplitude of axial peak strain is also enhanced at approximately constant speed, while the amplitudes of lateral and volumetric peak strains increase significantly under the saturated state. Compared with the natural state, the increase in amplitude of saturated samples＇ peak lateral and volumetric strains, and the post-peak cyclic loading and unloading period all conform to the linearly increasing relationship. Under natural and saturated states, the damage factor （the plastic shear strain） of each rock sample gradually increases with the increase of post-peak cyclic loading and unloading period, and the crack damage stress of each rock sample declines rapidly at first and tends to reach a constant value later with the increase in plastic shear strain. Under natural and saturated states, the wave velocities of rock samples all decrease in the process of post-peak cyclic loading and unloading with the increase in plastic shear strain. The wave velocities of rock samples and plastic shear strain conform to the exponential relationship with a constant. Saturation reduces the total absorption energy, dissipated energy, and elastic strain energy of rock samples.

Quantitative calculation for the dissipated energy of fault rock burst based on gradient-dependent plasticity

The capacity of energy absorption by fault bands after rock burst wascalculated quantitatively according to shear stress-shear deformation curves considering theinteractions and interplaying among microstructures due to the heterogeneity of strain softeningrock materials. The post-peak stiffness of rock specimens subjected to direct shear was derivedstrictly based on gradient-dependent plasticity, which can not be obtained from the classicalelastoplastic theory. Analytical solutions for the dissipated energy of rock burst were proposedwhether the slope of the post-peak shear stress-shear deformation curve is positive or not. Theanalytical solutions show that shear stress level, confining pressure, shear strength, brittleness,strain rate and heterogeneity of rock materials have important influence on the dissipated energy.The larger value of the dissipated energy means that the capacity of energy dissipation in the formof shear bands is superior and a lower magnitude of rock burst is expected under the condition ofthe same work done by external shear force. The possibility of rock burst is reduced for a lowersoftening modulus or a larger thickness of shear bands.

Dilation angle variations in plastic zone around tunnels in rocks-constant or variable dilation parameter

Dilation angle is a significant parameter needed for numerical simulation of tunnels.Even though dilation parameter is physically variable and dependent on confinement and experienced shear plastic strain based on the existing dilation models,numerical simulations of tunnels and underground openings with constant dilation parameter usually lead to satisfactory results in practical use.This study aims to find out why constant dilation angle is enough under practical conditions to simulate numerically tunnels and underground excavations in spite of the fact that dilation angle is variable in laboratory and experimental scale.With this aim,this work studies how mobilized dilation angle varies in a plastic zone surrounding a tunnel.For the circular tunnel under uniform in situ stress field,the stepwise finite difference approximation analytical solution considering strain softening rock mass behavior with mobilized dilation angle was used to study how mobilized dilation angle varies in plastic zone around tunnel under very different conditions.In practical conditions determined in this study,dilative behavior of all over the plastic zone around the tunnel can be approximated to constant dilation angle in the middle region of the plastic zone.Moreover,the plastic zone displacements for mobilized and constant dilation angle models are compared with each other.Further investigation under more general non-uniform in situ stress conditions and non-circular tunnels is performed by using the commercial finite difference software to numerically simulate the Mine-by experimental tunnel of AECL(Atomic Energy of Canada Limited)and the arched tunnel.Although the Mine-by and arched tunnels were numerically simulated based on the mobilized dilation angle model,the variability associated with dilation angle around the simulated Mine-by and arched tunnels is insignificant,and dilation angle is approximately constant in the plastic zone.

Development and verification of large deformation model considering stiffness deterioration and shear dilation effect in FLAC^(3D)

The existing constitutive models of rock with strain softening cannot successfully reflect the damageinduced anisotropy and nonlinearity of the post-peak failure behavior under progressive loading. In order to better reflect the nonlinear stress-strain behavior of rock, especially for the post-peak failure behavior,with expected stiffness degradation and large deformation, a modified constitutive model of rock considering stiffness degradation and dilatation behavior at large deformation was proposed in this study. This study analyzes and discusses various attenuation parameters in the proposed nonlinear plastic constitutive model using FLAC^(3D) software. The excavation-induced stress in rocks was calculated by FLAC^(3D) using the Mohr-Coulomb model, conventional strain model, and the proposed modified model. The obtained results of these models were analyzed and compared with field data. This study shows that the simulated results using the proposed new constitutive model matched much more closely with the measured field data, with an average error less than 5%. This new model can successfully reflect the damage-induced stiffness degradation at large deformation, and can provide a theoretical basis for stability design and evaluation of underground excavation.

Calibration and uniqueness analysis of microparameters for DEM cohesive granular material

The differential evolution(DE)algorithm was deployed to calibrate microparameters of the DEM cohesive granular material.4 macroparameters,namely,uniaxial compressive strength,direct tensile strength,Young’s modulus and Poisson’s ratio,can be calibrated to high accuracy.The best calibration accuracy could reach the sum of relative errors RE_(sum)<0.1%.Most calibrations can be achieved with RE_(sum)<5%within hours or RE_(sum)<1%within 2 days.Based on the calibrated results,microparameters uniqueness analysis was carried out to reveal the correlation between microparameters and the macroscopic mechanical behaviour of material:(1)microparameters effective modulus,tensile strength and normal-to-shear stiffness ratio control the elastic behaviour and stable crack growth,(2)microparameters cohesion and friction angles present a negative linear correlation that controls the axial strain and lateral strain prior to the peak stress,and(3)microparameters friction coefficient controls shear crack friction and slip mainly refers to the unstable crack behaviour.Consideration of more macroparameters to regulate the material mechanical behaviour that is dominated by shear crack and slip motion is highlighted for future study.The DE calibration method is expected to serve as an alternative method to calibrate the DEM cohesive granular material to its peak strength.

Safety Evaluation of Concrete Structures Based on a Novel Energy Criterion

In this article,the post-peak softening stage of the constitutive relation and the elastic stiffness degradation of concrete are investigated,and a highly reasonable constitutive relation curve is proposed.At the material level,the energy change in the concrete failure process is studied based on the different stress-strain curves of concrete under uniaxial tension and compression.The concrete failure criterion based on elastic strain energy density is deemed suitable and consistent with the experimental phenomena.The hysteresis phenomenon(lags behind the peak strength)is also discussed.At the structure level,the strength reduction method is employed for the stability analysis,the energy change in the failure process of the Long Xi-Kou Dam is examined,and the results show that the dam failure criterion based on elastic strain energy shows a greater significance in practical applications compared with other conventional structural failure criteria in engineering.This criterion is objective and can avoid subjective arbitrariness.

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.

节理面剪切应力–切向位移曲线峰值后区特性的初步研究

在节理面剪切试验中,许多剪切应力–位移过程曲线呈现出明显的峰值后区形态。针对这种结构面强度弱化特性,对一组结构面剪切应力–位移过程曲线进行分析,从曲线中获取节理面峰值强度与残余强度。采用一系列应力跌落与塑性流动过程模拟节理面强度弱化过程,通过数值方法再现剪切应力–位移全过程曲线;并进一步研究峰值后区应力–位移曲线与强度弱化的内在关系以及剪胀角演化规律对节理面法向变形的影响,研究成果有助于深化结构面强度与变形特性认识。

基于三维形貌的节理抗剪强度弱化规律研究

采用3D扫描和打印技术浇筑一系列具有相同表面形貌的节理试样,针对试样开展不同法向应力、不同剪切位移条件下的直剪试验。通过分析剪切试验曲线和节理面损伤特征,研究峰后剪切过程中节理表面形貌的劣化规律及其与抗剪强度弱化间的关系,发现采用基于Grassilli形貌参数的三维粗糙度参数可以直观地量化表征节理表面形貌的劣化规律。将三维粗糙度参数引入JRC_JMC抗剪模型,并在分析节理面吻合度与三维粗糙度参数在峰后剪切过程中的变化规律基础上,提出节理峰后抗剪强度弱化模型。基于提出模型的计算值与试验结果基本一致,表明提出的模型可以较好地表征峰后剪切段节理的抗剪强度弱化规律。