A statistical damage-based constitutive model for shearing of rock joints in brittle drop mode

Some rock joints exhibit significant brittleness,characterized by a sharp decrease in shear stress upon reaching the peak strength.However,existing models often fail to accurately represent this behavior and are encumbered by numerous parameters lacking clear mechanical significance.This study presents a new statistical damage constitutive model rooted in both damage mechanics and statistics,containing only three model parameters.The proposed model encompasses all stages of joint shearing,including the compaction stage,linear stage,plastic yielding stage,drop stage,strain softening stage,and residual strength stage.To derive the analytical expression of the constitutive model,three boundary conditions are introduced.Experimental data from both natural and artificial rock joints is utilized to validate the model,resulting in average absolute relative errors ranging from 3%to 8%.Moreover,a comparative analysis with established models illustrates that the proposed model captures stress drop and post-peak strain softening more effectively,with model parameters possessing clearer mechanical interpretations.Furthermore,parameter analysis is conducted to investigate the impacts of model parameters on the curves and unveil the relationship between these parameters and the mechanical properties of rock joints.Importantly,the proposed model is straightforward in form,and all model parameters can be obtained from direct shear tests,thus facilitating the utilization in numerical simulations.

A 3D microseismic data-driven damage model for jointed rock mass under hydro-mechanical coupling conditions and its application

Rock mass is a fractured porous medium usually subjected to complex geostress and fluid pressure simultaneously.Moreover,the properties of rock mass change in time and space due to mining-induced fractures.Therefore,it is always challenging to accurately measure rock mass properties.In this study,a three-dimensional(3D)microseismic(MS)data-driven damage model for jointed rock mass under hydro-mechanical coupling conditions is proposed.It is a 3D finite element model that takes seepage,damage and stress field effects into account jointly.Multiple factors(i.e.joints,water and microseismicity)are used to optimize the rock mass mechanical parameters at different scales.The model is applied in Shirengou iron mine to study the damage evolution of rock mass and assess the crown pillar stability during the transition from open-pit to underground mining.It is found that the damage pattern is mostly controlled by the structure,water and rock mass parameters.The damage pattern is evidently different from the two-dimensional result and is more consistent with the field observations.This difference is caused by the MS-derived damage acting on the rock mass.MS data are responsible for gradually correcting the damage zone,changing the direction in which it expands,and promoting it to evolve close to reality.For the crown pillar,the proposed model yields a more trustworthy safety factor.In order to guarantee the stability of the pillar,it is suggested to take waterproof and reinforcement measures in areas with a high degree of damage.

Parameter calibration of the tensile-shear interactive damage constitutive model for sandstone failure

The tensile-shear interactive damage(TSID)model is a novel and powerful constitutive model for rock-like materials.This study proposes a methodology to calibrate the TSID model parameters to simulate sandstone.The basic parameters of sandstone are determined through a series of static and dynamic tests,including uniaxial compression,Brazilian disc,triaxial compression under varying confining pressures,hydrostatic compression,and dynamic compression and tensile tests with a split Hopkinson pressure bar.Based on the sandstone test results from this study and previous research,a step-by-step procedure for parameter calibration is outlined,which accounts for the categories of the strength surface,equation of state(EOS),strain rate effect,and damage.The calibrated parameters are verified through numerical tests that correspond to the experimental loading conditions.Consistency between numerical results and experimental data indicates the precision and reliability of the calibrated parameters.The methodology presented in this study is scientifically sound,straightforward,and essential for improving the TSID model.Furthermore,it has the potential to contribute to other rock constitutive models,particularly new user-defined models.

An elasto-plastic and viscoplastic damage constitutive model for dilatancy and fracturing behavior of soft rock squeezing deformation

Soft rock squeezing deformation mainly consists of pre-peak damage-dilatancy and post-peak fracture-bulking at the excavation unloading instant,and creep-dilatancy caused by time-dependent damage and fracturing.Based on the classic elastoplastic and Perzyna over-stress viscoplastic theories,as well as triaxial unloading confining pressure test and triaxial unloading creep test results,an elastoplastic and viscoplastic damage constitutive model is established for the short-and long-term dilatancy and fracturing behavior of soft rock squeezing deformation.Firstly,the criteria for each deformation and failure stage are expressed as a linear function of confining pressure.Secondly,the total damage evolution equation considering time-dependent damage is proposed,including the initial damage produced at the excavation instant,in which the damage variable increases exponentially with the lateral strain,and creep damage.Thirdly,a transient five-stages elasto-plastic constitutive equation for the short-term deformation after excavation that comprised of elasticity,pre-peak damage-dilatancy,post-peak brittle-drop,linear strain-softening,and residual perfectly-plastic regimes is developed based on incremental elasto-plastic theory and the nonassociated flow rule.Fourthly,regarding the timedependent properties of soft rock,based on the Perzyna viscoplastic over-stress theory,a viscoplastic damage model is set up to capture creep damage and dilatancy behavior.Viscoplastic strain is produced when the stress exceeds the initial static yield surface fs;the distance between the static yield surface fs and the dynamic yield surface fd determines the viscoplastic strain rate.Finally,the established constitutive model is numerically implemented and field applied to the-848 m belt conveyer haulage roadway of Huainan Panyidong Coal Mine.Laboratory test results and in-situ monitoring results validate the rationality of the established constitutive model.The presented model takes both the transient and time-dependent damage and fracturing into consideration.

A damage constitutive model of rock-like materials containing a single crack under the action of chemical corrosion and uniaxial compression

To describe the deformation and strength characteristics of the corroded rock-like specimens containing a single crack under uniaxial compression,a damage constitutive model combining hydro-chemical damage with coupling damage of micro-flaws and macro-cracks is proposed.Firstly,based on phenomenological theory,the damage variable of the rock-like specimens subjected to water environment erosion and chemical corrosion is obtained.Secondly,a coupled damage variable for cracked rock-like specimens is derived based on the Lemaitre strain equivalence hypothesis,which combines the Weibull statistical damage model for micro-flaws and the fracture mechanics model for a macro single crack.Then,considering the residual strength characteristics of the rock-like materials,the damage variable is modified by introducing the correction coefficient,and the damage constitutive model of the corroded rock-like specimens with a single crack under uniaxial compression is established.The model is verified by comparing the experimental stress−strain curves,and the results are in good agreement with those provided in the literature.Finally,the correction coefficient of the damage variable proposed in this paper is discussed.The damage constitutive model developed in this paper provides an effective method to describe the stress−strain relationship and residual strength characteristics of the corroded rock-like specimens with a single crack under uniaxial compression.

Study on damages constitutive model of rocks based on lognormal distribution

The damage constitutive relation of entire rock failure process was established using the theory of representative volume element obeying the Iognormal distribution law, and the integrated damages constitutive model of rock under triaxial compression was established. Comparing with triaxial compression test result, it shows that this model correctly reflects the relationship of stress-strain. At the same time, according to the principle of the rock fatigue failure that conforms to completely the static entire process curve, a new method of establishing cyclic fatigue damage evolution equation was discussed, this method form is simple and the physics significance is clear, it may join preferably the damage relations of the rock static entire process curve.

Deformation characteristics and damage ontologies of soft and hard composite rock masses under impact loading

As one of the most common occurring geological landforms in deep rock formations, the dynamic mechanical properties of layered composite rock bodies under impact loading have been widely studied by scholars. To study the dynamic properties of soft and hard composite rocks with different thickness ratios, this paper utilizes cement, quartz sand and gypsum powder to construct soft and hard composite rock specimens and utilizes a combination of indoor tests, numerical calculations, and theoretical analyses to investigate the mechanical properties of soft and hard composite rock bodies. The test results reveal that:(1) When the proportion of hard rock increases from 20% to 50%, the strength of the combined rock body increases by 69.14 MPa and 87 MPa when the hard rock face and soft rock face are loaded, respectively;however, when the proportion of hard rock is the same, the compressive strength of the hard rock face impact is 9%-17% greater than that of the soft rock face impact;(2) When a specimen of soft and hard combined rock body is subjected to impact loading, the damage mode involves mixed tension and shear damage, and the cracks generally first appear at the ends of the specimen, then develop on the laminar surface from the impact surface, and finally end in the overall damage of the soft rock part. The development rate and the total number of cracks in the same specimen when the hard rock face is impacted are significantly greater than those when the soft rock face is impacted;(3) By introducing Weibull’s statistical strength theory to establish the damage variables of soft-hard combined rock bodies, combined with the DP strength criterion, the damage model and the Kelvin body are concatenated to obtain a statistical damage constitutive model, which can better fit the full stress-strain curve of soft-hard combined rock body specimens under a single impact load.

An Anisotropic Geomechanical Model for Jointed Rock Masses at Taishan Nuclear Power Station, Southern China

An anisotropic geomechanical model for jointed rock mass is presented. Simultaneously with deriving the orthotropic anisotropy elastic parameters along the positive axis, the equivalent compliance matrix for the deflection axis orthotropic anisotropy was derived through a three- dimensional coordinate transformation. In addition, Singh＇s analysis of the stress concentration effects of intermittent joints was adopted, based on two groups of intermittent joints and a set of cross- cutting joints in the jointed rock mass. The stress concentration effects caused by intermittent joints and the coupling effect of cross-cutting joints along the deflection-axis are also considered. The proposed anisotropic mechanics parameters method is applied to determine the deformation parameters of jointed granite at the Taishan Nuclear Power Station. Combined with the deterministic mechanical parameters of rock blocks and joints, the deformation parameters and their variability in jointed rock masses are estimated quantitatively. The computed results show that jointed granite at the Taishan Nuclear Power Station exhibits typical anisotropic mechanical characteristics; the elastic moduli in the two horizontal directions were similar, but the elastic modulus in the vertical direction was much greater. Jointed rock elastic moduli in the two horizontal and vertical directions were respectively about 24% and 37% of the core of rock, showing weakly orthotropic anisotropy; the ratio of elastic moduli in the vertical and horizontal directions was 1.53, clearly indicating the transversely isotropic rock mass mechanical characteristics. The method can be popularized to solve other rock mechanics problems in nuclear power engineering.

Distinct element modelling of fracture plan control in continuum and jointed rock mass in presplitting method of surface mining

Controlled blasting techniques are used to control overbreak and to aid in the stability of the remaining rock formation. Presplitting is one of the most common methods which is used in many open pit mining and surface blast design. The purpose of presplitting is to form a fracture plane across which the radial cracks from the production blast cannot travel. The purpose of this study is to investigate of effect of presplitting on the generation of a smooth wall in continuum and jointed rock mass. The 2D distinct element code was used to simulate the presplitting in a rock slope. The blast load history as a function of time was applied to the inner wall of each blasthole. Important parameters that were considered in the analysis were stress tensor and fracturing pattern. The blast loading magnitude and blasthole spacing and jointing pattern were found to be very significant in the final results.

AN ANALYSIS MODEL OF THE MECHANICS OF JOINTED ROCK MASS

The creep fracture damage model of jointed rock mass is proposed, the basic methods and properties of engineering structure forecast analysis in split surrounding rock mass is discussed, numericalized way is analyzed, and the computing program of RCFD rock mechanics problems known is modified.Moreover, this program is used to make practical forecast analysis for the stability of surrounding rock mass of one large section (vertical)shaft which is buried in the earth 300 m deep.

Mesoscopic fracture damage evolution and fractal damage constitutive model of heat-treated red sandstone under direct tensile impact loadings

Understanding the mesoscopic tensile fracture damage of rock is the basis of evaluating the deterioration process of mechanical properties of heat-damaged rock. For this, tensile tests of rocks under high-temperature treatment were conducted with a ϕ75 mm split Hopkinson tension bar (SHTB) to investigate the mesoscopic fracture and damage properties of rock. An improved scanning electron microscopy (SEM) experimental method was used to analyze the tensile fracture surfaces of rock samples. Qualitative and quantitative analyses were performed to assess evolution of mesoscopic damage of heat-damaged rock under tensile loading. A constitutive model describing the mesoscopic fractal damage under thermo-mechanical coupling was established. The results showed that the high temperatures significantly reduced the tensile strength and fracture surface roughness of the red sandstone. The three-dimensional (3D) reconstruction of the fracture surface of the samples that experienced tensile failure at 900 °C showed a flat surface. The standard deviation of elevation and slope angle of specimen fracture surface first increased and then decreased with increasing temperature. The threshold for brittle fracture of the heat-damaged red sandstone specimens was 600 °C. Beyond this threshold temperature, local ductile fracture occurred, resulting in plastic deformation of the fracture surface during tensile fracturing. With increase of temperature, the internal meso-structure of samples was strengthened slightly at first and then deteriorated gradually, which was consistent with the change of macroscopic mechanical properties of red sandstone. The mesoscopic characteristics, such as the number, mean side length, maximum area, porosity, and fractal dimension of crack, exhibited an initial decline, followed by a gradual increase. The development of microcracks in samples had significant influence on mesoscopic fractal dimension. The mesoscopic fractal characteristics were used to establish a mesoscopic fractal damage constitutive model for red sandstone, and the agreement between the theoretical and experimental results validated the proposed model.

A meso-damage-based constitutive model for yellow sandstone under dry-wet cycles

The mechanical properties of rocks weaken under dry-wet cycles.This weakening may significantly modify the safety reserve of underground caverns or reservoir bank slopes.However,meso-damage has not been carefully studied based on micromechanical observations and analyses.Therefore,in this study,meso-damage of a yellow sandstone is investigated and a meso-damage-based constitutive model for dry-wet cycles is proposed.First,computed tomography scanning and uniaxial compression tests were conducted on yellow sandstones under different dry-wet cycles.Second,the evolution of rock mesostructures and the damage mechanism subjected to dry-wet cycles were simulated using the discrete element method with Particle Flow Code in 2 Dimensions(PFC2D)software.Third,a constitutive model was proposed based on the meso-statistical theory and damage mechanics.Finally,this constitutive model was verified with the experimental results to check its prediction capability.It is found that the radius and number of pore throats in the sandstone increase gradually with the number of dry-wet cycles,and the pore structure connectivity is also improved.The contact force of sandstone interparticle cementation decreases approximately linearly and the continuity of the particle contact network is continuously broken.The meso-deformation and strength parameters show similar declining patterns to the modulus of elasticity and peak strength of the rock sample,respectively.This meso-damage-based constitutive model can describe well the rock deforma-tion in the initial pressure density stage and the damage stage under the coupling effect of dry-wet cycles and loads.

Creep damage constitutive model of rock based on the mechanisms of crack-initiated damage and extended damage

Since the classical element model cannot describe the nonlinear characteristics of rock during the entire compressive creep process,nonlinear elements and creep damage are generally introduced in the model to resolve this issue.However,several previous studies have reckoned that creep damage in rock only occurs in the accelerated creep stage and is only described by the Weibull distribution.Nevertheless,the creep damage mechanism of rocks is still not clearly understood.In this study,a reasonable representation of the damage variables of solid materials is presented.Specifically,based on the Gurson damage model,the damage state functions reflecting the constant creep stage and accelerated creep stage of rock are established.Further,the one-dimensional and three-dimensional creep damage constitutive equations of rock are derived by modifying the Nishihara model.Finally,the creep-acoustic emission tests of phyllite under different confining pressures are conducted to examine the creep damage characteristics of phyllite.And the proposed constitutive model is verified by analyzing the results of creep tests performed on saturated phyllite.Overall,this study reveals the relationship between the creep characteristics of rocks and the corresponding damage evolution pattern,which bridges the gap between the traditional theory and the quantitative analysis of rock creep and its damage pattern.

Responses of jointed rock masses subjected to impact loading

Impact-induced damage to jointed rock masses has important consequences in various mining and civil engineering applications. This paper reports a numerical investigation to address the responses of jointed rock masses subjected to impact loading. It also focuses on the static and dynamic properties of an intact rock derived from a series of laboratory tests on meta-sandstone samples from a quarry in Nova Scotia, Canada. A distinct element code(PFC2D) was used to generate a bonded particle model(BPM) to simulate both the static and dynamic properties of the intact rock. The calibrated BPM was then used to construct large-scale jointed rock mass samples by incorporating discrete joint networks of multiple joint intensities into the intact rock matrix represented by the BPM. Finally, the impact-induced damage inflicted by a rigid projectile particle on the jointed rock mass samples was determined through the use of the numerical model. The simulation results show that joints play an important role in the impactinduced rock mass damage where higher joint intensity results in more damage to the rock mass. This is mainly attributed to variations of stress wave propagation in jointed rock masses as compared to intact rock devoid of joints.

Damage constitutive model for strain-softening rock based on normal distribution and its parameter determination

Firstly, using the damage model for rock based on Lemaitre hypothesis about strain equivalence, a new technique for measuring strength of rock micro-cells by adopting the Mohr-Coulomb criterion was developed, and a statistical damage evolution equation was established based on the property that strength of micro-cells is consistent with normal distribution function, through discussing the characteristics of random distributions for strength of micro-cells, then a statistical damage constitutive model that can simulate the full process of rock strain softening under specific confining pressure was set up. Secondly, a new method to determine the model parameters which can be applied to the situations under different confining pressures was proposed, by deeply studying the relations between the model parameters and characteristic parameters of the full stress-strain curve under different confining pressures. Therefore, a unified statistical damage constitutive model for rock softening which can reflect the effect of different confining pressures was set up. This model makes the physical property of model parameters explicit, contains only conventional mechanical parameters, and leads its application more convenient. Finally, the rationality of this model and its parameters-determining method were identified via comparative analyses between theoretical and experimental curves.

Computing in-situ strength of rock masses based upon RQD and modified joint factor: Using pressure and damage sensitive constitutive relationship

In th is study, a n e w m odel w as p re se n te d for com p u tin g stre n g th o f rock m asses based u p o n in -situo bservations o f RQD p o pularly kno w n as rock quality d esignation. This m odel links u p th e rock m assp aram eters from in -situ investigations w ith th e stre n g th p a ram eters o f jo in ted rocks obtain ed fromlaboratory scale ex p erim en tal observations. Using th e co n stitu tiv e relation, th e a u th o r derived a p ressu reand d am age sensitive plastic p a ra m e te r to d ete rm in e stre n g th o f rock m asses for varied ex te n ts ofd isco n tin u ity an d p ressu re induced dam age. The te s t results show th a t plasticity characterized byhard en in g an d softening inclusive o f dam ag e invariably d e p en d s u p o n m ean p ressu re an d e x te n t ofdefo rm atio n s alread y experien ced by rock m asses. The p re se n t w ork explores th e te s t d a ta th a t revealth e d ep en d en c e o f in -situ stren g th on increm ental jo in t p ara m e te rs o b tain ed from th e jo in t num ber,jo in t orien tatio n , jo in t roughness, gouge p a ram eters an d w a te r pressure. S ubstituting th e relationshipb e tw e e n th e RQD and m odified jo in t factor w ith th a t b e tw e e n m odulus ratio an d stren g th ratio, th em odel show s successfully th a t using d am age inclusive plastic p a ra m e te r an d RQD provides a relationshipfor estim atin g th e stre n g th o f rock m asses. One o f th e m ain objectives o f this w ork is to illustrate th a t th ep re se n t m odel is sensitive to p la s tic ity a n d dam ag e to g e th e r in estim atin g in -situ stre n g th o f rock m assesin foundations, u n d e rg ro u n d excavation an d tunnels.

Damage characteristics and new constitutive model of sandstone under wet–dry cycles

The mechanical properties of rock deteriorate under repeated wet-dry(WD)cycles,causing the deformation and failure of the rock mass.A reasonable damage constitutive model can truly reflect the whole process of rock deformation and failure.Therefore,it is of great significance to study the damage characteristics and constitutive behaviour of rock subjected to numerous WD cycles.First,sandstone from Tingliang tunnel was sampled for the WD cycle experiment,and uniaxial and triaxial tests were carried out on the rock samples after various numbers of WD cycles to analyze their macroscale damage characteristics.Then,the damage mechanisms of the rock samples under the action of WD cycling were identified by X-ray diffraction(XRD)and scanning electron microscopy(SEM).Finally,based on the test data,the WD cycle-induced damage variable,Weibull distribution function,damage threshold,Drucker-Prager(D-P)yield criterion and residual strength correction coefficient were introduced,a wet-dry loading(WDL)constitutive damage model that considers the cracking stress of rock masses was established,and the expressions of the corresponding parameters were given.The results show that an increasing number of WD cycles induces considerable variations in the macroscopic physical and mechanical parameters(such as the rock sample mass,saturated water content,longitudinal-wave velocity,compressive strength and elastic modulus),and the rate of change presents two stages,the inflection point of their rate of change is the 15th WD cycle.Microscopically,the rock sample structure changes from intact and dense to fragmented and unconsolidated;additionally,the surface roughness increases,and the mineral composition changes.The established constitutive damage model exhibited good agreement with the experimental data;thus,this model can reflect the deformation and failure of rocks under WDL conditions,and the physical meaning of each parameter is clear.

Strength and deformation characteristics of irregular columnar jointed rock mass: A combined experimental and theoretical study

The irregularity of jointed network poses a challenge to the determination of field mechanical param-eters of columnar jointed rock mass(CJRM),and a reasonable prediction of deformation and strength characteristics of CJRM is important for engineering construction.The Voronoi diagram and three-dimensional printing technology were used to make an irregular columnar jointed mold,and the irregular CJRM(ICJRM)specimens with different dip directions and dip angles were prepared.Uniaxial compression tests were performed,and the anisotropic strength and deformation characteristics of ICJRM were described.The failure modes and mechanisms were revealed in accordance with the final appearances of the ICJRM specimens.Based on the model test results,the empirical correlations for determining the field deformation and strength parameters of CJRM were derived using the dip angle and modified joint factor.The proposed empirical equations were used in the Baihetan Project,and the calculated mechanical parameters were compared with the field test results and those obtained from the tunneling quality index method.Results showed that the deformation parameters determined by the two proposed methods are all consistent with the field test results,and these two methods can also estimate the strength parameters effectively.

Predicting the excavation damaged zone within brittle surrounding rock masses of deep underground caverns using a comprehensive approach integrating in situ measurements and numerical analysis

Excavation Damaged Zone(EDZ)scope is important for optimizing excavation and support schemes in deep underground caverns.However,accurately predicting the full EDZ scope within the surrounding rock masses of deep underground caverns during excavation remains a pressing problem.This study presents a comprehensive EDZ scope prediction approach(CESPA)for the brittle surrounding rock masses of deep underground caverns by coupling numerical simulation with quantitative analysis of borehole wall images and ultrasonic test results.First,the changes in both P-velocity(V_(p))and joint distribution of the surrounding rock masses before and after excavation damage are captured using ultrasonic tests and borehole digital cameras.Second,the quality Q-parameters of the surrounding rock mass before and after excavation damage are preliminarily rated with the rock mass descriptions provided by borehole wall images,and the rock mass V_(p)-parameter values are determined according to the V_(p)-borehole depth curves.Third,the Q-parameter ratings are further finely adjusted by updating the related Q-values to be similar with the Q-values estimated by V_(p)-parameter values.Fourth,the initial and residual mechanical parameters for the rock mass deterioration model(RDM)are estimated by the adjusted Q-parameter ratings based on the modified Q-based relations,and the elastic modulus deterioration index(EDI)threshold to describe the EDZ boundary is determined with the V_(p)-parameter values.Finally,EDZ scope is predicted using the elastoplastic numerical simulation with RDM and EDI based on the mechanical parameter estimates and EDI threshold.Analyses of applications in Sub-lab D1 in Jinping II project show that CESPA can provide a reliable and operable solution for predicting full EDZ scopes within the brittle surrounding rock masses of deep underground caverns.

Determination of mechanical parameters for jointed rock masses

Combining with empirical method, laboratory test and numerical simulation, a comprehensive system was presented to determine the mechanical parameters of jointed rock masses. The system has the following four functions: (1) Based on the field investigation of joints, the system can consider rock mass structures, by using network simulation technology. (2) Rock samples are conducted by numerical simulation with the input engineering mechanical parameters of rocks and joints obtained from laboratory tests. (3) The whole stress-strain curve of jointed rock masses under certain normal stress can be plotted from numerical simulation, and then the shear strength parameters of jointed rock masses can be obtained from the whole stress-strain curves under different normal stresses. (4) The statistical values of mechanical parameters of jointed rock masses can be determined according to numerical simulation. Based on the statistical values, combining with engineering experiences and geological investigations, the comprehensive mechanical parameters of jointed rock masses can be achieved finally. Several cases are presented to prove the engineering feasibility and suitability of this system.