Predicting the probability distribution of Martian rocks mechanical property based on microscale rock mechanical experiments and accurate grain-based modeling

The exploration of Mars would heavily rely on Martian rocks mechanics and engineering technology.As the mechanical property of Martian rocks is uncertain,it is of utmost importance to predict the probability distribution of Martian rocks mechanical property for the success of Mars exploration.In this paper,a fast and accurate probability distribution method for predicting the macroscale elastic modulus of Martian rocks was proposed by integrating the microscale rock mechanical experiments(micro-RME),accurate grain-based modeling(AGBM)and upscaling methods based on reliability principles.Firstly,the microstructure of NWA12564 Martian sample and elastic modulus of each mineral were obtained by micro-RME with TESCAN integrated mineral analyzer(TIMA)and nanoindentation.The best probability distribution function of the minerals was determined by Kolmogorov-Smirnov(K-S)test.Secondly,based on best distribution function of each mineral,the Monte Carlo simulations(MCS)and upscaling methods were implemented to obtain the probability distribution of upscaled elastic modulus.Thirdly,the correlation between the upscaled elastic modulus and macroscale elastic modulus obtained by AGBM was established.The accurate probability distribution of the macroscale elastic modulus was obtained by this correlation relationship.The proposed method can predict the probability distribution of Martian rocks mechanical property with any size and shape samples.

CHARACTERISTICS AND DEVELOPMENT MODEL OF DUNE ROCKS ON SOUTH CHINA COASTS

Dune riocks are aeolian sands cemented ty calcium carbonate under subaerial conditions. They have been found in many of the coastal belts of Fujian, Guangdong and Hainan Provinces in South China. The grain composition of the dune rocks is mainly quartz sands and shell fragments. The quartz sands are medium and fine sized, relatively well sorted and positively skewed. Their surface texture formed in aeolian environments is characterized ty dishshaped depressions, meniscus depressions and V-shaped depressions with rounded edges. The most common bedding type of the rocks is larg (thickness>1.5m), steeply dipping (32--40°) with cross strata tolaner and convex upward). Mg and Sr contents are very low in the rock chemical composition which is classified into low Mg and low Sr category. The typical species of microfossils in the dune rocks are mainly freshwater ones and lack of typical saltwaer or semi-saltwater ones with incomplete assemblage of marine species. The cement minerals in the rocks are mainly low-Mg calcite and the common cement fabrics are meniscus cement and gravitational cement in response to impermanent water in vadose zones. Therefore, the dune rocks may be apparently distinguished from the beach rocks.

Physical model test and numerical simulation on the failure mechanism of the roadway in layered soft rocks

To explore the failure mechanism of roadway in layered soft rocks,a physical model with the physically finite elemental slab assemblage(PFESA)method was established.Infrared thermography and a video camera were employed to capture thermal responses and deformation.The model results showed that layered soft roadway suffered from large deformation.A three-dimensional distinct element code(3 DEC)model with tetrahedral blocks was built to capture the characteristics of roadway deformation,stress,and cracks.The results showed two failure patterns,layer bending fracture and layer slipping after excavation.The layer bending fracture occurred at positions where the normal direction of layers pointed to the inside of the roadway and the layer slipping occurred in the ribs.Six schemes were proposed to investigate the effects of layered soft rocks.The results showed that the deformation of ribs was obviously larger than that of the roof and floor when the roadway passed through three types of strata.When the roadway was completely in a coal seam,the change of deformation in ribs was not obvious,while the deformation in the roof and floor increased obviously.These results can provide guidance for excavation and support design of roadways in layered soft rocks.

Coupled hydro-thermo-mechanical modeling of hydraulic fracturing in quasi-brittle rocks using BPM-DEM

This paper presents an improved understanding of coupled hydro-thermo-mechanical(HTM) hydraulic fracturing of quasi-brittle rock using the bonded particle model(BPM) within the discrete element method(DEM). BPM has been recently extended by the authors to account for coupled convective econductive heat flow and transport, and to enable full hydro-thermal fluidesolid coupled modeling.The application of the work is on enhanced geothermal systems(EGSs), and hydraulic fracturing of hot dry rock(HDR) is studied in terms of the impact of temperature difference between rock and a flowing fracturing fluid. Micro-mechanical investigation of temperature and fracturing fluid effects on hydraulic fracturing damage in rocks is presented. It was found that fracture is shorter with pronounced secondary microcracking along the main fracture for the case when the convectiveeconductive thermal heat exchange is considered. First, the convection heat exchange during low-viscosity fluid infiltration in permeable rock around the wellbore causes significant rock cooling, where a finger-like fluid infiltration was observed. Second, fluid infiltration inhibits pressure rise during pumping and delays fracture initiation and propagation. Additionally, thermal damage occurs in the whole area around the wellbore due to rock cooling and cold fluid infiltration. The size of a damaged area around the wellbore increases with decreasing fluid dynamic viscosity. Fluid and rock compressibility ratio was found to have significant effect on the fracture propagation velocity.

Size effects in the uniaxial compressive properties of 3D printed models of rocks:an experimental investigation

Transparent physical models of real rocks fabricated using three-dimensional(3D)printing technology are used in photoelas-tic experiments to quantify the evolution of the internal stress and deformation fields of rocks.Therefore,they are rendered as an emerging powerful technique to quantitatively reveal the intrinsic mechanisms of rock failure.The mechanical behav-ior of natural rocks exhibits a significant size effect;however,limited research has been conducted on whether transparent physical models observe similar size effects.In this study,to make the transparent printed models accurately demonstrate the mechanical behavior of natural rocks and reveal the internal mechanism of the size effect in rock mechanical behavior,the size effect in 3D printed models of fractured and porous rocks under uniaxial compressive loading was investigated.Transparent cylindrical models with different sizes that contained different fractured and porous structures were printed using the fracture and porous characteristics extracted from natural coal and sandstone.The variation in uniaxial compres-sive strength and elastic modulus of fractured and porous models for increasing model sizes were obtained through uniaxial compression experiments.Finally,the influence of internal discontinuous structural features,such as fractures and pores,on the size effect pertaining to the mechanical behavior of the model was analyzed and elaborated by comparing it with the mechanical properties of the continuous homogeneous model without fractures and pores.The findings provided support and reference to analyze the size effect of rock mechanical behavior and the effect of the internal discontinuous structure using 3D printed transparent models.

A microscopic approach to brittle creep and time-dependent fracturing of rocks based on stress corrosion model

A brittle creep and time-dependent fracturing process model of rock is established by incorporating the stress corrosion model into discrete element method to analyze the creep behavior and microcrack evolution in brittle rocks at a micro-scale level.Experimental validation of the model is performed,followed by numerical simu-lations to investigate the creep properties and microcrack evolution in rocks under single-stage loading,multi-stage loading,and confining pressure,at various constant stress levels.The results demonstrate that as the stress level increases in single-stage creep simulations,the time-to-failure progressively decreases.The growth of microcracks during uniaxial creep occurs in three stages,with tensile microcracks being predominant and the spatial distribution of microcracks becoming more dispersed at higher stress levels.In multi-stage loadingunloading simulations,microcracks continue to form during the unloading stage,indicating cumulative damage resulting from increased axial stress.Additionally,the creep behaviour of rocks under confining pressure is not solely determined by the magnitude of the confining pressure,but is also influenced by the magnitude of the axial stress.The findings contribute to a better understanding of rock deformation and failure processes under different loading conditions,and they can be valuable for applications in rock mechanics and rock engineering.

EFFECTS OF PHASE CONTINUITY ON RHEOLOGY OF TWO-PHASE ROCKS: A CONTINUUM MECHANICL MODEL

Based on continuum mechanics, we have developed a model for semi quantitative estimating effects of phase continuity on flow strength of two phase rocks including partially melted or crystallized rocks. Calculations of the bulk flow strength of composite rocks as functions of the volume fraction, geometrical shape and continuity of the constitutive phases involve in numerically solving two non linear equations and thus are easy to be performed. The model has been justified by a good agreement between the predicted and measured results on diabase (64% clinopyroxene and 36% plagioclase) in the range of experimental temperatures and strain rates. It is believed that the present model could provide an approximate estimate for the rheological evolution of magmatic rocks during their life cycle of melting crystallization deformation.

Anisotropic time-dependent behaviors of shale under direct shearing and associated empirical creep models

Understanding the anisotropic creep behaviors of shale under direct shearing is a challenging issue.In this context,we conducted shear-creep and steady-creep tests on shale with five bedding orientations (i.e.0°,30°,45°,60°,and 90°),under multiple levels of direct shearing for the first time.The results show that the anisotropic creep of shale exhibits a significant stress-dependent behavior.Under a low shear stress,the creep compliance of shale increases linearly with the logarithm of time at all bedding orientations,and the increase depends on the bedding orientation and creep time.Under high shear stress conditions,the creep compliance of shale is minimal when the bedding orientation is 0°,and the steady-creep rate of shale increases significantly with increasing bedding orientations of 30°,45°,60°,and 90°.The stress-strain values corresponding to the inception of the accelerated creep stage show an increasing and then decreasing trend with the bedding orientation.A semilogarithmic model that could reflect the stress dependence of the steady-creep rate while considering the hardening and damage process is proposed.The model minimizes the deviation of the calculated steady-state creep rate from the observed value and reveals the behavior of the bedding orientation's influence on the steady-creep rate.The applicability of the five classical empirical creep models is quantitatively evaluated.It shows that the logarithmic model can well explain the experimental creep strain and creep rate,and it can accurately predict long-term shear creep deformation.Based on an improved logarithmic model,the variations in creep parameters with shear stress and bedding orientations are discussed.With abovementioned findings,a mathematical method for constructing an anisotropic shear creep model of shale is proposed,which can characterize the nonlinear dependence of the anisotropic shear creep behavior of shale on the bedding orientation.

A creep model for ultra-deep salt rock considering thermal-mechanical damage under triaxial stress conditions

To investigate the specific creep behavior of ultra-deep buried salt during oil and gas exploitation,a set of triaxial creep experiments was conducted at elevated temperatures with constant axial pressure and unloading confining pressure conditions.Experimental results show that the salt sample deforms more significantly with the increase of applied temperature and deviatoric loading.The accelerated creep phase is not occurring until the applied temperature reaches 130℃,and higher temperature is beneficial to the occurrence of accelerated creep.To describe the specific creep behavior,a novel three-dimensional(3D)creep constitutive model is developed that incorporates the thermal and mechanical variables into mechanical elements.Subsequently,the standard particle swarm optimization(SPSO)method is adopted to fit the experimental data,and the sensibility of key model parameters is analyzed to further illustrate the model function.As a result,the model can accurately predict the creep behavior of salt under the coupled thermo-mechanical effect in deep-buried condition.Based on the research results,the creep mechanical behavior of wellbore shrinkage is predicted in deep drilling projects crossing salt layer,which has practical implications for deep rock mechanics problems.

Creep experiment and rheological model of deep saturated rock

By the methods of uniaxial single-stage loading and graded incremental cyclic loading, the creep experiments were performed on the deep saturated rock from Dongguashan Mine, and the creep curves of saturated rock under different loading stresses were obtained. By comparing with the creep rule of dry rock in the same location, the creep rule of deep saturated rock was analyzed. Based on the united rheological mechanical model, the rheological model of deep saturated rock was recognized, and the parameters of the model were determined. The results show that the creep curves are very smooth under low stress, but the phenomena of wave and catastrophe turn up under high stress, and the bearing capacity of rock is weakening over time. The rheological properties of saturated and dry rocks are very different under tlie condition of deep high stress, especially when unloading, degradation and damage of rock quality is more serious, and the effect of water cannot be neglected. The H--HIN--NJS model （Schofield-Scott-Blair model） was selected to represent the rheology rule of deep saturated rock, and the fitting curves of model agree well with the experiment data, so the selected model is reasonable.

Effect of pre-deformation on aging creep of Al-Li-S4 alloy and its constitutive modeling

A set of uniaxial tensile creep tests at different pre-deformations, aging temperatures and stress levels were carried out for Al-Li-S4 alloy, and the creep behavior and the effects of pre-deformation on mechanical properties and microstructures were determined under basic thermodynamics conditions of aging forming. The results show that pre-deformation shortens the time of primary creep and raises the second steady-state creep rate. Then, the total creep strain is greater, but in the range of test parameters it is still smaller than that without pre-deformation. In addition, transmission electron microscopy（TEM） observation shows that pre-deformation promotes the formation of T1 phase and θ′ phase and makes them distribute more dispersively, while inhibits the generation of δ′ phase, which leads to the improvement of mechanical properties of the alloy. A unified constitutive model reflecting the effects of aging mechanism, stress levels and different pre-deformations was established. The fitting results agree with the experimental data well.

A nonlinear creep damage model for gelled waxy crude

Yielding behaviors of waxy crude oil is one of the key issues of flow assurance challenges. The yielding of waxy crude under constant stress is actually a creep process of strain accumulation to structural failure,to describe the process completely and accurately is the basis of numerical simulation of restart process of the pipeline. The creep and yield behaviors of two gelled waxy crudes were investigated experimentally under different constant applied stresses. The results clearly show that the creep process of waxy crude is related to the applied stress and time. The greater the applied stress, and the longer the loaded time, the more obvious the nonlinear features. Based on the fractional calculus theory, a fractional viscous element was developed to describe the decelerated and steady creep process of gelled waxy crude. On the basis of the damage theory, an elastic damage element was proposed to describe the accelerated creep after the yielding. According to the idea of mechanical analogy, a nonlinear creep model was established by a fractional viscous element, an elastic damaged element, and an elastic element in series, which can accurately describe the whole creep and yielding process of gelled waxy crude.

A power function model for simulating creep mechanical properties of salt rock

In this paper,a new micro-creep model of salt rock is proposed based on a linear parallel bonded model(LPBM)using the two-dimensional particle flow code(PFC2D).The power function weakening form is assumed to describe the variation of the parallel bonded diameter(PBD)over time.By comparing with the parallel-bonded stress corrosion(PSC)model,a smaller stress fluctuation and smoother creep strain−time curves can be obtained by this power function model at the same stress level.The validity and adaptability of the model to simulate creep deformation of salt rock are verified through comparing the laboratory creep test curves and the Burgers model fitting result.The numerical results reveal that this model can be capable of capturing the creep deformation and damage behavior from the laboratory observations.

A CREEP DAMAGE EQUATION FOR ROCKS

In this paper,based on many experimental results,a creep damage equation for rocks with a creep modulus that can describe the history of damage has been deduced.According to the equation,a creep damage model for rock materials is constructed,and it is shown that the extent of their damage,or damage degree,during creep can be determined by means of simple experiments.

A new elastoplastic model for bolt-grouted fractured rock

Complexities in mechanical behaviours of rock masses mainly stem from inherent discontinuities,which calls for advanced bolt-grouting techniques for stability enhancement.Understanding the mechanical properties of bolt-grouted fractured rock mass(BGFR)and developing accurate prediction methods are crucial to optimize the BGFR support strategies.This paper establishes a new elastoplastic(E-P)model based on the orthotropic and the Mohr-Coulomb(M-C)plastic-yielding criteria.The elastic parameters of the model were derived through a meso-mechanical analysis of composite materials mechanics(CMM).Laboratory BGFR specimens were prepared and uniaxial compression test and variable-angle shear test considering different bolt arrangements were carried out to obtain the mechanical parameters of the specimens.Results showed that the anisotropy of BGFR mainly depends on the relative volume content of each component material in a certain direction.Moreover,the mechanical parameters deduced from the theory of composite materials which consider the short fibre effect are shown to be in good agreement with those determined by laboratory experiments,and the variation rules maintained good consistency.Last,a case study of a real tunnel project is provided to highlight the effectiveness,validity and robustness of the developed E-P model in prediction of stresses and deformations.

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

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

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.

Numerical modeling of failure mechanisms in phyllite mine slopes in Brazil

This paper presents three case studies comprising failure mechanisms in phyllite mine slopes at Quadrila- tero Ferrifero, State of Minas Gerais, Brazil. Numerical modeling techniques were used in this study. Fail- ure mechanisms involving discontinuities sub parallel to the main foliation are very common in these mines. Besides, failure through the rock material has also been observed due to the low strength of phyl- lites in this site. Results of this work permitted to establish unknown geotechnical parameters which have significant influence in failure processes, like the in situ stress field and the discontinuity stiffness.

A numerical test method of California bearing ratio on graded crushed rocks using particle flow modeling

In order to better understand the mechanical properties of graded crushed rocks （GCRs） and to optimize the relevant design, a numerical test method based on the particle flow modeling technique PFC2D is developed for the California bearing ratio （CBR） test on GGRs. The effects of different testing conditions and micro-mechanical parameters used in the model on the CBR numerical results have been systematically studied. The reliability of the numerical technique is verified. The numerical results suggest that the influences of the loading rate and Poisson＇s ratio on the CBR numerical test results are not significant. As such, a loading rate of 1.0-3.0 mm/min, a piston diameter of 5 cm, a specimen height of 15 cm and a specimen diameter of 15 cm are adopted for the CBR numerical test. The numerical results reveal that the GBR values increase with the friction coefficient at the contact and shear modulus of the rocks, while the influence of Poisson＇s ratio on the GBR values is insignificant. The close agreement between the CBR numerical results and experimental results suggests that the numerical simulation of the CBR values is promising to help assess the mechanical properties of GGRs and to optimize the grading design. Be- sides, the numerical study can provide useful insights on the mesoscopic mechanism.

Simulation of rock deformation and mechanical characteristics using clump parallel-bond models

To properly simulate hard rock with a high ratio of the uniaxial compressive strength to tensile strength(UCS/TS) and realistic strength-failure envelope,the rock deformation and mechanical characteristics were discussed in detail when the particle simulation method with the clump parallel-bond model(CPBM) was used to conduct a series of numerical experiments at the specimen scale.Meanwhile,the effects of the loading procedure and crack density on the mechanical behavior of a specimen,which was modeled by the particle simulation method with the CPBM,were investigated.The related numerical results have demonstrated that:1) The uniaxial compressive strength(UCS),tensile strength(TS) and elastic modulus are overestimated when the conventional loading procedure is used in the particle simulation method with the CPBM; 2) The elastic modulus,strength and UCS/TS decrease,while Poisson ratio increases with the increase of the crack density in the particle simulation method with the CPBM; 3) The particle simulation method with the CPBM can be used to reproduce a high value of UCS/TS(>10),as well as a high friction angle and reasonable cohesion strength; 4) As the confining pressure increases,both the peak strength of the simulated specimen and the number of microscopic cracks increase,but the ratio of tensile cracks number to shear cracks number decreases in the particle simulation method with the CPBM; 5) Compared with the conventional parallel-bond model,the CPBM can be used to reproduce more accurate results for simulating the rock deformation and mechanical characteristics.