Numerical modeling of blast-induced rock fragmentation in deep mining with 3D and 2D FEM method approaches

To optimize the excavation of rock using underground blasting techniques,a reliable and simplified approach for modeling rock fragmentation is desired.This paper presents a multistep experimentalnumerical methodology for simplifying the three-dimensional(3D)to two-dimensional(2D)quasiplane-strain problem and reducing computational costs by more than 100-fold.First,in situ tests were conducted involving single-hole and free-face blasting of a dolomite rock mass in a 1050-m-deep mine.The results were validated by laser scanning.The craters were then compared with four analytical models to calculate the radius of the crushing zone.Next,a full 3D model for single-hole blasting was prepared and validated by simulating the crack length and the radius of the crushing zone.Based on the stable crack propagation zones observed in the 3D model and experiments,a 2D model was prepared.The properties of the high explosive(HE)were slightly reduced to match the shape and number of radial cracks and crushing zone radius between the 3D and 2D models.The final methodology was used to reproduce various cut-hole blasting scenarios and observe the effects of residual cracks in the rock mass on further fragmentation.The presence of preexisting cracks was found to be crucial for fragmentation,particularly when the borehole was situated near a free rock face.Finally,an optimization study was performed to determine the possibility of losing rock continuity at different positions within the well in relation to the free rock face.

A review of discrete modeling techniques for fracturing processes in discontinuous rock masses

The goal of this review paper is to provide a summary of selected discrete element and hybrid finitediscrete element modeling techniques that have emerged in the field of rock mechanics as simulation tools for fracturing processes in rocks and rock masses. The fundamental principles of each computer code are illustrated with particular emphasis on the approach specifically adopted to simulate fracture nucleation and propagation and to account for the presence of rock mass discontinuities. This description is accompanied by a brief review of application studies focusing on laboratory-scale models of rock failure processes and on the simulation of damage development around underground excavations.

Modeling stress wave propagation in rocks by distinct lattice spring model

In this paper, the ability of the distinct lattice spring model （DLSM） for modeling stress wave propagation in rocks was fully investigated. The influence of particle size on simulation of different types of stress waves （e.g. one-dimensional （1D） P-wave, 1D S-wave and two-dimensional （2D） cylindrical wave） was studied through comparing results predicted by the DLSM with different mesh ratios （It） and those obtained from the corresponding analytical solutions. Suggested values of lr were obtained for modeling these stress waves accurately. Moreover, the weak material layer method and virtual joint plane method were used to model P-wave and S-wave propagating through a single discontinuity. The results were compared with the classical analytical solutions, indicating that the virtual joint plane method can give better results and is recommended. Finally, some remarks of the DLSM on modeling of stress wave propagation in rocks were provided.

3-D modeling of rock burst in pillar No. 19 of Fetr6 chromite mine

Fetr6 is an underground mine in which chromite is extracted using stope and pillar mining method. Despite of all improving works such as roof supporting and replacing of ore pillars with concrete pillars, pillar No. 19 failed and other pillars failed progressively as a domino effect and 4000 m2 of mine collapsed within a few minutes, consequently. For detail investigation, two 3-D numerical models were developed by 3Dec. The first, a base model, was used for estimation of stress on pillars just before failure and the other for investigation of rock burst in pillar No. 19. The results show that discontinuity parameters such as friction angle and shear stiffness is critical parameters in this pillar failure. In addition, it indicates that W/H ratio equal 0.3, the lack of ore extraction strategy and inadequate roof support are the major reasons for this failure. In this paper, the procedure of study was described.

Rock skeleton models and seismic porosity inversion

By substituting rock skeleton modulus expressions into Gassmann approximate fluid equation, we obtain a seismic porosity inversion equation. However, conventional rock skeleton models and their expressions are quite different from each other, resuling in different seismic porosity inversion equations, potentially leading to difficulties in correctly applying them and evaluating their results. In response to this, a uniform relation with two adjusting parameters suitable for all rock skeleton models is established from an analysis and comparison of various conventional rock skeleton models and their expressions including the Eshelby-Walsh, Pride, Geertsma, Nur, Keys-Xu, and Krief models. By giving the two adjusting parameters specific values, different rock skeleton models with specific physical characteristics can be generated. This allows us to select the most appropriate rock skeleton model based on geological and geophysical conditions, and to develop more wise seismic porosity inversion. As an example of using this method for hydrocarbon prediction and fluid identification, we apply this improved porosity inversion, associated with rock physical data and well log data, to the ZJ basin. Research shows that the existence of an abundant hydrocarbon reservoir is dependent on a moderate porosity range, which means we can use the results of seismic porosity inversion to identify oil reservoirs and dry or water-saturated reservoirs. The seismic inversion results are closely correspond to well log porosity curves in the ZJ area, indicating that the uniform relations and inversion methods proposed in this paper are reliable and effective.

Failure characteristics of three-body model composed of rock and coal with different strength and stiffness

Four different types of three-body model composed of rock and coal with different strength and stiffness were established in order to study the failure characteristics of compound model such as roof-coal-floor. Through stress analysis of the element with variable strength and stiffness extracted from the strong-weak interface, the tri-axial compressive strength of the weak body and strong body near the interface as well as the areas away from the contact surface was found. Then, on the basis of three-dimensional fast Lagrangian method of continua and strain softening constitutive model composed of Coulomb-Mohr shear failure with tensile cut-off, stress and strain relationship of the four three-body combined models were analyzed under different confining pressures by numerical simulation. Finally, the different features of local shear zones and plastic failure areas of the four different models and their development trend with increasing confining pressure were discussed. The results show that additional stresses are derived due to the lateral deformation constraints near the strong-weak interface area, which results in the strength increasing in weak body and strength decreasing in strong body. The weakly consolidated soft rock and coal cementation exhibit significant strain softening behavior and bear compound tension-shear failure under uni-axial compression. With the increase of confining pressure, the tensile failure disappears from the model, and the failure type of composed model changes to local shear failure with different number of shearing bands and plastic failure zones. This work shows important guiding significance for the mechanism study of seismic, rock burst, and coal bump.

Dolomite fracture modeling using the Johnson-Holmquist concrete material model:Parameter determination and validation

In this paper,the Johnson-Holmquist concrete(JHC)constitutive model is adopted for modeling and simulating the fracture of dolomite.A detailed step-by-step procedure for determining all required parameters,based on a series of experiments under quasi-static and dynamic regimes,is proposed.Strain rate coefficients,failure surfaces,equations of state and damage/failure constants are acquired based on the experimental data and finite element analyses.The JHC model with the obtained parameters for dolomite is subsequently validated using quasi-static uniaxial and triaxial compression tests as well as dynamic split Hopkinson pressure bar(SHPB)tests.The influence of mesh size is also analyzed.It shows that the simulated fracture behavior and waveform data are in good agreement with the experimental data for all tests under both quasi-static and dynamic loading conditions.Future studies will implement the validated JHC model in small-and large-scale blasting simulations.

Brittleness index and seismic rock physics model for anisotropic tight-oil sandstone reservoirs

Brittleness analysis becomes important when looking for sweet spots in tightoil sandstone reservoirs. Hence, appropriate indices are required as accurate brittleness evaluation criteria. We construct a seismic rock physics model for tight-oil sandstone reservoirs with vertical fractures. Because of the complexities in lithology and pore structure and the anisotropic characteristics of tight-oil sandstone reservoirs, the proposed model is based on the solid components, pore connectivity, pore type, and fractures to better describe the sandstone reservoir microstructure. Using the model, we analyze the brittleness sensitivity of the elastic parameters in an anisotropic medium and establish a new brittleness index. We show the applicability of the proposed brittleness index for tight-oil sandstone reservoirs by considering the brittleness sensitivity, the rock physics response characteristics, and cross-plots. Compared with conventional brittleness indexes, the new brittleness index has high brittleness sensitivity and it is the highest in oil-bearing brittle zones with relatively high porosity. The results also suggest that the new brittleness index is much more sensitive to elastic properties variations, and thus can presumably better predict the brittleness characteristics of sweet spots in tight-oil sandstone reservoirs.

The constructing of pore structure factor in carbonate rocks and the inversion of reservoir parameters

With a more complex pore structure system compared with clastic rocks, carbonate rocks have not yet been well described by existing conventional rock physical models concerning the pore structure vagary as well as the influence on elastic rock properties. We start with a discussion and an analysis about carbonate rock pore structure utilizing rock slices. Then, given appropriate assumptions, we introduce a new approach to modeling carbonate rocks and construct a pore structure algorithm to identify pore structure mutation with a basis on the Gassmann equation and the Eshelby-Walsh ellipsoid inclusion crack theory. Finally, we compute a single well＇s porosity using this new approach with full wave log data and make a comparison with the predicted result of traditional method and simultaneously invert for reservoir parameters. The study results reveal that the rock pore structure can significantly influence the rocks＇ elastic properties and the predicted porosity error of the new modeling approach is merely 0.74%. Therefore, the approach we introduce can effectively decrease the predicted error of reservoir parameters.

Thermal damage constitutive model for rock considering damage threshold and residual strength

With the gradual depletion of mineral resources in the shallow part of the earth,resource exploitation continues to move deeper into the earth,it becomes a hot topic to simulate the whole process of rock strain softening,deformation and failure in deep environment,especially under high temperature and high pressure.On the basis of Lemaitre’s strain-equivalent principle,combined with statistics and damage theory,a statistical constitutive model of rock thermal damage under triaxial compression condition is established.At the same time,taking into account the existing damage model is difficult to reflect residual strength after rock failure,the residual strength is considered in this paper by introducing correction factor of damage variable,the model rationality is also verified by experiments.Analysis of results indicates that the damage evolution curve reflects the whole process of rock micro-cracks enclosure,initiation,expansion,penetration,and the formation of macro-cracks under coupled effect of temperature and confining pressure.Rock thermal damage shows logistic growth function with the increase of temperature.Under the same strain condition,rock total damage decreases with the rise of confining pressure.By studying the electron microscope images(SEM)of rock fracture,it is inferred that 35.40 MPa is the critical confining pressure of brittle to plastic transition for this granite.The model parameter F reflects the average strength of rock,and M reflects the morphological characteristics of rock stress–strain curves.The physical meanings of model parameters are clear and the model is suitable for complex stress states,which provides valuable references for the study of rock deformation and stability in deep engineering.

Prediction of brittleness based on anisotropic rock physics model for kerogen-rich shale

The construction of a shale rock physics model and the selection of an appropriate brittleness index （B/） are two significant steps that can influence the accuracy of brittleness prediction. On one hand, the existing models of kerogen-rich shale are controversial, so a reasonable rock physics model needs to be built. On the other hand, several types of equations already exist for predicting the BI whose feasibility needs to be carefully considered. This study constructed a kerogen-rich rock physics model by performing the self- consistent approximation and the differential effective medium theory to model intercoupled clay and kerogen mixtures. The feasibility of our model was confirmed by comparison with classical models, showing better accuracy. Templates were constructed based on our model to link physical properties and the BL Different equations for the BI had different sensitivities, making them suitable for different types of formations. Equations based on Young＇s Modulus were sensitive to variations in lithology, while those using Lame＇s Coefficients were sensitive to porosity and pore fluids. Physical information must be considered to improve brittleness prediction.

Characteristics of different rocks cut by helical cutting mechanism

To research the loading charactefistc of rocks with different structures cut by helical cutting mechanism （HCM）, three different structures of rock （hard-soft-hard rock, soft-hard rock and soft-hard-soft rock） were built. And each type model was further divided into three types when the experiments were carried out. To reduce the errors of cutting load caused by manually configured rock in each test, the cutting load of soft rock was taken as a benchmark, and the differences of the cutting load of the different structures of rocks and the soft rock were used to reflect the cutting load change rules of the HCM. The results indicate that, the cutting load of only the HCM top cutting hard rock is larger than that of only the HCM bottom cutting hard rock for dextral HCM, and the cutting load fluctuation is larger, too. However, when the top and the bottom of the HCM cutting hard rock simultaneously, its cutting load is the largest, but the cutting load fluctuation is the least. And the HCM cutting load increment is increased linearly with the increase of rock compressive strength. The HCM cutting load increment is increased exponentially with the increase of hard rock cutting thickness.

Effects of confinement on rock mass modulus:A synthetic rock mass modelling(SRM) study

The main objective of this paper is to examine the influence of the applied confining stress on the rock mass modulus of moderately jointed rocks（well interlocked undisturbed rock mass with blocks formed by three or less intersecting joints）. A synthetic rock mass modelling（SRM） approach is employed to determine the mechanical properties of the rock mass. In this approach, the intact body of rock is represented by the discrete element method（DEM）-Voronoi grains with the ability of simulating the initiation and propagation of microcracks within the intact part of the model. The geometry of the preexisting joints is generated by employing discrete fracture network（DFN） modelling based on field joint data collected from the Brockville Tunnel using LiDAR scanning. The geometrical characteristics of the simulated joints at a representative sample size are first validated against the field data, and then used to measure the rock quality designation（RQD）, joint spacing, areal fracture intensity（P21）, and block volumes. These geometrical quantities are used to quantitatively determine a representative range of the geological strength index（GSI）. The results show that estimating the GSI using the RQD tends to make a closer estimate of the degree of blockiness that leads to GSI values corresponding to those obtained from direct visual observations of the rock mass conditions in the field. The use of joint spacing and block volume in order to quantify the GSI value range for the studied rock mass suggests a lower range compared to that evaluated in situ. Based on numerical modelling results and laboratory data of rock testing reported in the literature, a semi-empirical equation is proposed that relates the rock mass modulus to confinement as a function of the areal fracture intensity and joint stiffness.

Numerical analysis of confinement effect on crack propagation mechanism from a flaw in a pre-cracked rock under compression

In many situations rocks are subjected to biaxial loading and the failure process is controlled by the lateral confinement stresses. The importance of confinement stresses has been recognized in the literature by many researchers, in particular, its influence on strength and on the angle of fracture, but still there is not a clear description for the influence of confining stress on the crack propagation mechanism of rocks. This paper presents a numerical pro- cedure for the analysis of crack propagation in rock-like ma- terials under compressive biaxial loads. Several numerical simulations of biaxial tests on the rock specimen have been carried out by a bonded particle model （BPM） and the influ- ence of confinement on the mechanism of crack propagation from a single flaw in rock specimens is studied. For this purpose, several biaxial compressive tests on rectangular spec- imens under different confinement stresses were modeled in （2 dimensional particle flow code） PFC2D. The results show that wing cracks initiate perpendicular to the flaw and trend toward the direction of major stress, however, when the lat- eral stresses increase, this initiation angle gets wider. Also it is concluded that in addition to the material type, the initiation direction of the secondary cracks depends on confine- ment stresses, too. Besides, it is understood that secondary cracks may be produced from both tensile and shear mechanisms.

The construction of shale rock physics model and brittleness prediction for high-porosity shale gas-bearing reservoir

Due to the huge differences between the unconventional shale and conventional sand reservoirs in many aspects such as the types and the characteristics of minerals,matrix pores and fluids,the construction of shale rock physics model is significant for the exploration and development of shale reservoirs.To make a better characterization of shale gas-bearing reservoirs,we first propose a new but more suitable rock physics model to characterize the reservoirs.We then use a well A to demonstrate the feasibility and reliability of the proposed rock physics model of shale gas-bearing reservoirs.Moreover,we propose a new brittleness indicator for the high-porosity and organic-rich shale gas-bearing reservoirs.Based on the parameter analysis using the constructed rock physics model,we finally compare the new brittleness indicator with the commonly used Young’s modulus in the content of quartz and organic matter,the matrix porosity,and the types of filled fluids.We also propose a new shale brittleness index by integrating the proposed new brittleness indicator and the Poisson’s ratio.Tests on real data sets demonstrate that the new brittleness indicator and index are more sensitive than the commonly used Young’s modulus and brittleness index for the high-porosity and high-brittleness shale gas-bearing reservoirs.

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.

A New Example of Retrograde Solubility Model for Carbonate Rocks

Objective The dissolution and precipitation of carbonate during burial diagenetic process controls the reservoir property in deep buried strata. The geological process related with it has become a research focus during recent years. The most important dissolution fluids to carbonates are probably H2S and CO2 as byproducts of sulfate reduction in deep-buried setting with sulfate minerals, but carbonates are more soluble in relatively low temperature, which is the so-called retrograde solubility. Several geological processes can result in the decrease of temperature, including the upward migration of thermal fluids and tectonic uplift.

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.

Rock physics inversion based on an optimized MCMC method

Rock physics inversion is to use seismic elastic properties of underground strata for predicting reservoir petrophysical parameters.The Markov chain Monte Carlo(MCMC)algorithm is commonly used to solve rock physics inverse problems.However,all the parameters to be inverted are iterated simultaneously in the conventional MCMC algorithm.What is obtained is an optimal solution of combining the petrophysical parameters with being inverted.This study introduces the alternating direction(AD)method into the MCMC algorithm(i.e.the optimized MCMC algorithm)to ensure that each petrophysical parameter can get the optimal solution and improve the convergence of the inversion.Firstly,the Gassmann equations and Xu-White model are used to model shaly sandstone,and the theoretical relationship between seismic elastic properties and reservoir petrophysical parameters is established.Then,in the framework of Bayesian theory,the optimized MCMC algorithm is used to generate a Markov chain to obtain the optimal solution of each physical parameter to be inverted and obtain the maximum posterior density of the physical parameter.The proposed method is applied to actual logging and seismic data and the results show that the method can obtain more accurate porosity,saturation,and clay volume.

Numerical simulation study of the failure evolution process and failure mode of surrounding rock in deep soft rock roadways

Based on the safety coefficient method,which assigns rock failure criteria to calculate the rock mass unit,the safety coefficient contour of surrounding rock is plotted to judge the distribution form of the fractured zone in the roadway.This will provide the basis numerical simulation to calculate the surrounding rock fractured zone in a roadway.Using the single factor and multi-factor orthogonal test method,the evolution law of roadway surrounding rock displacements,plastic zone and stress distribution under different conditions is studied.It reveals the roadway surrounding rock burst evolution process,and obtains five kinds of failure modes in deep soft rock roadway.Using the fuzzy mathematics clustering analysis method,the deep soft surrounding rock failure model in Zhujixi mine can be classified and patterns recognized.Compared to the identification results and the results detected by geological radar of surrounding rock loose circle,the reliability of the results of the pattern recognition is verified and lays the foundations for the support design of deep soft rock roadways.