Horizontal Stress Distribution Research Articles

Evaluation of integrated geological engineering reservoir reconstruction in Block X of Bozi

The geological structure of the reservoir in Bozi-Dabei area is complex, and the longitudinal difference of rock mechanical properties of the reservoir is large. Most of the current evaluation techniques after reservoir reconstruction are based on the fitting of construction pressure based on the logging curve of a single well, so as to analyze the fracture morphology and the geometric dimensions of length, width and height after pressure. It is difficult to explain the fracture morphology and geometric parameters correctly because the interpretation methods used do not comprehensively consider the influence of natural fractures, 3D geological properties and 3D geomechanical properties. In order to explain the artificial fracture morphology more accurately, the target layer ant body is generated by using 3D original seismic data, and the natural fracture model of three different reservoir types in Bozi X block is generated, which provides geological basis for the integrated demonstration. By combining dynamic and static data and multidisciplinary methods, a one-dimensional rock mechanics profile model is established, and a three-dimensional geomechanical model of three different reservoir types in Block X of Bozi is established by combining geological model and deep diagenesis theory. The matching relationship between horizontal stress, fault strike and natural tensile fracture distribution is comprehensively analyzed and evaluated, providing a geomechanical basis for the evaluation of integrated reservoir reconstruction. Integrated geological model and geomechanical model are closely combined with engineering parameters to establish an integrated true three-dimensional artificial fracture model. On this basis, the optimization research and design of the parameters of displacement, liquid volume and sand ratio are completed. The optimal flow rate of Class I reservoir 6-7 (m³·min-1), Class II reservoir 5-6 (m³·min-1), Class III reservoir 4-5 (m³·min-1), Class I reservoir 600-700 m³, Class II reservoir 600-700 m³, Class III reservoir 500-600 m³, Sand ratio of 15%-20% for Class I reservoir, 15%-20% for class II reservoir and 20%-25% for class III reservoir are the optimal construction parameters, which provide guidance for field construction.

Deformative Response of Sheltering Structures Under the Debris Flow Impact

A relevant issue in the development of disaster risk reduction strategies is played by design of mitigation measures aimed at reducing risk to acceptable values. For rapid landslides, such as debris flows, sheltering structures are very common mitigation measures realized in exposed areas that allow to protect elements at risk and to stop flowing mass. For the design of these works, the debris flow–structure interaction mechanism is very important. The paper focuses on the evaluation of debris flow–structure interaction mechanism in earth reinforced embankments based on an uncoupled analysis of the interaction in two flow cases (dominant static and dynamic). In particular, a novel approach to evaluate the horizontal stress distribution at different time of the impact phenomenon along the upstream face height of deformable sheltering structures considering the dominant flow component has been proposed. First, impact force over the time against structure is calculated. Subsequently, assuming that debris flow is completely stopped by embankment according to a scheme of accumulation of material behind the obstacle, the deformative response of different geometrical types of embankment is obtained by FEM numerical analysis for considered flow cases. The results of numerical analyses are discussed in terms of horizontal displacements in different control points in sheltering structures. The analysis showed that the deformative response of two geometries of embankments depends on dominant static or dynamic components of impact force.

Reduction of ore dilution when mining low-thickness ore bodies by means of artificial maintenance of the mined-out area

Purpose. The research purpose is to study the effectiveness of artificial maintenance of the mined-out space based on the use of cable bolts to reduce the dilution coefficient when mining low-thickness ore bodies. Methods. Geotechnical mapping of the rock mass according to the Q, RMR, RQD and GSI rating classifications is conducted, as well as a linear survey of the fracture system in the hanging wall and footwall rocks is performed using a rock compass and the GEO ID application. Numerical analysis by the limit equilibrium method in the Unwedge software package is applied to determine the safety factor of a mass divided by fractures into wedges. Using a Schmidt test hammer, the uniaxial compressive strength of the mass rocks has been determined. The full-scale studies have been conducted using cable support in the conditions of the Akbakai deposit. Findings. It has been revealed that the footwall rocks are in a stable state, while the safety factor of the hanging wall rocks is 0.98, which requires artificial maintenance using cable bolts. The cable support parameters are calculated taking into account nonuniform distribution of horizontal and vertical stresses in the rock mass. It has been determined that when strengthening the hanging wall with cable bolts in inclined veins with a dip angle of up to 40º, the average ore dilution is 66.1%, and that of previously mined without fastening is 68.7%. In similar experiments in steep-dipping veins with a dip angle of more than 60º, dilution decreases from 62.8 to 48.7%. Originality. It has been revealed that in the conditions of the Akbakai deposit, cable fastening of the hanging wall rocks is effective at an ore deposit dip angle of more than 60º, at which the mined ore dilution coefficient decreases. Practical implications. The research results can be used to increase the stability of hanging wall rocks when mining low-thickness ore bodies with a sublevel caving system.

Microscopic mechanism of subgrade vibration compaction based on discrete element method

<abstract> <p>The discrete element is an important tool for vibration compaction simulation from the microscopic viewpoint. The irregular particle model was established by the disc filling method, and the linear contact model with anti-rolling was selected to reflect the contact characteristics between the particles, so as to establish the simulation model of subgrade vibratory compaction. Based on this model, the stress characteristics of the area below the center of the vibrating wheel and the surface area of the soil were studied, and the principle of vibratory compaction was discussed. The results show that the distribution of vertical stresses below the center of drum basically presents a decreasing trend in the depth range during vibration, with the stress amplitude of the lower structure increasing and the stress magnitude of the upper structure decreasing. The distribution of horizontal stresses in the area below the center of the vibrating wheel is similar to the stress distribution in the splitting test. The soil at the surface has an obvious pushing and squeezing effect, and the transmission distance of horizontal stresses is larger than that of vertical stresses. The soil at the surface is pushed and the horizontal stresses are transmitted at a greater distance than the vertical stresses, which, together with a certain degree of shear effect, causes a certain uplift deformation of the soil around the vibrating wheel. In general, the vibration compaction process is relatively consistent with the theory of repeated loading and the theory of alternating shear strain.</p> </abstract>

Geomechanical substantiation of the parameters for the mining system with ore shrinkage in the combined mining of steep-dipping ore bodies

Purpose. The research purpose is to substantiate a rational technology for mining steep-dipping ore bodies based on a complex of geomechanical studies in combined mining of deposits. Methods. Analysis of existing constructive methods for calculating the optimal mining system parameters when mining under-open-pit ore reserves in the zone of influence of surface mining operations, taking into account the natural stress-strain state of the rock mass. Numerical modeling is used to study the geomechanical processes occurring in the mass during the mining of under-open-pit reserves of steep-dipping ore bodies in order to substantiate the mining system with ore shrinkage. The geotechnical mapping of mine workings is conducted directly in the face to determine the mass rating. Findings. The calculation of the optimal parameters for the stope chamber, inter-chamber and inter-level pillars based on a complex of geomechanical studies has shown that the more intense horizontal stresses act in the bottom of the blocks and in the inter-block pillars, in which a large number of board gates have been driven. Originality. For the first time, using high-precision programs and given the nonuniform distribution of horizontal and vertical stresses acting in the mass for the Abyz Mine conditions, it has been revealed that when mining an individual block, the maximum horizontal stresses around the mined-out space reach 10-15 MPa; when mining a group of blocks – 20-25 MPa. Practical implications. The research results can be used in planning and mining with shrinkage of steep-dipping ore bodies during mining of under-open-pit reserves.

Analysis of the Stressed State of Sand-Soil Using Ultrasound

The maintenance of the ballast substructure is an important cost-driver for railway systems. The problem is that today’s condition monitoring methods are insufficient to collect detailed data on the compaction and stress allocation inside the ballast bed. That makes it challenging to improve the maintenance technology and organization. This study aimed to investigate the applicability of the ultrasound method for analyzing the state of stress of sand-soil and the relation between the residual stress and wave propagation velocity. The experiments on the sand in a box with different allocations of the ultrasonic receivers and pressure measurement cells were produced under different external loading. In addition, the vertical and horizontal stress distributions were measured. The results showed a correlation between the test load, the state of stress, and the ultrasound propagation velocity. Moreover, the residual stresses after the loading cycles were analyzed.

Analysis of force and deformation parameters in corrugated clad rolling

Corrugated clad rolling is an emerging and promising technology to produce composite plates with a three-dimensional corrugated interface and excellent performance. A new analytical model is proposed to predict and analyze force and deformation parameters in corrugated clad rolling using the slab method, which solves the problem that there is no suitable analytical model to improve the precision of automatic production control. The analytical model is proposed by selecting a differential element perpendicular to the rolling direction, analyzing the corresponding differential equilibrium equations and calculating the integral constants according to the yield and boundary conditions. Dynamic rolling forces under different contact states between the composite plate and rolls are presented creatively considering the special features of the new corrugated clad rolling that there are multiple complex shapes and stress states in the deformation zone and that there are various outlet conditions of the corrugated composite plate. The accuracy of the proposed analytical model is verified by the comparisons of the calculated values from the model, the FEM results, and the experimental measurements. The error of the proposed model is within 7.36%. The specific rolling pressure distributions along the projected contact arc, the specific horizontal stress distributions along the projected contact arc, the dynamic rolling forces, and the positions of the lower neutral point can be conveniently and accurately calculated by the proposed model, which can help to analyze the mechanism of the corrugated rolling with the variation of the rolling reduction rate, the shear yield stress ratio and the friction factor ratio. The proposed analytical model of dynamic rolling force and deformation parameters is especially suitable for the analysis of the new corrugated clad rolling and can provide technical support for the control precision of automatic production.

FORM-FINDING ANALYSIS OF HANGING MEMBRANE USING HORIZONTAL MEMBRANE STRESS DISTRIBUTION BY FINITE ELEMENT STRESS ANALYSIS

This paper proposes a simple method to obtain equilibrium membrane forms under the self-weight. The horizontal component of the membrane forces determined by the finite element analysis of an initial shell form is given as the known membrane stress distribution in the form-finding analysis. The form of the hanging membrane can be obtained by modifying the nodal z coordinates to be in equilibrium for the self-weight while maintaining the horizontal membrane stress distribution. Several numerical examples are presented to demonstrate the effectiveness of the proposed method.

Floor heave mechanism in water-rich soft rock roadways and a DS-IBA control approach

Severe floor heave in underground soft rock roadways heavily affects mine safety and production efficiency. In the present study, the context of the Shanghaimiao mining area is analyzed as the research object. In this regard, the floor heave mechanism and floor control in water-rich soft rock roadways are investigated through laboratory experiments, theoretical analysis, numerical simulation, and field tests. Moreover, a mechanical model of asymmetric floor heave is established. The obtained results reveal that: the main contributors to serious floor deformation in mining roadways are low rock stratum strength, hydrophysical behavior, and mining disturbance. It is found that the roadway floor stability is relevant to the stress concentration coefficient of the roadway side, the burial depth of the roadway, and the cohesion and internal friction angle of the floor rock. Meanwhile, the correlation between the upward resultant stress of the floor and the stress concentration coefficient of the roadway sides is established. Furthermore, the horizontal stress distribution of the roadway floor within 20 m of the advanced working face is simulated and analyzed. Based on the performed analyses and the obtained results, a novel double-seal deep and shallow inverted bottom arch (DS-IBA) floor support strategy is proposed. The proposed strategy is expected to provide a reference for dealing with similar water-rich soft rock roadways.

Implementation of the Non-Associated Elastoplastic MSDPu Model in FLAC3D and Application for Stress Analysis of Backfilled Stopes

The multiaxial Mises-Schleicher and Drucker-Prager unified (MSDPu) criterion has been shown to exhibit several specific features compared to other yield and failure criteria, including a nonlinear mean stress dependency, influence of the Lode angle, use of independent uniaxial compressive and tensile strength values and absence of an apex (singularity) on the envelope surface in the negative stress quadrant. However, MSDPu has been seldom used in practice to solve geotechnical and geomechanical engineering problems mainly because it had not yet been fully implemented into three-dimensional (3D) numerical codes. To fill this gap, a 3D elastoplastic MSDPu formulation is developed and implemented into FLAC3D. The proposed MSDPu elastic-perfectly plastic (EPP) constitutive model is then validated against existing analytical solutions developed for calculating the stress and displacement distributions around cylindrical openings. The FLAC3D MSDPu-EPP model is then applied to evaluate the vertical and horizontal stress distributions in a three-dimensional vertical backfilled stope. The numerical results obtained with the MSDPu-EPP model are compared with those obtained with the Mohr-Coulomb EPP model, to highlight key features of the new formulation.

Comprehensive Evaluation of Rock Mechanical Properties and in-situ Stress in Tight Sandstone Oil Reservoirs

Comprehensive research on reservoir rock mechanics and in-situ stress properties combined with petrophysical experiments, logging models and numerical simulation is an important means to achieve efficient development of tight sandstone oil reservoirs. In this study, a large number of rock mechanics and acoustic experiments, full-wave train array acoustic wave tests, hydraulic fracturing data and three-dimensional finite element simulations were used to study the rock mechanical properties and in-situ stress characteristics of continental tight oil reservoirs in the Yanchang Formation. The results show that under uniaxial conditions, the tight sandstone samples mainly suffer from tensional ruptures. With the increase of confining pressure, the tight sandstone samples undergo obvious shear ruptures. When the confining pressure is loaded to 35 MPa, a typical vertical shear fracture will be formed. The hydraulic fracturing calculation results show that the in-situ stress state of the target layer satisfies σv (vertical principal stress)>σH (maximum horizontal principal stress)>σh (minimum horizontal principal stress). Based on the results of rock mechanics and acoustic tests, we have constructed the dynamic and static mechanical parameter conversion models of tight oil reservoirs and the logging interpretation model of current in-situ stress. Furthermore, the finite element method is used to simulate the three-dimensional structural stress field of the target layer. The simulations show that the horizontal principal stress distribution in the work area is consistent with the applied environmental stress. The σH of the target layer is mainly distributed in 32–50 MPa, and the σh is mainly distributed in 20–34 MPa. Both σH and σh are relatively high in the southern uplift of the work area; among them, σH is usually greater than 44 MPa, and σh is usually greater than 24 MPa. The northern part of the study area developed several grooved areas with relatively low stress values. The regions with high stress values are often distributed in bands, which may be related to the compression caused by the deformation of the strata. For shear stress, left-handed and right-handed regions usually alternate with each other. However, the extent of the left-handed area in the southern uplift area is larger than that of the right-handed area, indicating that the tight oil reservoirs in the study area are mainly affected by left-handed activities.

Theoretical method for additional horizontal stress of isolation piles due to adjacent loading

AbstractIsolation piles are widely used to increase the horizontal resistance of high‐speed railway under adjacent loading in soft soils. This study proposes a theoretical model for horizontal additional stress of pile‐reinforced area subjected to adjacent loading. The isolation piles and the soil between piles in the reinforcement area are equivalent to a uniform medium in the proposed model. The Heaviside function is introduced to avoid the partition solution problem of pile‐reinforced area and the foundation soils. A combined method with the inverse Fourier transform, Gauss integral, Lagrange quadratic interpolation, and Simpson quadrature formula is employed in the calculation process. The theoretical model is validated by the finite element method. According to the calculated results, the distribution of horizontal additional stress is obtained. The horizontal soil displacements at the location of the railway increases in the depth range of 0–2.5 m and then gradually decreases. The proposed model with engineering significance is available for preliminary design of isolation piles.

Stability analysis of shield tunnel face under complex ground conditions

Current underground space development features ever-increasing scales. More and more planned tunnel lines have alignments that are characterized by varying passing depths. Both conditions make it more frequent that the shield tunnel face is exposed to heterogeneous ground consisting of distinct soil layers and hydraulic loads, which makes it remarkably challenging to maintain a stable shield face. This work presents a limit equilibrium model to analyze the face stability of shield tunnel under complex ground conditions. The model is consistent with the existing method of slices for uniform soil profile in that the effect of horizontal arching is considered without the need of an a priori assumption on the distribution of horizontal stresses, but extends it to the stratified ground by allowing the variation of failure mechanism across soil layers. Three-dimensional coupled pore fluid flow and stress finite element analyses are performed to study the tunnel face stability in heterogeneous ground consisting of horizontal layers and subjected to hydraulic loads. The results show that the multilayer wedge model can compute limit support pressures that are reasonably close to finite element solutions. Lastly, the finite element method and the multilayer wedge model are employed to analyze the stability of tunnel face in aquifer-aquitard alternate layers with confined water.

Fault Segmentation Pattern Controlled by Thickness of Brittle Crust

AbstractDuring large earthquakes, seismic sources tend to split in several sub‐events that rupture neighboring fault patches called fault segments. The scaling of such segmentation plays a decisive role in earthquake rupture dynamics, especially for strike‐slip events. Using numerical modeling we demonstrate that when a pristine layer of brittle material is sheared, the first oblique Riedel fractures nucleate with a regular spacing that is controlled by the thickness of that layer. During later localization of the deformation, those initial fractures control the spatial structuration of the entire fault system. Analyzing the horizontal stress distribution in fault‐parallel direction for different ratios between inter‐Riedel distance and material thickness, we identify a threshold at 1.5, beyond which the stress switches from compressional to tensional and leads to the nucleation of a new Riedel fracture. Thus, the inter‐Riedel segment length appears to be controlled by the vertical distribution of stress along the fault.

Investigation of Stress Arching Above Depleting Hydrocarbon Reservoirs and Its Effect on the Compaction Drive Mechanism

In this paper, the compression drive mechanism, which can be considered as the most related oil drive mechanism with the reservoir geomechanical properties, has been investigated. The constant total vertical stress on the reservoir and uniaxial reservoir compaction with zero lateral strain are two main assumptions in the conventional reservoir compaction modeling. These assumptions are not considering the stress arching, which leads to a reduction in the total vertical stress and also affects the distribution of vertical and horizontal stresses. In this paper, it was tried to investigate the effects of three keys elastic parameters, including Young's modulus, Poisson’s ratio, and Biot coefficient on the reservoirs stress paths and compaction drive mechanism using numerical modeling with ABAQUS software. Based on the modeling results the reservoirs stress paths is very different from simplifying assumption in uniaxial compaction models while the total compaction of reservoir obtained using numerical modeling and uniaxial model in some cases can be equal. Also, among the three geomechanical parameters, the ratio of Young's modulus of the reservoir and surrounding rocks has a significant effect on the reservoir stress paths and compaction. The results of modeling indicate when a reservoir rock is softer than its surrounding environment, due to the arching occurrence, the total vertical stress applied to the reservoir rock reduced even to half of the initial vertical stress, which leads to the oil recovery by the compression drive mechanism will be less than 50% of the predicted value.

Mechanical Analysis of the Failure Characteristics of Stope Floor Induced by Mining and Confined Aquifer

Mining above confined aquifer has become an important task for water inrush prevention in China. To study the failure characteristics of stope floor along the strike, a mechanical model under combined action of mining and confined aquifer was constructed, and the distribution of vertical stress, horizontal stress, and shear stress was obtained. Based on the Mohr–Coulomb criterion, the failure range of the floor is determined and verified by the in situ test. The results indicate the following. (1) Both vertical stress and horizontal stress in the stope floor take the junction of stress increasing area and stress decreasing area as the dividing line, forming two groups of “convex arches” at the solid coal side and the goaf side, respectively. (2) The vertical stress gradient in the solid coal side is significantly higher than that in the goaf side, while the horizontal stress gradient in the solid coal side is similar to that in the goaf side. The shear stress distribution is divided into three regions by the boundary between positive and negative shear stress, which makes the stope floor in this area to show compression shear or tension shear failure. (3) According to the in situ test, the maximum floor failure depth of 41503 working face is 11.38 m, which is quite close to the theoretical calculation result of 9.68 m. (4) Applying the mechanical model to five other coal mines with different mining conditions and stress states, the maximum absolute error between the measured and theoretical values of floor failure depth is 1.1 m, the average absolute error is 0.8 m, the maximum relative error is 8.2%, and the average relative error is 6.5%. The study provides a certain mechanical basis and reference for the floor failure mechanism induced by mining and confined aquifer.

Determination and Engineering Practice of Unsupported Roof Distance for Rapid Excavation of Roadway with Thick and Hard Basic Roof

In order to determine the reasonable empty roof distance during roadway excavation, a mechanical model of the direct roof rock beam was established, and the relationship between the direct roof tensile stress and the empty roof distance was obtained. According to the criterion of roof stability, that is, the tensile stress of the roof does not exceed the tensile strength, the expression of the empty roof distance during the roadway excavation is determined. Taking the 150,802 roadway in Liuzhuang coal mine as the research background, the horizontal and vertical stress distribution characteristics of the direct roof under different supporting forces are analyzed, and combined with the direct roof surplus safety factor, the reasonable empty roof distance during roadway excavation is determined as 2.0 m. By using FLAC3D numerical simulation software to analyze the distribution law of vertical stress and plastic zone when the empty roof distance is 2.0 m, it is obtained that the overall stability of the roadway surrounding rock within the empty roof area is better when the empty roof distance is 2.0 m, and it is applied to Liuzhuang Coal mine 150,802 roadway. The field application results show that when the empty roof distance is selected as 2.0 m during roadway excavation, the deformation of the roof and bottom of the roadway and the two sides are small, the stability is good, and the roadway excavation speed is increased by about 30%.

Maximising the efficiency of Menard pressuremeter testing in cohesive materials by a cookie-cutter drilling technique

Menard pressuremeter testing has been widely used in geotechnical engineering applications for 40 years and is an important technique in determining in-situ horizontal stress distributions. In this study, Menard pressuremeter testing is combined with a “cookie-cutter” insertion technique to determine horizontal stresses for a soft-rock in an operational Australian mine. The method presents an alternative to the Self-Bored Pressuremeter, with cookie-cutter drill rods allowing for sample recovery and further laboratory testing. The method accommodates for the presence of gravel and hard layered materials that present a risk of damage to cutting shoes of Self-Bored Pressuremeter devices. The combination of a sonic drill rig, coupled with the cookie cutter rods produces a close tolerance pocket resulting in “pseudo self boring pressuremeter tests”. The undrained shear strength, unload-reload shear modulus and in-situ horizontal stress are presented from pressuremeter tests conducted in the region for the first time. The undrained shear strength was observed in the range of 0.47–0.57 MPa, the unload-reload shear modulus between 17.43 and 18.25 MPa, the lift-off pressure in the range of 0.35–0.61 MPa. The K0 of coal was equal to 1, with interseam materials ranging from 2.1 to 3.5. Results of the cookie-cutter insertion method are compared with conventional drilling methods, with the cookie-cutter insertion test providing results in good agreement with both advanced triaxial laboratory tests and FEM numerical analysis. Cookie-cutter pressuremeter tests were conducted on cohesive soils at Australia's second-largest open-pit mine, with pressuremeter test results presented for Victorian brown coal for the first time.

Research on the Evolution Characteristics of Floor Stress and Reasonable Layout of Roadways in Deep Coal Mining

The safe and efficient mining of deep coal resources is severely restricted by the dynamic disasters caused by high gas and high ground stress. Taking a deep mine in China as the research background, a mechanical model of the front supporting stress with the working face was constructed through theoretical calculations. Based on the limit equilibrium theory, the stress distribution in the plastic zone and the elastic zone of the lateral working face was derived; based on semi-infinite plane mechanics model, the floor vertical and horizontal stress distribution was deduced. Then, the roadway surrounding rock stress and displacement field distribution evolution characteristics were revealed through numerical simulation. On this basis, the reasonable floor gas drainage roadway (FGDR) layout was determined: internal staggered layout was used with FGDR, the vertical distance to the working face is 20 m, and the horizontal distance to the working face end is 15 m; the open-off cut of FGDR was arranged in an external staggered layout, the vertical distance to the working face is 20 m, and the horizontal distance to the open-off cut of the working face is 15 m. It is an important practical significance for the layout of FGDR, the control of surrounding rocks, and the improvement of gas drainage effects under similar conditions through the research results.

A study of crack initiation and source mechanism in the Brazilian test based on moment tensor

It has been widely accepted that the Brazilian test can be used to obtain the indirect tensile strength of geo-materials. However, the effects of the contact conditions and the heterogeneity of the rock affect the micro-failure of the disc and the accuracy and feasibility of the Brazilian tensile strength (BTS), which typically leads to deviations from the results of the direct test. This study uses active and passive ultrasonic techniques and a three-dimensional flat-joint model (FJM3D) to quantitatively investigate the effects of these factors on the location and source mechanism with a Brazilian test, both in the laboratory and with numerical tests. During the laboratory tests, eight channels were used to record full waveform data continuously, and a total of 1090 and 928 acoustic emission (AE) events were located successfully under line loads and non-line loads, respectively. Both cases showed that the crack initiation points occurred away from the centre of the disc, indicating that the true tensile strength value may be somewhat underestimated. Three classification methods based on moment tensor inversion were used to quantitatively study the AE source analysis, which revealed that tensile micro-cracks that contain some deviatoric components predominantly occurred in micro-failure events. With the use of the FJM3D, the effects of the contact conditions and the heterogeneity of the rocks were analysed in detail. Four types of numerical tests were performed with different contact conditions and degrees of heterogeneity for comparison, indicating that the heterogeneity of rocks has a remarkable effect on the distribution of horizontal stress. This microcosmic and quantitative perspective can provide new data that can be used to modify the Brazilian test to obtain more accurate tensile strength values.