Two-dimensional Particle Flow Code Research Articles

Modelling of dynamic tensile failure of inclusion-bearing rocks

Natural and synthetic inclusions may modify the tensile strength and the failure pattern of surrounding rocks. Understanding the failure mechanism could improve rock failure prediction and induced geohazard mitigation. Due to difficulties in controlling the geometrical and mechanical properties of embedded inclusions in the laboratory, we simulate the dynamic tensile failure of inclusion-bearing rock specimens using a two-dimensional particle flow code model. We investigate the effects of strength ratio, loading rate, and treatment temperature on the nominal tensile strength of inclusion-bearing specimens and discuss the brittleness index to interpret the strength evolution. We identify the dominant effect on the nominal tensile strength as strength ratio for a low tensile strength inclusion and loading rate and treatment temperature for a high tensile strength inclusion. The change in dominant effect is associated with induced cracks primarily formed in the rock/inclusion part with lower tensile strength and highlights key factors to control inclusion-induced rock failure. This study also reveals that low strength, large size inclusions promote a decrease in brittleness index and accelerate the degradation of inclusion-bearing rocks.

Numerical simulation of mesomechanical properties of limestone containing dissolved hole and persistent joint

In order to reveal the complex mechanical properties and mesoscopic failure behavior of limestone rock mass containing both dissolved hole defect and persistent joint, numerical models are developed using the two-dimensional particle flow code (PFC2D) to carry out the uniaxial compressive strength (UCS) tests. The stress–strain, contact force chain, vertical stress field, and crack evolution characteristics of limestone samples containing circular holes and different dip angles persistent joints were analyzed. The results show that the UCS and elastic modulus of the rock samples can be reduced by the circular hole and the persistent joint, and the persistent joints with steep dip angles have a more obvious control effect on the mechanical properties of the rock samples. With the increase in loading stress level, the contact force chain in the hole-joint combination model gradually deflects slightly along the joint dip angle from the left and right sides of the hole and gradually spreads outward. Under uniaxial compression, the initiation cracks in persistent joints and rock blocks are primarily tensile cracks. The initiation positions first appear in the persistent joint, and the initiation positions in the rock block change from the upper and lower vertices of the circular hole to the junction below the joint with the increase of the joint dip angle. The crack initiation stress in the persistent joint is smaller than that in the corresponding rock block, and the control effect of the joint dip angle on the crack initiation stress of the whole rock sample is reduced.

Shear characteristics and shear strength model of rock mass structural planes

Accurately determining the shear strength of structural planes is crucial for evaluating the stability of rock masses. The shear test using the sawtooth structural plane usually captures the main influencing factors of its shear characteristics. In this study, the two-dimensional particle flow code (PFC2D) numerical simulation method was used to conduct shear tests on the sawtooth structural planes of rock masses with undulant angles of 10°, 20°, and 30°, respectively. With the increase in normal stress and the undulant angle, the shear failure of the structural planes was found to no longer be pure slip failure or shear failure but accompanied by a compression-induced fracture phenomenon. Based on the analysis of the shear test results, a peak shear strength model considering different undulant angles and normal stresses was proposed, and the hyperbolic function post-peak shear strength model was improved. The peak shear strength obtained from the physical direct shear tests was compared with those calculated using the proposed model, Parton model, and Shen model. The calculation error under low and high normal stress of the proposed method was found to be within an acceptable range. Additionally, when calculating the peak shear strength of a structural plane under high normal stress, applying the calculation method proposed in this study is a better option than applying the other models. Furthermore, although the variation trend of the post-peak shear strength was similar to that of the experimental results, the values obtained using the hyperbolic variation model were too large. The variation trend of the post-peak shear strength obtained using the improved function was essentially consistent with the experimental results, and the calculated values were close to the experimental results. The systematic research on the shear strength calculation model of rock mass structural planes contributes to the theoretical research of rock mass mechanics, and this study can act as a guide for landslide prediction and control projects.

Micromechanics of granulated rubber–soil mixtures as a cost-effective substitute for geotechnical fillings

Rubber–soil mixtures (RSM), formed by mixing two types of granules with vastly different mechanical properties, has the potential for serving as a cost-effective substitute for geotechnical fillings. Its micromechanical behavior at a microscopic scale, however, is not yet well understood. In this study, a numerical model of granulated RSM under biaxial compression conditions is established based on the discrete element theory and two-dimensional particle flow code. Microparameters of a particular RSM are studied and calibrated by comparison with triaxial consolidated drained shear tests. The volumetric fraction of sand is assigned as the index of the mixture, and the deviatoric stress–axial strain curves of RSM with different sand fractions are analyzed. Particle rotation, average coordination number, force chain structure, and energy dissipation with axial strains are further investigated to better understand the microscopic mechanisms of RSM. The main findings of the study include: (1) Rubber particles are highly deformable and fill the voids more easily than stiffer sand particles. This contributes to the high friction of sand–rubber interfaces, which delays or even inhibits the relative motion and tumbling of sand particles; (2) The force chains of sand particles are either braced from buckling until large axial strains by rubber particles occupying the intergranular voids or distributed by increased rubber–rubber contacts depending on the rubber content; and (3) RSM with a rubber volumetric content of 30–40% are optimal in that the force chain increases monotonically with axial strain with a stable load-deformation relationship. In addition, the sensitivity analysis of the effect of microparameters on the macroscopic behavior of RSM is presented, which can provide theoretical support for exploring the mechanical properties of similar mixed granular materials subjected to external loading.

Mechanical behaviours of sandstone containing intersecting fissures under uniaxial compression

Predicting rock cracking is important for assessing the stability of underground engineering. The effects of the intersecting angle α and the distribution orientation angle β of intersecting fissures on the uniaxial compressive strength and the failure characteristics of sandstone containing intersecting fissures are investigated through laboratory experiments and two-dimensional particle flow code (PFC2D). The relationship between the mechanical properties of sandstone and the intersecting angle α and the distribution orientation angle β is analysed. Crack initiation forms and the final failure modes are then categorised and determined via empirical methods. In addition, the cracking processes of intersecting fissures with different α and β values are discussed. The results show that variations in the peak stress, peak strain, average modulus, and crack initiation stress of sandstone containing intersecting fissures show a “moth” shape in the space of the α-β-mechanical parameters. Two crack initiation forms are identified: inner tip cracking (usually accompanied by one outer tip cracking) and only outer tips cracking. Two failure modes are observed: (1) the main fracture planes are created at the inner tip and one outer tip, and (2) the main fracture planes are formed at the two outer tips. Two main crack evolution processes of sandstone containing intersecting fissures under uniaxial compression are found. Approaches for quickly determining the crack initiation form and the failure mode are proposed. The combination of the determination equations for the crack initiation form and the failure mode can be used to predict the crack evolution. The approach for determining the crack evolution processes is hence proposed with acceptable precision.

Numerical analysis of mechanical behavior of stratified rocks containing a single flaw by utilizing the particle flow code

The evaluation of the mechanical properties of stratified rock masses with flaws is of great significance to geological engineering problems such as underground project and slope stability, etc. To investigate the mechanical properties of fractured stratified rock, the two-dimensional particle flow code (PFC2D) was used to conduct uniaxial compression simulation tests on stratified rock model containing a single flaw. To study the failure mechanism of the specimen, the stress-strain curve, acoustic emission events, mechanical parameters and cracking mode were recorded and analyzed. The simulation results showed that the stress-strain curves and AE events of specimens with different arrangements of flaw and stratification can be divided into three types, namely multi-peak type, pre-peak wave type and single peak with few fluctuations type. Inclined stratification caused the cracks to gradually propagate along the bedding planes, which weakened the strength and dominated the failure modes of the specimen. The flaw affected the stress distribution and played a role in connecting micro-cracks. The combined effect of stratification and flaw depended on the relative relationship between the stratification and the flaw, which determined the cracking path and failure modes.

Crack path at bedding planes of cracked layered rocks

The evolution of cracks in layered rocks is a basic issue in stability analyses of underground openings in layered rocks. This study presents the crack penetration/deflection behaviour of bedding planes in layered rocks with a designed three-layer system that consists of two pre-existing cracks. The effects of crack spacing (S, between two pre-existing cracks), layer thickness (T), and their ratio (S/T) on the cracking paths of a propagating crack are investigated. A semi-artificial (SA) method is suggested to prepare the test specimens, which includes a natural rock layer and artificial bedding planes. The SA specimens offer advantages over natural rocks and pure artificial materials. Numerical simulations of the crack penetration/deflection behaviours are also conducted based on a two-dimensional particle flow code. The results indicate that the crack path is determined by a critical S/T ratio. The propagating crack can deflect along the bedding planes and coalesce with pre-existing cracks if the S/T ratio is lower than the critical value. If the S/T ratio is greater than the critical value, the propagating crack will penetrate the bedding planes and rock layers without experiencing any crack coalescences. The critical S/T ratio decreases as the plane strength increases. Load-displacement responses and acoustic emission activities are also discussed to improve the understanding of crack/bedding plane interaction in layered rocks.

Cracking Behavior and Acoustic Emission Characteristics of Rock Containing a Single Preexisting Flaw

The existence of flaws in brittle rocks or rock-like materials has an obvious influence on the material mechanical properties and cracking behavior of civil engineering projects. In this work, the two-dimensional particle flow code PFC2D was used to study the deformation and strength properties, failure processes, and acoustic emission (AE) characteristics of mudstone with a single preexisting flaw. First, the procedure to construct a parallel bond model is introduced. The Weibull distribution is used to reflect the mechanical heterogeneity of rocks. Then, the microscopic parameters used in PFC2D are calibrated to the macroproperties of mudstone obtained from laboratory tests under the uniaxial compression. The results indicate that the increases of the flaw inclination lead to the increasing uniaxial compressive strength and elastic modulus. In terms of microcrack evolution, the initiation, propagation, and coalescence of microcracks are closely related to the force chain. Specifically, an “X” shaped tension force chain concentrated area around the preexisting flaw is founded, which is the most prone area for microcracks to initiate. With an increase in flaw inclination, the b value of AE also shows an increasing trend. By incorporating the AE event numbers into a damage variable, this paper derives a constitutive model, which is verified by numerical results on brittle rocks with a single preexisting flaw under uniaxial compression.

Numerical Modeling on Dynamic Characteristics of Jointed Rock Masses Subjected to Repetitive Impact Loading

A discrete element method code was used to investigate the damage characteristics of jointed rock masses under repetitive impact loading. The Flat-Joint Contact Model (FJCM) in the two-dimensional particle flow code (PFC2D) was used to calibrate the microparameters that control the macroscopic behavior of the rock. The relationship between macro- and microparameters by a series of uniaxial direct tension and compression numerical tests based on an orthogonal experimental design method was obtained to calibrate the microparameters accurately. Then, the Synthetic Rock Mass (SRM) method that incorporates joints into the calibrated particle model was used to construct large-scale jointed rock mass specimens, and the repetitive drop hammer impact numerical tests on SRM specimens with different numbers of horizontal joints and dip angle joints were carried out to study the damage evolution, stress wave propagation, and energy dissipation characteristics. The results show that the greater the number of joints, the greater the number of cracks generated, the greater the degree of damage, and the more energy dissipated for rock masses with horizontal joints. The greater the dip angle of joints, the less the number of cracks generated, the less the degree of damage, and the less energy dissipated for rock masses with different dip angles of joints. The impact-induced stress waves will be reflected when they encounter preexisting joints in the process of propagation. When the reflected stress waves meet with subsequent stress waves, the stress waves will change from compressional waves to tensile waves, producing tensile damage inside rock masses.

A simple discrete-element model for numerical studying the dynamic thermal response of granular materials

This paper aims to investigate the influence of periodicity temperature change on the properties of dry granular materials in macroscopic and microscopic. A series of cyclic thermal consolidation tests have been carried out based on the discrete element method (DEM) that incorporate particles’ volumetric thermal expansion coefficient. The simulation of the direct shear test was carried out on the samples after thermal cycling. Results showed that thermally-induced volumetric strain accumulation of the specimen can be calculated by the DEM model, based on the two-dimensional particle flow code (PFC2D) software. The lateral pressure degraded concomitantly thanks to decreases in particles’ horizontal contact during periodic thermal cycling. In addition, the shear dilatancy level decreases during the shearing process with the number of thermal cycles. Both the size and anisotropy of the normal contact force and contact number and the force chain are affected by the temperature cycle. Finally, the results of this paper have a certain reference for the engineering practice, such as thermal piles or others, when granular materials are subjected to thermal cycling.

Failure Characteristics and Mechanism of Multiface Slopes under Earthquake Load Based on PFC Method

Understanding the failure mechanism and failure modes of multiface slopes in the Wenchuan earthquake can provide a scientific guideline for the slope seismic design. In this paper, the two-dimensional particle flow code (PFC2D) and shaking table tests are used to study the failure mechanism of multiface slopes. The results show that the failure modes of slopes with different moisture content are different under seismic loads. The failure modes of slopes with the moisture content of 5%, 8%, and 12% are shattering-shallow slip, tension-shear slip, and shattering-collapse slip, respectively. The failure mechanism of slopes with different water content is different. In the initial stage of vibration, the slope with 5% moisture content produces tensile cracks on the upper surface of the slope; local shear slip occurs at the foot of the slope and develops rapidly; however, a tensile failure finally occurs. In the slope with 8% moisture content, local shear cracks first develop and then are connected into the slip plane, leading to the formation of the unstable slope. A fracture network first forms in the slope with 12% moisture content under the shear action; uneven dislocation then occurs in the slope during vibration; the whole instability failure finally occurs. In the case of low moisture content, the tensile crack plays a leading role in the failure of the slope. But the influence of shear failure becomes greater with the increase of the moisture content.

A coupled experimental and numerical simulation of concretejoints' behaviors in tunnel support using concrete specimens

The experimentally tested modelled specimens were simulated by a two-dimensional particle flow code to study the behavior of rock mass surrounding a tunnel interacted with a nearby rock joint or discontinuity. The specially prepared specimens are tested in the laboratory and the measured results are provided. Then a numerical modelling of these tests is accomplished by a calibrated two-dimensional particle flow code to study the rock tunnel behavior while interacting with a neighboring joint. The two-dimensional discrete element code was calibrated using Brazilian tensile test. Then the modelled specimens are provided so that various configurations of tunnel cross sections and the neighboring joints were tested under uniaxial compression condition. This study showed that the tensile cracks are the most dominant mode occurred in these modelled samples. The wing cracks initiated from the joint tips when the joints interacted in a position less than that of the tunnel height. These cracks are then propagated and interacted with the tunnel ceiling. When the joint interacting the tunnel head and the interaction angle is negative the tunnel can be in a stable position considering the joints effect on its instability situation. But for positive interaction angles and the case of joint existing near the tunnel head, the wing cracks may initiate and propagate towards the tunnel ceiling. As the distance of joint from the tunnel ceiling is increased its effect on the tunnel instability is decreased because the failure stress is increased. The number of joints and their distance with the tunnel boundary (ceiling) have also a profound effect on the stability condition of the tunnel. The failure stress reached its maximum value for the increase from -30 to -60 degrees or increase from 30 to 60 degrees. The failure stress also decreased as the number of notches and their lengths increased. In all these interaction scenarios, the corresponding numerical and experimental values compared and it is concluded that the failure stresses are very close to each other which verified the accuracy and applicability of the proposed modeling technic.

Effect of curing time on the mesoscopic parameters of cemented paste backfill simulated using the particle flow code technique

Several special mechanical properties, such as dilatancy and compressibility, of cemented paste backfill (CPB) are controlled by its internal microstructure and evolution. The mesoscopic structure changes of CPB during the development process were investigated. On the basis of the scanning electron microscopy (SEM) and mechanical test results of CPB, the particle size information of CPB was extracted, and a two-dimensional particle flow code (PFC) model of CPB was established to analyze the evolution rule of mesoscopic parameters during CPB development. The embedded FISH language in PFC was used to develop a program for establishing a PFC model on the basis of the SEM results. The mesoscopic parameters of CPB samples at different curing times, such as coordination number (Cn), contact force chain, and rose diagram, were obtained by recording and loading and used to analyze the intrinsic relationship between mesoscopic parameter variations and macroscopic mechanical response during CPB development. It is of considerable significance to establish the physical model of CPB using the PFC to reveal the mesoscopic structure of CPB.

Acoustic emission, damage and cracking evolution of intact coal under compressive loads: Experimental and discrete element modelling

In underground mining engineering, it is of considerable significance to focus on acoustic emission (AE), damage and cracking evolution inside coal. This article first performed a series of triaxial compressive tests on intact coal specimens simultaneously monitored AE signals; then evaluated the cracking behaviours of intact coal specimens under biaxial compression using a two-dimensional particle flow code (PFC2D). Before the specimens enter into the yield regime, it emits a small number of acoustic signals and generates stable crack initiation and propagation linked to Kaiser effect and modest damage. As increasing the compressive load upon to the ultimate strength, the strain energy in the simulation will reach the maximum value; subsequently, it decreases in the post-peak stage, which is consistent with the acoustic development in the experiments. Furthermore, confining pressure plays a vital role not only in strength and acoustic activity but also in crack growth and fracture patterns. The maximum AE count and maximum strain energy increase with the rise in confining pressure. Higher confining pressure will create a higher crack initiation threshold and hinder crack propagation and coalescence, thus contributing to a higher compressive strength. With increasing confining pressure, intact coal specimens are prone to shift from tensile-shearing mixed failure to shearing fracture. Additionally, once the axial strain exceeds approximately one per cent, brittle failure will occur accompanied by a strain-softening phenomenon. Unlike intact coal, tectonic coal typically exhibits a ductile failure with a strain-hardening phenomenon. Moreover, numerical results show that cracks within coal generally can be classified into six patterns. Tensile cracks, usually restricted to a ligament area, generate along the direction of principal stress in a relatively stable manner; whereas (primary, secondary, and quasi-parallel) shear cracks generally propagate and coalesce towards the boundary of specimens.

A modeling study of the micro-cracking behavior of brittle crystalline rocks under uniaxial loading considering different scenarios of grain-based models

The grain-based model (GBM) in two-dimensional Particle Flow Code (PFC2D) is widely used to simulate the deformation and brittle failure of crystalline rocks. However, the original GBM consisting of the parallel-bond (PB) and the smooth-joint (SJ) produces unrealistic micro-cracking processes in which excessive microcracks are distributed along the interfaces of mineral grains under uniaxial loading. To solve the problem, this research presents a discussion of the mechanical behavior of six GBMs composed of different contact models including PB, SJ, and flat-joint (FJ). After the uniaxial compressive and direct tensile tests of numerical granites, it is found that the different contact types in GBMs have a limited influence on the tensile strength (TS), elastic modulus (E), and Poisson’s ratio (ν) but have a great impact on the uniaxial compressive strength (UCS) and microcrack pattern. The UCS calculated by the PB/FJ GBM is higher than the actual value. Microcrack distributions simulated by the FJ/SJ and FJ/PB GBMs show that numerous mineral grains are cut across under uniaxial loading instead of their interfaces. While the FJ/SJ and FJ/PB GBMs may well reproduce the brittle failure process of crystalline rocks, it remains to be seen whether they will be applicable to other rock mechanics issues, including triaxial compression, thermal cracking, and hydraulic fracturing.

Failure characteristics and mechanical mechanism of study on red sandstone with combined defects

In this study, the strength and failure mechanism of red sandstones with combined defects were investigated by uniaxial compression tests on red sandstones with different crack angles using two-dimensional particle flow code numerical software, and their mechanical parameters and failure process were studied and analyzed. The results showed that the mechanical characteristics such as peak strength, peak strain, and elastic modulus of the samples with prefabricated combined defects were significantly inferior than those of the intact samples. With increasing crack angle from 15&deg to 60&deg, the weakening area of cracks increased, elastic modulus, peak strength, and peak strain gradually reduced, the total number of cracks increased, and more strain energy was released. In addition, the samples underwent initial brittle failure to plastic failure stage, and the failure form was more significant, leading to peeling phenomenon. However, with increasing crack angle from 75&deg to 90&deg, the crack–hole combination shared the stress concentration at the tip of the crack–crack combination, resulted in a gradual increase in elastic modulus, peak strain and peak strength, but a decrease in the number of total cracks, the release of strain energy reduced, the plastic failure state weakened, and the spalling phenomenon slowed down. On this basis, the samples with 30&deg and 45&degcrack-crack combination were selected for further experimental investigation. Through comparative analysis between the experimental and simulation results, the failure strength and final failure mode with cracks propagation of samples were found to be relatively similar.

Effects of flaw width on cracking behavior of single-flawed rock specimens

Cracking behavior of flawed samples has been extensively studied in rocks and rock-like materials using experimental and numerical approaches. However, the existing research mainly focuses on the effects of flaw length l and inclination angle α on rock mechanical behavior, a limited attention has been given to understand the role of flaw width b on crack initiation and propagation in relation to mechanical parameters of rocks. In this paper, a two-dimensional particle flow code (PFC2D)-based synthetic rock model, which is calibrated by the laboratory sandstone properties, is used to investigate the effects of flaw width on cracking behavior of single-flawed rock samples under uniaxial compression tests. Numerical simulation results show that the flaw width b has significant effects on the crack geometrical parameters (crack initiation location d and crack initiation angle θ). The values of θ and d significantly decrease with the increase of flaw width when b < 1.0 mm and their values tend to be stable with the further increase of flaw widths. It is also found that the mechanical properties (uniaxial compressive strength UCS and deformation modulus Es) of flawed rock samples are related to the crack geometrical parameters (θ and d) and the effects of flaw width on the values of UCS and Es of single-flawed rock specimens is significant when b < 1.0 mm for lower crack inclination angle (α < 60°).

Parameter studies on the mineral boundary strength influencing the fracturing of the crystalline rock based on a novel Grain-Based Model

The grain-based model (GBM) in two-dimensional Particle Flow Code (PFC2D) is widely employed to investigate the mechanical response characteristics of crystalline rocks under external load considering the realistic petrographic texture. However, due to the poor self-locking effect of the Parallel-Bond (PB) inside the minerals and unreasonable parametric assignment for the Smooth-Joint (SJ) at the mineral boundaries, the original GBM cannot reproduce the exact microcracking process of brittle rocks. To solve the problem, the novel grain-based model (nGBM) composed of the Flat-Joint (FJ) and the SJ was proposed in our previous research, which not only enhances the rotational resistance of particles, but also improves the simulation of the mineral boundaries. In this study, the nGBM was carefully established and calibrated based on the properties of Alxa porphyritic granite. A series of simulation tests of uniaxial compression, triaxial compression and direct tension under different mineral boundary parametric conditions were carried out to observe the deformation, microcracking and failure behaviors of the nGBM. Quantitative analyses of the mineral boundary properties and the mechanical behaviors of the numerical specimen revealed the extremely complicated relationships between them, which can help explain the micromechanical damage process of crystalline rocks and provide valuable reference for the model calibration.

Numerical investigation on effect of confining pressure on the dynamic deformation of sandstone

In deep buried rock engineering, in situ stress is a significant factor affecting the mechanical response of rocks to dynamic loads. This work focuses on the effect of confining pressure on dynamic deformation of rocks. Considering the limitation of observation in laboratory experiments, numerical simulation method is adopted. The numerical model of split Hopkinson pressure bar test system with confining pressure is established in a two-dimensional particle flow code. Dynamic compression tests of sandstone under different confining pressure conditions are then simulated. The axial dynamic compressive deformation, crack evolution, failure modes and dynamic dilation of specimen are obtained. The results indicate that confining pressure has a constraint influence on both axial and transverse deformation of rock. Under the compression of confining pressure, the axial dynamic deformation, and damage degree are weakened while the elasticity of rock may be enhanced. Compared with that without confining pressure, the failure modes of rock specimens are different under the confining pressure. Dynamic dilation of rock specimen is triggered synchronously with the crack initiation. Confining pressure can weaken the dilation, and contraction of rocks may even happen after the dynamic unloading under a high confining pressure, resulting in a secondary damage to rocks. The results can benefit to comprehend the dynamic deformation and failure of deep buried rocks.

Numerical Investigation of Injection-Induced Fracture Propagation in Brittle Rocks with Two Injection Wells by a Modified Fluid-Mechanical Coupling Model

Hydraulic fracturing is a key technical means for stimulating tight and low permeability reservoirs to improve the production, which is widely employed in the development of unconventional energy resources, including shale gas, shale oil, gas hydrate, and dry hot rock. Although significant progress has been made in the simulation of fracturing a single well using two-dimensional Particle Flow Code (PFC2D), the understanding of the multi-well hydraulic fracturing characteristics is still limited. Exploring the mechanisms of fluid-driven fracture initiation, propagation and interaction under multi-well fracturing conditions is of great theoretical significance for creating complex fracture networks in the reservoir. In this study, a series of two-well fracturing simulations by a modified fluid-mechanical coupling algorithm were conducted to systematically investigate the effects of injection sequence and well spacing on breakdown pressure, fracture propagation and stress shadow. The results show that both injection sequence and well spacing make little difference on breakdown pressure but have huge impacts on fracture propagation pressure. Especially under hydrostatic pressure conditions, simultaneous injection and small well spacing increase the pore pressure between two injection wells and reduce the effective stress of rock to achieve lower fracture propagation pressure. The injection sequence can change the propagation direction of hydraulic fractures. When the in-situ stress is hydrostatic pressure, simultaneous injection compels the fractures to deflect and tend to propagate horizontally, which promotes the formation of complex fracture networks between two injection wells. When the maximum in-situ stress is in the horizontal direction, asynchronous injection is more conducive to the parallel propagation of multiple hydraulic fractures. Nevertheless, excessively small or large well spacing reduces the number of fracture branches in fracture networks. In addition, the stress shadow effect is found to be sensitive to both injection sequence and well spacing.