《东北大学学报(自然科学版)》 创刊于1955年,是教育部主管、东北大学主办的理工类综合性学术期刊。现为月刊,每期152页,国内外公开发行。本刊的办刊宗旨是:以马克思主义、毛泽东思想、邓小平理论和“三个代表”重要思想为指导,全面落实科学发展观,及时报道高质量高水平的最新学术成果,以促进学术交流,培养科技人才。主要栏目有:信息科学与工程、材料与冶金、机械工程、资源与土木、管理科学、数理化力学等。本刊是全国中文核心期刊、Ei Compendex核心期刊。
15 March 2021, Volume 42 Issue 3 Previous Issue   
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Information & Control
Method of Lane Line Detection in Low Illumination Environment Based on Model Fusion
GU De-ying, WANG Na, LI Wen-chao, CHEN Long
2021, 42 (3):  305-309.  DOI: 10.12068/j.issn.1005-3026.2021.03.001
Abstract ( 173 )   HTML ( 43)   PDF (1436KB) ( 162 )  
Aiming at the problem of low accuracy and poor stability of lane line detection in low illumination environment, an algorithm of lane line detection in low illumination environment based on model fusion was proposed. The improved color balance algorithm based on ALTM(adaptive local tone mapping) algorithm is adopted for data enhancement processing, which is beneficial for the extraction of lane line features. The improved Deeplabv3+model and Unet model are fused to reduce the overfitting. The segmented lane line image is obtained by instance segmentation. The experimental results show that the mean_IOU(mean intersection-over-union) values of the improved Unet model and Deeplabv3+model reach 0.625 and 0.646, respectively, which are 2% and 4.6% higher than the original model. The final fusion result increased by 0.01%. The stability and accuracy of lane line detection are promoted in low illumination environment.
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Research on Calibration Transfer via Correcting Distributions Difference
ZHAO Yu-hui, LU Peng-cheng, LIU Xiao-dong, QI Tian-shu
2021, 42 (3):  310-317.  DOI: 10.12068/j.issn.1005-3026.2021.03.002
Abstract ( 69 )   HTML ( 9)   PDF (972KB) ( 54 )  
Aiming at the characteristics of high dimensionality of near-infrared spectroscopy data and serious multi-collinearity between features, a method of calibration transfer via correcting distributions difference(CT-CDD) was proposed without transfer standards. CT-CDD firstly establishes PLS(partial least square) model of the master instrument, and then latent variables of both the master instrument and the slave instrument are extracted by the PLS model. Next, the latent variables of the two instruments are clustered. The method is based on the assumption that the characteristic spectra of each part of the master and slave instruments after clustering is a single Gaussian distribution. Finally, the nearest sub-distribution of the two instruments is found, and the differences in data distribution is corrected by correcting mean and variance. The experimental results show that CT-CDD is generally more robust and can also achieve the lowest RMSEP (root mean squared error on prediction).
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A PWM Modulation Method Used to Suppress Current Fluctuation of Brushless DC Motor
BIAN Chun-yuan, JIA Yu-long, XING Hai-yang, LIU Shang-yue
2021, 42 (3):  317-324.  DOI: 10.12068/j.issn.1005-3026.2021.03.003
Abstract ( 88 )   HTML ( 6)   PDF (3386KB) ( 87 )  
In order to solve the current fluctuation problem of the brushless DC motor in the traditional half-bridge modulation mode, an improved PWM modulation strategy was proposed. First, the traditional H_OFF-L_PWM modulation method was analyzed in detail. Second, in order to reduce the current fluctuation in the H_OFF-L_PWM modulation mode, an improved H_OFF-L_PWM modulation strategy was proposed. This modulation strategy performs PWM chopping control on the switch tube of the lower bridge arm of the non-conduction phase in the non-freewheeling interval, so that the motor current is smoother, thereby further reducing the motor torque ripple. Finally, a simulation model of the brushless DC motor feedback power generation system was built on the PLECS simulation platform. Based on the TMS320F280049CPZS control chip, an experimental platform for the brushless DC motor feedback power generation system was built. Simulation and experimental results show that the proposed improved H_OFF-L_PWM modulation strategy can suppress the motor phase current fluctuations, thereby suppress the motor electromagnetic torque ripple.
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Materials & Metallurgy
Hot Deformation Behavior of a High-Mn TWIP Steel and Establishment of Strain-Compensated Constitutive Equation
CHEN Yong, WEN Guang-qi, ZHANG Xiao-ming, DING Hua
2021, 42 (3):  325-332.  DOI: 10.12068/j.issn.1005-3026.2021.03.004
Abstract ( 34 )   HTML ( 7)   PDF (1818KB) ( 45 )  
Hot deformation behaviors of a high-Mn twinning induced plasticity (TWIP) steel were investigated using isothermal hot compression tests at different temperature ranging from 850℃ to 1100℃ and constant strain rates of 0.01, 0.1, 1, 5 and 10s-1, respectively. The effects of deformation temperature and strain rate on flow behavior were analyzed. A developed constitutive equation considering the strain compensation was established and its accuracy was evaluated based on three standard statistical parameters. The results indicate that the flow stress is strongly sensitive to deformation temperature and strain rate, which decreases with the increase in temperature or the decrease in strain rate. Strain rate has a complex influence on the kinetics of dynamic recrystallization. Since the predicted flow stress is in good agreement with the experimental one, it proves that the strain-compensated constitutive equation can estimate the flow stress accurately.
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Preparation and Properties of Biodegradable Fe30MnxCa Alloys
ZHANG Ya-jing, WANG Yi-ming, LI Shuai-ping
2021, 42 (3):  333-339.  DOI: 10.12068/j.issn.1005-3026.2021.03.005
Abstract ( 42 )   HTML ( 7)   PDF (2484KB) ( 36 )  
The medical degradable Fe30MnxCa(x=0,1.5,3.0 and 4.5)alloy bars were prepared by mechanical alloying, powder pressing and hot extrusion. The effect of Ca addition on the microstructure and properties of the alloy was studied by optical metallographic microscope, scanning electron microscope (SEM), tensile test, electrochemical test and SBF solution immersion corrosion test. The results show that the Fe30MnxCa alloy is composed by the austenite phase and with the increasing mass fraction of Ca, the hardness increases, and the tensile strength and final elongation decrease.Meanwhile, the degradation performance of the alloy is significantly improved, where the corrosion rate increases from 0.1130mg/(cm2·d)of Fe30Mn to 0.2260mg/(cm2·d)of Fe30Mn4.5Ca in the corrosion tests. The cytotoxicity test indicates that the biocompatibility is 0 ~ 1grade.
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Experiment Study and Simulation for Friction Stir Welding Process of 7075 Aluminum Alloy
FENG Ying-ying, ZHAO Shuang, LIU Zhao-song, LUO Zong-an
2021, 42 (3):  340-346.  DOI: 10.12068/j.issn.1005-3026.2021.03.006
Abstract ( 39 )   HTML ( 1)   PDF (5567KB) ( 41 )  
Friction stir welding (FSW) is used to solve the problem of the poor solderability of 7075 aluminum alloy. However, the complex changes of temperature and flow field are prone to cause defects. In this work, FLUENT software was used to study the changes of temperature and flow field of 7075 aluminum alloy during welding and the simulated results were verified. It is found that the temperature on the advancing side is higher, the flow rate is lower, and the maximum temperature appears inside the shoulder edge. When the rotation speed of the stirring head is higher, the welding speed becomes smaller, associated with a higher welding temperature. Meanwhile, the flow rate is faster and less affected by the welding speed. Under the conditions of the rotation speed-welding speed parameters of 800r/min-100mm/min,the defect-free weld can be achieved.
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Experiment of Resistance Characteristics for Magnesite Pellets Packed Bed Based on Ergun Equation
ZHANG Sheng, ZHANG Xiao-hu, ZHAO Liang, DONG Hui
2021, 42 (3):  347-352.  DOI: 10.12068/j.issn.1005-3026.2021.03.007
Abstract ( 28 )   HTML ( 0)   PDF (707KB) ( 33 )  
The gas flow distribution in the magnesite shaft furnace is relatively complicated. Obtaining the resistance characteristics in the magnesite pellets packed bed is the basis for the research on the gas flow and gas-solid heat transfer process. Starting from the gas dynamics of the gas-solid packed bed, based on the Ergun equation, the key macroscopic properties of the magnesite pellets, including particle size distribution, density, sphericity and voidage, were systematically measured. The viscous resistance coefficient and the inertial resistance coefficient in the Ergun equation were corrected through cold experiments, and a relational equation suitable for describing the resistance characteristics of the magnesite pellet bed was obtained. The results showed that the sphericity and voidage increase with the increase of particle size. The pressure drop increases with the increase of gas flow rate, and the increasing trend gradually intensifies. On the contrary, it decreases with the increase of particle size.
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Experimental Study and Calculation of Ethane Flammability Limit Under O2/CO2Atmosphere
HU Xian-zhong, FENG Jing-wu, JIANG Lin-hong
2021, 42 (3):  353-358.  DOI: 10.12068/j.issn.1005-3026.2021.03.008
Abstract ( 34 )   HTML ( 0)   PDF (581KB) ( 36 )  
The flammability limit is an important parameter of combustion characteristics. In this paper, a flammability limit experimental device was set up based on the 5L cylindrical reactor. The flammability limits of ethane under CO2/O2 atmosphere were studied and compared with those in air atmosphere. The results showed that high concentration of CO2 reduces the upper flammability limit and increases the lower flammability limit of gas mixture. The influence of high concentration of CO2 on flammability limit was analyzed. The formula of calculation of flammability limit for C2H6/O2/CO2 was deduced according to the thermal theory. The average absolute deviation between the experimental values and calculated values is within 2.2%. The values of calculation are in agreement with the experimental data.
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Study on a Non-road Mobile Source Emission Inventory and Scenario Prediction in Northeast China
GAO Cheng-kang , YOU Huan , BA Qiao , LIANG Cheng-xu
2021, 42 (3):  358-366.  DOI: 10.12068/j.issn.1005-3026.2021.03.009
Abstract ( 42 )   HTML ( 2)   PDF (1600KB) ( 35 )  
Compared with other regions, Northeast China has its unique characteristics of non-road mobile source emission inventories due to its long and cold winter. In this paper, the analysis was divided into Liaoning Province and Harbin-Changchun Megalopolis. Firstly, the emission inventory of non-road mobile sources was established based on technical guide for preparation of air pollutant emission list of non-road mobile sources (trial), and its emission and spatial-temporal distribution characteristics were analyzed. Secondly, the emissions in 2030 were forecasted based on the scenario analysis, taking into account of the relevant policy objectives. Finally, reasonable emission reduction recommendations were made. The results show that: 1) the emissions of PM10, PM2.5, NOx, THC, and CO were 13.0×103, 12.5×103, 205.6×103, 37.0×103 and 101.1×103 t, respectively; 2) construction machinery accounts for the largest share of emissions in the two urban agglomerations with 44.5%and 44.8%, respectively; 3) the overall emission reduction can be improved by more than 50% under both the baseline scenario and the enhanced control scenario.
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Mechanical Engineering
Cross-Domain Fault Diagnosis of Rolling Bearings Using Domain Adaptation with Classifier Discrepancy
ZHANG Yong-chao, LI Qi, REN Zhao-hui, ZHOU Shi-hua
2021, 42 (3):  367-372.  DOI: 10.12068/j.issn.1005-3026.2021.03.010
Abstract ( 52 )   HTML ( 4)   PDF (1215KB) ( 53 )  
When diagnosing rolling bearing faults based on data-driven methods, the discrepancy in data distribution under different operating conditions may result in severe degradation of model diagnosis performance.To handle this issue, a cross-domain fault diagnosis method of rolling bearing based on domain adaptation with classifier discrepancy was proposed.Firstly, the convolutional neural network was used to extract the features of the labeled source domain samples and the unlabeled target domain samples.Then, the features were classified by two fully connected classifiers.Finally, the classification loss, the maximum mean discrepancy loss and the classifier discrepancy loss were optimized step by step to align the domain distribution discrepancy between the source domain and the target domain so as to implement the fault diagnosis of unlabeled target domain samples.The experimental results showed that the proposed method has a higher fault diagnosis accuracy rate than the mainstream domain adaptation methods, which verifies its rationality and feasibility.
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Early Fault Diagnosis Method of Rolling Bearings Based on Optimization of VMD and MCKD
WANG Xin-gang, WANG Chao, HAN Kai-zhong
2021, 42 (3):  373-381.  DOI: 10.12068/j.issn.1005-3026.2021.03.011
Abstract ( 67 )   HTML ( 5)   PDF (735KB) ( 46 )  
Considering the phenomenon that the early fault signals of rolling bearings are easily interfered by noise and background information and it is difficult to extract fault characteristics, a method combining K value optimization of variational mode decomposition (VMD) and particle swarm optimization (PSO) optimizing the maximum correlated kurtosis deconvolution (MCKD) parameters L, M was proposed to extract the fault characteristic frequency of rolling bearings. Firstly, the K value in VMD was calculated, and the signal was decomposed to obtain a series of modal components. EWK index was used to select the effective modal components that contain the most fault information for subsequent analysis and the optimized MCKD was used to enhance it. Finally, the enhanced signal was subjected to envelope demodulation to extract the fault characteristic frequency, which verified the effectiveness of the proposed method. Simulations and experiments showed that this method can accurately extract the fault characteristic frequency of the signal and realize fault diagnosis.
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Recognition Model of Fear of Heights Based on Brain Region Community Structure
WANG Qiao-xiu, WANG Hong, HU Fo, HUA Cheng-cheng
2021, 42 (3):  381-388.  DOI: 10.12068/j.issn.1005-3026.2021.03.012
Abstract ( 28 )   HTML ( 3)   PDF (4116KB) ( 21 )  
With high-rise buildings emerging, objective fear of heights detection is a key step in the standardization of the aerial work industry. Taking into account virtual reality, this paper designs an aerial exposure experiment, which studies the brain neural mechanism of fear of heights reaction, and proposes the functional brain network (FBN) to detect the fear of heights .By comparing the basic topological characteristics of FBNs, the brain regions closely related to fear of heights are found through thresholding. By dividing the community structures according to the brain regions, the recognition model of fear of heights is established . The results show that the more severe the fear of heights, the more complicated the FBN. The main brain regions involved in fear of heights include frontal lobe, central area, and occipital lobe. Using these brain regions to divide the community structures, the calculation accuracy of connection strengths on fear of heights can reach (97.37±0.58)%.
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Dynamic Thermal Mechanical Coupling Effect in Disc Grinding and Its Influence on Workpiece Material Removal Process
XIU Shi-chao, LU Yue, SUN Cong, LI Qing-liang
2021, 42 (3):  389-395.  DOI: 10.12068/j.issn.1005-3026.2021.03.013
Abstract ( 46 )   HTML ( 2)   PDF (3560KB) ( 27 )  
A theoretical modeling method based on dynamic thermal mechanical coupling effect is proposed for the thermodynamic distribution characteristics of contact surfaces in disc grinding. Firstly, the mathematical model of movement trajectory of multiple abrasive grains is established. Then, the surface grinding force of the workpiece is modeled analytically based on the dynamic distribution characteristics of movement trajectory and the height of effective abrasive grains. Subsequently, the dynamic thermal mechanical coupling process on the workpiece surface is analyzed with the finite difference method (FDM) according to the grinding force. Lastly, the finite element method (FEM) and disc grinding experiment are applied to verify the rationality of the theoretical analysis respectively. The results show that the workpiece surface profile height is different due to the homogenization degree of the dynamic thermal mechanical coupling. The workpiece surface profile can be improved by reducing the speed of grinding wheels.
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Theoretical Study on the Apparent Viscosity of Melt Inside the Fused Filament Fabrication Extrusion Liquefier Under Vibration Field
JIANG Shi-jie, CHEN Pi-feng, SUN Ming-yu, DONG Tian-kuo
2021, 42 (3):  395-401.  DOI: 10.12068/j.issn.1005-3026.2021.03.014
Abstract ( 30 )   HTML ( 2)   PDF (464KB) ( 23 )  
The apparent viscosity of the melt inside the extrusion liquefier is one of the key factors affecting the mechanical properties of fused filament fabrication (FFF) products. A method applying a longitudinal sinusoidal vibration to the FFF extrusion liquefier is proposed to improve the apparent viscosity of the internal melt. Then the theoretical model of the apparent viscosity of the melt inside the extrusion liquefier with vibration applied is carried out, and the experimental results from the existing literature are used to verify the correctness of the theoretical model. Finally, the variation of apparent viscosity with different-frequency vibrations applied is discussed through the model, and the corresponding mechanism is clarified. It is shown that the theoretical results agree well with the experimental ones,validating the model’s feasibility. When the vibration field is applied to the extrusion liquefier, the effective value of apparent viscosity will decrease with the increase of vibration frequency.
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Correlation Analysis of TBM Operating Parameters and Different Lithologic Strata
XIA Yi-min, KE Jie, QI Meng-xue, DENG Chao-hui
2021, 42 (3):  401-408.  DOI: 10.12068/j.issn.1005-3026.2021.03.015
Abstract ( 36 )   HTML ( 1)   PDF (2905KB) ( 31 )  
In order to study the correlation between TBM operating parameters and different lithologic strata, taking a Xinjiang water diversion project as the background, 300 m of tunneling parameter data was selected for typical lithologic strata. The correlation between 3 tunneling parameters and 6 lithologic strata was analyzed by using mathematical statistics. By analyzing the correlation among propulsion speed, total thrust and cutter speed under the six types of lithologic strata, the tunneling suggestions were put forward. The results show that the average value of propulsion speed and total thrust varies greatly among different lithologic strata. The cutter speed fluctuates little, and the average difference is small. In siliceous, andesite and tuff strata, the total thrust, cutter speed and propulsion speed are not correlated. In mylonite and sandstone strata, the total thrust, cutter speed and propulsion speed are positively correlated. In cataclastic rock strata, the total thrust is negatively correlated with the propulsion speed.
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Curve and Surface Fitting Algorithm for Measurement Data
GU Tian-qi, LUO Zu-de, HU Chen-jie, LIN Shu-wen
2021, 42 (3):  408-413.  DOI: 10.12068/j.issn.1005-3026.2021.03.016
Abstract ( 54 )   HTML ( 1)   PDF (2237KB) ( 44 )  
The moving least squares (MLS) method is widely used in curve and surface fitting due to its good approximation performance. However, the fitting accuracy is extremely unstable when processing data with gross error.In order to reduce the effect of gross error on the fitting accuracy, a moving least trimmed squares (MLTS)method was proposed. In this method, the least trimmed square (LTS) method was introduced in the influence domain to replace the least square (LS) method, and the optimal group of nodes without abnormal data was selected among all the nodes to determine the local fitting coefficient.Assigning weights or setting threshold values artificially is unnecessary, which avoids the influence of subjective operations. Numerical simulation and experimental data processing showed that the gross error of measurement data can be handled effectively, and the fitting results of the MLTS method are better than those of the MLS method, which has good fitting accuracy and robustness.
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Resources & Civil Engineering
Recovery Process of Iron from High-Iron Red Mud Through Suspension Magnetization Roasting-Low Intensity Magnetic Separation Technology
LIU Xiao , GAO Peng , LYU Yang , YUAN Shuai
2021, 42 (3):  414-421.  DOI: 10.12068/j.issn.1005-3026.2021.03.017
Abstract ( 39 )   HTML ( 0)   PDF (2366KB) ( 34 )  
High-iron red mud contains a lot of iron, which is a potential iron ore resource. Therefore, it is of great significance to develop innovative processes and technologies to realize the recycling of iron in red mud, and at the same time to achieve red mud reduction. A novel process of suspension magnetization roasting-low intensity magnetic separation was developed for the Bayer high-iron red mud. The effects of roasting temperature, roasting time, reducing gas CO concentration and total gas volume on the magnetization roasting effect were studied. The experiment results show that the desired indexes with iron grade of 56.40% and recovery of 88.46% were obtained from the roasted ore after the low intensity magnetic separation under the optimal roasting conditions. The results of XRD analysis, chemical phase analysis of iron, SEM-EDS analysis and VSM analysis indicate that hematite phase present in the raw material was transformed into magnetite phase during the suspension magnetization roasting process.
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New Sealing Techniques for Hydraulic Fracturing Experiment of Rock Under High Temperature and High Pressure Conditions
ZHANG Hong-wei, ZHANG Tong, WAN Zhi-jun, ZHOU Chang-bing
2021, 42 (3):  422-428.  DOI: 10.12068/j.issn.1005-3026.2021.03.018
Abstract ( 41 )   HTML ( 4)   PDF (3173KB) ( 40 )  
In order to solve the sealing problem in hydraulic fracturing experiments of rock sample under high temperature and high pressure (HTHP), theoretical analysis, numerical simulation and physical experiment were used to design a new type of sealing hydraulic fracturing experiment based on wedge-shaped metal buckled structure and its sealing effect under water injecting was analyzed by simulation. Furthermore, the HTHP hydraulic fracturing experiments were successfully conducted by using this proposed sealing technique. The results show that the high temperature, high pressure and high water-injecting pressure are all favorable conditions for the further sealing of the wedge-shaped buckled structure. Increasing the water-injecting pressure can realize the compressed sealing process. Finally, the hydraulic fracturing experiment of large-size rocks under HTHP is successfully conducted, which in turn verfies the sealing effect of this structure. The multiple hydraulic fracturing characteristics of rock is revealed by using this sealing technique.
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Analysis on Mechanical Properties of the Steel Plate Shear Wall with Fully Bolted and Welded Connections
MU Zai-gen, DA Hai, YANG Yu-qing, WANG Zhe
2021, 42 (3):  428-435.  DOI: 10.12068/j.issn.1005-3026.2021.03.019
Abstract ( 40 )   HTML ( 2)   PDF (5074KB) ( 47 )  
In order to avoid the residual stress caused by welding, the upper and lower steel plates are connected by the end-plate with bolts to form a fully bolted steel plate shear wall (SPSW) with better ductility and energy dissipation capacity. The models of fully bolted SPSW and welded SPSW were established and analyzed by the finite element method. The load-displacement curve, lateral bearing capacity, energy dissipation capacity, stiffness degradation, and bearing capacity degradation of the two kinds of steel plate shear walls under unidirectional push-over and reciprocating load were compared. The results show that, under the action of unidirectional push-over, the lateral bearing capacity of the SPSW with full bolted is close to that of the traditional form, but the initial stiffness is 11% lower than that of the traditional form. Under the reciprocating load, the SPSW with full bolted shows a better overall energy dissipation capacity, and the stiffness degrades slower. This form of SPSW is also convenient for production and installation, and worth to extensive promotion and application in the future engineering application.
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Stress-Reduction Model for Soil Arch and Its Application in Load Sharing Model for Landslide
LI Xing-ming, YAN E-chuan, TIAN Zhuang, ZHANG Yi
2021, 42 (3):  436-443.  DOI: 10.12068/j.issn.1005-3026.2021.03.020
Abstract ( 33 )   HTML ( 0)   PDF (456KB) ( 31 )  
Soil arching effect is the key research point for anti-slide piles coming into effect. Taking the stress change of soil arch as the research point, first, a reasonable arch axis for soil arch was specified, and then a new stress-reduction model for soil arch was further derived, based on which the calculation of the critical arch shape parameters of the soil arch was quantified, and last a new three-level load sharing model for landslide was proposed. Research shows that the model calculation has demonstrated an exponential reduction in the stress between and behind piles. The two equations of inclination angle at the foothold and the thickness of soil arch are more practical due to full consideration of effecting factors. According to the bearing capacity of soil arch behind and between anti-slide piles, the three-level load sharing model can be consistent with the phase characteristics of interaction between landslide mass and anti-slide pile. The research can deepen the understanding in soil arching effect theory, and can also provide theoretical guidance to the design of anti-slide piles in landslide programs.
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Discrete Element Investigation on the Interaction of Hydraulic Fracturing and Weak Plane in Deep Tunnels
LIU Shuai-qi, MA Feng-shan, GUO Jie, SUN Qi-hao
2021, 42 (3):  444-456.  DOI: 10.12068/j.issn.1005-3026.2021.03.021
Abstract ( 56 )   HTML ( 3)   PDF (14462KB) ( 48 )  
Hydraulic fracturing caused by high confined water is the root cause of water inrush in roadway. The discrete element fluid-solid coupling algorithm was improved, and the action mode of fluid channel length and water pressure on particles was updated. The interaction between the hydro-splitting fractures (HFs) and the weak planes (WPs) was simulated. Five different modes were obtained and the critical pressure values were calculated. The displacement, contact force of the specimen and the various of the stress at a specific point were analyzed. The research shows that: 1) with a constant injection pressure, the pressure value is the largest at the initial crack, then gradually decreases along the crack. 2) the displacement response are different under five interaction modes. The normal contact force has obvious vertical dominant surface in its contact direction, and the shear contact force generates four vertical dominant distribution directions. 3) the stress at Mc1 changes dramatically during the initiation stage, and the maxmium principal is always compressive. Stress response in Mc2 is relatively hysteretic. The diversity of principal stress is fundamentally determined by the interaction mode between HFs and WPs.
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