XI Shu , CHEN Xumei , LI Peikun , MA Jiaxin
2025, 57(11):1-11, 21. DOI: 10.11918/202410035
Abstract:To improve freeway operational efficiency and optimize spatiotemporal resource allocation in weaving area under the setting of dedicated lane for connected and autonomous vehicles (CAVs), a deep reinforcement learning-based integrated control strategy is proposed. This strategy aims to ensure the efficient and safe merging of CAVs into the dedicated lane. The research focuses on a three-lane freeway configuration, with the innermost lane designated for CAVs. A multi-objective reward function is developed to address the dedicated lane merging demand of CAVs while simultaneously considering the efficiency of mainline traffic and the length of ramp queue. The deep deterministic policy gradient (DDPG) algorithm is employed to implement the integrated control strategy, which encompasses entrance ramp signal control, variable speed limit at the lane level, and adjustment to the gaps between CAV platoon. A simulation environment for the freeway weaving area is designed using SUMO and Python to assess the effectiveness of the proposed control strategy. The results demonstrate that, with a CAV penetration rate of 30%, the integrated control strategy advances the longitudinal positioning of CAVs entering the dedicated lane, merging success rate increases of 19.34%, 22.86%, and 25.55% under low, medium, and high traffic demand scenarios, respectively. Additionally, average vehicle travel time is reduced by 5.42%, 17.41%, and 20.65% under the same conditions. The proposed integrated control strategy for weaving area demonstrates significant effectiveness by not only achieving effective guidance for CAV merging dedicated lane but also enhancing the traffic efficiency and operational safety of the mainline, providing a theoretical basis and technical reference for optimizing the traffic operation in weaving areas of freeway under CAV dedicated lane conditions.
TBZ〗MENG Yuhong , WANG Qiong , SU Wei , YE Weimin , CHEN Yonggui
2025, 57(11):12-21. DOI: 10.11918/202409082
Abstract:To elucidate the hydration-induced cracking phenomenon and the spatiotemporal evolution of crack network in bentonite during the self-sealing process of technological voids in deep geological repository of high-level radioactive wastes, a hydration test was conducted on the compacted bentonite with a radial technological void. Microfocus X-ray computed tomography was utilized for detecting the bentonite non-destructively at different hydration time. Qualitative and quantitative characterizations of the crack network were performed after the three-dimensional reconstruction. The results demonstrate that the bentonite sample experienced an evolvement from crack initiation and propagation to crack closure.Statistical analysis of morphological and geometric parameters revealed that Feret diameter and sphericity were respectively distributed within the ranges of 0.1-0.2 mm and 0.6~0.8, indicating that the crack network was composed of a large number of dotted cracks in isolation (>95%) and a small number of flaky cracks of interconnection. Notably, the latter accountted for over 80% of the total volume and surface area.The linear relation between the logarithm of hydration time and both the sample and technological void volume suggested that the expansive deformation of bentonite gradually slowed down in the hydration process. Furthermore, the linear relations of swelling rate, cracking rate and closing rate versus time in double logarithmic coordinates, as well as the persistent dominance of swelling rate over cracking and closure rates, reflected an intrinsic connection between expansion deformation and crack evolution. Specifically, the expansive deformation served as both a prerequisite for cracking and a necessary condition for crack closure.Through three-dimensional characterization and quantitative analysis, this study revealed the evolutionary regularity and underlying mechanism of hydration-induced cracks, thereby providing critical references for the design and optimization of the buffer/backfill materials.
CHEN Ke , WANG Chen , LIANG Fayun , WANG Zhongwei
2025, 57(11):22-32, 44. DOI: 10.11918/202408045
Abstract:This study investigates the critical state characteristics of kaolin across a wide suction range and clarifies their role in governing stress-dilatancy behavior. A series of constant-suction triaxial tests covering suctions from 0 to 367.54 MPa were performed to examine the evolution of the critical state stress ratio M, the critical state line, and the stress-dilatancy curves (D-η, where D is the dilatancy rate and η is the stress ratio). A normalization approach (Dη/M) was further employed to unify the stress-dilatancy relationships under different suction conditions. The results reveal that when suction exceeds a certain threshold, the critical state, shear strength, and stress-dilatancy behavior of kaolin cease to evolve with increasing suction. Below this threshold, M increases significantly with suction, while the slope of the critical state line in the v-p′ plane is only marginally affected. With respect to dilatancy, suction and net mean stress exert little influence on the slope of the D-η curves; instead, the principal effect of suction arises from its control of M, which enables normalization of the stress-dilatancy relationship as Dη/M. The findings demonstrate that the evolution of the critical state in unsaturated kaolin exhibits a distinct threshold feature and that the influence of suction on stress-dilatancy behavior can be consistently interpreted through changes in M. Building on this understanding, a modified stress-dilatancy equation within the framework of the Modified Cam-Clay model is proposed, which provides reliable predictions of suction effects and offers new experimental evidence and theoretical support for the development of constitutive models of unsaturated soils over a wide suction range.
CHAI Keli , LANG Xiaoming , SONG Zeren , XU Heng , JIANG An , HU Zheng
2025, 57(11):33-44. DOI: 10.11918/202409056
Abstract:In order to solve steady seepage filed for full-sectional leakage of a lined tunnel with grouting ring, a new conformal transformation method for both tunnel lining and grouting ring is proposed, and the explicit analytical solution without infinite series for head and water pressure in tunnel surrounding rock is obtained by variable separation method and orthogonality of trigonometric functions. Results of this analytical solution is compared with numerical simulation data by ABAQUS and existing literature data, which shows a reasonable agreement and verifies the correctness and applicability of this analytical solution. Parameter analysis of this analytical solution demonstrates that an increase in tunnel buried depth and a decrease in grouting ring thickness both increase the external water pressure on tunnel lining and lining water influx, whereas a reduction in lining thickness reduces water pressure outside tunnel lining, but increases lining water influx. Increases both in soil permeability coefficient and grouting ring permeability coefficient will increase water pressure outside tunnel lining and lining water influx, whereas an increase in lining permeability coefficient reduces water pressure outside tunnel lining, but increases lining water influx. This analytical solution provides a reference for size design of tunnel lining and grouting ring as well as the selection of materials.
GUO Ding , ZHANG Mingyu , LIU Yan , WU Yongquan
2025, 57(11):45-52. DOI: 10.11918/202401053
Abstract:Changes in water content alter soil mechanical properties. Current engineering theories for earth pressure calculation mainly use saturated soil theory. This study investigates unsaturated soil pressure under seepage effects with dynamic soil-water characteristic curves. Unsteady seepage is considered. The Richards equation during seepage process is solved. A theoretical solution for suction considering dynamic soil-water characteristic curves is obtained. Suction distribution patterns are analyzed. Using the suction solution with dynamic effects, the Rankine earth pressure equation for unsaturated soil under seepage is derived. The equation helps analyze dynamic effects on unsaturated soil pressure distribution. The theoretical earth pressure solution is applied to foundation pit support structures. Numerical software simulates earth pressure changes on support structures during rainfall infiltration with different intensities. Safety factors of support structures are calculated using unsaturated soil theory. Results show: Dynamic effects increase active earth pressure and decrease passive earth pressure. Larger suction leads to more significant differences. Under rainfall infiltration, dynamic effects make active earth pressure on support structures smaller than static effects. Faster infiltration rates cause greater pressure differences. Safety factors calculated by unsaturated soil theory exceed those by saturated soil theory. Considering dynamic effects reduces safety factors, indicating rainfall infiltration increases foundation pit instability risks.
ZHU Tantan , MA Fuwang , LI Ang , ZHU Haoyang , ZONG Xilei , HUANG Da , FENG Qiang
2025, 57(11):53-61. DOI: 10.11918/202409070
Abstract:To study the evolution of physical properties and mechanical behavior of sandstone under different uniaxial stress-induced damage conditions and freeze-thaw cycles, firstly, different axial stress levels were applied to sandstone samples to produce different damage degrees. Then, the stress-induced damaged sandstone samples were treated by freeze-thaw cycles. Finally, uniaxial compression tests were carried out on the damaged sandstone. The effects of damage inside the samples and freeze-thaw cycle on the deformation characteristics of sandstone were studied. The evolution laws of uniaxial compressive strength and elastic modulus of sandstone with different damage degrees were analyzed. The evolution mechanism of porosity, pore size, and pore structure fractal dimension before and after freeze-thaw cycle was revealed. The results show that the axial deformation of the samples increases significantly under the same stress after freeze-thaw cycles. The uniaxial compressive strength and elastic modulus of sandstone decrease gradually with the increase of damage stress and the number of freeze-thaw cycles. Before and after the freeze-thaw cycles, the porosity of sandstone increases gradually with the increase of damage stress, and the porosity of sandstone after the freeze-thaw cycle is obviously larger than that before the freeze-thaw cycles. The difference of sandstone porosity before and after the freeze-thaw cycles increases as the damage stress increases. With the increase of the equivalent radius, the proportion of sandstone pore number before the freeze-thaw cycle can be divided into three stages: gradually decreasing, first increasing and then decreasing, and gradually decreasing. After the freeze-thaw cycles, the proportion of sandstone pore number gradually decreases, and the proportion of pores with larger equivalent radius increases after the freeze-thaw cycle. The fractal dimension of sandstone pore structure after freeze-thaw cycles is larger than that before freeze-thaw cycles. The pore structure of sandstone samples after freeze-thaw cycle is more complex than that of sandstone samples before freeze-thaw cycle. Before and after the freeze-thaw cycles, the fractal dimension of sandstone pore structure increases gradually with the increase of damage stress, but the increase amplitude of the fractal dimension of sandstone pore structure after the freeze-thaw cycles is obviously smaller than that before the freeze-thaw cycle.
LUO Yikai , XU Jinhua , LI Yuran , LIU Chenghao , LI Yan
2025, 57(11):62-70. DOI: 10.11918/202407040
Abstract:A lane-level traffic flow prediction method was proposed to refine the spatial granularity of traffic flow prediction and address the limitations in traditional prediction methods which overlooked the interaction mechanisms brought by the lane differences. The soft-dynamic time warping was chosen as the measurement method to consider the variations in traffic flow time series caused by the lane positions. Then, the k-means algorithm was aggregated in the proposed algorithm to classify the lane cross-sections, which was utilized to analyze the temporal characteristics of flow at the selected lane cross-section type. The sequential variational mode decomposition was introduced to reduce the volatility of time series flow data and remove its noise, whose results can serve as inputs for the prediction model. Based on the previous results, the lane correlations can be determined by incorporating the Spearman correlation analysis in the proposed method. The heterogeneous spatiotemporal graph convolutional recurrent neural network model for predicting the flow of various lane types can be established by embedding the multi-head attention mechanism into the bidirectional gated recurrent unit and combining the lane correlations and their distance. The traffic count data from several freeways in Shanxi, China was selected to assess the effectiveness of the proposed method. The results indicate that the freeway′s lanes within the selected area can be classified to four categories: dense type, sparse type, morning peak type, and evening peak type, respectively. Compared to the autoregressive integrated moving average model, long-short term memory network model, and spatio-temporal graph convolutional network models, the proposed model reduces the mean absolute error and root mean square error by 11.21%-24.05% and 8.89%-24.43%, with the r-squared coefficient as 0.962 at the 5-minute granularity flow prediction for all the lanes. This result indicates the accuracy of the flow prediction can be further improved by considering the lane classification. When the prediction was accomplished at the 5-minute granularity with the step size within 12, the mean absolute error and root mean square error of the proposed model increased by 15.82% and 11.99% at most. The findings provide a basis for road planning and the development of intelligent transportation.
2025, 57(11):71-84. DOI: 10.11918/202406036
Abstract:In order to overcome the inadequacy of the current geocell reinforced coarse-grained soil constitutive model and the limitations of its finite element analysis method. Based on the three-parameter nonlinear shear expansion model and the mechanism of geocell reinforced additional constraints surrounding the pressure action, a nonlinear shear expansion model for geocell reinforced coarse-grained soil is proposed. In addition, a subroutine for the model was developed using the user-defined material subroutine UMAT interface provided by ABAQUS software. The triaxial test results of strain-softened and strain-hardened geocell-reinforced sandy soils were compared and verified with the simulation results of the model, respectively, and the computational results of the reinforced composite model in this paper were further compared and analyzed with those of the reinforced-soil-separated model. The level of performance of geocell parameters on the reinforcing effectiveness of coarse-grained soil was also evaluated. The results show that the constructed reinforced coarse-grained soil model can accurately simulate and reflect the shear expansibility characteristics of geocell-reinforced coarse-grained soil during the stressing process and its complex nonlinear mechanical behavior. Through the secondary development of this model, it can accurately predict the stress-strain curve relationship of different degree types of geocell strength under different perimeter pressures and relative density conditions of sand and soil. In the stage of reaching peak strength and before, the calculation accuracy of the reinforced composite model is basically comparable to that of the separated model, and it also has the advantages of simple modeling and efficient calculation. At the same time, the reinforced composite model solves the problem that the separated model cannot calculate the damage of the fill in geocells up to the Mohr-Coulomb yield function. The results of this research are of great value to the field of numerical analysis of geocell reinforced soil structures and can promote their application in engineering practice.
LIU Chenghao , XU Jinhua , LIANG Shujuan , SHAO Jin , LI Yan
2025, 57(11):85-94. DOI: 10.11918/202410063
Abstract:To improve transportation efficiency and reduce total costs, an optimization approach is adopted to address truck-drone flexible collaboration routing problem. Firstly, a mixed integer linear programming model with the goal of minimizing the operation cost and customer waiting cost is formulated, combining the characteristics of multiple-truck-drone flexible collaboration and drone continuous delivery. Secondly, a two-stage heuristic solution framework is designed to optimize the routes of drones and trucks respectively in two stages. Finally, a tailored adaptive hybrid neighborhood search algorithm based on destroy operator, repair operator and k-opt operator is proposed for routing in each stage. The Solomon dataset is selected for numerical experiments, and the results show that: compared with CPLEX solver, the proposed method can obtain satisfactory solutions with higher quality in a short time. Compared with iterative local search, variable neighborhood search and ant colony optimization algorithm, the solution quality of the proposed method is improved by 5.49%, 6.88% and 27.82% in small-, medium- and large-scale instances, respectively. Compared to pure truck transportation mode, the truck-drone collaborative transportation mode is more suitable for small- and medium-scale operations, achieving a 4.70% to 8.56% reduction in overall costs. The research results can provide theoretical basis for the practice of truck-drone collaborative transportation.
LI Zhenbao , ZHANG Qianqing , WANG Shujian , LIN Yanjun , CUI Wei
2025, 57(11):95-104. DOI: 10.11918/202410013
Abstract:To investigate the influence of core-pile interface friction characteristics on the bearing capacity of filled-core composite solidified soil precast piles, this study simulated the core-pile-precast-pile interfacial contact using annular shear specimens and systematically examined the frictional behavior at their interface. The experimental results demonstrated that: The ultimate interfacial frictional resistance increases with core pile diameter enlargement; The bonding coefficient between core pile and precast pile shows a positive correlation with the compressive strength of core-filling materials, with recommended values ranging from 0.02 to 0.10; An initial frictional resistance exists at the interface, and the shear-induced friction evolution exhibits three distinct phases-elastic deformation phase, brittle failure phase, and bond-slip phase, presenting a quasi-brittle failure mode. Through curve fitting of the interfacial shear stress versus relative displacement scatter plots using exponential and inverse hyperbolic models, a bond-slip load transfer model incorporating initial frictional resistance (τc) was established. This model effectively characterizes the load transfer mechanism in filled-core composite solidified soil precast piles under loading conditions. The proposed methodology provides theoretical support for analyzing the bearing behavior and interfacial interaction mechanisms of this novel pile foundation system.
CHENG Guozhu , ZHANG Xilong , XU Liang
2025, 57(11):105-114. DOI: 10.11918/202409063
Abstract:In order to ensure the safety and comfort of self-driving vehicles on expressways, research has been conducted on the design parameters for the longitudinal profile of highway sections suitable for autonomous vehicles, improves the calculation method of vertical curve radius and length of expressways suitable for self-driving vehicles, and puts forward a simulation test method of self-driving vehicle-road integration from the point of view of driving sight distance through LiDAR sensor based on PreScan and MATLAB/Simulink software. According to the safe driving speed, the adaptability of the highway with the design speed of 80140 km/h to the self-driving vehicle is analyzed, and the minimum length and radius of the highway vertical curve suitable for the self-driving vehicle are determined. The results show that the highway of 140 km/h is not enough to meet the safety requirements of self-driving vehicles at the present stage, and its design speed can be reduced to 130 km/h, and the speed can be increased when the technology is mature. Due to the lower system response time and higher sensor height of self-driving vehicles, the corresponding convex vertical curve radius can be reduced to 1 800 m, 2800 m, 5 600 m and 10 600 m when the design speed of expressway is 80 km/h, 100 km/h, 120 km/h and 130 km/h respectively. The radius of concave Symbol`@@vertical curve can be reduced to 2 000 m, 3 000 m, 4 000 m and 5 500 m. The research results of this paper can provide theoretical support for the design of fully automatic driving expressway in the future.
HUANG Yufan , DAI Siyang , CHEN Kangming , WU Qingxiong
2025, 57(11):115-123. DOI: 10.11918/202409033
Abstract:To facilitate the computation and analysis of the dynamic response of concrete-filled steel tubular (CFST) rigid-frame tied-arch bridges after tie rod fracture, a dynamic coefficient is introduced to account for the dynamic effects during the fracture process. An equivalent static calculation method incorporating the effect of tie rod fracture is proposed. The validity of the finite element modeling approach for simulating tie rod fracture was verified through comparisons with experimental results from a physical model test. A response analysis was carried out on a CFST rigid-frame tied-arch bridge to determine dynamic coefficients under various tie rod fracture scenarios. The results demonstrate that the tie rods should be regarded as the primary components in the dynamic analysis of such bridges after fracture. The in-plane bending moment of the piers and the horizontal displacement at the pier top can serve as supplementary indicators. In the case of single-side tie rod fracture, significant displacement occurs at the pier top on the fractured side, while displacement on the non-fractured side is negligible. The end crossbeam is subjected to shear and torsion. In contrast, under double-side fracture conditions, no torsion is generated in the end crossbeam on the fractured side, the axial force in the arch rib decreases, and the out-of-plane bending moment of the pier shows little variation. Based on the analysis, it is recommended to use a dynamic coefficient of 1.4 for single-side fracture and 1.6 for double-side fracture when applying the equivalent static method for assessing CFST rigid-frame tied-arch bridges considering the dynamic effect of tie rod fracture.
KOU Weibin , CAO Yue , ZHANG Shijie , LIU Chang
2025, 57(11):124-133. DOI: 10.11918/202410045
Abstract:To address the inefficiencies of pushback operation and the inadequate utilization of stand resources under traditional pushback mode in airport harbor areas, a grouping-based aircraft pushback method considering wake turbulence is proposed. Considering the special apron layout of harbor areas, the pushback modes of aircraft, and the effects of wake turbulence, the process and pattern for grouping-based aircraft pushback operations are established. The concept of "ultimate pushback spacing" is defined, and quantitative constraints are formulated for the scope and severity of wake turbulence impacts under different scenarios. By integrating grouping strategies, pushback strategies, and towing strategies, an optimization model for grouping-based aircraft pushback in harbor apron areas is developed, aiming to minimize the total aircraft grouping and pushback times. Due to the complexity of the nonlinear programming model, a two-stage linear iterative algorithm is designed to solve it. Finally, a case study based on Tianjin Binhai International Airport is conducted. The harbor area is divided into different zones, and specific parameters in the model are calibrated. The optimization results indicate that compared to the traditional single pushback mode, the optimized grouped pushback strategy reduces the total pushback time of all aircrafts by 17.48% in the current year and by 33.56% in the planed year 2030. Furthermore, under two additional scenarios that flights are reduced by 50% and increased by 50% respectively, it is indicated that the optimization effect of grouped pushback method consistently improves with growing number of aircrafts. The findings provide decision-making support for enhancing flight pushback efficiency and apron capacity in the harbor areas of large hub airports.
ZHENG Chuantian , ZHU Xingyu , ZHANG Zhiqiang
2025, 57(11):134-143. DOI: 10.11918/202405061
Abstract:To study the Macro-anisotropic progressive rupture characteristics and damage modes of gently inclined layered surrounding rock influenced by structural planes, we analytically deduced the mechanical response mechanism of the layered rock′s structural instability. Using a coupled discrete-finite-difference analysis method and results from indoor triaxial compression tests on sand-mudstone, we developed a numerical mechanical model to characterize the macro-mechanical properties of the gently inclined layered surrounding rock. This model was then used to systematically investigate the mechanical behavior of the rock under varying structural plane inclination angles and spacings. The rupture characteristics and rupture evolution of gently dipping layered rock under different structural plane inclination angle and spacing are systematically studied. The results indicate that: 1)analytical analysis based on beam plate structure can better reflect the progressive fracture process of layered surrounding rock and distinguish its failure mode; 2)The established discrete element finite difference coupled numerical model can better characterize the anisotropic macroscopic mechanical properties of layered sand and mudstone under triaxial stress state; 3)The fracture of the matrix changes significantly with the change of the inclination angle of the structural plane, and the cracks mainly appear in the direction perpendicular to the structural plane, as the inclination angle of the structural plane increases, the matrix fracture will undergo secondary deflection, and the critical angle for sliding failure of the surrounding rock will be calculated α1=24.43°, α2=55.29°; 4)As the spacing between structural planes decreases, the fragmentation of surrounding rock increases and the total number of cracks increases. When the spacing between structural planes is less than 30 cm, the fragmentation of surrounding rock significantly increases. The research results can provide a certain theoretical basis and play a guiding role for the control of stability and optimal design of supporting structures for gently inclined layered tunnels.
QU Faxian , LI Junjin , HU Mingwu , SHAN Deshan
2025, 57(11):144-159, 170. DOI: 10.11918/202410019
Abstract:To capture nonlinear variations in the mean and variance of seismic demand relative to seismic intensity measures, this study proposes a probabilistic seismic demand model based on a Gaussian mixture model (GMM). Grounded in statistical principles, the model estimates the joint and conditional probability distributions of seismic demand and intensity, subsequently established via Gaussian mixture regression (GMR). Using a 3-span, 30-meter continuous T-beam bridge as a case study, we analyze the model′s characteristics and compare them with traditional log-linear regression approaches. Results indicate that structural states exhibit distinct stage-dependent characteristics due to constraints from abutments and shear keys on girder displacement, coupled with backfill soil effects and pier column yielding. Consequently, the joint distribution of seismic demand and intensity displays significant multimodality, which the GMM effectively captures. Owing to its capacity to characterize nonlinear variations in seismic demand statistics, the GMM-based model demonstrates superior fitting performance, yielding fragility curves that differ discernibly from those generated by log-linear regression. Furthermore, mixture components of the joint probability distribution—alongside the mean and variance of the GMM-based model—show strong correlations with the structure′s stage-dependent behavioral phases.
MA Xuening , BAI Fan , WANG Le
2025, 57(11):160-170. DOI: 10.11918/202410012
Abstract:In order to improve the embedding effect of geogrid on reinforced aeolian sand, in this paper, four kinds of geogrids with new transverse ribs are designed by changing the thickness and shape of transverse ribs on the basis of ordinary biaxial geogrid. The pull-out test and DEM-FDM coupling method are used to study the influence of grid transverse ribs on the reinforcement effect and mechanism of aeolian sand. The reinforcement efficiency is introduced to evaluate the interface resistance characteristics of geogrid and soil, and the optimal geogrid transverse rib shape of reinforced aeolian sand is determined. The relationship between pullout force and pullout displacement and reinforcing efficiency under different thicknesses and shape of transverse ribs are analyzed at the macroscopic level. The evolution law of contact force chain and displacement field is studied at the mesoscopic level. The results show that the shape and thickness of the transverse ribs have a great influence on the shear strength of the reinforcement-soil interface. The pull-out force of the four new types of geogrids is about 1.1-3.6 times that of the ordinary biaxial geogrid. Combined with the concept of the material usage ratio of the geogrid, it is found that the rhombus transverse rib geogrid has the highest reinforcement efficiency. Through microscopic analysis, it is found that the strong contact force chain at the pull-out end is obviously denser during the pull-out process. Compared with the ordinary biaxial geogrid, the evolution trend of the contact force chain of the rhombus transverse rib geogrid is more significant, and the strong force chain is more denser, which indicated that the change of the shape and thickness of the transverse rib can mobilize more soil particles to resist the pull-out of the geogrid. During the pullout process, the displacement of the soil particles is lagging behind the displacement of the geogrid. Under the same pullout displacement, the participation of the surrounding soil of the rhombus transverse rib grid is higher than that of the biaxial geogrid during the pullout process, and the disturbance to the soil is also greater. The findings of this study can offer a significant reference for the development of new transverse rib geogrids and the reinforcement design of desert railway subgrades.
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