LI Yan , CUI Shilin , CHEN Yimin
2024, 56(3):1-8. DOI: 10.11918/202205002
Abstract:In order to consider the influence of the stayed cable breakage process characteristics and the time-varying characteristics of the bridge mode, and reflect the whole process characteristics of the structural dynamic response in the cable breaking accident, this paper proposes a dynamic response analysis method of the cable-stayed bridge under the action of the sudden cable-breaking process model and the structural modal information update strategy. Numerical simulation is mainly used to analyze the dynamic behavior characteristics of bridges under typical cable-stayed bridges and to study the influence of broken cables on the dynamic response characteristics of bridges when broken cables are held. The results show that the modal updating method considering the characteristics of cable breakage process increases the peak dynamic response of the bridge structure by nearly 10% compared to the case without considering it, and the overall response also shows a slight lag phenomenon; When a single main tower cable breaks in different parts, the types and peak positions of the dynamic response of the entire bridges main beam structure are summarized. It was found that when the duration of cable breakage is greater than the basic period of the structure, the dynamic amplification coefficient of the structure changes less and the amplitude approaches 1.0; When the suspension time is 0.011.0 times the basic period of the structure, the dynamic amplification coefficient of the structural response increases to its peak as the suspension time shortens. The research results can provide reference and guidance for the design and post structural evaluation of similar bridge types considering sudden cable breakage.
SONG Shengyuan , HUANG Di , SUI Jiaxuan , TAO Yong , MA Muye , LI Haojie
2024, 56(3):9-18. DOI: 10.11918/202307072
Abstract:In order to study the size effect of the shear characteristics of complex fractured rock mass, taking PDC3 adit of Songta Hydropower Station in Nujiang, Tibet as an example, on the basis of on-site fracture information collection, based on PFC3D software, a 3D fracture network was generated by statistical method and Monte Carlo principle, and the equivalent rock mass was constructed. The shear strength, internal friction coefficient and cohesion of fractured rock mass were obtained by large-scale direct shear test, and the size effect of the fractured rock mass was studied and the REV size under different parameters was determined. Then, the related parameters and sample sizes were fitted by nonlinear regression to explore their functional relationship. The results show that the shear strength, cohesion and internal friction coefficient tend to be stable with the change of sample size, and the REV obtained from different parameters are different. Comprehensive analysis of REV size of different parameters shows that the REV size of fractured rock mass for the shear characteristics in the study area is 11 m×11 m×11 m. By fitting the function relationship, there are exponential function relationships between shear strength, cohesion and internal friction coefficient and sample size. These results provide a basis for studying the mechanical REV of complex fractured rock mass and reasonably determining the mechanical parameters.
WEN Huiying , QIU Yinghan , ZHAO Sheng
2024, 56(3):19-28. DOI: 10.11918/202206120
Abstract:To improve the level of emergency management, this paper considers the uncertainty of the travel cost under the influence of an unexpected event to study urban traffic evacuation problem. Firstly, a spatio-temporal coupled network diagram based on the spatio-temporal characteristics of traffic evacuation problem is created, and a quantification method for the travel cost of urban traffic road networks is proposed, which contains a combination of the travel time cost and conflict risk cost. Furthermore, considering the influence of an upper limit to link resource weights for side constraints, a robust optimization model of the priori evacuation strategy based on the budgeted uncertainty set is constructed to minimize the total travel cost of road network evacuation process. Then, the model reconstruction technique is applied to transform the constructed robust model into a mixed integer linear programming model, and an adapted Lagrangian relaxation method is designed to decouple and solve. Finally, the SiouxFalls network is used for arithmetic analysis and the numerical results show that the growth rates of travel time cost and conflict risk cost increase by about 29.13% and 236.46%, respectively, with the growth of uncertainty set and model size. The model budget parameter is controlled in a certain interval, which can better trade off the robustness and optimality of solutions. The applicability of the proposed method in larger scale network calculations is verified through a case study of the Nanjing regional road network, and the results show the proposed method can obtain high-quality feasible solutions within fewer number of iterations than the traditional Lagrangian relaxation method. The results of this study can provide ideas for emergency command authorities to develop reliable traffic evacuation strategies.
ZHENG Kaifeng , FENG Xiaoyang , HE Xiaohui , HENG Junlin , LI Le , WANG Hongfu
2024, 56(3):29-37. DOI: 10.11918/202210041
Abstract:In order to improve the fatigue resistance of orthotropic steel decks (OSDs), the steel bridge deck was annealed to reduce the welding residual stress of key welds. This work at first presented a systematical review and discussion over the distribution pattern of welding residual stress in OSDs, in accordance with a conceptual analysis respecting the impact of residual stress on fatigue crack propagation. Then, the associated summarization and comparison were made on the common approaches to mitigate the welding residual stress in the worldwide. By referring to the manufacturing of pressure vessels, the authors suggested to reduce welding residual stress by introducing annealing treatment to OSDs. On this basis, the study focused on the rib-to-deck welded joints that demonstrates a relatively prominent fatigue issue. The residual stress measurements and fatigue tests were carried out using a total of sixteen full-scale specimens, i.e., nine annealed specimens and seven as-welded ones without any additional treatment. The test results showed a reduction in the residual stress of welded joint in OSDs by 80% after the annealing, and moreover, an enhancement in the fatigue strength by 23%. Obviously, the annealing can significantly reduce the residual stress of the weld joints and effectively improve the fatigue resistance of OSDs.
WANG Yonggang , LI Xiaokun , SONG Jie , LI Delin
2024, 56(3):38-45. DOI: 10.11918/202207089
Abstract:In order to reveal the formation and change of rear-end collision risk between the lead and following vehicles on sharp curves effectively, a typical accident-prone sharp curved segment is selected to collect traffic flow data by vertical aerial photography from unmanned aerial vehicles. Vehicle trajectory information is extracted via Tracker to determine the post-encroachment time (PET) variable of rear-end conflict cross the sharp curve. The results show that there is a spatial clustering feature in rear-end conflicts, which mainly concentrate in the upstream of the entry transition curve and the downstream of the circular and exit transition curves. Four types of rear-end conflicts make up 83.24% of all types of conflicts, and PET decreases both at threshold moment and within conflict risk range with the former is even more so than the latter, resulting in declines of DPET (derivative of PET) values. Also, four indicators as speed of FV, acceleration, difference in speed and acceleration between LV and FV have a significant impact on the DPET change at the threshold moment of rear-end conflicts. The mean value of DPET during the conflict evolution process of T10 (LV decelerates and FV accelerates) is the smallest with the PET sequence declines most sharply, which shows a significantly higher risk than other conflict modes.
LI Li , LI Shiqi , XU Zhigang , LI Guangze , WANG Guiping
2024, 56(3):46-55. DOI: 10.11918/202205090
Abstract:In order to improve prediction accuracy of vehicle′s car-following behavior in the complex environment, a car-following behavior modeling method is proposed under an ensemble learning framework to integrate theory-driven model and data-driven model. Based on the stacking ensemble learning framework, a theory-driven model, intelligent driver model (IDM), and two data-driven models, long-short term memory (LSTM) network and gate recurrent unit (GRU) network considering the factors of vehicle platoon and surrounding driving condition, are selected as the first-level learning algorithms of car-following behavior features. Three linear and eight nonlinear regression methods are taken as the candidates of second-level learning algorithms to integrate the features of the first-level learner outputs. By comparing trajectory prediction accuracy calculated from real vehicle trajectory data, the optimal car-following model is determined. Results show that the data-driven car-following models, which take the variables of vehicle platoon and surrounding driving condition into account, have the higher trajectory prediction accuracy than the IDM. In most cases, the ensemble learning car-following models with the nonlinear second-level learning algorithm predicts vehicle trajectory in the higher accuracy than the IDM, the data-driven models and the ensemble learning car-following models with the linear second-level learning algorithm. The IDM-LSTM-stacking model, which uses the GBRT regression as second-level learning algorithm, and the IDM-GRU-stacking model, which uses the random forest regression as second-level learning algorithm, give the highest trajectory prediction accuracy. The stability of integrated car-following model under external disturbance is prior to single theory-driven model and data-driven model. The ensemble learning method provides a new approach for modeling driving behaviors.
HE Min , LIANG Peng , LIU Jiuxian , YANG Fan , LIU Jie
2024, 56(3):56-67. DOI: 10.11918/202204079
Abstract:To reasonably simulate the stochastic traffic load on bridge site, a new cellular automata based on car following theory is proposed. Firstly, a new transformable cell which considers the vehicle as the core is proposed. The precise axle gap and axle weight are incorporated into the cell to fulfill the goal of precise vehicle load simulation. Then, the car following theory is introduced to propose the new transition rules, and the acceleration of each vehicle can be calculated based on the proposed transition rules. Finally, new boundary rules based on Weigh in Motion (WIM) is proposed. The vehicle sequence of any time period which matches the real one can be generated based on the WIM data, based on which the initial states of the vehicles to enter the road can be determined. Based on the proposed transition rules and the boundary rules, the spatiotemporal position of vehicles can be simulated, and the stochastic traffic load can be simulated with consideration of the new cell. The proposed model is validated using real WIM data, and the results indicate that the proposed new cell can precisely simulate the vehicle load. The proposed transition rules can compute the specific acceleration for each vehicle, and free driving and car following can be simulated. With simultaneously using the vehicle sequence generation method and the transition rules, the real traffic load of any time period can be reconstructed. The proposed CA model can be applied to simulate the stochastic traffic load of any time period on bridge site. With considering the precise axle load and reasonable traffic flow, the stochastic traffic load on bridge site can be successfully simulated.
ZHANG Changguang , WU Kai , MENG Xiangzhong , WANG Xiaolun
2024, 56(3):68-77. DOI: 10.11918/202212012
Abstract:In order to describe the variation of vertical earth pressure against culverts for different types of unsaturated soils under steady infiltration, the earth pressure coefficient at a sliding surface considering soil arching effect was derived by assuming the minor principal stress trajectory and Mohr stress circle. Based on the effective stress strength equation of unsaturated soils, the suction stress theory, and the vertical force equilibrium of a horizontal thin layer element, this study then respectively presented iterative solutions of vertical earth pressure against positive-buried/trench-buried culverts in unsaturated soils under steady infiltration along with providing application steps. Comparative validations and method extensions were also performed. Finally, simplified practical formulations of vertical earth pressure were introduced according to distribution laws of suction stress with depth. The results show that iterative solutions of vertical earth pressure against culverts can reasonably address comprehensive influences of soil type, water evaporation, rainfall infiltration, and soil arching effect. Moreover, these iterative solutions and their applicability to culverts in unsaturated soils are verified by comparing with the data of field measurements and theoretical calculations reported in the literature. Practical formulations of vertical earth pressure against culverts can be expressed explicitly with high accuracy, and they are readily to be adopted to estimate primary culvert loads under different steady infiltrations. Vertical earth pressure against culverts in sands could be determined as saturated soils due to ignoring the effect of unsaturated characteristics. The suction stress can be simplified as a linear profile with depth for culverts in silts and clays. The negative soil arching effect of a positive-buried culvert increases the vertical earth pressure, whereas the positive soil arching effect of a trench-buried culvert reduces the vertical earth pressure.
ZHAO Xiaokang , DONG Qiao , DONG Shi , CHEN Xueqin
2024, 56(3):78-88. DOI: 10.11918/202209022
Abstract:To investigate the healing behavior and healing occasion of cement stabilized macadam (CSM), the factors influencing the healing effect were analyzed based on the damage-healing model. Firstly, a 2D semicircular bending (SCB) numerical specimen of CSM was established through the Discrete Element Method (DEM). The damage factor was adopted to simulate the local damage and healing effect, and then the mesoscopic damage-healing model was constructed under a SCB loading mode. Secondly, the virtual SCB fatigue test was adopted to realize different degrees of load damage. The healing variable was established to simulate the healing behavior of local damage. Lastly, based on the damage-healing model, the healing effects were evaluated to reveal the influence of the initial damage state and healing degree of specimens. The optimal healing occasion of CSM was further studied. The results show that the proposed numerical damage-healing model can explain and simulate the mesoscale damage and healing behavior of CSM materials. The initial damage state and healing degree have nonlinear effects on healing effect. In the fatigue life stage of 70%-85%, local damage healing has a significant effect on strength improvement. According to the healing results, 70%-85% fatigue life is recommended as the optimal healing occasion for CSM materials. In addition, enough healing agent with moderate strength can help to maximize the healing effect of local damage.
SHI Yajun , MA Wei , YANG Chengsong , ZHANG Lianhai , SHANG Fei , CHEN Cheng
2024, 56(3):89-97. DOI: 10.11918/202302001
Abstract:To investigate the dynamic characteristics of adsorbed water and free water in silty clay during freezing and thawing and explore the physical processes between soil and water during these processes, a novel layered nuclear magnetic measurement technique was employed. Freezing-thawing experiments were conducted under closed conditions on silty clay with water contents (mass fractions) of 21.1%, 16.8%, and 12.0%, respectively. The microstructure of the soil at different depths after freezing and thawing was scanned using an electron microscope. The experimental results indicate that as the soil freezing process continues, both adsorbed water and free water decrease at different soil depths, and the relative decrease in free water is greater than that of adsorbed water in both the frozen and unfrozen zones. During thawing, both adsorbed water and free water increase at different soil depths. Furthermore, freezing and thawing lead to a decrease in adsorbed water and an increase in free water in the frozen zone, while both adsorbed water and free water decrease in the unfrozen zone. After freezing and thawing, the number and volume of pores increase in the frozen zone, while they decrease in the unfrozen zone. The dynamic differences in adsorbed water and free water during freezing are related to the inhomogeneous spatial distribution of water molecule interaction potential. The redistribution of adsorbed water and free water in the soil before and after freezing-thawing is the result of the combined effects of water migration and changes in soil microstructure.
LIU Jiahui , CHEN Ke , CHEN Qun
2024, 56(3):98-109. DOI: 10.11918/202203092
Abstract:Aiming at the problems of current intersection congestion and low utilization rate of bus lanes, this paper proposes a real-time sharing control method for dynamic bus lanes based at signal-controlled intersections. This method uses GPS to obtain real-time information on the locatin of the bus at the intersection, and obtains the number of vehicles in the bus lane through traffic detection equipment. Combined with the main signal display, the method comprehensively calculates the total delay of vehicles at the intersection before and after the bus lane sharing at the current moment. Based on the comparison results of the delay size feeding back, the lane signal shows red or green lights to tell drivers if they can enter the bus lane. This paper introduces the concept of affected vehicles, and establishes the bus lane sharing control model aiming at reducing the total vehicle delay at the intersection. Through the analysis of the two situations where the main signal showing red and green light at the current moment, this paper proposes a comprehensive calculation method for intersection delay of affected vehicles, considering the driver-occupant coefficient and the affected vehicles. The expression of the total delay difference of vehicles at the intersection before and after the bus lane sharing has been obtained. This paper numerically simulates the display of the lane signal in various scenarios to analyze the impact of factors on lane sharing, such as existing vehicles in the dedicated lane, the position of buses, and the status of the main signal display. The results demonstrate that the control method aligns well with real-world situations and effectively improves the utilization rate of the bus lane, making full use of green light time at the intersection. This method provides a new idea for synamically sharing of bus lanes and alleviating road congestion.
FU Helin , AN Pengtao , WU Yimin , LI Jie , CHEN Long
2024, 56(3):110-116. DOI: 10.11918/202112018
Abstract:The prediction accuracy of tunnel water inflow in water rich fracture area is poor, and the problem of water inflow has not been well solved. To solve this problem, considering the fractured surrounding rock and grouting area as heterogeneous and anisotropic media, and the initial support and secondary support structures as homogeneous and isotropic media, a simplified calculation model of tunnel water inflow under fractured surrounding rock is constructed. The calculation formula of tunnel water inflow in water rich fractured area is deduced based on the theory of underground hydraulics and the law of fluid mass conservation. Through the degradation analysis and the field measured data of the case project, the rationality of constructing the simplified calculation model of tunnel water inflow in the water rich fissure area and the correctness of the solution of the calculation formula of water inflow are verified. Finally, based on the analytical solution, the influence law of each characteristic parameter on the tunnel water inflow in the water rich fissure area is revealed, and the water inflow mechanism of the tunnel in the water rich fissure area is discussed. The research shows that the maximum error between the theoretical calculated value and the field measured value is 8.1%, which verifies the rationality of the model and the correctness of the formula derivation. The water inflow of the tunnel increases with the increase of the maximum width of the crack, which is approximately linear due to the joint restriction of the water shutoff structure. When the ratio of grouting area thickness to tunnel radius is less than 2 times, the tunnel water inflow is significantly affected by the thickness of grouting area. The water inflow of tunnel in water rich fracture area is restricted by the fracture distribution law and support structure, so we should pay attention to the investigation of fracture distribution.
LIU Tiexin , DONG Ziyan , GUO Yining
2024, 56(3):117-125. DOI: 10.11918/202304025
Abstract:The discontinuities are widely distributed in the rock mass and are difficult to analyze one by one. Therefore, it is of great engineering value and scientific significance to carry out the dominant grouping of the discontinuities. The existing research methods are sensitive to the initial information, the grouping results are not reliable, and it is difficult to accurately group the discontinuities with similar discontinuity orientations. To address these problems, this paper proposes a method for grouping discontinuities in rock masses based on the pelican optimization algorithm (POA). The POA algorithm is used to globally find the optimal initial clustering center and combine with the fuzzy C-mean algorithm (FCM) to fully group the discontinuity orientations. A Monte Carlo simulation technique is used to generate discontinuity orientations that conform to the Fisher distribution. Based on the orthogonal design, using the recognition error rate as the index, the new algorithm was compared with the traditional FCM algorithm, and the variation regulation of grouping accuracy was investigated under different number of discontinuities, number of discontinuities groups, clustering centers and dispersion degree. The results indicate that the cluster centers have a significant impact on grouping accuracy, and the proposed method is capable of effectively grouping structural data with unclear boundary of geological features, thereby improving the accuracy and reliability of the grouping results. Based on the data of the slope structural plane of a reservoir in Dalian, it is grouped and processed to verify the engineering practicability of the new method. This study can provide a basis for the three-dimensional network computer simulation of structural plane and the stability analysis of rock mass engineering.
CHENG Guozhu , ZHOU Chuanmiao , BIE Yiming
2024, 56(3):126-135. DOI: 10.11918/202208003
Abstract:In order to study the impact of road occupation construction events on the capacity of regional road network, based on the theory of bilevel programming, a calculation model of regional road network capacity considering the capacity constraints of road sections is constructed, and the solution algorithm is designed. Through VISSIM simulation software, the capacity benchmark value of the construction section is determined, the quantitative relationship between possible capacity and various influencing factors is analyzed, and the calculation method of possible capacity under the road occupation construction condition is given. Combined with the traffic flow distribution results, the boundary value, and the change rate of road network efficiency before and after deliberate destruction, the identification method of key sections in the occupied road construction period is given. Finally, taking the urban road network in Acheng District of Harbin City as a case, the travel demand distribution is obtained through the acquisition of mobile phone signaling data, the road network capacity before and after the road occupation construction is calculated, and the importance of the road network in Acheng District during the road occupation construction period is ranked. The research shows that the capacity of regional road network is 38 445 pcu/h under initial conditions and 36 865 pcu/h during construction, which reduces capacity of road network by 4.1%.
SUN Xianglong , ZHAO Hu , FENG Shumin , LI Zhenning
2024, 56(3):136-142. DOI: 10.11918/202307029
Abstract:In order to ensure the anti-glare effect of plants and avoid the formation of “wall effect”, from the perspective of road alignment combination, considering factors such as the number of lanes, vehicle type, and drivers vision, firstly, spacing models for plants on straight and curved sections, height models for superelevation or not superelevation horizontal curve, height models for concave and convex vertical curves, and a plant height limit model were constructed. Secondly, the models were calibrated based on the specifications and commonly used parameters in actual construction, and the theoretical values of the spacing and height at different speeds were obtained. Considering the cost of plants and the convenience of construction and maintenance, the recommended values were determined. Finally, taking Heida Highway as an example, the spacing and height models of plant anti-glare were validated, and the results showed that at a speed of 100 km/h, the spacing is 9 m and the height is 1.90 m in straight slope and straight concave vertical curve sections; The spacing and height of the superelevation horizontal curve section are 3 m and 1.95 m respectively; The spacing in convex vertical curve sections is 3 m, and the height is 1.90 m. The recommended values meet the design requirements for differentiation and precision under different alignment combination, while also facilitate construction and maintenance, and reduce costs.
ZHANG Youpeng , FENG Qiang , ZHAO Shanpeng , WANG Sihua
2024, 56(3):143-153. DOI: 10.11918/202207009
Abstract:The Lanzhou-Urumqi high-speed railway has suffered from wind disasters all year round. The construction of wind-break wall not only ensures the safety of train operation, but also intensifies the galloping of catenary positive feeder. In view of the deficiency of existing wind-break wall in gale areas that “only prevents trains but not catenary”. In this paper, a kind of perforated wind-break wall was designed, and a computational domain model was established based on the theory of fluid mechanics. The wind protection effect of the wind-break wall was evaluated, and the response laws of the porosity and opening angle of the wind-break wall to the aerodynamic characteristics of the positive feeder was analyzed by simulation. The results show that after the wind-break wall was set with a certain porosity, it will impact the vortex flow field behind the wind-break wall, making the flow field tend to be stable. With the increase of the porosity of wind-break wall, the range of the airflow growth zone at the positive feeder of the catenary decreases significantly, and the aerodynamic coefficient of the positive feeder shows a significant downward trend. When the porosity of the wind-break wall was 0.3, the residual coefficient of wind velocity at the leeward side of the wind-break wall was 0.46-0.69. At the same time, the drop rate of lift and drag coefficient of the positive feeder were more than 41.56% and 24.59%,respectively. When the porosity of the wind-break wall was 0.3 and the opening angle was 150°, the aerodynamic coefficient on the positive feeder decreases significantly compared with other angles, which can play a certain role in restraining the galloping of the positive feeder. The research results can provide a certain theoretical reference for the galloping prevention of the catenary positive feeder in gale areas of the Lanzhou-Urumqi high-speed railway.
WEI Wenjun , ZHANG Xuanming , YANG Liben
2024, 56(3):154-163. DOI: 10.11918/202206075
Abstract:In practice, the scarcity of failure data for bearings makes it challenging to meet the extensive training requirements of deep learning models. This paper leverages the fine-grained feature extraction capabilities of Convolutional Neural Networks and the classification ability of fuzzy clustering without the need for training, proposing a small-sample bearing fault diagnosis method based on fuzzy clustering and an improved Densenet network. Initially, the pretrained Densenet network is modified by removing the classification layer and retaining only the feature extraction layers, and designing an Adaptive Global Average Pooling (GAP) layer to replace the Fully Connected (FC) layer. Subsequently, fuzzy clustering is utilized instead of the Densenet networks softmax classification layer, eliminating the need for training to achieve classification. Experimental results demonstrate that by training the GAP layer parameters with small-sample data, the model significantly reduces the requirement for training samples. During diagnosis, bearing time-domain images are input into the network, outputting 1 920 feature data at the GAP layer. Feature vectors matrices are constructed from the feature data of different fault states. Fuzzy similarity matrices and fuzzy equivalence matrices are obtained using fuzzy clustering methods. As the confidence factor changes from high to low, dynamic clustering diagrams are derived from the corresponding Boolean matrices, thereby achieving bearing fault classification.
CHEN Keji , BIAN Rong , BAO Xuming , GU Yi , LOU Wenjuan , XU Haiwei , ZHANG Linlin
2024, 56(3):164-170. DOI: 10.11918/202204005
Abstract:To study the influence of vertical wind speed on the wind-induced swing of jump lines in mountainous micro-topography, the vertical wind load on the conductors, jump lines, and insulator strings was analyzed based on the rigid bar method. The maximum displacement of wind-induced swing at the jump lines was determined as the index of wind-induced swing. The geometric transform relation of the static balance plane of jump lines was established before and after the wind load. Then the wind-induced swing state equation was proposed considering the influence of vertical wind speed. A terrain model with a radius of 5 km was established, including the accident site of the wind-induced swing of jump lines and the micrometeorological station. The wind speed of the accident site was deduced from the wind speed of the micrometeorological station by using the numerical simulation method to obtain the accident wind speed of wind-induced swing considering the influence of the micro-topography. The parameters of the accident line and the vertical wind speed were substituted into the wind-induced swing state equation to obtain the critical horizontal wind speed of the wind-induced swing. Then the reliability of the wind-induced swing state equation was verified by comparing the accident wind speed and the critical horizontal wind speed. Finally, the influence of variable vertical wind speed on the critical horizontal wind speed of wind-induced swing was analyzed according to the wind-induced swing state equation. The results showed that with the increase in vertical wind speed, the critical horizontal wind speed of wind-induced swing decreased linearly. When the wind attack angle was 20°, the critical horizontal wind speed could be reduced by 16%. Therefore, the critical horizontal wind speed of the wind-induced swing was much safer considering the influence of vertical wind speed which should be considered in the design of jump lines for mountainous areas.
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