Purpose-The design goal for the tracking interval of high-speed railway trains in China is 3 min,but it is difficult to achieve,and it is widely believed that it is mainly limited by the tracking interval of train arr...Purpose-The design goal for the tracking interval of high-speed railway trains in China is 3 min,but it is difficult to achieve,and it is widely believed that it is mainly limited by the tracking interval of train arrivals.If the train arrival tracking interval can be compressed,it will be beneficial for China's high-speed railway to achieve a 3-min train tracking interval.The goal of this article is to study how to compress the train arrival tracking interval.Design/methodologylapproach-By simulating the process of dense train groups arriving at the station and stopping,the headway between train arrivals at the station was calculated,and the pattern of train arrival headway was obtained,changing the traditional understanding that the train arrival headway is considered the main factor limiting the headway of trains.Findings-When the running speed of trains is high,the headway between trains is short,the length of the station approach throat area is considerable and frequent train arrivals at the station,the arrival headway for the first group or several groups of trains will exceed the headway,but the subsequent sets of trains will havea headway equal to the arrival headway.This convergence characteristic is obtained by appropriately increasing the running time.Originality/value-According to this pattern,there is no need to overly emphasize the impact of train arrival headway on the headway.This plays an important role in compressing train headway and improving high-speedrailwaycapacity.展开更多
Purpose–The purpose of this study is to introduce the top-level design ideas and the overall architecture of earthquake early-warning system for high speed railways in China,which is based on P-wave earthquake early-...Purpose–The purpose of this study is to introduce the top-level design ideas and the overall architecture of earthquake early-warning system for high speed railways in China,which is based on P-wave earthquake early-warning and multiple ways of rapid treatment.Design/methodology/approach–The paper describes the key technologies that are involved in the development of the system,such as P-wave identification and earthquake early-warning,multi-source seismic information fusion and earthquake emergency treatment technologies.The paper also presents the test results of the system,which show that it has complete functions and its major performance indicators meet the design requirements.Findings–The study demonstrates that the high speed railways earthquake early-warning system serves as an important technical tool for high speed railways to cope with the threat of earthquake to the operation safety.The key technical indicators of the system have excellent performance:The first report time of the P-wave is less than three seconds.From the first arrival of P-wave to the beginning of train braking,the total delay of onboard emergency treatment is 3.63 seconds under 95%probability.The average total delay for power failures triggered by substations is 3.3 seconds.Originality/value–The paper provides a valuable reference for the research and development of earthquake early-warning system for high speed railways in other countries and regions.It also contributes to the earthquake prevention and disaster reduction efforts.展开更多
Concrete slabs are widely used in modern railways to increase the inherent resilient quality of the tracks,provide safe and smooth rides,and reduce the maintenance frequency.In this paper,the elastic performance of a ...Concrete slabs are widely used in modern railways to increase the inherent resilient quality of the tracks,provide safe and smooth rides,and reduce the maintenance frequency.In this paper,the elastic performance of a novel slab trackform for high-speed railways is investigated using three-dimensional finite element modelling in Abaqus.It is then compared to the performance of a ballasted track.First,slab and ballasted track models are developed to replicate the full-scale testing of track sections.Once the models are calibrated with the experimental results,the novel slab model is developed and compared against the calibrated slab track results.The slab and ballasted track models are then extended to create linear dynamic models,considering the track geodynamics,and simulating train passages at various speeds,for which the Ledsgard documented case was used to validate the models.Trains travelling at low and high speeds are analysed to investigate the track deflections and the wave propagation in the soil,considering the issues associated with critical speeds.Various train loading methods are discussed,and the most practical approach is retained and described.Moreover,correlations are made between the geotechnical parameters of modern high-speed rail and conventional standards.It is found that considering the same ground condition,the slab track deflections are considerably smaller than those of the ballasted track at high speeds,while they show similar behaviour at low speeds.展开更多
High speed photography technique is potentially the most effective way to measure the motion parameter of warhead fragment benefiting from its advantages of high accuracy,high resolution and high efficiency.However,it...High speed photography technique is potentially the most effective way to measure the motion parameter of warhead fragment benefiting from its advantages of high accuracy,high resolution and high efficiency.However,it faces challenge in dense objects tracking and 3D trajectories reconstruction due to the characteristics of small size and dense distribution of fragment swarm.To address these challenges,this work presents a warhead fragments motion trajectories tracking and spatio-temporal distribution reconstruction method based on high-speed stereo photography.Firstly,background difference algorithm is utilized to extract the center and area of each fragment in the image sequence.Subsequently,a multi-object tracking(MOT)algorithm using Kalman filtering and Hungarian optimal assignment is developed to realize real-time and robust trajectories tracking of fragment swarm.To reconstruct 3D motion trajectories,a global stereo trajectories matching strategy is presented,which takes advantages of epipolar constraint and continuity constraint to correctly retrieve stereo correspondence followed by 3D trajectories refinement using polynomial fitting.Finally,the simulation and experimental results demonstrate that the proposed method can accurately track the motion trajectories and reconstruct the spatio-temporal distribution of 1.0×10^(3)fragments in a field of view(FOV)of 3.2 m×2.5 m,and the accuracy of the velocity estimation can achieve 98.6%.展开更多
The high-speed on/off valve(HSV)serves as the fundamental component responsible for generating discrete fluids within digital hydraulic systems.As the switching frequency of the HSV increases,the properties of the gen...The high-speed on/off valve(HSV)serves as the fundamental component responsible for generating discrete fluids within digital hydraulic systems.As the switching frequency of the HSV increases,the properties of the generated discrete fluid approach those of continuous fluids.Therefore,a higher frequency response characteristic of HSV is the key to ensure the control accuracy of digital hydraulic systems.However,the current research mainly focuses on its dynamic performance,but neglect its FRC.This paper presents a theoretical analysis demonstrating that the FRC of the HSV can be enhanced by minimizing its switching time.The maximum switching frequency(MSF)is mainly determined by opening dynamic performance when HSV operates with low switching duty ratio(SDR),whereas the closing dynamic performance limits the MSF when HSV operates with high SDR.Building upon these findings,the pre-excitation control algorithm(PECA)is proposed to reduce the switching time of the HSV,and consequently enhance its FRC.Experimental results demonstrate that PECA shortens the opening delay time of HSV by 1.12 ms,the closing delay time by 2.54 ms,and the closing moving time by 0.47 ms in comparison to the existing advanced control algorithms.As a result,a larger MSF of 417 Hz and a wider controllable SDR range from 20%to 70%were achieved at a switching frequency of 250 Hz.Thus,the proposed PFCA in this paper has been verified as an effective and promising approach for enhancing the control performance of digital hydraulic systems.展开更多
The hydrodynamic performance of a high forward-speed ship in obliquely propagating waves is numerically examined to assess both free motions and wave field in comparison with a low forward-speed ship.This numerical mo...The hydrodynamic performance of a high forward-speed ship in obliquely propagating waves is numerically examined to assess both free motions and wave field in comparison with a low forward-speed ship.This numerical model is based on the time-domain potential flow theory and higher-order boundary element method,where an analytical expression is completely expanded to determine the base-unsteady coupling flow imposed on the moving condition of the ship.The ship in the numerical model may possess different advancing speeds,i.e.stationary,low speed,and high speed.The role of the water depth,wave height,wave period,and incident wave angle is analyzed by means of the accurate numerical model.It is found that the resonant motions of the high forward-speed ship are triggered by comparison with the stationary one.More specifically,a higher forward speed generates a V-shaped wave region with a larger elevation,which induces stronger resonant motions corresponding to larger wave periods.The shoaling effect is adverse to the motion of the low-speed ship,but is beneficial to the resonant motion of the high-speed ship.When waves obliquely propagate toward the ship,the V-shaped wave region would be broken due to the coupling effect between roll and pitch motions.It is also demonstrated that the maximum heave motion occurs in beam seas for stationary cases but occurs in head waves for high speeds.However,the variation of the pitch motion with period is hardly affected by wave incident angles.展开更多
Purpose–This review aims to give a critical view of the wheel/rail high frequency vibration-induced vibration fatigue in railway bogie.Design/methodology/approach–Vibration fatigue of railway bogie arising from the ...Purpose–This review aims to give a critical view of the wheel/rail high frequency vibration-induced vibration fatigue in railway bogie.Design/methodology/approach–Vibration fatigue of railway bogie arising from the wheel/rail high frequency vibration has become the main concern of railway operators.Previous reviews usually focused on the formation mechanism of wheel/rail high frequency vibration.This paper thus gives a critical review of the vibration fatigue of railway bogie owing to the short-pitch irregularities-induced high frequency vibration,including a brief introduction of short-pitch irregularities,associated high frequency vibration in railway bogie,typical vibration fatigue failure cases of railway bogie and methodologies used for the assessment of vibration fatigue and research gaps.Findings–The results showed that the resulting excitation frequencies of short-pitch irregularity vary substantially due to different track types and formation mechanisms.The axle box-mounted components are much more vulnerable to vibration fatigue compared with other components.The wheel polygonal wear and rail corrugation-induced high frequency vibration is the main driving force of fatigue failure,and the fatigue crack usually initiates from the defect of the weld seam.Vibration spectrum for attachments of railway bogie defined in the standard underestimates the vibration level arising from the short-pitch irregularities.The current investigations on vibration fatigue mainly focus on the methods to improve the accuracy of fatigue damage assessment,and a systematical design method for vibration fatigue remains a huge gap to improve the survival probability when the rail vehicle is subjected to vibration fatigue.Originality/value–The research can facilitate the development of a new methodology to improve the fatigue life of railway vehicles when subjected to wheel/rail high frequency vibration.展开更多
As High Speed Rail(HSR)has proliferated globally,so has a related research field dedicated to exploring and addressing its unique issues.Yet,studies to understand and classify the HSR research domain are limited.This ...As High Speed Rail(HSR)has proliferated globally,so has a related research field dedicated to exploring and addressing its unique issues.Yet,studies to understand and classify the HSR research domain are limited.This paper addresses the gap,using bibliometric analysis to identify future research areas and 20 candidate topics for literature review based on keyword analysis through VOSviewer.Article and review papers related to HSR published in the last 20 years(2003-2022)were retrieved from Scopus,and then analyzed to determine the split in knowledge between languages,the collaboration between countries and institutions,highly productive and cited journals,and research topics which have and have not been reviewed.Approximately 30%of the search results were published exclusively in Chinese,highlighting the importance of extending the evaluation to cover both languages.This is a novel aspect of the work,which has enabled the recognition of potential knowledge gaps.It is recommended that future reviews incorporate works in both languages,possibly through international collaboration.Institutions in China and other countries that are strong collaborators have been identified,as well as relevant,highly cited journals.展开更多
It was found that the steel plate in the composite plate in the WJ-8 fastener used in high speed rail is rusty. The objective of this study is to test the zinc coating of the steel plate. A literature review was condu...It was found that the steel plate in the composite plate in the WJ-8 fastener used in high speed rail is rusty. The objective of this study is to test the zinc coating of the steel plate. A literature review was conducted to identify the zinc coating techniques, and the companies that can provide different coating service was identified. A salt fog chamber was built that was in compliance with the ANSI B117 code, and the steel plates that were coated by the identified companies were tested using the salt fog chamber. The results indicated that the coating technique that had the best performance in preventing corrosion was the Greenkote plates with passivation. The galvanized option had the roughest coating layer, and it was the most reactive in the salt water solution. This makes it non-ideal for the dynamic rail environment because the increased friction of the plate could damage the supports, especially during extreme temperatures that would cause the rail to expand or contract. Greenkote with Phosphate and ArmorGalv also provided increased corrosion prevention with a smooth, strong finish, but it had more rust on the surface area than the Greenkote with ELU passivation. The ArmorGalv sample had more rust on the surface area than the Greenkote samples. This may not be a weakness in the ArmorGalv process;rather, it likely was the result of this particular sample not having the added protection of a colored coating.展开更多
The Balise Transmission Module(BTM)unit of the on-board train control system is a crucial component.Due to its unique installation position and complex environment,this unit has a higher fault rate within the on-board...The Balise Transmission Module(BTM)unit of the on-board train control system is a crucial component.Due to its unique installation position and complex environment,this unit has a higher fault rate within the on-board train control system.To conduct fault prediction for the BTM unit based on actual fault data,this study proposes a prediction method combining reliability statistics and machine learning,and achieves the fusion of prediction results from different dimensions through multi-method interactive validation.Firstly,a method for predicting equipment fault time targeting batch equipment is introduced.This method utilizes reliability statistics to construct a model of the remaining faultless operating time distribution considering uncertainty,thereby predicting the remaining faultless operating probability of the BTM unit.Secondly,considering the complexity of the BTM unit’s fault mechanism,the small sample size of fault cases,and the potential presence of multiple fault features in fault text records,an individual-oriented fault prediction method based on Bayesian-optimized Gradient Boosting Regression Tree(Bayes-GBRT)is proposed.This method achieves better prediction results compared to linear regression algorithms and random forest regression algorithms,with an average absolute error of only 0.224 years for predicting the fault time of this type of equipment.Finally,a multi-method interactive validation approach is proposed,enabling the fusion and validation of multi-dimensional results.The results indicate that the predicted fault time and the actual fault time conform to a log-normal distribution,and the parameter estimation results are basically consistent,verifying the accuracy and effectiveness of the prediction results.The above research findings can provide technical support for the maintenance and modification of BTM units,effectively reducing maintenance costs and ensuring the safe operation of high-speed railway,thus having practical engineering value for preventive maintenance.展开更多
In order to make further study on the mechanical property of CRTSIII type slab non-ballast track structures,which was self-designed in China,based on the method of the multiscale finite element model(FEM),the traditio...In order to make further study on the mechanical property of CRTSIII type slab non-ballast track structures,which was self-designed in China,based on the method of the multiscale finite element model(FEM),the traditional FEM of slab non-ballast track structures was improved.The multiscale FEM of CRTSII type slab nonballast track structures was established based on the general finite element program ABAQUs.Then the comparative calculation was made between various FEMs,showing that the high solution precision,fast modelling speed and high solution efficiency could be obtained.Therefore,the multiscale FEM was suitable for the parametric study on mechanical behaviour of CRTSII type slab non-ballast track structures,and then the key influence factor and constructions could be optimized.展开更多
Purpose–This method will become a new development trend in subgrade structure design for high speed railways.Design/methodology/approach–This paper summarizes the structural types and design methods of subgrade bed ...Purpose–This method will become a new development trend in subgrade structure design for high speed railways.Design/methodology/approach–This paper summarizes the structural types and design methods of subgrade bed for high speed railways in China,Japan,France,Germany,the United States and other countries based on the study and analysis of existing literature and combined with the research results and practices of high speed railway subgrade engineering at home and abroad.Findings–It is found that in foreign countries,the layered reinforced structure is generally adopted for the subgrade bed of high speed railways,and the unified double-layer or multi-layer structure is adopted for the surface layer of subgrade bed,while the simple structure is adopted in China;in foreign countries,different inspection parameters are adopted to evaluate the compaction state of fillers according to their respective understanding and practice,while in China,compaction coefficient,subsoil coefficient and dynamic deformation modulus are adopted for such evaluation;in foreign countries,the subgrade top deformation control method,the subgrade bottom deformation control method,the subsurface fill strength control method are mainly adopted in subgrade bed structure design of high speed railways,while in China,dynamic deformation control of subgrade surface and dynamic strain control of subgrade bed bottom layer is adopted in the design.However,the cumulative deformation of subgrade caused by train cyclic vibration load is not considered in the existing design methods.Originality/value–This paper introduces a new subgrade structure design method based on whole-process dynamics analysis that meets subgrade functional requirements and is established on the basis of the existing research at home and abroad on prediction methods for cumulative deformation of subgrade soil.展开更多
Nowadays,high mobility scenarios have become increasingly common.The widespread adoption of High-speed Rail(HSR)in China exemplifies this trend,while more promising use cases,such as vehicle-to-everything,continue to ...Nowadays,high mobility scenarios have become increasingly common.The widespread adoption of High-speed Rail(HSR)in China exemplifies this trend,while more promising use cases,such as vehicle-to-everything,continue to emerge.However,the Internet access provided in high mobility environments stllstruggles to achieve seamless connectivity.The next generation of wireless cellular technology 5 G further poses more requirements on the endto-end evolution to fully utilize its ultra-high band-width,while existing network diagnostic tools focus on above-IP layers or below-IP layers only.We then propose HiMoDiag,which enables flexible online analysis of the network performance in a cross-layer manner,i.e.,from the top(application layer)to the bottom(physical layer).We believe HiMoDiag could greatly simplify the process of pinpointing the deficiencies of the Internet access delivery on HSR,lead to more timely optimization and ultimately help to improve the network performance.展开更多
Purpose–The purpose of this paper is to summarize the status and characteristics of rail technology of high-speed railway in China,and point out the development direction of rail technology of high-speed railway.Desi...Purpose–The purpose of this paper is to summarize the status and characteristics of rail technology of high-speed railway in China,and point out the development direction of rail technology of high-speed railway.Design/methodology/approach–This study reviews the evolution of high-speed rail standards in China,comparing their chemical composition,mechanical attributes and geometric specifications with EN standards.It delves into the status of rail production technology,shifts in key performance indicators and the quality characteristics of rails.The analysis further examines the interplay between wheels and rails,the implementation of grinding technology and the techniques for inspecting rail service conditions.It encapsulates the salient features of rail operation and maintenance within the high-speed railway ecosystem.The paper concludes with an insightful prognosis of high-speed railway technology development in China.Findings–The rail standards of high-speed railway in China are scientific and advanced,highly operational and in line with international standards.The quality and performance of rail in China have reached the world’s advanced level.The 60N profile guarantees the operation quality of wheel–rail interaction effectively.The rail grinding technology system scientifically guarantees the long-term good service performance of the rail.The rail service state detection technology is scientific and efficient.The rail technology will take“more intelligent”and“higher speed”as the development direction to meet the future needs of high-speed railway in China.Originality/value–The development direction of rail technology for high-speed railway in China is defined,which will promote the continuous innovation and breakthrough of rail technology.展开更多
According to the characteristics of complex terrain and bad geological conditions in the southwest mountainous area of China, it is proposed that cast-in situ double-block ballastless track with layers and blocks stru...According to the characteristics of complex terrain and bad geological conditions in the southwest mountainous area of China, it is proposed that cast-in situ double-block ballastless track with layers and blocks structure should be adopted preferentially in the subgrade section of high-speed railway, which is conducive to the construction, prolongation of service life and maintenance of the ballastless track. Based on the finite element model, the dynamic performance, structural strength and stability of double-block ballastless track under high earthquake-intensity action are analyzed. The analysis shows that the relative displacement between the base slab of ballastless track and the subgrade may occur under 9 degree earthquake action. A new CRTS double-block ballastless track structure with a concave-convex structure between the base slab and the subgrade is proposed in the subgrade section, and its additional stress and relative displacement under earthquake are analyzed. The results show that the additional stress and relative displacement of the new ballastless track structure and the subgrade under 9-degree earthquake actions are small, which meet the high stability requirements of high-speed railway.展开更多
Some foreign media institutions have errantly characterized the Jakarta-Bandung High-Speed Railway(Jakarta-Bandung HSR)as a potential debt trap,claiming that the railway project could cause heavy debt burden for Indon...Some foreign media institutions have errantly characterized the Jakarta-Bandung High-Speed Railway(Jakarta-Bandung HSR)as a potential debt trap,claiming that the railway project could cause heavy debt burden for Indonesia.This is the biggest misunderstanding and misinterpretation of the project.展开更多
Purpose – This paper aims to propose a medium-term forecast model for the daily passenger volume of HighSpeed Railway (HSR) systems to predict the daily the Origin-Destination (OD) daily volume formultiple consecutiv...Purpose – This paper aims to propose a medium-term forecast model for the daily passenger volume of HighSpeed Railway (HSR) systems to predict the daily the Origin-Destination (OD) daily volume formultiple consecutivedays (e.g. 120 days).Design/methodology/approach – By analyzing the characteristics of the historical data on daily passengervolume of HSR systems, the date and holiday labels were designed with determined value ranges.In accordance to the autoregressive characteristics of the daily passenger volume of HSR, the Double LayerParallel Wavelet Neural Network (DLP-WNN) model suitable for the medium-term (about 120 d) forecast of thedaily passenger volume of HSR was established. The DLP-WNN model obtains the daily forecast result byweighed summation of the daily output values of the two subnets. Subnet 1 reflects the overall trend of dailypassenger volumes in the recent period, and subnet 2 the daily fluctuation of the daily passenger volume toensure the accuracy of medium-term forecast.Findings – According to the example application, in which the DLP-WNN modelwas used for the medium-termforecast of the daily passenger volumes for 120 days for typical O-D pairs at 4 different distances, the averageabsolute percentage error is 7%-12%, obviously lower than the results measured by the Back Propagation (BP)neural network, the ELM (extreme learning machine), the ELMAN neural network, the GRNN (generalizedregression neural network) and the VMD-GA-BP. The DLP-WNN model was verified to be suitable for themedium-term forecast of the daily passenger volume of HSR.Originality/value – This study proposed a Double Layer Parallel structure forecast model for medium-termdaily passenger volume (about 120 days) of HSR systems by using the date and holiday labels and WaveletNeural Network. The predict results are important input data for supporting the line planning, scheduling andother decisions in operation and management in HSR systems.展开更多
Financing of the African Integrated High-Speed Railway Network (AIHSRN) through Standard Gauge Railway (SGR) Projects is very expensive. As a result, most of the African countries seek financial supports from the Inte...Financing of the African Integrated High-Speed Railway Network (AIHSRN) through Standard Gauge Railway (SGR) Projects is very expensive. As a result, most of the African countries seek financial supports from the International Financial Institutions (IFIs). However, conditions provided by the IFIs through the Performance Standards (PS) of the International Financial Corporation (IFC) increase cost of the projects and thus, it becomes a burden to most of the African countries. This study aimed to explore the causes of IFC-PS through the SGR Projects that escalate costs and how to address them. The Tanzania SGR Lot 1 Project that covered 205 km from Dar es Salaam to Morogoro was selected as a case study. The methods used for data collection involved literature review, focus group discussions and interviews. The results and findings show a gap between the IFC-PS and the National Laws and Regulations that escalates costs of the projects if funds from the IFIs were to be secured. To bridge the gap, it is recommended that the African countries should engage into negotiations with the IFIs to agree to waive IFC-PS conditions that escalate costs provided they are adequately covered in the national laws and regulations;engagement of locally established national and regional financial institutions;and the responsible government institutions in the African countries should sit together for assessment and review of the IFC-PS against the national laws and regulations.展开更多
This paper proposes an adaptive unscented Kalman filter algorithm(ARUKF)to implement fault estimation for the dynamics of high⁃speed train(HST)with measurement uncertainty and time⁃varying noise with unknown statistic...This paper proposes an adaptive unscented Kalman filter algorithm(ARUKF)to implement fault estimation for the dynamics of high⁃speed train(HST)with measurement uncertainty and time⁃varying noise with unknown statistics.Firstly,regarding the actuator and sensor fault as the auxiliary variables of the dynamics of HST,an augmented system is established,and the fault estimation problem for dynamics of HST is formulated as the state estimation of the augmented system.Then,considering the measurement uncertainties,a robust lower bound is proposed to modify the update of the UKF to decrease the influence of measurement uncertainty on the filtering accuracy.Further,considering the unknown time⁃varying noise of the dynamics of HST,an adaptive UKF algorithm based on moving window is proposed to estimate the time⁃varying noise so that accurate concurrent actuator and sensor fault estimations of dynamics of HST is implemented.Finally,a five-car model of HST is given to show the effectiveness of this method.展开更多
A dynamic model test(CL = 4) at different velocities of train,namely different loading frequencies,is carried out to study the dynamic characteristics of a high-speed railway tunnel invert and its foundation soils.Not...A dynamic model test(CL = 4) at different velocities of train,namely different loading frequencies,is carried out to study the dynamic characteristics of a high-speed railway tunnel invert and its foundation soils.Not only are the accelerations,dynamic coefficients,dynamic stresses of the invert and foundation soils emphatically analyzed,their relationship with the velocity of the train are discussed in detail.Through laboratory testing,the attenuation of vibration propagating from up the rails is obtained and the calculation formula of the speed influence coefficient of the tunnel invert is preliminarily established.The depth of the foundation soils influenced by vibration is also determined in this study.It is shown that the responses of the tunnel invert and foundation soils to vibration are slightly increased with the velocity of the train;circumferential stresses in the bottom of the invert are tensile stresses and maximum stresses appear under the foot of the rails;the dynamic soil pressures of the foundation decrease quickly with the distance away from the tunnel invert and an exponential relationship exists between them.展开更多
基金State Railway Corporation of China Limited under the Science and Technology Research and Development Programme(2021X007)China Academy of Railway Research(2021YJ012)+1 种基金National Natural Science Foundation of China(52302417)Natural Science Foundation of Sichuan Province of China(2023NSFSC0906).
文摘Purpose-The design goal for the tracking interval of high-speed railway trains in China is 3 min,but it is difficult to achieve,and it is widely believed that it is mainly limited by the tracking interval of train arrivals.If the train arrival tracking interval can be compressed,it will be beneficial for China's high-speed railway to achieve a 3-min train tracking interval.The goal of this article is to study how to compress the train arrival tracking interval.Design/methodologylapproach-By simulating the process of dense train groups arriving at the station and stopping,the headway between train arrivals at the station was calculated,and the pattern of train arrival headway was obtained,changing the traditional understanding that the train arrival headway is considered the main factor limiting the headway of trains.Findings-When the running speed of trains is high,the headway between trains is short,the length of the station approach throat area is considerable and frequent train arrivals at the station,the arrival headway for the first group or several groups of trains will exceed the headway,but the subsequent sets of trains will havea headway equal to the arrival headway.This convergence characteristic is obtained by appropriately increasing the running time.Originality/value-According to this pattern,there is no need to overly emphasize the impact of train arrival headway on the headway.This plays an important role in compressing train headway and improving high-speedrailwaycapacity.
基金This research is supported by the R&D Fund Project of China Academy of Railway Science Corporation Limited[Grant No.2022Y253].
文摘Purpose–The purpose of this study is to introduce the top-level design ideas and the overall architecture of earthquake early-warning system for high speed railways in China,which is based on P-wave earthquake early-warning and multiple ways of rapid treatment.Design/methodology/approach–The paper describes the key technologies that are involved in the development of the system,such as P-wave identification and earthquake early-warning,multi-source seismic information fusion and earthquake emergency treatment technologies.The paper also presents the test results of the system,which show that it has complete functions and its major performance indicators meet the design requirements.Findings–The study demonstrates that the high speed railways earthquake early-warning system serves as an important technical tool for high speed railways to cope with the threat of earthquake to the operation safety.The key technical indicators of the system have excellent performance:The first report time of the P-wave is less than three seconds.From the first arrival of P-wave to the beginning of train braking,the total delay of onboard emergency treatment is 3.63 seconds under 95%probability.The average total delay for power failures triggered by substations is 3.3 seconds.Originality/value–The paper provides a valuable reference for the research and development of earthquake early-warning system for high speed railways in other countries and regions.It also contributes to the earthquake prevention and disaster reduction efforts.
基金Engineering and Physical Sciences Research Council (EPSRC) is also acknowledged for funding this work under Grant Number EP/N009207/1.
文摘Concrete slabs are widely used in modern railways to increase the inherent resilient quality of the tracks,provide safe and smooth rides,and reduce the maintenance frequency.In this paper,the elastic performance of a novel slab trackform for high-speed railways is investigated using three-dimensional finite element modelling in Abaqus.It is then compared to the performance of a ballasted track.First,slab and ballasted track models are developed to replicate the full-scale testing of track sections.Once the models are calibrated with the experimental results,the novel slab model is developed and compared against the calibrated slab track results.The slab and ballasted track models are then extended to create linear dynamic models,considering the track geodynamics,and simulating train passages at various speeds,for which the Ledsgard documented case was used to validate the models.Trains travelling at low and high speeds are analysed to investigate the track deflections and the wave propagation in the soil,considering the issues associated with critical speeds.Various train loading methods are discussed,and the most practical approach is retained and described.Moreover,correlations are made between the geotechnical parameters of modern high-speed rail and conventional standards.It is found that considering the same ground condition,the slab track deflections are considerably smaller than those of the ballasted track at high speeds,while they show similar behaviour at low speeds.
基金Key Basic Research Project of Strengthening the Foundations Plan of China (Grant No.2019-JCJQ-ZD-360-12)National Defense Basic Scientific Research Program of China (Grant No.JCKY2021208B011)to provide fund for conducting experiments。
文摘High speed photography technique is potentially the most effective way to measure the motion parameter of warhead fragment benefiting from its advantages of high accuracy,high resolution and high efficiency.However,it faces challenge in dense objects tracking and 3D trajectories reconstruction due to the characteristics of small size and dense distribution of fragment swarm.To address these challenges,this work presents a warhead fragments motion trajectories tracking and spatio-temporal distribution reconstruction method based on high-speed stereo photography.Firstly,background difference algorithm is utilized to extract the center and area of each fragment in the image sequence.Subsequently,a multi-object tracking(MOT)algorithm using Kalman filtering and Hungarian optimal assignment is developed to realize real-time and robust trajectories tracking of fragment swarm.To reconstruct 3D motion trajectories,a global stereo trajectories matching strategy is presented,which takes advantages of epipolar constraint and continuity constraint to correctly retrieve stereo correspondence followed by 3D trajectories refinement using polynomial fitting.Finally,the simulation and experimental results demonstrate that the proposed method can accurately track the motion trajectories and reconstruct the spatio-temporal distribution of 1.0×10^(3)fragments in a field of view(FOV)of 3.2 m×2.5 m,and the accuracy of the velocity estimation can achieve 98.6%.
基金Supported by National Natural Science Foundation of China (Grant No.52005441)Young Elite Scientist Sponsorship Program by CAST of China (Grant No.2022-2024QNRC001)+4 种基金Zhejiang Provincial Natural Science Foundation of China (Grant No.LQ21E050017)Zhejiang Provincial“Pioneer”and“Leading Goose”R&D Program of China (Grant Nos.2022C01122,2022C01132)State Key Laboratory of Mechanical System and Vibration of China (Grant No.MSV202316)Fundamental Research Funds for the Provincial Universities of Zhejiang of China (Grant No.RF-A2023007)Research Project of ZJUT of China (Grant No.GYY-ZH-2023075)。
文摘The high-speed on/off valve(HSV)serves as the fundamental component responsible for generating discrete fluids within digital hydraulic systems.As the switching frequency of the HSV increases,the properties of the generated discrete fluid approach those of continuous fluids.Therefore,a higher frequency response characteristic of HSV is the key to ensure the control accuracy of digital hydraulic systems.However,the current research mainly focuses on its dynamic performance,but neglect its FRC.This paper presents a theoretical analysis demonstrating that the FRC of the HSV can be enhanced by minimizing its switching time.The maximum switching frequency(MSF)is mainly determined by opening dynamic performance when HSV operates with low switching duty ratio(SDR),whereas the closing dynamic performance limits the MSF when HSV operates with high SDR.Building upon these findings,the pre-excitation control algorithm(PECA)is proposed to reduce the switching time of the HSV,and consequently enhance its FRC.Experimental results demonstrate that PECA shortens the opening delay time of HSV by 1.12 ms,the closing delay time by 2.54 ms,and the closing moving time by 0.47 ms in comparison to the existing advanced control algorithms.As a result,a larger MSF of 417 Hz and a wider controllable SDR range from 20%to 70%were achieved at a switching frequency of 250 Hz.Thus,the proposed PFCA in this paper has been verified as an effective and promising approach for enhancing the control performance of digital hydraulic systems.
基金supported by the National Natural Science Foundation of China(Grant Nos.52271278 and 52111530137)the Natural Science Foundation of Jiangsu Province(Grant No.SBK2022020579)the Newton Advanced Fellowships by the Royal Society(Grant No.NAF\R1\180304).
文摘The hydrodynamic performance of a high forward-speed ship in obliquely propagating waves is numerically examined to assess both free motions and wave field in comparison with a low forward-speed ship.This numerical model is based on the time-domain potential flow theory and higher-order boundary element method,where an analytical expression is completely expanded to determine the base-unsteady coupling flow imposed on the moving condition of the ship.The ship in the numerical model may possess different advancing speeds,i.e.stationary,low speed,and high speed.The role of the water depth,wave height,wave period,and incident wave angle is analyzed by means of the accurate numerical model.It is found that the resonant motions of the high forward-speed ship are triggered by comparison with the stationary one.More specifically,a higher forward speed generates a V-shaped wave region with a larger elevation,which induces stronger resonant motions corresponding to larger wave periods.The shoaling effect is adverse to the motion of the low-speed ship,but is beneficial to the resonant motion of the high-speed ship.When waves obliquely propagate toward the ship,the V-shaped wave region would be broken due to the coupling effect between roll and pitch motions.It is also demonstrated that the maximum heave motion occurs in beam seas for stationary cases but occurs in head waves for high speeds.However,the variation of the pitch motion with period is hardly affected by wave incident angles.
基金The author sincerely appreciates the help provided by the research team(Wheel/rail interaction,Vibration and Noise Research Team)and CRRC.In addition,this study has also been supported by Science and Technology Research Plan of China Railway General Corporation(No.P2019J002,N2022J009)China Association of Science and Technology Young Talent Support Project(No.2019QNRC001)+1 种基金National Natural Science Foundation(No.U1934203)Sichuan Science and Technology Program(No.2022NSFSC0469,2023NSFSC0374,2023YFH0049).
文摘Purpose–This review aims to give a critical view of the wheel/rail high frequency vibration-induced vibration fatigue in railway bogie.Design/methodology/approach–Vibration fatigue of railway bogie arising from the wheel/rail high frequency vibration has become the main concern of railway operators.Previous reviews usually focused on the formation mechanism of wheel/rail high frequency vibration.This paper thus gives a critical review of the vibration fatigue of railway bogie owing to the short-pitch irregularities-induced high frequency vibration,including a brief introduction of short-pitch irregularities,associated high frequency vibration in railway bogie,typical vibration fatigue failure cases of railway bogie and methodologies used for the assessment of vibration fatigue and research gaps.Findings–The results showed that the resulting excitation frequencies of short-pitch irregularity vary substantially due to different track types and formation mechanisms.The axle box-mounted components are much more vulnerable to vibration fatigue compared with other components.The wheel polygonal wear and rail corrugation-induced high frequency vibration is the main driving force of fatigue failure,and the fatigue crack usually initiates from the defect of the weld seam.Vibration spectrum for attachments of railway bogie defined in the standard underestimates the vibration level arising from the short-pitch irregularities.The current investigations on vibration fatigue mainly focus on the methods to improve the accuracy of fatigue damage assessment,and a systematical design method for vibration fatigue remains a huge gap to improve the survival probability when the rail vehicle is subjected to vibration fatigue.Originality/value–The research can facilitate the development of a new methodology to improve the fatigue life of railway vehicles when subjected to wheel/rail high frequency vibration.
文摘As High Speed Rail(HSR)has proliferated globally,so has a related research field dedicated to exploring and addressing its unique issues.Yet,studies to understand and classify the HSR research domain are limited.This paper addresses the gap,using bibliometric analysis to identify future research areas and 20 candidate topics for literature review based on keyword analysis through VOSviewer.Article and review papers related to HSR published in the last 20 years(2003-2022)were retrieved from Scopus,and then analyzed to determine the split in knowledge between languages,the collaboration between countries and institutions,highly productive and cited journals,and research topics which have and have not been reviewed.Approximately 30%of the search results were published exclusively in Chinese,highlighting the importance of extending the evaluation to cover both languages.This is a novel aspect of the work,which has enabled the recognition of potential knowledge gaps.It is recommended that future reviews incorporate works in both languages,possibly through international collaboration.Institutions in China and other countries that are strong collaborators have been identified,as well as relevant,highly cited journals.
文摘It was found that the steel plate in the composite plate in the WJ-8 fastener used in high speed rail is rusty. The objective of this study is to test the zinc coating of the steel plate. A literature review was conducted to identify the zinc coating techniques, and the companies that can provide different coating service was identified. A salt fog chamber was built that was in compliance with the ANSI B117 code, and the steel plates that were coated by the identified companies were tested using the salt fog chamber. The results indicated that the coating technique that had the best performance in preventing corrosion was the Greenkote plates with passivation. The galvanized option had the roughest coating layer, and it was the most reactive in the salt water solution. This makes it non-ideal for the dynamic rail environment because the increased friction of the plate could damage the supports, especially during extreme temperatures that would cause the rail to expand or contract. Greenkote with Phosphate and ArmorGalv also provided increased corrosion prevention with a smooth, strong finish, but it had more rust on the surface area than the Greenkote with ELU passivation. The ArmorGalv sample had more rust on the surface area than the Greenkote samples. This may not be a weakness in the ArmorGalv process;rather, it likely was the result of this particular sample not having the added protection of a colored coating.
基金supported by the Integrated Rail Transit Dispatch Control and Intermodal Transport Service Technology Project(Grant No.2022YFB4300500).
文摘The Balise Transmission Module(BTM)unit of the on-board train control system is a crucial component.Due to its unique installation position and complex environment,this unit has a higher fault rate within the on-board train control system.To conduct fault prediction for the BTM unit based on actual fault data,this study proposes a prediction method combining reliability statistics and machine learning,and achieves the fusion of prediction results from different dimensions through multi-method interactive validation.Firstly,a method for predicting equipment fault time targeting batch equipment is introduced.This method utilizes reliability statistics to construct a model of the remaining faultless operating time distribution considering uncertainty,thereby predicting the remaining faultless operating probability of the BTM unit.Secondly,considering the complexity of the BTM unit’s fault mechanism,the small sample size of fault cases,and the potential presence of multiple fault features in fault text records,an individual-oriented fault prediction method based on Bayesian-optimized Gradient Boosting Regression Tree(Bayes-GBRT)is proposed.This method achieves better prediction results compared to linear regression algorithms and random forest regression algorithms,with an average absolute error of only 0.224 years for predicting the fault time of this type of equipment.Finally,a multi-method interactive validation approach is proposed,enabling the fusion and validation of multi-dimensional results.The results indicate that the predicted fault time and the actual fault time conform to a log-normal distribution,and the parameter estimation results are basically consistent,verifying the accuracy and effectiveness of the prediction results.The above research findings can provide technical support for the maintenance and modification of BTM units,effectively reducing maintenance costs and ensuring the safe operation of high-speed railway,thus having practical engineering value for preventive maintenance.
基金supported by“111”Project(B18062)Fundamental Research Funds for the Central Universities(2019CDQYTM028).
文摘In order to make further study on the mechanical property of CRTSIII type slab non-ballast track structures,which was self-designed in China,based on the method of the multiscale finite element model(FEM),the traditional FEM of slab non-ballast track structures was improved.The multiscale FEM of CRTSII type slab nonballast track structures was established based on the general finite element program ABAQUs.Then the comparative calculation was made between various FEMs,showing that the high solution precision,fast modelling speed and high solution efficiency could be obtained.Therefore,the multiscale FEM was suitable for the parametric study on mechanical behaviour of CRTSII type slab non-ballast track structures,and then the key influence factor and constructions could be optimized.
基金The research was supported by the National Natural Science Foundation of China(Grant Nos.41731288 and 41972299)the Science and Technology Research and Development Program of China Railway(Grant No.P2018G050)+1 种基金the Young Top-Notch Talent Project of National“Ten Thousands Talent Program”(Grant No.2019YJ300)the Major Scientific Research and Development Project of China Academy of Railway Sciences Corporation Limited(Grant No.2019YJ026).
文摘Purpose–This method will become a new development trend in subgrade structure design for high speed railways.Design/methodology/approach–This paper summarizes the structural types and design methods of subgrade bed for high speed railways in China,Japan,France,Germany,the United States and other countries based on the study and analysis of existing literature and combined with the research results and practices of high speed railway subgrade engineering at home and abroad.Findings–It is found that in foreign countries,the layered reinforced structure is generally adopted for the subgrade bed of high speed railways,and the unified double-layer or multi-layer structure is adopted for the surface layer of subgrade bed,while the simple structure is adopted in China;in foreign countries,different inspection parameters are adopted to evaluate the compaction state of fillers according to their respective understanding and practice,while in China,compaction coefficient,subsoil coefficient and dynamic deformation modulus are adopted for such evaluation;in foreign countries,the subgrade top deformation control method,the subgrade bottom deformation control method,the subsurface fill strength control method are mainly adopted in subgrade bed structure design of high speed railways,while in China,dynamic deformation control of subgrade surface and dynamic strain control of subgrade bed bottom layer is adopted in the design.However,the cumulative deformation of subgrade caused by train cyclic vibration load is not considered in the existing design methods.Originality/value–This paper introduces a new subgrade structure design method based on whole-process dynamics analysis that meets subgrade functional requirements and is established on the basis of the existing research at home and abroad on prediction methods for cumulative deformation of subgrade soil.
基金supported by National Key Research and Development Plan,China(Grant No.2020YFB1710900)National Natural Science Foundation of China(Grant No.62022005 and 62172008).
文摘Nowadays,high mobility scenarios have become increasingly common.The widespread adoption of High-speed Rail(HSR)in China exemplifies this trend,while more promising use cases,such as vehicle-to-everything,continue to emerge.However,the Internet access provided in high mobility environments stllstruggles to achieve seamless connectivity.The next generation of wireless cellular technology 5 G further poses more requirements on the endto-end evolution to fully utilize its ultra-high band-width,while existing network diagnostic tools focus on above-IP layers or below-IP layers only.We then propose HiMoDiag,which enables flexible online analysis of the network performance in a cross-layer manner,i.e.,from the top(application layer)to the bottom(physical layer).We believe HiMoDiag could greatly simplify the process of pinpointing the deficiencies of the Internet access delivery on HSR,lead to more timely optimization and ultimately help to improve the network performance.
基金supported by the National Key R&D Program of China[Grant No.2022YFB2603402]the Task of Science and Technology R&D Program of China Railway Corporation[Grant No.K2023G013]the R&D Fund Project of China Academy of Railway Science Corporation Limited[Grant No.2022YJ165].
文摘Purpose–The purpose of this paper is to summarize the status and characteristics of rail technology of high-speed railway in China,and point out the development direction of rail technology of high-speed railway.Design/methodology/approach–This study reviews the evolution of high-speed rail standards in China,comparing their chemical composition,mechanical attributes and geometric specifications with EN standards.It delves into the status of rail production technology,shifts in key performance indicators and the quality characteristics of rails.The analysis further examines the interplay between wheels and rails,the implementation of grinding technology and the techniques for inspecting rail service conditions.It encapsulates the salient features of rail operation and maintenance within the high-speed railway ecosystem.The paper concludes with an insightful prognosis of high-speed railway technology development in China.Findings–The rail standards of high-speed railway in China are scientific and advanced,highly operational and in line with international standards.The quality and performance of rail in China have reached the world’s advanced level.The 60N profile guarantees the operation quality of wheel–rail interaction effectively.The rail grinding technology system scientifically guarantees the long-term good service performance of the rail.The rail service state detection technology is scientific and efficient.The rail technology will take“more intelligent”and“higher speed”as the development direction to meet the future needs of high-speed railway in China.Originality/value–The development direction of rail technology for high-speed railway in China is defined,which will promote the continuous innovation and breakthrough of rail technology.
基金supported by China Railway Eryuan Engineering Group Co.,Ltd。
文摘According to the characteristics of complex terrain and bad geological conditions in the southwest mountainous area of China, it is proposed that cast-in situ double-block ballastless track with layers and blocks structure should be adopted preferentially in the subgrade section of high-speed railway, which is conducive to the construction, prolongation of service life and maintenance of the ballastless track. Based on the finite element model, the dynamic performance, structural strength and stability of double-block ballastless track under high earthquake-intensity action are analyzed. The analysis shows that the relative displacement between the base slab of ballastless track and the subgrade may occur under 9 degree earthquake action. A new CRTS double-block ballastless track structure with a concave-convex structure between the base slab and the subgrade is proposed in the subgrade section, and its additional stress and relative displacement under earthquake are analyzed. The results show that the additional stress and relative displacement of the new ballastless track structure and the subgrade under 9-degree earthquake actions are small, which meet the high stability requirements of high-speed railway.
文摘Some foreign media institutions have errantly characterized the Jakarta-Bandung High-Speed Railway(Jakarta-Bandung HSR)as a potential debt trap,claiming that the railway project could cause heavy debt burden for Indonesia.This is the biggest misunderstanding and misinterpretation of the project.
基金supported by the National Natural Science Foundation of China(Grant Nos.72171236 and 71701216)the National Key R&D Program of China(Grant No.2020YFB1600400)+2 种基金the China Scholarship Council(202008360277)the Key Science and Technology Research Program of the Educational Department of Jiangxi Province(Grant No.GJJ200605)the Natural Science Foundation of Hunan Province(Grant No.2020JJ5783).
文摘Purpose – This paper aims to propose a medium-term forecast model for the daily passenger volume of HighSpeed Railway (HSR) systems to predict the daily the Origin-Destination (OD) daily volume formultiple consecutivedays (e.g. 120 days).Design/methodology/approach – By analyzing the characteristics of the historical data on daily passengervolume of HSR systems, the date and holiday labels were designed with determined value ranges.In accordance to the autoregressive characteristics of the daily passenger volume of HSR, the Double LayerParallel Wavelet Neural Network (DLP-WNN) model suitable for the medium-term (about 120 d) forecast of thedaily passenger volume of HSR was established. The DLP-WNN model obtains the daily forecast result byweighed summation of the daily output values of the two subnets. Subnet 1 reflects the overall trend of dailypassenger volumes in the recent period, and subnet 2 the daily fluctuation of the daily passenger volume toensure the accuracy of medium-term forecast.Findings – According to the example application, in which the DLP-WNN modelwas used for the medium-termforecast of the daily passenger volumes for 120 days for typical O-D pairs at 4 different distances, the averageabsolute percentage error is 7%-12%, obviously lower than the results measured by the Back Propagation (BP)neural network, the ELM (extreme learning machine), the ELMAN neural network, the GRNN (generalizedregression neural network) and the VMD-GA-BP. The DLP-WNN model was verified to be suitable for themedium-term forecast of the daily passenger volume of HSR.Originality/value – This study proposed a Double Layer Parallel structure forecast model for medium-termdaily passenger volume (about 120 days) of HSR systems by using the date and holiday labels and WaveletNeural Network. The predict results are important input data for supporting the line planning, scheduling andother decisions in operation and management in HSR systems.
文摘Financing of the African Integrated High-Speed Railway Network (AIHSRN) through Standard Gauge Railway (SGR) Projects is very expensive. As a result, most of the African countries seek financial supports from the International Financial Institutions (IFIs). However, conditions provided by the IFIs through the Performance Standards (PS) of the International Financial Corporation (IFC) increase cost of the projects and thus, it becomes a burden to most of the African countries. This study aimed to explore the causes of IFC-PS through the SGR Projects that escalate costs and how to address them. The Tanzania SGR Lot 1 Project that covered 205 km from Dar es Salaam to Morogoro was selected as a case study. The methods used for data collection involved literature review, focus group discussions and interviews. The results and findings show a gap between the IFC-PS and the National Laws and Regulations that escalates costs of the projects if funds from the IFIs were to be secured. To bridge the gap, it is recommended that the African countries should engage into negotiations with the IFIs to agree to waive IFC-PS conditions that escalate costs provided they are adequately covered in the national laws and regulations;engagement of locally established national and regional financial institutions;and the responsible government institutions in the African countries should sit together for assessment and review of the IFC-PS against the national laws and regulations.
基金the Department of Education of Liaoning Province(Grant No.JDL2020020)the Changzhou Applied Basic Research Program(Grant No.CJ2020007).
文摘This paper proposes an adaptive unscented Kalman filter algorithm(ARUKF)to implement fault estimation for the dynamics of high⁃speed train(HST)with measurement uncertainty and time⁃varying noise with unknown statistics.Firstly,regarding the actuator and sensor fault as the auxiliary variables of the dynamics of HST,an augmented system is established,and the fault estimation problem for dynamics of HST is formulated as the state estimation of the augmented system.Then,considering the measurement uncertainties,a robust lower bound is proposed to modify the update of the UKF to decrease the influence of measurement uncertainty on the filtering accuracy.Further,considering the unknown time⁃varying noise of the dynamics of HST,an adaptive UKF algorithm based on moving window is proposed to estimate the time⁃varying noise so that accurate concurrent actuator and sensor fault estimations of dynamics of HST is implemented.Finally,a five-car model of HST is given to show the effectiveness of this method.
基金the National Program on Key Basic Research Project of China(973 Program)under Grant No.2011CB013802the National Basic Research Program of China under Grant No.51108461 and No.51308270
文摘A dynamic model test(CL = 4) at different velocities of train,namely different loading frequencies,is carried out to study the dynamic characteristics of a high-speed railway tunnel invert and its foundation soils.Not only are the accelerations,dynamic coefficients,dynamic stresses of the invert and foundation soils emphatically analyzed,their relationship with the velocity of the train are discussed in detail.Through laboratory testing,the attenuation of vibration propagating from up the rails is obtained and the calculation formula of the speed influence coefficient of the tunnel invert is preliminarily established.The depth of the foundation soils influenced by vibration is also determined in this study.It is shown that the responses of the tunnel invert and foundation soils to vibration are slightly increased with the velocity of the train;circumferential stresses in the bottom of the invert are tensile stresses and maximum stresses appear under the foot of the rails;the dynamic soil pressures of the foundation decrease quickly with the distance away from the tunnel invert and an exponential relationship exists between them.