BEHAVIOUR OF TRACK STRUCTURE UNDER STATIONARY AND MOVING VERTICAL WHEEL LOADS

Abstract

To cope with the increased traffic and goods with regards to speed and loading, the stress variation in various components must be known accurately to evaluate useful life of each component and may provide guidance for its life assessment and therefore, the replacement of components after its useful life so as to have a more scientific maintenance of the track structure. To asses this, detailed analysis is necessary to develop the methodology of the design of various components of track structure under actual loading conditions. It is therefore, important to determine the behaviour of track structure, stresses in its components and finally its useful life. The track structure comprises of rail, rubber pad, sleeper, elastic fastenings, ballast and subgrade and these are used in the mathematical modelling of the track structure. A comprehensive and systematic investigation on the behaviour of track structure under stationary and moving vertical wheel loads is carried out and is summarised below. A critical review on the performance of various available models of vehicle and track structure developed is made. The finite element technique is adopted for the static analysis of track structure artd for dynamic analysis, the vehicle-track structure is idealised with spring-mass-dashpot system so that the role of each component can be identified while carrying out the parametric studies. Behaviour of track structure under stationary vertical wheel loads: Initially the rail seat loads have been determined by using the track modulus (TM) method as a first step. The stress analysis of three different track structures under stationary vertical wheel loads is carried out. Each track structure is idealised as (i) three dimensional, (ii) two dimensional plane strain and (iii) quasi-three dimensional problem using finite element modelling technique. The validation of computed results is carried out and is found in good agreement with the available test data and three models (MULTA, PSA and ILLITRACK). The Q3D IV analysis of longitudinal section of track structure using 20 degree angle of distribution (9) gives very close results to that of 3D analysis and it takes very less time for the input data preparation and computation than that of 3D analysis. The present investigations reveal that the role of sleeper and level filling of ballast is significant in the distribution of vertical displacement and stress of track structure. The bearing area of sleeper inside and outside the rail plays an important role and because of high relative stiffness of prestressed concrete sleeper, the punching shear phenomenon distributes the load through the ballast in between the sleeper and outside the sleeper. A detailed distribution of bearing stresses under the sleeper has been determined alongwith proper modified rail seat reaction for proper design of pad and clip. The parametric investigations are carried out and it is concluded that the increase in the moment of inertia of rail section, thickness of ballast and modulus of elasticity of subgrade soil decrease the static vertical displacement and stress in the different components of track structure except the static vertical stress in subballast and subgrade soil which increases with the increase of modulus of elasticity of subgrade soil. Behaviour of track structure under moving vertical wheel loads: A simple discrete-lumped-parameter mathematical model of track structure for dynamic analysis has been developed using a track element with three degrees of freedom (vertical displacement and rotation at the ends of rail and vertical displacement of sleeper) per node. This model includes the effect of rail clips which was not considered in the previous models. The equations of motion and matrices for track element are formulated. The rail is represented in two form: (i) an Euler beam and (ii) a Timoshenko beam which includes the effect of rotary inertia and shear deformation of rail. The development of computational algorithm for frequency domain analysis of track structure is carried out to compute the natural frequencies and associated normal modes, receptance and phase lag of track structure. The mathematical model of track structure developed is validated with the classical problem of beam on elastic foundation. The VI fundamental frequency of track structure is computed, which is found to be very close to the observed value. It is observed that there are three distinct zones of natural frequencies. The first mode (fundamental mode) is predominantly translational mode of rail. The second mode is rocking mode of rail where as other modes are bending mode of the rail. There are two regions of locally high receptance, one at approximately 31.33 Hz (resonance frequency) and the other about 470.0 Hz, separated by a region of low receptance around 190.0 Hz. The peak value of receptance of track structure is achieved at the resonance frequency in each case. The trend of the calculated receptance of track structure is the same for that theoretically calculated and experimentally observed by the other investigators. The parametric study shows that the influence of shear deformation, rotary inertia and length of rail is negligible on fundamental frequency, receptance and phase lag of the track structure. The fundamental frequency of track structure is also obtained same for all values of equivalent stiffness of pad, clip and sleeper (k ) and spacing of sleeper. It increases by the increase in equivalent stiffness of ballast and subgrade (k ) and reduces by the increase in mass of sleeper (m ). The natural frequencies of track structure upto 66 modes (zone-I) are uniformly decreased by the increase in m . The natural frequencies of track structure in zone-I (1 to 66 modes) tend to be constant by increasing the value of k and by decreasing the value of k . The mass of sleeper and the stiffness k do not change the natural frequencies of track structure in the zone-II (67 to 133 modes) and zone-Ill (134 modes onwards). The frequencies of track structure in all three zones reduce by increasing the spacing of sleeper. Four basic parameters namely vertical profile, cross level, gauge and alignment to describe the track have been identified. The PSD representation of track irregularities has been computed and plotted at four different speed of vehicle. The peak value of PSD for vertical profile, cross level and alignment track irregularities reduces with higher speed of vehicle. The PSD of gauge does not show significant variation with speed of vehicle. Vll For dynamic analysis, three vehicle models are developed to carry out the coupled time domain analysis of vehicle-track structure (i) one wheel axle vehicle (3 d.o.f.), (ii) two wheel axle vehicle (6 d.o.f.) and (iii) four wheel axle vehicle (10 d.o.f.). The dynamic equilibrium equations have been formulated to study the coupled behaviour of the vehicle and the two layer track structure modelled. The Newmark's predictor-corrector implicit scheme is adopted and computational algorithm is presented to solve the problem of dynamic interaction of vehicle-track structure. The validation of the developed mathematical models of vehicle-track structure is performed. The computed root mean square (rms) values and PSD of vertical acceleration at the CG of coach body of three vehicle model are compared with that of field measured data. The four wheel axle vehicle model gives the rms value close to the observed field value. The response of vertical displacement and force at the wheel-rail contact are determined for the first time and plotted under different wheels. Based on these contact forces, the dynamic augment factor is computed. The major conclusions based on parametric investigations carried out on the above vehicle-track structure are (i) the deflection of rail and sleeper and bending moment in rail decrease by increasing the damping of the track structure. These also increase with the increase in vehicle speed. (ii) The rms value of acceleration of coach body increases by increasing the speed of vehicle upto 150.0 kmph and at higher than this speed it reduces, (iii) The spacing of sleeper is significant for bending moment in rail only. The bending moment increases with the increase in the sleeper spacing, (vi) The dynamic response of track structure reduces with increasing values of equivalent stiffness of clip, pad, sleeper, ballast and subgrade. Finally, three software packages have been developed in FORTRAN language and using Starbase graphics libraries (on UNIX based HP 9000/330 computer) for computation of responses of the track structure under static and dynamic conditions. These are: (i) SATRACKS (Static Analysis of TRACK Structure), (ii) DATRACKS (Dynamic Analysis of TRACK Structure) and (iii) PLTRACKS (PLot the TRACK Structure).