Hem Hunt

Stochastic modelling of traffic-induced ground vibration

Abstract In this paper an entirely analytical method of calculating the power spectrum of ground vibration in the vicinity of a busy roadway is presented. It is based on the assumption that vehicles are sufficiently closely spaced that ground vibration can be considered to be a random and statistically stationary process. The assumption is valid at distances away from the road greater than or equal to the mean vehicle spacing. Random process theory is used to obtain expressions for the power spectra of horizontal and vertical vibration when given the power spectrum of road surface roughness, a dynamic vehicle model and a model for vibration transmission through a half-space. A suitable two-axle vehicle model is discussed in an accompanying paper [19], where allowances are made for the statistical variation of vehicle dimensions, weight, suspension characteristics and distribution along the road, and in particular for the effect of wheelbase filtering. Calculated ground-vibration power spectra compare favourably with measured vibration spectra in the vicinity of a busy road near Cambridge.

Modelling of road vehicles for calculation of traffic-induced ground vibration as a random process

Abstract To predict the level of ground vibration in the vicinity of a busy roadway, dynamic vehicle models are required from which tyre forces can be calculated for a given road-surface profile. A method has been devised by which a single model of a multi-axle vehicle can be used to represent all vehicles on the road. The model accounts for variation in vehicle mass, speed and wheelbase; it relies on the assumption that all vehicles have similar characteristic frequencies and damping ratios. The effect of wheelbase filtering, where a given combination of axle spacing and vehicle speed “tunes in” to road roughness of certain wavelengths, is found to be unimportant for calculations of traffic-induced ground vibration because vehicle speeds and wheelbase lengths are sufficiently varied among vehicles on a busy road. In this paper methods of vehicle modelling appropriate for the inclusion of some statistical variation between vehicles are described, while in an accompanying paper [1] its application to the calculation of ground-vibration power spectra is discussed.

Isolation of Buildings from Ground Vibration: A Review of Recent Progress

Many buildings near railways are mounted on rubber springs to isolate them from ground vibration. This paper reviews the theory of resiliently mounted buildings and discusses recent calculations of the effects of (a) different damping models and (b) piled foundations. The paper also describes site measurements in London and laboratory tests in Cambridge which are being made to support new analytical work.

Using the PiP Model for Fast Calculation of Vibration from a Railway Tunnel in a Multi-layered Half-Space

This paper presents a new method for calculating vibration from underground railways buried in a multi-layered half-space. The method assumes that the tunnel’s near-field displacements are controlled by the dynamics of the tunnel and the layer that contains the tunnel, and not by layers further away. Therefore the displacements at the tunnel-soil interface can be calculated using a model of a tunnel embedded in a full space. The Pipe-in-Pipe (PiP) model is used for this purpose, where the tunnel wall and its surrounding ground are modelled as two concentric pipes using elastic continuum theory. The PiP model is computationally efficient on account of uniformity along and around the tunnel. The far-field displacement is calculated by using another computationally efficient model that calculates Green’s functions for a multi-layered half-space using the direct stiffness method. The model is based on the exact solution of Navier’s equations for a horizontally layered half-space in the frequency-wavenumber domain.

Modelling of floating-slab track with discontinuous slab part 1: response to oscillating moving loads

This paper presents three different methods for modelling a track with discontinuous slab under oscillating moving loads. These are the Fourier-Repeating-unit method, the Periodic-Fourier method and the Modified-phase method. The first two methods, borrowed from the literature of periodic infinite structures, are accurate if careful consideration is taken when performing numerical integrations. The third method, not presented elsewhere before, is faster and simpler; it is only valid for velocities of moving loads lower than the critical velocity of the track, but this “velocity effect” is of no consequence for underground railways. Discontinuity of slab provides a parametric excitation for moving loads over floating-slab tracks. It is shown that in the frequency range of ground-borne vibration, more vibration propagates form such tracks at resonance frequencies of the slabs, compared with tracks with continuous slabs. It is found that the velocity effect is insignificant when calculating displacements of a typical floating-slab track under oscillating moving loads with velocities less than 100km/hr. However, a correction has to be made to account for the right phase between the input force and the output displacement.

Modelling of floating-slab track with discontinuous slab part 2: response to moving trains

A floating-slab track with discontinuous slab provides a spatially-varying stiffness under a constant moving load. When a train moves on such a track, even with the absence of rail roughness, a parametric excitation develops as wheels move up and down applying dynamic forces at the wheel-rail interface. The dynamic force is magnified if one of its principal frequencies matches with any of the train or the track resonance frequencies. In this paper, a new method based on a Fourier series representation is developed to couple a moving train to a track with discontinuous slab. A two-degree-of-freedom system is used to model a quarter of a train with four axles and two bogies moving on a track with constant velocity. The purpose of this work is to investigate the dynamic effect of slab discontinuity on trains running in underground railway tunnels, where the velocity is less than 100km/hr. For typical parameters of a train and a track, it is found that the force at the wheel-rail interface is only increased by 1% of its static value due to slab discontinuity. However, the dynamic effect may be more important in circumstances where high-speed or heavy-axled trains are used in underground tunnels.

A computationally efficient piled-foundation model for studying the effects of ground-borne vibration on buildings

Abstract Understanding the effects of ground-borne vibration on buildings is becoming increasingly important as pressure grows to construct high-quality buildings on existing urban sites, which are often close to busy roads or railways. The motivation behind the work presented here is the development of a computational model that enables engineers to evaluate the effectiveness of isolating buildings. This paper presents one component of such a model, namely a new three-dimensional model for modelling the propagation of ground-borne vibration through a piled foundation. A row of piles is considered, with the piles modelled using the solutions for an elastic bar and Euler beam, and the soil represented by an elastic half-space. The model is comprehensive in that it accounts for the longitudinal and transverse motion of the piles due to both external pile-head loads and interaction between neighbouring piles through wave propagation in the surrounding soil. Computational efficiency is achieved by assuming that the row comprises an infinite number of identical piles and using a combination of the boundary element method and periodic structure theory.

On the Performance of Base-Isolated Buildings

Base isolation is a means of reducing the transmission of vibration into buildings and was first used in the 1960s. Since then many buildings have been mounted on springs of various types in order to reduce the effects of ground-borne vibration from roads and railways. For most applications, the building rests on steel springs or laminated rubber bearings. A typical objective is a reduction in vibration transmission of at least 10 dB for frequencies above 10 Hz, but, while difficult to verify, such performance is probably rarely ever achieved. Current practice suggests that the choice of spring type has a significant effect on the efficiency of the vibration isolation, as well as having implications on the cost and implementation of the system. However, there remain unanswered a number of fundamental questions concerning the specification and design of isolation bearings for buildings. For example, what is the most appropriate stiffness of the bearings for a given application and to what extent is damping an important part of a good system? This paper reviews current methods of predicting isolation performance and introduces an alternative model which aims to model more fully the behaviour of base-isolated buildings. The benefits of a power-flow approach in assessing isolation performance are also discussed and it is argued that this enables a more appropriate measure of performance to be defined than one based on vibration amplitudes alone.

A generic model for evaluating the performance of base-isolated buildings

Ground-borne vibration has existed ever since the development of urban road and rail networks. Vibration generated by the moving traffic propagates through the ground and into buildings, resulting in unacceptable levels of internal noise and vibration. A common solution to this increasingly significant problem is the base-isolation of buildings by incorporating vibration isolation bearings between the buildings and their foundations. This technique has been employed for over forty years but the exact performance of base isolation remains uncertain. This paper describes a generic computational model; generic in that it accounts for the essential dynamic behaviour of a typical base-isolated building in order to make predictions of isolation performance. The model is a linear one, formulated in the frequency domain, and consists of a two-dimensional portal-frame model of a building coupled to a three-dimensional boundary-element model of a piled-foundation. Both components of the model achieve computational efficiency by assuming they are infinitely long and using periodic structure theory. Following an overview of the model, a virtual case study is presented to illustrate its practical application. Along with some initial observations, the case of a point-load surface excitation of the foundation is used to investigate the isolation performance of typical isolation bearings.

Types of Rail Roughness and the Selection of Vibration Isolation Measures

A procedure is outlined for quantifying the significance of various types of rail roughness for the purposes of predicting and controlling low-frequency ground vibration near railway lines. The effectiveness of resilient elements inserted beneath the rail is investigated. It is found that roughness mechanisms can be classified according to the effectiveness of added resilience. Vibration from a track with “Class A” roughness will be well controlled by resilient rail support; a track with “Class B” roughness cannot be controlled; and vibration from a track with “Class C” roughness will be increased. Examples of “Class A” roughness are those due to variations in trackbed roughness and in rail-support stiffness and these can be controlled through the insertion of additional under-rail resilience. The reduction in roughness level can easily result in a 10dB reduction in perceived roughness down to 5Hz for an urban metro system. This reduction is additional to any reduction due to the mass-on-spring effect of the unsprung mass on its resilient track. This not only explains the good insertion performance often measured of under-rail countermeasures, but also why there is often far less amplification at the track-system resonance than might otherwise be expected. In some cases the effect of adding resilience has less effect than in others. For example there is no beneficial effect found for the case of roughness due to a rail that is naturally bent (a condition built-in after leaving the rail-straightener in the rolling mill).