Abstract This article lays out a unified theory  for dynamics of vehicle–pavement interaction under moving and stochastic loads. It covers three major aspects of the subject: pavement surface, tire–pavement contact forces, and response of continuum media under moving and sto- chastic vehicular loads. Under the subject of pavement surface, the spectrum of thermal joints is analyzed using Fourier analysis of periodic function. One-dimensional and two-dimensional random field models of pavement surface are discussed given three different assumptions. Under the subject of tire–pavement contact forces, a vehicle is mod- eled as a linear system. At a constant speed of travel, random field of pavement surface serves as a stationary stochastic process exciting vehicle vibration, which, in turn, generates contact force at the interface of tire and pavement. The contact forces are analyzed in the time domain and the frequency domains using random vibration theory. It is shown that the contact force can be treated as a nonzero mean stationary process with a normal distribu- tion. Power spectral density of the contact force of a vehicle with walking-beam suspension is simulated as an illustration. Under the subject of response of continuum media under moving and stochastic vehicular loads, both time-domain and frequency-domain analyses are presented for analytic treatment of moving load problem. It is shown that stochastic response of linear continuum media  subject to a moving stationary load is a nonstationary  process. Such a nonstationary stochastic process can be converted to a stationary stochastic process in a follow-up moving coordinate.

Keywords Vehicle–pavement interaction · Random field · Continuum medium · Spectral analysis · Green’s function · Linear system

1 Introduction

The investment of the United States in the nation’s trans- portation infrastructure alone (highways, bridges, railways, and airports) amounted to $7 trillion by 1999. To preserve infrastructure longevity in a cost-effective manner, the research in pavement design and infrastructure manage- ment has been growing rapidly in recent years. From a pavement design point of view, pavement response, dam- age, and performance are essentially the result of long-term vehicle–pavement interaction. When vehicle speed is low, the dynamic effect of vehicular loads on pavements is insignificant. However, with the promotion of high-speed surface transportation in the world, this dynamic effect must be taken into account to develop more rational pavement design methods. For instance, real causative mechanisms that lead to fatigue damage of pavement material might be frequency dependent. From an infra- structure management point of view, vehicle–pavement interaction has a profound impact on the way that existing technologies of structural health monitoring, environmental vibration mitigation, nondestructive testing and evaluation, and vehicle weight-in-motion are to be improved, inno- vated and implemented. For instance, modern high-speed surface transportation systems are normally accompanied by rises in levels of noise and vibration that may cause a significant detrimental effect to the ecology. Vehicle– pavement interaction-induced structure-borne and ground- borne vibrations emit and propagate toward some extent. Residents may experience hardship from uncomfortable vibration, and high-precision equipment may suffer from malfunctioning to irreparable damage. To mitigate noise and vibration in surrounding areas of roadway, it is nec- essary to investigate predominant frequencies of vehicle– pavement interaction, the source of vibration, so as to develop effective noise and vibration countermeasures. The study of vehicle–pavement interaction also plays a critical role in developing better inversion algorithms for nonde- structive testing and evaluation of transportation infra- structure. In addition, taking into account dynamic effects of vehicle vibration caused by rough surface may consid- erably improve accuracy and reliability of weigh-in-motion systems, which measure a vehicle’s weight as it travels at a normal speed.