Study on Multiphase Discrete Random Medium Model and its GPR Wave Field Characteristics

Abstract

AbstractAsphalt concrete is a typical multiphase discrete random medium, which is composed of aggregate, asphalt mortar and air with different volume fraction. Aggregate, asphalt mortar and air usually have different sizes, shapes, dielectric properties, and distribute randomly in space. This paper is based on random medium theory, (1) we measured the dielectric constants of the asphalt concrete samples, and computed the statistical characteristics (such as mean values, standard deviations) of spatial random distribution of dielectric constants and the volume fraction of each component; (2) we calculated the autocorrelation function of asphalt concrete based on Wiener‐Khintchine theorem, and extracted its characteristic parameters (such as autocorrelation length, autocorrelation angle), and then classified the type of random media; (3) we developed the modeling algorithm of multiphase discrete random medium under quantization constrain, and constructed multiphase discrete random medium model based on intermixed elliptic autocorrelation function. Additionally, we studied the propagation characteristics of ground penetrating radar wave in multiphase discrete random medium model and compared the model with homogeneous medium model and continuous random medium model using numerical simulation. The calculated results show that the autocorrelation functions of a large number of asphalt concrete sections are approximate to ellipsoidal autocorrelation functions, which provide the foundation for using random medium theory to describe asphalt concrete. The multiphase discrete random medium model not only describes the statistical characteristics of spatial random distribution of asphalt concrete, but also describe the volume fractions of its compositions. For multiphase discrete random medium model and continuous random medium model, ground penetrating radar wave has strong scattering phenomenon. Random and disorderly scattering waves overlie and interfere with each other, which resulting random perturbations and noise in received waves. The reflected waves from anomalous body are with distortion and discontinuity and reduce the signal to noise ratio and resolution of ground penetrating radar data. When multiphase discrete random medium model and continuous random medium model have the same given model parameters, ground penetrating radar waves have stronger scattering in continuous random medium model. The study reveals that the multiphase discrete random medium model can describe asphalt concrete more comprehensive and precise than homogeneous medium model and continuous random medium model. The multiphase discrete random medium model also provides a new way for studying similar media or materials. The radar profile is more consistent with the field measured data, and more conducive to guide the interpretation of the ground penetrating radar profile data.