摘要
高速公路沥青混凝土路面是由骨料、沥青胶浆和空气组成的双相介质。骨料、沥青胶浆和空气的体积不等、形状各异、介电性质不同,在空间上随机分布。这类介质相对于高频电磁波波长来说,物性参数变化剧烈,是典型的随机介质。高频电磁波在随机介质中传播时,会发生散射,造成大量的不相干波至,导致接收波形也具有相应的随机特征。由于路用探地雷达天线的主频比较高,探测波长较短,散射相对较大,使得介质介电特性在空间上随机分布引起的波场变化被相对放大。因此,建立符合实际公路工程材料的随机介质模型,研究随机介质模型参数及其与之相关的探地雷达波场变化规律,是定量评估公路工程介质材料的物质基础。另外,探地雷达应用于公路结构层质量无损检测时,其探测对象是深度在一米以内,甚至在几厘米以内的极浅层介质,这是典型的近场问题。因此,建立探地雷达蝶形天线的数学模型,研究其辐射特性及其在随机介质中的电磁场近场特征,是提高探地雷达的探测效果和解释准确性的理论基础。
本文在建立符合沥青混凝土实际情况的双相离散随机介质和探地雷达蝶形天线数学模型的基础上,研究了探地雷达波场特征与双相离散随机介质参数、工程材料电性参数、典型工程缺陷之间的对应关系。本文的主要研究工作及其成果包括：
1.采用时域有限差分方法设计并实现了适用于随机介质的探地雷达三维正演数值模拟算法,为分析随机介质中的探地雷达波场提供了有力工具；
2.基于商用探地雷达平面蝶形天线的几何尺寸、电阻加载方式、激励及屏蔽吸波机理,采用时域有限差分方法建立了商用探地雷达蝶形天线的三维模型,通过三维数值模拟研究了蝶形天线几何学特征、电阻加载、屏蔽腔和吸波材料、介质介电特性等对蝶形天线辐射的影响,为验证、改进探地雷达蝶形天线的辐射性能提供科学依据；
3.采集了12个高速公路沥青混凝土芯样,实验测量了其组成材料的介电常数,分析了沥青混凝土路面不同结构层介电常数的空间随机分布特征,计算了其自相关函数,并估计了自相关长度、自相关角度,确定了其随机介质类型：通过改进随机介质建模方法,建立了多个符合沥青混凝土路面不同结构层介质实际情况的双相离散随机介质模型,为三维正演数值模拟探地雷达高频电磁波在沥青混凝土介质中的波场传播特征提供了基础,同时该项研究成果也为探地雷达资料的解释和反演提供了新的理论基础；
4.通过基于双相离散随机介质模型的三维探地雷达波场的数值模拟,检验了二种基于组成材料介电常数及其体积含量百分比的混合物等效介电常数计算模型的正确性和准确性：
5.模拟实际沥青混凝土路面结构及其组成材料,建立了不同空隙率的双相离散随机介质模型,通过三维数值模拟研究了沥青混凝土各结构层不同空隙率对探地雷达波场特征的影响,提出了定量计算沥青混凝土路面不同结构层的空隙率的方法,为探地雷达定量检测沥青混凝土路面不同结构层的空隙率提供了理论基础；
6.研究了双相离散随机介质中不同宽度的垂向裂缝、不同厚度的层间脱空相应的探地雷达波场变化规律,为定量计算裂缝的宽度、层间脱空的厚度提供了科学依据。
本文以“基于随机介质的高速公路探地雷达检测理论研究”为中心,全文共分六章：
第一章为绪论。简要地阐述了本文研究的目的和意义,分析了国内外研究现状及存在的问题,详述了本文的研究目标、研究内容、研究方案、主要研究成果及创新点；
第二章主要介绍探地雷达的理论基础与数值模拟方法。简要介绍了探地雷达系统组成与电磁波的基本传播理论,讨论了时域有限差分原理、迭代公式、数值稳定性与数值色散条件等,着重推导了UPML吸收边界条件的迭代公式,最后通过实例展示了UPML吸收边界条件的有效性；
第三章主要讨论探地雷达蝶形天线的数值模拟方法。分析了探地雷达蝶形天线所具有方向性、极化特性、振铃效应、屏蔽设计以及地下介质对蝶形天线的加载作用等特点；根据商用蝶形天线的几何学特征、激励波形、电阻加载方式及屏蔽吸波机理建立了其时域有限差分模型；数值模拟了蝶形天线的几何学特征、电阻加载方式、屏蔽吸波材料,天线离地高度和地下介质介电特性对蝶形天线辐射特性的影响；
第四章为沥青混凝土介质类型与特征及其建模研究。根据不同沥青混凝土路面结构层芯样测量结果及其横、纵切片的介电常数分布图,研究了沥青混凝土路面不同结构层介电常数在空间上的随机分布特征,估算了其自相关长度、自相关角度及自相关函数的类型：提出了双相离散随机介质的建模方法,建立了不同沥青混凝土路面结构层的双相离散随机介质模型；
在第五章中,针对不同空隙率的沥青混凝土双相离散随机介质模型,采用线性模型、CRIM模型估算了不同空隙率的双相离散随机介质模型等效介电常数,并对空隙率=4%的双相离散随机介质及其相应的等效介电常数均匀介质进行了基于探地雷达蝶形天线的三维正演数值模拟,对比了双相离散随机介质和均匀介质的探地雷达波场特征,同时验证了等效介电常数估算结果的准确性。基于探地雷达蝶形天线的波场特征,提出了定姑计算不同高速公路沥青混凝十路面结构层空隙率的方法；研究了双相离散随机介质中裂缝宽度与其顶部中点处振幅强度之间近似线性的变化规律；研究了双相离散随机介质中层间脱空厚度与其反射波振幅强度之间的对应变化规律,为定量计算裂缝宽度、层间脱空厚度提供了科学依据：
第六章为本文的最后一章,全面总结了本文的主要工作成果与结论,阐述了研究中存在的问题及以后的研究方向。
本论文的原创性工作主要表现在三个方面：
1.本文首次将沥青混凝土视作随机介质,研究了其介电常数在空间上的随机分布特征,确定了其随机介质类型,提出了双相离散随机介质模型的构建方法。经数值模拟验证,这种双相离散随机介质模型不仅能较好模拟沥青混凝土介质的结构,由此所估计的等效介电常数,以及电磁波在其中的传播特征都比较符合实际探地雷达测量结果,这一工作为高速公路沥青混凝土路面的质量检测提供了理论依据,也为类似介质或材料的研究开辟了新的途径；
2.提出了基于探地雷达蝶形天线的波场特征定量计算不同沥青混凝土结构层的空隙率的方法,探地雷达物理实验证实了其正确性,这对探地雷达定量化检测高速公路沥青混凝土路面质量具有重要意义；
3.采用以商用探地雷达蝶形天线作为激励源的探地雷达三维正演数值模拟方法,研究了双相离散随机介质中裂缝的宽度、层间脱空的厚度变化与其探地雷达波场之间的对应变化规律,为定量估算裂缝宽度、层间脱空厚度提供了科学依据。
Asphalt concrete pavement of highway is a kind of two-phase medium, which is composed of aggregate, asphalt mortar and air. Aggregate, asphalt mortar and air usually have different sizes, shapes, dielectric properties, and distribute randomly in space. Relative to the wavelength of high-frequency electromagnetic wave, the physical properties of this typical random medium change dramatically. Scattering will happen when high-frequency electromagnetic wave propagates in random medium, and would cause a lot of irrelevant wave arrival, which result in that the being received waveform also has corresponding random characteristics. Due to high dominant frequency of the antenna of Ground Penetrating Radar (GPR), Radar wave has the short wavelength and big scattering, which make the changes of wave field caused by the random distribution of medium's dielectric properties bigger relatively. So reconstructing the random medium model to approximate actual engineering material, and researching parameters of random medium model and the change law of GPR wave field associated with these parameters are the physical basis for the quantitative evaluation of highway engineering dielectric materials. Besides, when GPR is applied to the nondestructive testing on the quality of the road structural layer, its detecting object is very shallow medium whose depth is less than one meter, even within a few centimeters, which is a typical near-field problem. Therefore, building the model of the bow-tie antenna of GPR and studying its radiation and electromagnetic near-field characteristics in random medium is the theoretical basis of improving the effect and interpretation of ground penetrating radar detection.
This work proposes a two-phase discrete random medium that is in line with the physical truth of asphalt concrete and constructs the numerical model of the bow-tie antenna of GPR. Then, the typical corresponding relationships between the wave field characteristics of GPR and the parameters of the two phase discrete random medium, or the electrical parameters of engineering materials, or the typical engineering defects are studied. The main research and their results are as follows:
1. A numerical simulation algorithm is designed and implemented using finite-difference time-domain (FDTD) method. This algorithm is based on Maxwell equations and it can be applied to problems of the excitation and the propagation process of GPR electromagnetic waves in random medium. It provides a powerful tool for analyzing the GPR wave field in random medium.
2. A finite difference time domain (FDTD) model of commercial bow-ties antenna of ground penetrating radar is set up based on the geometry of the commercial bow-tie antenna, the way of resistive loading, the excitation and the shielding of absorbing mechanism. The effects of the geometry of bow-tie antenna, resistive loading, shielding cavity, wave-absorbing material, and the dielectric characteristics of media on the radiation of the bow-ties antenna are studied through3D numerical simulation, which provides a scientific basis for verifying and improving the radiation performance of GPR bow-ties antenna.
3.12core samples of asphalt concrete are collected from highways, and the dielectric constant of these samples" ingredient are measured. By analyzing spatial random distribution characteristics of the dielectric constants of core samples from different structural layers of asphalt concrete pavement. I calculated their autocorrelation functions of random media and estimated their autocorrelation lengths and autocorrelation angle, also classified the type of random media:Then I constructed several models of two-phase discrete random media corresponding to different structural layer media of asphalt concrete pavement by improving the random medium modeling method. The research results provide new theoretical basis for the interpretation and inversion of GPR data.
4. Through the3-D numerical simulation of Ground-penetrating radar wave field, we tested the correctness and accuracy of two kinds of model of CRIM and linear approach for estimating the effective dielectric constants of two-phase random media based on volume percentages of components within materials.
5. Through of simulating the real asphalt concrete pavement structure and its constituted materials. I constructed the two-phase discrete random medium models with the different void ratio. Then I also studied the effect of asphalt concrete layers of different porosity to GPR wave Held characteristics based on the3-D numerical simulation, and proposed the method to estimate quantitatively void ratio of different structure layer. All of these studies provide theoretical foundation for the quantitative detection of void ratio of asphalt concrete pavement structure using GPR.
6. The variation of GPR wave Held caused by the different width vertical crack and different thickness of the interlayer cavity in two-phase discrete random media are studied, which put forward a scientific basis for quantitative estimation of crack width and thickness of the interlaver cavity.
The full text is divided into six chapters.
The llrst chapter is introduction which briefly describes the purpose and significance of this study. The research status in domestic and foreign and the existing problems are analyzed, and also the research objectives, research contents, research programs, the main research results and my innovations are presented.
The second chapter mainly states the basic theory and numerical simulation method of the ground penetrating radar, as well as GPR system. The theory of finite difference in time domain, iterative formula, numerical stability and numerical dispersion conditions are discussed, and the iterative formula of UPML absorbing boundary condition is deduced. Finally, a few of examples show the validitv of the UPML absorbing boundary condition.
The third chapter mainly discusses the numerical simulation method of GPR bowtie antenna. The characteristic of GPR bowtie antenna, such as the direction, polarization, ringing effect, shielding design and the bowtie antenna loading on underground media are analyzed. According to the specification of bowtie antenna, for example, geometry, excitation waveform, and the load resistance. I established the Unite difference time domain model of the bowtie antenna, and simulated the effect of the bowtie antenna radiation to its geometry, the change in load resistance, the height of gap from antenna to the ground and the dielectric property of underground medium.
The fourth chapter is the research on types and characteristics of the asphalt concrete medium, and its modeling. According to the measurements of asphalt concrete core samples and the distribution of dielectric constant within the transverse and vertical section. I studied the characteristics of spatial random distribution of dielectric constants, such as autocorrelation length, angle and the type of autocorrelation function, in the different structural layer of the asphalt concrete pavement. I suggested the modeling method of two-phase discrete random medium, and established a few of the two-phase discrete random medium models for different structural layer of asphalt concrete pavement.
In the fifth chapter, assuming that asphalt concrete is two-phase discrete random medium, the CRIM model compared with linear model to estimate the effective dielectric constant for different porosity of asphalt concrete is more accurate. I also compared characteristics of ground-penetrating radar field between in two-phase discrete random media and in the effective homogeneous medium using three-dimensional numerical simulation. That proved the accuracy of the effective dielectric constant estimation. Quantitative method to estimate the porosity of pavement structural layer is proposed; Study on the relationship between the crack width and radar wave amplitude deduced a conclusion of approximate linear relationship. A similar linear relationship between the thickness of void-layer and the maximum reflection amplitude is got. These results provide scientific basis for quantitative estimation of the crack width and void-layer thickness.
Last chapter is the sixth chapter, which comprehensively summarizes my main work and the problems to be solved in the study and the future research directions.
The originality of my doctoral work mainly concludes the following three aspects:
1. The paper firstly regards asphalt concrete as medium containing randomly distributed dielectric composite in space. I studied the random distribution feature of asphalt concrete media, further confirmed the type of random media and suggested a method of modeling two-phase discrete random media. This model of two-phase discrete random medium tested by numerical simulation can simulate the interior structure of asphalt concrete medium. Thereby, the effective dielectric constant estimated from that and the characteristics of electromagnetic wave propagation in this random media are accordant with the actual measurements of ground-penetrating radar. This study provides a theoretical basis for the quality testing of asphalt concrete highway and paves a new way for studying similar media or materials.
2. A quantitative method is proposed to calculate the void ratio of structure layer of asphalt concrete based on the wave field characteristics of the ground-penetrating radar of bowtie antenna. The ground-penetrating radar physical experiments prove that is correct and reliable, which has important significance for quantitative detecting the quality of asphalt concrete highway.
3. The influence on the ground-penetrating radar field, caused by the width of the crack or thickness of void-layer in the two-phase discrete random media is studied using3D numerical GPR simulation method with the commercial bowtie antenna as excitation source, which shows approximate line relationship between maximum amplitude of radar wave and with either crack width or void-layer thickness.
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