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1、7钢筋混凝土路面的探地雷达数值模拟研究基金项目:国家自然科学基金资助项目(41374118,41074085);高等学校博士学科点专项科研基金项目(20120162110015),湖南省自然基金项目(13JJ5006)作者简介:戴前伟(1968-),男,教授,博导,主要从事电磁法方法及理论研究,E-mail:qwdai@mail.csu.edu.cn;*通讯作者:张彬(1984-),男,汉族,博士,电话:0731-88830217;E-mail:geophysic@csu.edu.cn摘要运用K.S.Yee建立的离散电场、离散磁场网格,采用二阶时间精度和二阶空间精度的中心隐式差分方程代
2、替Maxwell微分方程,设置传统的完全匹配层(PerfectlyMatchedLayer)吸收边界条件(AbsorbingBoundaryCondition)和Gauss脉冲源后,得到探地雷达(GroundPenetratingRadar)时域有限差分(FiniteDifferenceTime-Domain)正演推导方程组,编写了探地雷达二维Matlab正演程序,对几类典型的复杂钢筋混凝土路面模型进行了正演数值模拟,取得了较满意的效果,并对该正演数据的偏移结果进行了分析,同设置的实际模型相比较,表明了探地雷达高频天线的理论纵横向分辨率与实际模型中钢筋网的具体分布密度和型号有关,为以后
3、相关的复杂钢筋混凝土路面及缺陷探地雷达检测提供较好的参考。关键词钢筋混凝土路面;分辨率;探地雷达;时域有限差分;数值模拟StudyofGPRsimulationforreinforcedconcretepavementDAIQian-wei1,2,ZHANGbin1,2,YINXiao-bo1,31.SchoolofGeosciencesandInfo-Physics,CentralSouthUniversity,Changsha,410083,China;2.KeyLaboratoryofMetallogenicPredictionofNonferrousMetals,Ministr
4、yofEducation,Changsha410083,China;2.HunanZhongdaConstructionEngineeringTechniqueTestCo.Ltd.,Changsha,410205,ChinaAbstract:UsingthediscreteelectricandmagneticfieldofYee′sgrid,withsecondordertimeandspatialaccuracyoftheimplicitdifferenceequationinsteadofMaxwelldifferentialequations,settingthetradit
5、ionalPerfectlyMatchedLayerAbsorbingBoundaryConditionandtheGausspulsesource,derivingtheFiniteDifferenceTimeDomainofGroundPenetratingRadarforwardmodelingequations,writingatwo-dimensionalGPRforwardMatlabprogramforavarietyoftypicalreinforcedconcretegeoelectricmodelforwardnumericalsimulation,andsatis
6、factoryresultswereobtained,withthemigrationresultsoftheforwardmodelingdata,comparedwiththesetofactualmodel,itindicatesthatthehorizontalandverticalresolutionofhighfrequencyantennatheoryisrelatedwiththedistributiondensityofbar-matreinforcementinthepracticalmodel,whichcouldprovideapreferablereferen
7、ceforanycomplexreinforcedconcretepavementanddrawbackdetectionwithGPR.KeyWords:reinforcedconcretepavement;resolution;GroundPenetratingRadar;FDTD;Numericalsimulation1.引言目前,基于波动方程理论的探地雷达正演模拟已发展较为成熟,而时域有限差分法以其节约计算时间和存储空间、直接时域范围计