發(fā)布時(shí)間：2018-02-24 19:13

  本文關(guān)鍵詞： 探地雷達(dá) 有限單元法 透射邊界條件 數(shù)值模擬 非結(jié)構(gòu)化網(wǎng)格　出處：《湖南科技大學(xué)》2017年碩士論文　論文類型：學(xué)位論文

【摘要】：對(duì)于實(shí)際的地球物理模型的數(shù)值模擬,網(wǎng)格的劃分對(duì)于擬合地球物理模型具有十分重要的意義。它直接影響著有限元數(shù)值模擬的求解效率以及計(jì)算精度。一般情況下,網(wǎng)格生成技術(shù)可以分為結(jié)構(gòu)化網(wǎng)格和非結(jié)構(gòu)化網(wǎng)格兩大類。結(jié)構(gòu)化網(wǎng)格具有統(tǒng)一的結(jié)構(gòu)特點(diǎn),生成速度快,結(jié)構(gòu)單一,但是不能夠滿足復(fù)雜的地球物理模型的數(shù)值模擬。目前,非結(jié)構(gòu)化網(wǎng)格劃分技術(shù)在探地雷達(dá)的有限元數(shù)值模擬中應(yīng)用的較少,相關(guān)的研究文獻(xiàn)也相對(duì)較少。因此,本文研究了三角形非結(jié)構(gòu)化網(wǎng)格下的探地雷達(dá)有限元數(shù)值模擬,并且建立了多種地球物理模型,進(jìn)行了二維GPR有限元數(shù)值模擬、分析,歸納總結(jié)了雷達(dá)波在不同地質(zhì)地球物理模型中的傳播規(guī)律,對(duì)實(shí)際資料的解釋工作具有十分重要的意義。本文在前人研究的基礎(chǔ)上,重新推導(dǎo)了基于三角形網(wǎng)格劃分的探地雷達(dá)有限元波動(dòng)方程,并詳細(xì)的給出了波動(dòng)方程的解法。在數(shù)值模擬計(jì)算中,對(duì)加載透射了邊界條件和沒有加載透射邊界條件的均勻模型開展了數(shù)值模擬,分析了透射邊界的處理效果;簡(jiǎn)要分析了雷達(dá)波在介質(zhì)水和空氣的傳播規(guī)律,分析了其中的差異;建立了道路路基病害模型、隧道地質(zhì)超前預(yù)報(bào)模型以及頂管脫空模型等數(shù)學(xué)物理模型,分析了雷達(dá)波在不同模型中的傳播規(guī)律。通過數(shù)值模擬可以發(fā)現(xiàn):透射邊界條件能夠很好的抑制模型邊界處所產(chǎn)生的干擾波;可以通過雷達(dá)波在介質(zhì)中傳播的多次反射波特征來區(qū)別介質(zhì)水和介質(zhì)空氣;通過隧道地質(zhì)超前預(yù)報(bào)與實(shí)測(cè)數(shù)據(jù)相結(jié)合,對(duì)于更好的判斷雷達(dá)波在此類模型中的傳播特點(diǎn)提供依據(jù);通過對(duì)頂管脫空模型的進(jìn)行數(shù)值模擬,發(fā)現(xiàn)探地雷達(dá)對(duì)于水泥混凝土頂管脫空能夠取得很好的探測(cè)效果,對(duì)于鋼頂管的脫空效果并不明顯,與實(shí)測(cè)效果相符合。通過減小鋼頂管壁的厚度,能夠?qū)γ摽涨闆r進(jìn)行探測(cè),但是效果并不明顯。研究表明:非結(jié)構(gòu)化網(wǎng)格對(duì)于物性參數(shù)復(fù)雜的的地球物理模型具有很好的適應(yīng)性;非結(jié)構(gòu)化網(wǎng)格剖分的質(zhì)量好,單元易于控制,能夠很好的實(shí)現(xiàn)自適應(yīng)有限元,提高數(shù)值模擬的精度。
[Abstract]:For the numerical simulation of the actual geophysical model, the mesh division is very important for fitting the geophysical model. It directly affects the efficiency and accuracy of the finite element numerical simulation. Grid generation technology can be divided into structured grid and unstructured grid. Structured grid has the characteristics of uniform structure, fast generation speed and single structure, but it can not satisfy the numerical simulation of complex geophysical model. The unstructured mesh generation technique is seldom used in the finite element simulation of ground penetrating radar, and the related literatures are relatively few. Therefore, the finite element simulation of ground penetrating radar under triangular unstructured mesh is studied in this paper. Several geophysical models are established, 2D GPR finite element numerical simulation is carried out, and the propagation law of radar waves in different geophysical models is summarized. The interpretation of practical data is of great significance. Based on the previous studies, the finite element wave equation of ground penetrating radar based on triangular mesh division is rederived in this paper. The solution of wave equation is given in detail. In the numerical simulation, numerical simulation is carried out for the uniform model with and without the loading transmission boundary condition, and the processing effect of the transmission boundary is analyzed. The laws of radar wave propagation in medium water and air are analyzed briefly, and the difference between them is analyzed, and mathematical and physical models such as road subgrade disease model, tunnel geological advance prediction model and pipe jacking void model are established. The propagation law of radar wave in different models is analyzed. The numerical simulation shows that the transmission boundary condition can suppress the interference wave generated at the boundary of the model very well. It is possible to distinguish medium water from medium air by the characteristics of multiple reflection waves of radar wave propagating in medium, and combine tunnel geological advance prediction with measured data. Through numerical simulation of pipe jacking model, it is found that ground penetrating radar can achieve good detection effect for cement concrete pipe jacking. The emptying effect of steel jacking pipe is not obvious, which is consistent with the measured results. By reducing the thickness of steel jacking pipe wall, the void situation can be detected. But the effect is not obvious. The results show that the unstructured meshes have good adaptability to geophysical models with complex physical parameters, and the unstructured meshes are of good quality and easy to control. It can realize adaptive finite element well and improve the accuracy of numerical simulation.
【學(xué)位授予單位】：湖南科技大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：P631

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本文編號(hào)：1531385