本文選題：裂隙 + 閔可夫斯基函數(shù)�。� 參考：《寧夏大學(xué)》2017年碩士論文

【摘要】：目前,土壤干縮裂隙的發(fā)展規(guī)律以及形成機(jī)理尚不明確,為揭示農(nóng)田土壤表面干縮裂隙發(fā)展規(guī)律以及形成機(jī)理,本文對農(nóng)田土壤裂隙進(jìn)行了試驗研究。應(yīng)用數(shù)字圖像處理技術(shù)對農(nóng)田土壤裂隙試驗圖像進(jìn)行了二值化、去除噪點、提取裂隙邊緣等處理。閔可夫斯基面積、長度、歐拉數(shù)3個可以描述裂隙空間分布以及連通性的形態(tài)參數(shù)作為裂隙定量分析指標(biāo)。對裂隙試驗圖像進(jìn)行形態(tài)學(xué)膨脹與腐蝕運算,分析了運算后裂隙試驗圖像的面積、長度、歐拉數(shù)密度的變化規(guī)律。同時構(gòu)建了基于胡克定律的二維土壤開裂模型,模擬土壤收縮動態(tài)開裂的過程。模型假定水分蒸發(fā)是裂隙開裂的主要原因,生成裂隙的土層厚度足夠小。設(shè)置均值為ε,方差為δ2的正態(tài)分布N(ε,δ2)的土壤臨界應(yīng)變隨機(jī)場,并引入摩擦力f作為土壤靜態(tài)粘合力,以及表示土壤彈塑性性能的參數(shù)網(wǎng)絡(luò)結(jié)構(gòu)連接強(qiáng)度nit,在由結(jié)點組成的六邊形網(wǎng)絡(luò)結(jié)構(gòu)中持續(xù)減小結(jié)點間的距離模擬水分蒸發(fā),由此引起網(wǎng)絡(luò)結(jié)點受力改變發(fā)生斷裂的過程。本文比較了模擬裂隙圖像與試驗圖像面積、長度、歐拉數(shù)密度。結(jié)果表明:(1)應(yīng)用閔可夫斯基面積、長度、歐拉數(shù)密度函數(shù)可以有效描述裂隙形態(tài);形態(tài)學(xué)分析結(jié)果顯示裂隙的閔可夫斯基面積、長度、歐拉數(shù)密度函數(shù)具有不同的變化規(guī)律,其中面積密度函數(shù)表現(xiàn)為0-1之間的增函數(shù);長度密度函數(shù)表現(xiàn)為先增大后減小的變化規(guī)律,歐拉數(shù)密度函數(shù)表現(xiàn)為先增大,后減小再增大的變化規(guī)律。(2)運用基于胡克定律構(gòu)建的二維土壤開裂模型,模擬由于水分蒸發(fā)而引起土壤收縮開裂過程,計算采用蒙特卡洛方法模擬獲得裂隙面積、長度、歐拉數(shù)密度平均值μ以及標(biāo)準(zhǔn)差δ,試驗平均密度值基本分布在模擬密度值μ± δ之間,表明模擬結(jié)果較好。(3)試驗和模擬面積密度、歐拉數(shù)密度平均值相對誤差較小,面積密度相對誤差基本小于10%;歐拉數(shù)密度相對誤差在15%左右;長度密度平均值相對誤差較大,除過38-48 h之間小于10%,其余時段內(nèi)均大于25%,最大相對誤差達(dá)到37.38%。應(yīng)用數(shù)值方法模擬土壤表面裂隙,有助于研究農(nóng)田土壤裂隙的形成機(jī)理以及土壤裂隙隨時間變化過程中動態(tài)演化規(guī)律。
[Abstract]:At present, the development law and formation mechanism of soil dry shrinkage fissures are not clear. In order to reveal the development law and formation mechanism of dry shrinkage fissures on farmland soil surface, this paper has carried on the experiment research to the farmland soil fissures. The digital image processing technique was applied to the field soil fissures test images to be binary, to remove the noise and to extract the fissures edge and so on. Minkowski area, length and Euler number can describe the spatial distribution of fractures and the morphological parameters of connectivity as quantitative analysis indexes of fractures. Morphological expansion and corrosion operations were performed on the fracture test images. The changes of the area, length and Euler number density of the fracture test images were analyzed. At the same time, a two-dimensional soil cracking model based on Hook's law was constructed to simulate the dynamic cracking process of soil shrinkage. The model assumes that moisture evaporation is the main cause of crack cracking, and the thickness of soil layer is small enough. The soil critical strain random field of normal distribution N (蔚, 未 2) with mean value 蔚 and variance 未 2 is set, and friction force f is introduced as the static adhesion of soil. The connection strength of the network structure, which represents the soil elastoplastic properties, decreases the distance between the nodes in the hexagonal network structure and simulates the moisture evaporation, which leads to the fracture process of the network node. In this paper, the area, length and Euler number density of simulated fracture images and experimental images are compared. The results show that: (1) Minkowski area, length and Euler number density function can be used to describe fracture morphology effectively, and morphological analysis results show that Minkowski area, length and Euler number density function of fractures have different variation laws. The area density function is an increasing function between 0 and 1, the length density function increases first and then decreases, and the Euler number density function increases first. (2) the two-dimensional soil cracking model based on Hooke's law is used to simulate the soil shrinkage cracking process caused by water evaporation, and Monte Carlo method is used to calculate the crack area and length. The average value of Euler number density 渭 and the standard deviation 未, the experimental average density value basically distributed in the simulation density value 渭 鹵未, which indicated that the simulation result is better. (3) the relative error of the experimental and simulated area density and the Euler number density average value is small. The relative error of area density is less than 10; the relative error of Euler number density is about 15%; the average relative error of length density is larger than 10, except that after 38-48 hours, the other period is larger than 25 and the maximum relative error is 37.38. Numerical simulation of soil surface fissures is helpful to study the formation mechanism of soil fissures and the dynamic evolution of soil fissures with time.
【學(xué)位授予單位】：寧夏大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：S152

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