土地平整問(wèn)題

精選優(yōu)質(zhì)文檔-----傾情為你奉上精選優(yōu)質(zhì)文檔-----傾情為你奉上專心---專注---專業(yè)專心---專注---專業(yè)精選優(yōu)質(zhì)文檔-----傾情為你奉上專心---專注---專業(yè)土地平整問(wèn)題摘要隨著山區(qū)城市的發(fā)展，向山要地開發(fā)成為了一種必然的選擇。為了更好的確定平整地的起始點(diǎn)，做到節(jié)約成本的目的，我們根據(jù)幾個(gè)決定性因素利用散點(diǎn)法【1】、建立了相關(guān)的模型。主要討論如何在一片山地之中選擇合適的方位與開挖深度，從而使總的土石方量最小，使得在實(shí)際工程中達(dá)到最可靠，最節(jié)約成本。采用MATLAB軟件模擬功能，畫出了該工廠的這片土地的三維圖形與等高線圖，并對(duì)山地地形作出分析。在求解開挖位置時(shí)，我們只考慮連片地的一種放置位置，并通過(guò)平移求出海拔方差最小的區(qū)域，在此區(qū)域內(nèi)用散點(diǎn)法求出最小土石方量，從而決定從什么地方，什么海拔高度平整一塊固定大小的長(zhǎng)方形連片土地，能使總的土石方量最小，使工程施工經(jīng)濟(jì)上達(dá)到最優(yōu)。關(guān)鍵詞：合理開挖土地散點(diǎn)法最優(yōu)Ⅰ問(wèn)題重述1.1問(wèn)題背景土地整理在我國(guó)是一個(gè)較新的學(xué)科領(lǐng)域，面對(duì)“21世紀(jì)誰(shuí)來(lái)養(yǎng)活中國(guó)？”的嚴(yán)峻挑戰(zhàn)，積極推行土地整理，已成為解決各方土地矛盾，實(shí)現(xiàn)土地資源可持續(xù)利用和保持經(jīng)濟(jì)快速、健康發(fā)展的必然選擇【2】。但是如何在一片山地之中選擇合適的方位與開挖深度，從而使總的土石方量最小，就是一個(gè)有意義的命題了！1.2問(wèn)題提出某工廠為了在一片長(zhǎng)度為1500米，寬度為1000米的山地之中，開挖出一個(gè)800米×600米平坦連續(xù)的長(zhǎng)方形地塊作為工廠的廠房地基，前期已經(jīng)在本塊土地上測(cè)量出長(zhǎng)、寬每隔30米的網(wǎng)格的對(duì)應(yīng)網(wǎng)格點(diǎn)的海拔高度（詳細(xì)數(shù)據(jù)見附件（1））。問(wèn)題：①用附件（1）中的數(shù)據(jù)畫出工廠的這片土地的三維圖形與等高線圖；②從什么地方，什么海拔高度平整一塊800米×600米的連片土地能使總的土石方量最小？③如果允許平整出來(lái)的土地為二層的臺(tái)階狀地塊，要求各地塊的長(zhǎng)、寬不少于60米，又將從什么地方、什么海拔高度分別開挖，能使總的土石方量最小？Ⅱ問(wèn)題分析2.1問(wèn)題一分析我們可以利用MATLAB軟件直接調(diào)用surf函數(shù)和contour函數(shù)分別畫出這片土地的三維圖形和等高線圖。2.2問(wèn)題二分析考慮要平整一塊800米×600米的連片土地，且要使土石方量最小，我們需要確定這塊800米×600米的連片土地的底面投影區(qū)域，以及海拔高度，使得其土石方量最小。對(duì)于指定底面是800米×600米大小區(qū)域內(nèi)，在內(nèi)平移，取海拔的高度做方差，如果方差最小，說(shuō)明這片區(qū)域比較平坦，挖土或填土的土石方量近似最小。我們可以通過(guò)這個(gè)思路求出連片地的底面投影區(qū)域，即為求出滿足海拔方差值最小的底面位置的問(wèn)題。確定連片地的底面投影區(qū)域后，再通過(guò)散點(diǎn)法在施工場(chǎng)地計(jì)算高程，挖填土方量等因素，綜合協(xié)調(diào)的處理，從而達(dá)到土方運(yùn)輸量最小。而土方工程量的計(jì)算，采用散點(diǎn)法。一般來(lái)說(shuō)，只要基本按照自然地形的變化選取合適的特征點(diǎn)，將自然地形在某一方向上的變化簡(jiǎn)化為相似的折線變化，再求出折線與設(shè)計(jì)線之間的面積乘以高度，即可求得體積。2.3問(wèn)題三分析對(duì)于底面是800米×600米大小的為二層的臺(tái)階狀土地，均分為兩塊，取任意一塊在內(nèi)平移，取海拔的高度做方差，如果方差最小，說(shuō)明這片區(qū)域比較平坦，挖土或填土的土石方量近似最小。在確定一塊連片地后，在其四周取另一塊連片地，并使其海拔高度方差最小。Ⅲ模型假設(shè)在平整單元內(nèi)無(wú)土方進(jìn)出；只考慮800米×600米的連片土一種放置位置（見附錄1）；假設(shè)所求海拔即為連片地海拔高度的平均值；假設(shè)臺(tái)階高度沒(méi)有要求。Ⅳ符號(hào)說(shuō)明符號(hào)說(shuō)明連片土地平均高程實(shí)測(cè)的各點(diǎn)高程應(yīng)側(cè)區(qū)域的測(cè)點(diǎn)數(shù)挖方區(qū)的平均挖深填方區(qū)平均填高大于平均高程的各實(shí)測(cè)點(diǎn)的高程小于平均高程的各實(shí)測(cè)點(diǎn)的高程大于平均高程的測(cè)點(diǎn)數(shù)小于平均高程的測(cè)點(diǎn)數(shù)挖方量填方量挖方的面積填方的面積Ⅴ模型建立4.1問(wèn)題一模型1.通過(guò)MATLAB7.0編程（程序見附錄:2），畫出這片土地的三維圖如下：圖1山地三維圖2.這片土地等高線圖如下：圖2土地三維等高線圖3土地二維等高線4.2問(wèn)題二模型在山地內(nèi)，指定底面是800米×600米大小的連片地（圖4），并將連片地在山地內(nèi)平移（只考慮一種放置位置），并計(jì)算海拔高度的方差，如果方差最小，說(shuō)明這片區(qū)域比較平坦，挖土或填土的土石方量近似最小。圖4連片地放置根據(jù)地形情況布置測(cè)量點(diǎn)，考慮到計(jì)算的精確程度應(yīng)在的場(chǎng)地四邊的最高點(diǎn)、最低點(diǎn)、次高點(diǎn)、次低點(diǎn)以及一切能代表不同高程的各個(gè)位置上都均勻布置測(cè)點(diǎn)，將測(cè)點(diǎn)高程求算術(shù)平均值，此平均值即為設(shè)計(jì)的地面平均高程，計(jì)算公式為：在平整單元無(wú)土方進(jìn)出的條件下，根據(jù)挖填平衡，可由下面的方程組【3】分別求得挖填方面積：挖方面積：填方面積：將各實(shí)測(cè)點(diǎn)高程與平均高程相比較，大于平均高程的為挖方，小于平均高程的為填方，等于平均高程的表示不挖不填。以此算出各點(diǎn)高程與平均高程的差值，并算出總挖深、總填高?？偼谏睿嚎偺罡撸和诜搅浚禾罘搅浚?.3問(wèn)題三模型建立將臺(tái)階狀土地均分為兩片土地，取任意一塊在內(nèi)平移，取海拔的高度做方差，如果方差最小，說(shuō)明這片區(qū)域比較平坦，挖土或填土的土石方量近似最小。在確定一塊連片地后，在其四周取另一塊連片地，并使其海拔高度方差最小?？紤]到第一塊連片地放置位置不同，對(duì)第二塊連片地的選取會(huì)有影響，所以第一塊連片地的放置有兩種情況(圖5).4004006001500100040040060015001000圖5第一塊土地兩種放置位置Ⅵ模型求解5.1問(wèn)題一模型求解通過(guò)MATLAB7.0編程（程序見附錄2），畫出這片土地的三維圖。5.2問(wèn)題二模型求解通過(guò)MATLAB7.0編程（程序見附錄3）求出在此數(shù)據(jù)區(qū)域（x=0:600,y=690:1500）內(nèi)，平均海拔為12.095，海拔高度方差最小為8.4913，即：所挖填的土石方量最小。再通過(guò)Excel和散點(diǎn)法求得最小的土石方量為：。5.3問(wèn)題三模型求解通過(guò)MATLAB7.0編程（程序見附錄4）求出在此區(qū)域（x=210:810,y=750:1150）內(nèi)，平均海拔為5.095，海拔高度方差最小為5.6813，最小挖土量為：。再確定第一塊連片地后，只需在A、B處（圖6）分別計(jì)算第二塊連片的海拔方差，取最小值即可。A處海拔方差：7.6070B處海拔方差:10.8042A處海拔方差小于B處海拔方差，取A處為第二塊連片地位置，此處最小挖土量為：.8。圖6第一塊連片地位置600600400AB圖7AB位置Ⅶ模型評(píng)價(jià)與改進(jìn)模型的優(yōu)點(diǎn)在于對(duì)原始數(shù)據(jù)進(jìn)行整合時(shí)，使用MATLAB軟件描述山地的三維圖形和等高線圖形，在此基礎(chǔ)上可以得到具有很高的擬合度和適度性。對(duì)模型的進(jìn)一步討論便可以得到一系列可靠而實(shí)用的信息，所得結(jié)論與客觀事實(shí)很好地吻合，從而進(jìn)一步說(shuō)明模型是合理的。在解決合理開挖土地的問(wèn)題中，通過(guò)土石方量費(fèi)用最小的原則，確定平整土地的開挖位置和開挖高度。模型的缺點(diǎn)在于在建立模型時(shí)，只考慮了連片地的一種位置，偶然性較大，且不能得到大規(guī)模推廣。在確定開挖位置時(shí)可以采用枚舉法，具體思路如下：將平整塊區(qū)域投影到底面（XOY平面），確定開挖方向，即要確定平整塊的底面位置。顯然底面是800米×600米的矩形，假設(shè)矩形的四個(gè)頂點(diǎn)分別為A、B、C、D。山地是長(zhǎng)度為1500米，寬度為900米的矩形區(qū)域，因此平整塊底面投影矩形ABCD可以在1500×900的區(qū)域范圍內(nèi)任意移動(dòng)，四個(gè)頂點(diǎn)不能超出這個(gè)范圍我們要取遍所有可能的位置，必須枚舉所有的可能值。參考文獻(xiàn)[1]劉富民，土地整治中土方量測(cè)量及計(jì)算方法比較研究，科技信息，2012年3期，2012。[2]馮忠江，張艷東，張磊，淺談土地整理項(xiàng)目中的土地平整問(wèn)題，河北：資源與產(chǎn)業(yè)，2005.5。[3]江平，周連，何申泰，卓犖，土地整理中土地平整工程中的若干方法討論，國(guó)土資源管理，2007年5期，2007。附錄附錄1：附錄2：x=0:30:1500;y=0:30:900;[x1,y1]=meshgrid(x,y)z=[1.291.291.471.691.861.942.052.312.6833.123.183.363.673.873.723.342.982.822.853.023.223.263.012.592.131.751.471.320.921.031.231.491.812.112.282.262.121.991.982.092.342.612.712.572.352.232.192.11.881.621.291.291.471.691.861.942.052.312.6833.123.183.363.673.873.723.342.982.822.853.023.223.263.012.592.131.751.471.320.921.031.231.491.812.112.282.262.121.991.982.092.342.612.712.572.352.232.192.11.881.621.291.291.471.691.861.942.052.312.6833.123.183.363.673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