張大英，許啟鏗，王樹明，梁醒培

筒倉(cāng)動(dòng)態(tài)卸料過(guò)程側(cè)壓力模擬與驗(yàn)證

張大英1，許啟鏗2，王樹明3，梁醒培2

（1. 鄭州航空工業(yè)管理學(xué)院土木建筑工程學(xué)院，鄭州 450015；2. 河南工業(yè)大學(xué)土木建筑學(xué)院，鄭州 450001；3. 鄭州大學(xué)綜合設(shè)計(jì)研究院有限公司，鄭州 450002）

為了研究立筒倉(cāng)卸料過(guò)程中的側(cè)壓力及數(shù)值模擬技術(shù)，設(shè)計(jì)了有機(jī)玻璃筒倉(cāng)模型進(jìn)行試驗(yàn)研究，運(yùn)用ABAQUS有限元軟件中的自適應(yīng)網(wǎng)格劃分技術(shù)模擬了筒倉(cāng)的動(dòng)態(tài)卸料過(guò)程。結(jié)果表明，筒倉(cāng)動(dòng)態(tài)側(cè)壓力試驗(yàn)值大于靜態(tài)側(cè)壓力，但各測(cè)點(diǎn)超壓系數(shù)不同，在鄰近漏斗附近超壓系數(shù)最大為1.78，其次為倉(cāng)壁中上部2個(gè)測(cè)點(diǎn)超壓系數(shù)達(dá)到了1.73和1.61，其他位置超壓系數(shù)在1.45以內(nèi)；側(cè)壓力模擬值與計(jì)算值吻合度較好，靜態(tài)側(cè)壓力兩者相對(duì)誤差絕對(duì)值在0.43%～9.92%之間，動(dòng)態(tài)側(cè)壓力兩者相對(duì)誤差絕對(duì)值在1.14%～9.65%之間，驗(yàn)證了數(shù)值模擬技術(shù)的可行性；靜態(tài)和動(dòng)態(tài)側(cè)壓力的數(shù)值模擬曲線、公式計(jì)算曲線、試驗(yàn)曲線或試驗(yàn)擬合曲線都表明，隨著測(cè)點(diǎn)距筒倉(cāng)底部高度的增加，側(cè)壓力呈下降趨勢(shì)，即側(cè)壓力下大上小，而且靜態(tài)側(cè)壓力模擬曲線與試驗(yàn)曲線變化規(guī)律一致，相對(duì)誤差絕對(duì)值在1.83%～9.97%之間；由于試驗(yàn)時(shí)壓力傳感器精度、標(biāo)定試驗(yàn)誤差和試驗(yàn)次數(shù)等隨機(jī)因素的影響，動(dòng)態(tài)側(cè)壓力試驗(yàn)曲線不很規(guī)則，數(shù)值模擬曲線相對(duì)平滑，但動(dòng)態(tài)側(cè)壓力試驗(yàn)值的擬合曲線與數(shù)值模擬曲線變化趨勢(shì)基本相同，相對(duì)誤差絕對(duì)值在0.28%～9.93%之間。通過(guò)觀察漏斗附近Mises應(yīng)力分布圖發(fā)現(xiàn)，物料卸出前，應(yīng)力較大點(diǎn)發(fā)生在緊鄰漏斗附近的倉(cāng)壁處，卸料開始后，應(yīng)力較大點(diǎn)即轉(zhuǎn)向漏斗壁中部某范圍，而且隨著卸料時(shí)間的延長(zhǎng)，此應(yīng)力較大點(diǎn)的范圍有所增大。

筒倉(cāng)；模型；有限元分析；側(cè)壓力試驗(yàn)；動(dòng)態(tài)卸料模擬

0 引 言

筒倉(cāng)廣泛應(yīng)用于糧食、物流、電力、冶金等行業(yè)中，因此，合理進(jìn)行筒倉(cāng)結(jié)構(gòu)設(shè)計(jì)是關(guān)鍵。為此，眾多學(xué)者主要展開了以下方面的研究工作，對(duì)鋼筋混凝土筒倉(cāng)在內(nèi)外溫差作用下的研究[1-2]，通過(guò)有限元方法重點(diǎn)分析不同溫差下結(jié)構(gòu)的位移、外壁應(yīng)力或倉(cāng)底應(yīng)力，指出加大倉(cāng)壁環(huán)向配筋很重要；對(duì)鋼筒倉(cāng)倉(cāng)壁在溫度作用下的受力性能進(jìn)行研究[3]，提出高溫貯料鋼筒倉(cāng)倉(cāng)壁溫度荷載的計(jì)算方法，并對(duì)不均勻溫度場(chǎng)作用下的結(jié)構(gòu)響應(yīng)進(jìn)行分析研究；對(duì)落地鋼筒倉(cāng)在溫度荷載作用下的研究[4]，分析倉(cāng)壁、倉(cāng)底應(yīng)力與筒倉(cāng)直徑、倉(cāng)壁厚度的關(guān)系，發(fā)現(xiàn)倉(cāng)底處環(huán)向應(yīng)力和豎向應(yīng)力隨溫度荷載線性變化，溫度應(yīng)力隨筒倉(cāng)直徑、倉(cāng)壁厚度的變化呈拋物線型；對(duì)不同倉(cāng)型糧堆內(nèi)溫度場(chǎng)和水氣分壓場(chǎng)隨季節(jié)的變化規(guī)律的研究[5]，采用陣列式分布的溫度傳感器監(jiān)測(cè)糧堆溫度，利用溫度擬合算法構(gòu)建糧堆溫度場(chǎng)模型，重現(xiàn)糧堆在冬末春初之際和夏季的溫度場(chǎng)和水氣分壓場(chǎng)分布。對(duì)物料與倉(cāng)壁接觸作用的研究[6-9]，解決了松散物料與倉(cāng)壁接觸時(shí)接觸面上必須滿足的位移條件、力的傳遞關(guān)系以及力與位移的關(guān)系，從而得到接觸壓力變化規(guī)律。對(duì)靜態(tài)側(cè)壓力分布規(guī)律的研究，如周長(zhǎng)東等[10]基于亞塑性本構(gòu)理論，對(duì)鋼筋混凝土筒倉(cāng)倉(cāng)壁與散料顆粒體之間的靜態(tài)壓力作用進(jìn)行有限元模擬，得出對(duì)筒倉(cāng)-散料靜力相互作用影響較大的各類參數(shù)為：散料顆粒的種類、初始孔隙比、倉(cāng)內(nèi)散料臨界內(nèi)摩擦角、顆粒硬度和顆粒間應(yīng)變；楊鴻等[11]通過(guò)建立考慮散料與倉(cāng)壁相互作用的鋼筒倉(cāng)靜態(tài)散料壓力三維有限元分析模型，發(fā)現(xiàn)泊松比和內(nèi)摩擦角對(duì)側(cè)壓力的影響較大。對(duì)動(dòng)態(tài)側(cè)壓力問(wèn)題的研究，許多研究成果[12-23]主要集中在筒倉(cāng)中心卸料過(guò)程中動(dòng)態(tài)側(cè)壓力分布規(guī)律及物料流動(dòng)狀態(tài)的研究，主要是針對(duì)筒倉(cāng)模型內(nèi)物料卸出過(guò)程的試驗(yàn)及數(shù)值分析研究；還有些研究成果[24-25]集中在筒倉(cāng)偏心卸料過(guò)程的數(shù)值模擬和試驗(yàn)研究，如研究不同偏心的卸料口下物料流速模式，偏心漏斗口鋼筒倉(cāng)的側(cè)壓力分布研究。對(duì)大直徑筒倉(cāng)的計(jì)算與分析研究[26-28]，主要體現(xiàn)在復(fù)雜條件下大型筒倉(cāng)尤其是淺圓倉(cāng)側(cè)壓力的極限分析與彈塑性有限元分析；對(duì)大型筒倉(cāng)結(jié)構(gòu)與地基的動(dòng)力相互作用研究[29]，發(fā)現(xiàn)彈性地基上單體筒倉(cāng)結(jié)構(gòu)的動(dòng)力響應(yīng)大于群倉(cāng)結(jié)構(gòu)，剛性地基上群倉(cāng)結(jié)構(gòu)動(dòng)力響應(yīng)大于單倉(cāng)結(jié)構(gòu)。上述眾多研究成果中，裝料、靜止和卸料時(shí)物料對(duì)倉(cāng)壁的側(cè)壓力計(jì)算合理與否是非常重要的，然而，至今為止對(duì)側(cè)壓力的認(rèn)識(shí)尤其是倉(cāng)壁動(dòng)態(tài)側(cè)壓力問(wèn)題仍然處在研究階段，并沒(méi)有一個(gè)公認(rèn)的計(jì)算方法和手段。

為此本文采用試驗(yàn)和數(shù)值方法結(jié)合的手段，對(duì)筒倉(cāng)模型進(jìn)行裝卸料試驗(yàn)和數(shù)值模擬。研究對(duì)象為有機(jī)玻璃筒倉(cāng)模型，通過(guò)試驗(yàn)測(cè)試得到了物料對(duì)倉(cāng)壁的靜、動(dòng)態(tài)側(cè)壓力，尤其提出一種動(dòng)態(tài)卸料過(guò)程模擬技術(shù)，并通過(guò)與試驗(yàn)測(cè)試結(jié)果進(jìn)行對(duì)比分析， 驗(yàn)證了動(dòng)態(tài)卸料過(guò)程模擬技術(shù)的合理性，為合理設(shè)計(jì)筒倉(cāng)提供數(shù)值依據(jù)。

1 試驗(yàn)概況

1.1 模型設(shè)計(jì)

試驗(yàn)時(shí)為了觀察筒倉(cāng)內(nèi)物料（本試驗(yàn)中用的物料為細(xì)砂）的流動(dòng)狀態(tài)，采用有機(jī)玻璃制作模型筒倉(cāng)倉(cāng)壁，倉(cāng)壁高度取實(shí)際常用筒倉(cāng)合理尺寸的1/20，為1.2 m，倉(cāng)壁內(nèi)徑為0.5 m，壁厚為5 mm。考慮到模型筒倉(cāng)離地面有一個(gè)高度方便卸料，以及便于與地面固定模擬筒倉(cāng)基礎(chǔ)，設(shè)置鋼材支架支撐模型筒倉(cāng)。倉(cāng)壁下設(shè)鋼漏斗便于與鋼材支架很好的連接，漏斗傾角為30°。模型筒倉(cāng)及詳細(xì)尺寸標(biāo)注如圖1所示。

圖1 筒倉(cāng)模型及詳細(xì)尺寸Fig.1 Silo model and detailed dimensions

1.2 試驗(yàn)儀器及物料性質(zhì)

試驗(yàn)中用壓力傳感器直接測(cè)試得到筒倉(cāng)倉(cāng)壁的動(dòng)態(tài)側(cè)壓力，圖1b筒倉(cāng)截面左側(cè)倉(cāng)壁上的實(shí)心矩形即為壓力傳感器的所在位置，布設(shè)C1～C15共15個(gè)壓力傳感器，距倉(cāng)壁底部1/3高度范圍所布設(shè)傳感器較密，間距為50 mm，剩余2/3倉(cāng)壁高度范圍所布設(shè)壓力傳感器較稀疏，間距為100 mm。采用DHDAS-5920動(dòng)態(tài)信號(hào)采集分析系統(tǒng)進(jìn)行數(shù)據(jù)采集和分析。

試驗(yàn)用物料為福建平潭標(biāo)準(zhǔn)砂，總用量大約0.25 t。標(biāo)準(zhǔn)砂的顆粒密度為2.643 g/cm3，相對(duì)密實(shí)度為0.51，重力密度為17.4 kN/m3，最大和最小干密度分別為1.74 g/cm3和1.43 g/cm3，最大和最小孔隙比分別為0.848和0.519，粒徑不均勻系數(shù)為1.542，曲率系數(shù)為1.104。筒倉(cāng)的水力半徑取0.125 m，砂與倉(cāng)壁的摩擦因數(shù)取0.43。標(biāo)準(zhǔn)砂的顆粒級(jí)配列于表1中。

表1 標(biāo)準(zhǔn)砂的顆粒級(jí)配Table1 Grain composition of standard sand

對(duì)于標(biāo)準(zhǔn)砂的內(nèi)摩擦角采用電動(dòng)四聯(lián)等應(yīng)變直剪儀進(jìn)行現(xiàn)場(chǎng)測(cè)定，測(cè)試所得數(shù)據(jù)列于表2中。通過(guò)對(duì)測(cè)試數(shù)據(jù)進(jìn)行線性擬合，得到直線方程為y=1.656 2x+1.066 6，由此可得標(biāo)準(zhǔn)砂的內(nèi)摩擦角約為31.1°。

表2 標(biāo)準(zhǔn)砂的剪切試驗(yàn)數(shù)據(jù)Table2 Shear test data of standard sand

1.3 試驗(yàn)測(cè)試及結(jié)果

向筒倉(cāng)模型內(nèi)裝滿砂后，需待砂密實(shí)后首先記錄下砂對(duì)倉(cāng)壁的靜態(tài)側(cè)壓力，之后打開漏斗口，邊卸料邊記錄物料對(duì)倉(cāng)壁的動(dòng)態(tài)側(cè)壓力。在此過(guò)程中，可以很清楚地觀察到砂在筒倉(cāng)內(nèi)的流動(dòng)狀態(tài)為管狀流動(dòng)，如圖2所示。待卸料完畢得到測(cè)點(diǎn)C1～C15在整個(gè)卸料過(guò)程中的動(dòng)態(tài)側(cè)壓力變化曲線如圖3所示。同時(shí)，將各測(cè)點(diǎn)的靜態(tài)側(cè)壓力值和在卸料過(guò)程中的最大動(dòng)態(tài)側(cè)壓力值列于表3中。

分析研究圖3所示各個(gè)測(cè)點(diǎn)的動(dòng)態(tài)側(cè)壓力變化曲線，動(dòng)態(tài)側(cè)壓力值隨著卸料時(shí)間的延續(xù)均為先大后小最終趨于0，有個(gè)別測(cè)點(diǎn)（如圖3e測(cè)點(diǎn)C13、C14）動(dòng)態(tài)側(cè)壓力值趨于0后又轉(zhuǎn)為負(fù)值，這主要受測(cè)點(diǎn)本身側(cè)壓力試驗(yàn)誤差及標(biāo)定曲線方程的影響。對(duì)比分析各條曲線發(fā)現(xiàn)，越靠近倉(cāng)壁頂部測(cè)點(diǎn)，側(cè)壓力趨于0的時(shí)間亦越早，因此曲線總體變化趨勢(shì)是合理的。分析研究漏斗鄰近測(cè)點(diǎn)C1、C2、C7、C8和C9的動(dòng)態(tài)側(cè)壓力變化曲線，當(dāng)壓力增大到某一數(shù)值時(shí)，壓力不再增大，隨著卸料時(shí)間延續(xù)，壓力值基本趨于下降的趨勢(shì)并最終趨于0。分析研究其他測(cè)點(diǎn)的動(dòng)態(tài)側(cè)壓力變化曲線，在卸料某一局部過(guò)程內(nèi)，壓力具有先增大再減小而后又增大的明顯變化，當(dāng)此局部過(guò)程過(guò)后壓力值基本趨于下降的趨勢(shì)并最終趨于0。上述分析說(shuō)明在卸料過(guò)程中各點(diǎn)的側(cè)壓力變化并不完全一致，這與測(cè)點(diǎn)所處倉(cāng)壁位置、物料的流動(dòng)狀態(tài)等有關(guān)。

圖2 筒倉(cāng)卸料Fig.2 Discharging of sand

圖3 測(cè)點(diǎn)C1～C15的動(dòng)態(tài)側(cè)壓力變化曲線Fig.3 Dynamic wall pressure curves of C1-C15

表3 動(dòng)態(tài)和靜態(tài)壓力試驗(yàn)值變化Table3 Experiment values change of dynamic and static pressures

由表3可以得知，除了倉(cāng)壁與漏斗交接處的測(cè)點(diǎn)C1動(dòng)態(tài)側(cè)壓力小于靜態(tài)側(cè)壓力外，其余測(cè)點(diǎn)的動(dòng)態(tài)側(cè)壓力均大于靜態(tài)側(cè)壓力，而且最大超壓系數(shù)出現(xiàn)在距倉(cāng)壁底部高度為0.15 m的測(cè)點(diǎn)C4處，達(dá)到1.78，其次較大的超壓系數(shù)為1.73，距倉(cāng)壁底部高度為0.65 m的測(cè)點(diǎn)C11處。從側(cè)壓力增大幅度也可以看出，此超壓系數(shù)較大兩測(cè)點(diǎn)的壓力增大超過(guò)了70%。由此說(shuō)明此類筒倉(cāng)的超壓較大位置可能出現(xiàn)在鄰近倉(cāng)壁底部某一高度處及鄰近倉(cāng)壁的中部位置。

2 數(shù)值模擬

2.1 數(shù)值分析模型及材料參數(shù)

采用ABAQUS有限元軟件進(jìn)行筒倉(cāng)卸料模擬。由于筒倉(cāng)為中心對(duì)稱結(jié)構(gòu)，故取筒倉(cāng)連同物料剖面的一半建立有限元模型，將倉(cāng)內(nèi)標(biāo)準(zhǔn)砂看作一平面對(duì)稱單元，采用的單元名稱為CAX4R。由于倉(cāng)壁比標(biāo)準(zhǔn)砂的剛度大很多，故建模時(shí)將倉(cāng)壁設(shè)置為剛性線。有限元模型及網(wǎng)格劃分如圖4所示。

圖4 筒倉(cāng)有限元模型及網(wǎng)格剖分Fig.4 Finite element model and mesh generation of silo

計(jì)算時(shí)有機(jī)玻璃筒倉(cāng)的彈性模量取3 000 MPa，泊松比取0.3，重力密度取10 kN/m3。標(biāo)準(zhǔn)砂的彈性模量取為0.2 MPa，泊松比為0.4，并將標(biāo)準(zhǔn)砂考慮為塑性材料，選用子午線為線性的Druker-Prager模型模擬標(biāo)準(zhǔn)砂，標(biāo)準(zhǔn)砂的材料參數(shù)取值列于表4中。

表4 標(biāo)準(zhǔn)砂的材料參數(shù)取值Table4 Material parameters of standard sand

2.2 動(dòng)態(tài)卸料模擬技術(shù)及數(shù)值結(jié)果

定義物料單元和倉(cāng)壁之間的接觸摩擦系數(shù)為0.43，選擇有限滑動(dòng)選項(xiàng)后進(jìn)行網(wǎng)格剖分。計(jì)算分2個(gè)步驟：第一，通過(guò)模擬物料在自重作用下達(dá)到密實(shí)進(jìn)行靜態(tài)側(cè)壓力計(jì)算；第二，去掉靜態(tài)側(cè)壓力模擬時(shí)卸料口處的約束進(jìn)行筒倉(cāng)卸料模擬，計(jì)算動(dòng)態(tài)側(cè)壓力。模擬卸料過(guò)程中，線性施加物料重力，采用顯式動(dòng)態(tài)計(jì)算方法。在物料卸出過(guò)程中，網(wǎng)格會(huì)發(fā)生較大變形，因此利用ABAQUS軟件中的自適應(yīng)網(wǎng)格劃分功能，可以減小網(wǎng)格畸形，有效延長(zhǎng)卸料時(shí)間。在這一過(guò)程中，合理設(shè)置漏斗內(nèi)物料單元的網(wǎng)格大小和計(jì)算頻率是關(guān)鍵。

圖5所示為卸料不同時(shí)間段漏斗口附近的網(wǎng)格變形及漏斗附近Mises應(yīng)力分布圖，可以看出物料卸出前，應(yīng)力較大點(diǎn)發(fā)生在緊鄰漏斗附近的倉(cāng)壁處，卸料開始后，應(yīng)力較大點(diǎn)即轉(zhuǎn)向漏斗壁中部某范圍，而且隨著卸料時(shí)間的延長(zhǎng)，此應(yīng)力較大點(diǎn)的范圍有所增大。

圖5 簡(jiǎn)倉(cāng)卸料不同時(shí)刻物料單元的網(wǎng)格變形及應(yīng)力分布Fig.5 Mesh deformation and stress distribution during discharging of silo

3 靜態(tài)和動(dòng)態(tài)側(cè)壓力理論計(jì)算公式

根據(jù)目前成熟的Janssen理論，對(duì)立筒倉(cāng)倉(cāng)壁各測(cè)點(diǎn)的靜態(tài)側(cè)壓力可以按如下公式計(jì)算：

對(duì)于貯料對(duì)倉(cāng)壁的動(dòng)態(tài)側(cè)壓力，根據(jù)中國(guó)《鋼筋混凝土筒倉(cāng)設(shè)計(jì)規(guī)范》（GB50077-2003）[30]4.2.2條進(jìn)行計(jì)算：

公式（1）～（4）中各符號(hào)的含義如下：

Ch為深倉(cāng)貯料水平壓力修正系數(shù)，根據(jù)《鋼筋混凝土筒倉(cāng)設(shè)計(jì)規(guī)范》（GB50077-2003）表4.2.5計(jì)算，測(cè)點(diǎn)距倉(cāng)壁底部的深度h為0～0.8 m時(shí)Ch=2，h=0.85時(shí)Ch=1.875，h=0.95時(shí)Ch=1.625，h=1.05時(shí)Ch=1.375；γ為貯料的重力密度，kN/m3；ρ為筒倉(cāng)水平凈截面的水力半徑，m；μ為貯料與倉(cāng)壁的摩擦系數(shù)；k為側(cè)壓力系數(shù)；s為貯料頂面或貯料錐體重心至所計(jì)算截面的距離，m；φ為貯料的內(nèi)摩擦角，（°）。

4 結(jié)果分析

采用ABAQUS有限元軟件對(duì)筒倉(cāng)進(jìn)行靜態(tài)和動(dòng)態(tài)側(cè)壓力模擬后，得到了倉(cāng)壁不同深度測(cè)點(diǎn)的靜態(tài)和動(dòng)態(tài)側(cè)壓力值，將其描繪成曲線，如圖6所示，并將按公式（1）～（4）計(jì)算的各測(cè)點(diǎn)側(cè)壓力值一同描繪于圖6中以作比較?？梢钥闯觯o態(tài)側(cè)壓力計(jì)算值和模擬值比較吻合，相對(duì)誤差絕對(duì)值在0.43%～9.92%之間，在0～0.2 m高度處，模擬值大于計(jì)算值，其他位置模擬值小于計(jì)算值；動(dòng)態(tài)側(cè)壓力的模擬值與計(jì)算值吻合較好，相對(duì)誤差絕對(duì)值在1.14%～9.65%之間，除測(cè)點(diǎn)C14和C15以外，模擬值均小于計(jì)算值。總的來(lái)說(shuō)，各測(cè)點(diǎn)模擬曲線與計(jì)算曲線相對(duì)誤差絕對(duì)值均小于10%，在合理范圍，可以參見同領(lǐng)域相關(guān)文獻(xiàn)[31-32]的誤差范圍，由此可見所選取的立筒倉(cāng)有限元模型和動(dòng)態(tài)卸料模擬技術(shù)是可行的。計(jì)算和模擬得到的倉(cāng)壁各測(cè)點(diǎn)動(dòng)態(tài)側(cè)壓力均明顯大于靜態(tài)側(cè)壓力，而且越接近倉(cāng)壁下部，動(dòng)態(tài)側(cè)壓力值比靜態(tài)側(cè)壓力大的愈多，即超壓系數(shù)愈大，當(dāng)?shù)洁徑┒犯浇鼤r(shí)超壓系數(shù)達(dá)到某一較大值，隨后超壓減小，此側(cè)壓力變化趨勢(shì)與實(shí)驗(yàn)測(cè)試結(jié)果是相同的。

圖6 靜態(tài)和動(dòng)態(tài)側(cè)壓力模擬值和計(jì)算值曲線Fig.6 Static and dynamic wall pressure curve of numerical and calculated values

將倉(cāng)壁不同深度處測(cè)點(diǎn)的靜態(tài)和動(dòng)態(tài)側(cè)壓力模擬值和試驗(yàn)值描繪成曲線，如圖7所示?？梢钥闯觯o態(tài)側(cè)壓力模擬值和試驗(yàn)值曲線均較平滑，而且總體變化趨勢(shì)均為倉(cāng)壁下部大于上部；動(dòng)態(tài)側(cè)壓力模擬值曲線較平滑，變化趨勢(shì)與靜態(tài)側(cè)壓力變化趨勢(shì)相似，但是動(dòng)態(tài)側(cè)壓力的試驗(yàn)值隨倉(cāng)壁高度的變化為不規(guī)則曲線，主要是由于動(dòng)態(tài)卸料受隨機(jī)干擾因素影響較大，故將動(dòng)態(tài)側(cè)壓力試驗(yàn)值。擬合曲線一起繪于圖7b中，發(fā)現(xiàn)擬合曲線與模擬曲線變化趨勢(shì)相似，兩者吻合較好。

圖7 側(cè)壓力模擬值和試驗(yàn)值曲線Fig.7 Wall pressure curves of numerical and experimental values

為進(jìn)一步比較側(cè)壓力模擬值和試驗(yàn)值的差異性，將靜態(tài)側(cè)壓力模擬值和試驗(yàn)值及動(dòng)態(tài)側(cè)壓力模擬值和試驗(yàn)擬合值的相對(duì)誤差絕對(duì)值的最大值、最小值和平均值分別列于圖7中，可以發(fā)現(xiàn)相對(duì)誤差絕對(duì)值分別在1.83%～9.97%和0.28%～9.93%之間，各測(cè)點(diǎn)模擬與試驗(yàn)側(cè)壓力的相對(duì)誤差絕對(duì)值均小于10%，是比較合理的計(jì)算結(jié)果，可以參見同領(lǐng)域相關(guān)文獻(xiàn)[31-32]的誤差范圍，由此進(jìn)一步驗(yàn)證了動(dòng)態(tài)卸料模擬技術(shù)的可行性及相關(guān)參數(shù)選取的合理性。然而，無(wú)論是靜態(tài)側(cè)壓力還是動(dòng)態(tài)側(cè)壓力，相對(duì)誤差絕對(duì)值都有個(gè)別測(cè)點(diǎn)達(dá)到9%左右，主要有以下原因：

1）材料屬性問(wèn)題，試驗(yàn)狀態(tài)砂子為散體材料，模擬時(shí)雖然采用了Drucker-Prager準(zhǔn)則，但還是近似地按連續(xù)介質(zhì)考慮的；

2）流動(dòng)狀態(tài)問(wèn)題，筒倉(cāng)卸料時(shí)的流動(dòng)狀態(tài)一般分為整體流動(dòng)和管狀流動(dòng)，整體流動(dòng)時(shí)的動(dòng)態(tài)側(cè)壓力要大于管狀流動(dòng)，試驗(yàn)時(shí)砂子為管狀流動(dòng)，模擬時(shí)無(wú)法精細(xì)地反映這一流動(dòng)狀態(tài)，所以模擬值多數(shù)大于試驗(yàn)值；

3）試驗(yàn)尤其是動(dòng)態(tài)卸料試驗(yàn)，受隨機(jī)干擾因素的影響較靜態(tài)試驗(yàn)大，導(dǎo)致誤差亦較大，因此，后續(xù)研究中，應(yīng)加大試驗(yàn)次數(shù)，更為有效合理地進(jìn)行試驗(yàn)設(shè)計(jì)和數(shù)據(jù)處理，減小誤差，進(jìn)一步提高試驗(yàn)數(shù)據(jù)精度和可靠度。

5 結(jié) 論

通過(guò)運(yùn)用試驗(yàn)測(cè)試、數(shù)值模擬和計(jì)算公式3種方法對(duì)有機(jī)玻璃筒倉(cāng)模型的靜態(tài)和動(dòng)態(tài)側(cè)壓力及卸料過(guò)程中的應(yīng)力分布進(jìn)行了分析研究，得到了一些有價(jià)值的結(jié)論：

1）筒倉(cāng)動(dòng)態(tài)側(cè)壓力大于靜態(tài)側(cè)壓力，但是倉(cāng)壁不同深度處測(cè)點(diǎn)的側(cè)壓力增大幅度不同，因此超壓系數(shù)不同，在鄰近漏斗附近某位置測(cè)點(diǎn)的側(cè)壓力增大幅度最大，超壓系數(shù)達(dá)到1.78，在倉(cāng)壁中部位置側(cè)壓力增大幅度較大，超壓系數(shù)達(dá)到1.73和1.61，其他位置處側(cè)壓力增大幅度一般，超壓系數(shù)在1.45以內(nèi)。

2）靜態(tài)側(cè)壓力和動(dòng)態(tài)側(cè)壓力的模擬值與計(jì)算值、試驗(yàn)值或試驗(yàn)擬合值吻合度較好，說(shuō)明了模擬方法的可行性和合理性；經(jīng)過(guò)誤差分析發(fā)現(xiàn)，個(gè)別測(cè)點(diǎn)的相對(duì)誤差絕對(duì)值達(dá)到了9%左右，主要與模擬時(shí)的材料屬性和流動(dòng)狀態(tài)問(wèn)題及測(cè)試用壓力傳感器精度、標(biāo)定試驗(yàn)和試驗(yàn)次數(shù)等隨機(jī)因素有關(guān)，但大多數(shù)測(cè)點(diǎn)的誤差都很小，而且各測(cè)點(diǎn)壓力大小的分布規(guī)律比較合理。

3）數(shù)值模擬筒倉(cāng)卸料時(shí)，漏斗口附近網(wǎng)格會(huì)發(fā)生較大變形，因此需要利用ABAQUS軟件中的自適應(yīng)網(wǎng)格劃分功能，通過(guò)設(shè)置合理的網(wǎng)格以減小網(wǎng)格畸形導(dǎo)致計(jì)算中斷，在此過(guò)程中，合理設(shè)置漏斗內(nèi)物料單元的網(wǎng)格大小和計(jì)算頻率是關(guān)鍵。

[1] 張少坤. 大直徑鋼筋砼筒倉(cāng)溫度荷載和貯料荷載作用有限元分析[D]. 武漢：武漢理工大學(xué)，2008.

Zhang Shaokun. Temperature Load and Storage Material Load Finite Element Analysis of Large-diameter Reinforced Concrete Silo[D]. Wuhan: Wuhan University of Technology, 2008. (in Chinese with English abstract )

[2] 馬麗沙. 圓形筒倉(cāng)在環(huán)境溫度作用下的研究[D]. 西安：西安建筑科技大學(xué)，2015.

Ma Lisha. The Research of Temperature Effects on the Circular Silo[D]. Xi?an: Xi?an University of Architecture and Technology, 2015. (in Chinese with English abstract )

[3] 郭紅偉. 大型落地式鋼筒倉(cāng)溫度作用有限元分析[D]. 濟(jì)南：山東大學(xué)，2013.

Guo Honwei. The Finite Element Analysis of Temperature Effects on Large Flat-bottom Squat Steel Silos[D]. Jinan: Shandong University, 2013. (in Chinese with English abstract )

[4] 宋靖. 大型高溫貯料筒倉(cāng)受力性能分析[D]. 杭州：浙江大學(xué)，2014.

Song Jing. Mechanical Behavior Analysis of Large Silos Storage for High Temperature Stored Materials[D]. Hangzhou: Zhejiang University, 2014. (in Chinese with English abstract )

[5] 尹君，吳子丹，張忠杰，等. 不同倉(cāng)型的糧堆溫度場(chǎng)重現(xiàn)及對(duì)比分析[J]. 農(nóng)業(yè)工程學(xué)報(bào)，2015，31(1)：281－287.

Yin Jun, Wu Zidan, Zhang Zhongjie, et al. Comparison and analysis of temperature field reappearance in stored grain ofdifferent warehouses[J]. Transactions of the Chinese Society of Agricultural Engineering (Transactions of the CSAE), 2015, 31(1): 281－287. (in Chinese with English abstract )

[6] 王學(xué)文，樹學(xué)峰，楊兆建. 散料與錐倉(cāng)接觸模擬[J]. 農(nóng)業(yè)機(jī)械學(xué)報(bào)，2010，41(10)：86－90.

Wang Xuewen, Shu Xuefeng, Yang Zhaojian. Contact simulation on loose material and cone-shaped silo[J]. Transactions of the Chinese Society for Agricultural Machinery, 2010, 41(10): 86－90. (in Chinese with English abstract)

[7] Colonnello C, Reyes L I, Clémentb E, et al. Behavior of grains in contact with the wall of a silo during the initial instants of a discharge-driven collapse[J]. Physica A-Statistical Mechanics and Its Applications, 2014, 398: 35－42.

[8] Durmu? A, Livaoglu R. A simplified 3D.O.F.model of a FEM model for seismic analysis of a silo containing elastic material accounting for soil–structure interaction[J]. Soil Dynamic sand Earthquake Engineering, 2015, 77: 1－14.

[9] 劉立意，郝世楊，張萌，等. 基于CFD-DEM的稻谷通風(fēng)阻力數(shù)值模擬與試驗(yàn)[J]. 農(nóng)業(yè)機(jī)械學(xué)報(bào)，2015，46(8)：27－32，158.

Liu Liyi, Hao Shiyang, Zhang Meng, et al. Numerical simulation and experiment on paddy ventilation resistance based on CFD-DEM[J]. Transactions of the Chinese Society for Agricultural Machinery, 2015, 46(8): 27－32, 158. (in Chinese with English abstract)

[10] 周長(zhǎng)東，郭坤鵬，孟令凱，等. 鋼筋混凝土筒倉(cāng)散料的靜力相互作用分析[J]. 同濟(jì)大學(xué)學(xué)報(bào)：自然科學(xué)版，2015,，43(11)：1656－1661，1669.

Zhou Changdong, Guo Kunpeng, Meng Lingkai, et al. Static interaction analysis of RC silo structure-granular material[J]. Journal of Tongji University: Natural Science, 2015, 43(11): 1656－1661, 1669. (in Chinese with English abstract)

[11] 楊鴻，楊代恒，趙陽(yáng). 鋼筒倉(cāng)散料靜態(tài)壓力的三維有限元模擬[J]. 浙江大學(xué)學(xué)報(bào)：工學(xué)版，2011，45(8)：1423－1429. Yang Hong, Yang Daiheng, Zhao Yang. Three-dimensional finite element simulation of static granular material pressure for steel silos[J]. Journal of Zhejiang University: Engineering Science, 2011, 45(8): 1423－1429. (in Chinese with English abstract)

[12] 樓曉明，施廣換，陳飛，等. 環(huán)錐型散體材料對(duì)筒倉(cāng)側(cè)壁的主動(dòng)側(cè)壓力[J]. 巖土工程學(xué)報(bào)，2010，32(增刊2)：25－28. Lou Xiaoming, Shi Guanghuan, Chen Fei, et al. Active lateral pressure of loop-cone shaped granular material against silo wall[J]. Chinese Journal of Geotechnical Engineering, 2010, (Supp.2): 25－28. (in Chinese with English abstract )

[13] 陳小輝，徐志楊，秦廣樂(lè). 筒倉(cāng)卸料的離散單元法模擬[J].中國(guó)粉體技術(shù)，2011，17(5)：61－64.

Chen Xiaohui, Xu Zhiyang, Qin Guangle. Distinct element method simulation of discharging in coal silos[J]. China Powder Science and Technology, 2011,17(5): 61－64. (in Chinese with English abstract)

[14] 劉震，王學(xué)文，楊兆建. 基于EDEM的筒倉(cāng)靜置與卸料側(cè)壓力模擬[J]. 中國(guó)農(nóng)機(jī)化學(xué)報(bào)，2015，36(2)：104－106，72.

Liu Zhen, Wang Xuewen, Yang Zhaojian. Simulation of lateral pressure during stewing and discharging in silos based on EDEM[J]. Journal of Chinese Agricultural Mechanization, 2015, 36(2): 104－106, 72. (in Chinese with English abstract)

[15] U?ac R O, Vidales A M, Benegas O A, et al. Experimental study of discharge rate fluctuations in a silo with different hopper geometries[J]. Powder Technology, 2012, 225: 214－220.

[16] Choi K, Mogami T, Suzuki T, et al. Experimental study on the relationship between the charge amount of polypropylene granules and the frequency of electrostatic discharges while silo loading[J]. Journal of Loss Prevention in the Process Industries, 2014, 32: 1－4.

[17] 林紅，魏文暉，胡智斌，等. 鋼筋混凝土筒倉(cāng)庫(kù)側(cè)卸料靜動(dòng)態(tài)壓力分布研究[J]. 土木工程與管理學(xué)報(bào)，2014，31(2)：29－33.

Lin Hong, Wei Wenhui, Hu Zhibin, et al. Study on the static and dynamic lateral pressure of reinforced concrete silo under side discharge[J]. Journal of Civil Engineering and Management, 2014, 31(2): 29－33. (in Chinese with English abstract)

[18] Volpato S, Artoni R, Santomaso A C. Numerical study on the behavior of funnel flow silos with and without inserts through a continuum hydrodynamic approach[J]. Chemical Engineering Research and Design, 2014, 92: 256－263.

[19] Gallego E, Ruiz A, Aguado P J. Simulation of silo filling and discharge using ANSYS and comparison with experimental data[J]. Computers and Electronics in Agriculture, 2015, (118): 81－289.

[20] Wang Yin, Lu Yong, Jin Y O. Finite element modeling of wall pressures in a cylindrical silo with conical hopper using an Arbitrary Lagrangian-Eulerian formulation[J]. Powder Technology, 2014, 257(5): 181－190.

[21] Ding S, Li H, Ooi J Y, et al. Prediction of flow patterns during silo discharges using a finite element approach and its preliminary experimental verification[J]. Particuology, 2015, 18(2): 42－49.

[22] Volpato S, Artoni R, Santomaso A C. Numerical study on the behavior of funnel flow silos with and without inserts through a continuum hydrodynamic approach[J]. Chemical Engineering Research and Design, 2014, 92(2): 256－263.

[23] Mellmann J, Hoffmann T, Fürll C. Mass flow during unloading of agricultural bulk materials from silos depending on particle form, flow properties and geometry of the discharge opening[J]. Powder Technology, 2014, 253(2): 46－52.

[24] Ritwik M, Gargi D, Prasanta K D. Experiments on eccentric granular discharge from a quasi-two-dimensional silo[J]. Powder Technology, 2016, 31(11): 1054－1066.

[25] Ramírez A, Nielsen J, Ayuga F. Pressure measurements in steel silos with eccentric hoppers[J]. Powder Technology, 2010, 201(1): 7－20.

[26] 付建寶. 復(fù)雜條件下大型筒倉(cāng)側(cè)壓力的極限分析與彈塑性有限元分析[D]. 大連：大連理工大學(xué)，2006.

Fu Jianbao. Limit Analysis and Elastio-plastic Finite Element Analysis of Lateral Pressure of Large Diameter Silo Under Complicated Conditions[D]. Dalian: Dalian University of Technology, 2006. (in Chinese with English abstract)

[27] 李勝利，王朝霞，王小慧. 不同方法分析大直徑筒倉(cāng)的側(cè)壓力比較[J]. 露天采礦技術(shù)，2010，(3)：61－63.

Li Shengli, Wang Zhaoxia, Wang Xiaohui. Comparative analyses of large diameter silo lateral pressure with different methods [J]. Opencast Mining Technology, 2010, (3): 61－63. (in Chinese with English abstract)

[28] 孫巍巍，張園，孟少平，等. 基于三維離散單元法的大直徑淺圓倉(cāng)偏心卸料研究[J]. 南京理工大學(xué)學(xué)報(bào)，2014，38(3)：414－418，423.

Sun Weiwei, Zhang Yuan, Meng Shaoping, et al. Eccentric discharge of large diameter squat silos based on threedimensional discrete element method[J]. Journal of Nanjing University of Science and Technology, 2014, 38(3): 414－418, 423. (in Chinese with English abstract)

[29] 尹冠生，黃義. 大型筒倉(cāng)結(jié)構(gòu)與地基的動(dòng)力相互作用研究[J]. 空間結(jié)構(gòu)，2002，8(3)：41－50.

Yin Guansheng, Huang Yi. Analysis of dynamic interaction of large silo structure and ITS foundation[J]. Spatial Structures, 2002, 8(3): 41－50. (in Chinese with English abstract)

[30] GB50077-2003，鋼筋混凝土筒倉(cāng)設(shè)計(jì)規(guī)范[S].北京：中國(guó)計(jì)劃出版社，2003.

[31] 劉定華，王建華，楊建斌. 鋼筋混凝土筒倉(cāng)側(cè)壓力的試驗(yàn)研究[J]. 西安建筑科技大學(xué)學(xué)報(bào)，1995，27(1)：8－12.

Liu Dinghua, Wang Jianhua, Yang Jianbin. An experimental study of the lateral pressure on the wall of reinforced concrete silo[J]. Journal of Xi'an University of Architecture & Technology, 1995, 27(1):8－12. (in Chinese with English abstract)

[32] 劉定華，魏宜華. 鋼筋混凝土筒倉(cāng)側(cè)壓力的計(jì)算與測(cè)試[J].建筑科學(xué)，1998，14(4)：14－18.

Liu Dinghua, Wei Yihua. Calculation and testing of lateral pressure in a reinforced concrete silo[J]. Building Science, 1998, 14(4): 14－18. (in Chinese with English abstract)

Simulation and experimental validation of silo wall pressure during discharging

Zhang Daying1, Xu Qikeng2, Wang Shuming3, Liang Xingpei2
(1. School of Civil Engineering, Zhengzhou University of Aeronautics, Zhengzhou 450015, China; 2. School of Civil Engineering and Architecture, Henan University of Technology, Zhengzhou 450001, China; 3. Zhengzhou University Multi-functional Design and Research Academy Co.. Ltd., Zhengzhou 450002, China)

Wall pressure especially dynamic wall pressure of the single silo is crucial for the silo design. Therefore, it’s necessary to obtain static and dynamic wall pressures, as well as their change regularity along the silo wall. In view of this, 2 techniques were mainly used in this study containing experimental method and simulation technique in order to solve the aforementioned problem. Apparently, it is difficult and intractable to study and discuss wall pressures of the silo during discharging. Nevertheless, it is direct and efficient to carry out experiment on this issue, so we carried out this test in Structure Laboratory of Henan University of Technology. In this experiment, the test object was a miniature silo model of organic glass due to its transparency to materials. We could clearly observe flow patterns of materials inside the silo. The silo model was full of standard sand, and sensors were pasted on the internal surface of the silo wall to record test data. The static wall pressure was tested after the silo model was filled up, and the dynamic wall pressure was tested during discharging. In order to obtain accurate experimental results, tests with many times had been done. On the other hand, for mutual authentication, ABAQUS software was employed to simulate the flow of material during discharging. The finite element model (FEM) was two-dimensional (2D) model with a rigid line representing the silo wall and a plane representing the material. In this process, surface-to-surface contact was used, and the silo wall and the material boundary were set to the target and contact element respectively. What was more, adaptive mesh subdivision technology was very important, for time duration of material discharging was directly affected, and it lasted 0.25 s in the process. In addition, some phenomena appeared in Mises stress cloud charts. The larger the Mises stress changed from the silo wall to the hopper wall, the larger the stress area on the hopper wall increased over time. Moreover, in order to verify the experimental and numerical results, theoretical formulae in Chinese code were used to calculate static and dynamic wall pressures, and it was verified that the calculated values were large influenced by the wall pressure coefficient. After that, experimental results, simulation results and theoretical values were also obtained and compared with each other. It was shown that dynamic pressures were bigger than the static ones; the maximum overpressure coefficient reached 1.78 at 0.15 m, the second larger overpressure coefficient reached 1.73 at 0.65 m, and thus the dynamic pressures increased by over 70% compared with the static pressures for the 2 measure points. About the other measure points, the overpressure coefficient was less than 1.45, and the minimum was 0.99. The other comparative results showed that the difference between simulated values and theoretical values of the silo wall pressure was small. To some extent, it was more or less different between experimental values and simulated values due to sensor accuracy and calibration test errors, but the variation tendency of static wall pressure was almost the same; in addition the dynamic pressure was affected larger than the static pressure by the above factors, and therefore the experimental curve was a little irregular, while the simulated curve of it was more smooth. And then, some helpful phenomena appeared through data analysis of measure points, for example, dynamic wall pressure amplitude of each measure point was different, and the maximum was next to the hopper; the higher value was nearly in the middle of the silo wall. Through the above analysis, the proposed simulated and experimental method are also feasible to obtain static and dynamic wall pressures of the silo, and the obtained change regularity of pressures along the silo wall is useful for the silo design and further research.

silo; models; finite element method; experimental study on wall pressure; simulation technique during discharging

10.11975/j.issn.1002-6819.2017.05.039

TU317+.1

A

1002-6819(2017)-05-0272-07

張大英，許啟鏗，王樹明，梁醒培. 筒倉(cāng)動(dòng)態(tài)卸料過(guò)程側(cè)壓力模擬與驗(yàn)證[J]. 農(nóng)業(yè)工程學(xué)報(bào)，2017，33(5)：272－278.

10.11975/j.issn.1002-6819.2017.05.039 http://www.tcsae.org

Zhang Daying, Xu Qikeng, Wang Shuming, Liang Xingpei. Simulation and experimental validation of silo wall pressure during discharging[J]. Transactions of the Chinese Society of Agricultural Engineering (Transactions of the CSAE), 2017, 33(5): 272－278. (in Chinese with English abstract) doi：10.11975/j.issn.1002-6819.2017.05.039 http://www.tcsae.org

2015-11-30

2016-12-30

國(guó)家自然科學(xué)基金資助項(xiàng)目“基于環(huán)境激勵(lì)的鋼筋混凝土立筒群倉(cāng)動(dòng)力相互作用機(jī)理研究”（51178164）；鄭州市科技計(jì)劃項(xiàng)目“立筒倉(cāng)的動(dòng)力測(cè)試優(yōu)化與動(dòng)力特性研究”（20140586）

張大英，女（漢族），山東淄博人，講師，博士，主要從事糧倉(cāng)結(jié)構(gòu)動(dòng)力問(wèn)題計(jì)算、測(cè)試與分析。鄭州 鄭州航空工業(yè)管理學(xué)院土木建筑工程學(xué)院， 450015。Email：daying803@126.com