付 強(qiáng)，李 玥，李天霄，崔 嵩，劉 東（東北農(nóng)業(yè)大學(xué)水利與土木工程學(xué)院，哈爾濱 150030）

渠道滲漏HYDRUS模擬驗(yàn)證及影響因素分析

付 強(qiáng)，李 玥，李天霄，崔 嵩，劉 東
（東北農(nóng)業(yè)大學(xué)水利與土木工程學(xué)院，哈爾濱 150030）

渠道滲漏影響灌溉水利用效率，分析影響滲漏的主要因素，評(píng)估各影響因素對(duì)渠道滲漏的影響程度，可以為提高灌溉水利用效率提供理論參考。為了得到渠道滲漏的主要影響因素，進(jìn)行了渠道滲漏室內(nèi)模擬試驗(yàn)，觀測(cè)不同邊坡系數(shù)、入滲水頭、渠道底寬下的累積入滲量和濕潤鋒推進(jìn)過程，建立試驗(yàn)條件下的土壤水分運(yùn)動(dòng)模型，選用HYDRUS-2D軟件求解所建模型，并將求解得到的模擬值與實(shí)測(cè)值進(jìn)行比較，結(jié)果表明，模型模擬R2均高于0.9、均方根誤差為0.43～4.99 L，檢驗(yàn)了所建模型可以用于模擬渠道滲漏的土壤水分入滲過程。模擬表明，邊坡系數(shù)對(duì)濕潤鋒運(yùn)移距離和累積入滲量的影響很小，渠道底寬對(duì)渠道土壤水分入滲過程的影響較大，通過雙因素方差分析，渠道底寬對(duì)累積入滲量和濕潤鋒運(yùn)移距離的影響極顯著（P＜0.01），而入滲水頭對(duì)水平距離的影響顯著（P＜0.05），渠道底寬和入滲水頭之間不存在顯著的交互影響（P＞0.05）。研究結(jié)果可以為提高灌溉水利用效率、對(duì)灌溉渠道防滲提供技術(shù)參考。

渠道；入滲；數(shù)值分析；HYDRUS-2D；濕潤鋒；滲漏

0 引 言

灌溉水損失的一大部分來自渠道滲漏，渠道水滲漏會(huì)降低灌區(qū)的灌溉水利用效率，造成水資源的浪費(fèi)。由于通過大田試驗(yàn)研究渠道滲漏土壤入滲規(guī)律比較困難，室內(nèi)模擬試驗(yàn)開始受到關(guān)注：孫美等進(jìn)行了夾砂層狀土的渠道滲漏室內(nèi)模擬試驗(yàn)，發(fā)現(xiàn)夾砂層會(huì)使?jié)駶欎h出現(xiàn)不連續(xù)的現(xiàn)象，具有一定的阻水減滲效果[1]；張銳等開展了室內(nèi)土箱模擬試驗(yàn)，發(fā)現(xiàn)土壤體積質(zhì)量越大，入滲水頭越高，灌溉需水量越少[2]；Zhang等[3]實(shí)施了不同土壤類型、初始含水量和壟溝尺寸下的6組室內(nèi)試驗(yàn)，觀測(cè)了累積入滲量、濕潤鋒分布的變化，為設(shè)計(jì)壟溝種植系統(tǒng)提供了參考；Phogat等[4]利用土箱試驗(yàn)驗(yàn)證了二維水平衡模型，并分析了渠床高程對(duì)滲流和地下水位上升的影響；冀榮華等[5]在室內(nèi)模擬了負(fù)壓灌溉下的土壤水分運(yùn)動(dòng)，得到了灌水器半徑對(duì)土壤入滲有顯著影響的結(jié)論；聶衛(wèi)波等[6]通過模擬溝灌入滲，建立了溝灌土分運(yùn)動(dòng)數(shù)值模型，并以此為基礎(chǔ)，推導(dǎo)出溝灌條計(jì)算累積入滲量的方法。數(shù)值模擬方面，有限元計(jì)算機(jī)模型HYDRUS具有豐富的功能[7-12]：Bufon等[13]用HYDRUS-2D計(jì)算了滴灌條件的棉花含水量，發(fā)現(xiàn)計(jì)算結(jié)果與測(cè)量數(shù)據(jù)擬合程度較高；Kandelous等[14]用HYDRUS-2D模擬了地下滴灌系統(tǒng)的室內(nèi)和大田試驗(yàn)，并用均方根誤差對(duì)試驗(yàn)結(jié)果和模擬結(jié)果進(jìn)行了評(píng)價(jià)，認(rèn)為其對(duì)應(yīng)關(guān)系非常好；張勇勇[15]建立了壟溝灌溉下的土壤水動(dòng)力學(xué)模型，用HYDRUS-2D軟件進(jìn)行求解，得到了不同試驗(yàn)條件下的土壤含水量、累積入滲量和濕潤鋒運(yùn)移距離并驗(yàn)證了設(shè)立模型的合理性。以上研究成果表明，用HYDRUS-2D模擬土壤水分入滲過程具有較高的可靠性，但并未考慮渠道邊坡系數(shù)對(duì)土壤入滲的影響及各因素之間的交互特性；邊坡系數(shù)作為渠道的重要參數(shù)，其變化對(duì)渠道入滲的影響非常重要，而各因素之間的交互影響對(duì)渠道斷面的優(yōu)化設(shè)計(jì)也起著決定性的作用。本文開展渠道滲漏室內(nèi)模擬試驗(yàn)，建立試驗(yàn)條件下的土壤水分運(yùn)動(dòng)方程，通過試驗(yàn)和模擬方法分析邊坡系數(shù)、入滲水頭和渠道底寬及其交互作用對(duì)濕潤鋒運(yùn)移距離和累積入滲量的影響，研究渠道土壤水分運(yùn)動(dòng)的主要影響因素，以期為減少渠道水滲漏，提高灌溉水利用效率提供理論支持。

1 材料與方法

1.1 室內(nèi)試驗(yàn)

1.1.1 試驗(yàn)設(shè)備

試驗(yàn)設(shè)備由模擬土箱和供水設(shè)備2部分構(gòu)成，模擬土箱規(guī)格為60 cm×20 cm×110 cm，由有機(jī)玻璃制成，為了防止氣阻，土箱側(cè)面和正面均留有排氣孔；為了讀數(shù)方便，土箱后側(cè)玻璃板貼有刻度條。試驗(yàn)由馬氏瓶供水，馬氏瓶直徑20 cm，高80 cm[16-17]。試驗(yàn)土箱內(nèi)按照試驗(yàn)設(shè)計(jì)要求，設(shè)置恰當(dāng)?shù)那罃嗝娉叽?，試?yàn)裝置如圖1。

圖1 室內(nèi)模擬試驗(yàn)裝置Fig. 1 Indoor simulation experimental setup

1.1.2 供試土樣

試驗(yàn)土樣于2016年7月取自哈爾濱市東北農(nóng)業(yè)大學(xué)水利學(xué)院試驗(yàn)田（126°45′32″E、45°44′41″N）[18]。取樣深度為10～30 cm，土壤質(zhì)地為壤土，顆粒比較均勻，試驗(yàn)前，土樣風(fēng)干破碎，過2 mm篩，配置初始質(zhì)量含水率7%，按設(shè)計(jì)干容重1.4 g/cm3分層（10 cm）裝入試驗(yàn)土箱中，層間打毛[19]。

1.1.3 試驗(yàn)設(shè)計(jì)

室內(nèi)試驗(yàn)于2016年夏季在東北農(nóng)業(yè)大學(xué)水利學(xué)院水工廳內(nèi)進(jìn)行。試驗(yàn)采用三因素完全試驗(yàn)設(shè)計(jì)，設(shè)計(jì)的渠道底寬分別為5、10、15 cm；入滲水頭分別為3、6、9 cm；邊坡系數(shù)分別為1、1.2、1.5，共27個(gè)處理，各3次重復(fù)，需進(jìn)行81次試驗(yàn)?？紤]到工作量較大，而且試驗(yàn)?zāi)康氖菫榱四Ｐ秃侠硇苑治?，?shí)際進(jìn)行了15個(gè)處理試驗(yàn)。每次試驗(yàn)持續(xù)時(shí)間為480 min。

試驗(yàn)開始時(shí)首先按照設(shè)計(jì)的渠道斷形狀裝填土樣，隨后調(diào)節(jié)馬氏瓶進(jìn)氣管低端至設(shè)計(jì)入滲水頭高度，快速向土箱內(nèi)加水至設(shè)計(jì)水位，同時(shí)打開其止水夾，再對(duì)進(jìn)氣管低端高度進(jìn)行微調(diào)。試驗(yàn)開始后每隔5 min記錄馬氏瓶讀數(shù)，每隔10 min在土箱貼有刻度條的一側(cè)描繪濕潤峰曲線；試驗(yàn)進(jìn)行一段時(shí)間后根據(jù)濕潤鋒運(yùn)移距離和入滲速度適當(dāng)延長讀數(shù)、描繪時(shí)間間隔。試驗(yàn)結(jié)束后用分辨率為1334×750像素的相機(jī)拍下繪制的濕潤峰曲線，整理數(shù)據(jù)。

1.2 模型建立

1.2.1 渠道水分運(yùn)動(dòng)模型

設(shè)計(jì)試驗(yàn)條件下的渠道水分入滲過程可以簡(jiǎn)化為二維非飽和水平及垂直入滲土壤水分運(yùn)動(dòng)問題，采用Richards方程進(jìn)行描述[20]。

式中θ為土壤體積含水率，cm3/cm3；t為入滲時(shí)間，min；h為基質(zhì)勢(shì)，cm；x、z分別水平坐標(biāo)和垂直距離，cm；K(h)為土壤非飽和導(dǎo)水率，cm/min。

上述Richards方程中提及的非飽和導(dǎo)水率、土壤基質(zhì)勢(shì)及含水率的關(guān)系采用VG-M模型進(jìn)行描述[21-22]。

式中θr為殘余含水率，cm3/cm3；θs為飽和含水率，cm3/；KS為飽和導(dǎo)水率，cm/min；m、n、α為經(jīng)驗(yàn)系數(shù)，m=1-1/n。

根據(jù)離心機(jī)實(shí)測(cè)的土壤水分特征曲線，環(huán)刀法實(shí)測(cè)的飽和導(dǎo)水率等數(shù)據(jù)，采用MATLAB2012a擬合得到相關(guān)模型參數(shù)[23-26]：飽和含水率0.438 cm3/cm3；殘余含水率0.042 cm3/cm3；α為 0.029；n為1.274；飽和導(dǎo)水率0.049 cm3/cm3。

1.2.2 定解條件

所建模型的初始和邊界條件如圖2所示。

圖2 模型求解的邊界條件Fig. 2 Boundary conditions for model solving

初始條件：在設(shè)計(jì)的試驗(yàn)條件下，土壤水分剖面為穩(wěn)定剖面。因此，模型的初始條件為計(jì)算區(qū)域內(nèi)各點(diǎn)具有相同的水土勢(shì)。

式中H0為初始水土勢(shì)，cm；Ω為計(jì)算區(qū)域（即圖2中的陰影部分）；模擬區(qū)域最低點(diǎn)的z=0。

邊界條件：試驗(yàn)過程中EFQ保持恒定入滲水頭h0(cm)；上邊界QG和GC覆蓋塑料薄膜，可以忽略蒸發(fā)，視為零通量邊界；左邊界EA為對(duì)稱軸，水平通量為0；右邊界CB視為零通量面；下邊界AB設(shè)置了排水孔，而且在試驗(yàn)過程中濕潤鋒未到達(dá)土槽底部，不影響土壤水分入滲過程，保持恒定初始條件，設(shè)為自由排水邊界。

綜上，其邊界條件可表述為

式中t0為試驗(yàn)延續(xù)時(shí)間，min。

1.2.3 數(shù)值計(jì)算

為了求解上述偏微分方程，采用HYDRUS-2D軟件對(duì)試驗(yàn)設(shè)計(jì)方案下的濕潤鋒運(yùn)移水平、豎直距離和累積入滲量進(jìn)行數(shù)值模擬[27-29]，并將所得結(jié)果與試驗(yàn)結(jié)果進(jìn)行對(duì)比分析，采用均方根誤差（root mean square error，RMSE）和決定系數(shù)（R2）[30]檢驗(yàn)所建立的土壤水分運(yùn)動(dòng)方程的合理性。

2 結(jié)果與分析

2.1 模型驗(yàn)證

2.1.1 累積入滲量對(duì)比

從15組試驗(yàn)中隨機(jī)選取9組試驗(yàn)組合研究其累積入滲量實(shí)測(cè)值和模擬值動(dòng)態(tài)變化（圖3）。結(jié)果表明，模擬值與實(shí)測(cè)值變化趨勢(shì)一致，均表現(xiàn)出初期入滲較快，隨入滲時(shí)間的延長入滲速率逐漸降低，并趨向穩(wěn)定的狀態(tài)。各次試驗(yàn)累積入滲量的模擬值和實(shí)測(cè)值的RMSE和 R2如表1所示。由表1可知，RMSE的值在0.43～4.99 L之間變化，R2值在0.91～0.97之間變化（均高于0.9），說明實(shí)測(cè)值與模擬值之間的對(duì)應(yīng)關(guān)系較好，所建立的土壤水分運(yùn)動(dòng)方程合理。

表1 累積入滲量實(shí)測(cè)值和模擬值的統(tǒng)計(jì)分析Table 1 Statistical analysis of measured and simulated cumulative infiltration

圖3 各試驗(yàn)條件下累積入滲量的模擬值與實(shí)測(cè)值對(duì)比Fig. 3 Comparison of simulated and measured cumulative infiltration under various experimental conditions

2.1.2 濕潤鋒運(yùn)移距離對(duì)比

以4種組合試驗(yàn)為例（圖4），對(duì)比480 min內(nèi)濕潤鋒運(yùn)移距離模擬值和實(shí)測(cè)值，結(jié)果表明，各處理?xiàng)l件下濕潤鋒運(yùn)移距離的實(shí)測(cè)值與模擬值基本吻合，均表現(xiàn)出初期運(yùn)移速度較快，隨試驗(yàn)時(shí)間的延長漸漸減緩，并趨于穩(wěn)定。

綜上，實(shí)測(cè)數(shù)據(jù)與模擬結(jié)果吻合較好，可以認(rèn)為本文建立的土壤水動(dòng)力學(xué)模型是可靠的，選取的相關(guān)參數(shù)值是適當(dāng)?shù)?，用于模擬試驗(yàn)條件下的累積入滲量和濕潤鋒運(yùn)移過程是可行的。

2.2 基于HYDRUS模擬的累積入滲量影響因素分析

為了分析渠道底寬w、入滲水頭h0、邊坡系數(shù)f對(duì)累積入滲量的影響，用HYDRUS軟件模擬了27組渠道滲漏試驗(yàn)。以圖5為例表明累積入滲量隨三者的變化。由圖可知，累積入滲量隨渠道底寬和入滲水頭變化較大，但邊坡系數(shù)f對(duì)累積入滲量的影響很小。

圖4 各試驗(yàn)條件下濕潤峰的模擬值與實(shí)測(cè)值對(duì)比Fig. 4 Comparison of simulated and measured wetting front under various experimental conditions

圖5 各試驗(yàn)條件下的累積入滲量對(duì)比Fig. 5 Comparison of cumulative infiltration under different experimental conditions

對(duì)w和h0下渠道480 min累積入滲量做雙因素方差分析，結(jié)果見表2。由表2可以看出，w對(duì)累積入滲量影響的F值為59.46，遠(yuǎn)大于臨界值4.78，說明渠道底寬對(duì)入滲量的影響極顯著（P＜0.01）。當(dāng)f=1、h0=3 cm時(shí)，若w由5 cm增加到15 cm時(shí)，累積入滲量由7 688 mL增加到37 027 mL，增加了382%。表2還表明h0對(duì)累積入滲量影響的F值為2.612，小于臨界值4.778，說明其對(duì)累積入滲量的影響不顯著（P＞0.05）。二者之間交互影響F值為0.30，說明w和h0的交互作用不顯著（P＞0.05）。這是因?yàn)?，隨著f、h0和w的增加，濕周增加，入滲界面受水面積增加，因而累積入滲量增加。而f對(duì)濕周的影響很小，因此其對(duì)渠道入滲的影響不作考慮。且由表2可以看出，濕周隨w的增幅比隨h0的增幅大，因此w對(duì)累積入滲量的影響比h0顯著。

2.3 基于HYDRUS模擬的濕潤鋒運(yùn)移距離影響因素分析

不同水頭下底寬、邊坡系數(shù)對(duì)濕潤鋒運(yùn)移影響類似，故以水頭為9 cm表明不同底寬和邊坡系數(shù)對(duì)濕潤鋒運(yùn)移的影響，如圖6所示?？梢钥闯?，邊坡系數(shù)對(duì)濕潤鋒運(yùn)移距離幾乎沒有影響，而渠道底寬、入滲水頭與濕潤鋒運(yùn)移距離呈正相關(guān)。

方差分析表明（表2），w對(duì)水平距離影響的F值為59.55，垂直距離為7.42，均大于臨界值4.78，而且水平距離的F值遠(yuǎn)大于垂直距離，說明w對(duì)濕潤鋒運(yùn)移距離的影響顯著（P＜0.01），且對(duì)水平距離的影響特別顯著（P＜0.01），比如在t=480 min，f=1、h0=3 cm的條件下，當(dāng)w由5 cm增加到15 cm時(shí)，濕潤鋒運(yùn)移水平、垂直距離分別增加了55.89%和47.82%。這是因?yàn)樵趂和h0不變的情況下，隨著w的增加，入滲界面濕周增加，濕潤鋒運(yùn)移距離有所增加，而w的增加直接導(dǎo)致垂向入滲面積增加，因而對(duì)水平距離的影響更為顯著。入滲水頭對(duì)水平距離影響的F值為19.14，垂直距離為3.0。說明h0對(duì)水平距離的影響顯著（P＜0.05），如在w=5 cm的條件下，

當(dāng)h0由3 cm增加到9 cm時(shí)，濕潤鋒運(yùn)移水平增加了33.45%。在w和f不變的條件下，隨著h0增加，入滲界面壓力勢(shì)和受水面積增加，而h0的增加對(duì)垂向入滲面的影響較大，因而對(duì)水平距離的影響比較顯著。w、h0對(duì)濕潤鋒運(yùn)移水平、垂直距離的交互影響F值分別為0.15和0.004，說明w、h0對(duì)濕潤鋒運(yùn)移距離不存在顯著的交互作用（P＜0.05）。

圖6 各試驗(yàn)條件下的濕潤鋒運(yùn)移距離對(duì)比Fig. 6 Comparison of wetting front migration distance under different experimental conditions

2.4 入滲速率變化

所有試驗(yàn)條件下的入滲速率均展現(xiàn)出隨時(shí)間的延長漸漸減小并趨向穩(wěn)定的征象；在試驗(yàn)開始初期，入滲速率下降得較快，隨著時(shí)間的延長，土壤水土勢(shì)梯度漸漸減小，入滲速率也隨之減小并趨向一個(gè)定值。以f =1.5為例（圖7），在w和f相同的條件下，隨h0的增加，入滲速率增加。其原因?yàn)椋琱0增加時(shí)，入滲界面處壓力勢(shì)增大導(dǎo)致入滲速率增加；隨入滲時(shí)間的推移，土壤濕潤區(qū)域變大，水土勢(shì)不斷減小，并趨于穩(wěn)定，因此入滲速率漸漸趨于穩(wěn)定。在相同h0和f條件下，入滲速率隨渠道底寬的增加而增加，且增幅較大。其原因?yàn)?，渠道底寬增加，入滲界面濕周增加，受水面積變大，使得入滲速率增大。在w和h0相同的條件下，由于f對(duì)入滲斷面濕周的影響很小，因此f對(duì)入滲速率幾乎沒有影響。

圖7 邊坡系數(shù)為1.5時(shí)不同底寬和入滲水頭下的入滲率對(duì)比Fig. 7 Comparison of infiltration rates under different canal base width and infiltration head with slope coefficient of 1.5

3 結(jié) 論

選用基于Richards方程的有限元模擬軟件HYDRUS-2D進(jìn)行數(shù)值模擬得到的模擬值和實(shí)測(cè)值的的擬合程度較高（R2均高于0.9），可以契合地模擬試驗(yàn)條件下的渠道滲漏土壤水分入滲規(guī)律。

模擬結(jié)果均表明，邊坡系數(shù)對(duì)土壤水分入滲過程的影響較為微弱；累積入滲量、濕潤鋒運(yùn)移距離及入滲速率均隨入滲水頭增加而增加，且入滲水頭對(duì)濕潤鋒運(yùn)移水平距離的影響顯著（P＜0.05）；隨渠道底寬的增加，濕潤鋒運(yùn)移距離、累積入滲量以及入滲率均表現(xiàn)出增加的趨勢(shì)，且渠道底寬增加對(duì)累積入滲量和運(yùn)移距離的影響極顯著（P＜0.01）。當(dāng)邊坡系數(shù)為1、入滲水頭為3 cm時(shí)，若底寬由5 cm增加到15 cm時(shí)，480 min累積入滲量增加了382%，濕潤鋒運(yùn)移水平、垂直距離分別增加了55.89%和47.82%。通過雙因素方差分析，發(fā)現(xiàn)渠道底寬和入滲水頭之間的沒有顯著的交互作用。

本文只針對(duì)各影響因素對(duì)渠道滲漏的影響做了定性分析，如何確定各試驗(yàn)條件下累積入滲量和濕潤鋒運(yùn)移距離隨影響因素變化的定量關(guān)系，尋求最優(yōu)經(jīng)濟(jì)效益下的渠道斷面設(shè)計(jì)，將作為下一步研究的重點(diǎn)。

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HYDRUS simulation and verification of canal leakage and its influencing factors analysis

Fu Qiang, Li Yue, Li Tianxiao, Cui Song, Liu Dong
(School of Water Conservancy & Civil Engineering, Northeast Agricultural University, Harbin 150030, China)

Canal leakage is the main factor affecting the efficiency of irrigation water. In this paper, the main factors of canal leakage (referring to infiltration) were analyzed and numerical analysis was carried out. In order to obtain the main factors that affected canal leakage, the indoor leakage simulation experiment was carried out. The experimental site was located in Northeast Agricultural University, Harbin(126°45′32″E、45°44′41″N). The test case was made of Plexiglas material, with the size 60 cm ×20 cm×110 cm (length×width×height). Mariotte flask was used to ensure water supply and its diameter was 20 cm and the height was 80 cm. A total of 15 treatments with 3 replicates were conducted. During the experiment, the cumulative infiltration and wet front migration distance of each experiment were recorded. In addition, the soil water characteristic curve of the soil samples was tested and the relevant parameters in the VG model were fitted. The parameters of the fitting and the saturated hydraulic conductivity measured by the ring knife method were input into the HYDRUS-2D software to solve the soil water movement model under the experimental conditions, and the simulate values were obtained. The error analysis of the simulated and measured values was carried out. The root mean square error and the determination coefficient of each experiment were calculated. The results showed that the model was reasonable with the root mean square error of 0.43-4.99 L and the R2higher than 0.9, and the model could simulate the soil water movement process under the experimental conditions. Based on the measured and simulated values, the influence of the 3 factors on the canal leakage and the influence of these factors on the infiltration process were analyzed. The influence of the slope coefficient on the infiltration process was weak and its influence on the infiltration process could be ignored. Two-way analysis of variance was performed in order to analyze the influence of canal base width and infiltration head and its interaction on cumulative infiltration and wetting front migration distance. The results showed that the statistic value of the canal base width was 55.62 for the cumulative infiltration, 59.46 for the horizontal distance of wet front migration, and 7.42 for the vertical distance. All the 3 statistic values were greater than the critical value of 4.78 under the significance level of 0.01. It indicated that the canal base width had a significant impact on the cumulative infiltration and the wetting front migration distance. The statistic value of the infiltration head at the cumulative infiltration was 2.612, the statistic value of the horizontal distance of wet front migration was 19.14, and the vertical distance was 3.00. The infiltration head had a significant effect on the horizontal distance. The statistic values of the effects of canal width and infiltration head on the cumulative infiltration and the horizontal and vertical distance were 0.30, 0.15 and 0.004, respectively. They were less than the critical value of 3.47, indicating that there was no significant interaction between the canal width and infiltration head (P＞0.05). The results of the study can provide technical support for improving the utilization efficiency of irrigation water from the aspect of canal seepage control.

canals; infiltration; numerical analysis; HYDRUS-2D; wetting front; leakage

10.11975/j.issn.1002-6819.2017.16.015

TV732.6; S152.7+2

A

1002-6819(2017)-16-0112-07

付 強(qiáng)，李 玥，李天霄，崔 嵩，劉 東. 渠道滲漏HYDRUS模擬驗(yàn)證及影響因素分析[J]. 農(nóng)業(yè)工程學(xué)報(bào)，2017，33(16)：112-118.

10.11975/j.issn.1002-6819.2017.16.015 http://www.tcsae.org

Fu Qiang, Li Yue, Li Tianxiao, Cui Song, Liu Dong. HYDRUS simulation and verification of canal leakage and its influencing factors analysis[J]. Transactions of the Chinese Society of Agricultural Engineering (Transactions of the CSAE), 2017, 33(16): 112-118. (in Chinese with English abstract) doi：10.11975/j.issn.1002-6819.2017.16.015 http://www.tcsae.org

2017-02-24

2017-06-10

國家自然科學(xué)基金（51479032、51579044）；國家重點(diǎn)研發(fā)計(jì)劃（2017YFC0406002）

付 強(qiáng)，男，遼寧錦州人，教授，博士生導(dǎo)師，主要從事農(nóng)業(yè)水土資源系統(tǒng)分析、凍融土壤水熱作用機(jī)理等方面研究。哈爾濱 東北農(nóng)業(yè)大學(xué)水利與土木工程學(xué)院，150030。Email：fuqiang0629@126.com。