重力驅(qū)動指流的觀測和數(shù)學(xué)模擬研究綜述

李海龍,夏玉強

(1.中國地質(zhì)大學(xué)(武漢)環(huán)境學(xué)院,湖北 武漢 430074;2.中國地質(zhì)大學(xué)(北京)水資源與環(huán)境科學(xué)學(xué)院,北京 100083;3.美國天普大學(xué)土木與環(huán)境工程系,費城 19122)

重力驅(qū)動指流(gravity-driven fingers),又稱優(yōu)勢流,簡稱指流或指狀分支流,是地表水在重力作用下滲入非飽和土壤中時經(jīng)常發(fā)生的一種現(xiàn)象,其特征是滲入土壤中的水流在土壤中形成固定的指狀優(yōu)勢通道。Gerke[1]指出“指流包括水流和溶質(zhì)不經(jīng)其他土壤部分而沿某些特定通道運移的所有現(xiàn)象”。土壤中指流的存在大大加速了地表水在土壤中的滲流速度,提高了各種養(yǎng)分及污染物在包氣帶中的運移傳輸速度,加劇了工農(nóng)業(yè)生產(chǎn)排放的污染物對土壤的污染。因此,指流的研究已成為與農(nóng)業(yè)、林業(yè)、生態(tài)環(huán)境保護等行業(yè)密切相關(guān)的基礎(chǔ)研究課題之一。

1 指流的形成原因

指流的形成原因復(fù)雜多樣,一種眾所周知的簡單情形就是多孔介質(zhì)中孔隙的隨機分布導(dǎo)致一些較大的孔隙連在一起而形成“優(yōu)勢通道”。當水流在重力作用下滲入多孔介質(zhì)時,會傾向于沿著這樣的優(yōu)勢通道形成指流。指流研究的復(fù)雜性在于其產(chǎn)生原因的多樣性[2]。例如,Coppola等[3]在單個土體尺度上,根據(jù)指流產(chǎn)生機制的不同劃分了4種指流形式:大孔隙(非毛細管孔)流,結(jié)構(gòu)性孔隙流,濕鋒面不穩(wěn)定性引起的指流,以及由土壤濕潤度(或斥水性)空間分布的不規(guī)則性和時間動態(tài)性引起的指流?？傮w來說,導(dǎo)致指流的因素除土壤孔隙度和滲透性空間分布不均(非均質(zhì)性)外,還有非飽和土壤中孔隙水分布不均[4]、毛細作用及其滯后效應(yīng)[5]、土壤質(zhì)地和根系結(jié)構(gòu)[6-9]、孔隙類型和分布[10-11]、施加于土壤表面的入滲流量[12]、非飽和土壤中的氣流以及大氣波動效應(yīng)等。一個簡單而基本的例子是,在實驗室平板玻璃模型中人工選擇的嚴格均質(zhì)砂樣中同樣會產(chǎn)生指流。這種現(xiàn)象在宏觀均質(zhì)的多孔介質(zhì)中,包括在直徑變化范圍很小的玻璃珠堆成的人工多孔介質(zhì)中也會發(fā)生[13-14]。Wallach等[15]的最新研究結(jié)果表明,由于土壤的斥水性,土壤孔隙含水量的空間分布不一定取決于土壤孔隙和滲透性的非均質(zhì)性。

2 近10年來指流研究的主要內(nèi)容

指流研究始于20世紀60年代[16-18]。過去的10多年中,在國際土壤和水文環(huán)境領(lǐng)域中涌現(xiàn)了大量關(guān)于指流研究的文獻[4],表明指流的研究是該領(lǐng)域前沿研究的一個熱點。這些研究的內(nèi)容主要集中在以下幾個方面:①綜述性文章[1-3,4,10-11,19-36];②確定性理論模型和數(shù)值模擬[5,37-53];③室內(nèi)試驗、觀測方法改進和機理定性描述[6-7,12,26,41,54-72];④室內(nèi)試驗和機理分析(包括野外采樣后進行室內(nèi)分析)[2,13-15,49,61,73-93];⑤野外現(xiàn)場試驗(可能有室內(nèi)試驗)[9,94-106]。

通過對上述研究的分析整理,得出以下主要認識:①由于指流研究的復(fù)雜性,其試驗研究目前仍以室內(nèi)分析為主,野外研究較少且其尺度與室內(nèi)試驗差不多。②指流研究所涉及的主要數(shù)學(xué)工具仍然是以微分方程為主的確定性理論,很少有以隨機理論為主要工具來研究指流的文獻。一方面,隨機理論可以被用來確定數(shù)學(xué)模型中水文地質(zhì)參數(shù)的時空分布;另一方面,在這種分布被確定后,探討模型解的性質(zhì)如它是如何依賴于多孔介質(zhì)的水文地質(zhì)參數(shù)等,還需要微分方程所表示的確定性理論來完成。

目前國內(nèi)有關(guān)指流的研究主要集中于大孔隙流、試驗描述以及指流研究進展的介紹等,對于指流的理論研究偏少,尤其是缺少對指流數(shù)學(xué)模型的研究。因此,筆者將著重介紹和總結(jié)重力驅(qū)動指流的精細觀測及其數(shù)學(xué)模擬方面的國際研究進展。

3 重力驅(qū)動指流的觀測及其數(shù)學(xué)模擬研究的重要進展

3.1 新的高時空分辨率的觀測方法

隨著新的試驗觀測方法如X-射線斷層攝影術(shù)(X-raytomography,CT)以及光投射法(light transmission method,LTM)的應(yīng)用[28-29,56-57,62,107],在指流試驗中可實現(xiàn)對孔隙水飽和度的高分辨率測定,其時空分辨率分別可達1s和1mm。而Deinert等[41]所采用的中子射線實時攝影法的時空分辨率分別可達30ms和0.5mm。這種硬件觀測水平的提高為開展高水平的理論研究提供了可靠、翔實的試驗觀測數(shù)據(jù)和以前試驗中難以發(fā)現(xiàn)的新現(xiàn)象。例如DiCarlo[60]所做的飽和度觀測試驗表明,孔隙尺度水平上的物理過程控制著水飽和度在指流指尖處的峰值,從而控制了指流的進一步發(fā)展。又如 Bayer等[54]用X-射線斷層攝影術(shù)測得的毛細壓力在初始階段的增高過程與傳統(tǒng)描述非飽和帶水流的Richards方程所刻畫的單相流有著顯著的差異。

3.2 有關(guān)Richards方程或傳統(tǒng)的水-氣兩相流模型能否完整地刻畫和描述指流的爭論

Nieber[108]利用帶有毛細滯后效應(yīng)的Richards方程,在多孔介質(zhì)水飽和度初值為零的情形下模擬了指流的生成和持續(xù)過程。他發(fā)現(xiàn),為了能夠在數(shù)值模擬中得到指流,剖分節(jié)點間非飽和水力傳導(dǎo)系數(shù)的計算不得不采用下游加權(quán)格式。之后,Ritsema等[109]、Nguyen等[110-111]以及Nieber等[49]在進行斥水沙質(zhì)土壤中指流的數(shù)值模擬時得到了類似結(jié)果,其共同點是都采用了下游加權(quán)格式。此外,Ritsema等[109]給出了在斥水沙質(zhì)土壤中指流形成過程及其復(fù)發(fā)的野外現(xiàn)場圖像,并用水-氣兩相流數(shù)值模型和對液相采用下游加權(quán)格式,重現(xiàn)了某種斥水沙質(zhì)土壤中的指流。但未提及若對水和氣都用上游加權(quán)格式將會得出什么結(jié)果。

Eliassi等[44]考慮了Richards方程是否能夠完整地描述非飽和多孔介質(zhì)中指流的問題,懷疑Richards方程的解是否真的可以產(chǎn)生試驗中觀測到的水飽和度在指流指尖處的非單調(diào)峰值。他們認為,Nieber[108]和Ritsema等[109]所得到的具有水飽和度非單調(diào)峰值的“指狀”數(shù)值解只是一種由于數(shù)值解的振蕩和過飽和而引起的假象,而數(shù)值解的振蕩和過飽和是由于下游加權(quán)法和網(wǎng)格剖分不夠細引起的數(shù)值計算誤差。若利用上游加權(quán)法或者網(wǎng)格剖分足夠細,這種人為產(chǎn)生的“指狀”數(shù)值解就會消失。因此,他們認為 Richards方程或者與之等價的水-氣兩相流模型,加上由Mualem[112-113]和Van Genuchten[114]給出的關(guān)于相對滲透系數(shù)和毛細效應(yīng)滯后現(xiàn)象的基本關(guān)系式所構(gòu)成的數(shù)學(xué)模型不足以描述指流。

Braddock等[40]對 Eliassi等[44]的工作從數(shù)學(xué)角度進行了評論。評論指出:①在二維情形,Eliassi等[44]所提出的關(guān)于Richards方程解的單調(diào)性假設(shè)有待進一步驗證;②關(guān)于時間離散的截斷誤差引起了數(shù)值解的振蕩現(xiàn)象;③振蕩現(xiàn)象對毛細滯后關(guān)系中切換值的選擇造成了很大的困難。Eliassi等[46]回應(yīng)說雖然在二維情形下沒有Richards方程解的單調(diào)性的理論結(jié)果,但是已有的數(shù)百篇公開發(fā)表的論文所給出的二維情形下的解析和數(shù)值解,在均質(zhì)和初邊值條件為常數(shù)時都表現(xiàn)出了單調(diào)性質(zhì)。

Deinert等[59]對Eliassi等[44]的工作做了另一番評論。認為Eliassi等[44]對Nieber[108]所做工作的評論有些言過其實。因為Nieber[108]用簡單模型所得出的模擬結(jié)果和觀測資料相符。Nieber[108]所用的下游加權(quán)格式,只是在模擬觀測得到的指流及其不穩(wěn)定特征時所選擇的一個參數(shù)而已,這與 Deinert等[115]利用試驗所得到的一種類似于達西形式的表達式所定義的動態(tài)毛細壓力所描述的不穩(wěn)定性是一致的。Eliassi等[47]回應(yīng)Nieber[108]所做的數(shù)值模擬是基于下游加權(quán)格式的,因此只能說是假的指流。下游加權(quán)格式會產(chǎn)生足夠大的數(shù)值誤差,從而導(dǎo)致用數(shù)值方法所求解的方程實際上不是Richards方程本身。當網(wǎng)格被適當加密以后,數(shù)值誤差減小,而數(shù)值解所產(chǎn)生的人工指流也隨之消失。

試驗觀測和理論研究表明,在均質(zhì)非飽和土壤中,連續(xù)入滲條件下水飽和度曲線會在入滲前鋒處形成一個非單調(diào)的突起,這個突起不能用傳統(tǒng)的Richards方程來描述[5,60,82]。Nieber等[5]所做的線性穩(wěn)定性分析表明,傳統(tǒng)的Richards方程對無窮小擾動是無條件穩(wěn)定的,即不會產(chǎn)生指流;而把Richards方程和動態(tài)毛細壓力結(jié)合起來所得到的模型卻是有條件穩(wěn)定的,即有可能產(chǎn)生指流。他們對上述動態(tài)毛細壓力機制作了回顧并將之擴展到了含水量小于田間持水量的很干的土壤中。

DiCarlo[82]的最新研究進展表明,上述動態(tài)毛細壓力機制(DiCarlo在文中稱之為非平衡毛細壓力,其實是一樣的)也不能很好地描述指流。在傳統(tǒng)的Richards方程基礎(chǔ)上,加之以動態(tài)毛細壓力,雖然能使模型描述指流的情況大有改善,例如可以預(yù)測出指流發(fā)生的流量范圍等,但對指流尖端處水飽和度非單調(diào)突起的描述仍差強人意。而且當多孔介質(zhì)的固體顆粒尺寸和粗糙程度稍有變化時,為了能擬合指流發(fā)生的流量范圍,就需要對動態(tài)毛細壓力項做大幅度的調(diào)整。這些結(jié)果說明,現(xiàn)有的動態(tài)毛細壓力表達式尚未包含控制指流尖端處水飽和度非單調(diào)突起的物理機制[82]。DiCarlo[61]在實驗室中觀測到了在入滲前鋒處形成的毛細壓力的非單調(diào)突起,且和上述水飽和度曲線的非單調(diào)突起類似。

3.3 有關(guān)新機制和新效應(yīng)的模型

Eliassi等[37]研究了試驗觀測到的水飽和度在指流垂直剖面上呈現(xiàn)的稱之為“后推堆積”(hold-backpile-up)的效應(yīng),這種效應(yīng)是以多孔連續(xù)介質(zhì)為基礎(chǔ)的Richards方程無法描述的。他們對傳統(tǒng)的Richards方程作了若干不同形式的拓展,使之能夠描述這種效應(yīng)。每種拓展都由2項組成:即傳統(tǒng)的Darcy-Buckingham通量項和另一對應(yīng)于“后推堆積”效應(yīng)的項。但正如他們所總結(jié)的那樣,這種拓展在更一般意義上的有效性尚存在疑問,且其表達式在整個理論框架中的物理意義無完整的定義,有關(guān)參數(shù)也沒有進行測定。為了全面考察對“后推堆積”的模擬能力,有必要利用控制方程的各種拓展形式進行直接數(shù)值模擬試驗,以驗證其有效性。在孔隙尺度水平試驗觀測研究的基礎(chǔ)上,Glass等[85-86,116]提出了與現(xiàn)有的理論框架完全不同的新機理模型,即“修正的侵入滲透”模型(modifiedinvasion percolation)。這種模型包含了重力、沿相-相界面上的局部界面彎曲、濕潤和非濕潤流體的同時入侵以及再次入侵等因素對指流的影響,該模型在描述指流中發(fā)生的各種現(xiàn)象如水飽和度的非單調(diào)性、碎裂、跳動等方面取得了初步進展。Shiozawa等[13]在室內(nèi)用初始狀態(tài)是干的粒狀多孔介質(zhì)所作的一維向下限流量入滲試驗及其分析表明,從孔隙尺度的角度來看,在入滲水流前鋒所在的水氣交界處,孔隙含水量和水壓是不連續(xù)的,因此Darcy定律不能用在這樣的水氣界面上。DiCarlo等[43]在 Eliassi等[37]所提出的拓展形式的基礎(chǔ)上,將傳統(tǒng)的Richards方程擴展為帶有非單調(diào)的毛細壓力-飽和度曲線和雙曲項(水壓關(guān)于時間的二階導(dǎo)數(shù)項)的非線性波動方程,并推導(dǎo)出該方程的行波解。該解的水飽和度曲線在入滲前鋒處確實有非單調(diào)突起。若要保證該解的唯一性,則還需加上1個正則項。

4 研究體會

Ursino等[117]用 Richards方程討論了潮間帶濕地植物根部呼吸的通風狀況、蒸騰作用引起的水分運移以及植物生長狀態(tài)之間的相互關(guān)系,其模型忽略了氣流。筆者以TOUGH2數(shù)值模擬程序為基礎(chǔ),就同一問題用水-氣兩相流模型所做的工作[118]表明,Richards方程不足以完全描述植物根部呼吸的通風條件。對于同一類型的水力傳導(dǎo)系數(shù)在10-6～10-5m/s之間的沼澤地土壤,水 氣兩相流模型所給出的潮間帶濕地植物根圍空氣飽和度總是大于零。而根據(jù)Ursino等[117]的計算,Richards方程所給出的根圍空氣飽和度在海潮周期的某一段時間內(nèi)為零。這說明包氣帶中氣流對水流的影響非常顯著,不能忽略?；赗ichards方程的單相流模型由于忽略了氣流,不能用來定量地描述潮間帶濕地土壤的通風條件。

通過文獻搜集和研究整理的結(jié)果[119-120]表明,尚無文獻在氣流對指流影響方面做過專門探討。盡管如此,筆者認為氣流對指流的發(fā)生和發(fā)展會有重大影響,并相信在指流研究中氣流效應(yīng)不能被忽視,甚至它主導(dǎo)與指流相關(guān)的某些現(xiàn)象(如碎裂和跳動)。已有的實驗室研究(如Touma等[121])以及野外現(xiàn)場試驗(如Dixon等[122])都表明,當水流從土壤表面滲入土壤中時,被水流擠壓的空氣能顯著降低水流的入滲速度。而當氣壓充分高時,空氣會沖破土壤表層孔隙水對其的限制,從土壤表面逸出,從而造成土壤內(nèi)氣壓的急劇降低以及增加水流入滲速度[121]。這有可能引起指流的跳動和碎裂。

由于指流研究是一個多學(xué)科的問題,其機制的研究離不開定量的數(shù)學(xué)描述,而機制、試驗和定量的數(shù)學(xué)模型之間是相輔相成、互相驗證的關(guān)系。一個新的機制,只有經(jīng)過試驗和模型驗證之后才能證明它的正確性和適用范圍。因此,尋找既具有最少的模型參數(shù),又能刻畫水氣交界處水流和氣流流動的最簡單的、具有物理背景意義的數(shù)學(xué)模型,很可能是解開指流復(fù)雜性的關(guān)鍵所在。

5 幾個關(guān)鍵的科學(xué)問題

綜上所述,在指流的研究中,尚存在大量亟待解決的又很有意義的挑戰(zhàn)性前沿課題。主要概括為如下幾點:①能在更小的時空尺度上刻畫指流發(fā)生和發(fā)展機制的試驗觀測裝置。②能否以傳統(tǒng)的多孔介質(zhì)理論為基礎(chǔ),結(jié)合新的動態(tài)毛細壓力機制,來完整地描述已經(jīng)觀測到的但是現(xiàn)有模型還不能滿意地描述的指流尖端處水飽和度和壓力的非單調(diào)突起。③建立和完善有關(guān)新的機制和效應(yīng)的模型,例如孔隙尺度水平上的微觀模型以及上述“后推堆積”效應(yīng)模型。特別地,如何用數(shù)學(xué)模型簡單而自然地描述在入滲水流前鋒的水氣界面處的水-氣兩相流。④新模型的解,包括解的性質(zhì)分析和數(shù)值求解方法。指流的理論模型及數(shù)值模擬方面的突破,將打破其對相關(guān)學(xué)科發(fā)展的制約,不僅對土壤物理學(xué)和水文地質(zhì)學(xué)的理論基礎(chǔ)本身,而且對其他相關(guān)學(xué)科如應(yīng)用數(shù)學(xué)、環(huán)境資源、農(nóng)業(yè)和生態(tài)學(xué)等,都具有重要的推動作用。

[1]GERKE HH.Preferential flow descriptions for structured soils[J].Journal of Plant Nutrition and Soil Science-Zeitschrift Fur Pflanzenernahrung Und Bodenkunde,2006,169(3):382-400.

[2]WANG Zhi,JURY W A,TULI A,et al.Unstable flow during redistribution:controlling factors and practical implications[J].Vadose Zone Journal,2004,3(2):549-559.

[3]COPPOLA A,KUT íLEK M,FRIND E O.Transport in preferential flow domains ofthe soilporous system:measurement,interpretation,modelling,and upscaling[J].Journal of Contaminant Hydrology,2009,104(1/2/3/4):1-3.

[4]De ROOIJG H.Modeling fingered flow of water in soils owing to wetting front instability:a review[J].Journal of Hydrology,2000,231:277-294.

[5]NIEBER JL,DAUTOV RZ,EGOROV A G,et al.Dynamic capillary pressure mechanism for instability in gravity-driven flows;Review and extension to very dry conditions[J].Transport in PorousMedia,2005,58(1/2):147-172.

[6]陳風琴,石輝.岷江上游三種典型植被下土壤優(yōu)勢流現(xiàn)象的染色法研究[J].生態(tài)科學(xué),2006,25(1):69-73.

[7]李懷恩,攔繼元,史文娟,等.層狀土壤指流實驗研究[J].干旱地區(qū)農(nóng)業(yè)研究,2007,25(6):111-115.

[8]董賓芳,傅瓦利.土壤優(yōu)勢流的植物根系效應(yīng)[J].安徽農(nóng)業(yè)科學(xué),2006,34(23):6249-6251;6262.

[9]程竹華,張佳寶,徐紹輝.黃淮海平原三種土壤中優(yōu)勢流現(xiàn)象的試驗研究[J].土壤學(xué)報,1999,36(2):154-161.

[10]馮杰,郝振純.水及溶質(zhì)在有大孔隙的土壤中運移機制研究進展[J].河海大學(xué)學(xué)報:自然科學(xué)版,2002,30(2):63-70.

[11]郝振純,馮杰.水及溶質(zhì)在大孔隙土壤中運移的實驗研究進展[J].灌溉排水,2002,21(1):67-71.

[12]郭會榮.優(yōu)先流影響下的入滲補給過程及溶質(zhì)運移實驗與模擬[D].武漢:中國地質(zhì)大學(xué),2008.

[13]SHIOZAWA S,FUJIMAKI H.Unexpected water content profiles under flux-limited one-dimensional downward infiltration in initially dry granular media[J].Water Resources Research,2004,40(7):W07404.(doi:10.1029/2003WR002197).

[14]ANNAKA T,HANAYAMA S.Dynamic water-entry pressure for initially dry glass beads and sea sand[J].Vadose Zone Journal,2005,4(1):127-133.

[15]WALLACH R,BEN-ARIE O,GRABER E R.Soil water repellency induced by long-term irrigationwith treated sewage effluent[J].Journal of Environmental Quality,2005,34(5):1910-1920.

[16]SAFMAN P G,TAYLOR S G.The penetration of fluid into a porous medium or Hele-Shaw cell containing a more viscous liquid[J].Proc Roy Soc A,1958,245:312-329.

[17]PALMQUIST W N,JOHNSON A I.Vadose zone in layered non layered materials[J].Geol Surv Res,1962,199:142-143.

[18]TABUCHI T.Infiltration and ensuing percolation in columnsof layered glass particles packed in laboratory[J].Trans.Agric.Eng.Soc.Jpn,1961,1:13-19.

[19]劉亞平,陳川.土壤非飽和帶中的優(yōu)先流[J].水科學(xué)進展,1996,7(1):85-89.

[20]李賀麗,李懷恩,王智,等.多孔介質(zhì)中指流的研究綜述及展望[J].土壤,2008,40(1):27-33.

[21]DEBANO L F.Water repellency in soils:a historicaloverview[J].Journal of Hydrology,2000,231:4-32.

[22]CLOTHIER B E,GREEN S R,DEURER M.Preferential flow and transport in soil:progress and prognosis[J].European Journal of Soil Science,2008,59(1):2-13.

[23]K? HNE J M,K? HNE S,SIMUNEK J.A review of model applications for structured soils:a)water flow and tracer transport[J].Journal of Contaminant Hydrology,2009,104(1/2/3/4):4-35.

[24]K? HNE J M,K? HNE S,SIMUNEK J.A review of model applications for structured soils:b)pesticide transport[J].Journal of Contaminant Hydrology,2009,104(1/2/3/4):36-60.

[25]程竹華,張佳寶.土壤中優(yōu)勢流現(xiàn)象的研究進展[J].土壤,1998,6:315-319;331.

[26]馮杰,郝振純,陳啟慧.分形理論在土壤大孔隙研究中的應(yīng)用及其展望[J].土壤,2001,33(3):123-130.

[27]馮杰,郝振純.土壤大孔隙流研究中分形幾何的應(yīng)用進展[J].水文地質(zhì)工程地質(zhì),2001,28(3):9-13.

[28]馮杰,郝振純.CT在土壤大孔隙研究中的應(yīng)用評述[J].灌溉排水,2002,21(3):71-76.

[29]李德成,張?zhí)伊?VELDE B.CT分析技術(shù)在土壤科學(xué)研究中的應(yīng)用[J].土壤,2002,34(6):328-332.

[30]李偉莉,金昌杰,王安志,等.土壤大孔隙流研究進展[J].應(yīng)用生態(tài)學(xué)報,2007,18(4):888-894.

[31]倪余文,區(qū)自清.土壤優(yōu)先水流及污染物優(yōu)先遷移的研究進展[J].土壤與環(huán)境,2000,9(1):60-63.

[32]倪余文,區(qū)自清,應(yīng)佩峰.土壤優(yōu)先水流及溶質(zhì)優(yōu)先遷移的研究[J].應(yīng)用生態(tài)學(xué)報,2001,12(1):103-107.

[33]牛健植,余新曉.優(yōu)先流問題研究及其科學(xué)意義[J].中國水土保持科學(xué),2005,3(3):110-116;126.

[34]牛健植,余新曉,張志強.優(yōu)先流研究現(xiàn)狀及發(fā)展趨勢[J].生態(tài)學(xué)報,2006,26(1):231-243.

[35]秦耀東,任理,王濟.土壤中大孔隙流研究進展與現(xiàn)狀[J].水科學(xué)進展,2000,11(2):204-207.

[36]徐紹輝,張佳寶.土壤中優(yōu)勢流的幾個基本問題研究[J].水文地質(zhì)工程地質(zhì),1999,26(6):27-30;34.

[37]ELIASSI M,GLASS R J.On the porous-continuum modeling of gravity-driven fingers in unsaturated materials:extension of standard theory with a hold-back-pile-up effect[J].Water Resources Research,2002,38(11):1234.(doi:10.1029/2001WR001131).

[38]DiCARLO D A.Quantitative network model predictions of saturation behind infiltration fronts and comparison with experiments[J].Water Resources Research,2006,42(7):W07408.(doi:10.1029/2005WR004750).

[39]BENSON D A.A model of water streaking down a wall[J].Water Resources Research,2001,37(2):427-430.

[40]BRADDOCK R D,NORBURY J.Comment on“On the continuum-scale modeling of gravity-driven fingers in unsaturated porous media:the inadequacy of the Richards equation with standard monotonic constitutive relations and hysteretic equations of state”by M.Eliassi and R.J.Glass[J].Water Resources Research,2003,39(9):1249.(doi:10.1029/2002WR001565).

[41]DEINERT M R,PARLANGE J Y,STEENHUIS T,et al.Measurement of fluid contents and wetting front profiles by real-time neutron radiography[J].Journal of Hydrology,2004,290:192-201.

[42]DiCARLO D A,BLUNT M J.Determination of finger shape using the dynamic capillary pressure[J].Water Resources Research,2000,36(9):2781-2785.

[43]DiCARLODA,JUANESR,LAFORCET,etal.Nonmonotonic traveling wave solutions of infiltration into porous media[J].Water Resources Research,2008,44(2):W02406.(doi:10.1029/2007WR005975).

[44]ELIASSI M,GLASS R J.On the continuum-scale modeling of gravity-driven fingers in unsaturated porous media:the inadequacy of the Richards equation with standard monotonic constitutive relations and hysteretic equations of state[J].Water Resources Research,2001,37(8):2019-2035.

[45]ELIASSI M,GLASS R J.On the porous continuum-scale modeling of gravity-driven fingers in unsaturated materials:numerical solution of a hypodiffusive governing equation that incorporates a hold-back-pile-up effect[J].Water Resources Research,2003,39(6):1167.(doi:10.1029/2002WR001535).

[46]ELIASSI M,GLASS R J.Reply to comment by R.D.Braddock and J.Norbury on“On thecontinuum-scale modeling of gravity-driven fingers in unsaturated porous media:the inadequacy of the Richards equationwith standard monotonic constitutive relations and hysteretic equations of state”[J].Water Resources Research,2003,39(9):1250.(doi:10.1029/2002WR001753).

[47]ELIASSI M,GLASS R J.Reply to comment on“On the continuum-scale modeling of gravity-driven fingers in unsaturated porous media:the inadequacy of the Richards equation with standard monotonic constitutive relations and hysteretic equations of state”by Mehdi Eliassi and Robert J.Glass[J].Water Resources Research,2003,39(9):1264.(doi:10.1029/2003WR002053).

[48]MAJDALANI S,ANGULO-JARAMILLO R,Di PIETRO L.Estimating preferential water flow parameters using a binary genetic algorithm inversemethod[J].Environmental Modelling&Software,2008,23(7):950-956.

[49]NIEBER J L,BAUTERS T W J,STEENHUIS T S,et al.Numerical simulation of experimental gravity-driven unstable flow inwater repellent sand[J].Journal ofHydrology,2000,231:295-307.

[50]URSINO N.Linear stability analysis of infiltration,analytical and numerical solution[J].Transport in Porous Media,2000,38(3):261-271.

[51]程金花,張洪江,史玉虎,等.長江三峽庫區(qū)優(yōu)先流模型修正及驗證[J].山東農(nóng)業(yè)大學(xué)學(xué)報:自然科學(xué)版,2007,38(4):605-609.

[52]任理,秦耀東,王濟.非均質(zhì)飽和土壤鹽分優(yōu)先運移的隨機模擬[J].土壤學(xué)報,2001,38(1):104-113.

[53]馮杰,張佳寶,郝振純,等.水及溶質(zhì)在有大孔隙的土壤中運移的研究(Ⅱ):數(shù)值模擬[J].水文地質(zhì)工程地質(zhì),2004,31(4):77-82.

[54]BAYER A,VOGEL H J,ROTH K.Direct measurement of the soil water retention curve using X-ray absorption[J].Hydrology and Earth System Sciences,2004,8(1):2-7.

[55]CRIST J T,MCCARTHY J F,ZEVI Y,et al.Pore-scale visualization ofcolloid transportand retention in partly saturated porous media[J].Vadose Zone Journal,2004,3(2):444-450.

[56]DAR NAULT C J G,DiCARLO D A,BAUTERS T W J,et al.Measurement of fluid contents by light transmission in transient three-phase oil-water-air systems in sand[J].Water Resources Research,2001,37(7):1859-1868.

[57]DAR NAULT C J G,DiCARLO D A,BAUTERS T W J,et al.Visualization and measurement of multiphase flow in porous media using light transmission and synchrotron X-rays[J].Visualization and Imaging in Transport Phenomena,2002,972:103-110.

[58]DAR NAULT C J G,GARNIER P,KIM Y J,et al.Preferential transport of Cryptosporidium parvum oocysts in variablysaturated subsurfaceenvironments[J].Water Environment Research,2003,75(2):113-120.

[59]DEINERT M,PARLANGE J Y,CADY K B,et al.Comment on“On the continuum-scale modeling of gravity-driven fingers in unsaturated porousmedia:The inadequacy of the Richards equation with standard monotonic constitutive relations and hysteretic equations of state”by Mehdi Eliassi and Robert J.Glass[J].Water Resources Research,2003,39(9):1263.(doi:10.1029/2002WR001785).

[60]DiCARLO D A.Experimental measurements of saturation overshoot on infiltration[J].Water Resources Research,2004,40(4):W04215.(doi:10.1029/2003WR002670).

[61]DiCARLO D A.Capillary pressure overshoot as a function of imbibition flux and initialwater content[J].Water Resources Research,2007,43(8):W08402.(doi:10.1029/2006WR005550).

[62]NIEMET M R,SELKER J S.A new method for quantification of liquid saturation in 2D translucent porous media systems using light transmission[J].Advances in Water Resources,2001,24(6):651-666.

[63]NISSEN H H,MOLDRUP P,KACHANOSKI R G.Time domain reflectometry measurementsof solute transport across a soil layer boundary[J].Soil Science Society of America Journal,2000,64(1):62-74.

[64]COPPOLA A,COMEGNA V,BASILE A,et al.Darcian preferential water flow and solute transport through bimodal porous systems:experiments and modelling[J].Journal of Contaminant Hydrology,2009,104(1/2/3/4):74-83.

[65]KUTILEK M,GERMANN P F.Converging hydrostatic and hydromechanic concepts of preferential flow definitions[J].Journal of Contaminant Hydrology,2009,104(1):61-66.

[66]KUT íLEK M,JENDELE L,KREJCA M.Comparison of empirical,semi-empirical and physically based models of soil hydraulic functions derived for bi-modal soils[J].Journal of Contaminant Hydrology,2009,104(1/2/3/4):84-89.

[67]HINCAPIE I,GER MANN P F.Impactof initial and boundary conditions on preferential flow[J].Journal of Contaminant Hydrology,2009,104(1/2/3/4):67-73.

[68]ROSENBOM A E,THERRIEN R,REFSGAARD J C,et al.Numerical analysis of water and solute transport in variablysaturated fractured clayey till[J].Journal of Contaminant Hydrology,2009,104(1/2/3/4):137-152.

[69]李德成,VELDE B,DELERUE JF,等.利用土壤切片和數(shù)字圖像方法研究土壤孔隙的垂直空間變異性[J].土壤與環(huán)境,2000,9(2):135-138.

[70]李德成,VELDE B,DELERUE J-F,等.用于研究土壤孔隙三維結(jié)構(gòu)的連續(xù)數(shù)字圖像的制備[J].土壤與環(huán)境,2001,10(2):108-110.

[71]李賀麗.指流特性及其影響因素的實驗研究[D].西安:西安理工大學(xué),2007.

[72]王煥之.稻田土壤水分優(yōu)先流的發(fā)生、發(fā)展與模擬研究[D].杭州:浙江大學(xué),2002.

[73]BAUTERS T W J,DiCARLO D A,STEENHUIS T S,et al.Soil water content dependent wetting front characteristics in sands[J].Journal of Hydrology,2000,231:244-254.

[74]BAUTERS T W J,STEENHUIS T S,DiCARLO D A,et al.Physics of water repellent soils[J].Journal of Hydrology,2000,231:233-243.

[75]CHO H,De ROOIJ G H.Pressure head distribution during unstable flow in relation to the formation and dissipation of fingers[J].Hydrology and Earth System Sciences,2002,6(4):763-771.

[76]CHO H,De ROOIJ G H,INOUE M.The pressure head regime in the induction zone during unstable nonponding infiltration:theoryand experiments[J].Vadose Zone Journal,2005,4(4):908-914.

[77]CULLIGAN PJ,BANNOK,BARRYD A,etal.Preferential flow of a nonaqueous phase liquid in dry sand[J].Journalof Geotechnical and Geoenvironmental Engineering,2002,128(4):327-337.

[78]DAR NAULT C J G,STEENHUIS T S,GARNIER P,et al.Preferential flow and transport of Cryptosporidium parvum oocysts through the vadose zone:Experiments and modeling[J].Vadose Zone Journal,2004,3(2):736-736.

[79]DEKKER L W,RITSEMA C J.Wetting patterns and moisture variability in water repellent Dutch soils[J].Journal of Hydrology,2000,231:148-164.

[80]DEKKER L W,RITSEMA C J,OOSTINDIE K.Extent and significance of water repellency in dunes along the Dutch coast[J].Journal of Hydrology,2000,231:112-125.

[81]De ROOIJ G H,STAGNITTI F.Spatial and temporal distribution of solute leaching in heterogeneous soils:analysis and application to multisampler lysimeter data[J].Journal of Contaminant Hydrology,2002,54(3/4):329-346.

[82]DiCARLO D A.Modeling observed saturation overshoot with continuum additions to standard unsaturated theory[J].Advances in Water Resources,2005,28(10):1021-1027.

[83]DOERR S H,THOMAS A D.The role of soil moisture in controlling water repellency:new evidence from forest soils in Portugal[J].Journal of Hydrology,2000,231:134-147.

[84]GEIGER S L,DURNFORD D S.Infiltration in homogeneous sands and a mechanistic model of unstable flow[J].Soil Science Society of America Journal,2000,64(2):460-469.

[85]GLASS R J,CONRAD S H,YARRINGTON L.Gravitydestabilized nonwetting phase invasion in macroheterogeneous porousmedia:near-pore-scale macro modified invasion percolation simulation of experiments[J].Water Resources Research,2001,37(5):1197-1207.

[86]GLASS R J,YARRINGTON L.Mechanistic modeling of fingering,nonmonotonicity,fragmentation,and pulsation within gravity/buoyant destabilized two-phase/unsaturatedflow[J].Water Resources Research,2003,39(3):1058.(doi:10.1029/2002WR001542).

[87]JARAMILLO D F,DEKKER L W,RITSEMA C J,et al.Occurrence of soilwater repellency in arid and humid climates[J].Journal of Hydrology,2000,231:105-111.

[88]KIM Y J,DARNAULT C J G,BAILEYN O,et al.Equation for describing solute transport in field soils with preferential flow paths[J].Soil Science Society of America Journal,2005,69(2):291-300.

[89]KIM Y J,STEENHUIS T S,NAM K.Movement of heavy metals in soil through preferential flow paths under different rainfall intensities[J].Clean-Soil Air Water,2008,36(12):984-989.

[90]NEKTARIOS P A,PETROVIC A M,STEENHUIS T S.Effect of surfactant on fingered flow in laboratory golf greens[J].Soil Science,2002,167(9):572-579.

[91]NICHOLL M J,GLASS R J.Infiltration into an analog fracture:experimental observations of gravity-driven fingering[J].Vadose Zone Journal,2005,4(4):1123-1151.

[92]WANG Zhi,WU Q J,WU Lao-sheng,et al.Effects of soil water repellency on infiltration rate and flow instability[J].Journal of Hydrology,2000,231:265-276.

[93]WEISBROD N,NIEMET M R,SELKER J S.Imbibition of saline solutions into dry and prewetted porous media[J].Advances in Water Resources,2002,25(7):841-855.

[94]EGUCHI S, HASEGAWA S.Determination and characterization of preferential water flow in unsaturated subsoil of andisol[J].Soil Science Society of America Journal,2008,72(2):320-330.

[95]FRANKLIN D H,WEST L T,RADCLIFFE D E,et al.Characteristics and genesis of preferential flow paths in a piedmont ultisol[J].Soil Science Society of America Journal,2007,71(3):752-758.

[96]HANGEN E,GER KE H H,SCHAAF W,et al.Flow path visualization in a lignitic mine soil using iodine-starch staining[J].Geoderma,2004,120(1/2):121-135.

[97]HEILIG A,STEENHUIS T S,WALTER M T,et al.Funneled flow mechanisms in layered soil:field investigations[J].Journal of Hydrology,2003,279:210-223.

[98]ORR S.Enhanced heap leaching-Part 1:Insights[J].Mining Engineering,2002,54(9):49-56.

[99]KUNG K J S,KLADIVKO E J,GISHT J,et al.Quantifying preferential flow by breakthrough ofsequentially applied tracers:silt loam soil[J].Soil Science Society of America Journal,2000,64(4):1296-1304.

[100]PERSSON M,BERNDTSSON R.Transect scale solute transport measured by time domain reflectometry[J].Nordic Hydrology,2002,33(2/3):145-164.

[101]RITSEMA C J,DEKKER L W.Preferential flow in water repellent sandy soils:principles and modeling implications[J].Journal of Hydrology,2000,231:308-319.

[102]RITSEMA C J,Van DAM J C,DEKKER L W,et al.A new modelling approach to simulate preferential flow and transport in water repellent porous media:model structure and validation[J].Australian Journal of Soil Research,2005,43(3):361-369.

[103]SANDER T,GERKE H H.Preferential flow patterns in paddy fields using a dye tracer[J].Vadose Zone Journal,2007,6(1):105-115.

[104]SANDER T,GERKE H H.Modellingfield-dataof preferential flow in paddy soil induced by earthworm burrows[J].Journal of Contaminant Hydrology,2009,104(1/2/3/4):126-136.

[105]FUCHS J W,FOX G A,STOR M D E,et al.Subsurface transport of phosphorus in riparian floodplains:influence of preferential flow paths[J].Journal of Environmental Quality,2009,38(2):473-484.

[106]馮杰,張佳寶,郝振純,等.水及溶質(zhì)在有大孔隙土壤中運移的研究(I):田間實驗[J].水文地質(zhì)工程地質(zhì),2004,31(3):20-24.

[107]TIDWELL V C,GLASS R J.X-rayand visible-lighttransmission for laboratory measurement of 2-dimensional saturation fields in thin-slab systems[J].Water Resources Research,1994,30(11):2873-2882.

[108]NIEBER J L.Modeling finger development and persistence in initially dry porous media[J].Geoderma,1996,70(2/3/4):207-229.

[109]RITSEMA C J,DEKKER L W,NIEBER J L,et al.Modeling and field evidence of finger formation and finger recurrence in a water repellent sandy soil[J].Water Resources Research,1998,34(4):555-567.

[110]NGUYEN H V,NIEBER J L,ODURO P,et al.Modeling solute transport in a water repellent soil[J].Journal of Hydrology,1999,215:188-201.

[111]NGUYEN H V,NIEBER J L,RITSEMA C J,et al.Modeling gravity driven unstable flow in a water repellent soil[J].Journal of Hydrology,1999,215:202-214.

[112]MUALEM Y.Conceptual model of hysteresis[J].Water Resources Research,1974,10(3):514-520.

[113]MUALEM Y.New modelforpredicting hydraulic conductivityofunsaturated porous-media[J].Water Resources Research,1976,12(3):513-522.

[114]Van GENUCHTEN M T.A closed-form equation for predicting the hydraulic conductivity of unsaturated soils[J].Soil Sci Soc Am J,1980,44(5):892-898.

[115]DEINER T M,PARLANGE J Y,STEENHUIS T S,et al.Real-time measurement of water profiles in a sand using neutron radiography[C]RAMIREZ J A.Hydrology Days 2002:Proceedings of the 22ndAnnual American Geophysical Union Hydrology Days.FortCollins:ColoradoState Univers,2002:56-63.

[116]GLASS R J,YARRINGTON L.Simulation of gravity fingering in porous media using amodified invasion percolation model[J].Geoderma,1996,70(2/3/4):231-252.

[117]URSINO N,SILVESTRI S,MARANI M.Subsurface flow and vegetation patterns in tidal environments[J].Water Resources Research,2004,40(5):W05115.(doi:10.1029/2003WR002702).

[118]LI Hai-long,LI Ling,LOCKINGTON D.Aeration for plant root respiration in a tidal marsh[J].Water Resources Research,2005,41(6):W06023.(doi:10.1029/2004WR003759).

[119]JIAO J J,LI Hai-long.Subsurface airflow induced by natural forcings[J].Advances in Earth Sciences,2004,19(3):413-421.

[120]JIAO J J,LI Hai-long.Breathing of coastal vadose zone induced by sea level fluctuations[J].Geophysics Research Letters,2004,31:L11502.(doi:10.1029/2004GL019572).

[121]TOUMA J,VACHAUD G,PARLANGE J Y.Air andwater flow in a sealed,ponded vertical soil column:experimental and model[J].Soil Science,1984,137:181-187.

[122]DiXON R M,LINDEN D R.Soil air pressure and water infiltration under border irrigation[J].Soil Science Society of America Journal,1972,36:948-953.