李兆峰,周志芳,李明遠(yuǎn),周翠英

(1.中山大學(xué)工學(xué)院,廣東 廣州 510275; 2.中山大學(xué)巖土工程和信息技術(shù)研究中心,廣東 廣州 510275; 3.河海大學(xué)地球科學(xué)與工程學(xué)院,江蘇 南京 211100)

弱透水層釋水過程中水力參數(shù)響應(yīng)規(guī)律

李兆峰1,2,3,周志芳3,李明遠(yuǎn)3,周翠英1,2

(1.中山大學(xué)工學(xué)院,廣東 廣州 510275; 2.中山大學(xué)巖土工程和信息技術(shù)研究中心,廣東 廣州 510275; 3.河海大學(xué)地球科學(xué)與工程學(xué)院,江蘇 南京 211100)

為了提高地下水運(yùn)移模擬、地下水資源評價和地面沉降預(yù)測的精度,利用室內(nèi)試驗分析弱透水層釋水固結(jié)過程中水力參數(shù)的變化規(guī)律?；谙噜徍畬咏瞪詈愣ㄇ页跏紩r刻水流穩(wěn)定條件下弱透水層釋水量的解析解,提出參數(shù)求解的配線法,利用研制的試驗裝置進(jìn)行試驗研究。結(jié)果表明:弱透水層釋水過程中滲透系數(shù)和貯水率逐漸減小,固結(jié)系數(shù)變化不大。試驗中土層的滲透系數(shù)和貯水率分別減小了52%和59%。弱透水層水力參數(shù)恒定不變的假設(shè)會對其釋水量的計算造成較大誤差,取弱透水層固結(jié)變形初始階段的貯水率,計算結(jié)果比實(shí)際釋水量大;取固結(jié)變形結(jié)束階段的貯水率時則相反。

弱透水層;解析解;釋水量;水力參數(shù);滯后因子

地下水資源是人類淡水資源的重要組成部分,主要儲存在含水層和弱透水層組成的含水層系統(tǒng)中[1]。弱透水層作為含水層系統(tǒng)的重要組成部分,在地下水資源管理和預(yù)測中經(jīng)常被忽視[2-3]。弱透水層在沖積平原和沉積盆地中分布廣泛,且主要由黏土、亞黏土、粉質(zhì)黏土等細(xì)粒沉積物組成,具有低滲透性和高儲水性[4-7]。弱透水層的滲透系數(shù)一般小于10-8m/s,比含水層小幾個數(shù)量級[8-10],對地下水環(huán)境保護(hù)具有重要作用[11]。當(dāng)抽水含水層水位下降時,弱透水層內(nèi)部水壓力減小,有效應(yīng)力增加,弱透水層固結(jié)變形并釋水到抽水含水層[12-13]。由于弱透水層的貯水率比含水層大1～2個數(shù)量級,弱透水層釋水量相當(dāng)大,弱透水層釋水量的計算對于地下水資源評價極其重要[1-2]。弱透水層參數(shù)是其釋水量計算的重要影響因素,因此弱透水層水力參數(shù)的確定是含水層系統(tǒng)水流運(yùn)移模擬、地下水資源評價和地面沉降預(yù)測的關(guān)鍵。

弱透水層的水力參數(shù)包括滲透系數(shù)和貯水率,Field[14]指出固結(jié)系數(shù)的不確定性是傳統(tǒng)固結(jié)理論計算變形速率的極限性。很多水文地質(zhì)學(xué)研究者對弱透水層水文地質(zhì)參數(shù)進(jìn)行了大量研究.[15-16]。余闖等[17]推導(dǎo)出正常固結(jié)和超固結(jié)狀態(tài)下固結(jié)系數(shù)與有效應(yīng)力之間的表達(dá)式;張明等[18]利用統(tǒng)計分析得到固結(jié)系數(shù)與有效應(yīng)力的擬合關(guān)系。上述研究主要針對軟土的固結(jié)系數(shù)進(jìn)行分析。葉淑君等[19]利用圖解法對上海含水層系統(tǒng)中的弱透水層參數(shù)進(jìn)行研究。Zhou等[20]提出了配線法求解弱透水層的滲透系數(shù)和貯水率,并通過室內(nèi)試驗驗證了方法的可靠性。弱透水層釋水過程中水力參數(shù)變化規(guī)律的研究尚未發(fā)現(xiàn),特別是弱透水層的貯水率。筆者在Terzaghi固結(jié)理論的基礎(chǔ)上推導(dǎo)了弱透水層定降深條件下釋水量的解析解,利用該解析解提出相應(yīng)條件下求解弱透水層參數(shù)的配線法,并通過室內(nèi)試驗對弱透水層釋水過程中水力參數(shù)的響應(yīng)規(guī)律進(jìn)行研究。

1 原 理

圖1 含水層系統(tǒng)概念模型Fig.1 Conceptual model of aquifer system

Terzaghi一維固結(jié)理論在解決軟土地基變形控制和預(yù)測中發(fā)揮著重要作用,至今仍被廣泛應(yīng)用于計算各種荷載條件下土體的固結(jié)問題。為了研究弱透水層釋水過程中水力參數(shù)的響應(yīng)規(guī)律,建立了一個含水層系統(tǒng)概念模型,如圖1所示。假設(shè):(a)弱透水層是均質(zhì)的,且滲透系數(shù)和貯水率不隨時間變化;(b)弱透水層水平側(cè)向無限延伸;(c)弱透水層始終是飽和狀態(tài);(d)弱透水層中的水流為垂向一維流,且服從達(dá)西定律。通常情況下弱透水層的滲透系數(shù)比含水層小兩個數(shù)量級以上,因此,弱透水層中的水流可近似為一維流動。坐標(biāo)軸原點(diǎn)O位于弱透水層的上表面,厚度為l,坐標(biāo)z向下為正。

弱透水層的水壓力用降深(s)代替,根據(jù)Terzaghi一維固結(jié)理論[21]建立數(shù)學(xué)模型:

(1)

式中:cv——土樣的固結(jié)系數(shù)或者水力擴(kuò)散系數(shù);K、Ss——弱透水層的滲透系數(shù)和貯水率;t——時間。

初始時刻弱透水層內(nèi)部水頭線性分布,即其內(nèi)部水流是穩(wěn)定流。

(2)

式中:φ0——抽水含水層初始時刻的降深。

假設(shè)弱透水層上部含水層水位不變,即上邊界降深為0,t時刻下部含水層降深增加量為φ,則

(3)

式(1)～(3)所示的偏微分方程,利用分離變量法可以求得其解析解[22]。

(4)

根據(jù)Darcy定律,求得弱透水層底面的水流速度,并進(jìn)行無量綱化得

(5)

將式(5)取對數(shù)得

(6)

(7)

(8)

1—底座;2—容器主體;3—反濾層;4—黏土層;5—剛性桿;6—百分表;7—支架; 8—電子天平;9 —出水管;10—進(jìn)水管;11—定水頭供水槽;12—溢水口;13—蠕動泵圖2 試驗?zāi)Ｐ褪疽鈭DFig.2 Sketch of experimental model

2 試驗結(jié)果及討論

本文使用的試驗裝置是在前人試驗?zāi)Ｐ偷幕A(chǔ)上進(jìn)行改進(jìn),并盡量設(shè)計符合弱透水層固結(jié)滲流環(huán)境,模擬相鄰含水層定降深條件下弱透水層釋水過程中的水流運(yùn)移問題。模型由模型主體(內(nèi)徑19.1 cm)、沉降量測系統(tǒng)、流量監(jiān)測系統(tǒng)、供水水槽組成(圖2)。為了研究弱透水層釋水過程中水力參數(shù)的響應(yīng)規(guī)律,對同一個土層不同定降深條件下弱透水層的釋水規(guī)律進(jìn)行了研究,其中土層的下邊界降深(即相鄰含水層的降深)逐漸變大(當(dāng)降深變大時,確保上一次定降深試驗土層內(nèi)部水流已達(dá)到穩(wěn)定)。隨著土層下邊界降深增大,土層釋水量變大,根據(jù)試驗過程中土層下邊界流量,利用配線法計算土層水力參數(shù),分析參數(shù)的變化規(guī)律。

試驗所用土樣是從野外取回的粉質(zhì)黏土,將其風(fēng)干、碾碎并過篩(0.5 mm)。將制備的土樣填充到試驗設(shè)備的主體部分,試驗土樣初始時刻厚度l=30 cm。試驗初始時刻定降深ΔH=30 cm,待流量達(dá)到穩(wěn)定時,此過程視為第一次定降深條件下的弱透水層水流運(yùn)移試驗結(jié)束;然后將出水口降低30 cm,進(jìn)行第二次定降深條件下的弱透水層水流運(yùn)移試驗,待流量達(dá)到穩(wěn)定時,第二次試驗結(jié)束;依次進(jìn)行5次試驗至ΔH=150 cm。利用環(huán)刀法測得試驗土層的基本性質(zhì),黏性土的干密度為1.14×103kg/m3,土的初始孔隙比e0=1.07。

表2 土層參數(shù)計算結(jié)果

表1 配線法匹配點(diǎn)坐標(biāo)

5次試驗結(jié)束時土層的總變形量為3.1 cm,根據(jù)物質(zhì)守恒定律(飽和土層的變形體積等于土層的釋水量)可得試驗結(jié)束時土層的總釋水量為887 cm3。在Terzaghi一維固結(jié)理論中,假設(shè)土體固結(jié)變形過程中滲透系數(shù)和壓縮系數(shù)保持不變,若取試驗土層的滲透系數(shù)和貯水率值等于土體壓縮變形初始階段的值,弱透水層單位面積的釋水量可通過下式計算得到:Vw=lφSsA/2=1 499 cm3[2-3]。該計算結(jié)果偏大69%,高估了弱透水層的釋水量。同理,若取弱透水層的滲透系數(shù)和貯水率值等于土體壓縮變形結(jié)束階段的值,計算得Vw=611 cm3。該結(jié)果偏小31%,低估了弱透水層釋水量,因此假設(shè)弱透水層釋水固結(jié)過程中其水文地質(zhì)參數(shù)不變是不合理的。利用上述5次試驗得到的貯水率值,計算5次試驗中土層釋水量分別為300 cm3、174 cm3、154 cm3、131 cm3、111 cm3,總釋水量為870 cm3。計算結(jié)果與實(shí)際釋水量很接近,誤差為1.9%(主要由測量誤差和土層的飽和度引起),驗證了配線法計算弱透水層貯水率的精度。

弱透水層釋水滯后于相鄰含水層的降深,相鄰含水層定降深條件下弱透水層釋水現(xiàn)象的滯后時間為[12]

(9)

τ0取決于弱透水層的水力參數(shù)和厚度,將5次試驗的土層參數(shù)代入式(9)可得τ0分別為500 min、348 min、364 min、351 min、355 min。第一次試驗中,土層初始孔隙比較大,變形量較大造成滯后釋水完成所需時間較長;后面連續(xù)4次試驗土層的釋水現(xiàn)象完成時間約為355 min,即水流達(dá)到穩(wěn)定所需要的時間基本相同。

3 結(jié) 語

基于相鄰含水層降深恒定且初始時刻水流穩(wěn)定條件下弱透水層釋水量的解析解,提出參數(shù)求解的配線法,利用自發(fā)研制的試驗裝置,通過室內(nèi)試驗對弱透水層釋水過程中水力參數(shù)的響應(yīng)規(guī)律進(jìn)行研究。結(jié)果表明:弱透水層的釋水滯后于相鄰含水層的降深變化,釋水速度由大變小,至釋水現(xiàn)象結(jié)束變?yōu)榱?隨著弱透水層的釋水固結(jié),弱透水層的滲透系數(shù)和貯水率隨孔隙比的減小而逐漸減小,固結(jié)系數(shù)有減小趨勢,但變化不大,試驗土層孔隙比減小0.19(不足20%),滲透系數(shù)和貯水率分別減小了52%和59%;假設(shè)弱透水層水力參數(shù)不變會對其釋水量的計算造成較大誤差,試驗土層的滲透系數(shù)和貯水率分別取土層變形初始階段和結(jié)束階段的貯水率,弱透水層釋水量計算結(jié)果分別偏大69%和偏小31%;弱透水層滯后釋水現(xiàn)象的滯后因子在釋水固結(jié)過程中基本不變,即釋水現(xiàn)象完成的時間基本相同。

研究成果對地面沉降預(yù)測和地下水資源量計算具有一定的應(yīng)用價值。本文對弱透水層釋水固結(jié)過程中水力參數(shù)的變化規(guī)律進(jìn)行探討,未考慮弱透水層變形量較大時對水文地質(zhì)參數(shù)反演的影響,需作進(jìn)一步的研究。

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Variation of hydraulic parameters of aquitard during water release

LI Zhaofeng1,2,3, ZHOU Zhifang3, LI Mingyuan3, ZHOU Cuiying1,2

(1.SchoolofEngineering,SunYat-senUniversity,Guangzhou510275,China; 2.ResearchCenterforGeotechnicalEngineeringandInformationTechnology,SunYat-senUniversity,Guangzhou510275,China; 3.SchoolofEarthScienceandEngineering,HohaiUniversity,Nanjing211100,China)

In order to improve the accuracy of groundwater transport simulation, groundwater resources assessment, and land subsidence prediction, the variation of hydraulic parameters of an aquitard during water release was analyzed through laboratory testing. Based on the analytical solution of the water release quantity of an aquitard under the condition that the drawdown of the adjacent aquifer is constant and the flow in the aquitard is stable at the initial time, a type curve method for calculation of parameters is proposed, and experimental research was carried out using the self-developed test equipment. The experimental results show that the hydraulic conductivity and specific storativity decrease gradually with the water release from the aquitard, but the consolidation coefficient changes little. The hydraulic conductivity and specific storativity of the soil layer in the experiment were decreased by 52% and 59%, respectively. The assumption that hydraulic parameters are constant will lead to a significant error in the calculation of the water release quantity of the aquitard. The calculated water release quantity of the aquitard is larger than the actual value when the specific storativity in the initial stage of consolidation is used, but the opposite conclusion is obtained when the specific storativity in the final stage of consolidation is used.

aquitard; analytical solution; water release quantity; hydraulic parameter; delay index

10.3876/j.issn.1000-1980.2017.04.009

2016-06-12

國家自然科學(xué)基金(41572209);國家重點(diǎn)研發(fā)計劃(2016YFC0402803)

李兆峰(1987—),男,山東安丘人,助理研究員,博士,主要從事地質(zhì)資源與地質(zhì)工程研究。E-mail: Lizhfzx@gmail.com

P641

A

1000-1980(2017)04-0340-05