李同錄+王紅+付昱凱+梁燕
基金項目:國家自然科學(xué)基金項目(41372329);國家重點基礎(chǔ)研究發(fā)展計劃(“九七三”計劃)項目(2014CB744701)
摘要:通過室內(nèi)試驗?zāi)M自然沉積作用下黃土中水的滲透性,發(fā)現(xiàn)黃土垂直節(jié)理是地表水入滲過程中形成的。根據(jù)室內(nèi)模型試驗,建立一理想顆粒排列模型,利用TEN15型張力計實測的土水特征曲線,計算從飽和到非飽和狀態(tài)的變化過程中土顆粒的相互作用力的變化。結(jié)果表明:地表水在下滲過程中,初始沉積的黃土含水量發(fā)生變化,基質(zhì)吸力和表面張力產(chǎn)生的粒間引力也發(fā)生變化;粒間引力會隨著粒間距的減小而急劇增大,而且其隨含水量的變化規(guī)律與粒間距的大小有很大關(guān)系;由于初始沉積的黃土粉粒結(jié)構(gòu)疏松,粒間有極弱的支撐,改變含水量狀態(tài)產(chǎn)生的粒間引力在較小的量級便會使土顆粒相互靠近,而顆粒間距減小,則粒間引力急劇增大,土體整體收縮導(dǎo)致局部拉裂形成垂向裂隙,即垂直節(jié)理。
關(guān)鍵詞:黃土;垂直節(jié)理;形成機理;模型試驗;滲透;表面張力;基質(zhì)吸力;粒間引力
中圖分類號:P642.13+1文獻(xiàn)標(biāo)志碼:A
Test Simulation on the Forming Mechanism of Loess Vertical Joints
LI Tonglu1, WANG Hong1, FU Yukai1, LIANG Yan2,3
(1. School of Geology Engineering and Geomatics, Changan University, Xian 710054, Shaanxi, China;
2.School of Highway, Changan University, Xian 710064, Shaanxi, China; 3. Key Laboratory for Special
Area Highway Engineering of Ministry of Education, Changan University, Xian 710064, Shaanxi, China)
Abstract: It is observed that the loess vertical joints form in the process of rainfall penetration by the model test for simulating loess penetration under the sedimentation. According to the model test, an ideal model of soil particle arrangement was built; based on the soilwater characteristic curve of loess sample measured by TEN15 tension meter, the interaction force between soil particles under different moisture contents was induced by the relationship between matric suction and curvature radius of water shrink film. The results show that the vertical joint is caused by the change of interparticle force because of the matric suction and surface tension in the process of rainfall penetration; the interparticle force increases sharply with the decrease of the interparticle distance, and the relationship between the interparticle force and water content is significantly influenced by the interparticle distance; the structure of initial sediment loess is loose and the support of interparticle is weak, so that the particles will be close to each other because of the interparticle force at small order caused by the change of water content, and the interparticle force increases sharply with the decrease of the interparticle distance, and then the shrinkage of soil leads to local cracks and forms vertical joints.
Key words: loess; vertical joint; forming mechanism; model test; penetration; surface tension; matric suction; interparticle force
0引言
垂直節(jié)理是黃土中普遍發(fā)育的一種獨特構(gòu)造,是非構(gòu)造成因的一種破裂。垂直節(jié)理一般是地表水或地下水的運移通道,地表水灌入地下后,常沿節(jié)理發(fā)生潛蝕,使其導(dǎo)水性增強,加劇黃土的侵蝕,常對各類工程造成危害,因此,學(xué)者們對黃土區(qū)的滲透性進(jìn)行了大量研究[19]。
黃土中垂直節(jié)理的存在是被廣泛公認(rèn)的現(xiàn)象,關(guān)于其形成機理的研究較少,認(rèn)識尚不統(tǒng)一[10]。駱進(jìn)等通過模擬試驗研究認(rèn)為黃土不均勻濕陷產(chǎn)生的內(nèi)裂縫在上覆壓力作用下受到拉力作用,當(dāng)達(dá)到土體抗拉強度后,裂縫在豎直方向上擴張而形成垂直節(jié)理。采用擾動土樣,設(shè)置不同厚度的土層,通過浸水產(chǎn)生不均勻濕陷,在厚度變化處產(chǎn)生濕陷裂縫;現(xiàn)場觀察表明,黃土垂直節(jié)理和沉積時的地表起伏沒有關(guān)系,在完全水平層狀的黃土中同樣有垂直節(jié)理發(fā)育,而且垂直節(jié)理很少有豎向錯位,以水平拉張為主[11]。王正貴等則認(rèn)為重力在黃土體中大孔洞上下邊緣所引起的水平拉應(yīng)力是導(dǎo)致黃土產(chǎn)生垂直節(jié)理的基本原因,將垂直節(jié)理的出現(xiàn)歸結(jié)為上覆荷載形成的水平張力[12]。而實際上,黃土是風(fēng)積的散粒體,在橫向有約束的情況下,重力只能產(chǎn)生水平擠壓,不可能產(chǎn)生張力。馮連昌等對黃土節(jié)理的地域分布和外觀形狀進(jìn)行過考察和分類,提出結(jié)構(gòu)特征、水平張力和風(fēng)化作用是黃土中垂直節(jié)理形成的主要原因,但并沒有具體的討論分析[1314]。
黃土非飽和滲透試驗中,表層集中滲水后,黃土從飽和狀態(tài)到非飽和狀態(tài)轉(zhuǎn)變的過程中產(chǎn)生體積收縮,試樣上部土體周圍產(chǎn)生距離大致相等的豎直方向的張性裂縫,而且水分入滲深度有限,垂直裂隙只能在一定深度范圍內(nèi)出現(xiàn)[12,15]。這與野外垂直節(jié)理的表現(xiàn)一致,而且整個試驗過程與自然條件下雨水自地表入滲到地下、淺層黃土經(jīng)歷飽和到非飽和的過程是一致的。因此,該試驗現(xiàn)象可以反映自然黃土中垂直節(jié)理的形成過程。試驗表明,垂直裂隙的出現(xiàn)是由于黃土的非飽和特性所決定的,主要是黃土由飽和狀態(tài)到非飽和狀態(tài)轉(zhuǎn)變中基質(zhì)吸力產(chǎn)生的粒間作用力的變化引起的。筆者將進(jìn)一步分析了水分變化在黃土中引起的基質(zhì)吸力變化,揭示黃土中垂直節(jié)理的形成機理。
在模擬風(fēng)積黃土的非飽和滲透性時,黃土在地表滲水過程中會出現(xiàn)垂直楔形裂隙,此現(xiàn)象和黃土垂直節(jié)理的形成類似。基于此,筆者通過建立一理想模型,測定黃土土水特征曲線;當(dāng)含水量由高到低變化時,計算不同土粒間距黃土顆粒間由水氣界面表面張力和基質(zhì)吸力引起的粒間引力以及由此產(chǎn)生的拉應(yīng)力。
1試驗?zāi)P图胺椒?/p>
試驗土樣取自陜西省涇陽縣涇河南岸的黃土塬南緣的馬蘭黃土(Q3),現(xiàn)場分別取了原狀土樣和擾動土樣。利用原狀土樣測得試驗土基本物理性質(zhì):用環(huán)刀法測得天然密度為
136 g·cm-3,用烘干法測得含水量(質(zhì)量比,下同)為63%,用比重計法測得土粒密度為269 g·cm-3,用搓條法得到塑限為198%,用丟錐法測得液限為 30.2%。通過測得的數(shù)據(jù)計算得到該黃土的孔隙比為1101,干密度為128 g·cm-3 ,塑性指數(shù)為104%,液性指數(shù)為-13。
室內(nèi)模型試驗裝置為:壁厚7 mm、內(nèi)徑為236 cm、高H為2 m的圓柱形有機玻璃桶,桶壁一側(cè)有一排直徑均為8 mm的圓形小孔,孔間隔為5 cm(圖1)。將擾動土樣風(fēng)干碾壓,用0.5 mm的篩均勻篩到模型試驗桶中,模擬黃土的自然沉積過程。整個過程中保持土顆粒自然沉積直到容器內(nèi)的土樣達(dá)到所需高度(1.8 m),每次篩入土?xí)r都要稱重,累積篩入土的總質(zhì)量m為91.1 kg。利用烘干法測得模型試驗桶中土樣含水量w為26%。然后,在土樣頂部施加靜載(荷載為10 kg的砂袋和20 kg砝碼),壓密土樣3 d,模型試驗桶內(nèi)土樣高度沉降穩(wěn)定,取出砂袋和砝碼。此時測得土樣的高度h為178 cm。在土樣表面均勻鋪上10 cm厚的細(xì)砂,防止在滲水過程中試樣表層板結(jié)或沿側(cè)壁集中下滲。土樣密度ρ和孔隙比e計算公式為
ρ=mV=4mhπD2(1)
e=Gs(1+w)ρ(2)
式中:h為壓密后模型試驗桶中土樣高度;D為模型試驗桶內(nèi)徑;Gs為土粒相對密度。
由式(1)、(2)計算得到模型試驗桶內(nèi)土樣的平均密度為1.17 g·cm-3,孔隙比e為1.359。利用TST55滲透儀測得與模型試驗桶中相同密度土樣的飽和滲透系數(shù)k為6.42×10-4m·s-1。
圖1模型試驗桶及滲水后上部開裂現(xiàn)象
Fig.1Model Test Barrel and Fissure Phenomena After Water Penetration in the Top
試驗準(zhǔn)備工作完成后,采用灑水器向砂層表面噴水,模擬自然降雨。持續(xù)緩慢噴水30 min,總共加水1 500 mL,水分透過砂層在黃土表面形成飽和帶。然后靜置觀察,在含水量梯度作用下,飽和帶水分向下遷移,土樣周圍豎向裂縫出現(xiàn)。經(jīng)過60 min之后,黃土試樣上部形成9條距離大致相等的豎直方向的楔形張性裂縫[圖1(b)],此時在裂縫發(fā)展的地方用掏土烘干法測得土樣含水量為32%,各條垂直裂縫的長度和寬度見表1。模型試驗桶頂部密封,沒有繼續(xù)加水,周圍豎向裂縫沒有繼續(xù)發(fā)展,保持初始狀態(tài)。在豎向裂縫形成過程中,由于黃土濕陷性,土樣局部產(chǎn)生橫向裂縫,并隨時間持續(xù)擴張。
表1模型試驗桶中垂直裂縫大小
Tab.1Sizes of Vertical Joints in Model Test Barrel
裂縫編號裂縫深度/cm裂縫頂寬/mm
110.33.2
210.33.3
38.02.3
49.02.4
58.02.5
69.53.5
76.03.3
89.03.2
95.03.2
2黃土垂直節(jié)理形成機理
模型試驗表明,黃土中垂直節(jié)理的形成與水的作用有密切關(guān)系。為了分析水在垂直節(jié)理形成中的作用,建立一個理想化的模型,將黃土顆粒看成大小相同的均勻球體,球體直徑等于黃土試樣的平均粒徑,并認(rèn)為土顆粒均勻排列,不考慮細(xì)粒在粗粒之間的接觸支撐作用。
根據(jù)室內(nèi)模擬試驗測得模型試驗桶中黃土的基本物理指標(biāo)(Gs、ρ、w和e);然后,利用激光粒度分析儀測得模型試驗桶內(nèi)黃土的粒徑級配曲線(圖2),得到顆粒的中位粒徑d50為15.1 μm,則單個土顆粒平均體積Vp為
Vp=16πd350=1 803 μm3(3)
圖2黃土試樣的粒度累積曲線
Fig.2Particle Size Accumulated Curve of the Loess Sample
選擇邊長為100 μm的立方體模型,則模型總體積V為1.0×106 μm3,其中固體顆粒部分的總體積Vs為
Vs=V1+e=423 908 μm3(4)
則土顆粒的個數(shù)N為
N=VsVp=235
試驗土樣為擾動土樣,無固結(jié),因此,假定土粒按最疏松的一種情況排列,即土粒中心也按立方體排列,則沿立方體模型棱邊任一方向的土粒數(shù)n為
n=3N=6.2
則2個土粒的中心間距ac為
ac=161 μm
土粒數(shù)取整數(shù),按每個方向6個土顆粒,得到(100×100)μm2的水平截面,土粒排列見圖3。土顆粒間的中心間距為16.1 μm,土粒之間的凈間距為1.0 μm,由此可見土顆粒之間有收縮空間。
圖3土顆粒排列模型(單位:μm)
Fig.3Arrangement Model of Soil Particle (Unit:μm)
沉積開始后,表層土體疏散干燥,粒間沒有水分。集中滲水后,表層顆粒間空隙充滿水分,土體飽和。飽和帶水分的向下遷移或蒸發(fā)等引起土體從飽和狀態(tài)向非飽和狀態(tài)發(fā)展。此時有空氣進(jìn)入土體中,水氣界面產(chǎn)生表面張力,表面張力作用方向與收縮膜表面相切,其大小主要與溫度有關(guān)。水氣界面上的孔隙水壓力uw為負(fù)值(相對大氣壓來說),水氣共同作用產(chǎn)生基質(zhì)吸力ua-uw,其中ua為孔隙氣壓力。基質(zhì)吸力是由負(fù)孔隙水壓力和表面張力綜合作用在非飽和粒狀顆粒骨架內(nèi)產(chǎn)生的粒間作用力[15],宏觀表現(xiàn)為拉力作用,可使作用范圍內(nèi)的土顆粒相互靠近(圖4)。
圖4高含水量到低含水量狀態(tài)中土顆粒間收縮膜形態(tài)的發(fā)展過程
Fig.4Development Process of Shrink Film Form Between
Soil Particles from High Water Content to Low
收縮水膜受到土顆粒表面向外的拉力,土顆粒則受到水膜向內(nèi)的切向拉力,因此,任意兩個土顆粒受表面張力作用都有相互靠近的趨勢。垂直方向上有重力作用,土粒整體向下運移;而橫向上僅有張力作用,會在薄弱處拉裂,宏觀上表現(xiàn)為垂直方向的裂縫。
以上分析表明,土顆粒間的吸引力變化是垂直節(jié)理形成的基本原因。為了定量分析黃土從飽和到非飽和狀態(tài)過程中土顆粒之間作用力的變化,需要測定試驗土樣的土水特征曲線。實驗室常用的土水特征曲線測定方法包括軸平移法[1617]、張力計法[18]等。筆者采用TEN15張力計測定了試驗土樣的土水特征曲線。
具體試驗方法為:在體積為27 cm×17 cm×15 cm的制樣盒中制備干密度與模型試驗桶中相同的土樣;然后,通過逐步減濕(自飽和到干),配置不同含水量,每種含水狀態(tài)密封靜置7 d,使土樣內(nèi)水分分布均勻;再在試樣中心打孔,孔徑略大于吸力傳感器探頭直徑,孔深8 cm左右;將張力計排氣、充滿水后,豎直向下插入孔中,用相同濕度的土樣填充試驗鉆孔與張力計間的空隙;等張力計讀數(shù)穩(wěn)定后,測得相應(yīng)含水量下試樣的吸力值,同時取出探頭,采集探頭附近土樣少許,用烘干法測定土樣的含水量。利用式(5)將實測的質(zhì)量含水量轉(zhuǎn)化為體積含水量[19],繪出試樣土水特征曲線(圖5)。
圖5試樣土水特征曲線
Fig.5Soilwater Characteristic Curve of the Sample
質(zhì)量含水量w轉(zhuǎn)化為體積含水量θw的公式為
θw=SwGsSr+wGs(5)
式中:Sr為飽和度。
非飽和土中基質(zhì)吸力和表面張力的關(guān)系為[6]
(ua-uw)=Ts(1r1-1r2)(6)
其中r1=acos α-R
r2=atan α-r1
式中: Ts為表面張力;r1為收縮膜半徑;r2為毛細(xì)水柱半徑;a為兩個土顆粒中心間距的一半;α為填充角;R為理想球狀土顆粒半徑。
圖6顯示了兩個土顆粒在非飽和狀態(tài)下的微觀作用力。所有力的合力Fsum為
Fsum=uaπR2-(ua-uw)πr22-2πr2Ts(7)
圖6土顆粒受力狀態(tài)
Fig.6Strained Condition of the Soil Particles
空氣壓力只會改變土顆粒內(nèi)力的大小,不會改變(ua-uw)和Ts的大小,也就不會改變土顆粒的相互作用力。根據(jù)文獻(xiàn)[20]~[23],把氣壓設(shè)為0可以得到粒間引力Ps為
Ps=(ua-uw)πr22+2πr2Ts(8)
模型試驗加水過程中,土樣經(jīng)歷了非飽和→飽和→非飽和過程。這一階段是土樣由松到密的過程,土顆粒在粒間引力作用下相互靠近,為此選擇不同的顆粒間距計算粒間引力的大小,以便對比。取溫度為25 ℃時的表面張力(72.0 mN·m-1)和理想球狀土顆粒的半徑(7.55 μm),利用式(6)計算得到不同粒間距下不同含水量對應(yīng)的平均曲率半徑r1和r2,然后再利用式(8)得到對應(yīng)粒間距的粒間引力與體積含水量的關(guān)系曲線(圖7)。
圖7不同粒間距體積含水量和粒間引力的關(guān)系
Fig.7Relationship Between Volume Water Content and
Interparticle Force at Different Distances of the Particles
從圖7可以看出:相同體積含水量下,粒間距越小,粒間引力越大;隨著體積含水量的減小,不同粒間距的粒間引力差值增大。粒間距一定時,粒間引力隨體積含水量的變化趨勢有所不同。當(dāng)粒間距較大(775 μm
10.120.111.564.025.20.792.762.7912.24
15.730.117.956.526.50.882.872.7612.11
21.041.623.838.030.31.193.212.6911.80
23.045.526.222.035.51.723.662.5911.36
27.654.631.510.541.92.594.182.4710.83
31.562.335.93.048.93.944.722.3510.31
39.878.845.31.051.54.584.912.3010.09
注:飽和含水量為505%。
分散在粗顆粒表面和支撐點上作為弱的膠結(jié),形成具有大孔的架空結(jié)構(gòu),這種結(jié)構(gòu)是黃土具有濕陷性的原因。由此可推測,黃土的實際結(jié)構(gòu)比圖3的理想結(jié)構(gòu)模型更加疏松,更容易形成垂直節(jié)理。
3結(jié)語
(1)在模擬風(fēng)積黃土的非飽和滲透性時,黃土在地表滲水過程中會出現(xiàn)垂直的楔形裂隙,此現(xiàn)象和黃土垂直節(jié)理的形成類似。
(2)通過建立一理想模型,測定黃土土水特征曲線,計算出當(dāng)含水量由高到低變化時,不同土粒間距黃土顆粒間由水氣界面表面張力和基質(zhì)吸力引起的粒間引力以及由此產(chǎn)生的拉應(yīng)力。盡管粒間引力和拉應(yīng)力很小,但對于初始沉積、結(jié)構(gòu)疏松、具有弱支撐的黃土來講,足以引起收縮變形,垂直方向收縮導(dǎo)致其沉陷,水平方向收縮導(dǎo)致其在薄弱處拉裂形成張裂隙,這就是黃土垂直節(jié)理的形成機理。
(3)黃土的垂直節(jié)理是一種原生節(jié)理,在黃土沉積初期,由于降雨入滲導(dǎo)致黃土處于非飽和狀態(tài),從而在粒間產(chǎn)生引力導(dǎo)致節(jié)理產(chǎn)生。
參考文獻(xiàn):
References:
[1]李萍,李同錄,王阿丹,等.黃土中水分遷移規(guī)律現(xiàn)場試驗研究[J].巖土力學(xué),2013,34(5):13311339.
LI Ping,LI Tonglu,WANG Adan,et al.Insitu Test Research on Regularities of Water Migration in Loess[J].Rock and Soil Mechanics,2013,34(5):13311339.
[2]梁燕,謝永利,劉保健,等.非飽和黃土滲透性的試驗研究[J].水文地質(zhì)工程地質(zhì),2006,33(2):2730.
LIANG Yan,XIE Yongli,LIU Baojian,et al.A Test Study of the Permeability of Unsaturated Typical Loess[J].Hydrogeology and Engineering Geology,2006,33(2):2730.
[3]藺曉燕,李同錄,趙紀(jì)飛,等.甘肅黑方臺黃土固結(jié)滲透特性試驗研究[J].水文地質(zhì)工程地質(zhì),2014,41(1):4147.
LIN Xiaoyan,LI Tonglu,ZHAO Jifei,et al.Permeability Characteristics of Loess Under Different Consolidation Pressures in the Heifangtai Platform[J].Hydrogeology and Engineering Geology,2014,41(1):4147.
[4]梁燕,邢鮮麗,李同錄,等.晚更新世黃土滲透性的各向異性及其機制研究[J].巖土力學(xué),2012,33(5):13131318.
LIANG Yan,XING Xianli,LI Tonglu,et al.Study of the Anisotropic Permeability and Mechanism of Q3 Loess[J].Rock and Soil Mechanics,2012,33(5):13131318.
[5]王福恒,李家春,田偉平.黃土邊坡降雨入滲規(guī)律試驗[J].長安大學(xué)學(xué)報:自然科學(xué)版,2009,29(4):2024.
WANG Fuheng,LI Jiachun,TIAN Weiping.Test on Rainfall Filtration in Loess Slope[J].Journal of Changan University:Natural Science Edition,2009,29(4):2024.
[6]李家春,崔世富,田偉平.公路邊坡降雨侵蝕特征及土的崩解試驗[J].長安大學(xué)學(xué)報:自然科學(xué)版,2007,27(1):2326,49.
LI Jiachun,CUI Shifu,TIAN Weiping.Erosion Characteristic of Road Slope and Test of Soil Disintegration[J].Journal of Changan University:Natural Science Edition,2007,27(1):2326,49.
[7]王磊,馬骉.黃土地區(qū)公路排水系統(tǒng)病害防治[J].長安大學(xué)學(xué)報:自然科學(xué)版,2003,23(1):1518.
WANG Lei,MA Biao.Prevention and Treatment for Disasters of Highway Drainage System in Loess Area[J].Journal of Changan University:Natural Science Edition,2003,23(1):1518.
[8]劉巍然,高江平.壓實黃土路基中水分遷移的數(shù)值模擬[J].長安大學(xué)學(xué)報:自然科學(xué)版,2006,26(4):57.
LIU Weiran,GAO Jiangping.Numerical Modelling on Water Migration in Loess Subgrade[J].Journal of Changan University:Natural Science Edition,2006,26(4):57.
[9]雷勝友,李志遠(yuǎn),王吉慶,等.含水量對非飽和黃土強度的影響[J].交通運輸工程學(xué)報,2012,12(1):15.
LEI Shengyou,LI Zhiyuan,WANG Jiqing,et al.Effect of Water Content on Strength of Unsaturated Loess[J].Journal of Traffic and Transportation Engineering,2012,12(1):15.
[10]王鐵行,王娟娟,房江鋒.垂直節(jié)理影響的黃土隧道洞口段穩(wěn)定性分析[J].地下空間與工程學(xué)報,2012,8(1):6570.
WANG Tiehang,WANG Juanjuan,FANG Jiangfeng.Stability Analysis of Loess Tunnel Entrance Section Considering the Impact of Vertical Joints[J].Chinese Journal of Underground Space and Engineering,2012,8(1):6570.
[11]駱進(jìn),項偉,吳云剛,等.陜北黃土垂直節(jié)理形成機理的試驗研究[J].長江科學(xué)院院報,2010,27(3):3841,45.
LUO Jin,XIANG Wei,WU Yungang,et al.Experimental Study on Formation of Loess Vertical Joints in Northern Shaanxi Province[J].Journal of Yangtze River Scientific Research Institute,2010,27(3):3841,45.
[12]王正貴,康國瑾,馬崇武,等.關(guān)于黃土垂直節(jié)理形成機制的探討[J].中國科學(xué):B輯,1993,23(7):765770.
WANG Zhenggui,KANG Guojin,MA Chongwu,et al.The Discussion on Formation of Loess Vertical Joints[J].Science in China:Series B,1993,23(7):765770.
[13]馮連昌,鄭晏武.中國濕陷性黃土[M].北京:中國鐵道出版社,1982.
FENG Lianchang,ZHENG Yanwu.Collapse Loess in China[M].Beijing:China Railway Publishing House,1982.
[14]王永炎,林在貴.中國黃土的結(jié)構(gòu)特征及物理力學(xué)性質(zhì)[M].北京:科學(xué)出版社,1990.
WANG Yongyan,LIN Zaigui.The Structural Characteristics and Physics Mechanical Properties of Loess in China[M].Beijing:Science Press,1990.
[15]LU N,LIKOS W J.Unsaturated Soil Mechanics[M].New York:Wiley,2004.
[16]梅嶺,姜朋明,李鵬,等.非飽和土的土水特征曲線試驗研究[J].巖土工程學(xué)報,2013,35(增1):124128.
MEI Ling,JIANG Pengming,LI Peng,et al.Soilwater Characteristic Curve Tests on Unsaturated Soil[J].Chinese Journal of Geotechnical Engineering,2013,35(S1):124128.
[17]宋亞亞,盧廷浩,季李通,等.應(yīng)力作用下非飽和土土水特征曲線研究[J].水利與建筑工程學(xué)報,2012,10(6):147150.
SONG Yaya,LU Tinghao,JI Litong,et al.Research on Soilwater Characteristic Curve of Unsaturated Soil Under Stress State[J].Journal of Water Resources and Architectural Engineering,2012,10(6):147150.
[18]李萍,李同錄,王紅,等.非飽和黃土土水特征曲線與滲透系數(shù) Childs & CollisGeroge模型預(yù)測[J].巖土力學(xué),2013,34(增2):184189.
LI Ping,LI Tonglu,WANG Hong,et al.Soilwater Characteristic Curve and Permeability Perdiction on Childs & CollisGeroge Model of Unsaturated Loess[J].Rock and Soil Mechanics,2013,34(S2):184189.
[19]FREDLUND D G,RAHARDJO H.Soil Mechanics for Unsaturated Soils[M].New York:John Wiley and Sons,1993.
[20]LIU S H,SUN D A,WANG Y S.Numerical Study of Soil Collapse Behavior by Discrete Element Modelling[J].Computers and Geotechnics,2003,30(5):399408.
[21]GESSINGER G H.A Modified Model for the Sintering of Tungsten with Nickel Additions[J].Journal of the Less Common Metals,1972,27(2):129141.
[22]HEADY R B,CAHN J W.An Analysis of the Capillary Forces in Liquidphase Sintering of Spherical Particles[J].Metallurgical Transactions,1970,1(1):185189.
[23]KEMPER W D,ROSENAU R C.Soil Cohesion as Affected by Time and Water Content[J].Soil Science Society of America Journal,1984,48(5):10011006.
[24]欒茂田,李順群,楊慶.對“非飽和土的基質(zhì)吸力和張力吸力”討論的答復(fù)[J].巖土工程學(xué)報,2007,29(7):11131114.
LUAN Maotian,LI Shunqun,YANG Qing.Reply for the Discussion on “Matric Suction and Tension Suction of Unsaturated Soils”[J].Chinese Journal of Geotechnical Engineering,2007,29(7):11131114.
WANG Tiehang,WANG Juanjuan,FANG Jiangfeng.Stability Analysis of Loess Tunnel Entrance Section Considering the Impact of Vertical Joints[J].Chinese Journal of Underground Space and Engineering,2012,8(1):6570.
[11]駱進(jìn),項偉,吳云剛,等.陜北黃土垂直節(jié)理形成機理的試驗研究[J].長江科學(xué)院院報,2010,27(3):3841,45.
LUO Jin,XIANG Wei,WU Yungang,et al.Experimental Study on Formation of Loess Vertical Joints in Northern Shaanxi Province[J].Journal of Yangtze River Scientific Research Institute,2010,27(3):3841,45.
[12]王正貴,康國瑾,馬崇武,等.關(guān)于黃土垂直節(jié)理形成機制的探討[J].中國科學(xué):B輯,1993,23(7):765770.
WANG Zhenggui,KANG Guojin,MA Chongwu,et al.The Discussion on Formation of Loess Vertical Joints[J].Science in China:Series B,1993,23(7):765770.
[13]馮連昌,鄭晏武.中國濕陷性黃土[M].北京:中國鐵道出版社,1982.
FENG Lianchang,ZHENG Yanwu.Collapse Loess in China[M].Beijing:China Railway Publishing House,1982.
[14]王永炎,林在貴.中國黃土的結(jié)構(gòu)特征及物理力學(xué)性質(zhì)[M].北京:科學(xué)出版社,1990.
WANG Yongyan,LIN Zaigui.The Structural Characteristics and Physics Mechanical Properties of Loess in China[M].Beijing:Science Press,1990.
[15]LU N,LIKOS W J.Unsaturated Soil Mechanics[M].New York:Wiley,2004.
[16]梅嶺,姜朋明,李鵬,等.非飽和土的土水特征曲線試驗研究[J].巖土工程學(xué)報,2013,35(增1):124128.
MEI Ling,JIANG Pengming,LI Peng,et al.Soilwater Characteristic Curve Tests on Unsaturated Soil[J].Chinese Journal of Geotechnical Engineering,2013,35(S1):124128.
[17]宋亞亞,盧廷浩,季李通,等.應(yīng)力作用下非飽和土土水特征曲線研究[J].水利與建筑工程學(xué)報,2012,10(6):147150.
SONG Yaya,LU Tinghao,JI Litong,et al.Research on Soilwater Characteristic Curve of Unsaturated Soil Under Stress State[J].Journal of Water Resources and Architectural Engineering,2012,10(6):147150.
[18]李萍,李同錄,王紅,等.非飽和黃土土水特征曲線與滲透系數(shù) Childs & CollisGeroge模型預(yù)測[J].巖土力學(xué),2013,34(增2):184189.
LI Ping,LI Tonglu,WANG Hong,et al.Soilwater Characteristic Curve and Permeability Perdiction on Childs & CollisGeroge Model of Unsaturated Loess[J].Rock and Soil Mechanics,2013,34(S2):184189.
[19]FREDLUND D G,RAHARDJO H.Soil Mechanics for Unsaturated Soils[M].New York:John Wiley and Sons,1993.
[20]LIU S H,SUN D A,WANG Y S.Numerical Study of Soil Collapse Behavior by Discrete Element Modelling[J].Computers and Geotechnics,2003,30(5):399408.
[21]GESSINGER G H.A Modified Model for the Sintering of Tungsten with Nickel Additions[J].Journal of the Less Common Metals,1972,27(2):129141.
[22]HEADY R B,CAHN J W.An Analysis of the Capillary Forces in Liquidphase Sintering of Spherical Particles[J].Metallurgical Transactions,1970,1(1):185189.
[23]KEMPER W D,ROSENAU R C.Soil Cohesion as Affected by Time and Water Content[J].Soil Science Society of America Journal,1984,48(5):10011006.
[24]欒茂田,李順群,楊慶.對“非飽和土的基質(zhì)吸力和張力吸力”討論的答復(fù)[J].巖土工程學(xué)報,2007,29(7):11131114.
LUAN Maotian,LI Shunqun,YANG Qing.Reply for the Discussion on “Matric Suction and Tension Suction of Unsaturated Soils”[J].Chinese Journal of Geotechnical Engineering,2007,29(7):11131114.
WANG Tiehang,WANG Juanjuan,FANG Jiangfeng.Stability Analysis of Loess Tunnel Entrance Section Considering the Impact of Vertical Joints[J].Chinese Journal of Underground Space and Engineering,2012,8(1):6570.
[11]駱進(jìn),項偉,吳云剛,等.陜北黃土垂直節(jié)理形成機理的試驗研究[J].長江科學(xué)院院報,2010,27(3):3841,45.
LUO Jin,XIANG Wei,WU Yungang,et al.Experimental Study on Formation of Loess Vertical Joints in Northern Shaanxi Province[J].Journal of Yangtze River Scientific Research Institute,2010,27(3):3841,45.
[12]王正貴,康國瑾,馬崇武,等.關(guān)于黃土垂直節(jié)理形成機制的探討[J].中國科學(xué):B輯,1993,23(7):765770.
WANG Zhenggui,KANG Guojin,MA Chongwu,et al.The Discussion on Formation of Loess Vertical Joints[J].Science in China:Series B,1993,23(7):765770.
[13]馮連昌,鄭晏武.中國濕陷性黃土[M].北京:中國鐵道出版社,1982.
FENG Lianchang,ZHENG Yanwu.Collapse Loess in China[M].Beijing:China Railway Publishing House,1982.
[14]王永炎,林在貴.中國黃土的結(jié)構(gòu)特征及物理力學(xué)性質(zhì)[M].北京:科學(xué)出版社,1990.
WANG Yongyan,LIN Zaigui.The Structural Characteristics and Physics Mechanical Properties of Loess in China[M].Beijing:Science Press,1990.
[15]LU N,LIKOS W J.Unsaturated Soil Mechanics[M].New York:Wiley,2004.
[16]梅嶺,姜朋明,李鵬,等.非飽和土的土水特征曲線試驗研究[J].巖土工程學(xué)報,2013,35(增1):124128.
MEI Ling,JIANG Pengming,LI Peng,et al.Soilwater Characteristic Curve Tests on Unsaturated Soil[J].Chinese Journal of Geotechnical Engineering,2013,35(S1):124128.
[17]宋亞亞,盧廷浩,季李通,等.應(yīng)力作用下非飽和土土水特征曲線研究[J].水利與建筑工程學(xué)報,2012,10(6):147150.
SONG Yaya,LU Tinghao,JI Litong,et al.Research on Soilwater Characteristic Curve of Unsaturated Soil Under Stress State[J].Journal of Water Resources and Architectural Engineering,2012,10(6):147150.
[18]李萍,李同錄,王紅,等.非飽和黃土土水特征曲線與滲透系數(shù) Childs & CollisGeroge模型預(yù)測[J].巖土力學(xué),2013,34(增2):184189.
LI Ping,LI Tonglu,WANG Hong,et al.Soilwater Characteristic Curve and Permeability Perdiction on Childs & CollisGeroge Model of Unsaturated Loess[J].Rock and Soil Mechanics,2013,34(S2):184189.
[19]FREDLUND D G,RAHARDJO H.Soil Mechanics for Unsaturated Soils[M].New York:John Wiley and Sons,1993.
[20]LIU S H,SUN D A,WANG Y S.Numerical Study of Soil Collapse Behavior by Discrete Element Modelling[J].Computers and Geotechnics,2003,30(5):399408.
[21]GESSINGER G H.A Modified Model for the Sintering of Tungsten with Nickel Additions[J].Journal of the Less Common Metals,1972,27(2):129141.
[22]HEADY R B,CAHN J W.An Analysis of the Capillary Forces in Liquidphase Sintering of Spherical Particles[J].Metallurgical Transactions,1970,1(1):185189.
[23]KEMPER W D,ROSENAU R C.Soil Cohesion as Affected by Time and Water Content[J].Soil Science Society of America Journal,1984,48(5):10011006.
[24]欒茂田,李順群,楊慶.對“非飽和土的基質(zhì)吸力和張力吸力”討論的答復(fù)[J].巖土工程學(xué)報,2007,29(7):11131114.
LUAN Maotian,LI Shunqun,YANG Qing.Reply for the Discussion on “Matric Suction and Tension Suction of Unsaturated Soils”[J].Chinese Journal of Geotechnical Engineering,2007,29(7):11131114.