Lecture2Phasepropertiesandrelations

1、Unsaturated soil mechanicsDr. LI, Xu （李（李 旭）旭）Associate Processor, School of Civil EngineeringEmail: ceXuL2Phase propertiesl State of unsaturated soilsl 4 phases model of unsaturated soilsl Capillary in unsaturated soilsl Suction and humidityl Assignments3State of unsaturated soils4Pore-water and po

2、re-air phase in unsaturated soils5State of unsaturated soils6Three-phase or Four-phase?74 phasesl Solid particlel Void Pore-air Pore-water Contractile skin8Contractile skinl Surface tension表面張力表面張力 (surface tension, (surface tension, T Ts)s)定義：展開或收攏物質(zhì)相交界面上單位面積時所需的能量單位：J/m2，N/mContractile skinSurface

3、 tensionTsnUnbalanced force in the contractile skinnTs: Surface tension The tensile force per unit length along the contractile skin (N/m)11 = 濕潤角濕潤角 空氣空氣固體固體水水 lT = 界面張力界面張力d d = 毛管直徑毛管直徑Td=2rua-uwua-uw = 壓力差壓力差毛細(xì)現(xiàn)象毛細(xì)現(xiàn)象毛毛細(xì)細(xì)管管hc毛細(xì)水12Contractile skinl Contractile skin presents at the interface betwee

4、n pore-water and pore-airl What will happen?l ua = uw ?Water pressure, uwAir pressure, uaAir pressure, uaMercury pressure, umTs,wTs,m= ua - uwp = um - ua 13Pressure difference14Matric suction (基質(zhì)吸力基質(zhì)吸力)l Due to the presence of contractile skin, the pore-water pressure is different with the pore-air

5、pressure in unsaturated soilsl Whats that in saturated soils?l The pressure difference D Du=(ua-uw), is referred to as matric suctionWater pressure, uwAir pressure, uaAir pressure, uaMercury pressure, umTs,wTs,m= ua - uwp = um - ua Surface tension at soil-air-water interface表面張力表面張力交界面交界面兩個水滴之間的平衡兩個

6、水滴之間的平衡閥門打開會出現(xiàn)什么現(xiàn)象？交界面交界面兩個水滴之間的平衡兩個水滴之間的平衡小水滴曲率半徑小水滴曲率半徑R R1 1小于大水滴的曲率半徑小于大水滴的曲率半徑R R2 2 ，其內(nèi)的水壓，其內(nèi)的水壓力大于大水滴。因此閥門打開時，大水滴變得更大，小水力大于大水滴。因此閥門打開時，大水滴變得更大，小水滴變得更滴變得更小。小。當(dāng)當(dāng)小水滴進(jìn)入導(dǎo)管內(nèi)且形成了一個彎曲半徑等于小水滴進(jìn)入導(dǎo)管內(nèi)且形成了一個彎曲半徑等于R R2 2的彎液的彎液面時，管內(nèi)液體停止面時，管內(nèi)液體停止流動。流動。請問：請問：圖圖b b中左端界面時外凸還是內(nèi)凹的？中左端界面時外凸還是內(nèi)凹的？19Surface tension交界

7、面交界面接觸角接觸角定義：氣-水交界面上的切線與水-固交界面上直線之間的夾角 。固-液-氣三相體系內(nèi)任意兩相相互接觸物質(zhì)相的固有屬性毛細(xì)現(xiàn)象毛細(xì)現(xiàn)象Young-LaplaceYoung-Laplace方程方程毛細(xì)現(xiàn)象毛細(xì)現(xiàn)象Young-LaplaceYoung-Laplace方程方程 （自（自學(xué)）學(xué)）1806年，Young-Laplace利用勢能理論推導(dǎo)了基質(zhì)吸力與交界面幾何形狀關(guān)系的雙曲率模型公式取任意氣-水交界面上的一點O為研究對象，假設(shè)其達(dá)到了力學(xué)平衡積分毛細(xì)現(xiàn)象毛細(xì)現(xiàn)象Young-LaplaceYoung-Laplace方程方程Young-Laplace方程交界面交界面非飽和土非飽和土

8、25Capillary in soill The capillary phenomenon is illustrated by the rise of a water surface in a capillary tubel The weight of the water column is transferred to the tube through the contractile skinCapillary tubes showing the air-water interfaces at different radii of curvature水頭水頭 h h (Water Head,

9、 unit: m)(Water Head, unit: m)Water head profile Water head profile ( (under static hydraulic equilibriumunder static hydraulic equilibrium) )毛細(xì)現(xiàn)象毛細(xì)現(xiàn)象毛細(xì)上升高度毛細(xì)上升高度表面張力作用使得毛細(xì)管內(nèi)水上升，上升高度與孔徑大小有關(guān)容器中交界面平直，基質(zhì)吸力趨近于0：毛細(xì)管內(nèi)，基質(zhì)吸力為：從而有：2930Capillary height31Capillary in soilnSimple cylindrical modelnThe radius or

10、 opening of the tube is a significant factor controlling the capillary rise.nA soil can be viewed as a complex system where interconnected channels are the “real” tubes which may vary in size according to the structure of the soil.毛細(xì)上升高度毛細(xì)上升高度Guo et al. 2013, Global geology毛細(xì)上升高度毛細(xì)上升高度36Pore-water a

11、nd pore-air phase in unsaturated soils37Pore-water pressure in saturated soilsl 水壓力的作用水壓力的作用 一個顆粒處于孔隙水包圍之中，當(dāng)孔隙水壓力發(fā)生變化一個顆粒處于孔隙水包圍之中，當(dāng)孔隙水壓力發(fā)生變化時，顆粒是否會發(fā)生移動？時，顆粒是否會發(fā)生移動？ 當(dāng)土體受到剪應(yīng)力時，水壓力對土體抗剪有沒有作用？當(dāng)土體受到剪應(yīng)力時，水壓力對土體抗剪有沒有作用？l 顆粒之間的接觸力發(fā)生改變是否會導(dǎo)致土體顆粒顆粒之間的接觸力發(fā)生改變是否會導(dǎo)致土體顆粒移動？移動？38Pore-water pressure in saturated s

12、oils它它在各個方向相等，只能在各個方向相等，只能使土顆粒本身受到等向壓力使土顆粒本身受到等向壓力，不會，不會使土顆粒移動并導(dǎo)致孔隙體積發(fā)生變化。由于顆粒本身壓使土顆粒移動并導(dǎo)致孔隙體積發(fā)生變化。由于顆粒本身壓縮模量很大，故土粒本身壓縮變形極小縮模量很大，故土粒本身壓縮變形極小 水不能承受剪應(yīng)力水不能承受剪應(yīng)力，對土顆粒間摩擦、土粒的破碎沒有貢，對土顆粒間摩擦、土粒的破碎沒有貢獻(xiàn)，因而獻(xiàn)，因而對強度也沒有影響對強度也沒有影響 所以孔隙水壓力對變形、強度沒有直接影響，故稱為中性所以孔隙水壓力對變形、強度沒有直接影響，故稱為中性應(yīng)力應(yīng)力 So we have the concept of eff

13、ective stress, -uwSurface tension at soil-air-water interfaceContractile skinIt can withstand tensile stresses so it exerts soil stresses throughout the soil mass.Shear strength or ?Required to consider four-phase when understanding stress state analysis40Influence of suction on inter-particle force

14、sIn a soil the contractile skin compresses the soil resulting in an increase in its shear strength414243Think over the capillary phenomenon44Unsaturated soilsl Due to the presence of Contractile skin, ua is not equal to uwl if change ua or uwl Whats happen?45Development of an unsaturated soil by the

15、 withdrawal of the airwaterinterface at different stages of matric suction46Water in soil 自由水自由水重力水重力水毛細(xì)水毛細(xì)水在重力作用下可在土中自由在重力作用下可在土中自由流動流動 存在于固氣之間存在于固氣之間 在重力與表面張力作用下在重力與表面張力作用下 可在土粒間空隙中自由移可在土粒間空隙中自由移動動4748結(jié)合水：附著在粘土顆粒表面結(jié)合水：附著在粘土顆粒表面研究表明：研究表明：粘土顆粒的表面電荷，凈電荷通常為負(fù)電荷粘土顆粒的表面電荷，凈電荷通常為負(fù)電荷- - - - - - - - - - - -

16、 - - - - - - - - - -+粘土顆粒粘土顆粒水分子水分子陽離子陽離子49結(jié)合水結(jié)合水 排列致密、定向性強排列致密、定向性強 密度密度1g/cm1g/cm3 3 冰點處于零下幾十度冰點處于零下幾十度 具有固體的特性具有固體的特性 溫度高于溫度高于100100C C時可蒸發(fā)時可蒸發(fā)強結(jié)合水強結(jié)合水 位于強結(jié)合水之外，電場引位于強結(jié)合水之外，電場引 力作用范圍之內(nèi)力作用范圍之內(nèi) 外力作用下可以移動外力作用下可以移動 不因重力而移動，有粘滯性不因重力而移動，有粘滯性弱結(jié)合水弱結(jié)合水雙電層雙電層50雙電層決定了土粒表面結(jié)合水膜的厚度雙電層決定了土粒表面結(jié)合水膜的厚度結(jié)合水結(jié)合水?dāng)U散層厚度擴(kuò)

17、散層厚度增加增加減小減小土的塑性增加降低脹縮性增加降低強度降低增加結(jié)合水膜中的擴(kuò)散層結(jié)合水膜中的擴(kuò)散層（位于弱結(jié)合水區(qū)域）（位于弱結(jié)合水區(qū)域）土的性質(zhì)土的性質(zhì)有重要影響有重要影響51雙電層厚度雙電層厚度l 離子濃度增加l Ca2+ VS Na+ l 隨離子濃度增加，雙電層厚度線性遞減隨離子濃度增加，雙電層厚度線性遞減l 應(yīng)用：為什么用生石灰處理膨脹土？應(yīng)用：為什么用生石灰處理膨脹土？52土壤水土壤水土中水礦物中的結(jié)合水土孔隙中的水土粒表面結(jié)合水非結(jié)合水強結(jié)合水弱結(jié)合水液態(tài)水氣態(tài)水(水蒸氣)固態(tài)水(冰)重力水或自由水毛細(xì)水53Matric suctionrTuuswa2)(l At negati

18、ve pressures, the water is under tensionl The surface tension associated with the contractile skin results in a reaction force on the walls of the capillary tube.544 phases in unsaturated soils55Volume-mass relationsnVolumetric properties: porosity, void ratio, degree of saturationnGravimetric prope

19、rties: water content, soil densitynPorosity, n, is the ratio of the volume of voids, VV, to the total volume, V nEach phase can also be written as a percentage of total volume: Soil particle Contractile skin Water porosity nThe volume of the contractile skin can be assumed to be negligible.nThe poro

20、sity with respect to the water phase, nw, is equivalent to the volumetric water content, qw.nVoid ratio: ratio of the volume of voids, Vv, to the volume of soil solids, VsnRelation between void ratio and porositynVolumetric water content nDegree of saturation: Percentage of void space containing wat

21、er Continuous air phase when S90%nWater content: the ratio of the mass of water Mw, to the mass of soil solids, Ms.nBulk density (p): the ratio of the total mass, M, to the total volume of the soil, V. nDry density (ps): the ratio of the mass of the soil solids, Ms, to the total volume of the soil,

22、V:nSaturated densitynBuoyant densityBasic volume mass relationshipwGsSe n Specific Gravity of the soil particles, Gs, is defined as the dimensionless ratio between the density of the soil particles and the density of water at a temperature of 4oC under atmospheric pressure conditions (i.e., 101.3 kP

23、a). nTotal density, r, can be writtennSubstituting in the basic volume-mass relationship:n ornDry density rd, is obtained by eliminating the mass of water:634 phases in unsaturated soilsAir phasenAir is a mixture of several gases Air phasenThe ideal gas lawnDensity of airDensity of air is proportion

24、al to the absolute pressure 66Partial pressure67Saturation pressure of water vapor 68Water Vapor pressure69Air phasel Relative humidity: concentration of water vapor in air70RH vs suction71Dew point72Free energySoil suction Soil suction （吸力）（吸力）Matric Suction孔隙水與土顆粒間相互作用而產(chǎn)生的吸力中的各個部分毛細(xì)作用吸附作用Matric su

25、ction: Matric suction: Relative humidity decrease due to Relative humidity decrease due to the presence of curved water surfaces the presence of curved water surfaces produced by the capillary phenomenon produced by the capillary phenomenon 74Osmotic suctionSoil suction Soil suction （吸力）（吸力）OsmoticO

26、smotic suction: suction: Relative humidity Relative humidity decrease due to decrease due to the presence of dissolved the presence of dissolved saltssalts 因溶質(zhì)溶解作用而產(chǎn)生的吸力滲透作用OsmoticOsmotic suctionsuction ( (滲透吸力，化學(xué)勢）滲透吸力，化學(xué)勢）78Osmotic suctionOsmotic pressure as a function of dissolved solute concentr

27、ationSoil suction Soil suction （吸力）（吸力）Suction孔隙水與土顆粒間相互作用而產(chǎn)生的吸力中的各個部分因溶質(zhì)溶解作用而產(chǎn)生的吸力毛細(xì)作用吸附作用滲透作用Soil Suction (Soil Suction (吸力吸力,),)土中吸力反映土中水的自由能狀態(tài)土中吸力反映土中水的自由能狀態(tài)相對相對于自由水狀態(tài)來說，土中孔隙水勢能的于自由水狀態(tài)來說，土中孔隙水勢能的減少量減少量l毛細(xì)吸力，高于自由水面，勢能較低毛細(xì)吸力，高于自由水面，勢能較低l滲透吸力，濃度增大，勢能較低滲透吸力，濃度增大，勢能較低l重力勢重力勢/ /壓力勢壓力勢/ /水頭勢水頭勢水往低處流水往低

28、處流l毛細(xì)上升現(xiàn)象毛細(xì)上升現(xiàn)象l半透膜現(xiàn)象半透膜現(xiàn)象l河流河流81Soil Suction vs free energy水的摩爾質(zhì)量水的摩爾質(zhì)量 = 1*2+16 = 18 g/mol 化學(xué)勢能反映每單位質(zhì)量所包含的能量，其單位化學(xué)勢能反映每單位質(zhì)量所包含的能量，其單位為為J/mol或或J/kg；82Osmotic suctionvm is the partial molar volume of water (m3 /mol).水的摩爾質(zhì)量水的摩爾質(zhì)量 = 1*2+16 = 18 g/mol 化學(xué)勢能反映每單位質(zhì)量所包含的能量，其單位化學(xué)勢能反映每單位質(zhì)量所包含的能量，其單位為為J/mol或或

29、J/kg；83RH vs free energy化學(xué)勢能反映每單位質(zhì)量所包含的能量，其單位化學(xué)勢能反映每單位質(zhì)量所包含的能量，其單位為為J/mol或或J/kg；84Soil suction / total suctionl The free energy state of soil waterl Measured in terms of partial vapor pressure of the soil water (Richards 1965)l The thermodynamic relationship between soil suction and the partial pres

30、sure of the pore-water vapor: Suction Relative humidityR: Universal (molar) gas constant;T: absolute temperature;vm is the partial molar volume of water (m3 /mol). -135 MPa at 20oc85Soil suction VS RH86勢能換算勢能換算 土體孔隙水的勢能可以利用化學(xué)勢能、壓力勢能或水頭勢能的形式進(jìn)土體孔隙水的勢能可以利用化學(xué)勢能、壓力勢能或水頭勢能的形式進(jìn)行表征行表征。 化學(xué)勢化學(xué)勢能反映每單位質(zhì)量所包含的能量能

31、反映每單位質(zhì)量所包含的能量，其，其單位為單位為J/mol或或J/kg； 壓力勢壓力勢能反映每單位體積所包含的能量能反映每單位體積所包含的能量，其，其單位為單位為J/m3=N/m2=Pa； 水頭水頭勢能反映每單位重量所包含的能量勢能反映每單位重量所包含的能量，其，其單位為單位為J/N=m。8788Class exersisel RH 40% Ref to ? Suction? Ref to ? Potential units? Ref to ? Water headl RH 98% Ref to ? Suction? Ref to ? Potential units? Ref to ? Wate

32、r head孔隙水勢能孔隙水勢能capillaryosmoticelectricalvan der Waals隨著交界面曲率的增大（意味著含水量降低，負(fù)孔隙水壓力的數(shù)值變得更大），化學(xué)勢能會顯著降低孔隙水勢能孔隙水勢能隨著溶液溶質(zhì)濃度的增加，滲透壓力也逐漸增加，相應(yīng)隨著溶液溶質(zhì)濃度的增加，滲透壓力也逐漸增加，相應(yīng)的孔隙溶液的化學(xué)勢能的孔隙溶液的化學(xué)勢能卻卻降低降低當(dāng)土中有化學(xué)溶液輸運時，土中孔隙水的化學(xué)溶度發(fā)生當(dāng)土中有化學(xué)溶液輸運時，土中孔隙水的化學(xué)溶度發(fā)生改變，此時滲透吸力對土的性質(zhì)具有較大的影響。然而改變，此時滲透吸力對土的性質(zhì)具有較大的影響。然而就其它情況而言可忽略吸力中的滲透就其它情況

33、而言可忽略吸力中的滲透部分部分?？紫端畡菽芸紫端畡菽芤陨蟽墒奖砻鳎阂陨蟽墒奖砻鳎寒?dāng)當(dāng)水分子水分子相對相對遠(yuǎn)離遠(yuǎn)離土土顆粒表面時，電場和顆粒表面時，電場和范德華力引起的化學(xué)勢能的降低值要遠(yuǎn)小于水分子靠近土范德華力引起的化學(xué)勢能的降低值要遠(yuǎn)小于水分子靠近土顆粒表面是化學(xué)勢能的降低顆粒表面是化學(xué)勢能的降低值值?；|(zhì)吸力的探討基質(zhì)吸力的探討上述每種作用機(jī)理均造成了化學(xué)勢能的下降，這些下降只能的總和就上述每種作用機(jī)理均造成了化學(xué)勢能的下降，這些下降只能的總和就定義為土水系統(tǒng)的總定義為土水系統(tǒng)的總吸力吸力基質(zhì)吸力基質(zhì)吸力中的毛細(xì)部分和粘吸部分在概念上的區(qū)分是明顯的，但難以中的毛細(xì)部分和粘吸部分在概念上的區(qū)

34、分是明顯的，但難以通過試驗手段加以通過試驗手段加以區(qū)分區(qū)分基質(zhì)吸力中的各個部分對非飽和土行為影響的機(jī)理并不相同。對于低塑性的或較高含水量下的土體，基質(zhì)吸力中毛細(xì)部分占支配地位；然而對于高塑性的粘土或較低含水量下的土體，基質(zhì)吸力中粘吸部分占支配地位。當(dāng)基質(zhì)吸力很大時，只表明液相吸附到固相的程度很大，但絕不能認(rèn)為是傳統(tǒng)意義上的負(fù)孔隙壓力很大。然而，在以往的研究中，通常忽略基質(zhì)吸力中粘吸部分的作用，認(rèn)為基質(zhì)吸力僅由毛細(xì)作用產(chǎn)生，致使基質(zhì)吸力很大時，認(rèn)為負(fù)孔隙水壓力亦很大。目前針對非飽和土所建立的本構(gòu)模型多是基于毛細(xì)機(jī)理，因此這些模型對高塑性的粘土或低含水量下的土體的適用性是值得探討的。93Summa

35、ry of Soil suctionl Suction Matric suction Osmotic suction Total suctionl Relative humidity & total suction94Water phase transformationInteraction of water and airnAir and water can be an immiscible（不相溶） and/or miscible mixturenMiscible mixture can have two formsAir dissolves in waterWater vapor

36、 in the airSolubility(可溶性） of airnCoefficient of solubility (unit: gm/gm): nratio between the mass of each gas that can be dissolved in a liquid and the mass of the liquidWater molecules form a lattice structure with openings referred to as a “cage” that can be occupied by gas97Dissolved airl Approximately 2% of total volume98Disso