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表面张力表面张力 (surface tension, (surface tension, T Ts)s)定义：展开或收拢物质相交界面上单位面积时所需的能量单位：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 = 湿润角湿润角 空气空气固体固体水水 lT = 界面张力界面张力d d = 毛管直径毛管直径Td=2rua-uwua-uw = 压力差压力差毛细现象毛细现象毛毛细细管管hc毛细水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 (基质吸力基质吸力)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表面张力表面张力交界面交界面两个水滴之间的平衡两个

6、水滴之间的平衡阀门打开会出现什么现象？交界面交界面两个水滴之间的平衡两个水滴之间的平衡小水滴曲率半径小水滴曲率半径R R1 1小于大水滴的曲率半径小于大水滴的曲率半径R R2 2 ，其内的水压，其内的水压力大于大水滴。因此阀门打开时，大水滴变得更大，小水力大于大水滴。因此阀门打开时，大水滴变得更大，小水滴变得更滴变得更小。小。当当小水滴进入导管内且形成了一个弯曲半径等于小水滴进入导管内且形成了一个弯曲半径等于R R2 2的弯液的弯液面时，管内液体停止面时，管内液体停止流动。流动。请问：请问：图图b b中左端界面时外凸还是内凹的？中左端界面时外凸还是内凹的？19Surface tension交界

7、面交界面接触角接触角定义：气-水交界面上的切线与水-固交界面上直线之间的夹角 。固-液-气三相体系内任意两相相互接触物质相的固有属性毛细现象毛细现象Young-LaplaceYoung-Laplace方程方程毛细现象毛细现象Young-LaplaceYoung-Laplace方程方程 （自（自学）学）1806年，Young-Laplace利用势能理论推导了基质吸力与交界面几何形状关系的双曲率模型公式取任意气-水交界面上的一点O为研究对象，假设其达到了力学平衡积分毛细现象毛细现象Young-LaplaceYoung-Laplace方程方程Young-Laplace方程交界面交界面非饱和土非饱和土

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水头水头 h h (Water Head,

9、 unit: m)(Water Head, unit: m)Water head profile Water head profile ( (under static hydraulic equilibriumunder static hydraulic equilibrium) )毛细现象毛细现象毛细上升高度毛细上升高度表面张力作用使得毛细管内水上升，上升高度与孔径大小有关容器中交界面平直，基质吸力趋近于0：毛细管内，基质吸力为：从而有：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.毛细上升高度毛细上升高度Guo et al. 2013, Global geology毛细上升高度毛细上升高度36Pore-water a

11、nd pore-air phase in unsaturated soils37Pore-water pressure in saturated soilsl 水压力的作用水压力的作用 一个颗粒处于孔隙水包围之中，当孔隙水压力发生变化一个颗粒处于孔隙水包围之中，当孔隙水压力发生变化时，颗粒是否会发生移动？时，颗粒是否会发生移动？ 当土体受到剪应力时，水压力对土体抗剪有没有作用？当土体受到剪应力时，水压力对土体抗剪有没有作用？l 颗粒之间的接触力发生改变是否会导致土体颗粒颗粒之间的接触力发生改变是否会导致土体颗粒移动？移动？38Pore-water pressure in saturated s

12、oils它它在各个方向相等，只能在各个方向相等，只能使土颗粒本身受到等向压力使土颗粒本身受到等向压力，不会，不会使土颗粒移动并导致孔隙体积发生变化。由于颗粒本身压使土颗粒移动并导致孔隙体积发生变化。由于颗粒本身压缩模量很大，故土粒本身压缩变形极小缩模量很大，故土粒本身压缩变形极小 水不能承受剪应力水不能承受剪应力，对土颗粒间摩擦、土粒的破碎没有贡，对土颗粒间摩擦、土粒的破碎没有贡献，因而献，因而对强度也没有影响对强度也没有影响 所以孔隙水压力对变形、强度没有直接影响，故称为中性所以孔隙水压力对变形、强度没有直接影响，故称为中性应力应力 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细水毛细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动流动 存在于固气之间存在于固气之间 在重力与表面张力作用下在重力与表面张力作用下 可在土粒间空隙中自由移可在土粒间空隙中自由移动动4748结合水：附着在粘土颗粒表面结合水：附着在粘土颗粒表面研究表明：研究表明：粘土颗粒的表面电荷，净电荷通常为负电荷粘土颗粒的表面电荷，净电荷通常为负电荷- - - - - - - - - - - -

16、 - - - - - - - - - -+粘土颗粒粘土颗粒水分子水分子阳离子阳离子49结合水结合水 排列致密、定向性强排列致密、定向性强 密度密度1g/cm1g/cm3 3 冰点处于零下几十度冰点处于零下几十度 具有固体的特性具有固体的特性 温度高于温度高于100100C C时可蒸发时可蒸发强结合水强结合水 位于强结合水之外，电场引位于强结合水之外，电场引 力作用范围之内力作用范围之内 外力作用下可以移动外力作用下可以移动 不因重力而移动，有粘滞性不因重力而移动，有粘滞性弱结合水弱结合水双电层双电层50双电层决定了土粒表面结合水膜的厚度双电层决定了土粒表面结合水膜的厚度结合水结合水扩散层厚度扩

17、散层厚度增加增加减小减小土的塑性增加降低胀缩性增加降低强度降低增加结合水膜中的扩散层结合水膜中的扩散层（位于弱结合水区域）（位于弱结合水区域）土的性质土的性质有重要影响有重要影响51双电层厚度双电层厚度l 离子浓度增加l Ca2+ VS Na+ l 随离子浓度增加，双电层厚度线性递减随离子浓度增加，双电层厚度线性递减l 应用：为什么用生石灰处理膨胀土？应用：为什么用生石灰处理膨胀土？52土壤水土壤水土中水矿物中的结合水土孔隙中的水土粒表面结合水非结合水强结合水弱结合水液态水气态水(水蒸气)固态水(冰)重力水或自由水毛细水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孔隙水与土颗粒间相互作用而产生的吸力中的各个部分毛细作用吸附作用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 因溶质溶解作用而产生的吸力渗透作用OsmoticOsmotic suctionsuction ( (渗透吸力，化学势）渗透吸力，化学势）78Osmotic suctionOsmotic pressure as a function of dissolved solute concentr

27、ationSoil suction Soil suction （吸力）（吸力）Suction孔隙水与土颗粒间相互作用而产生的吸力中的各个部分因溶质溶解作用而产生的吸力毛细作用吸附作用渗透作用Soil Suction (Soil Suction (吸力吸力,),)土中吸力反映土中水的自由能状态土中吸力反映土中水的自由能状态相对相对于自由水状态来说，土中孔隙水势能的于自由水状态来说，土中孔隙水势能的减少量减少量l毛细吸力，高于自由水面，势能较低毛细吸力，高于自由水面，势能较低l渗透吸力，浓度增大，势能较低渗透吸力，浓度增大，势能较低l重力势重力势/ /压力势压力势/ /水头势水头势水往低处流水往低

28、处流l毛细上升现象毛细上升现象l半透膜现象半透膜现象l河流河流81Soil Suction vs free energy水的摩尔质量水的摩尔质量 = 1*2+16 = 18 g/mol 化学势能反映每单位质量所包含的能量，其单位化学势能反映每单位质量所包含的能量，其单位为为J/mol或或J/kg；82Osmotic suctionvm is the partial molar volume of water (m3 /mol).水的摩尔质量水的摩尔质量 = 1*2+16 = 18 g/mol 化学势能反映每单位质量所包含的能量，其单位化学势能反映每单位质量所包含的能量，其单位为为J/mol或或

29、J/kg；83RH vs free energy化学势能反映每单位质量所包含的能量，其单位化学势能反映每单位质量所包含的能量，其单位为为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势能换算势能换算 土体孔隙水的势能可以利用化学势能、压力势能或水头势能的形式进土体孔隙水的势能可以利用化学势能、压力势能或水头势能的形式进行表征行表征。 化学势化学势能反映每单位质量所包含的能量能

31、反映每单位质量所包含的能量，其，其单位为单位为J/mol或或J/kg； 压力势压力势能反映每单位体积所包含的能量能反映每单位体积所包含的能量，其，其单位为单位为J/m3=N/m2=Pa； 水头水头势能反映每单位重量所包含的能量势能反映每单位重量所包含的能量，其，其单位为单位为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孔隙水势能孔隙水势能capillaryosmoticelectricalvan der Waals随着交界面曲率的增大（意味着含水量降低，负孔隙水压力的数值变得更大），化学势能会显著降低孔隙水势能孔隙水势能随着溶液溶质浓度的增加，渗透压力也逐渐增加，相应随着溶液溶质浓度的增加，渗透压力也逐渐增加，相应的孔隙溶液的化学势能的孔隙溶液的化学势能却却降低降低当土中有化学溶液输运时，土中孔隙水的化学溶度发生当土中有化学溶液输运时，土中孔隙水的化学溶度发生改变，此时渗透吸力对土的性质具有较大的影响。然而改变，此时渗透吸力对土的性质具有较大的影响。然而就其它情况而言可忽略吸力中的渗透就其它情况

33、而言可忽略吸力中的渗透部分部分。孔隙水势能孔隙水势能以上两式表明：以上两式表明：当当水分子水分子相对相对远离远离土土颗粒表面时，电场和颗粒表面时，电场和范德华力引起的化学势能的降低值要远小于水分子靠近土范德华力引起的化学势能的降低值要远小于水分子靠近土颗粒表面是化学势能的降低颗粒表面是化学势能的降低值值。基质吸力的探讨基质吸力的探讨上述每种作用机理均造成了化学势能的下降，这些下降只能的总和就上述每种作用机理均造成了化学势能的下降，这些下降只能的总和就定义为土水系统的总定义为土水系统的总吸力吸力基质吸力基质吸力中的毛细部分和粘吸部分在概念上的区分是明显的，但难以中的毛细部分和粘吸部分在概念上的区

34、分是明显的，但难以通过试验手段加以通过试验手段加以区分区分基质吸力中的各个部分对非饱和土行为影响的机理并不相同。对于低塑性的或较高含水量下的土体，基质吸力中毛细部分占支配地位；然而对于高塑性的粘土或较低含水量下的土体，基质吸力中粘吸部分占支配地位。当基质吸力很大时，只表明液相吸附到固相的程度很大，但绝不能认为是传统意义上的负孔隙压力很大。然而，在以往的研究中，通常忽略基质吸力中粘吸部分的作用，认为基质吸力仅由毛细作用产生，致使基质吸力很大时，认为负孔隙水压力亦很大。目前针对非饱和土所建立的本构模型多是基于毛细机理，因此这些模型对高塑性的粘土或低含水量下的土体的适用性是值得探讨的。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