非饱和土力学讲义(Fredlund在香港科大)chapter2ustmod
非饱和土力学
非饱和土力学1. 简介非饱和土力学是土力学中的一个重要分支，研究非饱和土的力学性质和行为规律。
非饱和土是指含有一定空隙度和部分或全部未饱和的水分的土壤。
相比于饱和土，非饱和土具有一些特殊的力学性质和变形特性，因此对其力学行为的研究具有重要的实际意义。
2. 非饱和土特性非饱和土的特性主要包括以下几个方面：2.1 吸力吸力是非饱和土中水分存在的特殊状态所引起的一种力。
在非饱和土中，由于存在着未饱和水分，土颗粒表面会形成一种吸附力，即吸力。
吸力的大小与土壤的孔隙结构密切相关。
2.2 干湿收缩性非饱和土在干燥过程中会发生干缩现象，而在被湿润后会发生湿润膨胀。
这是因为非饱和土中的水分含量影响着土颗粒之间的接触状态和土壤体的结构。
2.3 孔隙气压非饱和土中的气体存在一定的孔隙气压，该气压与土壤孔隙水的张力有关。
在非饱和土力学中，孔隙气压的变化对土体的力学行为有重要影响。
3. 非饱和土力学实验为了研究非饱和土的力学性质和行为规律，人们进行了大量的实验研究。
常用的非饱和土力学实验包括以下几种：3.1 吸力试验吸力试验是用来测试非饱和土吸力大小的实验。
在吸力试验中，通常采用吸力仪器对土样进行测量，得到吸力与土壤含水量之间的关系。
3.2 干湿循环试验干湿循环试验是用来模拟非饱和土在干燥和湿润过程中的变形行为的实验。
通过反复进行干燥和湿润过程，可以观察并记录土样的收缩和膨胀行为。
3.3 压缩试验压缩试验是用来研究非饱和土的压缩变形特性的实验。
实验中通常使用压缩装置对土样施加压力，并记录土样的变形和力学参数的变化。
4. 非饱和土的工程应用非饱和土力学的研究对于土木工程的设计和施工具有重要的指导意义。
非饱和土的一些特性和行为规律在以下方面有着广泛的应用：4.1 坡面稳定性分析非饱和土在坡面稳定性分析中发挥着重要作用。
由于非饱和土具有较好的抗侵蚀和抗冲刷能力，因此在坡面设计中通常采用非饱和土力学原理。
4.2 基础工程在基础工程中，非饱和土的力学行为对基底承载力和变形进行了特别的研究。
[PPT]非饱和土力学大师Fredlund的演讲英文
![[PPT]非饱和土力学大师Fredlund的演讲英文](https://img.taocdn.com/s3/m/44c1cf8f3968011ca20091ab.png)
SHAPE and LOCATION are the driving force for a paradigm shift
Objectives of this Presentation:
To show the gradual change that is emerging in the way that slope stability analyses can be undertaken
Engineers are often surprised at the results they are able to obtain from Limit Equilibrium methods So Why Change?
There are Fundamental Limitations with Limit Equilibrium Methods of
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QUESTION: How can the Normal Stress at the base of a slice be most accurately computed?
Consider the Free Body Diagrams used to calculate the Normal Stress?
Assumption for all Limit Equilibrium Analysis
Soils behave as Mohr-Coulomb materials (i.e., friction, f', and cohesion, c')
Factor of safety, Fs, for the cohesive component is equal to the factor of safety for the frictional component
非饱和土力学讲义(Fredlund在香港科大)chapter8ustmod
•The mechanical behavior of an unsaturated soil is directly affected by changes in the pore-air and pore-water pressures. Undrained loading of an unsaturated soil generates pore pressures in both the air and water phases.•This chapter presents the pore-pressures generated as a result of the application of total stresses to the soil.•The compressibility of air, water, and air-water mixtures is presented along with the compressibility of the soil structure which is summarized in the form of a constitutive relationship.•The pore pressure response is expressed in terms of pore pressure parameters, which relate the development of pore-pressures to a change in total pressure applied to a soil mass. These parameters perform a useful role in visualizing unsaturated soil behavior.•Estimated pore pressures are required at the start of a transient consolidation type analysis.•Comparisons between the predictions and measurements of pore pressures generated by applied loads are presented and discussed.•This chapter addresses pore pressures generated under various loading conditions.Additional notes:•During undrained compression of an unsaturated soil, volume change occurs as a result of the compression of air and to a lesser extent, compression of the water. Consequently, the pore-air and pore-water pressures increase.•Soil solids can be considered to be incompressible for the stress ranges commonly encountered in engineering practice.•The compressibility of a material at a point can be defined on the volume-pressure curve during compression.•Isothermal compressibility is defined as the volume change of a fixed mass with respect to a pressure change per unit volume at a constant temperature.Additional notes:•Isothermal compressibility of air is defined as the volume change of a fixed mass of air as the pressure is changed.•The volume versus pressure relationship for air during isothermal, undrained compression can be expressed using Boyle’s law, and the final air volume, V a ,is a function of the applied absolute air pressure,•Differentiating the volume of air, V a , with respect to the absolute air pressure, defines an expression for the infinitesimal volume change of air with respect to an infinitesimal change in the absolute air pressure.•Combining this equation with Boyle’s law permits expressing the volume of air derivative with respect to the absolute air pressure.•Air compressibility can then be written as the inverse of the absolute air pressure, since the incremental change in absolute air pressure is equal to the incremental change in the gauge pressure.•The air compressibility decreases as the absolute air pressure increases.Additional notes:a u•Water compressibility can be expressed as the product of the inverse of the water volume and the water volume change with respect to a change in the water pressure.•Water compressibility measurements (Dorsey, 1940) are also a function of temperature.•Dissolved air in water produces an insignificant difference between the compressibility of water.Additional notes:•The air phase, water phase, and solid phase volumetric relations in an unsaturated soil are as shown above.•The volumetric relations are used in the formulation of the compressibility of air-water mixtures found in an unsaturated soil mass.Additional notes:•The compressibility of an air-water mixture can be derived using directproportioning of the air and water compressibilities.•The air, water and solid volumetric relations can be described in terms of the degree of saturation, S , and a porosity, n,for an unsaturated soil.•The total volume of the air-water mixture is the sum of the individual components, V a + V w . The dissolved air, V d , is within the volume of water.•The pore-air and pore-water pressures are u a and u w , with u a > u w . The soil is subjected to a compressive total stress, σ.•Applying an infinitesimal increase in total stress, d σ, to the undrained soil results in increases in both pore-air and pore-water pressures, while the volumes of air and water decreases.•The compressibility of an air-water mixture for an infinitesimal increase in total stress can be written using total stress as a reference.Additional notes:•The compressibility of an air-water mixture presented in the previous slide is slightly different from the compressibility equation proposed by Fredlund (1976) in that the pore-water pressure change, du w , was used as the reference pressure in the 1976 compressibility equation.•The term [d(V w -V d )/d σ] is considered to be equal to dVw since the dissolved air is a fixed volume internal to the water.•The total volume of water, Vw , is therefore used in computing the compressibility ofwater [ i.e., C w = -(1/V w )(dV w /du w )].•The total air volume change can be obtained directly using Boyle’s law byconsidering the initial and final pressures and the volumetric conditions with respect to the air phase.•The free and dissolved air can be considered as one volume with uniform pressure, and although the volume of dissolved air is a fixed quantity, it is carried along in the formulation.•The chain rule of differentiation can be applied to the compressibility equation.Additional notes:•The compressibility of an air-water mixture equation can be rearranged in the form shown in the first equation in order to permit the use of the volume relations, S,and the expressions previously defined for air compressibility,C a ,and water compressibility,C w , to yields the second equation shown above.•The isothermal compressibility of air, C a ,is equal to the inverse of the absolute air pressure, and therefore a third equation can be written.•The ratio between the pore pressure and the total stress change,(du/d σ), is referred to as a pore pressure parameter (Skempton, 1954; and Bishop, 1954).•The pore pressures parameters for air and water are different and depend primarily upon the degree of saturation of the soil.•The pore pressure parameters can also be experimentally measured in laboratory.•For isotropic loading conditions, the parameter is called the B pore pressure parameter.•In the absence of soil solids, the pore pressures parameters, B a and Bw , are equal to 1.0. •In the presence of soil solids, the surface tension effects and the compressibility of air, will cause the B a and B w values to be less than 1.0.Additional notes:•Several equations for the compressibility of an air-water mixture have been proposed by researchers.•The above equation is obtained by ignoring the first term of the previous equation for air-water mixture compressibility (i.e., the water compressibility term) andsetting the Ba and Bwvalues to 1.0.•The result is an equation applicable to the case where the air phase constitutes a significant portion of the fluid, and is similar to the equation proposed by Bishop and Eldin(1950).•Bishop and Eldin(1950) assumed the compressibility of air with reference to the initial volume of air, Vao, as shown in the second equation above.•Such an assumption yields a slightly different equation for the air compressibility,C a , as expressed by the third equation above which gives the average aircompressibility, (uao /ua2) during an air absolute pressure change from uaoto ua.•Replacing the air compressibility term (i.e., 1 / ua ) with the average aircompressibility term [i.e., (uao /ua2)] yields the air-water compressibility equationproposed by Bishop and Eldin(1950), expressed as the fourth equation above.•The last equation was suggested by Koning(1963) by expressing the pore-air and pore-water pressure changes as a function of surface tension. The solubility of air in water and the effect of matric suction were neglected.Additional notes:•Kelvin’s equation [i.e., (u a -u w ) = 2T s /R s ] relates matric suction to surface tension and the radius of curvature.•Attempts have been made to use Kelvin’s equation in writing an equation for the compressibility of air-water mixtures (Schuurrman, 1966; Barends, 1979).•In particular, problems arise in the case of occluded air bubbles in a soil with adegree of saturation greater than 85 %.•Kelvin’s equation results in the incorporation of the radius curvature,R s , as avariable. However, R s ,is not measurable in a soil element.•Kelvin’s equation describes a microscopic phenomenon within the soil element.The radii of the occluded air bubbles should not be incorporated into amacroscopic type formulation for compressibility.•Figure 8.6b shows a soil that is almost saturated and has its macroscopic behavior governed by effective stress. At a microscopic level, there exists numerous inter-granular stresses acting at the contacts between the soil particles in the element.•The net results of attempts to apply Kelvin’s equation, togetherHenry’s laws, to the compressibility of an air-water mixture is that an anomalyarises from a theoretical point of view. Such a formulation predicts that anincrease in matric suction occurs as the total stress is increased under undrainedloading (Fredlund and Rahardjo, 1993).Additional notes:•Experimental results indicate that the pore-air and pore-water pressures gradually increase towards a single value as the matric suction approaches zero and the total stress is increased under undrained loading. The process is gradual and in response to several increments of total stress.•The above figure illustrates the development of air and water pore pressures as well as the changes in both the shape and volume of the air bubbles within an unsaturated soil during undrained loading, as the total stress is increased.•Non-spherical air bubbles in Zone 1 could provide an explanation to justify that the decrease in free air volume is not necessarily accompanied by a decrease in the controlling radius of curvature. The assumption is made that only the controlling minimum radius is of relevance in Kelvin’s equation.•The above figure shows that although the volume of the continuous air phase in Zone 1decreases due to an increase in the pore-air pressure from ua1to ua2,the controlling radiusmay increase from Rs1to Rs2,and therefore the matric suction decreases.•Nevertheless, the increase in total stress will eventually cause the air bubbles to take on a spherical form, as shown in Zone 2.•For spherical air bubbles, a decrease in volume must be followed by a decrease in the radius. In this case, the increase of matric suction postulated by Kelvin’s equation, cannot be resolved.•It would appear that the presence of air bubbles merely renders the pore-fluid compressible. Therefore, it is recommended that the pore-air and pore-water pressures be assumed to be equal in Zone 2.Additional notes:•The pore-pressure response for a change in total stress during undrained compression has been expressed in terms of pore-pressure parameters (i.e., B a and B w ), in previous sections.•In this section , derivations are presented for pore-pressure parameters corresponding to various loading conditions.•The pore pressure parameters for the air and water phases of an unsaturated soil can be defined either as tangent-type or secant-type parameters.•These definitions are similar in concept to the tangent and secant moduli used in the theory of elasticity.•Isotropic loading is a particular case of the more general triaxial loading and is used to express the definition of the secant pore pressure parameter for the air phase.•The secant-type pore-air pressure parameter (i.e., B a ’) is defined as the ratio between the increase in pore-air pressure (i.e., response) and the increase in isotropic pressure (i.e., σ3) from the initial condition.Additional notes:•The secant-type pore-water pressure parameter (i.e., B w ’) is defined as the ratio of the increase in pore-water pressure (i.e., response) to the increase in isotropic pressure (i.e., σ3) from the initial condition.•The secant-type parameter requires the definition of initial conditions for the soil specimen in terms of both pore-pressures and applied total stress.Additional notes:•If an infinitesimal increase in the isotropic confining pressure is considered at a point along the pore-air pressure versus isotropic confining stress, σ3, relationship,the pore-air pressure response at that point can be expressed as the tangent, B a ,pore-air pressure parameter.•Similarly, a tangent pore-water pressure parameter, B w , can be defined.•The concepts of secant and tangent-type pore-air and pore-water pressure parameters are illustrated on the next slide.Additional notes:•A linear equation for total volume changes within a localized region of the constitutive surface can be written as proposed by Fredlund and Morgenstern (1976).•The compressibility parameters, m 1s and m 2s ,correspond to changes in the stress state variables, (σ-u a ) and (u a -u w ), respectively.•Total volume changes can then be predicted by using the constitutive surfaces when changes in the stress state variables are known.Additional notes:•The linear equation for pore-air volume changes can be written as proposed by Fredlund and Morgenstern (1976).•The compressibility parameters, m 1a and m 2a ,correspond to changes in the stress state variables, (σ-u a ) and (u a -u w ), respectively.•Air volume changes can be predicted using the constitutive surfaces when changes in the stress state variables are known.Additional notes:•A linear equation for pore-water volume changes can be written as proposed by Fredlund and Morgenstern (1976).•The compressibility parameters, m 1w and m 2w , correspond to changes in the stress state variables (σ-u a ) and (u a -u w ), respectively.•Water volume changes can be predicted by using the constitutive surfaces when changes in the stress state variables are known.•The continuity requirement for a referential element of an unsaturated soil can be expressed by equating total volume change to the summation of the air volume and water volume changes.•This requirement leads to the conclusion that there are two closed-formrelationships between the compressibility.Additional notes:•The application of an all-around, positive (i.e., compressive) total stress, d σ, either in drained or undrained loading, can cause a change in volume.•In drained loading, air and water are allowed to drain from the soil subsequent to the application of a total stress increment. The stress state variables in the soil are altered and the volume of the soil changes.•The volume change can be computed from the stress state variable changes in accordance with the constitutive relationship for the soil structure.•In undrained loading, the air and water are not allowed to drain from the soil. The total stress increase causes the pore-air and pore-water pressures to increase, and consequently the stress state variables also change.•The increase in the pore fluid pressures occurs in response to a compression of the pore fluid.•The volume change equivalent to the pore fluid compression, dVv , can becomputed by multiplying the compressibility of air-water mixture, C aw , by thepore fluid volume V v (i.e., V w + V a = nV ) and the total stress increment, d σ.•The volume change can also be expressed in terms of the stress state variable [i.e., (σ-u a ) and (ua -u w )] changes in accordance with the constitutive relationships for the soil structure. The equation at the bottom of the slide is the volume change due to an increase in net total stress, d(σ-u a ).Additional notes:•An increase in the total stress results in an increase in pore fluid pressures (i.e., air and water) in response to compression of the pore fluids. Therefore,there is a reduction in matric suction since the increase in pore-water pressure is greater than the increase in pore-air pressure.•The volume change due to a decrease in matric suction can be expressed by the above equation.•The total volume change can then be written as the summation of the two previous volume changes due to the changes in the stress state variables (i.e., (dVv /V o )1and (dV v /V o )2].•The last equation expresses the volume change obtained from the constitutiverelationships and can be equated to the volume change due to pore fluid compression.•The concepts involving drained and undrained volume changes are illustrated on the next slide.Additional notes:•The increase in total stress results in an increase in net normal stress and a decrease in matric suction. The stress state variable changes can be used to define the volumetric changes in the unsaturated soil mass by using the constitutive relationships.•The above figure shows the comparison between undrained loading and drained loading by using the constitutive surfaces combined with changes in stress state variables due to an increase in total stress under undrained compression.Additional notes:•In a saturated soil, the pore voids are filled with water. The pore fluidcompressibility is equal to the compressibility of water.•At saturated conditions, a total stress increase, d σ, in undrained loading is almost entirely transferred to the water phase (i.e., du w ≈d σ) and the pore-water pressure parameter approaches 1.0.•The effective stress in undrained loading remains essentially constant, and as a consequence, the volume change computed from the constitutive relationship for the soil structure is extremely small as shown in Figure 8.11a.•The soil volume change obtained from the pore fluid compression is also small because of the low compressibility of water.•In a dry soil, the pore voids are primarily filled with air which is much more compressible than the soil structure.•A total stress change during undrained loading is almost entirely transferred to the soil structure.•Figure 8.11b above illustrates a dry soil under undrained loading which also illustrates that the pore-air pressure remains constant (i.e., the B parameter is essentially zero).Additional notes:•The K o loading conditions are illustrated in the above figure where the total stress increment is applied in the vertical direction.•The total stress increment is denoted as, d σ, and the vertical direction is assumed to be the major principal stress direction.Additional notes:•The volume change equation previously presented, associated the soil volume change of the soil structure to the volume change due to the pore fluid compression (i.e., under undrained loading).•Using K o loading conditions, the pore pressure parameter equation can be expressed by the above equation where the compressibility parameters correspond to K o loading.•The last two equations extend the compressibility of the air-water mixture,C aw , by substituting the change in total stress with the soil response in terms of pore pressures. •The first term of the compressibility equation (i.e., C aw equation) refers to thecompression of the pore-water phase and the second term refers to the compression of the pore-air phase.Additional notes:•The previous volume change equation can be rearranged to yield an expression for the change in the pore-water pressure, du w , in response to a total stress change, d σ.•In the last equation, the compressibility, m 2s ,has been written as a ratio of the compressibility with respect to a total stress change, m 1k s ,which gives rise to the parameter, R sk .Additional notes:•The previous equation can be simplified by introducing the compressibility parameters, R 1k and R 2k•There are two unknowns, du w and d σy , and therefore a second independent equation is required.•The second equation is derived by considering the change in the volume of air. •The change in volume is described by the constitutive relationship for the air phase which is equated to the volume change of air due to the compressibility of the air term multiplied by pore fluid volume (i.e., nV).•In this equation, the compressibility parameter, m 1k a ,is introduced.•In a similar procedure to that used for the soil structure, the last equation introduces the parameter R ak , that is defined as the ratio between the air phase compressibility, m2a ,and the air phase compressibility with respect to a total stress change, m 1k a .Additional notes:•The previous equation can be rewritten to give the change in pore-air pressure, du a , due to a total stress increment, d σy .•The expression can be simplified by introducing the ratio parameters, R 3k , and R 4k , as illustrated above.Additional notes:•The pore-air and pore-water parameters for Ko undrained loading can be written as B ak and B w k parameters, respectively. These pore-pressure parameters are defined as tangent-type parameters referenced to a particular stress point.•The expressions for du a and du w are from the previous equations where the pore-air and pore-water responses, at any stress point during Ko undrained loading, are a directfunction of the B ak and B w k pore pressure parameters.Additional notes:•Hilf (1948) outlined a procedure to compute the change in pore pressure in compacted earth fills as a result of an applied total stress. This method has been extensively used by the United States Bureau of Reclamation (i.e., U.S.B.R.), and has proven to be to be quite satisfactory in engineering practice (Gibbs et al, 1960).•The derivation is based on the results of a one-dimensional oedometer test on acompacted soil, Boyle’s law, and Henry’s law. A relationship between total stress and pore-water pressure is derived.•Hilf (1948) stated: “... consider a sample of moist earth compacted in a laboratory cylinder, as illustrated before. If a static load is applied by means of a tight-fitting piston , permitting neither air nor water to escape, it is found that there is a measurable reduction in volume of the soil mass”.•The reduction in volume was assumed to be the result of compression of free air and free air dissolving into water. Free and dissolved air are considered as a single phase.•The initial and final conditions considered in Hilf’s analysis are shown in the next slide. The total volume of air associated with the initial condition, Vao , can be writtenas shown above, with the first and second terms representing thefree and dissolved air volumes.•The air volume change can be written as a change in porosity, ∆n , times the initial volume of soil, V o ,. Therefore, the total volume of air under final conditions, V af , can be expressed by the above equation. •The final absolute air pressure is shown in the last equation.Additional notes:•Boyle’s law can be applied to the initial and final conditions of the free and dissolved air.•By substituting the initial and final air volumes into the above equation, andrearranging, it yields an expression for the change in the pore-air pressure as a function of the initial pore-air pressure.•The above equation for the change in absolute pore-air pressure is commonly referred to as Hilf’s equation, which provides a relationship between the change in pore-air pressure and the change in pore-air volume (i.e., ∆n ).•In order to reach saturation, the soil volume change, ∆Vv , must equal the volume offree air (i.e., (1-S o ) n o V o ). The change in porosity corresponding to this condition is expressed above (i.e., ∆n ).•Substituting the equation for a change in porosity, ∆n,into the equation for thechange in pore-air pressure, gives the absolute pore-air pressure change (i.e., increase) required to saturate a soil.Additional notes:•The previous equation for pore-air pressure change can be written in an alternate way form by replacing the change in porosity, ∆n,with (∆V v /V o ), which expresses the volume change due to the compression of air.•Assuming that the change in matric suction is negligible, the total volume change can also be obtained from the constitutive surfaces relationship [i.e., as a function of ∆(σv -u a )].•Near saturation, the soil compressibility parameter, m 1s ,can be assumed to be equal to the coefficient, m v ,measured under saturated conditions.Additional notes:•The pore-pressure parameter for K o undrained loading can be derived using Hilf’s analysis by equating the volume change of the soil structure to the volume change due to the compression of air.•The second equation in this slide shows the expression for the change in pore-air pressure, which is obtained by rearranging the first equation shown.•The secant pore pressure parameter, B áh , derived from Hilf’s analysis is thenexpressed as the third equation on the above slide.Additional notes:•For an isotropic soil under three-dimensional loading, the constitutive relationship for the soil structure is expressed by the above equation.•In the case of isotropic loading, the total stress increments are equal in all directions.Therefore, the constitutive relationship for an isotropic soil under isotropic loading can be written as the second equation.•The compressibility of the air-water mixture, C aw , is obtained from the previously shown equations by using the isotropic pressure increment, d σ3, for the total stress increment, d σ.•Volume change due to the pore fluid compression, dVv , is computed from thecompressibility, C aw equation multiplied by the pore fluid volume, V v (i.e., nV ), and the isotropic pressure increment, d σ3.Additional notes:•The change in volume of the soil structure must be equal to the change in volume due to pore fluid compression, as expressed by the first equation on this slide.•That equation can be rearranged to express the change in pore-water pressure, du w , as a function of the change in pore-air pressure and the change in total confining stress.•Another equation can be derived by considering the continuity of the air phase. The constitutive relationship for the air phase of an isotropic soil under three-dimensional loading can be written as the third equation above.•For isotropic loading, the constitutive relationship for the air phase of an isotropic soil is obtained by substituting the condition of ( d σ1 = d σ2 = d σ3). The result is the fourth equation.•Volume change due to the compression of air, dV a , is also represented by the fifth equation which is the second term of the pore fluid compression equation , dV v .•The last equation is obtained by equating the volume change due to thecompression of air to the volume change predicted by the constitutive relationship.Additional notes:•Solving the previous equation for the change in pore-air pressure, du a , results the first equation given above.•The compressibility of the soil structure, m 2s ,can be expressed as a ratio of m 1s , as shown by the R s parameter.•The expression for the pore-water pressure change can then be written as shown by the third equation, and simplified, by using the R 1and R 2parameters.Additional notes:•Solving the previous equation for the change in pore-air pressure, du a , results in the first equation given above.•In a similar manner, the compressibility, m 2a , can be related to the m1acompressibility coefficient by the ratio R a,as shown in the first equation.•The expression for the pore-air pressure change can then be written in the form presented in the second equation, and simplified by using the R 3and R 4parameters to give the form presented in the third equation on the slide.•Therefore, the pore pressure parameters B a (i.e., du a /ds 3) and B w (i.e., du a /ds 3) can be expressed as shown above.Additional notes:。
非饱和土的力学理论
文章编号:1000-582x(2000)S0-0197-04非饱和土的力学理论Ξ陈正汉,王权民,李 刚,孙树国(后勤工程学院土木工程系,重庆 400041) 摘 要:介绍了笔者多年来在非饱和土力学领域研究的主要理论成果。
内容包括非饱和土的建模理论、应力理论、渗流理论、本构理论和固结理论,其中本构理论和固结理论都涉及线性、非线性、弹塑性、结构性、动力特性和热力特性等6个方面。
关键词:非饱和土;力学理论;渗流理论;本构模型;固结模型 中图分类号:TU43;O357.3 文献标识码:A 非饱和土的力学理论包括渗流理论、本构理论、强度理论和固结理论,其中非饱和土的固结涉及水气渗流和土骨架的变形两个方面,是一个综合问题。
非饱和土中渗流包括水流和气流,变形有线性、非线性、弹塑性、结构性、动力特性和热力特性之分,从而组成了非饱和土的本构模型谱系和固结模型谱系。
通过笔者的多年努力,这两个谱系已基本形成,笔者简要介绍有关研究成果。
1 非饱和土建模的公理化理论体系渗流理论、本构模型和固结模型都是数学模型,建模需要理论指南。
1994年,笔者融理性力学、不可逆过程热力学和土力学的精华于一体,建立了岩土力学的公理化理论体系[1]。
该理论体系包括5个基本定律和8个本构原理,对饱和土与非饱和土都适用。
5个基本定律是:质量守恒定律、动量守恒定律、动量矩守恒定律、能量守恒定律和热力学第二定律。
8个本构原理是:等存性原理、相容性原理、客观性原理、Curie对称原理、Onsager原理、压硬剪胀原理、有效应力原理和记忆原理。
2 非饱和土的应力理论[2,3]非饱和土是固-液-气三相复合介质,描述应力状态一般需要三个应力张量。
在不计土粒的压缩性时,则可用两个应力状态变量σij-u aδij和(u a-u w)δij描述,分别称为净总应力张量和吸力张量;也可用下式表达的有效应力刻划之:σ′ij=σij-u aδij+χ(u a-u w)δij称为Bishop公式,其中σij、σ′ij、u a、u w分别是总应力、有效应力、孔隙气压力和孔隙水压力,χ是有效应力参数,与土的饱和度及应力路径有关,且0≤χ≤1。
非饱和土力学
非饱和土力学
非饱和土力学是研究非饱和土的力学性质和行为的学科。
非饱和土是指土壤中含有水分但不是完全饱和状态的土壤。
在非饱和状态下，土壤的力学性质和行为与饱和状态下有很大的不同。
非饱和土力学主要研究以下几个方面：1.非饱和土的吸力特性：非饱和土中的水分存在于土颗粒之间的微小孔隙中，这些孔隙中的水分会受到吸力的作用。
吸力是非饱和土力学中的一个重要参数，它对土壤的力学性质和行为有很大的影响。
2.非饱和土的渗透特性：非饱和土的渗透特性与饱和状态下有很大的不同。
在非饱和状态下，土壤中的水分会受到吸力的作用，因此渗透速度会比饱和状态下慢很多。
3.非饱和土的力学性质：非饱和土的力学性质与饱和状态下也有很大的不同。
在非饱和状态下，土壤中的水分会受到吸力的作用，因此土壤的强度和变形特性会受到吸力的影响。
4.非饱和土的稳定性：非饱和土的稳定性也是非饱和土力学研究的一个重要方面。
在非饱和状态下，土壤中的水分会受到吸力的作用，因此土壤的稳定性会受到吸力的影响。
总之，非饱和土力学是一个非常重要的学科，它对于土壤工程和地下水工程的设计和施工都有着重要的意义。
非饱和土力学
非饱和土力学引言非饱和土力学是土力学的一个分支，研究非饱和土壤的力学性质和行为。
饱和土壤是指土壤中的孔隙完全充满水分，而非饱和土壤是指土壤中的孔隙中同时存在气体和水分。
非饱和土力学的研究对于土壤工程、农业、环境科学等领域具有重要的意义。
本文将介绍非饱和土力学的几个重要概念和应用。
概念非饱和土壤的吸力非饱和土壤中存在着气体和水分。
由于毛细现象的存在，非饱和土壤中的水分会受到一定的吸力作用。
吸力是指土壤颗粒表面附近的环境中存在的气体与土壤孔隙中的水分之间的一种力。
吸力是非饱和土力学研究的基础，它与土壤的水分含量、孔隙结构等因素密切相关。
孔隙水压力非饱和土壤中的水分受到吸力作用，会产生一定的压力，称为孔隙水压力。
孔隙水压力是非饱和土力学中的一个重要概念，它描述了土壤中水分的分布和移动情况。
孔隙水压力的变化会影响非饱和土壤的力学性质和行为。
非饱和土壤的力学性质非饱和土力学研究的一个重要目标是揭示非饱和土壤的力学性质。
非饱和土壤的力学性质与饱和土壤有一些明显的差异。
例如，非饱和土壤的抗剪强度和变形特性会受到吸力和孔隙水压力的影响。
非饱和土壤的力学性质的研究对于土壤工程的设计和施工具有重要的指导意义。
应用土壤含水量测定非饱和土力学的研究需要准确测定土壤中的水分含量。
常用的方法有重量法、电容法、压力传感器法等。
这些方法可以测定不同吸力下土壤中的水分含量，从而揭示土壤的吸力特性和水分传输规律。
非饱和土壤的稳定性分析非饱和土壤的力学性质和行为与饱和土壤存在一定的差异。
因此，非饱和土壤的稳定性分析需要考虑吸力和孔隙水压力等因素对土壤的影响。
非饱和土壤的稳定性分析可以用于土壤边坡、挡土墙、基础等工程的设计和施工。
土壤水分调控非饱和土力学的研究成果可以应用于农业、环境科学等领域。
例如，在农业生产中，了解土壤中的水分分布和移动规律，可以合理调控土壤水分，提高植物的生长和产量。
此外，在环境科学研究中，非饱和土力学的研究成果可以用于土壤污染防治和土壤水源涵养等方面。
5非饱和土强度 高等土力学课件
soil 10,2.35,-5,rain 36mm/h
/kPa
10
20
30
40
1h
0h
4h 6h 12h
b
Eq.(8)
-10 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
-10
soil 20,2.35,-5 rain 36mm/h
/kPa
0
10
20
30
40
1h 2h
0h
3h 5h 4h
29
3. 应力状态变量
(
x
ua
)
xy
xz
yx ( y ua )
yz
zx
zy
(
y
ua
)
(ua uw ) 0
0
(ua uw )
0
0
0
0
(ua uw ) 30
零位试验
31
Bishop和Donald (1961)
3 ua 13.8kPa
ua uw 58.6kPa
2c
K0
N
v
ua
N
2(ua
v
uw ) tan b
ua
N
（3）被动土压力
44
45
（4）自立高度
46
47
5.2 承载力
48
q us tan b
qu0
cu0
49
5.3 土坡稳定
50
X f (x)E
51
f (x) K exp[(Cnn ) / 2]
52
53
54
5.4 降雨入渗影响
9
1.1 总吸力测量
（1）Peltier型湿度计
非饱和土土力学(新)
温度
3 ua 200kPa
u a u w 100 kPa
15℃ 30℃ 45℃ 60℃
温度的影响
非饱和土土力学理论
4、非饱和土的应力应变关系及本构模型
（1）弹性模型
Fredlund和Morganstern(1976)、Fredlund(1979)提出了基于双应力变量 ( u a ) 和 (ua u w ) 的弹性应力应变关系：
强度分析：
固结变形分析：
传统（经典）土力学的局限
3、现有土工试验仪器主要是针对饱和土设计的
① 试验数据按饱和土相关理论来整理，不符合实际情况 。 ② 不能测负孔隙水压力。 ③ 未考虑气相影响。
单轴压缩
三轴压缩
非饱和土土力学理论
非饱和土物质组成：固体、气体和液体
固体
液体
气体
n
Vpores Vtotal
固结本构方程
Mechanical constitutive law
q w k grad( pw w z)
d v m dp
1 dp K
pw 1 p k 2 pw wm t 3 t
3-D consolidation
传统（经典）土力学的局限
2、固结变形和强度分析中有效应力的表现形式是不一致的
Vliquid Vgas Vtotal
Sl
Vliquid Vpores
Vliquid Vliquid Vgas
饱和度
1 Sg
空隙度
非饱和土土力学理论
非饱和土为固、液、气相及收缩膜组成的四相介质
非饱和土土力学理论
存在一个新的应力状态变量：吸力
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Soil Mechanics for Unsaturated Soils Professor Delwyn G. Fredlund•The study of a multi-phase system such as an unsaturated soil, requires an understanding of the properties of each component phase.rties of each phase of an unsaturated soil; ii.) an understanding of the interaction between air and water; iii.) establishment of useful volume-mass relations for solving engineering problems.Additional notes:Soil particles &contractile skinbehave as solidsAir & waterbehave as fluids•An unsaturated soil is commonly referred to as a 3-phase system composed of: i.) solids (soil particles); ii.) water; iii.) iii.) air.•The air-water interface (i.e., the contractile skin) warrants inclusion as an additional phase due to its unique and specific properties.•The contractile skin interacts with the soil particles in an independent manner and can significantly change the mechanical behavior of an unsaturated soil.fore can be neglected in volume-mass relationships.•The air phase might be present in an unsaturated soil either in a continuous or an occluded (bubbles) form.Additional notes:Required tounderstandthe stress stateanalysisSufficient forMapping phasechanges•Gravimetric and volumetric relationships for unsaturated soil are based on various mass and volume ratios of the component phases.•A rigorous microscopic analysis of the volume-mass properties of an unsaturated soil mass requires the inclusion of the contractile skin.•Using a macroscopic (phenomenological) approach, an unsaturated soil can be considered as a three-phase continuum system.•The most important property of the contractile skin is its ability to exert a tensile pull which is a consequence of the surface tension generated between the two pore-fluid phases (i.e., air and water).Additional notes:•Air is a mixture of several gases and varying amounts of water vapor. water vapor is present.•Air is compressible and its density requires additional considerations in terms of pressure and temperature.Additional notes:Air is a mixture of several gases that act in an independent manner•Air is considered to behave as an “ideal gas” under pressures and temperatures commonly encountered in geotechnical engineering. •The molecular mass of air , ωa , depends on the mixture of dry air and water vapor.lar mass ofwater vapor is 18.016 kg/kmol.from0.000002% to 5% (Harrison, 1965). Additional notes :Density is equal to mass per unit volume Density of air is directlyproportional to the absolute air pressure•Amounts of Nitrogen (N 2) and Oxygen (O 2) are essentially constant.•Carbon dioxide (CO 2) content in air may vary depending on the rate of consumption of fossil fuels. Additional notes:•Water is essentially a homogeneous substance the world over, except for variations due to salts and isotopes of hydrogen and oxygen (Dorsey, 1940).•Distilled water under the pressure of its saturated vapor is called pure, saturated water.•The density of water must be measured experimentally.•Variations in the density of water due to temperature differences are more significant than variations due to applied pressure.Additional notes:SURFACE TENSION •A molecule in the interior of the water experiences equal forces in all directions whilea water molecule in the contractile skin experiences an unbalanced force towards the interior of the water.actile skin.alled its surface tension,T s (i.e., units of N/m 2).•Contractile skin behaves like an elastic membrane.-water surface can be related to surface tensionand the radius of curvature by considering equilibrium.Additional notes:Surface Tension Phenomena•Surface tension is measured as the tensile force per unit length along the contractile skin (i.e., units of N/m).•Surface tension is tangential to the contractile skin surface. Its magnitude decreases as temperatures decreases.u a , that is greater than thewater pressure, u w .•The pressure difference, (u a -u w ) is referred to as matric suction.Additional notes:•Contractile skin forms a warped or saddle-shaped surface (i.e., 3-D membrane) that has different curvatures along two orthogonal (i.e., R 1and R 2for example).o C.-water interface.Additional notes:State Diagram for Water(from van Haveren and Brown, 1972) •Water phase can exist in one of three states: i.) solid state as ice; ii.) liquid state aswater; iii.) gaseous state as water vapor.•The vaporization curve is also called the vapor pressure curve of water.•The fusion curve separates the solid and liquid states.•The sublimation curve separates the solid and vapor states.•Triple point of water is achieved at a temperature of 0o C and a pressure of 0.61 kPa.Additional notes:•The vaporization curve represents an equilibrium condition between the liquid and vapor states of water.•At equilibrium, evaporation and condensation processes occur simultaneously at the same rate.•Rate of condensation depends on the water vapor pressure it reaches at itssaturation value on the vaporization value.•Evaporation rate depends only on temperature.•Water vapor is mixed with air in the atmosphere, and has no effect on thebehavior of the water vapor.•Water vapor may not be in equilibrium with adjacent water. Water vapor in air can be under-saturated, saturated or super-saturated depending on the partialpressure of water vapor.•The degree of saturation with respect to water vapor is referred to as relative humidity, RH.Additional notes:•Water molecules form a lattice structure with openings referred to as a “cage” that can be occupied by gas.•Air dissolves water and fills the “cages” which comprise approximately 2% by total volume.Additional notes:•The volumetric coefficient of solubility, h,varies slightly with temperature.•The rate at which mass is transferred across a unit area is equal to the product of the coefficient of diffusion, D,and the concentration gradient.•In the diffusion of air through water, the concentration difference is equal to the difference in density between the free air and the dissolved air in the water.•The pressure difference between the free air and the air dissolved in the water becomes the driving potential for the free air to diffuse into the water.•The coefficient of diffusion for air through the pore-water in a soil appears to differ by several orders of magnitude from that for air through free water.Additional notes:•Volume of air dissolved in water is essentially independent of air or water pressures.•Absolute pressure of the dissolved air is equal to the absolute pressure of the free air under equilibrium conditions.•Volume of air dissolved in water is constant for different pressures.•Ratio between the mass of each gas that can be dissolved in a liquid and the mass of the liquid is called the Coefficient of Solubility , H.•Coefficients of Solubility are referenced to a standard pressure of 101.3 kPa.•Ratio of the volume of dissolved gas, V d ,in a liquid to the volume of the liquid is the Volumetric Coefficient of Solubility , h.Additional notes :•A cylinder with a piston and porous stone analogy is useful in visualizing and analyzing the behavior of air-water mixtures.•The “porous stone” has pores equaling 2% of its volume. The “porto simulate the behavior of water.•An initial pressure is applied equally to the free air and the “•An imaginary valve is placed at the boundary between the free air and the “porous stone”.•When the piston is loaded, it compresses the free air above theporous stone inaccordance with Henry’s law.•Henry’s law states that the mass of gas dissolved in a fixed quantity of liquid, at constant temperature, is directly proportional to the absolute pressure of the gas above the solution (Sisler et al., 1953).•After several increases of the applied loading, all free air will have moved into the “porous stone”, and any additional applied load will be carriedAdditional notes:•The water lattice is relatively rigid and stable (Dorsey, 1940) and the density of water changes little as a consequence of the presence of the dissolved air.•Dissolved air has no measurable effect to the density of water at a temperature of about 22o C.Additional notes:•An unsaturated soil has air and water pressures at different magnitudes.•The mass of air going into or coming out of the water is time dependent.•The amount of gas dissolved in water is referred to as its Solubility .•The rate of solution of a gas is referred to as its Diffusivity .Additional notes:•The volume-mass relations of the soil particles, water, and air phases are useful properties in engineering practice, particularly for an unsaturated soil.•Both mechanical and hydraulic behaviors of an unsaturated soil mass are highly dependent on the relative proportion of the three component phases (i.e., solid, water and air).•Soil properties such as degree of saturation, porosity and void ratio express volumetric proportions involving the three phases of an unsaturated soil mass.•The above volumetric properties associated with the density of each phase allows the definition of all the index properties commonly utilized in engineering practice to characterize the state of a soil mass.Additional notes:•Each phase of an unsaturated can be expresses as a percentage of the totalvolume by using the definition of porosity.•The volume of the contractile skin can be assumed to be negligible.•The porosity with respect to the water phase, n w ,is equivalent to the volumetric water content, θw .•A soil mass might change its total volume in response to changes in the stress state applied. However, the volume of solid particles is constant.•Void ratio of a soil mass expresses the ratio of the void volume to the volume of the solid particles.Additional notes:•The degree of saturation expresses the percentage of void space filled by the liquid phase (i.e., water).dry (i.e., S = 0%),saturated (i.e., S = 100%) or unsaturated ( 0% < S < 100%).•The transition zone between a continuous air phase and occluded air bubbles occurs when the degree of saturation is between approximately 80-90%.•The water content can also be measured either in a gravimetric manner (i.e., ratio of water to solids mass) or in a volumetric manner (i.e., ratio of water volume to total volume).Additional notes:•Two commonly used soil density definitions are the total density and the dry density. Total density is called the bulk density.•Dry density of a soil mass is dependent upon the mineralogy of the solidphase, in terms of specific gravity,G s , and the porosity of the soil structure.•The saturated density of the soil is the total density of the soil for the casewhere the voids are filled with water (i.e., S = 100%).•The buoyant density of a soil is the difference between the saturated density of the soil and the density of water.•A “basic volume-mass relationship” for a soil mass can be derived by using the idealized diagram where each soil phase is defined by its volume and its mass.Additional notes:•Volume-mass relationships in engineering practice neglect the mass of airphase, but consider the volume of the air phase.•The expression (Se = wG s )is the basic volume-mass relationshipcommonly used in engineering practice and it represents the continuityequation for a soil mass.•Additional notes:•Density, ρis the ratio of mass to volume. Each soil phase has its own density.•Specific gravity of the soil particles, Gs ,is defined as the dimensionless ratio between thedensity of the soil particles and the density of water at a temperature of 4o C underatmospheric pressure conditions (i..e, 101.3 kPa).•Density of water at 4o C and at 101.3 kPa is 1000 kg/m 3.•Specific volume, v o ,is the inverse of density (i.e., ratio of volume to mass).•Unit weight, γis the product of density, ρ, and gravitational acceleration, g,(i.e., 9.81 m/s 2).Additional notes:•In engineering practice, the total density is often increased by imposing a reduction in the void volume of a soil mass.•Volume of pore-water in a soil mass is highly dependent uponenvironmental conditions and therefore is often a variable to be considered.•The dry density is independent of the volume of the pore-water and is often used in semi-empirical relationships for the soil.Additional notes:•The dry density curve corresponding to a degree of saturation of 100 % is called the “zero air voids”, ZAV, curve.•The dry density curves curves for different degrees of saturation should be presented in connection with soil compaction data.•Compaction is a mechanical process used to increase the dry density of soils (i.e., densification).Additional notes:-Start of process:•The basic volume-mass relationship (i.e., Se = w Gs ) applies to anycombination of S, e and w , and therefore it can be used to obtain changes in any of these properties when the other two properties are defined.•The basic volume-mass relationship can therefore be used to deriveequations associating changes of S, e and w .Additional notes:•Soil mixtures can occur in various forms in nature.•Mixture of soil particles and air constitutes a dry soil while a mixture of soil particles and water constitutes a saturated soil.•Unsaturated soils lie between dry and saturated soil conditions and constitute a mixture of soil particles, air and water in differing percentages.•The density of a soil mixture can also be formulated for situations where there is a change in the volume of air due to compression under undrained conditions. •The analogy of the piston-porous stone is a useful tool to derive the formulation of the density of the soil by considering the air compression.•In the above formulation, Boyle’s law is applied to the free and dissolved air under isothermal conditions.Additional notes:•Under isothermal conditions, the ratio of the density to the absolute pressure of the air phase (i.e., free and dissolved air) in a soil mixture is constant.•The final density of water is computed as the ratio of the total mass of water and dissolved air to the total volume of water and dissolved air under final equilibrium conditions.Additional notes:•The conservation of mass is herein applied to a system (i.e., soil mixture) under isothermal conditions, therefore, all the previous equations can be applied. •The total density of the soil mixture is therefore a function of the constant densities and volumes of water and solid phases as well as of the variable density and volume of the air phase.•The total density formulation can be applied to the definition of particular cases where one of the three phases (i.e., solid, water and air) in a soil mixture is not present.Additional notes:•The first equation above is a general mixture equation for density after the soil has been subjected to a change in air pressure.•The volume of dissolved air , V d ,is related to the volume of water, Vw ,by thevolumetric coefficient of solubility, h (i.e., V d = hV w ).•The equation incorporates the effect of air going into solution due to the change in the air pressure.•Where air does not have time to dissolve in water, the volumetric coefficient of solubility, h,might be set to zero.•The air-water mixture always has a density between that of air and water.•The density of an air-water mixture can be obtained from the general equation is obtained by setting the volume of the soil particles, Vs ,to zero, and the initial voidratio, e i ,becomes infinity.Additional notes:。