非饱和土的吸力与强度理论研究及其试验验证
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摘要
作为土力学基本框架的重要组成部分,饱和土的强度理论已经基本趋于成熟,而非饱和土在实际工程中分布更为广泛,其工程特性更为复杂,其强度理论尚不十分完善。在非饱和土力学中,应力理论和强度理论是非饱和土力学变形与稳定性分析理论及计算方法中的重要基础。因此,对于不同程度的非饱和土,必须建立合理的应力理论和强度理论。考虑到非饱和土的三相组成与各相组分的特点及其与饱和土的差异,在非饱和土中除了作用在土骨架上的净应力之外,分别作用在孔隙气与孔隙水上的孔隙气压力与孔隙水压力之差构成了非饱和土的基质吸力,对于非饱和土的变形与强度特性具有一定的影响。同时饱和度的高低或含水量的多少决定了非饱和土的孔隙水与孔隙气的分布形态及其相互迁移与渗透规律,从而直接或间接地影响着非饱和土的强度特性及其渗透特性。为了确定非饱和土的变形与强度特性,必须首先根据含水量或饱和度确定非饱和土的分类体系,进而针对不同形态的非饱和土确定净应力与基质吸力。因此为了探讨非饱和土的强度理论,必须确定非饱和土中的应力体系,其中关键在于确定吸力。为此,本文基于理论分析,对于非饱和的理想颗粒组成体系建立了吸力理论与强度理论,并试图利用这些理论阐明实际非饱和土的强度特性,进而采用非饱和土的试验研究对所提出的基本概念与理论体系进行验证,为非饱和土的工程特性及其本构模型研究奠定基础。本文研究工作主要包括下列内容。
1.在水封闭情况下,基于圆形弯液面假设、接触角协调性要求和热力学基本理论,针对规则等直径球形颗粒建立了颗粒间弯液面方程,运用迭代法对这一非线性方程组进行了求解,进而确定了理论意义上的基质吸力。基质吸力实际上是一个分布面力,其总体作用效应同时包括面力的大小及其作用面积两个因素。将作用于颗粒局部表面积上的基质吸力在整个颗粒表面上进行平均后作为等效基质吸力。进一步地,类似于描述吸力与饱和度之间关系的土—水特征曲线,将等效基质吸力与饱和度之间的关系曲线定义为广义土—水特征曲线。基于最松散堆积状态的理想模型分析表明,与基质吸力相比,由于考虑了面积效应,等效基质吸力较小,且随饱和度的变化并不象基质吸力那样十分显著;无论基质吸力还是等效基质吸力,均随颗粒空间排列间隙的增大而迅速减小:另外,土—水特征曲线和广义土—水特征曲线都依赖于孔隙水与固体颗粒之间接触角的变化。
2.目前,普遍接受的非饱和土分类方法把非饱和土分为水封闭、双开敞和气封闭等三类。液体表面存在表面张力作用,液面在颗粒表面的搭接使得表面张力对颗粒产生拉结作用。这种拉结作用类似于基质吸力的作用,但与基质吸力是两个完全不同的概念,其在基质吸力作用面积上的等效作用定义为张力吸力。孔隙水弯液面与土颗粒表面是否搭接决定了这种张力吸力存在与否。因此根据孔隙水弯液面与土颗粒表面的搭接状态,将双开敞非饱和土细分为搭接双开敞非饱和土和不搭接双开敞非饱和土。在水封闭非饱和土和搭接双开敞非饱和土中,由于孔隙水弯液面搭接在颗粒表面上,同时存在基质吸
As an essential portion of basic framework of soil mechanics, strength theory of saturated soils has been well established and widely used in geotechnical engineering practice. However, unsaturated soils are widely distributed and display more complex behaviour compared with saturated soils in engineering practice. Therefore the strength characteristics and strength theory of unsaturated soils have not been well recognized due to the complexity of their multi-phase constitution and interaction of particles, pore water and pore air occupied in the void. In fact, the theories of stress and strength of unsaturated soils are essential and fundamental for analysis of deformation and evaluation of stability of earth structures and foundations comprising of unsaturated soils. Therefore, it is necessary to establish the system of stresses and theory of strength for different degrees of unsaturated soils. Considering the fact that the three-phase composition and individual characteristics of different components as well as their difference from the saturated soils, the difference between the pore-air pressure and pore-water pressure constitutes a matric suction in addition to the net stress which is imposed on soil skeleton. The matric suction plays an important role in deformation and strength properties. The saturation or water content will define the distribution state and transport or seepage properties of pore air and pore water in the voids and then will directly or indirectly influence strength and permeability of unsaturated soils. In order to fully understand the engineering behaviour of unsaturated soils, it is of primary importance to establish the classification system of unsaturated soils according to the saturation and water content and then to define the net stress and matric suction for different states of unsaturated soils which is the key to establish the system of stresses of unsaturated soils. In this thesis, based on theoretical analyses for an ideal assembly of regular particles, the theories of suction and strength are established and then is attempted to be used for interpretation of strength characteristics of actual unsaturated soils. Then some especially-designed experimental tests are performed to verify the fundamental concepts and theory presented in theoretical analyses. These studies form the basis of unsaturated soil mechanics. The following portions are included in this dissertation.1. Based on thermodynamics and geometry, nonlinear formulae are established and numerically programmed with an iterative approach to determine three dimensional shape of contractive skin between two mono-sized ball particles and matric suction and saturation degree can be determined accordingly for an ideal assembly of regular ball-typed particles with isolated water. Considering both effects of magnitude and effective area of matric suction on granular media, equivalent matric suction is presented as average of total matric suctions imposed on all sections of a particle surface over the whole surface of the particle and generalized soil-water characteristic curve is given for relating the equivalent matric
suction to water content. It is shown that conventional matric suction is higher than its equivalent partner and the variation of equivalent matric suction with saturation degree is not as prominent as that of matric suction. Both matric suction and equivalent matric suction decrease rapidly with the increase of the spacing between particles. Additionally, both soil-water characteristic curve and generalized soil-water characteristic curve are dependent on the contact angle of pore water to the particle surface.2. In the most-popularly accepted classification for unsaturated soils, the unsaturated soils are classified as three types with different characteristics such as continuous water with discontinuous air (CWDA) and continuous water with continuous air (CWCA) and discontinuous water with continuous air (DWCA). In fact, surface tension exists on the surface of pore water. Overlapping of pore water along the surface of particle makes the surface tension impose a tension on the particle. Such a tension plays a similar role to that of matric suction and is different essentially from matric suction. The equivalent action of such a tension averaging over the action area of matric suction is defined as tension suction. Its existence is associated with overlapping condition of pore water along the surface of particle. Hence, it is necessary that CWCA unsaturated soils should be further divided into overlapping and non-overlapping CWCA unsaturated soils according to whether contractive skin is overlapping on the surface of soil particles or not. For the unsaturated soils in both DWCA and overlapping CWCA states, both matric suction and tension suction exist due to the overlapping of contractive skin on the surface of soil particles. Therefore, DWCA unsaturated soils and overlapping CWCA unsaturated soils can be combined into overlapping unsaturated soils in which direct effective on strength by surface tension exist in essence. Similarly, CWDA unsaturated soils and non-overlapping CWCA unsaturated soils can be also grouped into non-overlapping unsaturated soils. In this type of unsaturated soils, no direct effect of surface tension exists on strength while matric suction may exist or not exist depending on the conditions of pore water. In this way, the unsaturated soils can be grouped into two types such as overlapping and non-overlapping unsaturated soils according to the existence or non-existence of tension suction. By using such a classification system of unsaturated soils, the state of voids in unsaturated soils can be authentically related to the interaction mechanism between skeleton and voids. Therefore such a classification can interpret the essential behaviour of unsaturated soils and is more rational scientifically.3. In order to examine the characteristics of suction, theoretical analyses are made for an ideal assembly of mono-sized ball-typed particles under the state of discontinuous water with continuous air (DWCA). Based on thermodynamics and geometry, the equations respectively for computing the matric suction and tension suction are theoretically derived. The ratio of tension suction with respect to matric suction is defined as suction ratio in order to observe the correlation between tension suction and matric suction. For the assembly system of particles with zero spacing, the dependency of the suction ratio on saturation radius is observed through computations. It is shown that for unsaturated medium with
discontinuous water with continuous air (DWCA), the suction ratio is much larger than zero and generally lager than unity in most cases. Therefore the tension suction plays independent role in addition to matric suction and cannot be overlooked. Both an exponential-type empirical relation and a nonlinear formula are established respectively for the relationship between suction ratio and saturation radius and for the relationship between suction ratio and saturation by using curve-fitting technique. Furthermore, the sum of both tension and matric suctions is defined as resultant suction. At the same time, the equivalent tension suction and equivalent resultant suction are introduced in order to take the effect of action area into account. It is found that the equivalent tension suction increases while the equivalent matric suction decreases with the increase of saturation and the equivalent resultant suction is almost unvaried.4. For the ideal model of granularly assembled particles, the critical conditions among the DWCA and overlapping CWCA and non-overlapping CWCA states are developed through theoretical analyses. For the overlapping CWCA unsaturated medium, the equations respectively for computing the matric suction and tension suction are theoretically derived on the basis of thermodynamics and geometry. Through computation for different contact angles of contractive skin on the surface of ball-shaped particles, the dependency of both matric suction and tension suction and their equivalent partners on saturation are achieved. It is found that for unsaturated medium under the state of overlapping CWCA, the tension suction is higher than matric suction and both suctions are reduced rapidly with saturation. The matric suction will disappear at a certain lower saturation, around 30% while tension suction will vanish at a certain saturation about 35-45%. All types of suctions rapidly increase with contact angle of contractive skin on the surface of ideal particles. Therefore, both the concepts and determination procedure of all suctions proposed above can reproduce the overall effect of mineral components of soils on both various suctions and soil-water characteristic curves of unsaturated soils in a certain degree. When the saturation is lower than the critical saturation that is transition from DWCA state to overlapping CWCA state, the overlapping length of contractive skin on the surface of particles will increase with saturation, leading to increase of the tension suction with saturation. On the contrary, when the saturation is higher than the critical saturation, the overlapping length of contractive skin on the surface of particles will decrease with saturation, resulting in decrease of tension suction with saturation. At the same time, equivalent matric suction monotonically decreases basically with the increase of water content from zero to 100%.5. In the study of unsaturated soils, it is common to directly employ the equivalence hypothesis suggested by Bishop which can be stated as that the effect of interaction among particles on the deformation and strength behaviour of soils can be equivalently replaced by externally-applied average isotropic confining pressure. For an ideal system regularly assembled by mono-sized particles, the effects resulting from externally-applied hydrostatic confining pressure and attraction among particles are respectively analyzed foi two cases in
which there is no absence of particle and there exists absence of particle. It is shown that Bishop's hypothesis is rational in the case of no absence of particle while it is invalid in the case of existence of absence of particle. Under such a circumstance, the effect of confining pressure on friction along the interface among particles, interlocking and volumetric deformation are much more considerable than that of interaction or attraction among particles. However, it is rather difficult to define the effects of both confining pressure and internal attraction among particles on the deformation and strength of loosely-packed media as well as the interrelationship of both effects because of the limitation of current experimental and measurement techniques. Therefore, Bishop's hypothesis is still employed here to study contribution of various types of suction to strength in order to reduce the complexity. When linear Mohr-Coulomb's criterion is utilized, the strength of unsaturated soils induced by equivalent suctions increases linearly. When effective area of suctions on particle is taken into account, contribution of both matric suction and tension suction to strength can be superposed together and can be represented by the equivalent resultant suction. In order to define equivalent resultant suction, relationship between equivalent resultant suction and matric suction should be established since no proper procedure is currently available for directly defining or measuring the tension suction and the acting area of both tension and matric suctions. Empirical relation between matric suction and equivalent resultant suction is defined with use of curve-fitting technique based on the computed results. In the DWCA state, equivalent resultant suction is linearly related to matric suction and accordingly strength is linearly dependent on matric suction. In overlapping CWCA state, when matric suction disappears for a certain degree of saturation, tension suction may still exist independently and therefore non-zero equivalent resultant suction exists. The tension suction which may exist even under the condition that the matric suction vanishes yields non-zero resultant suction and therefore results in an intercept of ultimate strength. For the non-overlapping state, the unsaturated property of soils has no any effect on strength as no any suctions exist.6. Based on orthographic test principle, the experimental data of collective tests are re-evaluated to justify Fredlund's two stress-state variables for unsaturated soils respectively. The collected tests include unsaturated triaxial shear tests of both remolded loess soils and Nanyang expansive soils, the unsaturated direct shear tests of the Madrid grey clay, and unsaturated compression tests of reconstituted loess soils. It is demonstrated through the orthographic analyses that the dependencies of shear strength of unsaturated soil on net normal stress and matric suction are independent and there exists no cross interaction of the effects of net normal stress and matric suction on strength. Therefore the effects of net normal stress and matric suction on strength can be separately taken into consideration and then directly summed together to achieve the overall strength due to both net normal stress and matric suction. As a consequence, the overall strength induced by unsaturation of soils can be expressed by net normal stress and matric suction where the effect of the tension suction is implied. Based on the correlation relationship of matric suction and equivalent resultant
suction obtained for the ideal assemble of regularly-packed particles, in the range of saturation from 0 to 100%, the unsaturated state of unsaturated soils can be generally divided into two states which consists of generalized overlapping unsaturated state including both DWCA and overlapping CWCA and generalized non-overlapping unsaturated state including non-overlapping CWCA and CWDA. As a result, according to the existence and correlation of both matric suction and tension suction and the dependency of strength on suction or different unsaturated states, the strength behaviour of unsaturated soils can be described by four staged straight lines. Considering non-uniform of particle size and irregularity of particle shapes and multiply of grain size distribution as well as complexity of different mineral components in practice, an empirical formula of shear strength of unsaturated soils is proposed in terms of matric suction which is continuous and differentiable. The fundamental variation characteristics of strength with matric suction can be reproduced by the proposed formula, e.g., differential of strength with matric suction may approach to infinite due to the presence of tension suction when the matric suction vanishes while strength should approach to an asymptote at a higher value of matric suction.7. In order to verify the rationality and reasonability of the theories of suctions and strength of unsaturated soils proposed above, a number of experimental tests are well designed and performed. The conventional triaxial shear apparatus, pressure plate and GDS unsaturated triaxial shear apparatus are respectively employed to experimentally study fully saturated samples, unsaturated samples with higher saturation and naturally-dried unsaturated samples with iower saturation which are all initially saturated. The strength characteristics and failure features of unsaturated soils are examined at two extreme states including higher saturation and lower saturation or DWCA. It is displayed that the friction angle related to suction is larger than that associated with net normal stress for unsaturated soils under higher saturation while the strength linearly increases with increase of matric suction for unsaturated soils under lower saturation. It is implied that an internal force in addition to matric suction which exists in unsaturated soils will impose its contribution to the strength. Such an additional internal force may be resulted from the tension suction. It can be observed from the failure state of samples that the failure mechanism of unsaturated soils is different from that of saturated soils.8. By applying strength theory for unsaturated soils and Fredlund's theory of two stress-state variables, an one-dimensional constitutive model for vertical deformation of unsaturated soil under ^-consolidation state while the critical stable height of vertical cut slopes is evaluated with consideration of dry cracks at ground. (1) Unsaturated soils will undergo deformation as ground is soaked or underground water table rises. The increase in water content can result in, on one hand, compression due to rise in specific weight of soil, and on the other hand, rebound due to decrease in matric suction. The comprehensive effect is controlled by these two types of factors. Based on generalized Hook's law of elasticity and the empirical relationship between matric suction and saturation given by Brooks and Corey,
an incremental-type of constitutive model is established for unsaturated soils loaded under the condition of A^-consoilidation. Combined with the layer-wise summation method, the proposed model can be used to assess deformation of unsaturated soils induced by the soaking of ground, rise or lowering of water table as well as over-evaporation. Assessment on an example displays that deformation characteristics of the unsaturated soil is not only dependent on soil properties, but also associated with the variation of profile matric suction distribution and thickness of soil layer as well as stress states. The procedure can also be used to evaluate the settlement of footing on unsaturated soil foundation. (2) Based on the representation procedure of two stress state variables, the formulas for estimating the critical stable height of vertical cut slopes of unsaturated soils are established respectively for two cases that matric suction is constant or linearly decreased along depth. It is shown that the critical height is dependent on both matric suction and strength parameters. On one hand, matric suction can enhance stability of vertical slope since shear strength will increase with the matric suction. On the other hand, matric suction will initiate surface cracks on ground, leading to reduce the stability of slopes. Therefore it is not always true that the matric suction plays a positive rule in the slope stability. The feature of variation of the critical height with matric suction is associated with comprehensive effects of related parameters of soil. Compared with the condition that shrinkage cracks on ground are overlooked, the critical heights of slope considering dry shrinkage cracks get smaller. The study is instructive and useful in excavation of deep foundation pits without supports.
1.在水封闭情况下,基于圆形弯液面假设、接触角协调性要求和热力学基本理论,针对规则等直径球形颗粒建立了颗粒间弯液面方程,运用迭代法对这一非线性方程组进行了求解,进而确定了理论意义上的基质吸力。基质吸力实际上是一个分布面力,其总体作用效应同时包括面力的大小及其作用面积两个因素。将作用于颗粒局部表面积上的基质吸力在整个颗粒表面上进行平均后作为等效基质吸力。进一步地,类似于描述吸力与饱和度之间关系的土—水特征曲线,将等效基质吸力与饱和度之间的关系曲线定义为广义土—水特征曲线。基于最松散堆积状态的理想模型分析表明,与基质吸力相比,由于考虑了面积效应,等效基质吸力较小,且随饱和度的变化并不象基质吸力那样十分显著;无论基质吸力还是等效基质吸力,均随颗粒空间排列间隙的增大而迅速减小:另外,土—水特征曲线和广义土—水特征曲线都依赖于孔隙水与固体颗粒之间接触角的变化。
2.目前,普遍接受的非饱和土分类方法把非饱和土分为水封闭、双开敞和气封闭等三类。液体表面存在表面张力作用,液面在颗粒表面的搭接使得表面张力对颗粒产生拉结作用。这种拉结作用类似于基质吸力的作用,但与基质吸力是两个完全不同的概念,其在基质吸力作用面积上的等效作用定义为张力吸力。孔隙水弯液面与土颗粒表面是否搭接决定了这种张力吸力存在与否。因此根据孔隙水弯液面与土颗粒表面的搭接状态,将双开敞非饱和土细分为搭接双开敞非饱和土和不搭接双开敞非饱和土。在水封闭非饱和土和搭接双开敞非饱和土中,由于孔隙水弯液面搭接在颗粒表面上,同时存在基质吸
As an essential portion of basic framework of soil mechanics, strength theory of saturated soils has been well established and widely used in geotechnical engineering practice. However, unsaturated soils are widely distributed and display more complex behaviour compared with saturated soils in engineering practice. Therefore the strength characteristics and strength theory of unsaturated soils have not been well recognized due to the complexity of their multi-phase constitution and interaction of particles, pore water and pore air occupied in the void. In fact, the theories of stress and strength of unsaturated soils are essential and fundamental for analysis of deformation and evaluation of stability of earth structures and foundations comprising of unsaturated soils. Therefore, it is necessary to establish the system of stresses and theory of strength for different degrees of unsaturated soils. Considering the fact that the three-phase composition and individual characteristics of different components as well as their difference from the saturated soils, the difference between the pore-air pressure and pore-water pressure constitutes a matric suction in addition to the net stress which is imposed on soil skeleton. The matric suction plays an important role in deformation and strength properties. The saturation or water content will define the distribution state and transport or seepage properties of pore air and pore water in the voids and then will directly or indirectly influence strength and permeability of unsaturated soils. In order to fully understand the engineering behaviour of unsaturated soils, it is of primary importance to establish the classification system of unsaturated soils according to the saturation and water content and then to define the net stress and matric suction for different states of unsaturated soils which is the key to establish the system of stresses of unsaturated soils. In this thesis, based on theoretical analyses for an ideal assembly of regular particles, the theories of suction and strength are established and then is attempted to be used for interpretation of strength characteristics of actual unsaturated soils. Then some especially-designed experimental tests are performed to verify the fundamental concepts and theory presented in theoretical analyses. These studies form the basis of unsaturated soil mechanics. The following portions are included in this dissertation.1. Based on thermodynamics and geometry, nonlinear formulae are established and numerically programmed with an iterative approach to determine three dimensional shape of contractive skin between two mono-sized ball particles and matric suction and saturation degree can be determined accordingly for an ideal assembly of regular ball-typed particles with isolated water. Considering both effects of magnitude and effective area of matric suction on granular media, equivalent matric suction is presented as average of total matric suctions imposed on all sections of a particle surface over the whole surface of the particle and generalized soil-water characteristic curve is given for relating the equivalent matric
suction to water content. It is shown that conventional matric suction is higher than its equivalent partner and the variation of equivalent matric suction with saturation degree is not as prominent as that of matric suction. Both matric suction and equivalent matric suction decrease rapidly with the increase of the spacing between particles. Additionally, both soil-water characteristic curve and generalized soil-water characteristic curve are dependent on the contact angle of pore water to the particle surface.2. In the most-popularly accepted classification for unsaturated soils, the unsaturated soils are classified as three types with different characteristics such as continuous water with discontinuous air (CWDA) and continuous water with continuous air (CWCA) and discontinuous water with continuous air (DWCA). In fact, surface tension exists on the surface of pore water. Overlapping of pore water along the surface of particle makes the surface tension impose a tension on the particle. Such a tension plays a similar role to that of matric suction and is different essentially from matric suction. The equivalent action of such a tension averaging over the action area of matric suction is defined as tension suction. Its existence is associated with overlapping condition of pore water along the surface of particle. Hence, it is necessary that CWCA unsaturated soils should be further divided into overlapping and non-overlapping CWCA unsaturated soils according to whether contractive skin is overlapping on the surface of soil particles or not. For the unsaturated soils in both DWCA and overlapping CWCA states, both matric suction and tension suction exist due to the overlapping of contractive skin on the surface of soil particles. Therefore, DWCA unsaturated soils and overlapping CWCA unsaturated soils can be combined into overlapping unsaturated soils in which direct effective on strength by surface tension exist in essence. Similarly, CWDA unsaturated soils and non-overlapping CWCA unsaturated soils can be also grouped into non-overlapping unsaturated soils. In this type of unsaturated soils, no direct effect of surface tension exists on strength while matric suction may exist or not exist depending on the conditions of pore water. In this way, the unsaturated soils can be grouped into two types such as overlapping and non-overlapping unsaturated soils according to the existence or non-existence of tension suction. By using such a classification system of unsaturated soils, the state of voids in unsaturated soils can be authentically related to the interaction mechanism between skeleton and voids. Therefore such a classification can interpret the essential behaviour of unsaturated soils and is more rational scientifically.3. In order to examine the characteristics of suction, theoretical analyses are made for an ideal assembly of mono-sized ball-typed particles under the state of discontinuous water with continuous air (DWCA). Based on thermodynamics and geometry, the equations respectively for computing the matric suction and tension suction are theoretically derived. The ratio of tension suction with respect to matric suction is defined as suction ratio in order to observe the correlation between tension suction and matric suction. For the assembly system of particles with zero spacing, the dependency of the suction ratio on saturation radius is observed through computations. It is shown that for unsaturated medium with
discontinuous water with continuous air (DWCA), the suction ratio is much larger than zero and generally lager than unity in most cases. Therefore the tension suction plays independent role in addition to matric suction and cannot be overlooked. Both an exponential-type empirical relation and a nonlinear formula are established respectively for the relationship between suction ratio and saturation radius and for the relationship between suction ratio and saturation by using curve-fitting technique. Furthermore, the sum of both tension and matric suctions is defined as resultant suction. At the same time, the equivalent tension suction and equivalent resultant suction are introduced in order to take the effect of action area into account. It is found that the equivalent tension suction increases while the equivalent matric suction decreases with the increase of saturation and the equivalent resultant suction is almost unvaried.4. For the ideal model of granularly assembled particles, the critical conditions among the DWCA and overlapping CWCA and non-overlapping CWCA states are developed through theoretical analyses. For the overlapping CWCA unsaturated medium, the equations respectively for computing the matric suction and tension suction are theoretically derived on the basis of thermodynamics and geometry. Through computation for different contact angles of contractive skin on the surface of ball-shaped particles, the dependency of both matric suction and tension suction and their equivalent partners on saturation are achieved. It is found that for unsaturated medium under the state of overlapping CWCA, the tension suction is higher than matric suction and both suctions are reduced rapidly with saturation. The matric suction will disappear at a certain lower saturation, around 30% while tension suction will vanish at a certain saturation about 35-45%. All types of suctions rapidly increase with contact angle of contractive skin on the surface of ideal particles. Therefore, both the concepts and determination procedure of all suctions proposed above can reproduce the overall effect of mineral components of soils on both various suctions and soil-water characteristic curves of unsaturated soils in a certain degree. When the saturation is lower than the critical saturation that is transition from DWCA state to overlapping CWCA state, the overlapping length of contractive skin on the surface of particles will increase with saturation, leading to increase of the tension suction with saturation. On the contrary, when the saturation is higher than the critical saturation, the overlapping length of contractive skin on the surface of particles will decrease with saturation, resulting in decrease of tension suction with saturation. At the same time, equivalent matric suction monotonically decreases basically with the increase of water content from zero to 100%.5. In the study of unsaturated soils, it is common to directly employ the equivalence hypothesis suggested by Bishop which can be stated as that the effect of interaction among particles on the deformation and strength behaviour of soils can be equivalently replaced by externally-applied average isotropic confining pressure. For an ideal system regularly assembled by mono-sized particles, the effects resulting from externally-applied hydrostatic confining pressure and attraction among particles are respectively analyzed foi two cases in
which there is no absence of particle and there exists absence of particle. It is shown that Bishop's hypothesis is rational in the case of no absence of particle while it is invalid in the case of existence of absence of particle. Under such a circumstance, the effect of confining pressure on friction along the interface among particles, interlocking and volumetric deformation are much more considerable than that of interaction or attraction among particles. However, it is rather difficult to define the effects of both confining pressure and internal attraction among particles on the deformation and strength of loosely-packed media as well as the interrelationship of both effects because of the limitation of current experimental and measurement techniques. Therefore, Bishop's hypothesis is still employed here to study contribution of various types of suction to strength in order to reduce the complexity. When linear Mohr-Coulomb's criterion is utilized, the strength of unsaturated soils induced by equivalent suctions increases linearly. When effective area of suctions on particle is taken into account, contribution of both matric suction and tension suction to strength can be superposed together and can be represented by the equivalent resultant suction. In order to define equivalent resultant suction, relationship between equivalent resultant suction and matric suction should be established since no proper procedure is currently available for directly defining or measuring the tension suction and the acting area of both tension and matric suctions. Empirical relation between matric suction and equivalent resultant suction is defined with use of curve-fitting technique based on the computed results. In the DWCA state, equivalent resultant suction is linearly related to matric suction and accordingly strength is linearly dependent on matric suction. In overlapping CWCA state, when matric suction disappears for a certain degree of saturation, tension suction may still exist independently and therefore non-zero equivalent resultant suction exists. The tension suction which may exist even under the condition that the matric suction vanishes yields non-zero resultant suction and therefore results in an intercept of ultimate strength. For the non-overlapping state, the unsaturated property of soils has no any effect on strength as no any suctions exist.6. Based on orthographic test principle, the experimental data of collective tests are re-evaluated to justify Fredlund's two stress-state variables for unsaturated soils respectively. The collected tests include unsaturated triaxial shear tests of both remolded loess soils and Nanyang expansive soils, the unsaturated direct shear tests of the Madrid grey clay, and unsaturated compression tests of reconstituted loess soils. It is demonstrated through the orthographic analyses that the dependencies of shear strength of unsaturated soil on net normal stress and matric suction are independent and there exists no cross interaction of the effects of net normal stress and matric suction on strength. Therefore the effects of net normal stress and matric suction on strength can be separately taken into consideration and then directly summed together to achieve the overall strength due to both net normal stress and matric suction. As a consequence, the overall strength induced by unsaturation of soils can be expressed by net normal stress and matric suction where the effect of the tension suction is implied. Based on the correlation relationship of matric suction and equivalent resultant
suction obtained for the ideal assemble of regularly-packed particles, in the range of saturation from 0 to 100%, the unsaturated state of unsaturated soils can be generally divided into two states which consists of generalized overlapping unsaturated state including both DWCA and overlapping CWCA and generalized non-overlapping unsaturated state including non-overlapping CWCA and CWDA. As a result, according to the existence and correlation of both matric suction and tension suction and the dependency of strength on suction or different unsaturated states, the strength behaviour of unsaturated soils can be described by four staged straight lines. Considering non-uniform of particle size and irregularity of particle shapes and multiply of grain size distribution as well as complexity of different mineral components in practice, an empirical formula of shear strength of unsaturated soils is proposed in terms of matric suction which is continuous and differentiable. The fundamental variation characteristics of strength with matric suction can be reproduced by the proposed formula, e.g., differential of strength with matric suction may approach to infinite due to the presence of tension suction when the matric suction vanishes while strength should approach to an asymptote at a higher value of matric suction.7. In order to verify the rationality and reasonability of the theories of suctions and strength of unsaturated soils proposed above, a number of experimental tests are well designed and performed. The conventional triaxial shear apparatus, pressure plate and GDS unsaturated triaxial shear apparatus are respectively employed to experimentally study fully saturated samples, unsaturated samples with higher saturation and naturally-dried unsaturated samples with iower saturation which are all initially saturated. The strength characteristics and failure features of unsaturated soils are examined at two extreme states including higher saturation and lower saturation or DWCA. It is displayed that the friction angle related to suction is larger than that associated with net normal stress for unsaturated soils under higher saturation while the strength linearly increases with increase of matric suction for unsaturated soils under lower saturation. It is implied that an internal force in addition to matric suction which exists in unsaturated soils will impose its contribution to the strength. Such an additional internal force may be resulted from the tension suction. It can be observed from the failure state of samples that the failure mechanism of unsaturated soils is different from that of saturated soils.8. By applying strength theory for unsaturated soils and Fredlund's theory of two stress-state variables, an one-dimensional constitutive model for vertical deformation of unsaturated soil under ^-consolidation state while the critical stable height of vertical cut slopes is evaluated with consideration of dry cracks at ground. (1) Unsaturated soils will undergo deformation as ground is soaked or underground water table rises. The increase in water content can result in, on one hand, compression due to rise in specific weight of soil, and on the other hand, rebound due to decrease in matric suction. The comprehensive effect is controlled by these two types of factors. Based on generalized Hook's law of elasticity and the empirical relationship between matric suction and saturation given by Brooks and Corey,
an incremental-type of constitutive model is established for unsaturated soils loaded under the condition of A^-consoilidation. Combined with the layer-wise summation method, the proposed model can be used to assess deformation of unsaturated soils induced by the soaking of ground, rise or lowering of water table as well as over-evaporation. Assessment on an example displays that deformation characteristics of the unsaturated soil is not only dependent on soil properties, but also associated with the variation of profile matric suction distribution and thickness of soil layer as well as stress states. The procedure can also be used to evaluate the settlement of footing on unsaturated soil foundation. (2) Based on the representation procedure of two stress state variables, the formulas for estimating the critical stable height of vertical cut slopes of unsaturated soils are established respectively for two cases that matric suction is constant or linearly decreased along depth. It is shown that the critical height is dependent on both matric suction and strength parameters. On one hand, matric suction can enhance stability of vertical slope since shear strength will increase with the matric suction. On the other hand, matric suction will initiate surface cracks on ground, leading to reduce the stability of slopes. Therefore it is not always true that the matric suction plays a positive rule in the slope stability. The feature of variation of the critical height with matric suction is associated with comprehensive effects of related parameters of soil. Compared with the condition that shrinkage cracks on ground are overlooked, the critical heights of slope considering dry shrinkage cracks get smaller. The study is instructive and useful in excavation of deep foundation pits without supports.
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