非饱和土的理论探讨及膨润土加砂混合物的试验研究
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摘要
作为土力学理论的重要组成部分，饱和土力学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，理论尚不十分完善，强度理论和本构关系等需要进一步完善。由于非饱和土含有固相、液相和气相，使得非饱和土的力学性质相对于饱和土要复杂得多，在试验中试样的孔隙水压和气压的控制和测量较为复杂，非饱和土试验资料仍然十分缺乏。随着核能的利用，核技术的发展，所产生的高水平放射性核废料的处置越来越受到全世界范围内的关注，也成为亟待解决的世界性难题。许多国家都开展了对高水平放射性核废料深地质处置的研究工作。相比之下，我国起步较晚，在很多方面尚处于初级阶段，特别是对于作为核废料处置中缓冲、回填材料的膨润土加砂混合物的研究试验才刚刚开始，试验资料非常宝贵。因此，本文针对非饱和土理论中的本构关系、抗剪强度的非线性和非饱和膨胀土裂隙开展深度存在的一些问题进行了探讨研究，并以膨润土加砂混合物为试验研究对象，通过GDS非饱和土三轴试验系统和压力板仪等仪器进行了抗剪强度、膨胀特性和土水特征曲线的试验研究与详细分析。本文的主要研究工作包括下列方面：
1．针对修正膨胀土弹塑性模型中的微-宏观结构的变形耦合参数的具体计算式和非饱和土屈服吸力的确定进行了一定的探讨和研究。研究表明，干湿循环产生的微观结构层次的变形具有累积性，在干湿循环过程中不断产生变形累积，最终趋于稳定。由此可以认为微观结构层次的变形分为n个阶段，每个阶段对应着不同的微观参量，而当土结构在经历若干次干湿循环后，微-宏观结构的耦合胀缩变形趋于稳定，可以采用稳定时的干湿循环次数，作为微观结构层次变形所经历的阶段数，由此提出微-宏观结构变形耦合参数t具体计算式，加强了微-宏观参数之间的联系。从孔隙水的不同状态和不同排出方式出发，将LC和SI屈服曲线与两坐标轴所包围的区域重新划分为弹性和弹塑性两个区域，从而将非饱和土的吸力增加屈服过程划分为：弹性、弹塑性和塑性三个阶段，提出以分界吸力s_b作为弹性和弹塑性两个区域的分界线，并给出了分界吸力的计算公式，根据分界吸力进一步得到了屈服吸力s_y的确定方法和计算公式。
2．对非饱和膨胀土的裂隙开展深度进行了研究，将膨胀土的有效粘聚力c＇的影响引入到裂隙开展深度的线弹性理论解中，采用有效粘聚力折减系数来反映有效粘聚力在裂隙开展中的衰减变化程度，对非饱和膨胀土裂隙开展深度的线弹性理论解进行了推导，得出更能反映实际情况的非饱和膨胀土裂隙开展深度的理论关系式。进一步得到了地表基质吸力开裂值的表达式和膨胀土层不受地下水位深度影响时的裂隙开展深度表达式，并对关系式中泊松比、地下水位深度、有效内摩擦角、地表基质吸力等影响参数进行了比较和分析。在此基础上，分别就非饱和膨胀土层中的基质吸力的三种分布曲线形式，即基质吸力沿深度均匀分布、沿深度线性减小和沿深度呈抛物线减小，比较分析了干燥裂隙对非饱和膨胀土层中张拉区深度的影响。
3．随着非饱和土试验技术的不断发展，近年来大量的试验资料表明，单纯采用线性强度理论描述非饱和土的强度特性与试验结果不相符。许多非饱和土试验表明非饱和土的抗剪强度与基质吸力之间存在着非线性的关系，即可以反映出抗剪强度随基质吸力增加而增加的情况的角φ~b，并不如当初所假设的为一常数，而是随基质吸力(u_a-u_w)的变化而发生变化，即角φ~b为基质吸力(u_a-u_w)的函数。针对总粘聚力c与基质吸力(u_a-u_w)之间关系的非线性特征，提出了含有非线性系数m的总粘聚力c与基质吸力(u_a-u_w)的非线性关系式，并进一步得到了含有非线性系数的非饱和土的抗剪强度公式。采用四种不同类型的非饱和土的试验结果进行了验证与分析，发现非线性系数是与土的性质有关的参数，对特定的土体，与角φ~b不同的是，非线性系数与有效粘聚力和有效内摩角一样，不随基质吸力的变化而变化，可以取为常数，因而具有了更强的适用性；当非线性系数等于1时，含有非线性系数的非饱和土抗剪强度公式可以转变成与由Fredlund等人提出的线性非饱和土抗剪强度公式相同的形式，说明线性抗剪强度公式只是本文提出的非线性抗剪强度公式的一种特殊形式，含有非线性系数的抗剪强度公式将线性形式与非线性形式进行了较好的统一。采用GDS非饱和土三轴试验系统对作为核废料处置中的缓冲、回填材料的膨润土加砂混合物进行控制基质吸力的抗剪强度试验研究，并进一步验证了所提出的含有非线性系数的非饱和土抗剪强度公式的适用性。
4．土水特征曲线SWCC(Soil-water characteristic curve)是表示土体持水能力的重要曲线，反映了土体中基质吸力与体积含水率、质量含水率或饱和度之间的关系，是非饱和土力学研究中的一项重要内容。采用高进气值的压力板仪对不同初始干密度、不同干湿循环次数和不同配合比的膨润土加砂混合物进行了土水特征曲线的试验研究。测定了三种不同情况下的基质吸力与饱和度构成的膨润土加砂混合物的土水特征益线。试验结果表明对于不同初始干密度的混合物，随着初始干密度的增大，膨润土加砂混合物的进气值是增大的，这说明初始干密度大的混合物，连通性小，使饱和度降低所需要的气水压力差值更大，并且混合物进气值的对数与初始干密度之间存在着线性关系。对于经历不同干湿循环次数的混合物，土水特征曲线形状相似，随着干湿循环次数的增加，相同吸力下的饱和度是增大的，土水特征曲线也向上移动，并且与不同干湿循环次数相对应的混合物的进气值是不断增大的，进气值与干湿循环次数之间具有较好的线性关系，不同干湿循环次数下混合物的土水特征曲线的直线段的斜率是相近的。对于不同配合比的膨润土加砂混合物，进气值受相对孔隙填充率的影响，膨润土吸水膨胀后，将混合物中的孔隙填充，填充的密实度越高，混合物的进气值也相应提高。
5．采用GDS非饱和土三轴试验系统等试验仪器对膨润土加砂混合物的膨胀特性进行了一系列的一维膨胀试验和三轴膨胀试验研究。试验结果表明，膨润土加砂混合物的膨胀应变与试验历时之间的关系可以用双曲线形式进行表示，膨胀应变与吸水量之间呈线性关系，膨胀应变与应力的对数之间呈线性关系，吸水量与应力的对数呈线性关系。膨胀应力越大，试样的吸水量越小，膨胀应变也越小，而当膨胀应力减小时，试样就能越充分地吸水，膨胀性能表现的就越明显。所以在建立膨胀应变、应力和吸水量单个变量之间的关系式后，通过综合考虑应力与吸水量对膨胀应变的影响，建立了三者之间统一的膨胀本构关系式，由于考虑了混合物膨胀过程中吸水量的变化，此膨胀本构关系式可以反映出膨润土加砂混合物吸水膨胀的实际情况。膨润土加砂混合物的膨胀变形与上覆轴向压力和本身的干密度有着密切的关系，轴向应力大于混合物的最大的膨胀应力时，混合物吸水则发生相反的反应，即湿陷。这就要求在进行核废料深地处置系统的缓冲、回填材料—膨润土加砂混合物的施工时，要注意缓冲、回填材料的初始密实度，以及在压实过程中与围岩之间产生的应力反应，以避免膨润土加砂混合物遇水而发生湿陷现象，失去强自封闭和自愈合能力，从而达不到封堵人工屏障和天然屏障裂隙的作用。这些是以往的研究中没有指出的。并且在缓冲、回填材料的施工中控制合适的密实度，可以防止膨润土加砂混合物吸水膨胀产生过大的膨胀应力，对深地处置系统本身产生破坏作用，以保证系统各部分之间的协调性。进一步提出混合物状态参数的概念，根据标准砂颗粒最松散、最紧密接触状态线以及初始状态参数可以为选择混合物的配合比例和初始干密度提供参考依据。状态参数变化曲线反映出了在一定应力下混合物吸水变化的情况，并且反映出了状态参数与干密度之间的变化关系。
As the essential part of soil mechanics, saturated soil mechanics is applied in geotechnical engineering practice. However, unsaturated soils are widely existed in nature, with more complex behaviour. Nowadays, unsaturated soil mechanics is developing, in which shear strength theory and constitutive equations are far from perfect. Because unsaturated soil is composed of solid phase, fluid phase and gas phase, mechanical property is more complicated than that of saturated soil. The control and measurement of pore air pressure and pore water pressure in tests are very difficult. Testing data of unsaturated soils are also very shortage. Furthermore, with the use of nuclear energy and development of nuclear engineering, high-level radioactive nuclear waste disposal issues have gained increasing attention all over the world and become universal difficult problems. Research on the deep geological disposal of high-level radioactive nuclear waste is underway in all nuclear energy generation countries. In comparison, the research is at the initial stage in China, especially on bentonite-sand mixtures, which are used as the back-filling materials for high-level radioactive nuclear waste repositories. Testing data of bentonite-sand mixtures are very valuable. Thus, in this dissertation, studies are emphasized on constitutive equations, nonlinearity of shear strength and crack propagation depth of unsaturated expansive soils in unsaturated soil mechanics. Then, utilizing GDS unsaturated triaxial apparatus and pressure plate extractor, the shear strength, swelling properties and soil-water characteristic of bentonite-sand mixtures are studied carefully. The main investigations are as follows:
1. The coupling parameter between micro- and macro-structural deformation of the elasto-plastic model for unsaturated expansive soils, and yield suction of unsaturated soils are studied. Research results indicate that the amount of micro-structural strain accumulates and tends to a stationary value during wetting-drying cycles. So the micro-structural volumetric strain can be divided into n stages with different micro-structural parameters. The times of wetting-drying cycles can be used to difine the value of n. Equation of the coupling parameter between micro- and macro-structural deformation is put forward, which uses test results of wetting-drying cycles well and enhances the relationship of micro- and macro-parameters. Considerting different states of pore water and different discharge ways during isotropic compression test and triaxial shrinkage test of unsaturated soils, the definition and equation of boundary suction is established. The zone, which is enclosed by the yield curves (SI and LC) and the coordinate axes, is divided into two zones: elastic and elasto-plastic, by boundary suction. And there are three stages in the suction increasing process of unsaturated soils, that is, elastic, elasto-plastic and plastic stages. An estimating formula of yield suction of unsaturated soils is suggested.
2. The tensile crack propagation depth of unsaturated expansive soils is studid. A linear elastic solution of the tensile crack propagation depth is presented, which considers the contributions of effective cohesion and effective internal friction angle at the same time. Reduced coefficient of effective cohesion is definited, which considers the reduction of effective cohesion when cracks exit. Expressions for critical matrix suction at the ground surface, and the crack propagation depth with no influence of the depth of the groundwater level are derived from the equation of crack propagation depth. Relationships with influencing factors are compared, such as effective cohesion, reduced coefficient of effective cohesion, effective internal friction angle, Poisson's ratio, matrix suction at the ground surface and the depth of the groundwater level. Based on above, the influences of tensile cracks on tension zone depth are analyzed, considering three typical matrix suction profiles along the depth, that is, constant, linear and parabolic distributions.
3. Shear test results on unsaturated soils indicate that there exists nonlinearity in the shear strength versus matrix suction failure envelope. The angleφ~b is variable and a function of the applied matrix suction. The nonlinear relationship of total cohesion versus matrix suction is analyzed, and an equation with nonlinear coefficient is presented. Then a new shear strength equation for unsaturated soils is derived from it. The reliability and practicability of the shear strength equations with nonlinear coefficient are verified, using four kinds of shear test data on different unsaturated soils. Results show that nonlinear coefficient is a significant parameter for unsaturated soils, just like effective cohesion and effective internal friction angle, and do not vary with matrix suction. Different values can be taken to indicate nonlinear characteristics of different unsaturated soils. When the value of nonlinear coefficient is equal to 1, the new shear strength equation has a smooth transition towards the shear strength equation presented by Fredlund et al., one special form of the new shear strength equation in this study. Utilizing GDS unsaturated triaxial apparatus, the shear strength of bentonite-sand mixtures is studied, under the condition of controlling matrix suction. Mixtures of Heishan calcium-type bentonite and Fujian standard sand in a proportion of 50:50 are used. The relationship between the shear strength and matrix suction of unsaturated bentonite-sand mixtures is analyzed. Results indicate that the shear strength equation with nonlinear coefficient can express the shear strength of bentonite-sand mixtures well.
4. The soil-water characteristic curve (SWCC) represents the ability of a soil to retain water. SWCC reflects the relationship between water content or volumetric water content or degree of saturation versus suction. Utilizing the pressure plate apparatus with high air entry ceramic plate, the SWCCs of bentonite-sand mixtures between degree of saturation versus matrix suction are determined and analyzed. Three states of bentonite-sand mixtures are investigated, which are different dry density, different times of wetting-drying cycle and different proportions of mixture. Results show that for the bentonite-sand mixtures with different dry density, the logarithm of air-entry value increases linearly as dry density increases. It suggested that greater values of matrix suction are needed to reduce the values of degree of saturation, for the sake of greater values of dry density corresponding to smaller pores. For the bentonite-sand mixtures with different times of wetting-drying cycle, the SWCCs have the same shape. The air-entry values increase linearly as the times of wetting-drying cycle increase. The slope coefficients of straight-line section of the SWCCs are similar. For the bentonite-sand mixtures in different proportions of mixture, the air-entry value is influenced by relative packing ratio of pore. When bentonite absorbs water and swells, pores are packed. Greater packed density result in the greater air-entry values.
5. Utilizing GDS unsaturated triaxial apparatus and consolidation apparatus, a series of one dimension and triaxial swelling tests are conducted on bentonite-sand mixtures with different dry density and different initial water content in order to investigate the swelling properties. Based on the experimental data obtained, relationships between swelling strain and time, swelling strain and axial stress, swelling strain and water-absorbing volume, axial stress and water-absorbing volume are analyzed. The results show that the curves of swelling strain versus time can be expressed by the hyperbola well. Swelling strain increases linearly as water-absorbing volume increases. Swelling strain versus logarithm of stress has a relationship of linearity, the same as the relationship of water-absorbing volume versus logarithm of stress. Swelling strain increases as water-absorbing volume increases, but decreases as stress increases. Water-absorbing volume decreases as stress increases. For a given value of stress, water-absorbing volume has a maximum value at the end of swelling process. Then, a swelling constitutive equation of the bentonite-sand mixtures is established by the mothed of multiple linear regression analysis, which reflects the influences of axial stress and water-absorbing volume on swelling strain at the same time. It can reflect the swelling properties of bentonite-sand mixtures actually.
1．针对修正膨胀土弹塑性模型中的微-宏观结构的变形耦合参数的具体计算式和非饱和土屈服吸力的确定进行了一定的探讨和研究。研究表明，干湿循环产生的微观结构层次的变形具有累积性，在干湿循环过程中不断产生变形累积，最终趋于稳定。由此可以认为微观结构层次的变形分为n个阶段，每个阶段对应着不同的微观参量，而当土结构在经历若干次干湿循环后，微-宏观结构的耦合胀缩变形趋于稳定，可以采用稳定时的干湿循环次数，作为微观结构层次变形所经历的阶段数，由此提出微-宏观结构变形耦合参数t具体计算式，加强了微-宏观参数之间的联系。从孔隙水的不同状态和不同排出方式出发，将LC和SI屈服曲线与两坐标轴所包围的区域重新划分为弹性和弹塑性两个区域，从而将非饱和土的吸力增加屈服过程划分为：弹性、弹塑性和塑性三个阶段，提出以分界吸力s_b作为弹性和弹塑性两个区域的分界线，并给出了分界吸力的计算公式，根据分界吸力进一步得到了屈服吸力s_y的确定方法和计算公式。
2．对非饱和膨胀土的裂隙开展深度进行了研究，将膨胀土的有效粘聚力c＇的影响引入到裂隙开展深度的线弹性理论解中，采用有效粘聚力折减系数来反映有效粘聚力在裂隙开展中的衰减变化程度，对非饱和膨胀土裂隙开展深度的线弹性理论解进行了推导，得出更能反映实际情况的非饱和膨胀土裂隙开展深度的理论关系式。进一步得到了地表基质吸力开裂值的表达式和膨胀土层不受地下水位深度影响时的裂隙开展深度表达式，并对关系式中泊松比、地下水位深度、有效内摩擦角、地表基质吸力等影响参数进行了比较和分析。在此基础上，分别就非饱和膨胀土层中的基质吸力的三种分布曲线形式，即基质吸力沿深度均匀分布、沿深度线性减小和沿深度呈抛物线减小，比较分析了干燥裂隙对非饱和膨胀土层中张拉区深度的影响。
3．随着非饱和土试验技术的不断发展，近年来大量的试验资料表明，单纯采用线性强度理论描述非饱和土的强度特性与试验结果不相符。许多非饱和土试验表明非饱和土的抗剪强度与基质吸力之间存在着非线性的关系，即可以反映出抗剪强度随基质吸力增加而增加的情况的角φ~b，并不如当初所假设的为一常数，而是随基质吸力(u_a-u_w)的变化而发生变化，即角φ~b为基质吸力(u_a-u_w)的函数。针对总粘聚力c与基质吸力(u_a-u_w)之间关系的非线性特征，提出了含有非线性系数m的总粘聚力c与基质吸力(u_a-u_w)的非线性关系式，并进一步得到了含有非线性系数的非饱和土的抗剪强度公式。采用四种不同类型的非饱和土的试验结果进行了验证与分析，发现非线性系数是与土的性质有关的参数，对特定的土体，与角φ~b不同的是，非线性系数与有效粘聚力和有效内摩角一样，不随基质吸力的变化而变化，可以取为常数，因而具有了更强的适用性；当非线性系数等于1时，含有非线性系数的非饱和土抗剪强度公式可以转变成与由Fredlund等人提出的线性非饱和土抗剪强度公式相同的形式，说明线性抗剪强度公式只是本文提出的非线性抗剪强度公式的一种特殊形式，含有非线性系数的抗剪强度公式将线性形式与非线性形式进行了较好的统一。采用GDS非饱和土三轴试验系统对作为核废料处置中的缓冲、回填材料的膨润土加砂混合物进行控制基质吸力的抗剪强度试验研究，并进一步验证了所提出的含有非线性系数的非饱和土抗剪强度公式的适用性。
4．土水特征曲线SWCC(Soil-water characteristic curve)是表示土体持水能力的重要曲线，反映了土体中基质吸力与体积含水率、质量含水率或饱和度之间的关系，是非饱和土力学研究中的一项重要内容。采用高进气值的压力板仪对不同初始干密度、不同干湿循环次数和不同配合比的膨润土加砂混合物进行了土水特征曲线的试验研究。测定了三种不同情况下的基质吸力与饱和度构成的膨润土加砂混合物的土水特征益线。试验结果表明对于不同初始干密度的混合物，随着初始干密度的增大，膨润土加砂混合物的进气值是增大的，这说明初始干密度大的混合物，连通性小，使饱和度降低所需要的气水压力差值更大，并且混合物进气值的对数与初始干密度之间存在着线性关系。对于经历不同干湿循环次数的混合物，土水特征曲线形状相似，随着干湿循环次数的增加，相同吸力下的饱和度是增大的，土水特征曲线也向上移动，并且与不同干湿循环次数相对应的混合物的进气值是不断增大的，进气值与干湿循环次数之间具有较好的线性关系，不同干湿循环次数下混合物的土水特征曲线的直线段的斜率是相近的。对于不同配合比的膨润土加砂混合物，进气值受相对孔隙填充率的影响，膨润土吸水膨胀后，将混合物中的孔隙填充，填充的密实度越高，混合物的进气值也相应提高。
5．采用GDS非饱和土三轴试验系统等试验仪器对膨润土加砂混合物的膨胀特性进行了一系列的一维膨胀试验和三轴膨胀试验研究。试验结果表明，膨润土加砂混合物的膨胀应变与试验历时之间的关系可以用双曲线形式进行表示，膨胀应变与吸水量之间呈线性关系，膨胀应变与应力的对数之间呈线性关系，吸水量与应力的对数呈线性关系。膨胀应力越大，试样的吸水量越小，膨胀应变也越小，而当膨胀应力减小时，试样就能越充分地吸水，膨胀性能表现的就越明显。所以在建立膨胀应变、应力和吸水量单个变量之间的关系式后，通过综合考虑应力与吸水量对膨胀应变的影响，建立了三者之间统一的膨胀本构关系式，由于考虑了混合物膨胀过程中吸水量的变化，此膨胀本构关系式可以反映出膨润土加砂混合物吸水膨胀的实际情况。膨润土加砂混合物的膨胀变形与上覆轴向压力和本身的干密度有着密切的关系，轴向应力大于混合物的最大的膨胀应力时，混合物吸水则发生相反的反应，即湿陷。这就要求在进行核废料深地处置系统的缓冲、回填材料—膨润土加砂混合物的施工时，要注意缓冲、回填材料的初始密实度，以及在压实过程中与围岩之间产生的应力反应，以避免膨润土加砂混合物遇水而发生湿陷现象，失去强自封闭和自愈合能力，从而达不到封堵人工屏障和天然屏障裂隙的作用。这些是以往的研究中没有指出的。并且在缓冲、回填材料的施工中控制合适的密实度，可以防止膨润土加砂混合物吸水膨胀产生过大的膨胀应力，对深地处置系统本身产生破坏作用，以保证系统各部分之间的协调性。进一步提出混合物状态参数的概念，根据标准砂颗粒最松散、最紧密接触状态线以及初始状态参数可以为选择混合物的配合比例和初始干密度提供参考依据。状态参数变化曲线反映出了在一定应力下混合物吸水变化的情况，并且反映出了状态参数与干密度之间的变化关系。
As the essential part of soil mechanics, saturated soil mechanics is applied in geotechnical engineering practice. However, unsaturated soils are widely existed in nature, with more complex behaviour. Nowadays, unsaturated soil mechanics is developing, in which shear strength theory and constitutive equations are far from perfect. Because unsaturated soil is composed of solid phase, fluid phase and gas phase, mechanical property is more complicated than that of saturated soil. The control and measurement of pore air pressure and pore water pressure in tests are very difficult. Testing data of unsaturated soils are also very shortage. Furthermore, with the use of nuclear energy and development of nuclear engineering, high-level radioactive nuclear waste disposal issues have gained increasing attention all over the world and become universal difficult problems. Research on the deep geological disposal of high-level radioactive nuclear waste is underway in all nuclear energy generation countries. In comparison, the research is at the initial stage in China, especially on bentonite-sand mixtures, which are used as the back-filling materials for high-level radioactive nuclear waste repositories. Testing data of bentonite-sand mixtures are very valuable. Thus, in this dissertation, studies are emphasized on constitutive equations, nonlinearity of shear strength and crack propagation depth of unsaturated expansive soils in unsaturated soil mechanics. Then, utilizing GDS unsaturated triaxial apparatus and pressure plate extractor, the shear strength, swelling properties and soil-water characteristic of bentonite-sand mixtures are studied carefully. The main investigations are as follows:
1. The coupling parameter between micro- and macro-structural deformation of the elasto-plastic model for unsaturated expansive soils, and yield suction of unsaturated soils are studied. Research results indicate that the amount of micro-structural strain accumulates and tends to a stationary value during wetting-drying cycles. So the micro-structural volumetric strain can be divided into n stages with different micro-structural parameters. The times of wetting-drying cycles can be used to difine the value of n. Equation of the coupling parameter between micro- and macro-structural deformation is put forward, which uses test results of wetting-drying cycles well and enhances the relationship of micro- and macro-parameters. Considerting different states of pore water and different discharge ways during isotropic compression test and triaxial shrinkage test of unsaturated soils, the definition and equation of boundary suction is established. The zone, which is enclosed by the yield curves (SI and LC) and the coordinate axes, is divided into two zones: elastic and elasto-plastic, by boundary suction. And there are three stages in the suction increasing process of unsaturated soils, that is, elastic, elasto-plastic and plastic stages. An estimating formula of yield suction of unsaturated soils is suggested.
2. The tensile crack propagation depth of unsaturated expansive soils is studid. A linear elastic solution of the tensile crack propagation depth is presented, which considers the contributions of effective cohesion and effective internal friction angle at the same time. Reduced coefficient of effective cohesion is definited, which considers the reduction of effective cohesion when cracks exit. Expressions for critical matrix suction at the ground surface, and the crack propagation depth with no influence of the depth of the groundwater level are derived from the equation of crack propagation depth. Relationships with influencing factors are compared, such as effective cohesion, reduced coefficient of effective cohesion, effective internal friction angle, Poisson's ratio, matrix suction at the ground surface and the depth of the groundwater level. Based on above, the influences of tensile cracks on tension zone depth are analyzed, considering three typical matrix suction profiles along the depth, that is, constant, linear and parabolic distributions.
3. Shear test results on unsaturated soils indicate that there exists nonlinearity in the shear strength versus matrix suction failure envelope. The angleφ~b is variable and a function of the applied matrix suction. The nonlinear relationship of total cohesion versus matrix suction is analyzed, and an equation with nonlinear coefficient is presented. Then a new shear strength equation for unsaturated soils is derived from it. The reliability and practicability of the shear strength equations with nonlinear coefficient are verified, using four kinds of shear test data on different unsaturated soils. Results show that nonlinear coefficient is a significant parameter for unsaturated soils, just like effective cohesion and effective internal friction angle, and do not vary with matrix suction. Different values can be taken to indicate nonlinear characteristics of different unsaturated soils. When the value of nonlinear coefficient is equal to 1, the new shear strength equation has a smooth transition towards the shear strength equation presented by Fredlund et al., one special form of the new shear strength equation in this study. Utilizing GDS unsaturated triaxial apparatus, the shear strength of bentonite-sand mixtures is studied, under the condition of controlling matrix suction. Mixtures of Heishan calcium-type bentonite and Fujian standard sand in a proportion of 50:50 are used. The relationship between the shear strength and matrix suction of unsaturated bentonite-sand mixtures is analyzed. Results indicate that the shear strength equation with nonlinear coefficient can express the shear strength of bentonite-sand mixtures well.
4. The soil-water characteristic curve (SWCC) represents the ability of a soil to retain water. SWCC reflects the relationship between water content or volumetric water content or degree of saturation versus suction. Utilizing the pressure plate apparatus with high air entry ceramic plate, the SWCCs of bentonite-sand mixtures between degree of saturation versus matrix suction are determined and analyzed. Three states of bentonite-sand mixtures are investigated, which are different dry density, different times of wetting-drying cycle and different proportions of mixture. Results show that for the bentonite-sand mixtures with different dry density, the logarithm of air-entry value increases linearly as dry density increases. It suggested that greater values of matrix suction are needed to reduce the values of degree of saturation, for the sake of greater values of dry density corresponding to smaller pores. For the bentonite-sand mixtures with different times of wetting-drying cycle, the SWCCs have the same shape. The air-entry values increase linearly as the times of wetting-drying cycle increase. The slope coefficients of straight-line section of the SWCCs are similar. For the bentonite-sand mixtures in different proportions of mixture, the air-entry value is influenced by relative packing ratio of pore. When bentonite absorbs water and swells, pores are packed. Greater packed density result in the greater air-entry values.
5. Utilizing GDS unsaturated triaxial apparatus and consolidation apparatus, a series of one dimension and triaxial swelling tests are conducted on bentonite-sand mixtures with different dry density and different initial water content in order to investigate the swelling properties. Based on the experimental data obtained, relationships between swelling strain and time, swelling strain and axial stress, swelling strain and water-absorbing volume, axial stress and water-absorbing volume are analyzed. The results show that the curves of swelling strain versus time can be expressed by the hyperbola well. Swelling strain increases linearly as water-absorbing volume increases. Swelling strain versus logarithm of stress has a relationship of linearity, the same as the relationship of water-absorbing volume versus logarithm of stress. Swelling strain increases as water-absorbing volume increases, but decreases as stress increases. Water-absorbing volume decreases as stress increases. For a given value of stress, water-absorbing volume has a maximum value at the end of swelling process. Then, a swelling constitutive equation of the bentonite-sand mixtures is established by the mothed of multiple linear regression analysis, which reflects the influences of axial stress and water-absorbing volume on swelling strain at the same time. It can reflect the swelling properties of bentonite-sand mixtures actually.
引文
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