预剪对饱和松砂剪切特性的影响及亚塑性边界面本构模型改进
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摘要
土是最常用的土木工程材料之一,针对其强度与变形特性的研究对实际工程应用具有十分重要的意义。而由于土体所经受的应力历史具有较大的差异并且其后期的受力状态也十分复杂,这些影响因素必然会造成土体微观结构的剧烈变化与各向异性,从而强烈地影响着土材料的强度与变形特性。以波浪荷载为例,波浪荷载具有周期长,荷载作用时间长等特点,而且其作用比较频繁,这使得海工结构及其地基土体在经受较大波浪荷载作用,并导致破坏之前已经受到若干小振幅波浪荷载作用,形成所谓的循环预剪作用。这些前期波浪荷载的循环预剪作用势必将对海床土体产生明显的影响。另外,建筑物地基内各个部位处土单元的应力状态也是各不相同的,沿着某一潜在滑动面,各点的初始主应力方向随其位置而改变。而且,饱和弹性孔隙介质理论分析表明:波浪等循环荷载在土体中所产生的循环应力的主要特点之一是正应力偏差与剪应力所形成的循环偏应力的幅值保持不变,而主应力方向发生了连续旋转,这也将对土的强度与变形特性产生显著的影响。因此,作为建筑物地基稳定性评价中的一个基本而重要问题,探讨砂土的变形与强度特性时必须考虑应力历史的影响以及各向非均等的复杂初始应力状态和复杂的循环应力变化模式。然而,由于土工实验技术的限制,三轴剪切试验及扭转剪切试验等传统的土工试验无法完全实现上述的复杂初始应力条件和复杂加载模式。为此,大连理工大学于2001年起对于自日本诚研舍株式会社引进的“土工静力—动力液压—三轴扭转多功能剪切仪”进行了不断的开发与完善,这套新型土工试验系统可以同时施加和独立地控制轴向压力W、扭矩M_T、外室压力p_o与内室压力p_i及其组合。由此可重现土在不同复杂应力条件下的固结及加载路径。以此为基础,本文针对饱和松砂,进行了大量的考虑静力预剪与循环预剪作用的单调剪切试验与循环剪切试验研究,进而针对不同形式的静力预剪与循环预剪作用对饱和砂土的变形与强度特性进行了比较全面而系统的分析。并在原有亚塑性边界面模型的基础上,根据现有的试验结果建立起相关模型参数与主应力方向角之间的函数关系,在原有亚塑性边界面本构模型的基础上进行改进,使之能够考虑主应力方向角对饱和松砂单调剪切特性影响的。
为了探讨静力预剪作用对饱和砂土循环剪切特性的影响,分别针对实心圆柱状试样和空心圆柱状试样进行了不同方式静力预剪作用的循环三轴剪切试验。
对于实心圆柱状试样,分别针对均等固结条件、二向非均等固结条件和K_o固结条件进行了循环三轴剪切试验,并通过试验探讨了固结应力比与固结方式对饱和砂土循环剪切特性的影响。试验研究表明,周围压力对静止侧压力系数K_o的测定有一定的影响,但是随着周围压力的不断增加,其对K_o值的影响也越来越小。固结应力比与固结方式的不同对饱和砂土的循环剪切特性具有较大的影响。均等固结条件下的应变是对称发展的,且振动初期应变发展不明显,将要达到破坏时发展比较明显,而由于固结过程中静力预剪作用的影响,二向非均等固结和K_o固结条件下的应变主要向初始预剪的方向不断累积,加载初期应变发展较快,后期则逐渐趋于稳定。另外,二向非均等固结条件下,在动应力施加的第一周,随着竖向应力的增加,试样产生较大的正孔隙水压力,而K_o固结条件下,在动应力施加的第一周,随着竖向应力的增加,试样的孔隙水压力发展方向却与前者截然相反,产生了较大的负孔隙水压力。分析其原因主要是两种固结方式的不同固结过程造成的。
对于空心圆柱状试样,分别针对初始固结主应力方向角α_0=0°、30°、45°、60°和90°时进行了循环三轴剪切试验。试验研究表明,不同初始主应力方向角的静力预剪作用对饱和砂土不排水循环三轴剪切条件下的应力—应变发展模式以及各应变分量的发展均具有较为显著的影响。
为了探讨饱和砂土未发生液化条件下的循环预剪作用对饱和砂土液化强度的影响,分别针对实心圆柱状试样和空心圆柱状试样进行了循环三轴剪切试验和考虑主应力轴连续旋转的轴向—扭转双向耦合剪切试验。试验研究表明,循环预剪作用对孔隙比的影响并不大,在循环三轴试验中,孔隙比的变化幅度不超过0.2%,而在循环耦合试验中,其变化幅度也未超过0.3%。因此,较小的孔隙比变化不足以引起饱和砂土液化强度的较大改变。另外,无论是循环三轴试验还是循环耦合试验,无论是均等固结条件还是非均等固结条件,在未发生液化条件下,循环预剪作用对土体的应变发展特性和孔隙水压力发展模式影响较小,而对饱和砂土二次加载液化强度却有较为显著的提高,尤其当循环预剪应力幅值较大时,砂土液化强度提高的更为显著。分析其原因,主要是由于砂土孔隙的均匀化以及砂土颗粒间咬合作用的增强使饱和砂土形成了更为稳定的结构。
为了探讨静力预剪作用与循环预剪作用对饱和砂土单调剪切特性的影响,针对实心圆柱状试样进行了循环预剪后固结排水的不排水单调剪切试验与循环预剪后不固结排水的不排水单调剪切试验,针对空心圆柱状试样进行了考虑不同初始固结状态与加载方式的单调剪切试验。试验研究表明,饱和砂土在经受循环预剪作用后,无论是固结排水后再进行单调剪切加载,还是不固结排水,在存在残余孔隙水压力的条件下直接进行单调剪切加载试验,当预剪过程中试样未发生液化破坏时,循环预剪作用对饱和砂土后期的单调剪切特性影响并不显著。发展过程都是在剪切加载的初期饱和砂土发生剪缩,而后发生剪胀,整体上呈现硬化变形的特征,并最终达到稳定状态。而当饱和砂土在循环预剪过程中发生液化破坏时,其对后期的单调剪切加载特性具有十分显著的影响。在剪切过程中,试样均呈现出十分明显的剪胀特性,孔隙水压力以下降为主。
另外试验结果表明,当饱和砂土试样具有水平沉积面时,初始固结主应力方向与剪切方向的不同组合形成了单调剪切过程中总的主应力方向的不同,从而显著地影响着饱和砂土不排水单调剪切特性。当总的主应力方向不断发生变化时,剪切过程中任意时刻饱和砂土所表现出的单调剪切特性也不相同。
为了能够考虑初始固结主应力方向与单调剪切方向的各种组合所产生的剪切过程中变化的总主应力方向对饱和砂土单调剪切特性的影响,根据现有的试验结果建立起相关参数与主应力方向角之间的函数关系,并将其重新应用到亚塑性边界面模型之中,进而与部分试验实测所得到的结果进行了对比分析,由此论证了所改进的亚塑性边界面模型的适用性。对比分析表明所改进和推广的本构模型能够合理地反映出不同初始固结主应力方向和单调剪切方向的各种组合条件对饱和砂土应力—应变关系的硬化与软化特征、剪胀与剪缩特征以及有效应力路径等方面的影响,能够较为准确的反映出剪切过程中变化的主应力方向对饱和砂土单调剪切特性的影响。
The soils is one of the commonly used civil engineering materials. It is very important for the engineering application to study on the strength and deformation behaviors of soils. However, the stress history soils suffered is different extremely, and the loading model is also complex, which certainly will make the microstructure of soil change markedly and anisotropic. And the changes and anisotropic of the soil structure will effect the strength and deformation behavior of soil significantly. For example the wave loading, the sea floor has been suffered different degrees wave loading before suffering stronger wave loading, which forms so-called cyclic preloading effect. And the cyclic preloading of the previous wave loading has an important effect on the behaviors of ocean sand. Moreover, the stress states of soil elements located at different parts in the foundation of ocean structures are all different. The orientations of initial stresses of all the points along a potential sliding surface strongly depend on the location of the point. And the cyclic stresses induced by wave loading are characterized by the fact that the amplitude of the cyclic deviatoric stress originated from the deviation of normal stresses and the shear stress keeps unchanged but the orientation of principal stress axe rotate progressively, which has influence on the shear behavior of saturated sand. For this sake, as a basic and important issue in evaluation of the stability of seabed and ocean engineering structures, the stress history, the complex initial anisotropic stress state as well as the complex variation pattern of cyclic stress must be taken into consideration for studies of deformation and strength properties of sands. However, this has been handicapped by the difficulties in soil experimental technology. The conventional geotechnical tests such as triaxial shear test and torsional shear test are not able to reproduce the above-mentioned complex initial stress condition and cyclic loading pattern. Therefore, unceasing efforts have been made by Dalian University of Technology to develop and improve soil static and dynamic universal triaxial and torsional shear apparatus, which was manufactured by Seiken Corp., Inc., Japan. This well-designed system is capable to simultaneously apply and individually control the four components including axial pressure W, torque M_T, outer chamber pressure p_o and inner chamber pressure p_i. Therefore different consolidation and shear loading can be implemented by various combinations of four independent components under different complex stress conditions of soil. It constitutes a well-performed universal test system that makes possible to conduct a great number of experimental tests of saturated sand under various complex stress conditions. Furthermore comprehensive and systematic analyses on the effect of both static and cyclic preloading on the deformation and strength characteristics of saturated sands are carried out. And in the basic of hypoplasticity bounding surface model, the functional relationships between the related parameters and the orientation of principal stress are established according to the test results and then develop the hypoplasticity bounding surface model to be able to consider the effect of orientation of principal stress.
In order to investigate the effect of static preloading on the cyclic shearing behavior of saturated sand, using the solid cylindrical specimen and the hollow cylinder specimen, a series of cyclic shearing tests are performed under the conditions of static preloading.
For the solid cylindrical specimens, the tests are performed under both isotropic and two-directional anisotropic consolidation as well as K_0-consolidation conditions. And the effect of the consolidation stress ratio and consolidation style on the cyclic shearing behavior of saturated sand is investigated. It is shown that the confining pressure influence the determination of K_0 in some degree, and with the increasing of confining pressure the effect is more and more little. Moreover, different consolidation stress ratio and consolidation style have significant influence on the cyclic shearing behavior of saturated sand. Under the isotropic consolidation condition, the accumulated residual deformation develops Symmetrically. In the beginning of shearing the deformation is small, and bigger at failure. However, under the two-directional anisotropic and K_0 consolidation conditions, for the sake of static preloading, the deformation is mainly accumulative in the preloading direction, In the beginning of shearing, the deformation develops rapidly, and tends to be stable later. Moreover, for the condition of two-directional anisotropic consolidation the pore water pressure develops rapidly in positive direction with the increasing of axial stress in the first cycle. Contrarily larger negative pore water pressure is generated for the K_0 consolidation conditions in the first cycle, which seems to be relative to the different consolidation style.
For the hollow cylindrical specimens, the tests are performed under the conditions ofα_0=0°、30°、45°、60°and 90°. It is shown that the static preloading of different orientation of major principal stress has significant influence on the stress-strain development pattern and every components of strain development in the cyclic triaxial shearing tests.
In order to investigate the effect of cyclic preloading on the liquefaction resistance of saturated sands, using the solid cylindrical specimens and the hollow cylinder specimen, a series of cyclic triaxial shearing tests and vertical-torsional coupling shearing tests considering the continuous rotation in principal stress direction are performed. It is shown that the effect of cyclic preloading on the void ratio is extremely little under the condition that the saturated sand has not liquefied in the process of cyclic preloading. The rate of variation is less than 0.2% in triaxial tests and is less than 0.3% in vertical-torsional coupling tests. Therefore, the decrease of the void ratio induced by the cyclic preloading is so little that it can not have remarkable effect on the liquefaction resistance of saturated sand. Moreover, under the condition that the saturated sand has not liquefied, cyclic preloading has no significant influence on the strain development and pore water pressure development pattern, no matter cyclic triaxial test or cyclic vertical-torsional coupling test and no matter isotropic consolidation or anisotropic consolidation. But the previous cyclic preloading can improve the liquefaction resistance of saturated sand significantly, especially for the higher degree of cyclic preloading. The main reason is the uniformization of sand pores and the enhanced interlocking of the particles in the process of cyclic preloading and the structure of saturated sand is more stable.
In order to investigate the effect of static and cyclic preloading on the monotonic shearing behavior of saturated sand, using the solid cylindrical specimens and the hollow cylinder specimen, a series of monotonic shearing tests are performed. It is shown that the influence of cyclic preloading on monotonic shearing behavior is not significant under the condition that the saturated sand has not liquefied in the process of cyclic preloading. And the samples are all shearing contraction in the beginning of loading and shearing dilatation later. The characteristic of strain hardening is remarkable in the process of loading. However, when the saturated sand has liquefied in the process of cyclic preloading, the influence of cyclic preloading on the monotonic shearing behavior is significant. In the process of loading, the samples are all shear dilatation, and the pore water pressure mainly deceases.
Moreover, the test results show that when the saturated sand sample has horizontal sedimentary plane, the different combinations of initial orientation of major principal stress and direction of monotonic shearing make the actual orientation of major principal stress different during the shearing, which affecting the undrained monotonic shearing behavior of sand remarkably. And the monotonic shearing behavior of saturated sand is different when the orientation of major principal stress is different at any time.
In order to consider the effect of the orientation of major principal stress on the monotonic shearing behavior of saturated sand, the functional relationships between the model parameters and the orientation of principal stress are established according to the test results and then develop the hypoplasticity bounding surface model to be able to consider the effect of orientation of principal stress. Through comparing with the test results, it is shown that the improved hypoplasticity bounding surface model can reflect the influence of the orientation of major principal stress monotonic shearing behavior of saturated sand.
为了探讨静力预剪作用对饱和砂土循环剪切特性的影响,分别针对实心圆柱状试样和空心圆柱状试样进行了不同方式静力预剪作用的循环三轴剪切试验。
对于实心圆柱状试样,分别针对均等固结条件、二向非均等固结条件和K_o固结条件进行了循环三轴剪切试验,并通过试验探讨了固结应力比与固结方式对饱和砂土循环剪切特性的影响。试验研究表明,周围压力对静止侧压力系数K_o的测定有一定的影响,但是随着周围压力的不断增加,其对K_o值的影响也越来越小。固结应力比与固结方式的不同对饱和砂土的循环剪切特性具有较大的影响。均等固结条件下的应变是对称发展的,且振动初期应变发展不明显,将要达到破坏时发展比较明显,而由于固结过程中静力预剪作用的影响,二向非均等固结和K_o固结条件下的应变主要向初始预剪的方向不断累积,加载初期应变发展较快,后期则逐渐趋于稳定。另外,二向非均等固结条件下,在动应力施加的第一周,随着竖向应力的增加,试样产生较大的正孔隙水压力,而K_o固结条件下,在动应力施加的第一周,随着竖向应力的增加,试样的孔隙水压力发展方向却与前者截然相反,产生了较大的负孔隙水压力。分析其原因主要是两种固结方式的不同固结过程造成的。
对于空心圆柱状试样,分别针对初始固结主应力方向角α_0=0°、30°、45°、60°和90°时进行了循环三轴剪切试验。试验研究表明,不同初始主应力方向角的静力预剪作用对饱和砂土不排水循环三轴剪切条件下的应力—应变发展模式以及各应变分量的发展均具有较为显著的影响。
为了探讨饱和砂土未发生液化条件下的循环预剪作用对饱和砂土液化强度的影响,分别针对实心圆柱状试样和空心圆柱状试样进行了循环三轴剪切试验和考虑主应力轴连续旋转的轴向—扭转双向耦合剪切试验。试验研究表明,循环预剪作用对孔隙比的影响并不大,在循环三轴试验中,孔隙比的变化幅度不超过0.2%,而在循环耦合试验中,其变化幅度也未超过0.3%。因此,较小的孔隙比变化不足以引起饱和砂土液化强度的较大改变。另外,无论是循环三轴试验还是循环耦合试验,无论是均等固结条件还是非均等固结条件,在未发生液化条件下,循环预剪作用对土体的应变发展特性和孔隙水压力发展模式影响较小,而对饱和砂土二次加载液化强度却有较为显著的提高,尤其当循环预剪应力幅值较大时,砂土液化强度提高的更为显著。分析其原因,主要是由于砂土孔隙的均匀化以及砂土颗粒间咬合作用的增强使饱和砂土形成了更为稳定的结构。
为了探讨静力预剪作用与循环预剪作用对饱和砂土单调剪切特性的影响,针对实心圆柱状试样进行了循环预剪后固结排水的不排水单调剪切试验与循环预剪后不固结排水的不排水单调剪切试验,针对空心圆柱状试样进行了考虑不同初始固结状态与加载方式的单调剪切试验。试验研究表明,饱和砂土在经受循环预剪作用后,无论是固结排水后再进行单调剪切加载,还是不固结排水,在存在残余孔隙水压力的条件下直接进行单调剪切加载试验,当预剪过程中试样未发生液化破坏时,循环预剪作用对饱和砂土后期的单调剪切特性影响并不显著。发展过程都是在剪切加载的初期饱和砂土发生剪缩,而后发生剪胀,整体上呈现硬化变形的特征,并最终达到稳定状态。而当饱和砂土在循环预剪过程中发生液化破坏时,其对后期的单调剪切加载特性具有十分显著的影响。在剪切过程中,试样均呈现出十分明显的剪胀特性,孔隙水压力以下降为主。
另外试验结果表明,当饱和砂土试样具有水平沉积面时,初始固结主应力方向与剪切方向的不同组合形成了单调剪切过程中总的主应力方向的不同,从而显著地影响着饱和砂土不排水单调剪切特性。当总的主应力方向不断发生变化时,剪切过程中任意时刻饱和砂土所表现出的单调剪切特性也不相同。
为了能够考虑初始固结主应力方向与单调剪切方向的各种组合所产生的剪切过程中变化的总主应力方向对饱和砂土单调剪切特性的影响,根据现有的试验结果建立起相关参数与主应力方向角之间的函数关系,并将其重新应用到亚塑性边界面模型之中,进而与部分试验实测所得到的结果进行了对比分析,由此论证了所改进的亚塑性边界面模型的适用性。对比分析表明所改进和推广的本构模型能够合理地反映出不同初始固结主应力方向和单调剪切方向的各种组合条件对饱和砂土应力—应变关系的硬化与软化特征、剪胀与剪缩特征以及有效应力路径等方面的影响,能够较为准确的反映出剪切过程中变化的主应力方向对饱和砂土单调剪切特性的影响。
The soils is one of the commonly used civil engineering materials. It is very important for the engineering application to study on the strength and deformation behaviors of soils. However, the stress history soils suffered is different extremely, and the loading model is also complex, which certainly will make the microstructure of soil change markedly and anisotropic. And the changes and anisotropic of the soil structure will effect the strength and deformation behavior of soil significantly. For example the wave loading, the sea floor has been suffered different degrees wave loading before suffering stronger wave loading, which forms so-called cyclic preloading effect. And the cyclic preloading of the previous wave loading has an important effect on the behaviors of ocean sand. Moreover, the stress states of soil elements located at different parts in the foundation of ocean structures are all different. The orientations of initial stresses of all the points along a potential sliding surface strongly depend on the location of the point. And the cyclic stresses induced by wave loading are characterized by the fact that the amplitude of the cyclic deviatoric stress originated from the deviation of normal stresses and the shear stress keeps unchanged but the orientation of principal stress axe rotate progressively, which has influence on the shear behavior of saturated sand. For this sake, as a basic and important issue in evaluation of the stability of seabed and ocean engineering structures, the stress history, the complex initial anisotropic stress state as well as the complex variation pattern of cyclic stress must be taken into consideration for studies of deformation and strength properties of sands. However, this has been handicapped by the difficulties in soil experimental technology. The conventional geotechnical tests such as triaxial shear test and torsional shear test are not able to reproduce the above-mentioned complex initial stress condition and cyclic loading pattern. Therefore, unceasing efforts have been made by Dalian University of Technology to develop and improve soil static and dynamic universal triaxial and torsional shear apparatus, which was manufactured by Seiken Corp., Inc., Japan. This well-designed system is capable to simultaneously apply and individually control the four components including axial pressure W, torque M_T, outer chamber pressure p_o and inner chamber pressure p_i. Therefore different consolidation and shear loading can be implemented by various combinations of four independent components under different complex stress conditions of soil. It constitutes a well-performed universal test system that makes possible to conduct a great number of experimental tests of saturated sand under various complex stress conditions. Furthermore comprehensive and systematic analyses on the effect of both static and cyclic preloading on the deformation and strength characteristics of saturated sands are carried out. And in the basic of hypoplasticity bounding surface model, the functional relationships between the related parameters and the orientation of principal stress are established according to the test results and then develop the hypoplasticity bounding surface model to be able to consider the effect of orientation of principal stress.
In order to investigate the effect of static preloading on the cyclic shearing behavior of saturated sand, using the solid cylindrical specimen and the hollow cylinder specimen, a series of cyclic shearing tests are performed under the conditions of static preloading.
For the solid cylindrical specimens, the tests are performed under both isotropic and two-directional anisotropic consolidation as well as K_0-consolidation conditions. And the effect of the consolidation stress ratio and consolidation style on the cyclic shearing behavior of saturated sand is investigated. It is shown that the confining pressure influence the determination of K_0 in some degree, and with the increasing of confining pressure the effect is more and more little. Moreover, different consolidation stress ratio and consolidation style have significant influence on the cyclic shearing behavior of saturated sand. Under the isotropic consolidation condition, the accumulated residual deformation develops Symmetrically. In the beginning of shearing the deformation is small, and bigger at failure. However, under the two-directional anisotropic and K_0 consolidation conditions, for the sake of static preloading, the deformation is mainly accumulative in the preloading direction, In the beginning of shearing, the deformation develops rapidly, and tends to be stable later. Moreover, for the condition of two-directional anisotropic consolidation the pore water pressure develops rapidly in positive direction with the increasing of axial stress in the first cycle. Contrarily larger negative pore water pressure is generated for the K_0 consolidation conditions in the first cycle, which seems to be relative to the different consolidation style.
For the hollow cylindrical specimens, the tests are performed under the conditions ofα_0=0°、30°、45°、60°and 90°. It is shown that the static preloading of different orientation of major principal stress has significant influence on the stress-strain development pattern and every components of strain development in the cyclic triaxial shearing tests.
In order to investigate the effect of cyclic preloading on the liquefaction resistance of saturated sands, using the solid cylindrical specimens and the hollow cylinder specimen, a series of cyclic triaxial shearing tests and vertical-torsional coupling shearing tests considering the continuous rotation in principal stress direction are performed. It is shown that the effect of cyclic preloading on the void ratio is extremely little under the condition that the saturated sand has not liquefied in the process of cyclic preloading. The rate of variation is less than 0.2% in triaxial tests and is less than 0.3% in vertical-torsional coupling tests. Therefore, the decrease of the void ratio induced by the cyclic preloading is so little that it can not have remarkable effect on the liquefaction resistance of saturated sand. Moreover, under the condition that the saturated sand has not liquefied, cyclic preloading has no significant influence on the strain development and pore water pressure development pattern, no matter cyclic triaxial test or cyclic vertical-torsional coupling test and no matter isotropic consolidation or anisotropic consolidation. But the previous cyclic preloading can improve the liquefaction resistance of saturated sand significantly, especially for the higher degree of cyclic preloading. The main reason is the uniformization of sand pores and the enhanced interlocking of the particles in the process of cyclic preloading and the structure of saturated sand is more stable.
In order to investigate the effect of static and cyclic preloading on the monotonic shearing behavior of saturated sand, using the solid cylindrical specimens and the hollow cylinder specimen, a series of monotonic shearing tests are performed. It is shown that the influence of cyclic preloading on monotonic shearing behavior is not significant under the condition that the saturated sand has not liquefied in the process of cyclic preloading. And the samples are all shearing contraction in the beginning of loading and shearing dilatation later. The characteristic of strain hardening is remarkable in the process of loading. However, when the saturated sand has liquefied in the process of cyclic preloading, the influence of cyclic preloading on the monotonic shearing behavior is significant. In the process of loading, the samples are all shear dilatation, and the pore water pressure mainly deceases.
Moreover, the test results show that when the saturated sand sample has horizontal sedimentary plane, the different combinations of initial orientation of major principal stress and direction of monotonic shearing make the actual orientation of major principal stress different during the shearing, which affecting the undrained monotonic shearing behavior of sand remarkably. And the monotonic shearing behavior of saturated sand is different when the orientation of major principal stress is different at any time.
In order to consider the effect of the orientation of major principal stress on the monotonic shearing behavior of saturated sand, the functional relationships between the model parameters and the orientation of principal stress are established according to the test results and then develop the hypoplasticity bounding surface model to be able to consider the effect of orientation of principal stress. Through comparing with the test results, it is shown that the improved hypoplasticity bounding surface model can reflect the influence of the orientation of major principal stress monotonic shearing behavior of saturated sand.
引文
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