中主应力系数对应力主轴循环旋转条件下砂土变形特性的影响

采用香港科技大学的空心圆柱扭剪仪对日本标准丰浦砂进行了四个系列、每个系列包含中主应力系数b=0.1,0.5和1.0三种不同情况的纯应力主轴循环旋转排水试验,即试验过程中控制作用在砂样上的有效主应力的幅值不变,仅应力主轴在0°～180°循环旋转。试验发现中主应力系数b对应力主轴循环旋转条件下砂土的变形特性有显著影响,着重分析了这一参数对纯应力主轴循环旋转条件下砂土的应变分量和体应变的发展、剪应力剪应变关系曲线及流动规律等变形特性的影响。     

Behavior of Liquefied Sands Under Extremely Large Strain Levels in Cyclic Torsional Shear Tests

In order to study the cyclic behavior of liquefied sands at extremely large strain levels up to double amplitude shear strain of about 100%, a series of undrained cyclic torsional shear tests while keeping the specimen height constant was performed on saturated Toyoura sand under different densities, two kinds of in-situ frozen sandy samples and their reconstituted specimens. Due correction was made for the effect of membrane force on the measured shear stress. After exceeding a certain level of overall shear strain, the specimen deformation became non-uniform, which is called as “strain localization” in the present study. The initiation of such localization was associated with the changes in the cyclic amplitude of deviator stress and the increment of shear strain. In the case of Toyoura sand, the limiting value of shear strain to initiate strain localization was found to increase with decrease in the relative density, and such a trend was consistent with the empirical correlation of soil liquefaction when the relative density is higher than 30%. In the case of in-situ frozen sandy samples, their limiting shear strain values were smaller than those of the reconstituted specimens, suggesting that their soil structures were different from each other under different degrees of natural aging effects.     

Accumulated Deformation of Sand with Initial Shear Stress and Effective Stress State Lying Near Failure Conditions

This study concerns the development of residual deformations in soil subjected to static shear and cyclic stress components. This problem plays an important role in such situation as natural slopes, slopes of embankments and dams, quay walls. Among them, the present study focuses in particular on cyclic undrained behavior with static shear stress. Furthermore, in the case of structures with static shear stress and subjected to the earthquake shaking, the forces acting in the shear plane are generally one-way cyclic loading without reversing its direction. Experimental research was focused on the accumulation of shear strain in the soil element during one-way cyclic loading (torsional stress loading only on positive or negative side). Series of torsional shear tests on hollow cylindrical specimens of Toyoura sand with relative density of 40% and 60%, with isotropic stress condition under effective pressure of 98 kPa, 196 kPa and 294 kPa as well as anisotropic conditions were made in order to investigate the incremental shear strain per cycle during cyclic loading. The level of static shear stress was set equal to half of the ultimate stress under drained conditions (factor of safety equal to two). The experimental results showed that the presence of static shear stress increases the resistance of sandy soil. The experimental results of the shear strain increment per cycle and the number of cycles were plotted in a logarithmic scale to show a linear relationship with each other. Based on these findings a simple model for prediction of shear strain was developed.     

Comparison of Liquefaction-Induced Ground Deformation Between Results from Undrained Cyclic Torsional Shear Tests and Observations From Previous Model Tests and Case Studies

In order to investigate liquefaction-induced ground displacement, we conducted a series of undrained cyclic torsional shear tests on saturated Toyoura sand using a modified torsional apparatus capable of applying and measuring double amplitude shear strain up to about 100%. The limiting value of double amplitude shear strain, at which strain localization appears during undrained cyclic loading tests, was evaluated from the test results with reference to the change in the deviator stress during liquefaction. The limiting strain values, which increase with a decrease in the relative density of the specimen, were found to be consistent with the maximum amounts of liquefaction-induced ground displacement observed in the previous shaking table model tests and most of the relevant case studies. This feature is reasonable considering the reduction in the mobilized cyclic shear stress in liquefied soil due to the degradation of the shear resistance. As long as the liquefied soil layer remains in uniform deformation, these limiting strain values may be used in estimating the maximum amount of liquefaction-induced ground displacement.     

Influence of strain histories on liquefaction resistance of sand

The liquefaction resistance of sand increases with cyclic pre-shearing and pre-shaking as a result of earthquakes if the strain level in the pre-shearing is small. When larger shear strains are imposed, liquefaction resistance decreases. These complicated effects of pre-shearing histories on the liquefaction resistance are investigated in this study through a series of cyclic triaxial tests. Various combinations of cyclic stress amplitude and number of cycles of pre-shearing are examined. The tested sand is Toyoura Sand at 45% relative density, under a confining pressure of 50 kPa. Test results indicate that for the range of shear strain amplitude in pre-shearing smaller than 0.35%, the liquefaction resistance increases with pre-shearing. The increase in the liquefaction resistance depends strongly on the volumetric strain in the pre-shearing, and several effects of the shear stress amplitude and number of cycles can be negligible. Small volumetric strain of the order of 1% doubled the liquefaction resistance. Meanwhile, in the range of shear strain amplitude larger than 0.6%, the liquefaction resistance decreases. The liquefaction resistance decreases as the shear strain amplitude increases. Shear strain amplitude is one of the factors dominating this degrading effect, and the volumetric strain exerts beneficial effects to a certain extent. In this study, another series of tests are conducted to investigate the combined effects of small and large strain amplitude pre-shearing. It is observed that small shear strain pre-shearing cycles subsequent to large shear strain cycles erased the degrading effect of the latter. However, a large shear strain pre-shearing after small strain cycles degrades the beneficial effect of the small shear strain pre-shearing cycles previously applied to the specimens; however, the effects of the former small strain pre-shearing remains.     

Effects of initial static shear on liquefaction and large deformation properties of loose saturated Toyoura sand in undrained cyclic torsional shear tests

This study focused on the role which static shear plays on the large deformation behavior of loose saturated sand during undrained cyclic loading. A series of undrained cyclic torsional shear tests was performed on saturated Toyoura sand specimens up to single amplitude shear strain exceeding 50%. Three types of cyclic loading patterns, i.e., stress reversal, intermediate and non-reversal, were employed by varying the initial static shear level and the cyclic shear stress amplitude. The observed types of failure could be distinguished into liquefaction (cyclic and rapid flow) and residual deformation by comparing both monotonic and cyclic undrained behavior. It was found that the presence of initial static shear does not always lead to an increase in the resistance to liquefaction or strain accumulation; they could either increase or decrease with an increasing initial static shear level depending on the type of loading pattern and failure behavior. In addition, according to the failure behavior which the specimens exhibited, three modes of development of large residual deformation were observed.     

Strain localization characteristics of loose saturated Toyoura sand in undrained cyclic torsional shear tests with initial static shear

Strain localization, or the formation of shear bands, is a key aspect in understanding soil failure mechanisms. While efforts have been made in terms of measuring the shear band properties and the stress–strain behavior within shear bands, there are still uncertainties regarding when shear bands initiate and their influence on the development of large ground deformation. In this paper, the limiting value of shear strain, at which strain localization appears during undrained cyclic torsional shear tests with initial static shear, performed on loose Toyoura sand specimens (Dr=44–48%) up to a single amplitude of shear strain exceeding 50%, was evaluated. Non-uniform specimen deformation was observed at strain levels larger than 20%. However, the onset of strain localization could not be defined on the basis of visual observations. Therefore, the limiting values for half of the double amplitude (γ_DA/2) and single amplitude (γ_SA) shear strain, to initiate strain localization, were determined from test results based on changes in the deviator stress response and strain accumulation properties as well as changes in the strain-softening behavior during cyclic shear. It was found that γ_SA is a more appropriate parameter than γ_DA/2. Irrespective of the static shear stress level, the limiting strain value for γ_SA was evaluated to be in the range of 23–28% for liquefied loose Toyoura sand specimens (i.e., stress reversal and intermediate tests). Alternatively, the limiting strain value could not be properly defined when liquefaction did not occur (i.e., non-reversal stress tests), although various methods were employed.     

Numerical study on liquefaction characteristics of granular materials under Rayleigh-wave strain conditions using 3D DEM

In liquefaction analyses, liquefaction is conventionally assumed to originate from the vertical propagation of shear waves. However, some field and theoretical evidence has demonstrated that the risk of liquefaction may be induced or increased by surface waves. In this study, the liquefaction characteristics of K₀-consolidated granular materials under Rayleigh-wave strain conditions, ideal deformation conditions under the assumption of constant volume, were investigated by the three-dimensional discrete element method (3D DEM). The results indicate that Rayleigh-wave strain conditions combine pure and simple shear modes. As the ratio of the shear strain amplitude to the normal strain amplitude (RSN) increases from 1 to +∞, granular materials tend to have a slower liquefaction rate and higher liquefaction resistance; however, the difference in the undrained responses is negligible when the RSN is less than 1. The distribution of the magnitude and orientation of the contact forces also varies with the RSN, while it is similar when the RSN is less than 1. The degradation of the skeleton structure and the evolution of the structural anisotropy accelerate the liquefaction of granular materials. Moreover, in situations with the same accumulated equivalent strain per cycle, the Rayleigh-wave strain condition with a low RSN value will make granular materials more vulnerable to liquefaction compared with Love- and SH-wave strain conditions.     

Comparison of liquefaction behavior of granular material under SH- and Love-wave strain conditions by 3D DEM

In the study of liquefaction behavior associated with seismic loading conditions, it is often assumed that liquefaction occurs owing to the upward propagation of shear waves, despite evidence that liquefaction damage may result from or be aggravated by horizontally propagating surface waves. In this study, a series of numerical tests, based on the three-dimensional discrete element method, is performed to examine the liquefaction behavior of granular materials under Love-wave strain conditions. The response of granular packings under horizontally polarized shear- (SH-) and Love-wave strain conditions is discussed at both macro- and microscales. The simulation results indicate that, at the macroscale, the effective stress reduction ratio increases more rapidly under Love-wave strain conditions than under SH-wave strain conditions. Based on the concept of energy, the granular materials under Love-wave strain conditions can be considered more vulnerable to liquefaction than those under SH-wave strain conditions. Microscale analysis indicates the spatial rotation of the dominant direction of backbone force-chains under Love-wave strain conditions. In addition, focus here is placed on the coordination number, which represents the average contact number per particle. The difference in the degradation speed of the skeleton structure of the granular packings between the SH- and Love-wave strain conditions may not appear until the coordination number has decreased to a critical value of around 4. After the coordination number has approached approximately 3, the granular packings become unstable and soon liquefy. The minimum mean effective stress is discussed herein.     

砂土液化大变形的弹塑性循环本构模型

循环剪切过程中饱和砂土的3个体积应变分量(有效球应力变化引起的体变、剪切引起的可逆性体变和不可逆性体变)的变化规律决定了液化后剪应变的发展。基于上述机理、对剪切引起的可逆性和不可逆性体变的数学描述、体积相容性条件以及边界面本构理论框架,建立了一个可描述饱和砂土液化后大变形的弹塑性循环本构模型。通过对饱和砂土排水和不排水循环扭剪试验结果的模拟表明,该模型不仅可以合理地模拟饱和砂土循环加载条件下从液化前到液化后、从小剪应变到大剪应变的变形发展过程,而且可以合理地模拟饱和砂土液化后再固结大体变的累积特性。本文的研究为定量描述砂土液化后大变形提供了一条合理而有效的途径。     

Stress–dilatancy relationships of sand in the simulation of volumetric behavior during cyclic torsional shear loadings

In order to describe the volumetric behavior of soil subjected to shearing, a relationship that deals with the ratio of plastic strain increments to stress ratio (i.e. a stress–dilatancy relationship) is required in addition to the stress–shear strain relationship. In view of the above, stress–dilatancy relationships during cyclic torsional shear loadings were experimentally investigated in the current study. Based on the experimental results, a bilinear non-unique stress–dilatancy model was proposed for stress controlled drained cyclic torsional shear loading. The stress–dilatancy relationships during virgin loading and subsequent cyclic loading were modeled separately by considering the effects of stress history (over-consolidation or normal consolidation). Then the volume change of Toyoura sand specimens subjected to cyclic torsional shear loading was simulated by combining the simulation of stress–shear strain relationship with the proposed stress–dilatancy relationships. It was observed from the comparison of the experiment results with the simulation of volumetric strain that, after combining with accurate modeling of stress–shear strain relationship, the proposed stress–dilatancy relationship can reasonably simulate the volumetric behavior of sand subjected to various drained cyclic torsional shear loadings.     

Effects of small and large shear histories on multiple liquefaction properties of sand with initial static shear

It has been reported that soils belonging to slope grounds show different types of liquefaction behavior than those belonging to horizontal grounds. Some research has also revealed that liquefaction histories can significantly affect the shear behavior of sandy soils. However, the combined effects of the slope angle and the magnitude of past shear histories on the liquefaction properties of soils have not been studied comprehensively. Based on this background, several multiple liquefaction tests with initial static shear were conducted on Toyoura sand. In each of these tests, a single specimen was sheared several times up to small or large double amplitude shear strain under a constant volume condition using a specially designed stacked-ring shear apparatus. The behavior of the Toyoura sand observed in these tests was discussed considering various perspectives, such as the increase in relative density, the induced anisotropy, the change in liquefaction resistance, and the shear strain accumulation. The findings of this study established that shear histories of smaller magnitude had relatively less influence on densification and induced anisotropy than those of larger magnitude. Moreover, shear histories of smaller magnitude also resulted in the relatively higher liquefaction resistance of sand specimens against the next cyclic shear, while the opposite trend was observed in the case of specimens subjected to shear histories of larger magnitude. Finally, shear strain accumulated less easily in tests with small shear histories than in those with large shear histories.     

Yielding Characteristic and Non-Coaxiality of Toyoura Sand on p′-Constant Shear Stress Plane

In order to investigate the deformation characteristics under a wide selection of stress history, ten series of stress probing tests on p′-constant shear stress plane on dense Toyoura sand are conducted by using hollow cylinder apparatus. This paper presents yielding behavior and non-coaxiality of Toyoura sand obtained from the tests. The stress probing tests consist of ten series of shearing tests each of which starts from systematically chosen individual initial stress point. Each initial stress point is subjected to load-unload stress history. The yielding characteristic is interpreted by means of a concept of multiple yield surfaces model which has three yield surfaces representing linearly elastic behavior limit, commencement point of rapid development in plastic strain and elasto-plastic range. As a result, an experimental evidence of the isotropic hardening, i.e., isotropic expansion of yield surface, induced by anisotropic loadings is obtained. This is what was tacitly assumed in the application of plastic flow rules. However, misalignment of directions between principal stress and principal plastic strain increment is observed. Moreover, plastic strain increment direction is found to be influenced by the given stress increment direction. These facts suggest the non-coaxiality between stress and plastic strain increment due to shear stress increment, even during monotonic loading with isotropic hardening. The plastic strain increment direction diverges from the normal direction to a surface which is a circle with its center nearly at the origin on p′-constant plane and which passes through the current stress point.     

主应力方向循环变化对饱和松砂不排水动力特性的影响

利用新研制的土工静力-动力液压三轴-扭转多功能剪切仪进行了主应力轴循环变化的多种模式竖向和扭转双向耦合循环剪切及普通循环扭剪试验。针对福建标准砂, 在均等固结条件下着重研究了振动过程中主应力方向的不同变化模式对饱和松砂不排水循环特性的影响。试验研究结果表明: 振动过程中主应力方向的变化方式对饱和砂土不排水动强度具有显著的影响, 在所采用的五种类型循环剪切应力路径中, 主应力方向连续旋转条件下的动强度最低。进一步的研究发现: 对于初始均等固结条件,分别采用初始平均有效固结压力和循环破坏次数归一化的循环孔隙水压力比与循环次数比之间的关系与振动过程中主应力方向变化方式无关, 这种归一化循环孔隙水压力比随广义剪应变的变化规律及累积广义剪应变与循环次数比之间关系均与振动过程中主应力方向变化方式无关。     

松散砂土不稳定性试验研究

 对松散丰浦砂进行三轴不排水和常偏应力排水剪切(constant shear drained,简写为CSD)试验。试验采用高精度变围压三轴仪可实现CSD试验全过程偏应力不变,得到比以往研究更为可靠的试验结果。试验发现,在不排水试验中,同一孔隙比的试样在不同围压下具有相同的不稳定线,但同一围压下不稳定线的斜率随孔隙比的增大逐渐减小并趋于稳定。试样在完全排水条件下会发生不稳定,即试样产生明显塑性变形,轴向应变和体积应变迅速增大。以往的研究中CSD应力路径的施加采用轴向力不变,试验过程中偏应力的减小会对不稳定性的判断造成影响,这可能是不同研究者得出不一致结论的重要原因。对松散砂土在不排水和排水条件下不稳定性的区别与联系进行分析,得出如下结论：松散砂土无论在不排水条件下还是在完全排水条件下,相同孔隙比的试样均是在同一应力比下达到不稳定状态。试验结果为排水条件下不稳定性机制研究提供更强有力的试验依据,可用于解释某些边坡的破坏机制。     

砂土的双硬化特性与弹塑性本构模型

 基于高精度的丰浦砂三轴等向加卸载试验与多应力路径平面应变压缩试验结果,提出平面应变条件下的修正塑性功体积硬化函数,得到双硬化框架下的修正塑性功剪切硬化函数,建立应力路径不相关的丰浦砂修正塑性功剪切–体积双硬化函数。在该双硬化函数基础上,推导基于修正塑性功的增量型剪切–体积双硬化弹塑性刚度矩阵,构建可以考虑多种变形强度影响因素的丰浦砂本构模型。数值计算与室内试验结果的比较表明,该砂土双硬化弹塑性本构模型可以合理地模拟砂土材料的变形强度特性。     

静力与动力组合应力条件下饱和松砂变形特性的试验研究

利用大连理工大学新引进与研制开发的土工静力-动力液压三轴-扭转多功能剪切仪,针对福建标准砂,在相对密度为Dr=3 0 %的松散状态下,在不同的三向非均等固结应力状态下进行了应力控制式循环扭剪试验和竖向-扭转耦合剪切试验,通过对比试验结果着重探讨了初始固结主应力方向与循环应力变化模式对饱和松砂动应力-应变关系特性的影响,并采用相对有效应力比峰值与广义剪应变作为参变量对应力-应变模式进行了探讨。试验结果表明,相对有效应力比峰值与广义剪应变之间符合良好的双曲线关系,初始固结主应力方向对砂土的应力-应变关系特性具有不容忽视的影响。     

基于改进角点理论的砂土非共轴模型及其应用

基于传统角点理论建立的非共轴模型虽然能够描述砂土的非共轴行为,但却具有一定的理论缺陷。提出了一种改进的角点理论并将其应用到了砂土状态相关剪胀模型中,从而建立了一个新的砂土非共轴模型。该模型仅在主应力方向改变的加载条件下给出非共轴塑性变形,克服了传统角点模型的不足。构建了模型的隐式积分算法和相应的一致性切线刚度张量,并通过Toyoura砂的单剪试验对算法进行了验证,证明了算法的正确性。最后,利用建立的模型分析了条形基础的承载力,预测结果表明:非共轴塑性的引入使得地基模型整体刚度下降,导致力学响应表现出一些软化特征,忽略非共轴塑性的影响可能导致工程设计偏于危险。     

Post-erosion mechanical responses of internally unstable gap-graded soil under drained torsional simple shear and triaxial compression

Internal erosion is a major threat to hydraulic earth structures, such as river levees and dams. This paper focuses on suffusion and suffosion phenomena which are caused by the movement of fine particles in the granular skeleton due to seepage flow. The present study investigates the impact of internal erosion on the dynamic response under cyclic torsional shear and monotonic responses under triaxial compression and torsional simple shear. A series of experiments, using a gap-graded silica mixture with a fines content of 20%, is performed under loose, medium, and dense conditions using a novel erosion hollow cylindrical torsional shear apparatus. The erosion test results indicate that the critical hydraulic gradient and the rate of erosion are density-dependent, where a transition from suffosion to suffusion is observed as the seepage continues. Regardless of the sample density, variations in the radial strain and particle size distribution, along the specimen height after erosion, are no longer uniform. Furthermore, the dynamic shearing results show that the small-strain shear modulus increases, but the initial damping ratio decreases after internal erosion, probably due to the removal of free fines. In addition, the elastic threshold strain and reference shear strain values are found to be higher for the eroded and non-eroded specimens, respectively. Finally, based on drained monotonic loading, the post-erosion peak stress ratio increases remarkably under triaxial compression, while that under torsional simple shear depends on the relative density where the direction of loading is normal to the direction of seepage. These observations indicate that the horizontal bedding plane becomes weaker, while the vertical one becomes stronger after downward erosion.