From solid to granular gases: the steady state for granular materials

This paper aims at extending the well‐known critical state concept, associated with quasi‐static conditions, by accounting for the role played by the strain rate when focusing on the steady, simple shear flow of a dry assembly of identical, inelastic, soft spheres. An additional state variable for the system, the granular temperature, is accounted for. The granular temperature is related to the particle velocity fluctuations and measures the agitation of the system. This state variable, as is in the context of kinetic theories of granular gases, is assumed to govern the response of the material at large strain rates and low concentrations. The stresses of the system are associated with enduring, frictional contacts among particles involved in force chains and nearly instantaneous collisions. When the first mechanism prevails, the material behaves like a solid, and constitutive models of soil mechanics hold, whereas when inelastic collisions dominate, the material flows like a granular gas, and kinetic theories apply. Considering a pressure‐imposed flow, at large values of the normal stress and small values of the shear rate, the theory predicts a nonmonotonic shear rate dependence of the stress ratio at the steady state, which is likely to govern the evolution of landslides. Copyright © 2013 John Wiley & Sons, Ltd.     

砂土渗透系数的细粒效应与其状态参数关联性

利用常规渗透仪进行了不同细粒含量砂土的渗透性能试验,通过引入粒间状态参量概念,探讨砂土渗透系数的细粒效应及其与表征砂土各种状态参数的相互关联性。发现砂土渗透系数总体上随细粒含量增加而减小,当细粒含量小于5%时影响较小;细粒含量在5%～10%时,渗透系数随细粒含量增加而急剧减小;而当细粒含量大于25%后,砂土的渗透系数则基本趋向相对稳定值。基于5种不同表征状态参数的拟合分析,表明采用现有常用的经验模型尚难以简便、有效地预测各种细粒含量砂土的渗透系数,而利用粉粒间孔隙比则能更好地反映细粒含量对渗透系数的影响,且其与渗透系数在半对数坐标内基本呈现线性关系,说明粒间状态参量适宜用来描述砂土渗透系数的细粒效应     

细粒含量对饱和砂类土液化强度的影响

为研究细粒含量FC对不同密实状态饱和砂类土液化强度CRR的影响,将不同FC的砂类土试样分为3组：（1）相同的相对密实度 50%;（2）相同的孔隙比 0.90;（3）相同的骨架孔隙比 1.20,对不同FC和密实状态（ 、e和 ）的砂类土进行了一系列不排水循环三轴试验。试验结果显示：e或 相同的砂类土CRR随着FC的增加逐渐降低;具有相同 砂类土的CRR随FC的增加迅速增大,砂类土的CRR与 、e或 都没有较好的相关性。分析表明：不同FC和密实状态砂类土的CRR随等效骨架孔隙比 的增大而降低,两者呈现较好的负幂函数关系,这表明考虑细粒影响程度的 是合理表征不同种类砂类土CRR的一个物理状态指标。通过对比已有的砂类土的试验结果发现：砂类土中的砂粒是影响CRR的重要因素,且随着砂粒的形状从圆状向角状变化,砂类土的总体CRR逐渐增大。     

Modeling for critical state line of granular soil with evolution of grain size distribution due to particle breakage

Determination of the critical state line(CSL)is important to characterize engineering properties of granular soils.Grain size distribution(GSD)has a significant influence on the location of CSL.The influence of particle breakage on the CSL is mainly attributed to the change in GSD due to particle breakage.However,GSD has not been properly considered in modeling the CSL with influence of particle breakage.This study aims to propose a quantitative model to determine the CSL considering the effect of GSD.We hypothesize that the change of critical state void ratio with respect to GSD is caused by the same mechanism that influences of the change of minimum void ratio with respect to GSD.Consequently,the particle packing model for minimum void ratio proposed by Chang et al.(2017)is extended to predict critical state void ratio.The developed model is validated by experimental results of CSLs for several types of granular materials.Then the evolution of GSD due to particle breakage is incorporated into the model.The model is further evaluated using the experimental results on rockfill material,which illustrates the applicability of the model in predicting CSL for granular material with particle breakage.     

细粒含量对饱和砂土动弹性模量与阻尼比的影响研究

利用GDS循环三轴试验系统,进行一系列不同细粒含量砂土的不排水动三轴试验,研究细粒含量对饱和砂土动弹性模量与阻尼比的影响。试验结果表明,砂土的动弹性模量随细粒含量的增加而减小,但当超过细粒含量的临界值30%后,变化趋势则相反;阻尼比随着细粒含量的增加呈现先增大后减小的趋势,其细粒含量的临界值也为30%。当细粒含量小于30%时,砂土的动力特性主要由粗粒决定,粗粒间形成的骨架孔隙比随细粒含量的增加而增大,相同应变水平下抵抗变形的能力随之减弱,从而使动弹性模量减小。同时,土颗粒间接触点的减少使应力波在土中传播速度变慢,使得土体对动荷载反应的滞后性增强,阻尼比随之增加;当细粒含量大于30%后,砂土的动力特性主要由细粒决定,细粒间孔隙比随着细粒含量的增加而减小,从而使砂土的动弹性模量与阻尼比呈现出相反的变化趋势     

Cyclic liquefaction screening of sand with non-plastic fines:Critical state approach

There have been significant advances in the application of critical state,CS,in liquefaction potential assessment.This was done by comparing state parameter,j with estimated characteristic cyclic stress ratio,CSR due to an earthquake.A cyclic resistance ratio,CRR curve,which can be determined from cyclic liquefaction tests,separates historical liquefied and non-liquefied data points(j,CSR).On the other hand,the concepts of equivalent granular state parameter,j*,which was developed for sands with fines,can be used in lieu j to provide a unifying framework for characterizing the undrained response of sands with non/low plasticity fines,irrespective of fines content(fc).The present work combines these two propositions,and by merely substituting j*for j into the aforementioned CS approach to capture the influence of fc.A series of static and cyclic triaxial tests were conducted,separately and independently of the concept of j*,for sand with up to fc of 30%.The clean sand was collected from Sabarmati river belt at Ahmedabad city in India which was severely affected during the Bhuj earthquake,2001.The experimental data gave a single relation for CRR and j*which was then used to assess liquefaction potential for a SPT based case study,where fc varies along the depth.The prediction matched with the field observation.     

Steady state and liquefaction characteristics of gravely sands

Liquefaction of loose and saturated soils during earthquakes and strong ground motions has been a major cause of damage to buildings and earth embankments as well as other civil engineering structures. In order to evaluate the liquefaction potential and steady state characteristics of gravely sand of south west Tehran,a subsoil exploration program conducted dividing the region into 10 zones. In each zone of 500 m × 500 m a borehole of 20 m deep was drilled. SPT was performed at one meter intervals in each borehole and a total of 200 samples were recovered. Soils of similar grain size distribution have been considered to have similar steady state characteristics,therefore consolidated undrained triaxial tests were performed on these soils of similar grain size distribution to evaluate the steady state strength. The steady state line for each soil type was derived. Comparing the steady state strengths with the shear stress due to an earthquake with a PGA of 0.35 g,the potential of sand liquefaction and .ow failure in soil layers has been evaluated and the settlement of soil due to the liquefaction phenomena is calculated. Finally some recommendations for estimating the steady state strength from simple SPT test in gravely sands are presented.     

颗粒材料的微观临界状态理论模型

存在临界状态是颗粒材料的一个重要特性。基于孔隙胞元的颗粒离散元方法对二维颗粒体进行双轴加载数值试验,在详细分析数值模拟结果的基础上,从微观几何组构的角度揭示了临界状态的存在机制。基于剪胀性原理,提出了以接触价键表征的微观临界状态理论模型,得到了接触价键与塑性剪切应变的关系表达式,理论模型的结果和二维离散元数值模拟得到的结果吻合较好。通过比较不同情况下数值结果和理论模型中的参数,得到以下结论：表征微观临界状态的参数（临界接触价键和达到临界状态所需要的塑性剪切应变）依赖于颗粒体的微观特性,如颗粒形状、表面摩擦性质、颗粒体的围压和初始孔隙比。     

基于接触价键的颗粒材料微观临界状态

用颗粒离散元法,分别对二维圆形、椭圆形颗粒体进行了双轴压缩数值模拟。微观尺度的变形是基于孔隙胞元和其中的变形来计算的,而单个孔隙胞元的变形通过周围颗粒的相对运动来计算。针对该方法提出了以接触价键（每个孔隙胞元的边数）来表征颗粒材料微观临界状态的理论。为了定义临界接触价键的极限值,分别讨论了摩擦系数较大、较小时的两种情况。文中给出了微观几何织构（包括接触价键、孔隙胞元的形状、孔隙比）随压缩变形的演变过程,比较了不同颗粒形状、颗粒间摩擦系数以及颗粒体的固结压力对颗粒体的微观力学性能的影响。计算结果表明,颗粒材料的微观临界状态并不是可以唯一表征的,而是受围压、摩擦系数,颗粒形状等参数的共同影响。     

The effect of drained pre-shearing on the undrained behaviour of loose sand with a small amount of fines

Stress history is recognised to play a major role in determining stress–strain behaviour of soil in undrained shearing. Most experimental studies on the effects of stress history on undrained behaviour are mainly limited to clean sand. In this paper, an experimental study carried out to investigate the effect of stress history on the undrained behaviour of loose sand with a small amount of fines is presented. Four series of triaxial compression tests, with different types of drained stress histories to near-failure prior to commencement of undrained shearing, were conducted. The experimental results indicate that drained pre-shearing to near-failure affects significantly the undrained behaviour of loose sand. In general, the drained pre-shearing improves the subsequent undrained behaviour of loose sand to the extent that liquefaction may not occur. It is shown that the effect of drained pre-shearing cannot be explained by the reduction in void ratio induced by drained pre-shearing. However, for specimens subjected to drained pre-shearing, $ p_{{{\text{d}}0}}^{\prime } $ / $ p_{{{\text{u}}0}}^{\prime } $ can be used as a parameter for analysing the effects of preloading history. It is also shown that for different preloading histories that brought the same change in void ratio or state parameter, drained pre-shearing to near-failure is the most effective, whereas pre-compression alone is the least effective in improving subsequent undrained behaviour of loose sand.     

饱和黄土稳态强度特性的试验研究

饱和黄土的稳态强度（残余强度）是黄土边坡是否发生流滑的关键因素,为了评价饱和黄土的残余强度就需要很好地了解饱和黄土的不排水剪切性能。通过对重塑黄土的固结不排水三轴试验,研究了饱和黄土的稳态强度特性。试验研究发现饱和黄土有两种典型的不排水剪切特性：稳态特性和准稳态特性,且大多数情况下饱和黄土总表现为稳态特性,只有疏松的黄土表现出准稳态特性。根据试验结果得出了黄土的稳态线与稳态强度线,用来分析黄土边坡的流滑机理。同时证明了饱和黄土稳态线的存在性和惟一性;探讨了描述黄土稳态性质的参数内摩擦角和黏聚力的物理含义;比较了饱和黄土与砂土稳态特性的差异。     

Simulation of liquefaction of unsaturated soil using critical state soil model

Several researchers have reported that the mean effective stress of unsaturated soils having a relatively high degree of saturation gradually decreases under fully undrained cyclic loading conditions, and such soils can be finally liquefied like saturated soils. This paper describes a series of simulations of fully undrained cyclic loading on unsaturated soils, conducted using an elastoplastic model for unsaturated soils. This model is a critical state soil model formulated using effective stress tensor for unsaturated soils, which incorporates the following concepts: (a) the volumetric movement of the state boundary surface containing the critical state line owing to the variation in the degree of saturation; (b) the soil water characteristic curve considering the effects of specific volume and hydraulic hysteresis; and (c) the subloading surface concept for considering the effect of density. Void air is assumed to be an ideal gas obeying Boyle's law. The proposed model is validated through comparisons with past results. The simulation results show that the proposed model properly describes the fully undrained cyclic behavior of unsaturated soils, such as liquefaction, compression, and an increase in the degree of saturation. Finally, the effects of the degree of saturation, void ratio, and confining pressure on the cyclic strength of unsaturated soils are described by the simulation results. The liquefaction resistance of unsaturated soils increases as the degree of saturation and the void ratio decrease, and as the confining pressure increases. Furthermore, the degree of saturation has a greater effect on the liquefaction resistance than the confining pressure and void ratio. Copyright © 2017 John Wiley & Sons, Ltd.     

非塑性细粒对饱和砂土液化特性影响的试验研究

利用空心圆柱扭剪仪对含非塑性细粒的饱和砂土进行单调加载和循环扭剪试验,研究了不同细粒含量饱和砂土的液化特性。试验结果表明：（1）最大孔隙比与最小孔隙比均随着细粒含量的增加呈先减小后增大的趋势,分别在20%和40%时达到最小。（2）细粒含量从0%增加到20%,体积应变逐渐增加;细粒含量从20%增加到40%时,体积应变逐渐减小;之后随着细粒含量从40%增加到60%,体积应变再次增大;细粒含量超过60%以后,体积应变再次递减。（3）随着细粒含量的增加,土样的峰值强度随之降低,应力-应变关系从应变硬化特征发展为理想的弹塑性。相变角在细粒含量为30%时达到最小值。（4）细粒含量越大,达到液化所需的循环次数越小,液化时的应变越小。（5）抗液化强度曲线与抗液化应力比的变化趋势一致,在小于界限细粒含量（30%）时,随着细粒含量的增加而减小。在界限细粒含量附近（30%～50%）时,随着细粒含量的增加而增大。在细粒含量增加到60%时出现明显的骤减,之后再次随着细粒含量的增加而增大。界限细粒含量在40%左右。     

基于判别分析法的地震砂土液化预测研究

将距离判别分析方法应用于砂土液化的预测问题中,建立了砂土液化预测的距离判别模型。选用震级、研究深度、震中距、标贯击数、地下水位及地震持续时间等6项指标作为判别因子,以大量的工程实例数据作为学习样本进行训练,建立了线性判别函数对待评样本进行了评价。研究结果表明,距离判别分析模型判别砂土液化效果良好,预测准确度高,回判估计误判率低,可望成为砂土液化预测的有效手段。     

A simple critical state interface model and its application in prediction of shaft resistance of non-displacement piles in sand

A simple semi-hyperbolic state-dependent constitutive model for sand-structure interfaces is proposed. The model formulation is consistent with critical state soil mechanics since void ratio evolves continuously with shear strain from initial state towards asymptotic critical state at extremely large shear strains. The model takes into account influence of normal stiffness on volume change and stress path. The proposed interface model is implemented in a pile segment analysis scheme for simulation of shaft resistance mobilization in non-displacement piles. Results reveal that the proposed pile segment analysis can well predict shaft resistance of model piles embedded in different sands.     

饱和粉砂不稳定性的试验研究

通过对净砂和级配良好粉砂(含10 %粉土)进行一系列三轴固结不排水试验（CU）,研究了粉土、孔隙比和围压对饱和粉砂不稳定性的影响。试验结果表明,净砂与粉砂在不排水剪切条件下均会出现应变软化现象（即不稳定性）。同一围压下脆性指数(IB)随孔隙比增加,但不稳定线的应力比随孔隙比增加而减小。引用等效粒间孔隙比(ege)后,净砂和粉砂在ege-ln p?平面上拥有基本相同的临界状态线。在临界状态理论及等效粒间孔隙比的基础上,提出在同一修正状态参数(?ge)下净砂和级配良好粉砂有相似的不稳定性。     

Compressional behavior of clayey sand and transition fines content

Clayey sand can be considered as a composite matrix of coarse and fine grains. The interaction between coarser and finer grain matrices affects the overall stress–strain behavior of these soils. Intergranular void ratio, e_s (which is the void ratio of the coarser grain matrix) can be utilized as an alternative parameter to express the compressive response of such soils. Oedometer tests conducted on reconstituted kaolinite–sand mixtures indicate that initial conditions, percentage of fines, and stress conditions influence the compression characteristics evidently. Tests showed that, up to a fraction of fines, which is named as transition fines content (FC_t), compression behavior of the mixtures is mainly controlled by the sand grains. When concentration of fines exceeds FC_t, kaolinite controls the compression. It was found that FC_t varies between 19% and 34% depending on the above mentioned factors. This range of fines content is also consistent with various values reported in literature regarding the strength alteration. Performed direct shear tests revealed that there is also a close relationship between transition fines content and shear strength, which is harmonic with the oedometer test results.     

On the modeling of the state dependency of granular soils

Experimental studies have revealed that principal elements of the mechanical behavior of granular soils like the angles of internal peak friction and dilatancy are highly influenced by the combined effect of soil density and mean principal effective stress. In the literature, various empirical correlations between these elements and some parameters indicating soil state have been suggested. Herein, by using two well-known empirical expressions for state dependent peak friction and dilatancy angles, proper constitutive equations are derived and implemented in a stress ratio-based bounding surface plasticity framework. It is shown that the modified model is capable of simulating sand response in either loose or dense states using a unique set of parameters.     

掺砂率对膨润土与砂混合物膨胀特性的影响

膨润土与砂混合物的膨胀特性是评估核废料深层地质处置工程长期性能的重要指标。对比不同膨润土及其与砂混合物的膨胀试验结果可知,对纯膨润土及其低掺砂率混合物,浸水膨胀完成后蒙脱石孔隙比em与竖向应力?v在双对数坐标内呈惟一的线性关系,利用该线性关系可预测浸水完成后不同竖向应力下的体积变化量及不同初始状态对应的膨胀力;对高掺砂率混合物,在砂骨架形成之前,em-?v线性关系成立,随着竖向应力的增大,砂骨架形成,对应的em值脱离em-?v线性关系,混合物中掺砂率越大,脱离该线性关系时的竖向应力就越小。砂骨架形成前,砂颗粒被蒙脱石包围,外力由蒙脱石承担,最终变形量由试样中单位体积蒙脱石的含量决定;砂骨架形成后,竖向应力最终由砂骨架和蒙脱石共同承担。利用砂骨架孔隙比的概念可确定各种不同掺砂率混合物形成砂骨架时的应力起偏点。同时,还可确定混合物能够形成砂骨架的掺砂率范围。