The prediction of equivalent granular steady state line of loose sand with fines

Void ratio has been used as a state variable for predicting the liquefaction behaviour of soils under the critical state, sometimes also referred to as the steady state, framework. Recent publications show that void ratio may not be a good parameter for characterising sand with fines because the steady state line (or curve) in the e-log(p′) space moves downward with increase in fines content until it reaches a threshold value referred to as the threshold fines content (TFC). Recently, an alternative state variable, referred to as the equivalent granular void ratio, has been proposed to resolve this problem. To calculate this alternative state variable, an additional parameter ‘b’ is needed. This parameter ‘b’ represents the fraction of fines that actively participate in the force structure of the solid skeleton. However, predicting the ‘b’ value is problematic. This paper examines the factors affecting the ‘b’ value based on published work on binary packing. This leads to a simple semi-empirical equation for predicting the ‘b’ value based on fines size and fines content. The proposed equations were evaluated with published data sets. Then, the concept of an equivalent granular steady state line is proposed. This concept was used to predict the location of SSLs for sand with different fines content from either the SSL of clean sand or the SSL of sand with a given fines content. The predictions agree well with experimental results.     

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.     

Modelling undrained behaviour of sand with fines and fabric anisotropy

Acta Geotechnica - Fabric anisotropy and fines content (fc) in sands modify significantly their mechanical behaviour, particularly as related to static liquefaction under undrained conditions. The...     

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。     

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.     

Liquefaction triggering in silty sands: effects of non-plastic fines and mixture-packing conditions

Acta Geotechnica - During recent seismic events, such as 2010 Darfield and 2016 Ecuador earthquakes, widespread liquefaction has been observed in sand deposits with silt content. Nevertheless, the...     

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     

Limited flow characteristics of sand with fines under cyclic loading

Experimental studies on a sand with a well-graded low plasticity fines were conducted to study a number of issues related to limited flow. Cyclic behaviour in relation to instability and limited flow are compared with corresponding monotonic behaviour. A single set of rules for a range of fines contents was proposed to correlate cyclic and monotonic behaviour.     

含细粒砂土反常剪切行为的数值模拟研究

针对含细颗粒砂土的反常剪切行为,开展了双轴剪切试验的数值模拟,从宏细观角度分析了其反常剪切行为发生的内在机制。数值模拟结果表明,增加围压能提高含细颗粒砂土的抗剪切液化能力,该反常行为的根本原因在于围压上升使得粗细颗粒更有效地参与了力链传递,增加了颗粒间的接触,增强了土体的密实度。细颗粒在土骨架中的移动对砂土的液化起着至关重要的作用,而粗颗粒仅起次要作用。研究表明,细颗粒在剪切过程中会持续从有效土骨架中移出成为无效颗粒,而部分粗颗粒也因失去细颗粒的支撑作用会脱离土骨架,直至试样最终液化。细颗粒一般参与土骨架中的弱力链,而粗颗粒则一般参与强力链,导致细颗粒较粗颗粒更容易在土骨架中移动。     

The response of flexible pipes buried in sand to static surface stress

A series of laboratory tests on thin-walled PVC-U (i.e. very flexible) pipes buried in sand is described. The tests were conducted in a glass-fronted test tank, the pipe being positioned up against the glass with its longitudinal axis perpendicular to the glass. This allowed direct observation of the sand–pipe interactions. Photographs were taken through the glass allowing discrete measurement of pipe and soil displacements during pipe installation and subsequent surface loading. This paper discusses the influences on pipe response of installation method, cover depth and pipe stiffness as increasing static surface stress was applied. The results of the laboratory tests indicate very clearly the importance of well-controlled backfilling around flexible buried pipes to ensure their long-term performance. The stiffness of the pipe affects the way it behaves and hence its performance in resisting applied stresses. This is demonstrated by the observed changes in arching effects above pipes of different stiffness. The effect of increasing cover depth is demonstrated and confirms previous research findings regarding the influence of the ground surface on pipe performance. The results clearly demonstrate the valuable insight afforded by direct observation of the soil–pipe interaction during installation and the subsequent loading of flexible pipes.     

Experimental and theoretical investigation of the high‐pressure,undrained response of a cohesionless sand

Key in predicting stability in sands during dynamic events is gaining a fundamental understanding of the physics of its deformation and failure at high pressures. In this paper are reported results of an experimental investigation into the high‐pressure (up to 700 MPa) mechanical response of Quikrete sand. During all triaxial compression tests, the material exhibited hardening up to failure while both compressibility and dilatancy regimes of the volumetric response were observed. Furthermore, the transition from compressibility to dilatancy was found to be highly dependent on confining pressure. By performing triaxial compression tests with several creep stages followed by unloading–reloading cycles, the time influence of the overall response was detected. Using the experimental data, a new model that captures both compressibility and dilatancy has been developed. Comparison between model predictions and data showed that the proposed model describes well the main characteristics of the high‐pressure response of sand. Copyright © 2012 John Wiley & Sons, Ltd.     

Micromechanics of undrained response of dilative granular media using a coupled DEM-LBM model: A case of biaxial test

In this paper the Discrete Element Method (DEM) is coupled with the Lattice-Boltzmann Method (LBM) to model the undrained condition of dense granular media that display significant dilation under highly confined loading. DEM-only models are commonly used to simulate the micromechanics of an undrained specimen by applying displacements at the domain boundaries so that the specimen volume remains constant. While this approach works well for uniform strain conditions found in laboratory tests, it doesn’t realistically represent non-uniform strain conditions that exist in the majority of real geotechnical problems. The LBM offers a more realistic approach to simulate the undrained condition since the fluid can locally conserve the system volume. To investigate the ability of the DEM-LBM model to effectively represent the undrained constraint while conserving volume and accurately calculating the stress path of the system, a two dimensional biaxial test is simulated using the coupled DEM-LBM model, and the results are compared with those attained from a DEM-only constant volume simulation. The compressibility of the LBM fluid was found to play an important role in the model response. The compressibility of the fluid is expressed as an apparent Skempton’s pore pressure parameter B. The biaxial test, both with and without fluid, demonstrated particle-scale instabilities associated with shear band development. The results show that the DEM-LBM model offers a promising technique for a variety of geomechanical problems that involve particle-fluid mixtures undergoing large deformation under shear loading.     

DEM studies on the effect of particle breakage on the critical state behaviours of granular soils under undrained shear conditions

Acta Geotechnica - A number of discrete element analyses of undrained triaxial shear tests on crushable assemblies are performed using 3-dimensional particle flow code (PFC3D). The undrained shear...     

基于统一状态参数模型的砂中柱孔扩张分析

目前关于不同初始状态砂土砂中柱孔扩张的研究结果还缺乏更深层次的分析,并且由于没有考虑砂土屈服面形状因素的影响,造成许多研究成果难以在不同类型砂土中推广。采用统一状态参数模型（clay and sand model,CASM）和Rowe剪胀方程来描述砂的弹塑性变形特点,结合大变形理论并引入辅助变量,推导了基于拉格朗日描述的弹塑性区内砂土体积和有效应力的一阶偏微分方程组,在此基础上结合弹塑性区的边界条件和柱孔扩张弹性解,建立了饱和砂中的排水柱孔扩张半解析解。结果表明,CASM可以通过改变应力状态参数n和间距比r*的值使砂的屈服面形状发生改变,进而使文中解答能够用于不同类型饱和砂中的排水柱孔扩张计算,其中n、r*值越大,松砂初次屈服时的偏应力和后续砂中的扩孔压力越大,但中密、密实砂土中的情况与松砂完全相反。极限扩孔压力随砂土初始状态参数的减小而增大,相应的砂土体积也从一直剪缩变为先剪胀后剪缩,弹塑性区半径先减小后增大,硬化行为从一直硬化变为先软化后硬化。静止侧压力系数增大时,极限扩孔压力也增大,但对砂的体积变化规律影响不大。本研究可为相关岩土工程问题分析提供可靠理论支持。     

基于Eshelby张量和Mori-Tanaka等效方法的砂卵石土等效弹性模量研究

砂卵石土是物理力学性质既不同于砂土也不同于完整岩体的离散体,将其简化为砂土为基体,卵石为椭球形夹杂的两相复合材料。在小变形条件下,考虑卵石的含量和分布,采用Eshelby张量和Mori-Tanaka等效方法,运用替换迭代方式,从理论上推导出等效柔度张量一般性计算方程;重点研究卵石为球形时（椭球的一种特殊情况）砂卵石土等效弹性模量,通过编写程序求得其数值解,并与相关数值试验和理论进行对比。结果表明,此理论计算方法精度较以前的理论计算方法精度有大幅提高,当卵石体积分数小于50%时,理论计算结果与数值试验结果吻合较好,其结果可用于判断砂卵石土宏观力学特性,有利于地下工程应用;当体积分数大于50%时,理论计算结果和数值试验结果有一定误差。     

Effect of grading characteristics on the undrained shear strength of sand: review with new evidences

In this paper, the shear strength of saturated pure sand and sand–silt mixture is evaluated by monotonic undrained triaxial tests that were carried out on reconstituted specimens at same relative densities and a constant confining pressure (σ ₃?=?300 kPa). The test results were used to conclude on the effect of low non-plastic contents (0–20 %) and grading characteristics on the liquefaction resistance of the sand. The test results indicate that the undrained residual strength reduced with the increase of non-plastic fine content. Also, shear strength of gap-graded sand mixed with low non-plastic fine content increases with decrease in effective size (D ₅₀). In other words, in this state, we can use the D ₅₀ as a parameter to control of silty sand’s undrained resistance. Besides, the undrained residual strength of pure sand specimens with same effective size increases due to increase of coefficient of uniformity (C _u).     

Coupling pore-water pressure with distinct element method and steady state strengths in numerical triaxial compression tests under undrained conditions

The undrained shear behaviour of sands has been a key topic after the devastating geo-disasters during the 1964 Niigata Earthquake in Japan. Extensive geo-technical soil tests, especially undrained triaxial compression tests, have revealed that the liquefaction phenomenon was the major cause for the disaster expansions. To numerically reproduce the liquefaction phenomenon, the pore-water pressure was coupled with a distinct element method. In this model, the dynamic changes in pore-water pressure were taken into consideration by the changes in volumetric strain and modulus of compressibility of water in the respective measurement spheres. Fluid-flows among the measurement spheres were controlled by Darcy’s law. The effective stress paths and steady state strengths in undrained triaxial compression tests associated with the wide ranges of initial void ratio were investigated. The effective mean stresses of medium-dense to dense numerical specimens at the steady state were negatively proportional to the initial void ratio. Loose numerical specimens reproduced quasi-liquefaction with the effective mean stresses that were less than 25% of the initial value. The medium-dense numerical specimens reproduced the phase transformation that was a typical characteristic of granular materials. The rolling restraints did not much influence of the effective angle of internal friction but strongly affected pore-water pressure behaviour within a certain range of initial void ratio.     

减饱和松砂静态液化的水-气两相流耦合分析

减饱和法是一种通过减小饱和砂土地基中的饱和度,提高地基抗液化强度的新方法。基于水-气两相流反应与土体骨架变形的耦合模拟方法,建立了单调加载条件下减饱和砂土静态液化的数值分析模型。开展了减饱和松砂的三轴不排水试验数值模拟研究,与室内试验结果对比,发现两相流模型能够准确描述减饱和砂土加载过程中的应力-应变关系、应力路径及孔隙水压力增长规律,验证了两相流模拟方法的正确性。数值分析结果还表明,加载过程中减饱和松砂中的饱和度会增加,直至达到一个稳定值,当围压一定时,减饱和松砂加载结束时的饱和度与初始饱和度呈线性关系;且砂土中气体会在荷载作用下被压缩,使得减饱和砂土在不排水条件下发生剪缩。计算发现,当砂土饱和度从100%减小到94.5%时,孔隙水压力系数B值会减小约80%,最大孔隙压力值会降低40%~50%,不排水剪切强度提高2.0~2.5倍,残余强度会提升10倍以上,由此可知,此为减饱和法抗液化的主要机制,而基质吸力不是减饱和法提高砂土抗剪强度的主要原因。     

Evaluation of deformation parameter for deep excavation in sand through case histories

This study back analyzed deformation parameters of in situ sand through two excavation case histories in Kaohsiung, Taiwan. Two main features are highlighted; deformation prediction based on monitoring data at the first excavation stage and in situ Young’s modulus evaluation for sand considering monitoring data at the overall excavation stages. The former tends to establish a reliable method to predict the wall deflection at the critical stage based on the data at the first stage and the latter to enrich the limited database of Young’s modulus correlation for sand, specifically applicable for deep excavations analysis. The two constitutive models, linear elastic perfectly plastic and non-linear stress–strain constitutive models, were selected. The stiffness parameters of the models were discretely distributed along the subdivided soil body mesh to reflect the effect of overburden pressure on the in situ soil. In addition, relationship between Standard Penetration Test value (SPT-N value) and Young’s modulus and relationships for estimating the in situ Young’s modulus of the Kaohsiung sand as a function of depth were evaluated. The results greatly enhanced a framework for estimating the in situ Young’s modulus of sand.     

Discrete element modeling of static liquefaction of shield tunnel face in saturated sand

The failure mechanism and limit support pressure are essential factors for the stability assessment of tunnel face during shield tunneling. Previous studies were mostly based on the assumption that soil fails when the plastic limit is reached. The static liquefaction of saturated sand at pre-failure state often largely reduces shear strength; a stable tunnel face could be destabilized and even collapses abruptly. This paper aims to explore the static liquefaction failure of tunnel face in saturated sands by 3D discrete element simulation. The particle shape is considered by using clump composed of two identical spheres, and the micro-material parameters are calibrated by fitting against triaxial tests. The tunnel face is initially supported by the earth pressure at rest, and then the pressure is reduced by applying a displacement on the free surface until soil body completely collapses. The second-order work during the unloading process is calculated, and a negative value denotes the initiation of static liquefaction. The distribution of negative second-order work point shows the initiation and propagation of static liquefaction. The ultimate failure mode is shown to be composed of a sliding wedge and an overlying chimney, and the chimney is confined to a local area for soil arching. The experienced stress path of tunnel face verifies the existence of static liquefaction instability, indicating the stability analysis should consider static liquefaction rather than simply using the conventional plastic limit state analysis.