Equivalent granular state parameter and undrained behaviour of sand�Cfines mixtures

State parameter defined using void ratio, e, and the steady-state line has been shown to be effective in predicting the undrained behaviour of sand. However, steady-state line for sand with fines is dependent on fines content. To overcome this problem, the concept of equivalent granular void ratio, e*, has been well investigated. However, the conversion from e to e* has been essentially a back-analysis process. A methodology for converting e to e* without the need of a back-analysis process was first presented. The concept of equivalent granular state parameter, ψ*, defined in terms of e*, and equivalent granular steady-state line was then developed. An extensive experimental study was conducted to investigate whether ψ* can capture the effects of fines content, and thus can be used to correlate undrained behaviour of sand–fines mixtures without the need of separately considering the effects of fines content. This study suggested that the effective stress path and deviatoric stress–strain responses in undrained shearing can be correlated with the ψ* value at the start of undrained shearing irrespective of fines content.     

Comprehensive laboratory study on stress–strain of granular soils at constant global void ratio: combined effects of fabrics and silt content

The published literature has revealed conflicting results regarding the effect of low plastic fines fraction (I_p?≤?5.0%) on the mechanical behavior of sandy soils. For this reason, the use of different sample initial structures as (initial relative density approach, global void ratio index approach, etc.) could explain these different mechanical responses of granular materials. Thus, it is necessary to evaluate the quantitative aspect of the low plastic fines effects on the undrained monotonic response of sand-silt mixtures using the global void ratio approach. To achieve this goal, an experimental testing program through controlled monotonic triaxial tests was carried out on reconstituted saturated Chlef sand containing from 0 to 50% silt with an interval of 10% at three global void ratios (e?=?0.64, 0.66 and 0.68) and subjected to constant confining pressure (σ'₃?=?100 kPa). The different samples were reconstituted using two different preparation techniques: DFP and MT. The obtained results show that the low plastic fines content appears as a very relevant parameter in the characterization of the mechanical response of sand-silt mixture samples reconstituted at constant global void ratios, where the steady state shear strength and instability shear strength decreased with the increase in low plastic fines content up to the limiting fines contents (F_c?=?40% and F_c?=?10%) considering both studied initial structures (Dry funnel pluviation and Moist tamping), respectively. Beyond these thresholds fines contents, a reverse trend was observed for all parameters under study. Moreover, the test results indicate that the brittleness index, flow potential (V_f), friction index, equivalent void ratio (e*) and equivalent relative density (Dr*) could be considered as reliable parameters in the prediction of the mechanical behavior of the silty sand soils under study.

     

Experimental Study on Mechanical Behavior of Unsaturated Silty Sand in Constant Equivalent Granular Void Ratio

In this paper effect of fine mineralogy on mechanical behavior of unsaturated silty sand in different fine contents and divers confining pressure has been studied. All samples were molded with constant equivalent granular void ratio well-known parameter already proposed for characterizing silty sand behavior in saturated state. This manner of study allow to investigate also the validity of equivalent granular void ratio concept in unsaturated state. For this purpose, a series of triaxial tests were performed on the sand specimens with different percentages of silt in the undrained saturated (CU) and unsaturated (CW) conditions. The results showed that the material types and aggregate distribution of the fines have enormous effects on the silty sand behavior. In addition, the shear strength in the unsaturated specimens changed as a function of the initial applied matric suction. A fewer performance of equivalent intergranular void ratio in the case of unsaturated state in comparison of saturated states was observed.

     

Exploring the influence of interparticle friction on critical state behaviour using DEM

Understanding the extent to which discrete element method (DEM) simulations can capture the critical state characteristics of granular materials is important to legitimize the use of DEM in geomechanics. This paper documents a DEM study that considered the sensitivity of the critical state response characteristics to the coefficient of interparticle friction (μ) using samples with gradings that are representative of a real soil. Most of the features that are typically associated with sand behaviour at the critical state were seen to emerge from the DEM simulation data. An important deviation occurs when high μ values (μ ≥ 0.5) are used, as has been the case in a number of prior DEM studies. While there is a systematic variation in the critical state behaviour with μ for μ < 0.5, when μ ≥ 0.5, the behaviour at the critical state seems to be insensitive to further increases in μ. In contrast to observations of conventional soil response, when μ ≥ 0.5, the void ratio at the critical state initially increases with increasing mean effective stress (p′). Analysis of the DEM data and use of simple models of isolated force chains enabled some key observations. When ‘floating’ particles that do not transmit stress are eliminated from the void ratio calculation, the void ratio at the critical state decreases consistently with increasing p′. There is a transition from sliding to rolling behaviour at the contact points as μ increases. Beyond a limiting value of μ, further increases in μ do not increase the buckling resistance of individual strong force chains. Copyright © 2014 John Wiley & Sons, Ltd.     

Undrained shear strength response under monotonic loading of Chlef (Algeria) sandy soil

During the last mid-century, the Chlef area was strongly affected by two earthquakes. From the geological context, there were numerous ejections onto the ground level of great masses of sandy soils and large displacements of various forms of some building foundations. These damages are due to soil liquefaction problem. This loss of shear strength can be attributed to many factors. History of recent cases indicates that sand deposited with silt content is much more liquefiable than clean sand. Therefore, a deep understanding of silty sand behavior is needed for the liquefaction assessment of silty sandy soils. Moreover, during seismic shaking, the post-liquefaction behavior of silty sand and, consequently, the stability of structures founded on liquefied soil depend on the steady-state shear strength of soil. The objective of this laboratory investigation is to show the effect of silt contents and the relative density on the mechanical behavior of such soils in monotonic loading. In this context, a series of undrained triaxial tests were performed on reconstituted saturated silty sand samples with different fines content ranging from 0% to 40%. In all tests, the confining pressure was held constant to 100 kPa. The fines content and the global void ratio are expressed by means of the equivalent void ratio. Linear correlations relating the undrained residual shear strength of loose, medium dense, and dense (D _r?=?12%, 50%, and 90% before consolidation) sand–silt mixtures to the equivalent void ratio are obtained. The concept of the equivalent void ratio will then be used as a key parameter to express the dilatancy behavior of both clean and silty sand soils. Moreover, from the experimental results obtained, it is clear that the global void ratio cannot be used as a state parameter and may not represent the actual behavior of the soil as well.     

Rapid estimation of maximum and minimum void ratios of granular soils

Maximum and minimum void ratios (e_max and e_min) of granular soils are commonly used as indicators of many engineering properties. However, few methods, apart from laboratory tests, are available to provide a rapid estimation of both e_max and e_min. In this study, we present a theoretical model to map the densest and the loosest packing configurations of granular soils onto the void space. A corresponding numerical procedure that can predict both e_max and e_min of granular soils with arbitrary grain size distributions is proposed. The capacity of the proposed method is evaluated by predicting the maximum and minimum void ratios of medium to fine mixed graded sands with different contents of fines. The influence of the grain size distribution, characterized quantitatively by uniformity parameter and the fractal dimension, on e_max and e_min is discussed using the proposed method. Moreover, application of this method in understanding the controlling mechanism for the void ratio change during grain crushing is presented.

     

Constitutive modelling of granular materials using a contact normal-based fabric tensor

This paper presents a fabric tensor-based bounding surface model accounting for anisotropic behaviour (e.g. the dependency of peak strength on loading direction and non-coaxial deformation) of granular materials. This model is developed based on a well-calibrated isotropic bounding surface model. The yield surface is modified by incorporating the back stress which is proportional to a contact normal-based fabric tensor for characterising fabric anisotropy. The evolution law of the fabric tensor, which is dependent on both rates of the stress ratio and the plastic strain, rules that the material fabric tends to align with the loading direction and evolves towards a unique critical state fabric tensor under monotonic shearing. The incorporation of the evolution law leads to a rotational hardening of the yield surface. The anisotropic critical state is assumed to be independent of the initial values of void ratio and fabric tensor. The critical state fabric tensor has the same intermediate stress ratio (i.e. b value) and principal directions as the critical state stress tensor. A non-associated flow rule in the deviatoric plane is adopted, which is able to predict the non-coaxial flow naturally. The stress–strain relation and fabric evolution of model predictions show a satisfactory agreement with DEM simulation results under monotonic shearing with different loading directions. The model is also validated by comparing with laboratory test results of Leighton Buzzard sand and Toyoura sand under various loading paths. The comparison results demonstrate encouraging applicability of the model for predicting the anisotropic behaviour of granular materials.

     

Prediction of flow liquefaction instability of clean and silty sands

Adding a small amount of non-plastic silt to clean sands may lead to dramatic loss of shear strength and a noteworthy tendency toward contraction when the mechanical behavior of the mixture is compared with that of the clean host sand. Thus, simulation of the behavior of silty sands with varying fines content is still a challenging subject in geomechanics. A unified constitutive model for clean and silty sands is presented in this paper. To eliminate the factitious decrease of void ratio associated with inactive silt particles in various silty sand mixtures, the concept of equivalent void ratio is used in the model formulation instead of the global void ratio. In addition, the instantaneous soil state is expressed in terms of intergranular state parameter taking into account the combined influence of intergranular void ratio, mean principal effective stress and fines content. Then, dilatancy and plastic hardening modulus are directly linked to the intergranular state parameter. To improve the model capacity in simulation of cyclic tests, new features are added to the plastic hardening modulus. It is shown that the proposed model can reasonably reproduce the mechanical behavior as well as the onset of flow liquefaction instability of clean and silty sands using a unique set of parameters.     

Effect of fines content and void ratio on the saturated hydraulic conductivity and undrained shear strength of sand–silt mixtures

The hydraulic conductivity represents an important indicator parameter in the generation and redistribution of excess pore pressure of sand–silt mixture soil deposits during earthquakes. This paper aims to determine the relationship between the undrained shear strength (liquefaction resistance) and the saturated hydraulic conductivity of the sand–silt mixtures and how much they are affected by the percentage of low plastic fines (finer than 0.074 mm) and void ratio of the soil. The results of flexible wall permeameter and undrained monotonic triaxial tests carried out on samples reconstituted from Chlef river sand with 0, 10, 20, 30, 40, and 50 % non-plastic silt at an effective confining pressure of 100 kPa and two initial relative densities (D _r = 20, 91 %) are presented and discussed. It was found that the undrained shear strength (liquefaction resistance) can be correlated to the fines content, intergranular void ratio and saturated hydraulic conductivity. The results obtained from this study reveal that the saturated hydraulic conductivity (k _sat) of the sand mixed with 50 % low plastic fines can be, in average, four orders of magnitude smaller than that of the clean sand. The results show also that the global void ratio could not be used as a pertinent parameter to explain the undrained shear strength and saturated hydraulic conductivity response of the sand–silt mixtures.     

A compression model for sand–silt mixtures based on the concept of active and inactive voids

A compression model for sand–silt mixtures is needed in geotechnical engineering, for example in the analysis and prediction of deformation of levees and embankments due to internal erosion. In this paper, we introduce a novel concept of dividing the voids of a granular material into two hypothetical fractions: active and inactive voids. The active voids are kinematically available to the compression process. The inactive voids are kinematically unavailable to the compression process. The volume of active voids is dependent on the initial density and effective stress level. The volume of inactive voids is dependent on the amount of fines in the mixture. The current paper considers 1-D and isotropic compression behavior of sand–silt mixtures at stress levels lower than 2 MPa, so no substantial particle breakage is expected to occur. To successfully predict the void ratio for a sand–silt mixture during compression loading, we need (1) a mathematical expression for the evolution of the active void ratio during compression and (2) a relationship between the inactive void ratio and fines content of the mixture. For sand–silt mixtures with any amount of fines, the proposed model requires five material parameters, which are determined from two compression tests, and four minimum void ratio tests on sand–silt mixtures with different fines content. The performance of the proposed model is verified for six different types of sand–silt mixture with various fines contents, by comparing the predicted void ratios with the measured data from the experiments. The comparisons show a good agreement between the predictions and the measured data and prove the suitability of the proposed model for the prediction of compressibility of sand–silt mixtures with any amount of fines.     

Dominant grains network and behavior of sand–silt mixtures: stress–strain modeling

Stress–strain modeling of sand–silt mixtures is important in the analysis and design of earth structures. In this paper, we develop a stress–strain model that can predict the behavior of sand–silt mixtures with any amount of fines content. This model is based on a micromechanics approach, which involves mean‐field assumptions. For the mixtures with low amount of fines, the mechanical behavior is dominated by sand grains network. On the other hand, for the mixtures with high amount of fines, the mechanical behavior is dominated by silt grains network. Using this concept of dominant grains network, the behavior of mixtures with any amount of fines can be predicted from knowing the behavior of sand and silt, alone. We also modeled the critical state friction angle, critical state void ratio, and elastic stiffness for the mixtures as a function of fines content. The applicability of this developed stress–strain model is shown by comparing the simulated and measured results for two different types of sand–silt mixtures with full range of fines content. Copyright © 2012 John Wiley & Sons, Ltd.     

A study on the limit void ratio characteristics of medium to fine mixed graded sands

The minimum and maximum void ratios, corresponding to states of densest and loosest packing, of 111 systematically prepared mixed graded sand samples are determined with Method 2A and Method B according to ASTM D 4253 and ASTM D 4254 standards, respectively. Although, those standards are applicable to soils that may contain up to at most 15% fines content, for the harmony of the results even for samples having fines content greater 15%, no other methods are used throughout the experimental program. The test results show that 3rd degree polynomial equations derived from existing experimental data, as a function of packing material percentage, are quite reasonable (R² ≈ 1.0) to estimate the variation of minimum and maximum void ratios for the sands considered. Furthermore, error analysis of the limit void ratios is also carried out. It is found that predictability of maximum void ratio for the soil types and gradations considered is more accurate than that of minimum void ratio.     

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.     

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。     

The Effects of Fines on the Behaviour of a Sand Mixture

Intergranular void ratio, e _s, can be used as an alternative indicator to assess the mechanical properties of composite matrix of coarse and fine grains. In this paper, an intensive laboratory study of saturated coarse rotund sand and fine angular sand mixtures with various mix ratios is investigated by a series of oedometer and direct shear tests. Oedometer tests performed on the mixtures show that fines percentages and stress conditions affect the compression behaviours. Tests indicated that, up to a fraction of fines, which is named as transition fines content (FC_t), compression behaviour of the mixture is mainly governed by the sand grains. As the percentage of fines exceeds FC_t finer grains govern the compression. Performed direct shear tests revealed that there is a relationship between the FC_t and shear strength, which is harmonic with the oedometer test results.     

Laboratory Investigation into the Effects of Silty Fines on Liquefaction Susceptibility of Chlef (Algeria) Sandy Soils

In a number of recent case studies, the liquefaction of silty sands has been reported. To investigate the undrained shear and deformation behaviour of Chlef sand–silt mixtures, a series of monotonic and stress-controlled cyclic triaxial tests were conducted on sand encountered at the site. The aim of this laboratory investigation is to study the influence of silt contents, expressed by means of the equivalent void ratio on undrained residual shear strength of loose, medium dense and dense sand–silt mixtures under monotonic loading and liquefaction potential under cyclic loading. After an earthquake event, the prediction of the post-liquefaction strength is becoming a challenging task in order to ensure the stability of different types of earth structures. Thus, the choice of the appropriate undrained residual shear strength of silty sandy soils that are prone to liquefaction to be used in engineering practice design should be established. To achieve this, a series of undrained triaxial tests were conducted on reconstituted saturated silty sand samples with different fines contents ranging from 0 to 40 %. In all tests, the confining pressure was held constant at 100 kPa. From the experimental results obtained, it is clear that the global void ratio cannot be used as a state parameter and may not characterize the actual behaviour of the soil as well. The equivalent void ratio expressing the fine particles participation in soil strength is then introduced. A linear relationship between the undrained shear residual shear strength and the equivalent void ratio has been obtained for the studied range of the fines contents. Cyclic test results confirm that the increase in the equivalent void ratio and the fines content accelerates the liquefaction phenomenon for the studied stress ratio and the liquefaction resistance decreases with the increase in either the equivalent void ratio or the loading amplitude level. These cyclic tests results confirm the obtained monotonic tests results.     

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.     

Formulation of a unified constitutive model for clays and sands

This paper presents a new generalized effective stress model, referred to as MIT-S1, which is capable of predicting the rate independent, effective stress–strain–strength behaviour of uncemented soils over a wide range of confining pressures and densities. Freshly deposited sand specimens compressed from different initial formation densities approach a unique condition at high stress levels, referred to as the limiting compression curve (LCC), which is linear in a double logarithmic void ratio, e, mean effective stress space, p′. The model describes irrecoverable, plastic strains which develop throughout first loading using a simple four-parameter elasto-plastic model. The shear stiffness and strength properties of sands in the LCC regime can be normalized by the effective confining pressure and hence can be unified qualitatively, with the well-known behaviour of clays that are normally consolidated from a slurry condition along the virgin consolidation line (VCL). At lower confining pressures, the model characterizes the effects of formation density and fabric on the shear behaviour of sands through a number of key features: (a) void ratio is treated as a separate state variable in the incrementally linearized elasto-plastic formulation: (b) kinematic hardening describing the evolution of anisotropic stress–strain properties: (c) an aperture hardening function controls dilation as a function of ‘formation density’; and (d) the use of a single lemniscate-shaped yield surface with non-associated flow. These features enable the model to describe characteristic transitions from dilative to contractive shear response of sands as the confining pressure increases. This paper summarizes the procedures used to select input parameters for clays and sands, while a companion paper compares model predictions with measured data to illustrate the model capability for describing the shear behaviour of clays and sands. Copyright © 1999 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。