Predicting onset of cyclic instability of loose sand with fines using instability curves

This study utilises the equivalent granular state parameter, ψ^⁎, as a key parameter for studying static and cyclic instability and their linkage. ψ^⁎ can be considered as a generalisation of the state parameter as first proposed by Been and Jefferies so that the influence of fines content in addition to stress and density state can be captured. Test results presented in this study conclusively showed that ψ^⁎ at the start of undrained shearing and η_IS, the stress ratio at onset of static instability, can be described by a single relationship irrespective of fines content for both compression and extension shearing. This single relationship is referred as instability curve. However, the instability curve in extension shearing is different from that of compression. In this paper, the capacity of the instability curve in predicting triggering of cyclic instability was evaluated experimentally. An extensive series of undrained one-way (compression) and non-symmetric two-way cyclic triaxial tests, in addition to monotonic triaxial tests in both compression and extension were conducted for this evaluation. Furthermore, a published database for Hokksund sand with fines was also used. Test results show that cyclic instability was triggered shortly after the cyclic effective stress path crossed the estimated η_IS-zone(s) as obtained from instability curve(s) irrespective of whether instability occurs in the compression or extension side.     

Intergrain contact density indices for granular mixes I： Framework

Mechanical behavior such as stress-strain response, shear strength, resistance to liquefaction, modulus, and shear wave velocity of granular mixes containing coarse and fine grains is dependent on intergrain contact density of the soil. The global void ratio e is a poor index of contact density for such soils. The contact density depends on void ratio, fine grain content （Cv）, size disparity between particles, and gradation among other factors. A simple analysis of a two-sized particle system with large size disparity is used to develop an understanding of the effects of Cv, e, and gradation of coarse and fine grained soils in the soil mix on intergrain contact density. An equivalent intergranular void ratio （ec）oq is introduced as a useful intergrain contact density for soils at fines content of less than a threshold value Crth. Beyond this value, an equivalent interfine void ratio （ef）eq is introduced as a primary intergrain contact density index. At higher values of Cv beyond a limiting value of fine grains content CVL, an interfine void ratio ef is introduced as the primary contact density index. Relevant equivalent relative density indices （Drc）eq and （Drf）eq are also presented. Experimental data show that these new indices correlate well with steady state strength, liquefaction resistance, and shear wave velocities of sands, silty sands, sandy silts, and gravelly sand mixes.     

Evaluation of static and dynamic properties of sand–fines mixtures through the state and equivalent state parameters

The results of an experimental investigation on sands with low plastic fines content are presented. Specimens with a low plastic fines content of 0%, 15%, 30%, 40%, 50% and 60% by weight were tested in drained and undrained triaxial compression tests. The soil specimens were tested under three different categories: (1) at a constant void ratio index; (2) at the same peak deviator stress in a triaxial test; and (3) at a constant relative density. By a combination with our published experimental data in recent years, the critical state line and various state parameters have been proposed and discussed for a further understanding the behavior of sand–fines mixtures. Results indicated that a unique critical line was obtained from drained and undrained triaxial compression tests for each fines content. The effects of fines content on critical state line (CSL) were recognized and discussed. In addition, the results revealed that normalized peak undrained shear stress, cyclic resistance ratio, and compression index were found to be a good correlation with state parameter Ψ as well as equivalent state parameter Ψ*. An increasing state parameter decreased the normalized peak undrained shear stress, and cyclic resistance ratio; however, the compression index increased with an increase in state parameter. Finally, there were no correlations such as the coefficient of consolidation–state parameter and maximum shear modulus–state parameter due to the different testing condition.     

Intergrain contact density indices for granular mixes II： Liquefaction resistance

Whether the presence of non-plastic silt in a granular mix soil impact its liquefaction potential and how to evaluate liquefaction resistance of sand containing different amounts of silt contents are both controversial issues. This paper presents the results of an experimental evaluation to address these issues. Two parameters, namely, equivalent intergranular void ratio （ec）eq and equivalent interfine void ratio （ef）eq, proposed in a companion paper （Thevanayagam, 2007） as indices of active grain contacts in a granular mix, are used to characterize liquefaction resistance of sands and silty sands. Results indicate that, at the same global void ratio （e）, liquefaction resistance of silty sand decreases with an increase in fines content （Cv） up to a threshold value （Crth）. This is due to a reduction in intergrain contact density between the coarse grains. Beyond Crth, with further addition of fines, the interfine contacts become significant while the inter-coarse grain contacts diminish and coarse grains become dispersed. At the same e, the liquefaction resistance increases and the soil becomes stronger with a fttrther increase in silt content. Beyond a limiting fines content （CrL）, the liquefaction resistance is controlled by interfine contacts only. When Cr〈Crth, at the same （e）eq, the liquefaction resistance of silty sand is comparable to that of the host clean sand at a void ratio equal to （ec）eq. When CF〉CFth, at the same （ef）eq, the cyclic strength of a sandy silt is comparable to the host silt at a void ratio equal to （ef）eq.     

Effect of physical parameters on static undrained resistance of sandy soil with low silt content

Previous researches concerning the behavior of sand mixed with non-plastic fine show that the void ratio related to sand grains (e_c) plays a more important role in comparison with the total void ratio, where soil undrained resistance will be improved due to increase in FC at the constant e_c. In spite of this fact, the recent works indicate that e_c is unable to show perfectly the role of the non-plastic fines that are in voids between sand grains. For this reason, an equivalent void ratio (e_c)_eq has been defined that takes into account the non-plastic fine participation ratio in the soil bearing skeleton. In the present work, the generality of the expression of (e_c)_eq is verified. For this, a set of static undrained triaxial tests were performed. The results of tests indicate that the undrained behavior of a given sand mixed with different percentages of non-plastic fine can be described by (e_c)_eq. But if the grading curves of sand change, we cannot find a logic retention between (e_c)_eq and undrained resistance of soil, unless the physical and mechanical characteristics of soil are well introduced in expression of (e_c)_eq.     

Liquefaction characteristics of gap-graded gravelly soils in K0 condition

A series of undrained cyclic direct simple shear tests, which used a soil container with a membrane reinforced with stack rings to maintain the K₀ condition and integrated bender elements for shear wave velocity measurement, were performed to study the liquefaction characteristics of gap-graded gravelly soils with no fines content. The intergrain state concept was employed to categorize gap-graded sand–gravel mixtures as sand-like, gravel-like, and in-transition soils, which show different liquefaction characteristics. The testing results reveal that a linear relationship exists between the shear wave velocity and the minor fraction content for sand–gravel mixtures at a given skeleton void ratio of the major fraction particles. For gap-graded gravelly sand, the gravel content has a small effect on the liquefaction resistance, and the cyclic resistance ratio (CRR) of gap-graded gravelly sands can be evaluated using current techniques for sands with gravel content corrections. In addition, the results indicate that the current shear wave velocity (V_s) based correlation underestimates the liquefaction resistance for V_s values less than 160 m/s, and different correlations should be proposed for sand-like and gravel-like gravelly soils. Preliminary modifications to the correlations used in current evaluations of liquefaction resistance have thus been proposed.     

Shear wave velocity-based evaluation and design of stone column improved ground for liquefaction mitigation

The evaluation and design of stone column improvement ground for liquefaction mitigation is a challenging issue for the state of practice. In this paper, a shear wave velocity-based approach is proposed based on the well-defined correlations of liquefaction resistance (CRR)-shear wave velocity (V _s)-void ratio (e) of sandy soils, and the values of parameters in this approach are recommended for preliminary design purpose when site specific values are not available. The detailed procedures of pre- and post-improvement liquefaction evaluations and stone column design are given. According to this approach, the required level of ground improvement will be met once the target V _s of soil is raised high enough (i.e., no less than the critical velocity) to resist the given earthquake loading according to the CRR-V _s relationship, and then this requirement is transferred to the control of target void ratio (i.e., the critical e) according to the V _s-e relationship. As this approach relies on the densification of the surrounding soil instead of the whole improved ground and is conservative by nature, specific considerations of the densification mechanism and effect are given, and the effects of drainage and reinforcement of stone columns are also discussed. A case study of a thermal power plant in Indonesia is introduced, where the effectiveness of stone column improved ground was evaluated by the proposed V _s-based method and compared with the SPT-based evaluation. This improved ground performed well and experienced no liquefaction during subsequent strong earthquakes.     

Effect of overconsolidation ratio on dynamic properties of binary mixtures of silica particles

Overconsolidated soils are ubiquitous in nature due to multiple mechanisms; however, the stress-history-based studies of small strain stiffness on binary mixtures, such as silty sand, are limited even though natural sand deposits are commonly mixtures of sand particles with varying amounts of fines. Consequently, this study quantified the stress-history-based dynamic properties of binary mixtures, such as sand-sand mixtures with different size small particles, and silty sand mixtures with small amounts of non-plastic fines, up to the critical fines content. By performing bender element tests on those mixtures according to fines content, size ratio, and overconsolidation ratio, the stress-history-based G_max of binary mixtures was evaluated. For the relevant data analysis, the OCR (overconsolidation ratio) exponent in the G_max formulation was expressed in terms of stress exponents during loading and unloading. It was found that the effect of OCR on the estimation of G_max increased with a decrease in size ratio (or increase in size difference), since the stress exponents during loading increased more significantly with a decrease in size ratio due to the pronounced change in interparticle coordination between large grains. However, the variation of stress exponents during unloading of different mixtures was relatively small due to the prevalent elastic deformation. It was demonstrated that the maximum stress history effect of tested mixed soils was observed at a fines content of approximately 5%, which was smaller than critical fines content of silty sand. This behavior was attributable to the delay in critical fines content observed during unloading, when compared to that observed during loading.     

Absolute18O content of standard mean ocean water

The absolute values of the¹⁸O/¹⁶O ratio (R_s) and the relative¹⁸O content (X_s) in SMOW have been determined by comparing SMOW mass spectrometrically with well-defined synthetic mixtures of pure D₂¹⁸O and H₂¹⁶O. The results are:R_S = (2005.20 ± 0.45) × 10^?6, X_S = (2000.45 ± 0.45) × 10^?6     

TDR pressure cell for monitoring water content retention and bulk electrical conductivity curves in undisturbed soil samples

The water retention curve (θ(ψ)), which defines the relationship between soil volumetric water content (θ) and matric potential (ψ), is of paramount importance in characterizing the hydraulic behaviour of soils. However, few methods are so far available for estimating θ(ψ) in undisturbed soil samples. We present a new design of TDR‐pressure cell (TDR‐Cell) for estimating θ(ψ) in undisturbed soil samples. The TDR‐Cell consists of a 50‐mm‐long and 50‐mm internal diameter stainless steel cylinder (which constitutes the outer frame of a coaxial line) attached to a porous ceramic disc and closed at the ends with two aluminium lids. A 49‐mm‐long and 3‐mm‐diameter stainless steel rod, which runs longitudinally through the centre of the cylinder, constitutes the inner rod of a coaxial TDR probe. The TDR‐Cell was used to determine the θ(ψ) curves of a packed sand and seven undisturbed soil samples from three profiles of agricultural soils. These θ(ψ) curves were subsequently compared to those obtained from the corresponding 2‐mm sieved soils using the pressure plate method. Measurements of bulk electrical conductivity, σ_a, as a function of the water content, σ_a(θ), of the undisturbed soil samples were also performed. An excellent correlation (R² = 0·988) was found between the θ values measured by TDR on the different undisturbed soils and the corresponding θ obtained from the soil gravimetric water content. A typical bimodal θ(ψ) function was found for most of the undisturbed soil samples. Comparison between the θ(ψ) curves measured with the TDR‐Cell and those obtained from the 2‐mm sieved soils showed that the pressure plate method overestimates θ at low ψ values. The σ_a(θ) relationship was well described by a simple power expression (R² > 0·95), in which the power factor, defined as tortuosity, ranged between 1·18 and 3·75. Copyright © 2011 John Wiley & Sons, Ltd.     

Correlation of shear wave velocity with liquefaction resistance based on laboratory tests

According to the results of cyclic triaxial tests on Hangzhou sands, a correlation is presented between liquefaction resistance and elastic shear modulus. Material-dependent but independent of confining stress, shows the linear relation of (σ_d/2)^1/2 with G_max. For its application to different soils, a method proposed by Tokimatsu [Tokimatsu K, Uchida A. Correlation between liquefaction resistance and shear wave velocity. Soils Found 1990:30(2):33–42] is utilized to normalize the shear modulus with respect to minimum void ratio. A simplified equation is established to evaluate the liquefaction potential by shear-wave velocity. The critical shear-wave velocity of liquefaction is in linear relation with 1/4 power of depth and the peak horizontal ground surface acceleration during earthquakes. The equation proposed in this paper is compared with previous methods especially the procedure proposed by Andrus [RD Andrus, KH Stokoe. Liquefaction resistance of soils from shear-wave velocity. J Geotech Geoenviron Eng 2000:126(11):1015–25]. The results show its simplicity and effectiveness when applied to sands, but more validation or modification is needed for its application to sand with higher fines content.     

Instability of sand–silt mixtures

The instability of the sand–silt mixtures with different amount of fines contents were studied in this paper. It showed that the slope of the instability lines increases with the increasing relative densities, and it approaches the slope of the failure line (steady state line) at a high relative density. The relationship between the peak stress ratio and the intergranular void ratio can be described by a common curve for all the mixtures with fines contents less than the transitional fines content. There may also exist a unique curve for the relationship between the peak stress ratio and interfine void ratio for the mixtures with fines contents higher than the transitional fines content. If the yield strength ratio is used instead of the peak stress ratio, the relationships can be characterized in the same way.     

Non-plastic silty sand liquefaction,screening, and remediation

Assessing liquefaction potential, in situ screening using cone penetration resistance, and liquefaction-remediation of non-plastic silty soils are difficult problems. Presence of silt particles among the sand grains in silty soils alter the moduli, shear strength, and flow characteristics of silty soils compared to clean host sand at the same global void ratio. Cyclic resistance (CRR) and normalized cone penetration resistance (q_c1N) are each affected by silt content in a different way. Therefore, a unique correlation between cyclic resistance and cone resistance is not possible for sands and silty sands. Likewise, the response of silty soils subjected to traditional deep dynamic compaction (DC) and vibro-stone column (SC) densification techniques is influenced by the presence of silt particles, compared to the response in sand. Silty soils require drainage-modifications to make them amenable for dynamic densification techniques. The first part of this paper addresses the effects of silt content on cyclic resistance CRR, hydraulic conductivity k, and coefficient of consolidation C_v of silty soils compared to clean sand. The second part of the paper assesses the effectiveness of equivalent intergranular void ratio (e_c)_eq concept to approximately account for the effects of silt content on CRR. The third part of the paper explores the combined effects of silt content (viz effects of (e_c)_eq, k, and C_v) on q_c1N using laboratory model cone tests and preliminary numerical simulation experiments. A possible inter-relationship between q_c1N, CRR, accommodating the different degrees of influence of (e_c)_eq, k, and C_v on q_c1N and CRR, is discussed. The fourth part of the paper focuses on the detrimental effects of silt content on the effectiveness of DC and SC techniques to densify silty soils for liquefaction-mitigation. Finally, the effectiveness of supplemental wick drains to aid drainage and facilitate densification and liquefaction mitigation of silty sands using DC and SC techniques is discussed.     

Evaluation and modeling of runoff and sediment yield for different land covers under simulated rain in a semiarid region of Brazil

This paper quantifies the runoff and sediment yield for four different land covers in a semiarid region of Brazil. The WESP model, a distributed, event-oriented runoff-erosion model, was applied and its physical parameters, N_s and K_R, were adjusted based on observed runoff and sediment yield data using simulated rainfall with an average intensity of 53 mm h^-1. The sediment yield obtained was 53.02 kg ha^-1 (caatinga vegetation), 231.96 kg ha^-1 (bare soil), 309.75 kg ha^-1 (beans), and 847.38 kg ha^-1(corn). The results showed that caatinga cover yields the lowest erosion and runoff when compared to the other treatments. The results also show that the sediment yield and runoff values simulated with N_s, K_I, and K_R parameters were well calibrated, within acceptable deviations. The caatinga vegetation was more effective in protecting the soil, when compared to the other types of coverage. The beans and corn covers had the highest values of runoff and sediment yield, even higher than those observed for bare soil.     

Hard X-ray generation in the turbulent plasma of solar flares

The influence of scattering of accelerated electrons in the turbulent plasma on the transformation of their distribution function is studied. The turbulence is connected with the emergence of magnetic inhomogeneities and ion-sound mode. The level of ion-sound turbulence is specified by the ratio W ^s/nk _B T _e = 10^?3, while the value of magnetic fluctuations is δB/B = 10^–3. Different initial angular distributions of the function of accelerated-electron source are regarded: from isotropic to narrow directional distributions. For the chosen energy-density values of the ion-sound turbulence and the level of magnetic fluctuations, it is shown that both types of turbulence lead to a qualitative change in the hard X-ray brightness along the loop, moreover their influence was found to be different. Models with magnetic fluctuations and the ion sound can be distinguished not only by the difference in the hard X-ray distribution along the loop but also by the photon spectrum.     

Cyclic resistance and liquefaction behavior of silt and sandy silt soils

The liquefaction behavior and cyclic resistance ratio (CRR) of reconstituted samples of non-plastic silt and sandy silts with 50% and 75% silt content are examined using constant-volume cyclic and monotonic ring shear tests along with bender element shear wave velocity (V_s) measurements. Liquefaction occurred at excess pore water pressure ratios (r_u) between 0.6 and 0.7 associated with cumulative cyclic shear strains (γ) of 4% to 7%, after which cyclic liquefaction ensued with very large shear strains and excess pore water pressure ratio (r_u>0.8). The cyclic ring shear tests demonstrate that cyclic resistance ratio of silt and sandy silts decreases with increasing void ratio, or with decreasing silt content at a certain void ratio. The results also show good agreement with those from cyclic direct simple shear tests on silts and sandy silts. A unique correlation is developed for estimating CRR of silts and sandy silts (with more than 50% silt content) from stress-normalized shear wave velocity measurements (V_s1) with negligible effect of silt content. The results indicate that the existing CRR–V_s1 correlations would underestimate the liquefaction resistance of silts and sandy silt soils.     

Intergrain contact density indices for granular mixes——Ⅰ: Framework

Mechanical behavior such as stress-strain response, shear strength, resistance to liquefaction, modulus, and shear wave velocity of granular mixes containing coarse and fine grains is dependent on intergrain contact density of the soil. The global void ratio e is a poor index of contact density for such soils. The contact density depends on void ratio, fine grain content (CF), size disparity between particles, and gradation among other factors. A simple analysis of a two-sized particle system with large size disparity is used to develop an understanding of the effects of CF , e, and gradation of coarse and fine grained soils in the soil mix on intergrain contact density. An equivalent intergranular void ratio (ec)eq is introduced as a useful intergrain contact density for soils at fines content of less than a threshold value CFth. Beyond this value, an equivalent interfine void ratio (ef)eq is introduced as a primary intergrain contact density index. At higher values of CF beyond a limiting value of fine grains content CFL, an interfine void ratio ef is introduced as the primary contact density index. Relevant equivalent relative density indices (Drc)eq and (Drf)eq are also presented. Experimental data show that these new indices correlate well with steady state strength, liquefaction resistance, and shear wave velocities of sands, silty sands, sandy silts, and gravelly sand mixes.     

Intergrain contact density indices for granular mixes-Ⅰ: Framework

Mechanical behavior such as stress-strain response, shear strength, resistance to liquefaction, modulus, and shear wave velocity of granular mixes containing coarse and fine grains is dependent on intergrain contact density of the soil. The global void ratio e is a poor index of contact density for such soils. The contact density depends on void ratio, fine grain content (CF), size disparity between particles, and gradation among other factors. A simple analysis of a two-sized particle system with large size disparity is used to develop an understanding of the effects of CF, e, and gradation of coarse and fine grained soils in the soil mix on intergrain contact density. An equivalent intergranular void ratio (ec)eq is introduced as a useful intergrain contact density for soils at fines content of less than a threshold value CFth. Beyond this value, an equivalent interfine void ratio (ef)eq is introduced as a primary intergrain contact density index. At higher values of CF beyond a limiting value of fine grains content CFL, an interfine void ratio ef is introduced as the primary contact density index. Relevant equivalent relative density indices (Drc)eq and (Drf)eq are also presented. Experimental data show that these new indices correlate well with steady state strength, liquefaction resistance, and shear wave velocities of sands, silty sands, sandy silts, and gravelly sand mixes.     

Experimental and conceptual evidence about the limitations of shear wave velocity to predict liquefaction

Based on the liquefaction performance of sites with seismic activity, the normalized shear wave velocity, V_s1, has been proposed as a field parameter for liquefaction prediction. Because shear wave velocity, V_s, can be measured in the field with less effort and difficulty than other field tests, its use by practitioners is highly attractive. However, considering that its measurement is associated with small strain levels, of the order of 10⁻⁴–10⁻³%, V_s reflects the elastic stiffness of a granular material, hence, it is mainly affected by soil type, confining pressure and soil density, but it is insensitive to factors such as overconsolidation and pre-shaking, which have a strong influence on the liquefaction resistance. Therefore, without taking account of the important factors mentioned above, the correlation between shear wave velocity and liquefaction resistance is weak.In this paper, laboratory test results are presented in order to demonstrate the significant way in which OCR (overconsolidation ratio) affects both shear wave velocity and liquefaction resistance. While V_s is insensitive to OCR, the liquefaction resistance increases significantly with OCR. In addition, the experimental results also confirm that V_s correlates linearly with void ratio, regardless of the maximum and minimum void ratios, which means that V_s is unable to give information about the relative density. Therefore, if shear wave velocity is used to predict liquefaction potential, it is recommended that the limitations presented in this paper be taken into account.     

Influence of fines content on liquefied strength of silty sands

Critical state soil mechanics is a useful framework to understand sand behavior. In this paper, a relationship is developed for estimating undrained critical shear strength of sands based on the critical state framework. The relationship is validated by comparison with laboratory test results and sand liquefied strength from field liquefaction failure case histories. Using this relationship, the influence of fines content on undrained critical shear strength is studied for different combinations of effective stress and density. The parametric study indicates that depending on soil void ratio, effective stress, and the shape and mineralogy of the fine particles, undrained critical strength may increase, remain the same, or decrease as the amount of fines content increases. Both the susceptibility to liquefaction and the severity of strain-softening are affected by adding fines. It is suggested that the critical state parameter is inadequate for describing the behavior of liquefiable sands and sand shearing-compressibility should be taken into account in liquefaction analysis.