Intergranular Void Ratio Research Articles

A Review of Particle Packing Models and Their Applications to Characterize Properties of Sand-Silt Mixtures

This paper reviews particle packing models and explores their application in geotechnical engineering, specifically for sand-silt mixtures. The review covers key models, including limiting case, linear, and non-linear packing models, focusing on their mathematical structures, physical principles, assumptions, and limitations through the concept of excess free volume. The application of particle packing models in geotechnical engineering is explored in characterizing the properties of sand-silt mixtures, offering insights into maximum, minimum, and critical void ratios and inter-granular void ratio, and the prediction of mechanical properties.

On the undrained shear behavior of sand mixtures with non-plastic fines subjected to large shear displacement

Fluidized landslides pose significant hazards owing to the catastrophic failure and flow-like behavior with high mobility and long traveling distances. Non-plastic fines can be abundant in many fluidized landslides with 30%–40% content of relatively fine-grained particles. However, the role of fine particles in the initiation and movement of these landslides is not well understood. To investigate the effects of non-plastic fines content (FC) on the undrained shear behavior of the mixture, undrained ring shear tests were performed on mixtures of silica sand (D50 = 0.16 mm) with varying weight proportions of non-plastic fines (D50 = 0.035 mm) with different initial densities. We showed that liquefaction potential increased as fines content increased and initial density decreased. Peak strength (τp), steady-state strength (τss), and total dissipated shear energy to the steady state (Wss) increased against increasing density of the sample. Given the same initial density, τp, τss, and Wss decreased with the increases of FC. Using intergranular void ratio (es) and equivalent intergranular void ratio (es⁎), we found that plots of τp, τss, and Wss against es⁎ merged to a relatively narrow domain, indicating es⁎ can serve as a comprehensive indicator for evaluating the FC's effects on undrained shear behavior. An optimum es⁎ existed for the mixtures, which corresponds to the minimal brittleness index IB, that is used for analyzing liquefaction associated with post-failure behavior. The Wss in the log scale continuously decreased with increasing es⁎. We inferred that the addition of fine particles could change the inter-particle force transfer. When the FC increases, a greater proportion of fines can actively engage in the forces transferring structure as active fine particles, resulting in increasing liquefaction potential and reducing the energy dissipation throughout the entire shearing process of the saturated mixtures, thereby facilitating the fluidization and mobility of landslides. This study provides an evaluation of the full liquefaction process of fines-rich mixtures and further explains the fines' role in the high mobility of fluidized landslides based on the energy dissipation view.

Monotonic and cyclic behaviour of sand-silt mixtures through the equivalent state parameter

This paper presents the results of a laboratory investigation into the effect of non-plastic fines on the monotonic and cyclic behaviour of sand-silt mixtures. For this purpose, drained and undrained triaxial monotonic and undrained stresscontrolled cyclic triaxial tests were performed on clean sand and its mixtures with non-plastic silt. The Critical State theory known as a characteristic state of soil behaviour and the equivalent state concept were used to the interpretation of the laboratory tests results. By estimating parameter b, which recognizes that different percentages of fines contribute differently to the strength of the sand and consequently the equivalent intergranular void ratio, (eg)eq, a single Critical State Line, CSL, is determined in the (eg)eq-log(p΄) plane, and a single liquefaction resistance curve at the CRR15-(eg)eq, independently of fines content, fc, based on the monotonic and cyclic tests results, respectively. It is shown that parameter b depends on the fines content, fc, and on the loading type of the laboratory test conducted, while (eg)eq proves to be a suitable parameter for the estimation of the monotonic behavior and undrained critical state strength as well as the liquefaction resistance of granular mixtures up to the threshold fines content value, fcth, independently of their fines content. The effectiveness of state parameter, ψ, and equivalent state parameter, (ψg)eq, in the estimation of the undrained critical state strength and liquefaction resistance of sand-silt mixtures is confirmed.

Assessing the influence of non-plastic fines on rainfall-induced landslide initiation and propagation: Flume test findings

Numerous fluidized landslides with long runout distances and fast movements have been triggered by heavy rainfall under climate change. Non-plastic fines are frequently involved in many fluidized landslides. However, the role of fines in the initiation and movement of landslides has not been well understood. This study aimed to investigate the role of non-plastic fines in the initiation and movement of rainfall-induced landslides in a flume test setup. The experiments were conducted using mixtures of silica sand (D50 = 0.16 mm) with different non-plastic fines (D50 = 0.035 mm) content under different initial densities. The results demonstrated that the behavior of landsliding greatly depends on fines content (FC) and initial packing density (presented by density index, Id) of the soil layers in the flume. The landsliding phenomena could be classified into five failure modes, including slow and fast retrogressive individual sliding, sudden multiple sliding, and deep-seated and shallow fluidized sliding. As the FC increased or Id decreased, the landsliding behavior gradually evolved from slow retrogressive individual sliding to shallow fluidized sliding. For the tests with Id ≥ −0.06, the peak velocity (Vp) of the landsliding increased continuously with FC. Conversely, for the tests with Id ≤ −0.19, an optimal FC of 30 % was identified at which Vp reached its maximum. Additionally, for FC ≤ 10 %, Vp decreased with the increasing Id, while for FC ≥ 20 %, an optional Id existed at which Vp reached its maximum for a given FC, and the value of optimal Id (−0.2 ∼ −0.04) varied with FC (20 % ∼ 40 %). The peak pore-water pressure (PWP) (up) generally increased with the increase of FC. Furthermore, an optimal Id existed at which the PWP built up after landsliding occurrence (Δu) reached its maximum. The equivalent intergranular void ratio (es*) and equivalent interfine void ratio (ef*), which are calculated by considering both FC and void ratio, are found to be appropriate indices for evaluating and explaining the role of fines in the observed landsliding behavior. In conclusion, the addition of non-plastic fines can change the structure of test materials and result in different failure modes and mobility of landslides by affecting both interparticle contacts and PWP responses. These findings provide insights into the mechanisms of landsliding behavior and have implications for the assessment and mitigation of landslides in geotechnical engineering.

Effects of seepage flow on liquefaction resistance of uniform sand and gap-graded soil under undrained cyclic torsional shear

Internal erosion is the transportation of soil particles from within or beneath geotechnical structures, caused by seepage flow, that impacts the subsequent mechanical and hydraulic behaviour of the soil. However, it is difficult to predict the liquefaction resistance of eroded soil due to several factors related to the soil fabric. The present study investigates the impact of seepage flow on the undrained cyclic behaviour of two types of soil: uniform sand and gap-graded soil with a fines content of 20%, using a novel erosion hollow cylindrical torsion shear apparatus. From the results for the uniform sand, the soil fabric formed by moist tamping (MT) leads to higher liquefaction resistance than that formed by air-pluviation (AP). However, after applying seepage flow, the liquefaction resistance of the eroded MT specimens becomes even lower than that of the non-eroded AP specimen. Therefore, the liquefaction resistance of soil is expected to decrease due to the rearrangement of the initially stable coarse particles during seepage flow. On the other hand, the liquefaction resistance of the gap-graded soil tends to increase after the removal of fines as the number of stable contacts between the coarse particles is increased. Under these test conditions, the latter effect is found to be greater for the given gradation, leading to a slight increase in the liquefaction resistance of the tested gap-graded soil after internal erosion. Furthermore, the intergranular void ratio and small-strain shear modulus are seen to be well correlated with the liquefaction resistance of the tested soil.

Investigation of the critical state behavior of unsaturated silty sand with different fine contents in terms of net and effective stresses

This paper investigates the effect of fine content and matric suction on the behavior of silty sand soil through both net and effective stress variables in the critical state soil mechanics framework. For this purpose, a set of CD triaxial tests in saturated and unsaturated states were performed on the samples of sand with different fine contents. The results showed that in term of net stress variables the position of the critical state line (CSL) in stress space for a given non-plastic fine depend on suction. However, these lines approach each other by choosing a proper effective stress relationship. The CSLs in the coordinates of the void ratio in the term of effective stress changed as a function of the non-plastic fine content and matric suction. However, using the concept of the equivalent intergranular void ratio and considering a special mean effective stress variable depending on suction, the CSLs were converged so that a single line can be defined to describe the behavior of the silty sand at the critical state. Finally, the stress-dilatancy relationship of two constitutive models was examined and it was shown that the use of the equivalent state parameter could facilitate the use of these relationships.

Applicability of the concept of equivalent intergranular void ratio to sand-plastic fines mixtures below threshold fines content

The technical note presents findings of an experimental study on the applicability of equivalent intergranular void ratio e*eq concept in sand-plastic fines mixtures under monotonic and cyclic loading. The results of undrained triaxial tests conducted on mixtures of Hostun sand with varying amounts (0% to 20%) and types of plastic fines (kaolin and calcigel bentonite) were already presented in two previous studies. The e*eq for the mixtures under various initial densities was calculated using the parameter b. Preliminary results show that the concept of e*eq seems to hold valid in the e-p space considering monotonic tests as well as being able to capture the variation of the cyclic resistance ratio for a predefined number of cycles to initial liquefaction from cyclic undrained tests even in mixtures with plastic fines below threshold fines content. However, the need for further studies is duly acknowledged.

A Simplified Silty Sand Model

A unified critical state model has been developed for both clean sand and silty sand using the modified Cam-clay model (MCC). The main feature of the proposed model is a new critical state line equation in the e-ln(p) plane that is capable of handling both straight and curved test results. With this feature, the error in calculating plastic volumetric strain is, in theory, eliminated. Another crucial feature of the model is the transformed stress tensor based on the SMP (spatially mobilized plane) criterion, which takes into account the proper shear yield and failure of soil under three-dimensional stresses. Additionally, the proposed model applies the intergranular void ratio with the fines influence factor for silty sand. Only eight soil parameters are required for clean sand, and a total number of twelve soil parameters are needed for silty sand. This model not only enhances the predictive accuracy for granular soils but also broadens the applicability of the model to encompass silty sand in both drained and undrained analyses.

An energy-based model for the generation of excess pore water pressure in saturated coral sand

A series of undrained cyclic shear tests was carried out on saturated coral sands, with different initial physical states, as they were subjected to rotations of 90° in the paths of cyclic stress with various initial orientations under isotropic conditions. An important finding is that the cumulative dissipated energy required for liquefaction (W s) was significantly affected by their fines content (FC), relative density (D r), and effective stress of consolidation ( p ′ 0 ), but was independent of the conditions of cyclic loading. W s increased significantly with the increase in p ′ 0 . When FC was less than the threshold fines content, W s increased with FC and decreased with an increase in D r. The equivalent intergranular void ratio (e*) was introduced to reflect the effects of FC, physical states of the particles, and inter-particle contact on the physical properties of coral sand. The results revealed a unique relationship between e* and W s at p ′ 0 = 100 kPa. Furthermore, the unified model of the relation between the normalized cumulative dissipated energy and the ratio of excess pore water pressure (EPWP) followed an arc-tangent function. This model can be used to characterize the generation of EPWP with the cumulative dissipated energy of fine-grained sand under isotropic consolidation conditions.

Shear-Induced Instability of Sand Containing Fines: Using the Equivalent Intergranular Void Ratio as a State Variable

Shear-Induced Instability of Sand Containing Fines: Using the Equivalent Intergranular Void Ratio as a State Variable

Mechanics of the instability of sand and non-plastic silt mixture using equivalent intergranular void ratio

Mechanics of the instability of sand and non-plastic silt mixture using equivalent intergranular void ratio

Effects of internal erosion on the cyclic and post-cyclic mechanical behaviours of reconstituted volcanic ash

Internal erosion is the transportation of soil particles from within or beneath the main structure inside the ground due to seepage flow. Internal erosion impacts the mechanical and hydraulic behaviour of soil. The present study investigates the impact of internal erosion on the cyclic and post-cyclic mechanical behaviours of volcanic ash sampled from Satozuka, Japan. A series of experiments using volcanic ash with loose, medium, and dense conditions have been performed using an erosion triaxial apparatus. Further, reconsolidation after application of cyclic loading was considered to study the impact of reconsolidation on the post-cyclic mechanical behaviour. The results show that the cyclic resistance of eroded specimens is improved regardless of the percentage of eroded fines and the initial relative density. The higher cyclic resistance for the eroded specimens is found to be due to a decrease in the intergranular void ratio after the erosion, change in fabric, and pre-strain history during erosion. Reduction in the critical state friction angle (φcri) and peak stress ratio (Rpeak) for the monotonic loading due to cyclic loading is greater for the eroded specimens. However, reconsolidated eroded specimens show increases in φcri and Rpeak, which are lower than those of the non-eroded and eroded specimens without cyclic loading. This could be due to the change in the soil fabric during cyclic loading where the positive impact of erosion is lost after cyclic loading. Such limited recovery of deviatoric stress with deformation is density-dependent.

Investigation of the static and dynamic characteristics of TDA-subballast mixtures

TDA (tire-derived aggregate) has great potential in ballasted railway engineering due to its excellent wear resistance and vibration absorption capacity. Thus, engineering insight into the effect that TDA has on the static and dynamic behavior of TDA-subballast mixtures is in high demand. In this investigation, different size ratios and shapes of TDA were used, and a series of large-scale monotonic and cyclic triaxial tests with different confining pressures and tire contents were conducted to evaluate the mechanical properties of the TDA-subballast mixtures. The experimental results indicate that TDA leads to a decrease in the stiffness, shear dilatancy, and modulus of resilience and an increase in the energy dissipation capacity of the mixtures. Then, the equivalent intergranular void ratio eeq is introduced to further evaluate the contribution of TDA granules to the shear behaviors of mixtures. A series of equations were established to discuss the evolution of the peak deviatoric stress, energy dissipation, and resilient modulus with eeq. Furthermore, based on the test indexes, the performance of mixtures with different TDA shapes and contents was comprehensively evaluated, and the optimal volumetric content of tires was found to be approximately 20%. The test results further promote the application of TDA in railway engineering and the effective use of waste tires.

Influence of Fabric on Stress Distribution in Gap-Graded Soil

The combined influence of density and stress-induced fabric anisotropy on the nature of stress transmission in gap-graded soils with cohesionless fines has been explored using the discrete element method (DEM). Various particle size ratios and fines contents were considered in simulations of constant mean stress triaxial compression. Analysis of the available particle-scale data focused on understanding how stress was distributed among and between the finer and coarser particles. While the study confirms that stress is transferred from the coarser to the finer fraction with increasing fines content, the concept of a threshold fines content at which there is a definitive transition in the nature of stress transmission is not supported. Rather, there is a gradual evolution of the distribution of stresses between the two size fractions with increasing fines content, and the relationship between fines content and stress in the finer fraction depends on the size ratio, density, and fabric anisotropy. For the denser samples considered, the stress transmitted by the finer fraction systematically reduced during shearing. An alternate definition of granular void ratio is introduced, which accounts for the nonactive fine and coarse particles and is formulated in a consistent manner to capture both the intergranular and interfine void ratios commonly found in the literature, along with the equivalent granular void ratio. The anisotropy of the network of contacts formed by the interactions of coarse particles was observed to be the dominant contributor to fabric anisotropy.

Intergranular void ratio and undrained monotonic behavior of Chlef sand containing low plastic fines

Stability analysis of soils prone to static liquefaction based on their monotonic undrained shear strength characteristics is an indispensable challenge in earthquake geotechnical engineering. This paper presents a laboratory study on the static behavior of Chlef sand–silt mixtures (with a silt content fc range from 0 to 50%); under low confining pressures. The experimental program includes undrained triaxial monotonic tests which were carried out for five types of samples, consolidated under different confining pressures (σʹc = 20, 50, 100, 150, and 200 kPa). On the samples preparation, the dry pluviation funnel has been used with a medium relative density (Dr = 60%). Main results obtained indicate that the fines content and initial confining pressure have a significant influence on instability stress and steady-state ratios of sand–silt mixtures. Moreover, the obtained data confirm the existence of a simple correlation between undrained instability stress, steady-state ratios, fines content, void ratios, and effective confining pressure. From the results obtained, nevertheless it can be concluded that the global void ratio does not represent the actual behavior of the soil under study, and the undrained residual strength decreases with a logarithmic manner with the increase of the intergranular void ratio, and a similar trend is occurring with the fine content of the sand–silt mixtures up to 50% as well.

Experimental investigation on static and dynamic characteristics of granulated rubber-sand mixtures as a new railway subgrade filler

Because of their low unit weight, strong linear elastic deformation ability, good durability and high energy dissipation, mixtures of waste tire rubber and sand have been increasingly used as a new type of subgrade filler in railway engineering. To investigate static and dynamic characteristics of granulated rubber-sand mixtures as a new filler, consolidated undrained monotonic and cyclic triaxial tests were carried out. The monotonic triaxial tests reveal that the shear strength of mixtures first increases and then decreases with increasing granulated rubber content and is maximized when the rubber content is approximately 10%. Based on the theory of an equivalent intergranular void ratio, a new equation for estimating the peak deviatoric stress of mixtures is proposed. The cyclic triaxial tests reveal that the addition of granulated rubber can constrain the generation and accumulation of dynamic pore water pressure and improve the liquefaction resistance of mixtures. The change in shear modulus is inversely proportional to the change in granulated rubber content and frequency, and directly proportional to the change in confining pressure. A new equation is also established for calculating the maximum shear modulus considering the effect of the equivalent intergranular void ratio and confining pressure. By comparing the maximum shear modulus of the new railway subgrade filler with that of other subgrade filler, it is concluded that a granulated rubber content of less than 20% can meet engineering requirements related to shear stiffness. The damping ratio is correlated with granulated rubber content, negatively correlated with confining pressure and insensitive to loading frequency. The relationship between the damping ratio and shear strain conforms to the equation proposed by Hardin and Drnevich. Based on the analysis of static and dynamic characteristics of granulated rubber-sand mixtures with different rubber content, the optimum granulated rubber content should be approximately 10%.

The permeability of composite soils

Many natural soils (e.g. glacial tills, residual soils and alluvial soils) and artificial soils (e.g. engineered fill and environmental barriers) are composite soils formed of a range of particle sizes and types. These soils are often difficult to sample and test when following standard site investigation practice; thus, it is necessary to resort to empirical correlations, most of which were developed for either coarse-grained (e.g. clean sands) or fine-grained soils (e.g. pure clays). The hydraulic conductivity of clean sands is a function of the void ratio and particle size distribution, and for clays, of the clay type and void ratio. This suggests that the hydraulic conductivity of composite soils will be a function of these properties and the clay content. Composite soils formed of four clay minerals and two sands were consolidated from slurry to determine the variation in hydraulic conductivity with clay content, clay type and void ratio. With matrix-dominated soils, soils that have more than 35% fines content, the flow is a function of the matrix void ratio and clay type; and for clast-dominated soils, soils that have less than 20% fines content, the intergranular void ratio and particle size distribution. The behaviour of soils with a fines content between 20 and 35% depends on the confining pressure and density.

Coarse-fine mixtures subjected to repetitive Ko loading: Effects of fines fraction, particle shape, and size ratio

This study explores the effects of fines fraction, particle shape, and size ratio on the long-term response of sand-silt mixtures with fines fraction FF = 0-to-100% during Ko-loading cycles i = 104. The void ratio for all specimens evolves toward the asymptotic terminal void ratio eT that captures the transition from coarse-to-fine controlled behavior. Shear wave velocity versus intergranular eC and equivalent intergranular (eC)eq void ratios estimates the participation rate of fines-in-sand for the force chain. More fine particles contribute to the load-carrying skeleton as the particle shape becomes rounder and the size ratio decreases. In contrast, shear wave velocity against interfine eF and equivalent interfine (eF)eq void ratios reflects the reinforcing effect of coarse grains floating in the load-carrying fines matrix. The rounder sand in the fine-dominant matrix leads to more significant fabric changes. Clearly, there is a transition from coarse-to-fine controlled repetitive load-deformation response that promotes the reassessment of current soil classification systems.

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.

Influence of non-plastic fine on static iquefaction and undrained monotonic behavior of sandy gravel

Many geological hazards such as landslide, liquefaction, slope failure and rockfall occur in mixed gravelly alluvium or colluvium deposits, highlighting the importance of studying gravel–sand–silt mixtures. Although many natural strata are built using these mixtures, they are not entirely understood. A fundamental experimental study was designed to explore the influence of non-plastic fine content on the undrained behavior of gravel-sand-silt mixtures as common geomaterials in nature. Undrained monotonic triaxial tests were carried out. Three types of sandy gravels with different sand-to-gravel ratios were selected as base gravels. The impacts of the non-plastic fine content on the stress–strain behavior, static liquefaction potential, steady sate line, residual strength and critical state friction angle were studied. The laboratory results show that both sand-to-gravel ratio and non-plastic fine content have significant impacts on the undrained response of gravelly mixtures. It was observed that mixtures with zero non-plastic fines content exhibit the non-flow liquefaction behavior. However, adding silt content up to 45% shows the limited liquefaction or flow behavior, depending on the base gravelly soils and fine content percentage. A threshold for non-plastic fine content was found to be 35%–45%. Below this threshold, the steady state line shifts downward as silt content increases, and then shifts upward with further increase in the silt contents. The identical trend was also noted for residual strength and critical state friction angle. For silt contents below the threshold, the equivalent intergranular void ratio concept (modified with a new logical assumption) was used to analyze the behavior of gravelly mixtures. The results clearly indicate that the accurate value of equivalent intergranular void ratio can fully explain the behavior of sandy gravel-fine mixtures, similar to sand-fine mixtures. From a microstructure perspective, both sand and silt content act as fine-grains in gravelly mixtures and should be considered when studying the mechanical properties of theses mixtures.