Critical State Behavior Research Articles

Compression and critical-state behaviors of calcareous sand–diatom mixtures

Compression and critical-state behaviors of calcareous sand–diatom mixtures

Critical state behaviour of an unsaturated kaolin mixture

In this paper, a series of suction-controlled triaxial tests were conducted to investigate the hydromechanical behaviour of an unsaturated kaolin mixture. The studied variables included the mean net stress, suction, and initial dry density. The suction was controlled over a wide range – in the span of 0–390 MPa using the axis translation method and the vapour equilibrium technique, aiming to holistically study the mechanical response of unsaturated soils. The discussion focused on the critical state behaviour and dilatancy characteristics of the tested soil. The experimental results indicate that the ductility of the soil decreases and shifts towards brittleness with increasing suctions. The critical state stress ratio (Ma) of the soil exhibits a significant increase with suction, and this increase becomes more pronounced with higher initial dry density. Conversely, the impact of suction on the critical state line in the specific volume-mean net stress plane (v-lnpnet plane) diminishes with higher initial dry density. Furthermore, suction notably influences the stress-dilatancy relationship of kaolin mixtures, while the effect of confining pressure appears to be marginal. The influence of suction on the stress-dilatancy relationship primarily stems from its impact on the critical stress ratio (Ma), which can be normalized by dividing the stress ratio by the critical state stress ratio. Lastly, the stress-dilatancy equation of the modified Cam-clay model is extended to capture the effect of suction on the dilatancy characteristics of unsaturated soils.

DEM simulation of microscopic structure and macroscopic mechanical behavior of clay in oedometer and triaxial compression tests

An updated DEM simulation scheme for clay is implemented by incorporating convex polygon shaped platelets and robust algorithm for physico-chemical–mechanical interaction between clay platelets. Clays with two typical microscopic structures, i.e., card-house structure and book-house structure, are simulated in oedometer test and triaxial compression test. Virtual Mercury Intrusion Porosimetry (MIP) and pore segmentation algorithms are utilized to extract pore statistics from the numerical samples. The simulation results and experimental results from the literature are thoroughly compared at both macroscopic and microscopic scales. It is found that the implemented DEM simulation scheme can satisfactorily reproduce the experimentally observed macroscopic behavior of clay. Especially, in triaxial compression tests, the critical state behavior, stress-dilatancy relationship and over-consolidation effects are generally consistent with existing experimental results. General consistency in pore size, orientation and shape distributions in DEM simulations and experiments can be observed. Clay platelets tend to rotate to align their normal directions along the major principal stress direction, while pores tend to align their long-axis directions in the confinement direction, leading to dynamically evolving fabric anisotropy. In the book-house structure clay, clay domains experience multiple deformation modes, including uniaxial compaction, shear distortion, spatial spin, and their combinations.

Stress–Dilatancy and Critical-State Behavior of Geogrid-Reinforced Recycled Waste Materials

Stress–Dilatancy and Critical-State Behavior of Geogrid-Reinforced Recycled Waste Materials

Non-stationary anisotropy-dependent critical state for clays

In this paper, the effect of fabric anisotropy on the critical state behaviour of clays is investigated. An original concept of moving critical state is elaborated by a novel state parameter-based rotational hardening rule that is subsequently used to formulate a complete anisotropic elastoplastic constitutive model for clays. It is shown that some of the distinctive pre-failure and critical state responses of clays can be explained by adopting a non-stationary critical state line. Furthermore, an enhanced definition for the state of the soil is proposed that provides a more realistic correspondence between the shearing behaviour of an overconsolidated clay and its initial consolidation state. The proposed model is validated by simulating the experimental data from triaxial tests on a number of clays.

A hypoplastic model for unsaturated sand accounting for drying and wetting cycles

Existing constitutive models for unsaturated sand cannot capture the irreversible volumetric strain in the drying and wetting (DW) cycles. This study develops a novel hypoplastic model that aims to capture the behaviour of unsaturated soils, with a specific emphasis on the DW cycles experienced by unsaturated sand. The formulation integrates a hypoplastic model proposed by von Wolffersdorff for saturated sand with Bishop's effective stress. The simulation of soil water characteristic curve hysteresis is achieved through the implementation of the scanning rule for the main drying/wetting curve and scanning curve. The incorporation of a new tensorial term, Hs, into the hypoplastic equations, captures the irreversible volumetric strain in the DW cycle. A novel pyknotropy factor, referred to as fus, is proposed to replicate the rate at which irreversible volumetric strain accumulates during the DW cycle. Furthermore, the influence of suction effects on the critical state line is taken into account to represent the shear behaviour of unsaturated sand. The evaluation of the model performance is conducted through existing element tests on unsaturated sand. The comparison illustrates that the proposed model has the capability to capture certain essential characteristics, such as irreversible volumetric strain in the DW cycles and critical state behaviour of unsaturated sand. Due to its simplicity, the proposed model lends itself to straightforward implementation and potential utilization in future engineering applications, particularly in the analysis of slope stability in the presence of rainfall-induced conditions.

DEM simulations of critical state behaviour of granular materials under various drained triaxial stress path tests

DEM simulations of critical state behaviour of granular materials under various drained triaxial stress path tests

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.

DEM-based study on the mechanical behaviors of sand-rubber mixture in critical state

This paper presents a numerical method to investigate the critical-state behaviors of the soft-rigid mixture via DEM simulation. First, according to a series of laboratory tests of sand-rubber mixtures, a systematic calibration framework is proposed to acquire the numerical parameters. Then, cubic compression tests are conducted with different rubber contents and confining pressures. The evolution of micro-scale properties, including the internal structure, stress network, and fabric anisotropy, is investigated to reveal the influences of rubber content and confining pressure on the micromechanical behaviors of sand-rubber mixtures. Through the investigation of the macroscopic responses, a unified hypoplasticity constitutive model is established and the relationships between the critical state parameters and rubber content are explored. The results show that the critical state shear strength of sand-rubber mixtures decreases with increasing rubber content and does not correlate with confining pressure. Additionally, the influence of rubber content on shear behaviors of SRMs is highly dependent on confining pressure, e.g., SRMs are more likely to exhibit soft-like behaviors under higher confining pressure. This study lays a foundation for the engineering design of geotechnical structures with an appropriate filling of the sand-rubber mixture. Moreover, this study also paves a viable way for a comprehensive investigation of other soft-rigid mixtures in the critical state.

Experimental study on critical state behaviour of unsaturated silty sand under constant matric suctions

There are relatively few experimental studies on the hydromechanical and critical state behaviours of unsaturated silty sand. In this paper, suction-controlled, consolidated, drained triaxial shear tests were conducted on silty sand under saturated (net confining pressures of 100, 200, 300 and 400 kPa) and unsaturated (suctions of 30, 100 and 200 kPa and net confining pressures of 100, 200 and 300 kPa) conditions. For unsaturated silty sand, the effects of dry density, matric suction and net confining pressure on the hydromechanical and critical state behaviour were investigated, and the critical state parameters were obtained. The main findings for unsaturated silty sand included shear shrinkage at low dry density (1·6 g/cm3) and dilatancy at higher density (1·96 g/cm3). The peak shear strength was positively correlated with dry density, matric suction and net confining pressure. The critical state volumetric strain and critical state degree of saturation were negatively correlated with dry density and matric suction but positively correlated with net confining pressure. A new dilatancy equation that includes the state parameter for unsaturated silty sand was established. A unique critical state line passes through the origin in the effective stress [Formula: see text]–deviator [Formula: see text] plane, and its slope is the saturated critical state stress ratio [Formula: see text]. In the lnp*–v plane ([Formula: see text] is the specific volume), the critical state lines corresponding to different matric suctions are parallel.

Instability of a Gold Mine Tailings Subjected to Different Stress Paths

Static liquefaction of mine tailings has been the interest of many studies as these materials are generally deposited in a loose condition and stored at high saturation ratios. Yet few researchers have investigated the behavior of mine tailings in stress paths involving extensional consolidation or shearing in extension. In this study, the results of a set of experiments aimed at investigating the static liquefaction behavior of saturated loose gold mine tailings samples in triaxial compression and extension shear tests are described. Monotonic tests are carried out on isotropically and K0-consolidated samples to assess the effect of stress-induced anisotropy and mode of shearing on the instability and critical state behaviors of tailings. The comparison of undrained extension and compression shearing behaviors of samples consolidated to similar densities and stress conditions show a profound difference in their undrained shearing responses. This is attributed to the angular shapes of tailings particles that amplify the effects of particle orientation and sample fabric, as well as microstructural changes induced by different loading paths. Postliquefaction and yielding undrained shear strengths and effective friction angles from different modes of consolidation and shearing are examined. In both undrained compression and extension tests, tailings samples exhibit a limited liquefaction behavior after yielding, followed by a strain-hardening (dilative) behavior. Differences in tailings behavior under different loading directions and anisotropic stresses indicate the importance of considering the effects of these phenomena on the stability analysis of mine tailings dams.

Applicability of discrete element method with spherical and clumped particles for constitutive study of granular materials

Discrete element method (DEM) has been intensively used to study the constitutive behaviour of granular materials. However, to what extent a real granular material can be reproduced by virtual DEM simulations remains unclear. This study attempts to answer this question by comparing DEM simulations with typical features of experimental granular materials. Three groups of models with spherical and clumped particles are investigated from four perspectives: (i) deviatoric stress and volumetric behaviour; (ii) critical state behaviour; (iii) stress-dilatancy relationship; and (iv) the evolution of principal stress ratio against axial strain. The results demonstrate that DEM with spherical or clumped particles is capable of qualitatively describing macroscopic deviatoric stress responses, volumetric behaviour, and critical state behaviour observed in experiments for granular materials. On the other hand, some qualitative deviations between experiments and the investigated DEM simulations are also observed, in terms of the stress-dilatancy behaviour and principal stress ratio against axial strain, which are proven to be critical for constitutive modelling. The results demonstrate that DEM with spherical or clumped particles may not necessarily fully capture experimental features of granular materials even from a qualitative perspective. It is thus encouraged to thoroughly validate DEM with experiments when developing constitutive models based on DEM observations.

Thermodynamic Constitutive Model for Sands with Consideration of Distributed Fabric

A micromechanics-inspired fabric-dependent thermodynamic model is developed to simulate the critical-state and phase-transformation behavior of sands. A generalized fabric tensor that considers the statistical distribution of granular fabric is proposed. The fabric tensor is the sum of three families of a transversely isotropic tensor, which is assumed to be characterized by the probability density function of the normal distribution. The new tensor variable is incorporated into the reversible and irreversible thermodynamic models, and the fabric-dependent hyperelastic and plastic constitutive relations are then derived. The hyperelastic instability leads to a yield criterion that depends on fabric distribution and its evolution. Plastic strain development is linked to fabric distribution by a concept of accumulative yielding probability transitions, which in turn provides smooth transition from macroscopic elasticity to plasticity and finally to the critical state upon shearing. Using this theoretical framework, the physical mechanism underlying the phase-transformation and critical-state behavior of sands are interpreted from the evolution of fabric distribution. The performance of the model is verified by simulating various shear tests of Toyoura sand and a discrete element method (DEM)-modeled sand. The effects of b-value and principal stress direction on the stress-strain behavior are related to the evolution of fabric distribution. The noncoaxiality among stress, strain, and fabric is also captured by the model.

Effect of root orientation on the strength characteristics of loess in drained and undrained triaxial tests

Ecological engineering measures are gaining popularity in the control of mountain hazards, particularly in shallow landslides, in which plant roots improve the shear strength of shallow soil. To measure such improvement, a series of drained and undrained triaxial tests were performed to investigate the role of Cunninghamia R. Br roots in loess soil mechanical behavior collected from Longchi Forest Center, southwest China. The specimens were prepared by distributing roots in four (4) distinct spatial orientations types, i.e., Horizontal, Vertical, Horizontal-Vertical (grid), and Randomly mixed in the soil. All specimens were first fully saturated and subsequently sheared in compression tests under drained and undrained conditions. The test results are evaluated in terms of monotonic stress-strain behavior, volume change, development of excess pore water pressure, and critical state behavior. The results showed that the addition of roots increased the soil shear strength, provides additional resistance to volumetric deformations and increased the positive excess pore water pressure as compared to plain loess soil. The results also revealed that the mechanical response of the soil-root composite depends on the type of root orientation. The shear strength improved highest with horizontal-vertical (grid) root orientation in both drained and undrained conditions among four root orientations. In contrast, the horizontal root orientation showed the least shear strength improvement. Additionally, for the same root orientation type, the shear strength improvement was more pronounced in undrained conditions compared to drained conditions. The plain and soil-root composite shear strength parameters showed that the addition of roots increased the cohesion with little effect on the mobilized angle of friction in both drained and undrained conditions. The findings of this research will provide a strong baseline for developing a predictive constitutive model for soil–root composite.

Laboratory and Constitutive Modeling of Critical State Behavior of Rockfill Aggregates Mixed with Polymer

Abstract In order to increase the strength and deformation properties of coarse aggregates, the polymer was used as an additive. In this study, a series of triaxial tests were performed to analysis the effect of polymer content on the strength, deformation, and critical state of rockfill aggregates. It is found that the deformation properties are the same for different polymer contents. As the polymer content increases, the peak stress increases, and the volume strain decreases. The addition of polymer mainly led to inducing cohesion in rockfill aggregates while showing a marginal influence on friction angle. The average effective stress, which considered the cohesion of polymer as additional effective stress, was modified. It was observed that the critical state envelopes in q–p′pc and e–p′pc were not much influenced by the addition of polymer. A state parameter is used as a function of void ratio and pressure. A boundary surface model of polymer rockfill aggregates based on the critical state approach was proposed. The performance of the model is demonstrated by the results of triaxial tests. The study shows the model could effectively capture the influence of polymer contents and confining pressures on strength and deformation characteristics of rockfill aggregates.

Strength–dilatancy and critical state behaviours of binary mixtures of graded sands influenced by particle size ratio and fines content

Binary granular soil mixtures, as common heterogeneous soils, are ubiquitous in nature and man-made deposits. Fines content and particle size ratio are two important gradation parameters for a binary mixture, which have potential influences on mechanical behaviours. However, experimental studies on drained shear behaviour considering the whole range of fines content and different particle size ratios are scarce in the literature. For this purpose, a series of drained triaxial compression tests was performed on dense binary silica sand mixtures with four different particle size ratios to investigate systematically the effects of fines content and particle size ratio on the drained shear behaviours. Based on these tests, the strength-dilation behaviour and critical state behaviour were examined. It was observed that both fines content and particle size ratio have significant influence on the stress–strain response, the critical state void ratio, the critical state friction angle, the maximum dilation angle, the peak friction angle and the stress–dilatancy relation. The underlying mechanism for the effects of fines content and particle size ratio was discussed from the perspective of the kinematic movements at particle level.

Strength and Microstructural Assessment of Reconstituted and Stabilised Soft Soils with Varying Silt Contents

The study of the strength of reconstituted and stabilised soft soils is very important in geotechnical engineering. The soil particles, such as clay, sand, and silt play important roles in determining the behaviour of soils. The behaviour of clay and sand particles are unique; however, the behaviour of silt particles lie in a transitional form between sand and clay. Therefore, this paper seeks to investigate (a) the effect of silt contents on the strength of soft soils; (b) the effect of silt content on the strength of cement-stabilised soft soils; and (c) the microstructure of the soft soil specimens stabilised by cement with varying particle size distribution. A series of tests consisting in consolidated, isotropic undrained (CIU) triaxial tests, unconfined compressive strength (UCS) tests, and scanning electron microscope (SEM) images were conducted in this study to achieve these objectives. In conclusion, the relationship between the silt content and critical state behaviour of soft soils (both clay and silt particles) are proposed. For the cement-stabilised specimens, the unconfined compressive strength increases with the increase in silt content when the cement content is 10%. However, the UCS decreases with the increase in silt content when cement content is 30%. With cement content ranging from 15–25%, the UCS increases at first with the increase of silt content but decreases once the silt content reaches a ‘saturation’ point.

The critical state behaviour of granular material in triaxial and direct simple shear condition: A DEM approach

The critical state (CS), the anchor concept in the critical state soil mechanics (CSSM) framework, has been comprehensively evaluated in triaxial stress conditions, where all the principal stresses are known but the pure shear stresses in the shear directions are absent. Therefore, the evolution of first and second invariants of the stress tensor (σ′) i.e. the mean effective stress (p′) and deviatoric stress (q) along with volumetric strain (εv) is often used to identify the CS. However, the same does not apply for a direct simple shear (DSS) test, which is more representative of the real ground condition, as in most cases the minor principal stresses are not measured. This leads to the challenge of determining the CS line in the e-log(p') space and thus the concept of state parameter (ψ) cannot be used to characterise soil behaviour. Using DEM, this study evaluates CS for DSS, using evolution σ′ and εv, in the e-σ'N space, compare its location with triaxial CS lines in the e-log(p') space. The CS line for DSS in e-σ'N space was then used to define a modified state parameter, ψ, (ψm). It was found that both ψ and ψm showed good correlations with characteristic behaviour e.g. onset of liquefaction, phase transformation state, fabric anisotropy etc. Therefore, ψm maybe a good alternative of ψ for DSS test where the minor principal effective stresses are not measured to define a CSL in e-log(p') space.

Behaviour of granular matter under gravity-induced stress gradient: A two-dimensional numerical investigation

Gravity is the most important load source in mining and geotechnical engineering, which causes both the stress level and stress gradient inside geomaterials. Different from the stress level, the influence of gravity-induced stress gradient on the behaviour of the material is still unknown. An in-deep study on it will help to promote the understanding of material behaviour, especially for those cases related to unconventional gravity such as terrestrial ng physical modelling and extraterrestrial resource exploitation (g is the terrestrial gravitational acceleration). In this study, a high-order homogenization for granular materials is proposed at first, in which the stress gradient is drawn into the constitutive representation by adopting a representative volume element (RVE). The consolidation and shear strength behaviour of RVE are then investigated by performing numerical biaxial tests. The results show that all the compressibility, shear strength, shear stiffness, volumetric deformation, and critical state behaviour show a stress gradient dependence. A coupling between stress gradient, stress level, and material properties is also observed. These observations suggest that, besides the stress level, extra attention needs to be paid to material responses related to stress gradient during engineering practices.

Effect of Initial Density, Particle Shape, and Confining Stress on the Critical State Behavior of Weathered Gap-Graded Granular Soils

Weathered gap-graded soils are a common geological body in mountainous regions, and they are widely used as construction materials. The shear strength is the controlling parameter for the design of civil projects; however, there is still a controversy on the coarse fraction effect on the shear strength of gap-graded soils. To this end, 22 triaxial shear tests are performed on gap-graded soils, and the factors affecting the coarse fraction effect have been analyzed, including the confining stress, the particle shape of aggregates, and the initial density of sand matrix. Partial contacts and sand bridges between aggregates are responsible for the transmission of loading and thus affect the coarse fraction effect. The results of triaxial tests reveal: (1) The overall shear strength of sand-beads mixtures is rather independent of the confining stress and the coarse fraction, and even the volume of aggregates is as high as 44.5%. (2) The effect of the shape of aggregates is effective only at a high coarse volume fraction (44.5%) for loose-sand-gravel mixtures, where the partial contacts between aggregates play an important role in forming the interaggregate structure. (3) The overall shear strength of gap-graded soils with a denser matrix increases continuously with a rising coarse fraction. The formation of a densified sand bridge is correlated with the initial density of sand matrix, contributing to the loading transmission in the interaggregate structure and, in turn, affecting the overall critical state behavior of gap-graded soils. The insights drawn from this study provide a reference for assessing the deformation behavior of weathered residual soils.