Unique Critical State Line Research Articles

Deformational response of a marine silty-clay with varying organic content in the triaxial compression space

This study characterises the effects of naturally varying organic content on the compression and shear behaviour of a marine silty-clay from the Netherlands. Index properties and mechanical properties are determined through laboratory tests, including oedometer and multistage loading-unloading triaxial stress paths. The results indicate a significant impact of the organic content on the compression response, with both the loading and reloading indexes increasing as the loss on ignition increases from 3% to 7%. Additionally, the study suggests a directional response of the compression behaviour, with the loading index increasing with the stress ratio. The influence of the organic content on shear strength appears to be less significant. No brittle response is observed during shearing, and a similar ultimate stress ratio is attained by all samples. However, a unique critical state line can only be identified for samples with similar organic content, as its intercept and slope are found to increase with increasing organic content. The experimental results from stress paths at constant stress ratio reveal an anisotropic pre-failure plastic deformation mode, which depends on the previous stress history and loading direction. This suggests that the stress–dilatancy relationship cannot be formulated as a unique function of the stress ratio. The high-quality experimental data presented in the study enlarge the database on soft organic soils in view of the development of advanced constitutive models.

Uniqueness of the Normal Consolidation Line for Gold Tailings

Abstract Depending on the stress state, mine tailings are generally accepted to be susceptible to static liquefaction. A common method to assess the in situ stress state of tailings in relation to static liquefaction susceptibility involves the use of the state parameter. Because most tailings materials are normally consolidated (NC), this type of assessment requires knowledge about the normal consolidation line (NCL). It has been shown experimentally that the uniqueness of the NCL is vastly different for fine-grained and coarse-grained soils, with clays usually exhibiting a unique NCL and clean sands exhibiting an infinite number of parallel NCLs. Gold tailings, a sandy silt, fall between clays and clean sands, and there are limited experimental data regarding their compression behavior over a range of initial void ratios. This lack of data results in inconsistent interpretation of the uniqueness of the NCL for gold tailings in the industry. This can influence the results of designs and safety evaluations of tailings dams. In this study, a number of oedometer tests were conducted on gold tailings sourced from an active tailings dam in South Africa. Several specimens were prepared at various initial densities and were consolidated in small increments to a high effective stress. The oedometer tests were supplemented with triaxial compression tests, from which a unique critical state line was identified. Across the oedometer and triaxial tests, it was found that the behavior of the NC and overconsolidated samples was consistent with that typically observed for fine-grained soils. Therefore, for practical purposes, it appears that the gold tailings tested can be viewed in a framework with a unique NCL. No significant influence of particle crushing was noted.

Exploring the undrained behaviour of granular clumps after isotropic and Ko-consolidation paths using DEM

This paper investigates the undrained behaviour of granular clumps after isotropic and Ko-consolidation paths using a three-dimensional discrete element method (3D-DEM). Four randomly chosen clumped particles with a wide range of densification indexes, ID, and mean confining stresses, p' were considered. The specimens were sheared to the deviatoric strain, εq of 40 % to reach the critical state (CS) conditions. It was found from the results that a unique critical state line (CSL) was achieved, irrespective of consolidation paths. The micro-mechanical quantities such as the average coordination number (CN) and von Mises fabric in terms of the second invariant of deviatoric fabric, FvM, also reached CS values. Irrespective of the consolidation paths, unique relationships were found between e−log(p′)and CN−log(p′). The stress-fabric joint invariant, KF established a unique relationship with p′and e, which forms a relationship in the KF−p′−e space and the projection of this relationship in the e−log(p′) plane confirms the classical CSL. Moreover, the flow potential (uF), stress ratio at instability (ηIS), and average coordination number at instability (CNIS) showed no dependency on the consolidation paths, while a dependency was observed for the second-order deviator fabric, FvM.

Role of grain size and shape on undrained monotonic shear, liquefaction, and post-liquefaction behaviour of granular ensembles

This paper presents a fundamental study to explore the independent effects of grain size and shape on the pre-liquefaction, liquefaction, and post-liquefaction shearing behaviour of granular ensembles through a series of multi-stage constant volume simple shear tests. Three different granular materials (glass ballotini, river sand, and manufactured sand) of three different sizes (fine, medium, and coarse) with distinct shape descriptors were chosen for the study. Shape parameters of the granular materials, including roundness, sphericity, regularity, and angularity, and their grain level kinematic behaviour were determined from the microscopic images using image analysis algorithms. Experiments were carried out on reconstituted specimens prepared at different relative densities of 15, 30, and 45%, and the results were interpreted in the light of the critical state framework. Undrained monotonic shear tests showed that ensembles with similar grain shapes exhibit a unique critical state line (CSL) and also exhibit a unique phase transformation line (PTL), irrespective of the grain size. However, ensembles with different grain shapes exhibited different CSLs and different PTLs. Irrespective of grain shape, an increase in grain size increased the liquefaction resistance because of an increase in the tendency for dilation. Irrespective of grain size, an increase in particle angularity and irregularity increased the liquefaction resistance due to an increase in the interlocking tendency at grain contacts. Grain size and shape significantly affected the post-liquefaction shear strength of the granular ensembles. The post-liquefaction initial and secondary shear moduli were found to be highly dependent on the grain size and shape.

Strength, Deformation, and Particle Breakage Behavior of Calcareous Sand: Role of Anisotropic Consolidation

The effect of an anisotropic stress state on the monotonic behavior of calcareous sand has been rarely investigated, although calcareous sands in the field mainly experience anisotropic consolidation rather than isotropic consolidation. This study provides a laboratory study of the undrained and drained behaviors of dense calcareous sand consolidated anisotropically under various initial mean effective stresses (p0′) and anisotropic stress ratios (Kc), where significant effects of p0′ and Kc on the strength-deformation-degradation characteristics of calcareous sand can be observed. For undrained tests, higher deviatoric stress can be reached under a lower p0′. This could be due to the buildup of negative excess pore-water pressure (u) induced by sample dilatancy. As Kc increased, the negative u accumulated more distinctly, whereas the maximum and minimum u decreased. For drained tests, the maximum deviatoric stress decreased as Kc increased, even though more dilatancy occurred. Undrained loading generally resulted in a higher extent of particle breakage due to the buildup of negative u that increased the mean effective stress. A unique critical-state line was observed in both isotropic and anisotropic samples regardless of the loading condition. However, unlike quartz sand, a pseudosteady state that defined the transition from a dilatancy-dominant nonflow response to breakage-dominant stress degradation was observed in calcareous sand before reaching the critical state. Results also reveal the negligible effect of Kc on the peak-state stress ratio at undrained conditions. However, Kc had significant effect on stress ratio at peak or phase-transformation state in experiments under drained conditions, which can be well represented by using the concept of state dependence. Moreover, Kc had an adverse effect on the initial secant modulus.

Exploring packing density, critical state, and liquefaction resistance of sand-fines mixture using DEM

A series of monotonic and cyclic triaxial shearing tests are simulated by discrete element method (DEM) to explore packing density, critical state, and liquefaction resistance of sand-fines binary mixtures. It is found that there is a threshold fines content (FCth) that makes void ratio reach the minimum value and it is affected by the relative density of the mixture. A unique critical state line (CSL) is obtained in equivalent skeleton void ratio-mean effective stress (e*-p') plane regardless of the fines content. The critical stress ratio of the mixture slightly increases as fines content increases, and its average value is around 1.20. The e* and ψe* (state parameter based on e*) can unifiedly characterize the cyclic liquefaction resistance of the mixtures with different fines contents. The active particles of binary mixtures that participate in the force chains are explored from a microscope perspective. It reveals that there is a unique micro CSL in the mechanical coordination number-mean effective stress (MCN-p') plane despite of fines contents, and the micro state parameter (ψMCN) can also successfully and unifiedly characterize the cyclic liquefaction resistance of sand-fines mixtures.

Effect of fiber-reinforcement on the mechanical behavior of sand approaching the critical state

Several types of ground improvement methods that employ fiber-reinforcement have been developed in recent years. A series of consolidated drained triaxial compression tests has been conducted here to examine the effect of short fibers on the mechanical properties of Toyoura sand. Sand with 0%, 0.2%, 0.4%, and 1% fiber contents, prepared to yield random distribution, was sheared under several confining pressures and controlled via their initial relative densities. The test results showed that the maximum and residual deviatoric stresses increased, whereas the volumetric expansion decreased with an increase in fiber content. Although the stress ratio η ( =q / p ′) and specific volume changed depending on the fiber content and confining pressure with shear progression, they each reached the same values for a definite fiber content at the end of shearing, independent of initial relative density. In other words, the unique critical state line can be found for a definite fiber content. Moreover, the greater the fiber content, the larger the slope of the critical state line at the end of shearing. Additionally, as the length of fibers shortened with the same percentage of fiber inclusions in sand, the deviatoric stress and the stress ratio decreased, approaching the shear-strain-volumetric response of unreinforced sand.

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.

Soil Fabric and Transitional Behavior in Completely Decomposed Granite: An Example of Well-Graded Soil

Unlike sedimentary soils, limited studies have dealt with completely decomposed granite (CDG) soils, even though they are plentiful and used extensively in several engineering applications. In this paper, a set of triaxial compression tests have been conducted on well-graded intact and disturbed CDG soils to study the impact of the fabric on soil behavior. The soil behavior was robustly affected by the soil fabric and its mineral composition. The intact soil showed multiple parallel compression lines, while a unique isotropic compression line was present in the case of disturbed soil. Both the intact and disturbed soils showed unique critical state lines (CSL) in both the e-log p′ and q-p′ spaces. The intact soil showed behavior unlike other transitional soils that have both distinct isotropic compression lines ICLs and CSLs. The gradient of the unique ICL of the disturbed soil was much more than that of the parallel compression lines of the intact soil. In the intact soil, the slope of the unique CSL (M) in the q-p′ space was higher than that of the disturbed soil. The isotropic response was present for both the intact and disturbed soils after erasing the inherited anisotropy as the stress increased with irrecoverable volumetric change. Soil fabric is considered the dominant factor in the transitional behavior and such a mode of soil behavior is no longer restricted to gap-graded soil as previously thought.

DEM analysis of monotonic and cyclic behaviors of sand based on critical state soil mechanics framework

A series of monotonic and cyclic triaxial shearing tests on Toyoura sand are simulated by discrete element method (DEM) incorporating rolling resistance. The input parameters are calibrated against laboratory triaxial test data considering different initial states and monotonic loading paths. The calibrated DEM model successfully captures the density and stress dependency of sand behavior under both monotonic and cyclic conditions. It is shown that when approaching liquefaction, contact yielding alters from sliding-dominant to rolling-dominant. The expression of mechanical redundancy index (IR) is derived considering both effects of contact sliding and rolling. The IR = 1.0 condition is shown to be a unified criterion distinguishing between solid state and liquid state upon both monotonic and cyclic liquefactions. A unique micro critical state line (CSL) is obtained in MCN-p′ plane. The cyclic resistance ratio is exponentially correlated with both the macro state parameter (ψe0) derived from the e-p′ CSL and the micro state parameter (ψMCN0) determined from the MCN-p′ CSL. The specimens with the same ψe0 may have distinct cyclic behaviors, while cyclic behaviors of specimens with the same ψMCN0 are close to each other, indicating that ψMCN0 is a more plausible state variable for characterizing the behavior of sand than ψe0.

Mechanical behaviour of low–medium density destructured White Chalk

Low- and medium-density White Chalk often destructures during civil engineering works, forming a putty that exhibits problematic low strengths in the short term but may build-up strength with time. The underlying mechanisms that control the mechanical performance of the material are not well understood. This paper explores the prospect of developing a framework to characterise the behaviour of chalk putty. To this end, triaxial tests were carried out using low- and medium-density reconstituted chalks produced by different methods. Using void ratio against mean effective stress results, a unique critical state line (CSL) is proposed, regardless of parent rock origin or the crushing process used to generate the putty material. The CSL was also found to satisfactorily fit independent test data by various authors, even though each independent sample material may have had different ‘intrinsic’ CSLs. This was suggested to stem from the similar particle characteristics of the chalks used. An assessment of the ageing effect indicates increases in strength as a result of densification due to consolidation and secondary compression, however, the end-of-test state could still be described using the CSL.

A study of completely decomposed volcanic rock with a transitional mode of behaviour

A transitional mode of behaviour is seen in some soils where the specific volumes of samples do not converge to the same values at the same stress state within the ranges of strains that can be achieved in laboratory tests so there are no unique normal compression or critical state lines. This type of behaviour has been found in different soils but not previously in soils resulting from decomposed igneous rocks. In order to investigate the possibility of transitional mode of behaviour in a decomposed volcanic rock, an extensive series of one-dimensional compression and triaxial tests were conducted on samples in reconstituted and intact states. The important features of transitional mode of behaviour in soils have been identified, that is, the presence of non-unique and parallel normal compression and critical state lines. The behaviour of the soil is therefore dependent on the initial specific volume. The degree of transitional behaviour is strong, particularly in the reconstituted samples, but it is less clearly identified in the intact samples due to the small range of initial specific volumes available. These observations indicate that the transitional mode of behaviour, previously seen in sedimentary soils and artificial soil mixtures, can be extended to some weathered igneous rocks. Determining the effects of structure is difficult due to the non-unique intrinsic properties, but nevertheless, the effects of structure have been identified and discussed.

Influence of Initial Void Ratio on Critical State Behaviour of Poorly Graded Fine Sands

The application of critical state framework depends on the presence of either a unique critical state line (CSL). However, many authors have observed that a transitional behaviour occurs in certain granular intermediate soils in which the fines content and the initial void ratio have a significant effect on the location of this line. This work investigates these effects in poorly graded granular soils as previous studies reported that this type of soil does not exhibit transitional behaviour. Results from this study reveal that poorly graded fine-grained sand exhibits transitional behaviour similar to that of intermediate soils, and subsequently, it can be grouped into ranges of initial densities in which each group approaches a unique CSL in v:lnp’ space. A unique state boundary surface is identified by determining the critical state parameters from each group and using these parameters to normalise the stress paths; this shows that the critical state framework can be successfully applied to this type of soil.

Critical state behaviour of an unsaturated high-plasticity clay

This paper describes a series of tests carried out to examine triaxial compression and shearing of a high-plasticity compacted clay. Reconstituted and compacted samples which were saturated are used as a basis for interpreting the unsaturated test results within a critical state soil mechanics (CSSM) framework. The shear strength behaviour of unsaturated soils have previously been found to be reasonably well captured in a CSSM framework, whereas the volume change behaviour has been more difficult to rationalise. Based on test results presented using the Bishop effective stress, the volume change behaviour during shear suggests that a unique critical state line is approached, independent of the applied suction. The normalised shearing behaviour of the compacted unsaturated soil is interpreted to be analogous to that of saturated-structured soils.

Instability of saturated granular materials in biaxial loading with polygonal particles using discrete element Method (DEM)

Sandy soils may become unstable under loading which causes large deformations and consequently, impose damages to existing structures. In this research, Discrete Element Method (DEM) is used to simulate 2D drained and undrained behavior of polygonal granular materials to investigate instability occurrence. The so-called cylinder method is applied to simulate the undrained behavior that a pipe is assumed between neighboring pores to allow fluid flow. The applicability of this method was evaluated with constant-volume approach. The advantage of the cylinder method is to assess the distribution of fluid pressure. Comparison of the results indicate good match. Based on both drained and undrained simulations, a unique critical state line was obtained; however, the position of instability line was influenced by the initial void ratio. At the onset of potential instability, the central pore pressure increases highly; however, it reduces afterwards and the fluid pressure is almost distributed uniformly throughout the sample.

Quantifying “transitional” soil behaviour

The last decade has seen an increasing amount of research on so called “transitional” soils that are characterised by incomplete convergence to unique normal compression lines and/or critical state lines in simple laboratory tests. This topic has often provoked reaction, perhaps because some have seen it as a challenge to critical state frameworks of soil behaviour. A particular issue is whether incomplete testing or other test defects might cause such an apparent behaviour. Confusion around the topic has not been helped by the wide range of degrees of convergence seen for different materials and differences seen between convergence in compression and shearing. This paper proposes a unifying means of plotting laboratory test data from such soils that will hopefully provide a rational framework for such discussions, since it makes explicit the degree of convergence towards unique volumetric states for different forms of loading. Data are examined for three “transitional” soils. The results show that bringing about convergence for these soils would require strains beyond those that may easily be applied and that the lack of convergence cannot solely be an artefact of test defects. Plastic volumetric strain was found to cause much faster convergence than plastic shear strain.

Mineralogy, Micro-fabric and the Behavior of the Completely Decomposed Granite Soils

The main objective of this study is to investigate the impact of the micro-fabric and soil mineralogy on the overall macro-behavior of the completely decomposed granite soil through a set of drained and undrained triaxial shearing and isotropic compression tests on a medium-coarse grading completely decomposed granite soil. The mineral composition of the soil was a substantial factor governing the compressive behavior. The soil compressibility increased significantly in the case of existence crushable and weak minerals within the soil minerals like fragile feldspar, as well as the high content of fines, especially the plastic fines. The scanning electron microscopic photos indicated that the micro-fabric of the soil had a paramount impact on the compressive behavior. The mechanism of the volumetric change depended on the stress levels, the soil mineral composition and the grain morphology. In the low consolidated stress levels, the soils’ grains rearrangement was the prevailing mechanism of the volumetric change, particularly with the absence of weak and crushable minerals. On the other hand, at the high consolidated stress levels, particles’ crushing was the prevailing mechanism in the volumetric change. Both the mechanisms of volume change could occur simultaneously at the low stress levels in the case of presence crushable minerals in addition to micro-cracks in the soil grains. The soil showed an isotropic response after 250 kPa, as this stress level erased the induced anisotropy from the moist tamping preparation method. Under the drained shearing conditions, the soil showed a contractive response, while during the undrained shearing conditions, the soil exhibited both the contractive and dilative responses with phase transformation points. The studied soil showed a unique critical state line, irrespective of the drainage conditions and initial states, the critical state line was parallel to the isotropic compression line in the void ratio effective stress space. In the deviator effective mean stresses space, the studied soil approached a unique CSL with a critical stress ratio equal 1.5, corresponding to critical friction angle of 36.8°.

Mechanical behaviour of Panzhihua iron tailings

Safety problems have concerned many researchers studying tailings dams in recent years, as they have a high risk of failure due to liquefaction. Existing analysis of liquefaction in tailings within a critical state framework has relied on the critical state line (CSL) being unique in the volumetric plane. However, recent advances have highlighted a so-called “transitional” behaviour in which the location of the normal compression line (NCL) and CSL is a function of the density of the soils at deposition. This paper presents a detailed investigation of the mechanics of tailings taken from three locations of an iron tailings impoundment. Reconstituted samples were prepared by different methods and at different densities. No transitional behaviour was found, although the results show that the rate of convergence of the compression curves changes, with the finest pond material reaching a unique NCL earliest. The preparation method was found not to have a large effect on the behaviour for these tailings. Unique CSLs could be clearly identified for all the three tailings, but with different shapes, giving rise to a changing susceptibility to liquefaction. This susceptibility tends to increase from the pond to the upper beach.

Transitional behavior in well-graded soils: An example of completely decomposed granite

This study presents the results of a series of isotropic compression tests and drained and undrained triaxial shearing tests on naturally graded and reconstituted completely decomposed granite soils to investigate their compressive response and transitional behavior. Naturally graded soils exhibited unique isotropic compression and critical state lines within the stress levels studied. Soils reconstituted by increasing the sand content by 5% and 10% revealed non-unique isotropic compression lines; however, unique critical state lines were present in the e-log p' space. The degree of non-convergence increased as the sand content increased. The value of the m parameter, which is used to quantify the transitional mode and is defined as the ratio between the changes in the final and initial specific volumes (i.e., m = ∆v2/∆v1; see Fig. 1), increased from 0 in the case of naturally graded soil to 0.3 and 0.73 for reconstituted soils with increased sand content of 5% and 10%, respectively. For naturally graded soils, the initial void ratio affects only the initial compression response, and its influence does not extend to the normal compression line. In the case of reconstituted soils, the fabric that results from various compaction efforts exerts a significant effect on the soil′s compressive response. However, this fabric cannot withstand large strain during the shearing path and is completely destroyed, producing a unique fabric in the critical state. Both natural and reconstituted soils revealed isotropic responses during the loading and unloading compression paths with unrecoverable volume change. The transitional behavior is no longer limited to gap-graded soils, and grading is no longer the only dominant factor in this behavior. The transitional mode occurs due to relatively inconsiderable changes in soil mineralogy, grading, and microstructure.

Strength Behavior of Sedimented Gypsum Slurry

Abstract Rapid increases in the production of gypsum waste from the Flue Gas Desulphurization process necessitates that proper impoundments be built with an adequate understanding of the strength behavior of the sedimented gypsum slurry. This article presents laboratory experimental results that describe its physical characteristics and strength behavior. The physical characterization includes a particle size analysis and specific gravity of solids, which conform to ASTM standards. The strength behavior is described from a series of consolidated isotropically undrained triaxial compression tests that is performed at six levels of effective confining stress with two tests for each effective confining stress. The results and parameters are presented via critical state analyses in q-p’ and e-p’ spaces as well as a Mohr-Coulomb model. The analysis reveals two distinguishable regimes during shearing, which are classified as structured and destructured regimes, at which the sediment undergoes a change in strength behavior from being an intact structure to becoming a broken structure. A unique critical state line is found to be unparalleled with the isotropic compression line.