Constant Mean Effective Stress Research Articles

A Hydraulic Gradient and Stress-Controlled Erosion Apparatus for Assessing Soil Internal Erosion

Abstract Among the four dominant mechanisms of internal erosion, suffusion appears as one of the most complex. It is indeed the result of the combination of three processes: dislodgement of fine particles, transport of them, and filtration of some fluidized fine particles. These processes depend on the soil’s stress state and on the hydraulic gradient path. Thus, to ensure the repeatability of the suffusion test and to study with accuracy the influence of the aforementioned parameters, a new apparatus was developed. This apparatus is designed to test specimens under a vertical downward flow in hydraulic gradient controlled condition while controlling the confining pressure and the stress deviator, which can be either positive or negative. Ten tests on one cohesionless soil were performed in triaxial conditions, with the same mean effective stress and four different values of stress deviator. To compare with conventional suffusion results, one test is also performed in rigid wall conditions. For all performed tests, the same hydraulic gradient path was applied and particular attention is paid to the repeatability, which implies control of each test step. At the end of each test, the specimen was divided into four layers to measure post-suffusion grain size distributions. The time evolutions of the hydraulic conductivity and the erosion rate permit to identify four different phases. Each phase is characterized by two methods: one based on the hydraulic gradient and the second based on the expended energy by the fluid. The results show the great influence on the suffusion kinetics of the preferential flow paths, which localize in the body of the specimen in triaxial conditions and on the circumference in rigid wall ones. Under a constant mean effective stress, the effect of the stress deviator on the suffusion kinetics appears limited, for the tested soil and shear stress ratios.

Linking the macro-scale response of granular materials during drained cyclic loading to the evolution of micro-structure, contact network and energy components

This study has considered the behaviour of granular materials subjected to drained cyclic loading under constant mean effective stress. Using the discrete element method, cubical, isotropically compressed samples were subjected to 50 loading cycles at different values of mean stress (p' = 100, 200, 300 kPa) and different loading amplitudes (zeta = 5%, 10% and 20% of p'). At low cycle numbers, the deformation mechanism is controlled by contractive volumetric strains, before transitioning to the ratcheting regime, characterised by the persistent accumulation of plastic strains. An energy/work analysis showed that the volumetric work per cycle decreased as hysteresis loops tighten. During ratcheting, most boundary work was dissipated by contact sliding. The mechanical response was controlled by zeta, with little to no influence of p'. For zeta = 5%, deformations were confined to the elastic range, with no increase in secant stiffness G_{sec} or shear strength after cyclic loading. For zeta = 10%, G_{sec} and the shear strength increased after cyclic loading, although no significant expansion of the yield surfaces was observed. The largest loading amplitude (zeta = 20%) induced yielding at low cycles, leading to significant changes in the fabric, volume and yield surfaces of the samples, and a significant increase of shear strength and G_{sec}. At the micro-scale, graph theory was used to quantify the evolution of the contact network. After sim 20 loading cycles, the network reached a steady-state of constant but persistent topology changes in the material, with most of the topology retained between loading cycles.

On the influence of drained cyclic preloadings on the cyclic behaviour of Zbraslav sand

This article experimentally evaluates the influence of directional drained cyclic preloadings on the subsequent undrained monotonic and cyclic response of Zbraslav sand. The cyclic tests were performed on dense samples and under triaxial conditions. The experiments considered several different preloading directions, magnitude of the maximum deviatoric stress reached during the drained preloading stage and deviatoric stress amplitudes during the undrained shearing stage. The experimental results suggested that the rate of strains and pore water pressure accumulation, and therefore, the number of cycles to reach initial liquefaction or failure conditions are remarkably affected by the direction of the drained preloading history. In addition, the preloading direction plays a major role on the contractive/dilative response during the subsequent undrained monotonic loading. In particular, directional drained cyclic preloadings toward positive deviatoric stresses at constant mean effective stress and isotropic compression led to more dilative responses. Contrary, preloadings toward negative deviatoric stresses at constant mean effective stress led to more contractive responses. The results suggest that these major variations cannot be associated to the rather small changes in the relative density of the samples but likely due to fabric changes and induced anisotropy caused by the drained preloading history.

Critical State and Grading Evolution of Rockfill Material under Different Triaxial Compression Tests

One of the most important features of soil behavior is the dependence of stress path. A series of large-scale triaxial compression tests was conducted to investigate the effect of stress path on critical state and particle breakage–induced grading evolution of rockfill material. All tests were first consolidated under constant principle stress ratio condition, and then sheared under three different stress paths, including constant lateral stress σ3, constant mean effective stress p′, and constant vertical stress σ1. Test results indicate that the mean effective stress p′, deviatoric stress q, and void ratio e along different stress paths reached the consistent critical state line (CSL) in the p′-q-e space. There was a power function between p′ and q, and a linear relation between e and (p′/pa)ξ with ξ=0.5 at the critical state. The particle breakage under different stress paths was found to be consistent at the same critical state, and a unique relation among e, p′, and the particle grading parameters at the critical state existed irrespective of stress paths. The test results at the critical state formed a straight line in the e-(p′/pa)0.5-IG space.

The influence of particle-size distribution on critical state behavior of spherical and non-spherical particle assemblies

This paper presents an investigation into the effects of particle-size distribution on the critical state behavior of granular materials using discrete element method (DEM) simulations on both spherical and non-spherical particle assemblies. A series of triaxial test DEM simulations examine the influence of particle-size distribution (PSD) and particle shape, which were independently assessed in the analyses presented. Samples were composed of particles with varying shapes characterized by overall regularity (OR) and different PSDs. The samples were subjected to the axial compression through different loading schemes: constant volume, constant mean effective stress, and constant lateral stress. All samples were sheared to large strains to ensure that a critical state was reached. Both the macroscopic and microscopic behaviors in these tests are discussed here within the framework of the anisotropic critical state theory. It is shown that both OR and PSD may affect the response of the granular assemblies in terms of the stress–strain relations, dilatancy, and critical state behaviors. For a given PSD, both the shear strength and fabric norm decrease with an increase in OR. The critical state angle of shearing resistance is highly dependent on particle shape. In terms of PSD, uniformly distributed assemblies mobilize higher shear strength and experience more dilative responses than specimens with a greater variation of particle sizes. The position of the critical state line in the e–p′ space is also affected by PSD. However, the effects of PSD on critical strength and evolution of fabric are negligible. These findings highlight the importance of particle shape and PSD that should be included in the development of constitutive models for granular materials.

Dilative behavior of kaolinite under drained creep condition

This paper studies the dilative behavior of clay during drained creep along triaxial tests under constant mean effective stress, where the volumetric strain is caused by the sole deviatoric stress variation. Tests were conducted on a saturated reconstituted clayey material by the use of a GDS stress path control apparatus. The development of the axial and volumetric strains was studied with respect to time, stress level (SL) and overconsolidation ratio (OCR). Analysis of the results ascertained that both dilatancy and contractancy phenomena could occur during creep. The magnitude of the dilatancy/contractancy during creep was guided by the test conditions (SL and OCR), which specifically governed the direction of the volumetric strain variations. The position of the stress level vis-a-vis the different volumetric domains defined by monotonic triaxial tests in the (p′–q) plane controls the evolution of the volumetric creep strain. The failure of an overconsolidated specimen could be observed for a stress level located under the maximum strength envelope, but above the critical state line in the p′–q plane, accompanied by a significant dilative behavior during creep.

Experimental and numerical investigation on the effect of moisture on coal permeability

Coalbed methane is a kind of clean energy source and also a kind of hazardous gas threatening the safety of coal mine production. Permeability is a key parameter to evaluate gas migration capability. However, the permeability is influenced by moisture content. Here, a series of seepage experiments were conducted to analyze the development tendency of flux and permeability to reveal the impact mechanism. Experimental results show that permeability tends to be a sharp drop with increasing moisture, but it had a slight fluctuation with relative gas pressure increasing under the constant mean effective stress. Considering the effect of moisture and gas sorption, a new gas–solid coupling model was developed based on experimental results and theoretical analysis and was implemented into FEM software for simulation. The numerical results of the new gas–solid coupling model were in good accordance with the experimental results and have a priority to cube law in precision. This study reveals that, on the one hand, the moisture can influence the adsorption-induced strain and, on the other hand, it can lead to a significant decrease in porosity due to pore volume occupation.

Changing anisotropy of G0 in Hostun sand during drained monotonic and cyclic loading

The inherent and stress-induced anisotropy of saturated Hostun sand has been examined by means of shear wave velocity measurements under drained monotonic and cyclic triaxial conditions. Tests were carried out on samples prepared by moist tamping for a wide range of initial densities in a fully instrumented stress-path triaxial apparatus equipped with bender element instrumentation in three directions. Data have been normalised to account for the variations in void ratio and mean effective stress. The evolution of shear stiffness under anisotropic stress conditions has been explored by performing both constant mean effective stress tests and constant radial stress tests in compression and extension. Some samples were subsequently subjected to multiple drained deviatoric loading cycles, and the evolution of shear stiffness was examined. The tests showed that the initial inherent anisotropy was small, namely, lower than that previously observed in dry pluviated samples of the same sand in a cubical cell apparatus. Changing stress levels in compression or extension resulted in stress-induced anisotropy even when there were no changes in the values for p′, indicating that the widely-used empirical expressions for G0 under isotropic stress states are not strictly applicable under anisotropic stress conditions. The comparison between stress-induced anisotropy in compression and in extension is discussed, and the evolution of shear stiffness during drained cyclic loading is examined. It is concluded that the changes in inherent anisotropy during these tests were small, but that new constitutive models should account for such changes in state with appropriate normalization.

Breakage of an artificial crushable material under loading

The mechanical behaviour of granular materials depends on their grading. Crushing of particles under compression or shear modifies the grain size distribution, with a tendency for the percentage of fine material to increase. It follows that the frictional properties of the material and the critical states are modified as a consequence of the changes in grain size distribution and the available range of packing densities. This paper illustrates an extended experimental investigation of the evolution of the grading of an artificial granular material, consisting of crushed expanded clay pellets under different loading conditions. The changes of grading of the material after isotropic, one-dimensional and constant mean effective stress triaxial compression were described using a single parameter based on the ratio of the areas under the current and an ultimate cumulative particle size distribution, which were both assumed to be consistent with self similar grading with varying fractal dimension. Relative breakage was related to the total work input for unit of volume. For poorly graded samples, the observed maximum rate of breakage is practically independent of initial uniformity. Further experiments at higher confining stress are required to investigate the mechanics of breakage of better graded samples.

Three-dimensional drained behavior of normally consolidated anisotropic kaolin clay

A series of consolidated-drained true triaxial tests with a constant mean effective stress and constant Lode angles during shear is performed on cross-anisotropic kaolin clay. All tests are performed in a fully automated true triaxial testing apparatus. The relative magnitude of the intermediate principal stress, expressed in terms of the b-value, and initial cross-anisotropy show significant influence on the stress–strain, strength, and shear band formation characteristics of the clay. Shear bands form and appear to cause failure in all true triaxial tests performed, except in triaxial compression. The initiation and development of shear bands is observed to take place, when the clay undergoes volumetric contraction. The lower strength exhibited in the shear bands is caused by alignment of the clay particles. This shear band mechanism is different from that observed in granular materials, in which the lower shear strength is reached due to dilation in the shear bands.

A constitutive model for sand based on non-linear elasticity and the state parameter

The paper describes the development of a constitutive model for a poorly graded sand, which was used in geotechnical experiments on buried pipes (reported elsewhere). The sand was tested extensively in the laboratory to determine the state parameter constants. Triaxial tests on the sand included conventional drained triaxial compression tests, as well as more specialized shearing tests at constant mean effective stress and others at constant volume. Single element simulation of the triaxial tests was performed to validate the proposed constitutive model. The adopted model allowed non-linear elastic behaviour prior to yielding. After yielding of the sand, the state parameter-based model for the sand permitted non-associated plastic flow. Dilation and frictional strength were both dependent on the current value of the state parameter. The combination of laboratory testing and single element modelling resulted in the selection of a single set of material constants for the soil, which adequately described the full range of triaxial tests. Subsequently the model was applied to the problem of a plate loading test on the sand and the model predictions were compared with the test data.

Discrete element simulation of crushable soil

Computer simulations of crushable agglomerates were performed using the PFC3D computer code, which adopts the distinct element method (DEM). Agglomerates were made by bonding elementary spheres in ‘crystallo-graphic’ arrays, and by giving each sphere an existence probability of 0·8. Weibull statistics of the crushing strength of the resulting agglomerates, when tested singly between parallel platens, matches that of real silica sand grains. Triaxial tests on a cubical sample made of 389 agglomerates were then simulated. Curves of isotropic compression are shown, and the effect of loading rate on the position of the compression curves is discussed in relation to the practical question of performing DEM simulations as fast as possible without creating inertia errors. Other stress paths, including conventional ‘drained’ triaxial compression, constant mean effective stress, and constant-volume paths, were also simulated from different initial stresses along the virgin e–log p′ curve. The numerical results are compared quantitatively with the testing data of the silica sand. They are also discussed in relation to characterising crushable soils during normal compression, yield, and critical states. Simulation of crushable soils using DEM provides valuable insights concerning the micromechanical origins of soil plasticity.

Discrete element simulation of crushable soil

Computer simulations of crushable agglomerates were performed using the PFC3D computer code, which adopts the distinct element method (DEM). Agglomerates were made by bonding elementary spheres in ‘crystallo-graphic’ arrays, and by giving each sphere an existence probability of 0·8. Weibull statistics of the crushing strength of the resulting agglomerates, when tested singly between parallel platens, matches that of real silica sand grains. Triaxial tests on a cubical sample made of 389 agglomerates were then simulated. Curves of isotropic compression are shown, and the effect of loading rate on the position of the compression curves is discussed in relation to the practical question of performing DEM simulations as fast as possible without creating inertia errors. Other stress paths, including conventional ‘drained’ triaxial compression, constant mean effective stress, and constant-volume paths, were also simulated from different initial stresses along the virgin e–log p′ curve. The numerical results are compared quantitatively with the testing data of the silica sand. They are also discussed in relation to characterising crushable soils during normal compression, yield, and critical states. Simulation of crushable soils using DEM provides valuable insights concerning the micromechanical origins of soil plasticity.

Shear strength and small-strain stiffness of a natural clay under general stress conditions

In this paper the results of an experimental investigation into the mechanical behaviour of a natural stiff clay are presented. A set of drained true triaxial tests was performed, following rectilinear stress paths with constant mean effective stress, having different directions in the deviatoric stress plane. In addition, the small-strain shear stiffness of the soil in the vertical and horizontal planes was measured in the triaxial apparatus, during isotropic and anisotropic compression. To this purpose, three pairs of differently oriented bender elements were used. True triaxial failure data made it possible to plot the failure envelope in the deviatoric plane, and showed that the clay is slightly anisotropic with respect to strength. The analysis of the stress–strain response showed that the soil stiffness depends on the stress-path direction. For shear strains smaller than about 0·01% it was observed that, for monotonic loading conditions, the stress–strain relationships can be described with reasonable accuracy using a non-linear cross-anisotropic elastic model. Bender element test results confirmed that the clay is anisotropic with respect to stiffness, and that the small-strain shear modulus in the horizontal plane is larger, by about 22%, than that measured in the vertical plane. Such results also demonstrated that the small-strain stiffness increases with increasing values of the effective stress ratio experienced by the samples during constant-η compression paths, though this effect was not large because of the overconsolidated state of the soil. A reasonable agreement was finally observed between the shear stiffness of the clay obtained, at small strains, from true triaxial and bender element tests.

On the Stress-Strain Behaviour of Lightly Cemented Clay Based on an Extended Critical State Concept

ABSTRACT In order to evaluate the effects of increasing cementation on the mechanical properties of lightly cemented soils, artificially cemented clay was prepared and a series of standard consolidation tests, undrained triaxial compression tests and constant mean effective stress tests was performed. Based on the experimental considerations, the effects of light cementation on the stress-strain behaviour and strength property are discussed. In addition, based on the theoretical considerations within the framework of the critical state concept, several basic concepts for the development of a constitutive model for lightly cemented clays are presented. The special characteristic of the presented model is the introduction of an internal variable which controls the effects of cementation. The following conclusions are obtained: 1) The failure state of lightly cemented clay may be determined in the balance of cementation, void ratio and stress condition. 2) The failure state line in the p — q space is parallel to that of an uncemented clay and has a certain intercept pr, which characterizes the cementation effect. The slope of the failure state line in the e—In (p + pr) space becomes steeper with any increase in cementation effect. 3) A constitutive model incorporating cementation is proposed. Introduction of a soil constant pr is effective in estimating the mechanical properties of lightly cemented clay.

Triaxial testing of dry, cohesive powder and its application to a modified Cam-clay constitutive model

Triaxial tests were performed on wheat flour to determine the constitutive parameters for a modified Cam-clay model. This elastoplastic model consists of three critical-state parameters: λ, κ, and M. Additionally, there are two parameters representing the initial conditions of a material: e 0 and p c. All critical-state parameters were determined directly from four different triaxial tests: drained compression, undrained compression, constant mean effective stress and hydrostatic compression. The material parameters for the tested wheat flour, following standard statistical techniques, were: λ=0.13, κ=0.022 and M=2.1. The model was tested by comparing model-calculated deformation under triaxial loading conditions identical to those used to determine the parameters. The comparisons between the modified Cam-clay model calculated values and measured values showed that drained triaxial compression tests and constant mean effective stress tests were within the 95% confidence interval. The investigation proved that (1) standard triaxial tests and constitutive models can be successfully applied to dry, cohesive powders, and (2) constitutive parameters defined in soils models can be determined for dry powders by modifying the parameter determination procedure.

Triaxial testing of Lopez Fault gouge at 150 MPa mean effective stress

Triaxial compression experiments were performed on samples of natural granular fault gouge from the Lopez Fault in Southern California. This material consists primarily of quartz and has a self-similar grain size distribution thought to result from natural cataclasis. The experiments were performed at a constant mean effective stress of 150 MPa, to expose the volumetric strains associated with shear failure. The failure strength is parameterized by the coefficient of internal friction μ, based on the Mohr-Coulomb failure criterion.