Deviatoric Stress Paths Research Articles

An extended graphical solution for undrained cylindrical cavity expansion in K0‐consolidated Mohr–Coulomb soil

AbstractThis paper develops a general and complete solution for the undrained cylindrical cavity expansion problem in nonassociated Mohr‐Coulomb soil under nonhydrostatic initial stress field (i.e., arbitrary values of the earth pressure coefficient), by expanding a unique and efficient graphical solution procedure recently proposed by Chen and Wang in 2022 for the special in situ stress case with . It is interesting to find that the cavity expansion deviatoric stress path is always composed of a series of piecewise straight lines, for all different case scenarios of K0 being involved. When the cavity is sufficiently expanded, the stress path will eventually end, exclusively, in a major sextant with Lode angle θ in between and or on the specific line of . The salient advantage/feature of the present general graphical approach lies in that it can deduce the cavity expansion responses in full closed form, nevertheless being free of the limitation of the intermediacy assumption for the vertical stress and of the difficulty existing in the traditional zoning method that involves cumbersome, sequential determination of distinct Mohr–Coulomb plastic regions. Some typical results for the desired cavity expansion curves and the limit cavity pressure are presented, to investigate the impacts of soil plasticity parameters and the earth pressure coefficient on the cavity responses. The proposed graphical method/solution will be of great value for the interpretation of pressuremeter tests in cohesive‐frictional soils.

Numerical modelling of contact adhesion in a random assembly of elastic–plastic particles

The prediction of tensile strength properties of powder compacts remains an important industrial issue. In particular, one of the main problems of the powder compaction process is the failure of compacts. Indeed, some powder compacts exhibit cracks which appear during compaction. Such defects occur due to localised tensile or shear stresses, for example close to geometrical singularities. They are also related to the ability of a powder to create enough adhesion at contacts between particles to withstand tensile stresses. Therefore, cracks are a consequence of phenomena occurring at the particle scale and below, down to the molecular scale. To help understanding this mechanism, a particle-scale, numerical method called the multi-particle finite-element method was developed using the finite-element software suite Abaqus (Abaqus 6.14 Documentation, 2016). Such a method allowed to explicitly model the microstructure of a granular media idealised as an assembly of elastic–plastic spheres. The particles were meshed such that their deformations were fully taken into account, using a continuum-mechanics-based material model. The interactions between particles were managed using finite-element contact formulations. A multi-scale, adhesive contact model was developed based on the literature and implemented into the multi-particle finite-element code. The contact model was based on a surface energy formulation weighted by the roughness model developed by Pullen and Williamson (1972). It introduced a novel aspect, the development of adhesion under the effect of external mechanical loads, which is consistent with the cold compaction process. This model was then applied to predict the mesoscopic properties of a packing of spheres, i.e. its response to mechanical stresses of any type, in particular strongly deviatoric stress paths. Such a method intends to be a help toward the development of an efficient continuum model for the modelling of the powder compaction process.

New perspectives on preshearing history in granular soils

The design of deep dump slopes for opencast mines usually requires information about the soil resistance to liquefaction during earthquakes. This resistance depends not only on the initial stress, the initial density, and the amplitude of the cyclic loading, but also on the preshearing, that is, the deviatoric stress path applied to the soil before the cyclic loading. To explore the influence of preshearing on the subsequent soil behaviour, a set of triaxial tests with a combination of undrained preshearing and drained stress cycles using two sample preparation methods is presented. It is shown that the preshearing as well as the preparation method have a major influence on the strain accumulation upon cyclic loading. Simulations of the experiments with four advanced constitutive models reveal that neither the long-lasting effect of preshearing nor the preparation method can adequately be captured by all of the models. This deficiency of the constitutive models can lead to unsafe designs due to the overestimation of the cyclic resistance to liquefaction and to the underestimation of long term settlements.

Experimental quantification of 3D deformations in sensitive clay during stress-probing

Unique four-dimensional (4D) deformation data are collected during drained triaxial tests on intact specimens of a natural sensitive clay. This requires the development of a miniature triaxial cell for advanced stress path testing, specifically designed for X-ray computed tomography. Salient features include the omission of a membrane, and a mounting procedure that minimises disturbance by the experimenter. Three distinct drained stress ratios are studied for pseudo-isotropic, K0, and highly deviatoric loading paths. The results indicate that the K0path shows the most uniform deformation mechanism, where the measured ratio of deviatoric and volumetric strain increments reach the stress ratio applied at boundary value level for large magnitudes of total strain. The pseudo-isotropic test also reaches a strain ratio close to η at large total strain levels; however, the deformation field is less uniform. Furthermore, the highly deviatoric stress path shows the most heterogeneous deformation fields commensurate with the applied stress ratio, although the ratio of deviatoric and volumetric strain increments falls above the η applied. The mean value of the three-dimensional spatial fields of strain corresponds well with the changes observed at boundary level, supporting prior research on drained stress-probing on clays for which there are no 4D deformation data available.

Observed responses of saturated sand under constant deviatoric stress path considering influence of loading amplitude

The soil in embankment dams and slopes may accumulate irreversible deformation due to water level variations. During this process, the soil skeleton experiences a constant deviatoric stress path, along with cyclic mean effective stress. In this work, triaxial drained tests were conducted on saturated sand under a low rate of strain to investigate the strain response along such stress paths, considering the influence of loading amplitude. The test results demonstrated that the volumetric strain of the saturated sand varied when the consolidation stress conditions were different. When the consolidation deviatoric stress was increased from 300 kPa to 900 kPa, the effect of cyclic load amplitude on the volumetric strain was strengthened, while the cumulative effect was weakened. The shear strain curves under different loading amplitudes were parallel to each other regardless of the consolidation stress condition. However, the cumulative shear strain showed great differences. The accumulation of shear strain was increased with the enhancement of loading amplitude. When the consolidation deviatoric stress was held constant at a low stress level, the effect of loading amplitude on volumetric strain was greater than that on shear strain. However, with the enhancement of stress level, the effect on shear strain was significantly enhanced.

Instability of municipal solid waste along the constant deviatoric stress path and its engineering significance

To investigate the instability behaviours of municipal solid waste under the reduction of effective means stress, consolidated undrained (CU), constant shear drained (CSD) and constant shear undrained (CSU) tests were conducted on artificial waste specimens. In CU tests, the effective stress paths were modified by considering the particle compressibility, and the waste specimens did not exhibit pre-failure softening behaviours. Instability of the waste was observed in CSD tests, but was not observed in CSU tests. When the waste specimens became unstable, the axial strains increased rapidly and the volume was severely dilated. Softening of the waste specimens, manifested in the inability to maintain constant deviatoric stresses, was also observed. For waste specimens with similar void ratios, the instability points were located around an instability line (IL), and the slope of the IL decreased with an increase in the void ratio. Some factors, including the stress path and deformation characteristic of waste, may lead to the instability of waste specimens in CSD tests by influencing the effects of reinforcements. In engineered landfills, high pore pressure is often generated in waste mass and then leads to the obvious reduction of the effective stress of waste; thus, waste instability needs to be considered in the safety evaluation of waste slopes.

Comparison of Deformation Behavior of Saturated Sand under Constant and Variable Deviatoric Stress

The cyclic triaxial tests were carried out on Fujian standard sand under two stress paths, the constant deviatoric stress path (CDS) and constant stress-ratio path (variable deviatoric stress, VDS), and the influence of cyclic deviatoric stress on the development characteristics of saturated sand was preliminarily discussed. Under the condition of the same consolidation stress state and amplitude of cyclic spherical stress, the amplitude of deviatoric stress under the two stress paths was different. The test results indicated that cyclic deviatoric stress had significant effect on the volumetric and shear strain in soil. When the consolidation deviatoric stress was relatively small, the volumetric and shear strain curves under these two stress paths almost coincided. However, the cyclic deviatoric stress had a stronger effect with an increase in the consolidation deviatoric stress. During the loading and unloading stages, the slope of the volumetric strain curve under the VDS path was smaller than that under the CDS path. The accumulated volumetric strain under the VDS path was greater than that under the CDS path. In the loading stage, the growth rate of shear strain under the VDS path was greater than that under the CDS path, but the opposite relationship was observed in the unloading stage. The presence of cyclic deviatoric stress accelerated or slowed down the accumulation of shear strain. These phenomena were related to the positional relationship between the stress state of soil and the critical state line.

Microstructural organization of remoulded clays in relation with dilatancy/contractancy phenomena

This experimental work aimed to identify local mechanisms in remoulded clays under different triaxial loading conditions. The behaviour at a given stress level reached by two different stress paths, i.e. the conventional constant σ′3 stress path and the purely deviatoric stress path, and the behaviour at two different stress levels along a given stress path were examined. The investigation concerned both normally consolidated and overconsolidated saturated specimens of remoulded kaolin clay. The microstructural states of the clay specimens induced by different triaxial loading paths were examined at two different scales using the scanning electron microscopy and the X-ray microtomography. The results highlighted five particle orientation modes that could be activated. These modes seem to be highly dependent on the stress level, the overconsolidation ratio and the stress path. Mesocracks were found to develop within strongly overconsolidated specimens accompanied by the occurrence of dilatancy. The proposed conceptual modes provide an interesting approach to understand the mechanical behaviour of remoulded clays, especially the macroscale dilatancy phenomenon, through the possible activation of different mechanisms at micro- and mesoscales.

Creep behavior of unsaturated cohesive soils subjected to various stress levels

This paper presents the results of an experimental investigation carried out on disturbed clay samples to analyze their creep behavior. The experimental program included compression triaxial tests with varied degree of saturation of the samples and stress level. Triaxial tests were performed at imposed strain rate varied from 0.005 to 0.10%/min. Various stress paths have also been tested including isotropic consolidation and deviatoric stress. The obtained results showed that shear deformation increases with the initial degree of saturation and stress level of clay samples. At fixed stress level and for both isotropic and deviatoric stress paths, the initial degree of saturation and the second invariant of the strain tensor varied with a similar trend. The variation of axial creep strain is correlated with time in a semi-logarithmic function.

Linking permeability to crack density evolution in thermally stressed rocks under cyclic loading

AbstractTo improve our understanding of the complex coupling between circulating fluids and the development of crack damage, we performed flow‐through tests on samples of Etna basalt and Westerly granite that were cyclically loaded by deviatoric stresses. The basalt was naturally microfractured, while the relatively crack‐free Westerly granite was thermally pretreated to 500°C and 800°C to generate microcrack damage. Samples were repeatedly loaded and then unloaded under deviatoric stress paths and ultimately to failure. Permeability and water volume content were measured throughout the loading history together with the differential stress. Permeability decreases at low differential stresses and increases at intermediate differential stresses up to a steady value at failure. We use water volume content as a proxy for fluid storage and show that both permeability and storage evolve with damage and evolution of crack density. We use crack models to represent the evolution of permeability as a function of loading state and are able to independently link it to the observed evolution of deformability, used as an independent measure of crack density.

Coupled water retention and shrinkage properties of a compacted silt under isotropic and deviatoric stress paths

Although it is generally recognized that unsaturated soil behavior is governed by two constitutive variables (matric suction and net normal stress) and that the hydromechanical behavior of unsaturated soil is coupled, a water retention curve obtained from tests under zero stress and assuming no volume change is still fairly common. A relatively limited number of studies on the stress path–dependent water retention curve (SDWRC), particularly under a broader range of stress paths, exist in the literature. In this paper, the SDWRC, shrinkage curve, and swelling curve of a compacted silt subjected to isotropic and deviatoric stress paths are presented. The test results show that the air-entry value (AEV) increases, but the hydraulic hysteresis loop decreases with an increase in net mean stress. Furthermore, for a given stress level, the K0-compressed specimen exhibits higher AEV, but a smaller hysteresis loop than that of the isotropically compressed specimen. A nonlinear shrinkage curve is observed and the gradient of the post-yield shrinkage curve depends on the degree of saturation and net mean stress, but is independent of the stress path. For the range of suction studied, the gradient reduces with a decreasing degree of saturation, but with an increasing net mean stress. Finally, the test results are compared with the prediction of a model based on two independent constitutive stress variables.

Evaluation of Dang Van stress in Hertzian rolling contact

ABSTRACTThe equivalent Dang Van stress under Hertzian contacts is evaluated over the subsurface space using four computational approaches. The accuracy and computational efficiency of the different models is assessed. It is found that an approach consisting in finding the minimum circumscribed hypersphere to the deviatoric stress path in time gives a good trade‐off between accuracy and efficiency. It is also shown that a very computationally cheap approximation employing half the peak Tresca shear stress results in good agreements in the entire subsurface space for conditions relevant under wheel–rail contacts.

A Modified Triaxial Apparatus for Measuring the Stress Path-Dependent Water Retention Curve

Abstract This article reports a modified triaxial apparatus for measuring the stress path-dependent water retention curve (SDWRC) of unsaturated soils under isotropic and deviatoric stress conditions. In this modified triaxial apparatus, an open-ended, bottle-shaped inner cell is installed together with a differential pressure transducer to measure the total volume change of a specimen accurately for the correct determination of the degree of saturation of an SDWRC. Details of the calibration and test procedures are described and discussed. Some test results from compacted samples of a completely decomposed tuff, i.e., silt of low plasticity, are also presented in order to demonstrate the key features of the modified apparatus.

Modeling Failure and Deformation of an Assembly of Spheres with Frictional Contacts

A novel mesoscale granular continuum model is derived by homogenizing the mechanical behavior of six particles in contact forming an octahedron structure. The elastic behavior at the particle contacts is simulated in accordance with Hertz theory and the frictional behavior is taken into account by means of an evolution law for the contact shear stiffness. The mesoscale continuum model is calibrated on discrete element simulations of a cuboidal volume filled with identical spheres and loaded under axisymmetric compression. By imposing a set of radial deviatoric stress paths, the failure contour is computed in the deviatoric plane of the principal stress space.

Behavior of Uncemented Sands and Grouted Sands Before Peak Strength

ABSTRACT The results of triaxial tests carried out on both uncemented sands and sands injected by a microfine cement grout are presented in order to highlight and compare the main features of their mechanical behavior. The device used to prepare homogeneous samples of grouted sands in the laboratory is first described. The effect of the grout injection on the strength properties of three granular soils is then shown. By use of bender elements, the different evolutions of the shear modulus GVh,max in the small strain domain along isotropic and deviatoric stress paths are presented for both uncemented and grouted sands.

Stress–strain behaviour of a loosely compacted volcanic-derived soil and its significance to rainfall-induced fill slope failures

The stress–strain behaviour of a soil is crucial to the recognition of the mechanism of slope failure. Triaxial tests, composed of isotropically consolidated drained (ICD) and undrained compression (ICU) tests and anisotropically consolidated constant deviatoric stress path (CQD) tests, were carried out with the aim of investigating the stress–strain behaviour of loosely compacted volcanic-derived soils. The fact that the critical states are the same for ICU, ICD and CQD tests may show that the critical state is independent of the above three stress paths. The critical state line, as defined in critical state soil mechanics, is obtained from the e–log p′ and q– p′ plots based on the results of the above tests. The initial state of the consolidated specimens at initiation of failure may be classified as dilative or contractive in the light of the locations of the soil state relative to the critical state line. For contractional soils, the increased pore water pressure generated by rainfall infiltration leads to a contractive failure in a drained manner, giving rise to high excess pore water pressure. The excess pore water pressure caused by contraction cannot be dissipated instantly, resulting in a decrease in the shear resistance of the soil. The failure process is rapid. The failed soil mass is prone to flow after failure under the action of gravity due to its high moisture content and inflow of surface runoff and rainwater. For dilational soils, the increased pore water pressure resulting from infiltration leads to dilation, which reduces pore water pressure and thus increases the shear resistance of the soil. However, continued rainfall infiltration may be able to equilibrate the reduction in pore water pressure caused by dilation and, therefore, the dilation or displacement can continue. In Hong Kong, volcanic-derived soil is characterized by high permeability. Both the high permeability of volcanic-derived soil and a shallow failure surface make it possible for the reduction in pore pressure to equilibrate relatively quickly. Therefore, the failure is also rapid, at least for poorly compacted fill slopes.

Analysis of rainstorm-induced slide-debris flows on natural terrain of Lantau Island, Hong Kong

Lantau Island, the largest outlying island of the territory of Hong Kong, experienced a severe rainstorm on 4–5 November 1993, which induced >800 slope failures on natural terrain there. Detailed field investigations were carried out to study the failure modes, in relation with various influencing factors. It was found that the occurrence of slide-debris flows has a close relationship with bedrock geology, slope gradient, vegetation cover and micro landform. The failure modes of slide-debris flows may be classified into translational slides and rotational slides, and the former are predominant. Analysis of the hydrological response of colluvial slopes during the rainstorm indicated that the majority of the failures were caused by the development of a perched water table in the thin surface layer of colluvium of volcanic origin due to infiltration during the heavy rain. Undisturbed soil samples from south Lantau have been subjected to anisotropically consolidated undrained compression tests at comparatively low stress levels. Constant deviatoric stress path tests (CQD) simulating the stress path in the field at in situ stress levels have been performed to investigate soil behavior. The CQD test results indicate that the material of slopes at undisturbed state is brought to dilation because of the increase in pore water pressure caused by infiltration of rain water. For a translational slide, the displacement, resulting from dilation, may destroy cohesion along the failure surface and locally within the interior of the slide. The surplus water during the intense rainstorm was able to equilibrate the reduction in pore pressure caused by dilation, and the dilation and displacement may be further increased. The strain-softening after significant strains triggered debris flow mobilization. However, for a rotational slide, the increase in pore water pressure caused by surplus water infiltration during the intense rainstorm could not equilibrate the reduction in pore pressure caused by dilation, much or even all of the sliding block could not mobilize into a debris flow.

Correspondence between Strain Path and Stress Path in Plastic Deformation.

This paper deals with the connections between the local geometries of associated paths of stress and strain under plastic deformation. This is a classical topic; nevertheless, some practically important aspects remain to be investigated in depth. The studies of the mutual relations between these paths reported in the literature have been performed in plane deformation, where the shape of stress path on the (σ1, σ2) plane is compared with the strain path shape on the (ε1, ε2) plane. However, even though plane stress deformation is assumed, there exists an ε3 component. Hence, the planar shape of strain path on the (ε1, ε2) plane does not show the real path shape, but is only the projection of the three-dimensional path to this plane. The strain in plastic deformation is always constraint on the deviatoric plane passing through the origin, and its shape correlates with the shape of deviatoric stress path. Therefore, the intrinsic correlation between strain and stress should be discussed on that plane, where Levy-Mises theory gives a very simple correspondence showing that the stress vector changes its angle with a rate equal to the curvature of the strain path. Taking into account the stress rate dependence in the constitutive equations used, the effect of this dependence on the shape correspondence between these paths is discussed.

Collapse of dry sand

Loose cohesionless saturated materials have proved responsible for a number of serious or catastrophic flow slides. Liquefaction failures with no obvious triggering mechanism have also been recorded. This phenomenon of sudden liquefaction without a presence of cyclic shear stresses is often referred to as spontaneous or static liquefaction. Results from previously published studies suggest that liquefaction is triggered not by the undrained loading and generation of pore pressures but by the collapse of the metastàble sand structure, which in turn generates the driving pore pressures in a saturated material. Hence, the collapse is a characteristic response of a material to certain stress states rather than a result of some enforced undrained loading. This theory is evaluated on very loose dry Ottawa sand. It is shown that the very loose dry sand when subjected to a constant deviatoric stress path significantly changes its behavior at a certain discreet stress state, increases compressibility, and becomes increasingly unstable. This results in collapse – vigorous contraction of the specimen. This structural collapse appears to be equivalent to the pore-pressure generation in collapsing, very loose saturated sand. Key words : dry sand, collapse, liquefaction, stress path, triaxial cell.