Stress-dilatancy Theory Research Articles

Cyclic stress–dilatancy relations and plastic flow potentials for soils based on hypothesis of complementarity of stress–dilatancy conjugates

Soil, rocks and rock masses dilate or compact when sheared, i.e., distortion necessitates volume change. This coupling between distortional strains and volumetric strains, described by stress–dilatancy theories, endows soils with manifestation of peculiar characteristics when they are subjected to shear. Stress–dilatancy theories have become central in describing the mechanical energy dissipation mechanism and further establishing flow rules in constitutive modelling of soils. The classical stress–dilatancy theories, such as Taylor's and Rowe's, are endowed with simplicity and descriptive power, but they were developed for describing the dilatancy behaviour of soils subjected to loading in shear (mobilizing away from isotropic stress state) and needed to be extended for describing plastic dissipation and shear-induced volumetric changes when soils are subjected to cyclic shear. In this paper, hypothesis of complementarity of stress–dilatancy conjugates is proposed as a unifying hypothesis for deriving stress–dilatancy relations for both loading in shear and unloading in shear. Then, plastic potential functions are derived based on the resulting stress–dilatancy relations. In so doing, the resulting stress–dilatancy relations and plastic potential functions are rendered with a quality to be used for the modelling of deformation behavior of soils subjected to both monotonic and cyclic shearing. The theoretical framework is applied first for plane strain and axisymmetric stress–strain conditions; and then extended for the general stress condition considering the Lode angle dependency of the shear strength of soils, using the multilaminate framework and applying the Matsuoka–Nakai spatial mobilized plane.

Influence of density on the post-suffusion behavior of gap-graded sand with fines

Suffusion erosion, characterized as the selective detachment and transportation of finer particles by seepage flow, is hazardous to the stability and serviceability of geotechnical structures. The removal of finer particles deteriorates the structure and fabric of the soil, leading to the degradation of its mechanical properties. Studies into the effects of suffusion on mechanical behavior have so far produced disparate results depending on the pre-erosion relative density of the specimens tested. To investigate this issue, small cyclic and monotonic loading tests were performed on intact and eroded gap-graded silty sand specimens in three dispersed density states, using a triaxial cell modified for the purpose of erosion. The variation of Young's modulus showed an inverse relationship with the pre-erosion density of the specimen, as the small strain stiffness decreased in the dense cases and increased in the loose cases. Conversely, Poisson's ratio increased in value as suffusion progressed regardless of the initial density of the specimens. In the contractive phase of monotonic loading, the densification of the coarse soil skeleton by the downward seepage flow resulted in a decrease in contractiveness and an increase in secant stiffness. In the dilative phase, the increase in porosity by the erosion of finer particles reduced the dilatancy and peak strength of the specimens. The results suggest that the pre-suffusion density determines the primary locus of affected mechanical behavior in triaxial compression, which shifts from the contractive phase to the dilative phase with the increase in pre-suffusion density. The critical state strength, inferred using stress–dilatancy theory, was largely unaffected by the erosion of finer particles. As the results indicate, pre-erosion density may be of practical significance in assessing the vulnerability to deterioration and collapse of geotechnical formations and structures subjected to suffusion erosion.

A cohesionless micromechanical model for gas hydrate-bearing sediments

Proper representation and understanding of the mechanical response of the sediment is a prerequisite for successful future gas production from gas hydrate-bearing sediments, in view of the geotechnical issues encountered in recent field trials. Recent investigations have indicated that the increase of sediment strength, due to hydrate existence, is of frictional nature and associated with changes in the kinematic response, and not necessarily due to cementation. Following this idea, this paper presents a non-cohesive micro model for methane-hydrate-bearing sediments, where the hydrate is represented as solid particles precisely positioned between sand particles, contributing to the skeleton response even for small strains. Analytical expressions relating between the geometry, inter-particle properties, and the mechanical response of the hydrate-bearing sediment are developed in the paper. Global stress-strain response is evaluated under simulated triaxial loading, exhibiting stiffer, stronger and more dilative response compared to pure sand samples. It is shown that a trade-off exists between the particle size and the inter-particle friction, which can be unified using a participation factor related to the pore size distribution. As observed in recent experimental investigations, the suggested model results in a cohesionless response when analyzed using Rowe’s stress dilatancy theory.

Modeling Stress–Dilatancy Behavior of Compacted Silty Sand Under Suction-Controlled Axisymmetric Shearing

A thorough stress–dilatancy analysis of statically compacted silty sand is presented based on results from a comprehensive suction-controlled (drained) triaxial test program. Induced soil suction values, via axis-translation and relative humidity techniques, ranged between 0.05 to 300 MPa, with net confining pressures varying from 100 to 300 kPa. A first companion paper documented the strength, stiffness, and stress-induced anisotropy of the same soil under similar test conditions and variables. This paper focuses on the dilatancy rate, stress–strain and volume change responses, shear band formations, and peak as well as critical strength characteristics of isotropically consolidated silty sand under suction-controlled axisymmetric shearing. Augmentation in the peak stress ratio is found to be heavily dependent on the level of matric or total suction imposed, the maximum induced dilatancy, and the critical stress ratio. Experimental observations are also used to substantiate, or further refine, existing stress–dilatancy theories, which has led to the postulation of a simplified new formulation for predicting peak friction angle over the entire test suction range applied.

The Deformation Mechanism of a High Rockfill Dam during the Construction and First Impoundin

The Masjed-e-Soleyman dam is a high rockfill dam with clay core, located in Iran. During construction and first impounding, a considerably high excess pore water pressure has been developed inside the core and has been being dissipated with a very slow rate, so the consolidation deformations have been insignificant. However, there have been reports of noticeable internal deformations in the dam, the crest has also exhibited quick settlements during the first impounding. The main objective of this paper was to identify the deformation mechanism of this dam. For this purpose, the data recorded by its instruments were carefully studied and then a three-dimensional numerical model of the dam was developed. The mechanical behavior of materials was idealized by a hardening strain constitutive model. A numerical method was proposed, based on this constitutive model and Rowe’s stress–dilatancy theory, to simulate the deformation behavior of coarse-grained materials, like rockfills, due to particle size distribution, particle breakage, rotation, and rearrangement under shearing. The results show that significant development of pore pressure in the core and its insignificant dissipation, plastic shear deformations inside the core and extensive collapse settlements of the upstream shell are the main causes influencing the deformation mechanism.

Earth pressure coefficients for reinforcement loads of vertical geosynthetic-reinforced soil retaining walls under working stress conditions

Based on the nonlinear elastic theory and stress-dilatancy theory, two earth pressure coefficients were proposed to analyze the reinforcement loads at the potential failure surface of vertical geosynthetic-reinforced soil retaining walls under working stress conditions. The earth pressure coefficients take into account the force equilibrium and compatible deformations between soil and reinforcement, and can be obtained by solving two implicit functions by an iterative or graphic method. The effects of backfill compaction and facing restriction are taken into account in the earth pressure coefficients by two additional stress factors, which have been derived analytically using straightforward approaches. To validate the effectiveness of the proposed methods, comparisons were made with the results from large scale tests and numerical simulations. It was demonstrated that the reinforcement loads predicted by the proposed methods were in good agreement with the experimental or numerical results.

The lack of true cohesion in hydrate-bearing sands

The mechanical behavior of hydrate-bearing sands is affected by the hydrate quantity, hydrate morphology in the pores, soil skeleton characteristics, stress confinement and more. It has been traditionally assumed that bonding exists between hydrate and sand particles, which affects the global sediment strength. However, this paper shows, extending previous work, that the mechanical effect of hydrate in the sediment has kinematic rather than cohesive nature, based on comparison of mechanical and visual evidences with cemented sand. The visual analysis includes comparison between micro-scale X-ray images of sand containing either hydrate or cement agent. The mechanical analysis includes examining drained triaxial test results of hydrate-bearing sands with cemented sand results, using investigation through stress-dilatancy theories. The paper concludes that all mentioned hydrate-related effects should be interpreted by their influence on the sediment kinematics, rather than on strength characteristics. For a given kinematic response of hydrate-bearing sand, it is shown that the full mechanical behavior can be described using a single friction parameter.

Bonding degradation and stress–dilatancy response of weakly cemented sands

ABSTRACTThe progressive bond breakage of artificially cemented sands induced by shear straining was investigated through conventional isotropically consolidated drained triaxial compression tests. Sand specimens were prepared with a low degree of cementation by adopting a chemical grout. Test results were interpreted in terms of two stress–dilatancy theories for cohesive-frictional materials proposed in literature. The influence of debonding on the stress–dilatancy behaviour of cemented sands was analysed with particular emphasis on the ‘delayed dilatancy’ phenomenon. A bonding degradation curve was determined for each test relating the interparticle cohesion (c) to the magnitude of the total plastic strain vector (εd) and a bond degradation rate factor (Dc) was assessed from each curve. The maximum value of interparticle cohesion (c0) before the onset of bond degradation under shearing was found to correspond with a sharp decrease in the soil stiffness of the specimens. The influence of the effective confining stress (p′c) on both c0 and Dc parameters gathered from each test was also ascertained.

A modified elasto-plastic model with double yield surfaces and considering particle breakage for the settlement analysis of high rockfill dams

This paper improves the elasto-plastic model with double yield surfaces in the context of the hardening soil model for the simulation of the settlement behavior of high rockfill dams. The stress-dependent stiffness values (E50 and Eoed control the shear hardening and the cap yield surfaces, respectively) are modified to exhibit different degrees of evolution with changes in the stress state. A modification of Rowe's stress-dilatancy theory is proposed to account for the influence of particle breakage. Good quantitative agreement between simulated and measured stress-strain relationships can be achieved; in particular, the volumetric strain is much improved from the original model. The developed model is applied to predict the settlement of Nam Ngum 2, a 182 m high rockfill dam, during the construction stage, in conjunction with a three-Dimensional (3D) Finite Element (FE) analysis. The findings show that a good agreement between computed settlements and dam field monitoring data can be achieved.

Modeling the Stress-Dilatancy Relationship of Unsaturated Silica Sand in Triaxial Compression Tests

AbstractIt is well known that partial saturation increases the shear strength and dilatancy of unsaturated sand. However, little research has been carried out on the actual stress-dilatancy relationship. This paper shows that the increase in peak shear strength caused by partial saturation is consistent with an increase in dilatancy, and that conventional stress-dilatancy theories are still valid for unsaturated sand. The use of state indexes as a proxy for dilatancy were investigated and extended to unsaturated sands. Additionally, these indexes can be used to establish a critical state line that is based on material properties only. The validity of the stress-dilatancy theories and the use of state indexes offer simplicity in modeling the shear behavior of unsaturated sand. This will be demonstrated in this paper with the Nor-Sand model, with which the wetting collapse can be explained as a consequence of a loss of dilatancy characteristics.

Rowe’s Stress-Dilatancy Theory for Hydrate-Bearing Sand

AbstractThis note examines the strength characteristics of hydrate-bearing sands using Rowe’s 1962 stress-dilatancy theory. The model was examined through comparison with experimental results, covering a wide range of hydrate saturations and different hydrate formation methods. Using the model, and based on measured volumetric strains with shearing, the stress–strain response was predicted without using a cohesion component in the Mohr-Coulomb failure criteria, using the same friction value, regardless of hydrate saturation. This infers that kinematics, rather than cementation, may possibly be a key point in understanding the effect of hydrate on the apparent strength.

Stress-Strain Response and Dilatancy of Sandy Gravel in Triaxial Compression and Plane Strain

AbstractThe strength and stress-dilatancy of uniform sands has been studied extensively in geotechnical investigations, and practitioners can draw on a wealth of previously reported data for the estimation of their volumetric response. However, the suitability of accepted stress-dilatancy theory and empiricism has not been evaluated for well-graded gravelly soils. Axisymmetric, isotropically consolidated drained compression, and pure shear, plane strain quasi-K0 consolidated drained tests were performed on well-graded Kanaskat gravel using confining pressures ranging over three orders of magnitude to determine its stiffness, strength, and stress-dilatancy response. The plane strain stiffness, strength, and stress-dilatancy of Kanaskat gravel is observed from tests performed using a large cubical true-triaxial device with flexible bladders. The observed response is interpreted with a view of experimental boundary conditions and their impact on the volumetric response. The observed plane strain shear modulu...

Evaluation of Dilatancy Behavior of Asphalt Mixtures Using Partial Triaxial Compression Tests

Dilatancy behavior plays a key role in the rutting of asphalt mixtures; therefore, it is important to study its behavior to better predict and mitigate rutting of asphalt pavements. In this study, a partial triaxial compression test (PTCT) was developed and employed to characterize the dilatancy of asphalt mixtures. On the basis of the analysis of the principles and the testing method of the PTCT, the parameters of the specimen and the pedestals were determined using the finite-element method to ensure that the specimen could provide a similar confining pressure to that in an actual asphalt pavement. The diameters and heights of the pedestal and specimen were determined to be 50×30 mm and 100×80 mm, respectively, by considering the aspect ratio of the specimen, actual pavement thickness, and numerical results. The test results were analyzed using the strain ratio and stress-dilatancy theories, considering the coupled effects of dilation gradient, distortional strain, and volumetric strain of the asphalt mixtures. It is shown that the degree of dilatancy changed with the strain ratio, which is sensitive to the air void content and loading rate. The stress-strain relationships of the asphalt mixtures indicate that dilation is related to the air void content and testing time. The asphalt mixtures contracted at the beginning of testing and then dilated after the peak stress, and the dilation increased continuously with increase of the axial strain. The specimen contracted when the dilation parameter d (d = 1−volumetric strain increment/axial strain increment) was less than 1.0 and dilated if d was greater than 1.0. The dilation gradation was strongly correlated with the factors, including the stress-strain relationship, air void content, loading rate, and testing time. This study demonstrated that PTCT is a good and accurate test method to evaluate the dilation of asphalt mixtures.

The strength-dilatancy characteristics embraced in hypoplasticity

The strength-dilatancy characteristics of frictional materials embraced in the hypoplastic model proposed by Gudehus and Bauer are investigated and compared with the revised model suggested by Huang. In the latter the deviatoric stress in the model by Gudehus and Bauer is replaced by a transformed stress according to the stress transformation technique proposed by Matsuoka. The flow rule, the failure state surface equation and the strengthdilatancy relationship embraced in both models are derived analytically. The performance of the two hypoplastic models in reproducing the relationship between the peak strength and the corresponding dilation rate under triaxial compression, plane compression and plane shearing are then extensively investigated and compared with experimental results and with the predictions made by particular classical stress-dilatancy theories. Numerical investigations show that the performance in reproducing the strength-dilatancy relationship is quite satisfactory under triaxial compression stress state in both models and the predictions made by the transformed stress based model are closer to the results obtained from classical stress-dilatancy theories for plane compression and plane shearing problems.

Formulation and validation of a constitutive model for sands in monotonic shear

A constitutive model for sands in monotonic shear is presented. The model is designed to simulate the behavior of sands in the whole stress and strain range of engineering interest with enough accuracy for practical usage. Material parameters were chosen to be state independent and easy to calibrate using conventional testing procedures. The formulation is based on effective stresses, pressure-dependent hyperelasticity, non-associative elastoplasticity, an isotropic hardening law and Rowe’s stress-dilatancy theory. The implementation of Rowe’s stress-dilatancy theory within the framework of elastoplasticity theory is discussed. It is found that Rowe’s theory produces a volumetric plastic strain rate function that has a discontinuity in its first derivative w.r.t. stress, and a smoothed form is proposed instead. Finally, some experimental tests are simulated and the results are briefly discussed.

Numerical simulation of the shear behavior of rockfills

A strain hardening model is proposed for simulation of the shear behavior of rockfills, including the non-linear stress–strain relationship, stress-dependence of stiffness, non-linear strength envelope, and particularly the shearing contraction and dilatancy. This model utilizes the Mohr–Coulomb yield criterion, which is defined by the mobilized friction angle varying with plastic octahedral shear strain. The development of Rowe’s stress dilatancy theory is reviewed, with its limitation for rockfills highlighted. A modified solution is then proposed to derive the mobilized dilatancy angle of rockfills. Compared with large-scale triaxial testing results, it has been demonstrated that this simple model is capable of predicting the shear behavior of rockfills with fair accuracy.

Slope Failure Reanalysis of a Dilatant Dense Sand from CPTU and Laboratory Tests

Geotechnical properties of dense to very dense sands at Channel Island Harbor in Oxnard, California, are re-evaluated after slope failures to select appropriate strength parameters for remedial and extension works. The revetment is excavated at a slope of 2:1 (horizontal: vertical) in estuarine and dune sands and covered with a geotextile filter and armor rock. Reanalysis of the slope stability explores laboratory and in situ strength conditions of peak, constant volume and residual angles for the sands. A stress-dilatancy theory provides the framework used in re-characterization of the soil and observed slope failure mechanisms. Effective friction angles are recommended for further slope stability analysis at that location.

On double shearing in frictional materials

AbstractThis paper evaluates the mechanical behaviour of yielding frictional geomaterials. The general Double Shearing model describes this behaviour. Non‐coaxiality of stress and plastic strain increments for plane strain conditions forms an important part of this model. The model is based on a micro‐mechanical and macro‐mechanical formulation. The stress–dilatancy theory in the model combines the mechanical behaviour on both scales.It is shown that the general Double Shearing formulation comprises other Double Shearing models. These models differ in the relation between the mobilized friction and dilatancy and in non‐coaxiality. In order to describe reversible and irreversible deformations the general Double Shearing model is extended with elasticity.The failure of soil masses is controlled by shear mechanisms. These shear mechanisms are determined by the conditions along the shear band. The shear stress ratio of a shear band depends on the orientation of the stress in the shear band. There is a difference between the peak strength and the residual strength in the shear band. While peak stress depends on strength properties only, the residual strength depends upon the yield conditions and the plastic deformation mechanisms and is generally considerably lower than the maximum strength. It is shown that non‐coaxial models give non‐unique solutions for the shear stress ratio on the shear band. The Double Shearing model is applied to various failure problems of soils such as the direct simple shear test, the biaxial test, infinite slopes, interfaces and for the calculation of the undrained shear strength. Copyright © 2006 John Wiley & Sons, Ltd.

The shearing behaviour of a sugar aggregate

To better understand the behaviour of sugar within industrial centrifuges or silos, drained triaxial tests were performed on loose, dry or moist sugar aggregates under low confining pressures (15–90 kPa). Particular attention is paid to test reproducibility and grain damage level. Rowe's stress-dilatancy theory is used to improve characterisation of the critical state, at which the aggregate of grains could participate in frictional flow at constant volume. The effects of strain rate, mean grain size and moisture upon internal friction and dilatancy are each investigated. Additionally, initial elastic properties are identified.

Crushing and plastic deformation of soils simulated using DEM

Cheng and co-workers showed how to make numerical simulations of crushable soils by the discrete element method (DEM). Stress-path tests on triaxial elements comprising crushable agglomerates have now been simulated. The plastic behaviour of this numerically generated soil closely resembles that of real sand. Crushing in the aggregate begins at stresses less than one tenth of the characteristic strength of single grains. The yield surfaces of isotropic ‘lightly overconsolidated’ DEM simulations are also contours of breakage, and are elliptical on Cambridge-style (q, p′) plots and symmetrical about the p′ axis. The points of maximum deviator stress at yield lie along lines of stress ratio My = ±0·8, but the plastic strain increments at yield are non-associated, giving more contraction than normality would allow. Significantly, therefore, the stress ratio My was found not to coincide with critical states. All stress-path simulations yielding with q/p′ > My were found to satisfy the requirements of stress–dilatancy theory. In particular, their yielding was best described using a unique Mohr–Coulomb angle of internal friction ϕ, correlated with dilatancy rate. Points of zero dilation were found within this regime, providing a critical-state friction angle ϕcrit = 42° for these very ‘rough’ agglomerates. They also coincided with the location of a critical-state line on an e–log p′ plot. The peak angle (ϕpeak) developed in a variety of tests showed a unique correlation, reducing by progressive grain crushing as log σ′1 increased. As macroscopic stress levels approached the characteristic crushing strength of grains, it was impossible even to mobilise ϕ = ϕcrit, owing to large strains and high degress of breakage.