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Journal ArticleDOI

Review of Proposed Stress-dilatancy Relationships and Plastic Potential Functions for Uncemented and Cemented Sands

30 Sep 2019-Journal of Geological Research (Bilingual Publishing Co.)-Vol. 1, Iss: 2
TL;DR: In this paper, the proposed stress-dilatancy relations for compressive monotonic loading for cohesionless and cemented sand constitutive models are summarized and the proposed potential function can be calculated by integration of stress-dlatancy relationship.
Abstract: Stress-dilatancy relationship or plastic potential function are crucial components of every elastoplastic constitutive model developed for sand or cemented sand. This is because the associated flow rule usually does not produce acceptable outcomes for sand or cemented sand. Many formulas have been introduced based on the experimental observations in conventional and advanced plasticity models in order to capture ratio of plastic volumetric strain increment to plastic deviatoric strain increment (i.e. dilatancy rate). Lack of an article that gathers these formulas is clear in the literature. Thus, this paper is an attempt to summarize plastic potentials and specially stress-dilatancy relations so far proposed for constitutive modelling of cohesionless and cemented sands. Stress-dilatancy relation is usually not the same under compression and extension conditions. Furthermore, it may also be different under loading and unloading conditions. Therefore, the focus in this paper mainly places on the proposed stress-dilatancy relations for compressive monotonic loading. Moreover because plastic potential function can be calculated by integration of stress-dilatancy relationship, more weight is allocated to stress-dilatancy relationship in this research.

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Citations
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Journal ArticleDOI
05 Sep 2020
TL;DR: In this paper, the results of triaxial compression tests under drained conditions for Erksak sand were analyzed using the frictional state concept and the relationship between the stress ratio and dilatancy was described.
Abstract: Analyzing the results of triaxial compression tests under drained conditions for Erksak sand published in the literature, the stress–dilatancy relationships were described using the frictional state concept. At all phases of shearing, the linear stress ratio–plastic dilatancy relationship can be expressed by the critical frictional state angle and two parameters of the frictional state concept. At failure, dense sand exhibits purely frictional behavior (α = 0, β = 1) and the stress ratio–dilatancy relationship may be correctly described by the Rowe, Bolton, and frictional state concept relationships. Very loose Erksak sand sheared under drained triaxial compression at the ultimate state reaches a stable condition, but the reached stress ratio is significantly smaller than the one at a critical state.

3 citations


Cites background from "Review of Proposed Stress-dilatancy..."

  • ...The most well-known stress–dilatancy relationships were collected by Rahimi [17]....

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  • ...The complex stress–plastic dilatancy relationship can be obtained by differentiating the plastic potential function proposed in classical elastoplastic models [17]....

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Journal ArticleDOI
TL;DR: In this paper , a modified yielding function and fractional stress-dilatancy ratio enriched by fabric tensor is proposed to enhance the model performance and simplify the calibration process.

2 citations

Journal ArticleDOI
TL;DR: In this article , the results of triaxial compression tests of some naturally and artificially bonded soils presented in the literature were analyzed, and it was shown that the three characteristic stages of plastic flow during shear can be identified.
Abstract: In this study, the results of triaxial compression tests of some naturally and artificially bonded soils presented in the literature were analysed. It was shown that the three characteristic stages of plastic flow during shear can be identified. In all stages, the stress-dilatancy behaviour could be approximated by the general linear stress-dilatancy equation of the Frictional State Concept. For many shear tests, the failure states and newly defined dilatant failure states are not identical. The points representing dilatant failure states lie on a straight line, for which the position and slope in the η-D plane depend on the soil type and the amount of cement admixture. This line defines the critical frictional state angle, and its slope for bonded soils is greater than for unbonded soils.

2 citations

15 Apr 2005
TL;DR: A summary of recent work on cemented soils at Milan University of Technology (Politecnico) can be found in this paper, where a simple but powerful elasto-plastic bonded soil model is employed to select testing procedures and interpret the results obtained.
Abstract: ABSTRACT This paper presents a summary of recent work on cemented soils at Milan University of Technology (Politecnico). Oedometric and triaxial tests have been performed on lightly bonded soils of medium to very high porosity. Soils tested vary from a rather conventional silica sand-lime mixture to more unusual materials, including expanded clay aggregates, fragmented marine shells or stabilized metallurgical residues. A simple but powerful elasto-plastic bonded soil model is employed to select testing procedures and interpret the results obtained. Both experimental results and model simulations are employed here to illustrate and explore the onset of compaction bands, a new form of localization previously observed in rocks but whose appearance is here first signaled for bonded soils.

1 citations

Journal ArticleDOI
TL;DR: In this article , the authors analyzed the stress-strain behaviour of fiber-reinforced sand using the results obtained by drained triaxial compression tests presented in the literature, and they showed that the characteristic shear phases can only be determined when the η−Dp relationships are used.
Abstract: This paper analyses the stress–strain behaviour of fibre-reinforced sand using the results obtained by drained triaxial compression tests presented in the literature. The general stress–plastic dilatancy equation of the Frictional State Concept has been used to describe the behaviour of fibre-reinforced sand for different shear phases. The behaviour of pure sand is taken as a reference for the behaviour of sand with added fibres. It is shown that the characteristic shear phases can only be determined when the η−Dp relationships are used, which are very rarely demonstrated in the results of shear tests presented in the literature. It has been shown that tensile strains must occur in order to achieve the strengthening effect of fibre reinforcement. A reduction in the stiffness of the fibre–sand composite is observed in the absence of tensile strains below certain threshold values.
References
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Book
26 Apr 1991
TL;DR: In this article, the basic ingredients of a family of simple elastic-plastic models of soil behaviour are described and used in numerical analyses. But the models on which this book concentrates are simple, understanding of these will indicate the ways in which more sophisticated models will perform.
Abstract: Soils can rarely be described as ideally elastic or perfectly plastic and yet simple elastic and plastic models form the basis for the most traditional geotechnical engineering calculations. With the advent of cheap powerful computers the possibility of performing analyses based on more realistic models has become widely available. One of the aims of this book is to describe the basic ingredients of a family of simple elastic-plastic models of soil behaviour and to demonstrate how such models can be used in numerical analyses. Such numerical analyses are often regarded as mysterious black boxes but a proper appreciation of their worth requires an understanding of the numerical models on which they are based. Though the models on which this book concentrates are simple, understanding of these will indicate the ways in which more sophisticated models will perform.

1,671 citations


"Review of Proposed Stress-dilatancy..." refers background in this paper

  • ...They, however, assigned a value of one for A. (14) Ling and Yang [30]: Ling and Yang [30] used a combination of work of Nova and Wood [36] and Li and Dafalias [29] to define their stress-dilatancy relation as follows: (39) (40) where αg and m are positive constants and ξ is the state parameter. αg and m can be determined using the volumetric strain vs. deviator strain curve....

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  • ...(2) Nova and Wood [36]: One of the oldest and most popular stress-dilatancy relationships proposed for cohesionless sands was first suggested by Nova and Wood [36]....

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  • ...Weng [65] -identical to Nova and Wood [36]’s stress-dilatan- cy equation....

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  • ...It appears that the formula was proposed based on Nova and Wood [35]’s relation as follows: DOI: https://doi.org/10.30564/jgr.v1i2.864 Distributed under creative commons license 4.0 (15) where N is a material parameter and d is the dilatancy rate which is defined as plastic volumetric strain increment to plastic deviatoric strain increment....

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  • ...(9) Weng [65]: In his generalized plasticity model for sandstone, Weng [65] used Nova and Wood [36]’s stress-dilatancy relationship which has been proposed for cohesionless sands....

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Journal ArticleDOI
TL;DR: In this paper, the authors studied the relationship between the rate of dilatancy and the maximum stress ratio for any ideal packing and showed that the Mohr-Coulomb criterion of failure is strictly applicable to a continuum and does not have general application to a discontinuous assembly of particles.
Abstract: The dilatancy and strength of an assembly of individual particles in contact when subjected to a deviatoric stress system is found to depend on the angle of friction $\phi\_\mu$ between the particle surfaces, on the geometrical angle of packing, $\alpha$, and on the degree of energy loss during remoulding. The Mohr-Coulomb criterion of failure which is strictly applicable to a continuum is shown not to have general application to a discontinuous assembly of particles. A theoretical and experimental study of ideal assemblies of rods and uniform spheres establishes expressions for the relation between the rate of dilatancy and the maximum stress ratio for any ideal packing. The solution is extended to the case of a random assembly of irregular particles by investigating the conditions under which the mass dilates such that the rate of internal work absorbed in frictional heat is a minimum. Experiments on random masses of steel, glass, and quartz in which all the physical properties are measured independently show that the minimum energy criterion is closely obeyed by highly dilatant dense over-consolidated and reloaded assemblies throughout deformation to failure. An additional rate of energy has to be supplied to account for losses due to rearranging of loose packings, when the value of $\phi$ to satisfy the theory increases to $\phi\_f$ by an amount dependent on the degree of remoulding. The external stresses applied to an assembly are to be integrated over the $\alpha$-plane defined with reference to figure 14(a) as a plane of repetition of pattern over which the particles interlock, and the resulting forces are to be in equilibrium for sliding on particle interfaces at (45-$\frac{1}{2}\phi_f$) to the direction of the major principal stress. For the special case of no volume change these two planes are identical and the solution agrees then with that based on the Mohr-Coulomb theory. The well-known slip plane in drained discontinuous assemblies is proved to be the result of failure and nothing whatsoever to do with the peak strength. The findings are discussed in the light of previous contributions to the subject.

1,522 citations

Book ChapterDOI
01 Jan 1984
TL;DR: In this article, the authors consider three types of models of increasing complexity: the first model is a perfectly-plastic model, which employs Young's modulus and Poisson's ratio for describing the elastic properties; and a cohesion and a friction angle for the determination of the strength.
Abstract: With reference to practical engineering problems it is shown that considerable differences may be encountered between the results from associated and those from nonassociated plasticity theories. Next, the need for a non-associated plasticity theory is demonstrated by considering test results for sand, concrete and rock. Elementary material parameters are discussed such as Young's modulus and Poisson's ratio for the description of the elastic properties; and a cohesion and a friction angle for the determination of the strength. The salient difference from associated plasticity theory concerns the introduction of a dilatancy angle which controls the inelastic (plastic) volume changes. This dilatancy angle is not only a suitable parameter for the description of soils, but also appears to be useful for concrete and rock. Basically, the paper consists of three parts as we consider three types of models of increasing complexity. The first model is a perfectly-plastic model, which employs the five aforementioned parameters. It is based on test data rather than on Drucker's hypothesis of material stability. The consequences thereof are examined. The second model is a straightforward extension of the first model by augmenting it with friction hardening and cohesion softening. This novel idea is introduced to account for the degradation of the cohesion of cemented granular materials with increasing inelastic deformation. The model is employed in an analysis which shows that plastic deformations tend to localize in thin shear bands, which may occur even before peak strength is reached. Finally, a review is given of concepts for modelling hysteresis and strain accumulation in cyclic loading. The concept of a bounding surface in addition to a yield surface is discussed and is adapted for use in a sophisticated model for loose and cemented granular materials under cyclic loading.

842 citations

Journal ArticleDOI
TL;DR: Within the critical state soil mechanics framework, the two-surface formulation of plasticity is coupled with the state parameter to construct a constitutive model for sands in a general stress spa as mentioned in this paper.
Abstract: Within the critical state soil mechanics framework, the two-surface formulation of plasticity is coupled with the state parameter to construct a constitutive model for sands in a general stress spa...

735 citations


"Review of Proposed Stress-dilatancy..." refers background or result in this paper

  • ...Manzari and Dafalias [33] Mf =M+mξ ξ is the state parameter....

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  • ...(11) Dafalias and Manzari ([33]): Dafalias and Manzari [33] proposed their stress-dilatancy equation based on difference between the current stress ratio η and the dilatancy stress ratio MPT which is known as the phase transformation stress ratio....

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  • ...Dafalias and Manzari [33] -a fabric dependent stress-dilatancy equation based on difference between the current stress ratio and the phase transformation stress ratio....

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  • ...[16] -similar to equation of Dafalias and Manzari ([33]), however, it is not fabric dependent....

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  • ...Interested reader is referred to Dafalias and Manzari ([33])....

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Journal ArticleDOI
TL;DR: In this article, a theory was presented that treats the dilatancy as a state-dependent quantity within the framework of critical state soil mechanics, which is a major obstacle to unified modelling of the response of a cohesionless material over a full range of densities and stress levels (before particle crushing).
Abstract: Dilatancy is often considered a unique function of the stress ratio η = q/p′, in terms of the triaxial stress variables q and p′. With this assumption, the direction of plastic flow is uniquely related to η, irrespective of the material internal state. This obviously contradicts the facts. Consider two specimens of the same sand, one is in a loose state and the other in a dense state. Subjected to a loading from the same η, the loose specimen contracts and the dense one dilates. These two distinctly different responses are associated with a single η but two different values of dilatancy, one positive and the other negative. Treating the dilatancy as a unique function of η has developed into a major obstacle to unified modelling of the response of a cohesionless material over a full range of densities and stress levels (before particle crushing). A theory is presented that treats the dilatancy as a state-dependent quantity within the framework of critical state soil mechanics. Micromechanical analysis is u...

678 citations


"Review of Proposed Stress-dilatancy..." refers background or methods in this paper

  • ...Ling and Yang [30] -a combination of relationships proposed by Nova and Wood [36] and Li and Dafalias ([29])....

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  • ...Modified Cam Clay d=(M(2)f -η (2))/2η Jefferies (([17]) d=(Mf -η)/(1-N) Li and Dafalias [29] d=d0(Mf -η)/M Rowe [47] d=9(Mf -η)/(9+3Mf -2Mfη)...

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  • ...0 Li and Dafalias [29] Mf =Mexp(mξ) ξ is the state parameter....

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  • ...(14) Ling and Yang ([30]): Ling and Yang [30] used a combination of work of Nova and Wood [36] and Li and Dafalias [29] to define their stress-dilatancy relation as follows:...

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  • ...(19) Qu and Huang ([39]): Similar to Li and Dafalias ([29]), dilatancy of sand was related to state parameter ξ and the current stress ratio η= by Qu and Huang [39] as follows:...

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