Fundamental relations of the stress state and the strength of sandy ground

Lomize, G. M.; Kryzhanovskii, A. L.

doi:10.1007/bf01703495

Cited by 7 publications

(4 citation statements)

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“…Analysis of results of triaxial load tests performed with independent control of principal stresses [5,6] indicated that the peak Mohr-Coulomb strength of the soil will depend on the form of the stress state, as determined by the parameter µ σ = (2σ 2 − σ 1 − σ 3 )(σ 1 − σ 3 ). It is obtained from these tests that the peak strength in triaxial-compression (µ σ = −1) is somewhat lower than that for other forms of stress state.…”

Section: Comparison Of Theoretical and Experimental Resultsmentioning

confidence: 99%

“…Identification of the slip platform as an octahedral platform is valid for small soil dilatancy [1]. The dilatance relationship can be adopted in the form of the equation (5) where is the increment of plastic shear strain on the octahedral platform, and Λ is the coefficient of dilatancy, which links the increments of bulk and shear octahedral plastic strain. The following relationships for the principal plastic-strain increments ensue from (3) and (5)…”

Section: Alternate Model For Nonassociative Plastic Flowmentioning

confidence: 99%

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Plastic flow of a soil bed

Mironov

Sof’in

Gudii

2008

Soil Mech Found Eng

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Mathematical models describing the mechanical behavior of soils loaded with different degrees of physical certainty are used in analyzing beds and earthen structures; this results in discrepancy between theoretical and experimental strength and deformability values. The accuracy of these calculations will depend to a significant degree on the consideration given to the most significant characteristic features of soil deformation in the mathematical model.The theory of plastic flow is currently preferred for description of nonlinear deformation of soils. Here, the principal problem is the determination of the yield condition and the load surface corresponding to the latter in stress space, on the attainment of which plastic deformations develop.In our study, we propose an alternate scheme of model for nonassociative plastic flow of a soil, which generalizes constitutive equations for the special case of the plastic flow of an incompressible medium [1] during arbitrary dilatancy. Alternate Model for Nonassociative Plastic FlowWe will consider that total strain increments are summed from the elastic and plastic increments. Then,can be written for the principal strain increments. The principal elastic-strain increments are related to the principal stress increments by Hooke's lawA model of the elasto-plastic deformation of soils prone to dilatational softening is proposed. The deformations of softening soils are calculated on the basis of equations developed with use of experimental curves of the coefficients of friction and dilatancy versus bulk plastic strain. The interaction between a rigid square plate and a sandy bed is modeled numerically.

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Section: Comparison Of Theoretical and Experimental Resultsmentioning

confidence: 99%

Section: Alternate Model For Nonassociative Plastic Flowmentioning

confidence: 99%

Plastic flow of a soil bed

Mironov

Sof’in

Gudii

2008

Soil Mech Found Eng

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“…Figure 2 shows theoretically predictable Mohr-Coulomb angles of internal friction as a function of the parameter µ σ in comparison with experimental data derived from determination of the peak strength of sands, which were obtained by Green and Bishop [8] and Lomize and Kryzhanovskii et al [9].…”

mentioning

confidence: 99%

“…Constitutive relations can be sought in a form such that after their substitution in the familiar formulas (9) the result will be identical to expressions (5). The relations (10) where is an infinitely small scalar factor ( > 0), satisfy this result.…”

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confidence: 99%

Strength and deformability of soils in a complex stress state

Mironov

Sof’in

Gudii

2007

Soil Mech Found Eng

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Coulomb's friction law and soil failure in a three-dimensional stress-strain state

Kryzhanovskii¹

1982

Hydrotechnical Construction

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The Coulomb dry-friction law I~lult =tg eco+Cc, (i) (where ~C is the angle of friction, C C is cohesion) is a decisive regularity in the theory of soil mechanics and in the solution of practical problems of the design of foundations of structures and earth structures. For a fixed shear plane (in experiments on shear boxes) Eq. (I) found experimental confirmation with respect to cohesive and cohesionless soils [I].To use (i) when determining the strength of soils in the general case of a three-dimensional stress state it is necessary additionally to indicate the orientation of the area of the limit state on which this equation is fulfilled.Let the orientation of the normal to the area of the limit state in a system of principal stresses ~ o2~ ~ be determined by the values of the direction cosines l, m, n. Then in conformity with the Coulomb friction we have I~, lult = tg ~c~, +OK.(2)The practical use of (2) without an indication of the values of l, m, n is impossible.In various theories of the strength of soils the values of ~, m, n are assigned differently.For example, in the Mohr--Coulomb theory I = cos(45~177 m = O~ n = /1 --12; in the Mises--Schleicher--Botkin theory 12 = m 2 = n 2 = 1/3. It can be considered that the theory for describing the strength of soil is true if equal values of the parameters ~ and C are obtained from the results of experiments with a different relationship between principal stresses oi, 02, ~3 and with a different history of variation of these stresses on approaching the state of limit equilibrium.Only in this case, having experimentally established the values of ~ and C in the particular case of a three-dimensional stress state, can one use these same values for an arbitrary relationship between ~i, 02, ~3, which occurs when solving practical problems of soil mechanics.The inconstancy of the values of ~ and C can be due also to the inadmissibility of (2) for describing soil strength in the general case of a three-dimensional stress state.We will examine below proof of the validity of the Coulomb dry-friction law (2) in various stress--strain states of the soil and simultaneously the need to determine the orientation of the area of limit equilibrium as a function of increments of plastic deformations.Practical Significance of the Problem Being Discussed.The data of determining ~ in shear boxes and apparatus with independently controlled principal stresses with a different relationship between dl, ~2, a3 ( in processing with the use of the Mohr--Coulomb theory) for a wide variety of clay, sand and coarse-skeletal soils differ considerably.In the case when 02 = ~3 the difference in the values of ~ reach 4~ when 02 = (oi + 03)/2, the difference is l0 ~ and under conditionsof plane strain it is 8 ~ and more of the indicated values. These differences cannot be explained by imperfection of the design of the shear box or apparatus with independently controlled principal stresses, since, on one hand, there are varieties of soils where the results practically coincide and, on the other, th...

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Fundamental relations of the stress state and the strength of sandy ground

Cited by 7 publications

References 1 publication

Plastic flow of a soil bed

Plastic flow of a soil bed

Strength and deformability of soils in a complex stress state

Coulomb's friction law and soil failure in a three-dimensional stress-strain state

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