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At present, considerable attention is being devoted to investigating the deformability and strength characteris'tics of soils in the cam of three-dimensional stress."The following data on the strength and deformability of soils obtained on apparatus with independently controlled principal stresses are considered in the design model.~" Strength. For many soils the Mohr andMises-Botkin strength theories (used in traditional calculations withrespect to the first limiting state) prove to be substantially invariant to the form of three-dimensional stress. Inother words, the parameters of these strength theories depend on the relationship between the principal messes at which the experiment is set up (see, e.g., [5]). Figure In the calculation results presented below we treated the laboratory data by the method proposed by 8otkin [6] and supplemented by consideration of the dependence of strength on I1" 7 -~ 11"~ (I: , where I~ o is the value of II o at soil failure. The specific expression of gq. (1) was described earlier [2]; in addition to effect on strength, /~o reflects the substantially nonlimar relation II~ =II~ (Io)(for vo = const), observed at a high stress level.In soil mechanics the ratio of the sine of the angle of deflection to the sire of the angle of friction is considered for determining the degree of approximation to limit equilibrium [7]. /~ nalogously, with consideration of Eq. (1), we introduce the ratiowhere II o is calculated on the basis of the actual stresses at a point.The stress eondi~tion that is safe from the standpoint of the possibility of failure (condition of hydrostatic pressure) corresponds to the value fl --0; the state of limit equilibrium corresponds to the value ~ = 1. If we calculate

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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...

For the most common soils in construction practice the elastoplastic deformation in the consolidation region is characterized predominantly by the plastic (residual) component. The main form of failure of such soils is plastic flow of the stressed mass with progressive rates of strain. The soil is regarded as a continuous, quasi-homogeneous, and quasi-isotropic mass.The main feature of soils is the marked difference in their tensile and compressive strengths as a consequence of the dependence of strength on forces of internal friction and volumetric changes. Due to this soil characteristic, in soil mechanics we usually use Molar's theory of strength, which proposes as a criterion of failure some experimentally established functional relation between the half-difference and the half-sum of the principal stresses characteristic of the limiting soil state. The equation of Mohr's envelope of curves correlates with the Coulomb law and leads to the well-known, but not fanltless treatment of the forces of internal friction and cohesion. Here various cases of three-dimensional stresses are not analyzed and the effect of the intermediate principal stress onsoil strength is disregarded. The defects of Mohr's theory led to an attempt to tie in the strength condition with octahedral stresses and by this extend the Mises-Schleicher proposition to soils [1]. Thus, the condition of strength is expressed in terms of the basic invariants V+ I(~ + ,,, + (~ depending on a11 three princ:ipal stresses. Bm in so doing the uniqueness of the solution remains unproved, since in a solution holding tree for any type of three-dimensional stress two invariants can give a multitude of combinations of the three principal stresses. * The resuks of our experimemal investigations which shed light on certain problems of constructing a general theory of soil strength are given below.Plastic deformations of soil in the region between the elastic limit and strength limit resuk mainly from tile disturbance of existing and the occurrence of new bonds in the soft structure. As long as this process causes a gain in strength (consolidation) of the structure, the soil can establish new forms of equilibrium between the external and imernal forces. Having reached the limit of structural strength, the soil fails. Failure is a limiting state of deformation in the strength-gain (consolidation) region. Thus, if a gain of soil strength upon loading is associated mainly with plastic deformation, then the development of deformation in the consolidation region and failure should be regarded as a single process comrolled by general principles [6]. It follows from the above that a joim study of strength and the state of stress and strain of the soil mass in the prelimiting region of its loading is needed.On examining the stress-strain state which ends in failure, we assume loading to be monotonic and active and deformations to be small. We will consider that loading is active if the principal invariant characterizing stress at a given point and at a given instant of t...