Rotation Of Principal Stress Axes Research Articles

Deformation Behavior of Anisotropic Dense Sand Under Principal Stress Axes Rotation

In order to investigate the fundamental deformation behavior of sand under the more general stress condition involving the rotation of principal stress axes, a series of drained tests was carried out on a dense anisotropic sand using a hollow cylinder torsional shear apparatus. The hollow cylindrical specimens have an anisotropic fabric formed by the parallel alignment of particles induced during deposition, and are tested under the principal stress axes rotation keeping the values of three principal stresses constant. The experimental results showed that the shear deformation of sand due to the rotation of principal stress axes are not negligible as compared with that due to the shear with fixed principal stress axes and the effects of inherent anisotropic fabric on the shear deformation and volume change behavior are considerably large. The mode of anisotropic effects on the deformation characteristics depends strongly on whether the rotation of principal stress axes are involved or not. It was also indicated that the anisotropic deformation characteristics under the principal stress rotation can be explained by taking account of the predominant sliding occurring on the bedding plane, irrespective of whether the principal stress axes rotate or not. This consideration is supported by the fact that the bedding plane has the lowest value of the resistance against shear stress according to the horizontal alignment of subelongated sand particles.

Undrained strength of sand undergoing cyclic rotation of principal stress axes : Towhata, I; Ishihara, K Soils FoundV25, N2, June 1985, P135–147

Undrained strength of sand undergoing cyclic rotation of principal stress axes : Towhata, I; Ishihara, K Soils FoundV25, N2, June 1985, P135–147

Shear Work and Pore Water Pressure in Undrained Shear

When a loose sand is subjected to a cyclic rotation of principal stress axes during an undrained test, excess pore water pressure is generated. To study the nature of pore pressure buildup, several series of laboratory tests were conducted using a hollow cylindrical torsion shear apparatus. Tests were conducted employing different kinds of cyclic loading schemes in which specimens were subjected to cyclic shear stresses with or without continuous rotation of principal stress axes. Based on the test results, accumulated shear work per unit volume was calculated at each stage of shear stress application, and its correlation with the pore water pressure was examined. It was found that, at each state of shear stress alteration, there exists a unique relationship between the shear work and the pore water pressure, independent of the shear-stress history. This observation enables contour lines of equal shear work to be drawn in the stress space. (Author/TRRL)

Undrained Strength of Sand Undergoing Cyclic Rotation of Principal Stress Axes

This study concerns the effects of continuous rotation of principal stress axes on excess pore water pressure development during cyclic loading. Continuous rotation of principal stress axes has been known to exert some influence on the development of excess pore water pressure and failure of sand during cyclic loading. In an effort to investigate this aspect of the problem, several series of cyclic undrained tests were carried out in a static manner on saturated sampes of sand using a triaxial torsion shear apparatus. In this test apparatus, a hollow cylindrical soil specimen is subjected to a simultaneous application of both triaxial and torsional modes of shear stresses, which brings about the continuous rotation of principal stress axes. The test results indicated that, while the angle of internal friction remains unaffected, the continuous rotation of principal stress axes substantially reduces the resistance of sand to liquefaction by generating a greater amount of excess pore water pressure than in the case without the rotation. Some special tests were also performed to examine the effects of previous liquefaction on the undrained behavior of sand during the subsequent cyclic loading. The results show that the sand having previously experienced large deformations due to liquefaction exhibit a highly anisotropic stress-strain characteristics, whereby reducing the resistance of the sand drastically when sheared in certain directions.

Multi‐laminate model of clays—a numerical evaluation of the influence of rotation of the principal stress axes

AbstractA new framework for the development of constitutive models based on certain aspects of physical theories of plasticity is proposed. The resulting Multi‐laminate model of clays has the same response as the Critical state model provided no rotation of principal stress axes takes place during plastic flow.The influence of rotation of the principal stress axes on the volumetric and deviatoric plastic strains has been numerically evaluated. In undrained saturated, normally consolidated clays considerable excess pore pressure may build up due to rotation of the principal axes only. Numerical studies of the collapse of footings indicate that significant rotations do not take place in this class of problems and consequently the collapse load is only marginally reduced.

Rotation of principal stress axes caused by faulting

This note describes a simple procedure for determining the local rotation of principal stress axes caused by slip on a fault. The procedure employs Eshelby's solution for the elastic field of an ellipsoidal inclusion. An example is used to illustrate that this procedure may be useful in interpreting observations, such as the rotation of compression axes recently inferred from focal mechanisms of earthquakes near the San Andreas fault.

On bifurcation in elastic-plastic solids

In Shanley's model of bifurcation, a perturbed motion is assumed to occur with increasing co-axial load. In this paper a new approach is used to derive constitutive equations during perturbed motion of inelastic solids; specifically, the rotation of principal stress axes due to stress-increment is considered and its effect on subsequent plastic deformation is allowed for. The basis for the derivation is (i) Lévy-von Mises flow rule, and (ii) the dependence of total plastic strain-increments on the loading path. It is found, as a result, that the incipient value of the shear modulus in the constitutive relation could be lower than the elastic value.

Formation of shear bands in sand bodies as a bifurcation problem

AbstractThe paper reports on the results of theoretical and experimental investigations on the spontaneous formation of shear bands in sand bodies. The phenomenon is considered as a bifurcation problem. Consequently, material response and configuration‐dependent loading determine the bifurcation mode. Both Coulomb's and Roscoe's solutions of inclination of the shear band can be correct theoretically and experimentally. The first one holds for non‐rotating stress axes, the second one for co‐rotating stress and strain increment axes during failure. Values in between can occur if the rotation of principal stress axes is not equal to one of these limits. If Coulomb's inclination of shear band occurs, there is a thin deforming material layer separating rigid bodies. Inside the shear band non‐coaxiality of strain increment and stress holds from the beginning. If Roscoe's inclination of shear band occurs, it is separating two deforming bodies. Inside the shear band strain increment and stress are coaxial at peak.

Microscopic Deformation Mechanism of Granular Material in Simple Shear

The deformation of granular material was simulated by an assembly of cylinders (made -of photoelastic material) packed at random in a two-dimensional simple shear apparatus. From the detailed observations on the change of granular fabric due to shear, and from the analyses of interparticle contact force among grains, we obtained some experimental facts which must be taken into account in proposing a granular model of sand. With the increase of shear stress in the simple shear test and direct shear test, the normals Ni to the contact planes tend to concentrate toward the maximum principal stress axis. This tendency of the concentration of Ni is not determined by the magnitude of applied shear displacement but by the intensity of mobilized stress ratio τ/σN. The preferred direction of Ni gradually rotates with the rotation of principal stress axes during shear deformation. The sliding in microscopic scale at contact is, at any one instant, confined at some preferred contacts. According to the microscopic study of granular fabric of sand deformed in the direct shear apparatus, the similar characters are also observed.

Effect of rotating secondary principal axes in scattered-light photoelasticity

A set of equations is presented and the effect of rotation of the secondary principal stress axes is discussed. The equations, general and relatively simple, adequately describe observed results. In studying the equations, a better understanding of the rotational effect can be achieved, and a technique is suggested which can eliminate any error resulting from rotation. This technique and the concepts involved are substantiated with experimental evidence and reported in this paper.