In practice, there are verry few problems in which a state of axial sym metry exists as in the triaxial test. In practica l states of stress the intermediate principal stress is not usually equal to the minor prrincipal stress and the principal stress directions can undergo rotation as the failure co ndition is approached. A common condition is that of plane strain in which the strain in the direction of the intermediate principal stress is zero due to restraint imposed by vi rtue of the length of the structure in question. In the triaxial test, consolidation proceed s under equal all-round pressure (i.e. isotropic consolidation)whereas in-situ consolidation takes place under anisotropic stress conditions.
Tests of a more comple x nature, generally employing adaptions o f triaxial equipment, have been devised to simulate the more complex states of stress en countered in practice but these are used principally in research. The plane strain test uses a prismatic specimen in which strain in one direction (that of the intermediate principal stress) is maintained at zero throughout the test by means of two rigid side plates tied together. The all-round pressure is the minor principal stress and the sum of the applied axial stress and the all-round pressure the major principal stress. A more sophisticated test, also using a prismatic specimen, enables the values of all three principal stresses to be controlled independently, two side pressure bags or jacks being used to apply the intermediate principal stress. Independent control of the three principal stresses can also be achieved by means of tests on soil specimens in the form of hollow cylinders in which different values of external and internal fluid pressure can be applied in addition to axial stress. Torsion applied to the hollow cylinders results in the rotation of the principal stress directions. Because of its relative simplicity it seems likely that the triaxial test will continue to be the main test for the determination of shear strength characteristics. If considered necessary, corrections can be applied to the results of triaxial tests to obtain the characteristics under more complex states of stress.
SHEAR STRENGTH OF SANDS
The shear strength characteristics of a sand can be determined from the results of either direct shear tests or drained triaxial tests, only the drained strength of a sand normally being relevant in practice. The characteristics of dry and saturated sands are the same, provided there is zero excess pore water pressure in the case of saturated sands. Typical curves relating shear stress and shear strain for initially dense and loose sand specimens in direct shear tests are shown in Figure. Similar curves are obtained relating principal stress difference and axial strain in drained triaxial compression tests.
In a dense sand there is a considerable degree of interlocking between particles. Before shear failure can take place, this interlocking must be overcome in addition to the frictional resistance at the points of contact. In general, the degree of interlocking is greatest in the case of very dense, well-graded sands consisting of angular particles. The characteristic stress-strain curve for an initially dense sand shows a peak stress at a relatively low strain and thereafter, as interlocking is Progressively overcome, the stress decreases with increasing strain. The reduction in the degree of interlocking produces an increase in the volume of the specimen during shearing as characterized by the relationship, shown in Figure , between volumetric strain and shear strain in the direct shear test.
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