# direct shear - The University of Missouri Columbia Civil...

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The University of Missouri – Columbia Civil and Environmental Engineering DIRECT SHEAR TEST INTRODUCTION One of several methods available for measuring the shear strength of soils is the direct shear test. The idea of the test is as follows. Suppose that two blocks' are in contact as indicated in Fig. 1. A normal force (P) is applied, and a shearing force (F) is applied and gradually increased until failure occurs. Denote the normal stress ( σ ) as: σ= P/A (1) and the shear stress ( τ ) as: τ = F/A (2) where A is the area of contact. If the shearing force is gradually increased, sliding will eventually occur. If μ is the coefficient of friction between the two materials, then: F = μ P (3) Figure 1 -- Two Blocks in Direct Shear. With soil, a sample is formed or trimmed into a direct shear box (Fig. 2) where it is sheared along a plane that passes more-or-less through the center of the sample. The test is usually performed by first consolidating the sample to some desired normal stress and then increasing the horizontal (shear) force until failure occurs. The shear stress as failure is plotted as a function of normal stress, e.g., as indicated in Fig. 3. Such plots

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The University of Missouri – Columbia Civil and Environmental Engineering Direct Shear Test p. 2 Figure 2 -- Typical Direct Shear Box Figure 3 -- Mohr-Coulomb Diagrams for Conditions at Failure.
The University of Missouri – Columbia Civil and Environmental Engineering Direct Shear Test p. 3 are termed'"Mohr-Coulomb diagrams" and can be described with the equation: φ σ + = τ tan c (4) where c and φ are termed the effective cohesion and effective angle of internal friction (effective stresses are used in the nomenclature here, since most direct shear tests are performed on the basis of effective stress, but total stress could also be used if the test is performed on the basis of a controlled total normal stress). The purpose of the direct shear test is either to determine the shear stress at failure for some particular normal stress, or to perform a series of tests at different normal stress to define curves such as shown in Fig. 3 so that the shear strength parameters (effective cohesion and effective angle of internal friction) can be determined. DIMENSIONS OF SOIL SAMPLE The direct shear box is usually designed to accomodate a block-shaped sample of soil (with a square cross section), although disc-shaped samples (with a circular cross section) are sometimes used. The diameter or width of the sample is usually between 2 and 4 inches. The thickness of the sample is controlled by several conflicting requirements. The thickness should be as small as possible because the shearing time for fully drained tests decreases approximately with the square of the thickness of the sample. Further, in a test that is performed properly, the shear is not applied to the soil by the box but rather by application of shear to the flat upper and lower surfaces. If the soil sample is relatively thin, it is more likely that the shear

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direct shear - The University of Missouri Columbia Civil...

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