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4 a frictional component (I,I') and a non-frictional component, or cohesion (c, c’). Figure 1 below graphically depicts the Mohr-Coulomb failure criterion. Figure 1: Mohr-Coulomb failure criterion. Mohr-Coulomb failure envelopes can be developed through the use of Mohr’s circles of stress representing the stress states at failure for a series of tests (often three tests). As seen in Figure 1, both total and effective stress failure envelopes can be developed. Failure envelopes for soils are often curved. However, for mathematical simplicity, an analyst will approximate the failure envelope as linear over the normal stress range of interest for the analysis. The Mohr-Coulomb failure criterion is, therefore, represented by a straight line (failure envelope) with a slope designated as the friction angle (I,I') and an intercept called the cohesion (c, c’). The normal (or vertical) stress (ı,ı’) acting on soil in an embankment at a given depth, is represented by the horizontal axis, and can be either total stress or effective stress. Note that the greater the normal stress, the greater the frictional component and overall shear strength. Shear strength tests are performed on soils using a range of consolidation pressures to develop the strength envelope from Mohr-Coulomb plots. The following section will discuss various laboratory tests used to evaluate the shear strength of soils, and which laboratory tests are appropriate for drained and undrained loading conditions. Laboratory Shear Strength Tests The five types of laboratory tests most widely used to estimate shear strength in soils are:direct shear, unconfined compression,triaxial shear,direct simple shear, and torsional ring shear. These five tests are described in detail below and are performed in accordance with ASTM standards. The ASTM standard for each test outlines sample preparation, failure criterion, and procedures for saturation, consolidation, loading, and pore pressure measurements (where applicable). Direct Shear Test The oldest and simplest shear strength test is the direct shear (DS) test. DS testing is performed as described in ASTM D3080. In the DS test, a thin soil sample is placed in a shear box that is split horizontally into halves. A normal force (Pv) is applied to the top of the loading head. The normal force typically ranges from 0 to 150 pounds per square inch (psi). The lower half of the box is fixed, while a shear force (Ph) is applied to the upper half, thereby moving the upper half parallel to the lower half and forcing the soil specimen to fail along a horizontal shear plane. A schematic of the test apparatus is shown in Figure 2. Figure 2: Direct shear test apparatus. The DS test is performed in a strain-controlled (deformation-controlled) manner per ASTM D3080. In the strain-controlled test, a constant rate of shear displacement is applied to the top half of the box by a motor that acts through gears. Shear displacement ('H) of the top half of the box is measured by a horizontal dial gauge or displacement transducer. The resisting shear force of the soil can be measured by a horizontal proving ring or load cell. A dial gauge or displacement transducer on the upper loading plate Reference: Bowles (1988)