A Simple Test to Determine Friction Angle of Clean Coarse-Grained Soils:

The critical state friction angle, f9cs, for a clean coarse-grained soil can be found by pouring the soil into a loose heap on a horizontal surface and measuring the slope angle of the heap relative to the horizontal. This angle is sometimes called the angle of repose, but it closely approximates f9cs.

 

Shear Box or Direct Shear Test:
A popular apparatus to determine the shear strength parameters is the shear box. This test is useful when a soil mass is likely to fail along a thin zone under plane strain conditions. The shear box (Figure ) consists of a horizontally split, open metal box. Soil is placed in the box, and one-half of the box is moved relative to the other half. Failure is thereby constrained along a thin zone of soil on the horizontal plane (AB). Serrated or grooved metal plates are placed at the top and bottom faces of the soil to generate the shearing force.

 

Vertical forces are applied through a metal platen resting on the top serrated plate. Horizontal forces are applied through a motor for displacement control or by weights through a pulley system for load control. Most shear box tests are conducted using displacement control because we can get both the peak shear force and the critical shear force. In load control tests, you cannot get data beyond the maximum or peak shear force. The horizontal displacement, Dx, the vertical displacement, Dz, the vertical loads, Pz, and the horizontal loads, Px, are measured. Usually, three or more tests are carried out on a soil sample using three different constant vertical forces. Failure is determined when the soil cannot resist any further increment of horizontal force. The stresses and strains in the shear box test are diffi cult to calculate from the forces and displacements measured. The stresses in the thin (dimension unknown) constrained failure zone (Figure ) are not uniformly distributed, and strains cannot be determined.

 

Only the results of one test at a constant value of Pz are shown in Figure . The results of (Px)p and (Px)cs plotted against Pz for all tests are shown in Figure . If the soil is dilatant, it would exhibit a peak shear force (Figure 10.19a, dense sand) and expand (Figure , dense sand), and the failure envelope would be curved (Figure , dense sand). The peak shear stress is the peak shear force divided by the cross-sectional area (A) of the test sample; that is,

The critical shear stress is

In a plot of vertical forces versus horizontal forces (Figure), the points representing the critical horizontal forces should ideally lie along a straight line through the origin. Experimental results usually show small deviations from this straight line, and a “best-fi t” straight line is conventionally drawn. The angle subtended by this straight line and the horizontal axis is fcs. Alternatively,

For dilatant soils, the angle between a line from the origin to each peak horizontal force that does not lie on the “best-fi t” straight line in Figure and the abscissa (normal effective stress axis) represents a value of f9p at the corresponding vertical force. Recall from Section 10.5 that f9p is not constant, but varies with the magnitude of the normal effective stress (Pz/A). Usually, the normal effective stress at which f9p is determined should correspond to the maximum anticipated normal effective stress in the fi eld. The value of f9p is largest at the lowest value of the applied normal effective stress, as illustrated in
Figure . You would determine f9p by drawing a line from the origin to the point representing the peak horizontal force at the desired normal force, and measuring the angle subtended by this line and the horizontal axis. Alternatively,

You can also determine the peak dilation angle directly for each test from a plot of horizontal displacement versus vertical displacement, as illustrated in Figure 10.19b. The peak dilation angle is

We can fi nd ap from

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