A soil element beneath a pavement experiences principal stress rotations when the wheel load, W passes over it and moves away, as shown in Figure 10.47. In this case, the wheel load has passed over points A and B, and is now over point C. The general state of stress at these points is similar to the one shown by a stress

Block at point D. The phenomenon of principal stress rotation influences the permanent deformation behavior of the pavement layers. Let us now investigate how the magnitude and the orientations of the principal stresses vary with distance from the point of application of the wheel load. Consider the case shown in Figure 10.47. A layer of aggregate for an unpaved road of thickness 610 mm and unit weight of 19.4 kN / m3 is placed over a soil sub grade. A typical single-axle wheel load, W = 40 kN, is applied uniformly over a circular contact area of radius, R = 150 mm (tire pressure of 565 kN/m2). The horizontal and shear stresses at each point are calculated from a linear elastic finite element analysis for a two-layer pavement and are presented in the following table.

1. Use Eq. (10.27) to calculate the vertical stress increases at soil elements A, B, and C, located at radial distances 0.457, 0.267, and 0 m, respectively, from the center of the load. Determine the total vertical stress (sy) due to wheel load and the overburden pressure at each point and enter these values in the table.
2. Use the pole method to determine the maximum and minimum principal stresses (s1 and σ3) for elements A, B, and C. Also, determine the orientation (ai) of the principal stress with respect to the vertical. Enter these values in the above table.
3. Plot the variations of σ1 and ai with normalized radial distance, r/R, from the center of loading.

Rolling Wheel Load. W#40 kN Direction of travel a1 305 mm 3 Aggregate layer = 19.4 kN/m" 305 mm Soil subgrade Radlal Horizonta Shea Vertical distance, r* stress., stress, stress, (KN/m3 (kN/) 25 32 (kN/m2 17 45 0 Element at (n) (KN/m2) (kN) (deg) 0457 0.267 *r-distance measured from the center of the circular contact area.