A circular wheel load having radius a = 152 mm and uniform loading pressure q 552 kPa is applied on a two-layer flexible pavement system, as shown in Figure 1-1. The surface Hot Mixed Asphalt (HMA) layer has the elastic modulus E-280 MPa, and the subgrade layer has the elastic modulus E2-35 MPa, and. Both of the layers have the Poisson ratio u=0.5. Determine the vertical stress, the vertical strain, and the vertical deflection at point A due to the circular loading. Point A of analysis is located z = 152 mm below the surface and on the centerline of the loading area. It is at the interface of the two layers. The to-circular-loading response charts for a single-layer system (a structure with the subgrade layer only) are shown in Figure 1-2 through Figure 1-5 on the next two pages. Notes: (1) the layer conversion approximation factor is assumed as 1.0 (f=1.0); and (2) please mark the values you choose, if any, on the reference charts. HMA: E=280 MPa H=0.5 Subgrade: E=35 MPa M=0.5 q=552 kPa A I a=152mm z=152mm h=152mm Interface Centerline of loading (r=0) Figure 1-1: A two-layer system with a circular loading B/Z 8/2 1 2 3 7 0.1 8 0.1 9 0 10 1 2 3 7 8 9 0.2 0.30.4 0.6 0.81.0 10 10 igure 1-2: Vertical stress (0) due to circular loading (the subgrade-based single-layer system) 0.2 0.3 0.4 0.5 0.7 1.0 0.25 x 100 (%) 1.0 2 1.5 456 810 x 100 (%) 20 30 40 5060 80 100 q 2 3 4 5 678 10 1.0 1.5 -0.75 0.5 Numbers on Curves Indicate r/a 0.25 20 30 405060 80 100 OSTO Numbers on Curves Indicate r/a igure 1-3: Radial stress (o,) due to circular loading (the subgrade-based single-layer system) Po z/a 1 2 3 0.1 8.1 1 2 3 4 9 7 00 Figure 1-4: Tangential stress (o,) due to circular loading (the subgrade-based single-layer system) 8 9 0.2 0.3 0.4 0.6 0.81.0 -7.0 8,0 2.5 6.0 0.15 0.2 2.0 (7 9. x 100 (%) 3.0/ 2 3 4 5 6 8 10 F 0.3 0.4 0.5 0.6 0.70.8 0.9 1.0 qa W = F E 20 30 40 50 60 80 100 Numbers on Curves Indicate r/a Numbers on Curves Indicate r/a 2051 0 1.5 40.25 2.0 3.0 10 Figure 1-5: Vertical deflection factor F and vertical deflection w (the subgrade-based single- layer system)