Pavement Structural Analysis TwoLayer Systems Vertical interface deflection

Pavement Structural Analysis Two-Layer Systems (Vertical interface deflection) Highway and Transportation Engineering Al-Mustansiriyah University 2020 -2021 Dr. Abeer K. Jameel Dr. Rana Amir Yousif Yoder; E. J. and M. W. Witczak, “Principles of Pavement Design”, A Wiley- Interscience Publication, John Wiley & Sons Inc. , U. S. A. , 1975.

References Ø Nicholas J. Garber and Lester A. Hoel. ”Traffic and Highway Engineering”, Fourth Edition. Ø Yoder; E. J. and M. W. Witczak, “Principles of Pavement Design”, A Wiley. Interscience Publication, John Wiley & Sons Inc. , U. S. A. , 1975. Ø Yaug H. Huang, “Pavement Analysis and Design”, Prentic Hall Inc. , U. S. A. , 1993. Ø “AASHTO Guide for Design of Pavement Structures 1993”, AASHTO, American Association of State Highway and Transportation Officials, U. S. A. , 1993. Ø Oglesby Clarkson H. , “Highway Engineering”, John Wiley & Sons Inc. , U. S. A. , 1975. Yoder; E. J. and M. W. Witczak, “Principles of Pavement Design”, A Wiley- Interscience Publication, John Wiley & Sons Inc. , U. S. A. , 1975.

Two-Layer Systems Vertical Interface Deflection: The vertical interface deflection has also been used as a design criterion. Figure 2. 19 can be used to determine the vertical interface deflection in a two-layer system (Huang, 1969 c). The deflection is expressed in terms of the deflection factor F by: (2. 16) Yoder; E. J. and M. W. Witczak, “Principles of Pavement Design”, A Wiley- Interscience Publication, John Wiley & Sons Inc. , U. S. A. , 1975.

Two-Layer Systems (Vertical Interface Deflection) Yoder; E. J. and M. W. Witczak, “Principles of Pavement Design”, A Wiley- Interscience Publication, John Wiley & Sons Inc. , U. S. A. , 1975.

Two-Layer Systems (Vertical Interface Deflection) The deflection factor is a function of: 1. The modulus ratio El/E 2. 2. Thickness–radius ratio h 1/a. 3. r/a. Where : r: is the radial distance from the center of loaded area. Yoder; E. J. and M. W. Witczak, “Principles of Pavement Design”, A Wiley- Interscience Publication, John Wiley & Sons Inc. , U. S. A. , 1975.

Two-Layer Systems (Vertical Interface Deflection) Steps to Solve Two-Layer Systems (Vertical Interface Deflection): Step 1 ØFind Ø Find value. Yoder; E. J. and M. W. Witczak, “Principles of Pavement Design”, A Wiley- Interscience Publication, John Wiley & Sons Inc. , U. S. A. , 1975.

Two-Layer Systems (Vertical Interface Deflection) Steps to Solve Two-Layer Systems: Step 2 As example (if =4, = 1 and = 1. 5 ) from Figure 2. 19 please follow the chart Then F= 0. 3 can obtain. 1 Yoder; E. J. and M. W. Witczak, “Principles of Pavement Design”, A Wiley- Interscience Publication, John Wiley & Sons Inc. , U. S. A. , 1975. 2

Two-Layer Systems (Vertical Interface Deflection) Example: Figure 2. 20 shows a set of dual tires, each having contact radius 4. 52 in. (115 mm) and contact pressure 70 psi (483 k. Pa). The center-tocenter spacing of the dual is 13. 5 in. (343 mm). Layer 1 has thickness 6 in. (152 mm) and elastic modulus 100, 000 psi (690 MPa) ; layer 2 has elastic modulus 10, 000 psi (69 MPa). Determine the vertical deflection at point A, which is on the interface beneath the center of one loaded area. ? Yoder; E. J. and M. W. Witczak, “Principles of Pavement Design”, A Wiley- Interscience Publication, John Wiley & Sons Inc. , U. S. A. , 1975.

Two-Layer Systems (Vertical Interface Deflection) Solution: Given = 100, 000/10, 000 = 10 = 6 / 4. 542 = 1. 33 The deflection factor at point A due to the left load where : =0 from Figure 2. 19 F = 0. 56 Yoder; E. J. and M. W. Witczak, “Principles of Pavement Design”, A Wiley- Interscience Publication, John Wiley & Sons Inc. , U. S. A. , 1975. E 1/E 2

Two-Layer Systems (Vertical Interface Deflection) Solution: The deflection factor at point A due to the right load where : = 13. 5 / 4. 52 = 2. 99 from Figure 2. 19 F = 0. 28 By superposition F = 0. 56 + 0. 28 = 0. 84 From Eq. 2. 16 w = 70 * 4. 52/10, 000 * 0. 84 = 0. 027 in. (0. 69 mm) Yoder; E. J. and M. W. Witczak, “Principles of Pavement Design”, A Wiley- Interscience Publication, John Wiley & Sons Inc. , U. S. A. , 1975. E 1/E 2

Two-Layer Systems THANKS FOR ATTENTION Dr. Rana Amir Yousif & Dr. Abeer K. Jameel Yoder; E. J. and M. W. Witczak, “Principles of Pavement Design”, A Wiley- Interscience Publication, John Wiley & Sons Inc. , U. S. A. , 1975.