Pavement Structural Analysis Insights

Pavement Structural Analysis 3rdStage Lecture 4 Dr. RanaAmir Yousif & Dr. Abeer K. Jameel Highway and Transportation Engineering Al-Mustansiriyah University 2020-2021 Yoder; E. J. and M. W. Witczak, Principles of Pavement Design , A Wiley- Interscience Publication, John Wiley & Sons Inc., U.S.A., 1975.

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

Stresses in Pavements 2.1.2. Solutions at Axis of Symmetry When the load is applied over a single circular loaded area, the most critical stress ,strain, and deflection occur under the center of the circular area on the axis of symmetry, where = 0 and r = t, so z and r, are the principal stresses . Flexible Plate : The load applied from tire to pavement is similar to a flexible plate with a radius a and a uniform pressure q. The stresses beneath the center of the plate can be determined from z is independen t of E and v r is independent of E Yoder; E. J. and M. W. Witczak, Principles of Pavement Design , A Wiley- Interscience Publication, John Wiley & Sons Inc., U.S.A., 1975.

Stresses in Pavements The vertical deflection w can be determined from Yoder; E. J. and M. W. Witczak, Principles of Pavement Design , A Wiley- Interscience Publication, John Wiley & Sons Inc., U.S.A., 1975.

Stresses in Pavements When v = 0 .5, Eq. 2.6 can be simplified to Note On the surface of the half-space, z = 0 ; from Eq . 2 .6 , Yoder; E. J. and M. W. Witczak, Principles of Pavement Design , A Wiley- Interscience Publication, John Wiley & Sons Inc., U.S.A., 1975.

Example (2.2) : Same as Example 2 .1, except that only the left loaded area exists and the Poisson ratio is 0.3, as shown in Figure 2.8 . Determine the stresses, strains, and deflection at point A . Yoder; E. J. and M. W. Witczak, Principles of Pavement Design , A Wiley- Interscience Publication, John Wiley & Sons Inc., U.S.A., 1975.

Solution Example (2.2) : Given :- q = 50 psi z = 10.0 in a value = D/2 a = 5.0 in From Eq. 2.2, = 14.2 psi With v = 0.3, from Eq. 2.3 , = -0.25 psi The negative sign indicates tension which is in contrast to a compressive stress of 0 .8 psi (5.5 kPa) when v = 0 .5. Yoder; E. J. and M. W. Witczak, Principles of Pavement Design , A Wiley- Interscience Publication, John Wiley & Sons Inc., U.S.A., 1975.

Solution: From Eq .2.4, = 0 .00144. From Eq .2.5, = -0 .00044. From Eq .2.6, = 0 .0176. The results obtained from KENLAYER are z = 14.2 psi r = -0 .249 psi which are nearly the same as those derived from the formulas. Yoder; E. J. and M. W. Witczak, Principles of Pavement Design , A Wiley- Interscience Publication, John Wiley & Sons Inc., U.S.A., 1975.

Rigid Plate : All the above analyses are based on the assumption that the load is applied on a flexible plate, such as a rubber tire . If the load is applied on a rigid plate, such as that used in a plate loading test, the deflection is the same at all points on the plate , but the pressure distribution under the plate is not uniform. The differences between a flexible and a rigid plate are shown in Figure 2.9 . The pressure distribution under a rigid plate can be expressed as (Ullidtz, 1987 ) Yoder; E. J. and M. W. Witczak, Principles of Pavement Design , A Wiley- Interscience Publication, John Wiley & Sons Inc., U.S.A., 1975.

in which: r is the distance from center to the point where pressure is to be determined and q is the average pressure, which is equal to the total load divided by the area . The smallest pressure is at the center and equal to one-half of the average pressure . The pressure at the edge of the plate is infinity . By integrating the point load over the area , it can be shown that the deflection of the plate is A comparison of Eq . 2.10 with Eq. 2 .8 indicates that the surface deflection under a rigid plate is only 79% of that under the center of a uniformly distributed load . This is reasonable because the pressure under the rigid plate is smaller near the center of the loaded area but greater near the edge . The pressure near the center has a greater effect on the surface deflection at the center . Although Eqs .2.8 and 2.10 are based on a homogeneous half-space, the same factor, 0 .79, can be applied if the plates are placed on a layer system, as indicated by Yoder and Witczak (1975) . Yoder; E. J. and M. W. Witczak, Principles of Pavement Design , A Wiley- Interscience Publication, John Wiley & Sons Inc., U.S.A., 1975.

Example (2.3) : A plate loading test using a plate of 12-in . (305-mm) diameter was performed on the surface of the sub-grade, as shown in Figure 2.10 . A total load of 8000 lb (35 .6 kN) was applied to the plate, and a deflection of 0 .1 in . (2.54 mm) was measured . Assuming that the sub-grade has Poisson ratio 0 .4, determine the elastic modulus of the sub-grade . Solution: The average pressure on the plate is q = 8000/(367r) = 70 .74 psi (488 kPa) . From Eq. 2.10, E = all 0 .16) x 70 .74 x 6/(2 x 0 .1) = 5600 psi (38 .6 MPa) . Yoder; E. J. and M. W. Witczak, Principles of Pavement Design , A Wiley- Interscience Publication, John Wiley & Sons Inc., U.S.A., 1975.

Class work: 1 A plate loading test using a plate of 12-in . diameter was performed on the surface of the sub-grade, as shown in Figure below . A total load of 9500 lb was applied to the plate, and a deflection of 0.11 in . was measured . Assuming that the sub-grade has Poisson ratio 0 .3, determine the elastic modulus of the sub-grade . 12 in. 9500 lb Rigid Plate Deflects 0.11in v=0.3 E=? Yoder; E. J. and M. W. Witczak, Principles of Pavement Design , A Wiley- Interscience Publication, John Wiley & Sons Inc., U.S.A., 1975.

Pavement Structural Analysis 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.