LAUTECH Journal of Engineering and Technology

10

Authors: Akinleye M.T. Salami L.O. Okpidi A.O. Ayeni I.M., .Laoye A.A.

Rutting, which is permanent deformation or consolidation of asphalt pavement, is one of the flexible pavement failures. Research has shown that one of the ways of resisting this failure is by modifying the rheological properties of bitumen. This modification can be achieved by the addition of dissolved plasticwater sachet (DPWS), a well-known waste in Nigeria, to bitumen. This study was conducted to investigate the effect of DPWS on the rheological properties of bitumen and at the same time reduce the environmental hazard associated with PWS disposalwith consequential pavement material improvement. Bituminous blends containing DPWS at various percentages 0, 1, 3, 5, 7, 9, 11, 13, 15 and 17% by weight of conventional bitumen were used for the study. Tests on rheological properties such as dynamic viscosity, phase angle, peak shear stress and peak shear strainwere carried out on unmodified and DPWS modified hot and warm bitumen blendsto determine the corresponding complex shear modulus and complex shear modulus elastic portion. Results obtained fromthe tests were compared between control sample (0% DPWS) and DPWS modified bitumen samples. The test results showed that the dynamic viscosity increased upon addition of the DPWS at 135°C and at 165°C, it initially increased upon addition of DPWS up to 7%before it became constant till 17% DPWS addition; and the phase angle decreased upon addition of DPWS at both 135°C and 165°C for hot mix bituminous samples. Likewise, for the warm bituminous samples, the absolute viscosity increased and phase angle decreased upon addition of DPWS at both 135°C and 165°C. The best complex shear modulus elastic portion resultsoccurred upon 9% and 17% DPWS addition for hot mix bituminous samples and upon 5% and 17% DPWS addition for warm mix bituminous samples when subjected to temperatures of 135°C and 165°C respectively. These percentages are the best to resistrutting on our traffic roads from this study

11

Authors: Usman, M.A.,Shittu, M.T. Solanke, O.O and Onitilo,S.A

In this study, the solution to Klein-Gordon equations with focus on analytical methods is discussed. The analytical methods used in this research are the Variational Iteration Method (VIM) developed by Ji-Huan He, Adomian Decomposition Method (ADM) by Adomian and New Iterative Method (NIM) developed by Daftardar Gejji and Jafari. The modified Adomian Decomposition method by Wazwaz was used to solve the linear inhomogeneous and nonlinear Klein-Gordon equations to accelerate the convergence of the solution and minimizes the size of calculation while still maintaining high accuracy of the analytical solution.All the problems considered yield the exact solutions with few iterations. The solutions obtained were compared with the exact solution and the solutions obtained by other existing methods. The solutions obtained by the three methods yield the same results and all the problems considered show that the Variational Iteration Method, Adomian Decomposition Method and New Iterative Method are very powerful and potent in solving Klein-Gordon equations and can be used to obtain closed form solutions of linear and nonlinear differential equations (ordinary and partial).