Ali Nikkar

One of the significant problems in geo-environmental and geotechnical engineering is the unsaturated flow of soil in unsaturated soils. The model of this phenomenon in porous media is governed by the Richards equation. In this paper a new, efficient, iterative method is used to handle the Richards equation. This new technique is obtained from the variational iteration method by a simple reconstruction that is the Laplace iteration method (LIM). In order to evaluate the efficiency and accuracy of the solutions obtained by the proposed method, two representative examples were investigated. The obtained results show that the Laplace iteration method is a very effective method, simplifies the difficulty of classical techniques and is quite accurate for systems of partial differential equations.

In this paper, a mathematical model of large amplitude vibration of a uniform cantilever beam arising in the structural engineering is proposed. Two efficient and easy mathematical techniques called variational iteration method and He's variational approach are used to solve the governing differential equation of motion. To assess the accuracy of solutions, we compare the results with the Runge-Kutta 4th order. An excellent agreement of the approximate frequencies and periodic solutions with the numerical results and published results has been demonstrated. The results show that both methods can be easily extended to other nonlinear oscillations and it can be predicted that both methods can be found widely applicable in engineering and physics.

The drainage of liquid foams involves the interplay of gravity, surface tension, and viscous forces. Foaming occurs in many distillation and absorption processes. In this study, a new reliable technique is used to handle the foam drainage equation. This new method resulted from VIM by a simple modification, that is, variational iteration method-II (VIM-II). It has been shown that the VIM-II is a powerful technique in obtaining accurate solutions that cannot be given otherwise by perturbation and other methods. The accuracy and convergence of the method are also investigated and compared with other methods. The results showed that there are good agreements between the results.

Seismic design loads for tunnels are characterized in terms of the deformations imposed on the structure by surrounding ground. The free-field ground deformations due to a seismic event are estimated, and the tunnel is designed to accommodate these deformations. Vertically propagating shear waves are the predominant form of earthquake loading that causes the ovaling deformations of circular tunnels to develop, resulting in a distortion of the cross sectional shape of the tunnel lining. In this paper, seismic behavior of circular tunnels has been investigated due to propagation of shear waves in the vertical direction using quasi-static analytical approaches as well as numerical methods. Analytical approaches are based on the closed-form solutions which compute the forces in the lining due to equivalent static ovaling deformations, while the numerical method carries out dynamic, nonlinear soil-structure interaction analysis. Based on comparisons made, the accuracy and reliability of the analytical solutions are evaluated and discussed. The results show that the axial forces determined using the analytical approaches are in acceptable agreement with numerical analysis results, while the computed bending moments are less comparable and show significant discrepancies. The differences between the analytical approaches are also investigated and addressed.

Evaluation of the accuracy of the pseudostatic approach is governed by the accuracy with which the simple pseudostatic inertial forces represent the complex dynamic inertial forces that actually exist in an earthquake. In this study, the Upper San Fernando and Kitayama earth dams, which have been designed using the pseudostatic approach and damaged during the 1971 San Fernando and 1995 Kobe earthquakes, were investigated and analyzed. The finite element models of the dams were prepared based on the detailed available data and results of in situ and laboratory material tests. Dynamic analyses were conducted to simulate the earthquake-induced deformations of the dams using the computer program Plaxis code. Then the pseudostatic seismic coefficient used in the design and analyses of the dams were compared with the seismic coefficients obtained from dynamic analyses of the simulated model as well as the other available proposed pseudostatic correlations. Based on the comparisons made, the accuracy and reliability of the pseudostatic seismic coefficients are evaluated and discussed.