Journal of Advanced Materials in Engineering (Esteghlal)

---

Solving traffic equilibrium problem, or “traffic assignment”, as the last step in Transportation Planning, distributes OD trip demands of a transportation network over the network links with regard to Traffic Equilibrium Law, and estimates the link flows. In formulations of traffic equilibrium which are based on path saving, the memory consumption is considerably affected by the number of effctive OD pairs (ODs with non zero demand), thus making it impossible to solve a real life transportation problem in a computer’s conventional memory. This paper attempts to present some methods to show that, reducing the number of effective OD pairs and compensating for the error, it is possible to solve a real life traffic equilibrium problem in a reasonable amount of computer memory and up to an acceptable precision. To do so, the traffic equilibrium problem of the city of Mashhad, as a case of a real life problem, is considered and The Aashtiani complementary algorithm which requires path saving is applied to solve the problem. Solving such a problem in a PC’s conventional memory is normally impossible. Nevertheless, the methods presented in this paper allow us to solve it in a conventional memory. Comparison between the results of these methods with the original answer shows that the errors generated via these methods are quite low and acceptable. A brief comparison is finally made among the different methods.

---

The cross-stream migration of a deformable drop in two-dimensional Poiseuille flow at finite Reynolds numbers is studied numerically. In the limit of a small Reynolds number (<1), the motion of the drop depends strongly on the ratio of the viscosity of the drop fluid to the viscosity of the suspending fluid. For a viscosity ratio 0.125, the drop moves toward the centre of the channe while for the ratio 1.0, it moves away from the centre until halted by wall repulsion. The rate of migration increases with the deformability of the drop. At higher Reynolds numbers (5-50), the drop either moves to an equilibrium lateral position about halfway between the centerline and the wall according to the so-called Segre-Silberberg effect or undergoes oscillatory motions. The steady-state position depends only weakly on the various physical parameters of the flow but the length of the transient oscillations increases as Reynolds number is raised, the density of the drop is increased, or the viscosity of the drop is decreased. Once the Reynolds number is high enough, the oscillations appear to persist forever and no steady state is observed. The numerical results are in good agreement with experimental observations, especially for drops that reach steady-state lateral position.

---

Stability of reinforced slopes is almost always carried out using limit equilibrium methods and controlled by the shear strengths of the slope materials and the extension force of reinforcements. According to limit equilibrium methods, the stability of slopes is assessed by dividing the whole failure wedge into several vertical elements. In order to determine the safety factor of the reinforced slopes, a new approach is proposed based on the inclined slices method. According to this approach, a 4n formulation is introduced which uses fewer unknowns and a simpler formulation to calculate the extension forces of reinforcements and safety factors of the slopes. Additionally, moment and forces equilibrium in all slices are taken into account while the tensile force of each reinforcing element is independently calculated. Comparisons revealed differences at 5 to 10 percent level between analytical results obtained from this method and those of ReSSA software.