Application of Mapping and Superimposing Rule for Solution of Parabolic PDE in Porous Medium under Cyclic Loading

This paper presents an analytical method to solve governing consolidation parabolic partial differential equation (PDE) for inelastic porous Medium (soil) with consideration of variation of equation coefficient under cyclic loading. Since under cyclic loads, soil skeleton parameters change, this would introduce variable coefficient of parabolic PDE. Classical theory would not rationalize consolidation phenomenon in such condition. In this research, a method based on time space mapping to a virtual time space along with superimposing rule is employed to solve consolidation of inelastic soils in cyclic condition. Changes of consolidation coefficient applied in solution by modification of loading and unloading duration by introducing virtual time. Mapping function is calculated based on consolidation partial differential equation results. Based on superimposing rule a set of continuous static loads in specified times used instead of cyclic load. A set of laboratory consolidation tests under cyclic load along with numerical calculations were performed in order to verify the presented method. Numerical solution and laboratory tests results showed accuracy of presented method.

Using Non-Linear Programming Techniques in Determination of the Most Probable Slip Surface in 3D Slopes

Among many different methods that are used for optimizing different engineering problems mathematical (numerical) optimization techniques are very important because they can easily be used and are consistent with most of engineering problems. Many studies and researches are done on stability analysis of three dimensional (3D) slopes and the relating probable slip surfaces and determination of factors of safety, but in most of them force equilibrium equations, as in simplified 2D methods, are considered only in two directions. In other words for decreasing mathematical calculations and also for simplifying purposes the force equilibrium equation in 3rd direction is omitted. This point is considered in just a few numbers of previous studies and most of them have only given a factor of safety and they haven-t made enough effort to find the most probable slip surface. In this study shapes of the slip surfaces are modeled, and safety factors are calculated considering the force equilibrium equations in all three directions, and also the moment equilibrium equation is satisfied in the slip direction, and using nonlinear programming techniques the shape of the most probable slip surface is determined. The model which is used in this study is a 3D model that is composed of three upper surfaces which can cover all defined and probable slip surfaces. In this research the meshing process is done in a way that all elements are prismatic with quadrilateral cross sections, and the safety factor is defined on this quadrilateral surface in the base of the element which is a part of the whole slip surface. The method that is used in this study to find the most probable slip surface is the non-linear programming method in which the objective function that must get optimized is the factor of safety that is a function of the soil properties and the coordinates of the nodes on the probable slip surface. The main reason for using non-linear programming method in this research is its quick convergence to the desired responses. The final results show a good compatibility with the previously used classical and 2D methods and also show a reasonable convergence speed.

Mathematical Approach for Large Deformation Analysis of the Stiffened Coupled Shear Walls

Shear walls are used in most of the tall buildings for carrying the lateral load. When openings for doors or windows are necessary to be existed in the shear walls, a special type of the shear walls is used called "coupled shear walls" which in some cases is stiffened by specific beams and so, called "stiffened coupled shear walls". In this paper, a mathematical method for geometrically nonlinear analysis of the stiffened coupled shear walls has been presented. Then, a suitable formulation for determining the critical load of the stiffened coupled shear walls under gravity force has been proposed. The governing differential equations for equilibrium and deformation of the stiffened coupled shear walls have been obtained by setting up the equilibrium equations and the moment-curvature relationships for each wall. Because of the complexity of the differential equation, the energy method has been adopted for approximate solution of the equations.

Transportation and Physical Development around Kumasi, Ghana

This research explores the links between physical development and transportation infrastructure around Kumasi, Ghana. It utilizes census data as well as fieldwork and interviews carried out during July and December 2005. The results suggest that there is a weak association between transportation investments and physical development, and that recent housing has generally occurred in poorly accessible locations. Road investments have generally followed physical expansion rather than the reverse. Hence policies designed to manage the fast growth now occurring around Ghanaian cities should not focus exclusively on improving transportation infrastructure but also strengthening the underlying the traditional land management structures and the official land administrative institutions that operate within those structures.

Experimental Estimation of Mixed-Mode Fracture Properties of Steel Weld

The modified Arcan fixture was used in order to investigate the mixed mode fracture properties of high strength steel butt weld through experimental and numerical analysis. The fixture consisted of a central section with "butterfly-shaped" specimen that had central crack. The specimens were under pure mode I (opening), pure mode II (shearing) and all in plane mixed mode loading angles starting from 0 to 90 degrees. The geometric calibration factors were calculated with the aid of finite element analysis for various loading mode and different crack length (0.45≤ a/w ≤0.55) and the critical fracture loads obtained experimentally. The critical fracture toughness (KIC & KIIC) estimated with experimental and numerical analysis under mixed mode loading conditions.