Homotopy Analysis Approach of Boussinesq Equation for Infiltration Phenomenon in Unsaturated Porous Medium.

Boussinesq’s equation is one-dimensional nonlinear partial differential equation which represents the infiltration phenomenon. This equation is frequently used to study the infiltration phenomenon in unsaturated porous medium. Infiltration is the process in which the groundwater of the water reservoir has entered in the unsaturated soil through vertical permeable wall. An approximate analytical solution of nonlinear partial differential equation is presented by homotopy analysis method. The convergence of homotopy analysis solution is discussed by choosing proper value of convergence control parameter. The solution represents the height of free surface of infiltrated water.

Comparison of Numerical Methods for Calculation of Vertical Soil Pressures on Buried Piping due to Truck Loading

Calculation of pressures in a soil body due to finite loads imposed on the soil surface is a necessary step in the design and analysis of buried commodities. This study compares two commonly-applied numerical methods used to develop the vertical soil pressure profiles applied to buried pipes. The methods compared in this study differ in theory, basis, assumptions, complexity, and results, and therefore the comparison is meaningful. Provided is a comparison between design vertical forces on different sizes of buried pipes at a range of soil depth, determined using an integration of Boussinesq’s equation [1] and the method specified by AASHTO [2]. The Boussinesq equation is defined as a function of location in varying two dimensional soil planes and the integration is performed over the boundary of the pipe as well as the applied soil surface footprint. The soil surface loading considered in this study includes the AASHTO Design Truck and the AASHTO Design Tandem, positioned as required by the AASHTO LRFD code [2]. Recommendations for application of the results is provided based upon the resulting force magnitude calculated and ease of application of the methods. Consideration of the effects of redistribution of loading due to pavements or other rigid surfaces is outside the scope of this study.

Numerical Solution of Axisymmetric Problem for an Elastic Footing

Based on formulas of elastic mechanics, the axisymmetric problem applied to an elastic footing is analyzed. Using Hankel transform and finite difference method, the arbitrary points’ displacement and stress solutions of the axisymmetric elastic footing problem is obtained. Compared with recursive substitution method and transfer matrix method, this method is simple because it avoids complex formulas and exponential function calculation. The half space model is more flexible to simulate an actual footing. The numerical solutions are compared with Boussinesq’s Equation and results show that finite difference method is applicable to solve axisymmetric elastic footing problem. But in the application of finite difference method, there are a few factors that could cause calculation errors. Effective measures are needed to obtain exact solutions.