Fuzzy Analytical Solution of Horizontal Diffusion Equation into the Vadose Zone

An analytical solution for estimating percolation rate by fitting temperature profiles in the vadose zone.

We present a simple analytical solution for one-dimensional steady heat transfer with convection and conduction through a multilayer system such as a vadose zone. We assume that each layer is homogeneous and has a constant thermal diffusivity. The mass/heat flow direction is perpendicular to the layers, and the mass flow rate is a constant. The analytical solution presented in this study also a...

Incorporating the Vadose Zone into the Budyko Framework

The Budyko framework provides a quantitative description of long-term average annual evapotranspiration at catchment scales in terms of macro-climatic variables. This framework, however, makes no reference to the vadose zone because it neglects changes in subsurface storage in the catchment water balance. Recent studies have shown clearly that vadose-zone water storage cannot be neglected at su...

Analytical solution for vacuum preloading considering the nonlinear distribution of horizontal permeability within the smear zone

The vacuum preloading is an effective method which is widely used in ground treatment. In consolidation analysis, the soil around prefabricated vertical drain (PVD) is traditionally divided into smear zone and undisturbed zone, both with constant permeability. In reality, the permeability of soil changes continuously within the smear zone. In this study, the horizontal permeability coefficient ...

The analytical solution and numerical solution of the fractional diffusion-wave equation with damping

Fractional partial differential equations have been applied to many problems in physics, finance, and engineering. Numerical methods and error estimates of these equations are currently a very active area of research. In this paper we consider a fractional diffusion-wave equation with damping. We derive the analytical solution for the equation using the method of separation of variables. An imp...

Biodegradation in the Vadose Zone