Determination of the Nonlinear Equation Coefficients for Flow through Coarse Alluvium Foundations

As a result of the limitations in the application of Darcy Law (V=ki) to linear-laminar flow regimes through porous media and due to the fact that in coarse alluviums, the Reynolds number may exceed its critical value, the so-called Laplas equation cannot be used for precise analyses of coarse granular foundations. A more general relationship is, therefore, required for such cases. However, a common relationship between piezometric gradient i and the approach velocity v within porous media shown as i=mVn leads to major difficulties in undertaking complicated tests to determine the values of m and n. It is shown that by combining the above-mentioned relationship with the continuity equation, a differential equation may be obtained to give piezometric head and a potential function Φ, which in turn, leads to the uplift force distributions and the seepage quantities through porous media. To overcome difficulties associated with m and n estimations in the model and as a result of fulfilling an extensive research programme, a fresh and reliable procedure has been developed and explained to assess m and n by means of a simple stepped pump-out test. The practical applicability of the method for a given confined aquifer is also examined. Findings indicates that the proposed procedure a) makes the use of the differential equation for turbulent flow in porous media possible, and b) provides means to determine the nonlinear equation parameters (m&n) at an acceptable precision. The computed values of the parameters are also submitted.

Keywords: Turbulent flow, Rock fill, Alluvium foundation, Reynolds number, Aquifer