Keywords: soil, Kosugi, bi-modal, saturation, retention, hydraulic conductivity, constitutive model, fitting.

The paper presents a numerical procedure for fitting the material parameters of the Kosugi model that has been extended for bi-modal soils [1]. It is used to predict soil water saturation and hydraulic conductivity curves. The model was successfully used for several soil types and delivers more accurate results than other well established models. The fitting procedure itself employs the Quasi-Newton, Powell or Levenberg-Maquardt method. Based on our experience, the Powell method is recommended. The constitutive model is characterized by the following two equations:

The first one predicts degree of effective soil saturation S_i as a function of the hydraulic head of the capillary pressure h_i. The second equation is used to calculate the soil relative hydraulic conductivity K_Ri. The model is employed for bi-modal soils, i.e. the two equations must be written separately for the matrix, (i=1) and structural pores, (i=2) and the procedure of fitting searches for optimal values of parameters h_m1, h_m2, , , , , , , , , K_s1, K_s2. The process of the parameters fitting consists of several steps. They are now described for the case of parameters h_m1, h_m2, , , i.e. for the prediction of the soil saturation curve.

1. Read measured saturation curve data points, i.e. k data pairs (theta_k, h_k).
2. Calculate residual and saturated volumetric water contents theta_r,theta_s and calculate soil effective saturation S_k, (in all the k points).
3. Set value of h_A, i.e. a capillary pressure at separation of matrix and structural pores. This value is indicated by a peak in dS/d(ln(h)). Calculate theta_s1, which is saturated volumetric water content for matrix domain.
4. Based on theta_s1 calculate (measured) matrix and structural saturations S₁, S₂ in k points and compute the first approximation of the parameters h_m1, h_m2, , , (for prediction).
5. Use the Powell or any other method to find the best approximation of S. S₁+S₂ is compared against measured S and it yields new values for h_m1, h_m2, , . The value of h_A can be fixed or optimized. Our experience shows that manual setting of h_A usually ensures better results.

In the next phase, carry on similar procedure to optimize the parameters for relative hydraulic conductivity prediction, i.e. , , , , , . Note that in this case we do npt have a good guess approximation similar to item 4. Hence, good starting values for the parameters are obtained simply by scanning the space of , , , (in many equally distributed points) for the best fit. Thereafter, the relevant parameters are optimized in similar way as described for the parameters h_m1, h_m2, , . It follows the same to find optimal values for K_s1 and K_s2.

The procedure described proves robust and efficient. It converges within a reasonably short time, thereby it allows use of the Kosugi model for bi-modal soils. Based on the present procedure a computer program was developed to automate the whole process of the parameter fitting.

1

M. Kutilek, "Soil hydraulic properties as related to soil structure", Soil Tillage Res, 79, 175-184, 2004. doi:10.1016/j.still.2004.07.006

purchase the full-text of this paper (price £20)

go to the previous paper
go to the next paper
return to the table of contents
return to the book description
purchase this book (price £75 +P&P)