Alternative Analytical Expressions for the General van Genuchten–Mualem and van Genuchten–Burdine Hydraulic Conductivity Models

The van Genuchten expressions for the unsaturated soil hydraulic properti es, fi rst published in 1980, are used frequently in various vadose zone fl ow and transport applicati ons assuming a specifi c relati onship between the m and n soil hydraulic parameters. By comparison, probably because of the complexity of the hydraulic conducti vity equati ons, the more general soluti ons with independent m and n values are rarely used. We expressed the general van Genuchten–Mualem and van Genuchten–Burdine hydraulic conducti vity equati ons in terms of hypergeometric functi ons, which can be approximated by infi nite series that converge rapidly for relati vely large values of the van Genuchten–Mualem parameter n but only very slowly when n is close to one. Alternati ve equati ons were derived that provide very close approximati ons of the analyti cal results. The newly proposed equati ons allow the use of independent values of the parameters m and n in the soil water retenti on model of van Genuchten for subsequent predicti on of the van Genuchten–Mualem and van Genuchten–Burdine hydraulic conducti vity models, thus providing more fl exibility in fi ƫ ng experimental pressure-head-dependent water content, θ(h), and hydraulic conducti vity, K(h), or K(θ) data.