Ponded infiltration experiment is a simple test used for in-situ determination of soil hydraulic properties, particularly saturated hydraulic conductivity and sorptivity. It is known that infiltration process in natural soils is strongly affected by presence of macropores, soil layering, initial and experimental conditions etc. As a result, infiltration record encompasses a complex of mutually compensating effects that are difficult to separate from each other. Determination of sorptivity and saturated hydraulic conductivity from such infiltration data is complicated. In the present study we use numerical simulation to examine the impact of selected experimental conditions and soil profile properties on the ponded infiltration experiment results, specifically in terms of the hydraulic conductivity and sorptivity evaluation. The effect of following factors was considered: depth of ponding, ring insertion depth, initial soil water content, presence of preferential pathways, hydraulic conductivity anisotropy, soil layering, surface layer retention capacity and hydraulic conductivity, and presence of soil pipes or stones under the infiltration ring. Results were compared with a large database of infiltration curves measured at the experimental site Liz (Bohemian Forest, Czech Republic). Reasonably good agreement between simulated and observed infiltration curves was achieved by combining several of factors tested. Moreover, the ring insertion effect was recognized as one of the major causes of uncertainty in the determination of soil hydraulic parameters.
Let $$ A=\left [ \begin {matrix} 1 & 2 \\ 0 & 1 \end {matrix} \right ],\quad B_{\lambda }=\left [ \begin {matrix} 1 & 0 \\ \lambda & 1 \end {matrix} \right ]. $$ We call a complex number $\lambda $ “semigroup free“ if the semigroup generated by $A$ and $B_{\lambda }$ is free and “free” if the group generated by $A$ and $B_{\lambda }$ is free. First families of semigroup free $\lambda $'s were described by J. L. Brenner, A. Charnow (1978). In this paper we enlarge the set of known semigroup free $\lambda $'s. To do it, we use a new version of “Ping-Pong Lemma” for semigroups embeddable in groups. At the end we present most of the known results related to semigroup free and free numbers in a common picture.