In the field, it has been recognized that cylindrical macropores, predominant in vertical direction, exist in some stratum and these macropores play an important role in soil water flow under saturated condition. In this paper, in order to clarify the heterogeneity of saturated hydraulic conductivity (
Ks) in the stratum mensioned above, a pore structure model is proposed. In the model, the macropores are represented by a bundle of straight parallel capillaries of different diameters, and an inverse relation between the pore diameter and its number per unit area is assumed. Based on the model, means, variances and frequency distributions of
Ks in samples with different volume (same in height, but different in area) were examined theoretically by using probability theory. Under the assumptions that
Ks is approximately determined by the numbers of macropores included in the sample and no spatial structure exists for
Ks, the results are summarized as follows.
1. The expected value of the mean of
Ks is independent on the area of the individual sample.
2. The expected value of the variance of
Ks is inversely proportional to the area of the individual sample.
3. There is no analytic solution about the frequency distribution of
Ks. For the help of the numerical simulation, it is considered that the frequency distribution of
Ks is fitted to lognormal distribution for the smaller area of the individual sample, and it is fitted to both normal and lognormal distribution for the larger area of the individual sample.
4. From the results described above, the sampling scheme to estimate the mean of
Ks in the field was discussed. The conclusions are, (i) a factor related to the accuracy of estimating the mean of
Ks is the total area of the samples, (ii) the area of the individual sample and the number of samples should be determined for the convenience of measurement to match the total area of samples to the accuracy of estimation required.
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