Are the values truly zero to 6 decimal places?  Zero is a problem when trying to transform data.  Even if the samples only move a mm a month, you should see if you can get a value, and no rounding of values.  You need a non-zero value, even if it looks weird in tabular form.  If you end up with non normal distribution, which appears obvious, there are probably ways to deal with that.  Log Pearson Type III is one approach hydrologists deal with flood data that is skewed, but that may be unsuitable for the hydraulic conductivity data, where 25% of data is at one extreme.  It's been too long for me to advise you further, without reviewing information myself.  And you may need to look for ways to stratify sampling such as by soil type.  If you have so many samples with zero ability to move water under saturated conditions, the next question may be why.

Are the values truly zero to 6 decimal places?  Zero is a problem when trying to transform data.  Even if the samples only move a mm a month, you should see if you can get a value, and no rounding of values.  You need a non-zero value, even if it looks weird in tabular form.  If you end up with non normal distribution, which appears obvious, there are probably ways to deal with that.  Log Pearson Type III is one approach hydrologists deal with flood data that is skewed, but that may be unsuitable for the hydraulic conductivity data, where 25% of data is at one extreme.  It's been too long for me to advise you further, without reviewing information myself.  And you may need to look for ways to stratify sampling such as by soil type.  If you have so many samples with zero ability to move water under saturated conditions, the next question may be why.  If the study was done under extremely dry conditions, could the limited amount of water from your sample just be evaporating before it can be measured?  If so, try humidifying the analysis area during testing to help limit evaporation.

Dear Hansen,

Thanks for your suggestions.

I will explain here. The measurement was done using constant head method in the laboratory which maintains 4cm of water above soil column which is 3 cm. The data is not round off values of decimal. It is 0 due to water not moving at all. Even after a week no single drop of water conducted down the soil column. It is due to very high Na and Mg in soils and the ESP ranged from 18 to 46 in these samples. This information is available in my question description above. These soils are highly sodic and calcareous and occupy significant part of study area. This data (0values) can't be ignored in terms of pedology and this impaired hydraulic conductivity of these soils severely affects crop performance and other soil properties.