In water, carbonate and bicarbonate always occur together in solution in equilibrium with one another, with the pH and with atmospheric carbon dioxide.

In irrigation water that has a pH less than 7, carbonate and bicarbonate are at low concentrations and there are generally no problems. However at higher concentrations, in soils with pH greater than 7, carbonate becomes an issue.
This is because, although all bicarbonates are soluble, calcium carbonate is relatively insoluble, therefore irrigation with this water tends to enhance the sodium in the soil water (in solution) by removing calcium from solution so that sodium and magnesium dominate.

Below the soil surface where the respiration of organisms is at work, concentrations of carbon dioxide in the soil atmosphere may be 100 times higher than in the above ground atmosphere. This lowers the concentration of carbonate in favour of bicarbonate. However, near the soil surface carbonate concentration is higher and may become even more elevated as transpiration and evaporation of water occurs.
In extreme cases where pH and the concentration of carbonate in irrigation water are high, the soil will progressively become alkaline as well as sodic so that nutrient availability is also impaired.

Source: Murray R, Grant C. 2007. The Impact of Irrigation on Soil Structure. The National Program for Sustainable Irrigation