## ABSTRACT

When developing an analytical expression to determine swelling of clay soil during its moistening, the authors proceeded from the fact that the volume of clay soil increases by the amount of water absorbed into it. Based on simple mathematical operations, an equation to determine soil swelling is obtained, where the product of the unit weight of soil skeleton in the initial state by the difference in moisture contents of soil in the swollen and initial states is presented in the numerator of the fraction expression, and water density is presented in the denominator of the same expression. A method to derive a basic equation to determine shrinkage of clay soil is identical to the method mentioned above. An equation to determine shrinkage is obtained, where the product of the unit weight of clay soil at initial moisture by the difference in moisture contents in the initial state and after shrinkage is presented in the numerator of the fraction expression, and the product of water density by the sum of one and soil moisture in the initial state is presented in the denominator of the same expression.