A field compaction test using a nuclear densometer measures a wet density of 20.0 kN/m³ and a moisture content of 18%. What is the dry density of this compacted soil?

The objective is to determine the dry density of the compacted soil. Wet density is the total weight of the soil per unit volume, encompassing both the soil solids and the water present within the soil pores. In this scenario, the nuclear densometer measures a wet density of 20.0 kN/m³. Moisture content, often denoted by 'w', is a measure of the amount of water in a soil sample relative to the weight of its dry soil solids, expressed as a percentage. An 18% moisture content means that for every 100 units of dry soil weight, there are 18 units of water weight. Dry density is the weight of only the solid soil particles per unit volume, excluding the weight of any water. It is a fundamental parameter used to assess the degree of compaction achieved in a soil, as it directly reflects the amount of soil solids packed into a given space. The relationship between wet density, dry density, and moisture content is defined by the formula: wet density equals dry density multiplied by the sum of one plus the moisture content. To find the dry density, we rearrange this formula: dry density equals wet density divided by the sum of one plus the moisture content. Before using the moisture content in the formula, it must be converted from a percentage to a decimal by dividing it by 100. Thus, 18% becomes 0.18. Now, we substitute the given values into the rearranged formula. Dry density equals 20.0 kN/m³ divided by (1 + 0.18). This simplifies to 20.0 kN/m³ divided by 1.18. Performing the calculation, the dry density of the compacted soil is approximately 16.95 kN/m³.