Geotechnical Engineering

Weight–Volume Problems Involving Defined Quantities of soil

Weight-volume problems may be divided into two categories: those where there is a defined quantity of soil, and those where the quantity of soil is not defined and it is only desired to make conversions among relationships. The solution to problems of the first category is discussed first; discussion of the second category follows. Problems of the first category can be solved in four steps:
1. A blank phase diagram is sketched and known weights, volumes, and unit weights are entered on the diagram.
2. Known volumes are multiplied by their respective unit weights to obtain weights. Known weights are divided by unit weights to obtain volumes. Where values of some relationships are given, additional weight and volume values are calculated using the definitions of Eqs. (15.6), (15.7), (15.10), and (15.11). To numerically balance the phase diagram it is recommended that all calculations be carried to at least four significant digits.

3. Multiplication and division horizontally across the diagram and addition and subtraction vertically along the sides is continued until all weights, volumes, and unit weights are determined and found to numerically balance.
4. All desired values and relationships can now be calculated from the completed and checked diagram.

Related Articles