Earthwork Quantity Calculations

Earth is almost never at the desired elevation at the intended location of a structure, and even if it was the case, almost always modifications must be done, to serve as a foundation base material that is capable of supporting the loads and at the same time settling only within tolerable limits. Therefore, earthwork operations are performed to bring the soil to correct elevation. Bringing the soil to desired properties will be covered under ground improvement and soil stabilization sections.

To modify the elevation of natural soil, there are basically two types of activities. When the natural soil is higher than the intended elevation of the bottom level of the foundation of the structure, the soil is removed, which is called “cut” or “excavation”. The opposite, where natural ground elevation is lower than the bottom of intended foundation of the structure, new earth material must be brought in, which is called “fill” or “backfill”. The filled soil is compacted by compaction equipment. Note that before filling, still some cut may be necessary, up to a depth determined by engineer, if the natural ground is not made of strong enough material. Also, in case of roads or pavements, the bottom level of the foundation means the bottom level of the sub base materials.

To plan earthwork operations, area of excavation or fill is determined and the cut and fill volume is calculated based on this area (or route in the case of roads) times the average cut or fill depth or elevation for that area. Based on these volumes, equipment, crew and work schedule is planned, and costs are estimated. The road projects should be laid out so that the cut and fill amounts should be minimized and also immediately following each other to the greatest extent possible, so that the cut soil could be easily transported to areas that needs fill for only a short distance (as the heavy earth hauling equipment are expensive to operate), provided that it is suitable, and allowed by the engineer to be compacted and placed as fill.

Calculation of earthwork volume required for structures and their surrounding sitework is quite straightforward. First, the natural ground elevation map should be obtained. On top of this map, the proposed structure foundations and sitework layout map is imposed, and the elevation differences are multiplied by area.

For road projects, the logic is the same, only that this time, we do not compare only one area but the whole route of the road. We compare the natural ground with the proposed elevation of the road, along the whole rout of the road and come up with cut and fill quantities. This method is a little more complicated than just calculating volume of an area, but it is still straightforward geometry in the end as we divide the route into many intervals, and for each interval we estimate cut and fill quantities and them add them up.

One important thing to mention about earth material volumes is that the same amount of material occupy different volume (i.e. has different density) depending on whether it is in its in natural state, or after it was excavated and being transported in loose form, or after it is placed as backfill and compacted. All of these volumes can be different for the same amount of soil. The soil in its natural state is called “bank” volume, the soil after excavation but before backfill is called “loose” volume, and the soil after backfilling and compaction is called compacted volume. These are measured in cubic yards in countries that use imperial system, and in cubicmeters in countries that use metric system. For example, 1 cubic meters of soil in its natural state, may occupy 1.3 cubic meters of volume after excavated and being transported to dump site or fill site, and it may occupy only 0.9 cubic meters after being placed as fill and compacted. All these volume calculations affect the pricing and schedule of equipment usage. Phase relationships of soil, which was covered earlier, play important role in these volume, mass and density calculations. The density of solid soil particles, the moisture content of soil both before and after excavation and backfilling, play a very important role in these calculations, as we have also seen under phase relationships and soil compaction test sections.

As a result of backfilling and compaction, engineers usually want to see 90-95% of degree of compaction. This means, the soil placed as fill should be compacted to 95% of its optimum dry density value, which is a value determined by laboratory compaction test as we have seen before, which is a theoretical maximum degree of compaction of the soil. This value can never be achieved in practice, although very close values could be obtained by greater compaction effort and under optimum moisture content, which is just enough water to facilitate better compaction but not too much to occupy unnecessary volume, as was described during explaining compaction test of soil. Clay, sand, silt, gravel and their mixes all have different values for these. The relationship of dry density and moisture content of soil was shown as a graph also when describing compaction test of soil.

Before we move on to talk about earthwork equipment, one final thing to mention. Relative density (Dr), which is a quantity often used in earthwork calculations, can be found as:

Relative density is used for granular (coarse grained) soils only. Here as always, “e” is the void ratio, as we have seen previously. The relative density is a measure that is used in specifications for earthwork to be performed on site. Here in this equation emax is the void ratio of the soil in it’s loosest possible, and that is why it is called the maximum void ratio.

Relative density tells us the state of compactness of a granular soil with respect to it’s loosest and densest states, in other words, the in-situ denseness or looseness of a granular soil. The number 100 in this equation is only used to give it as a percentage. The value of relative density may vary from 0 % to 100 %. So for example, if we have the loosest possible in-situ soil, our e would be equal to emax and this would mean, top side of the equation would be zero, and the relative density would be 0%. If we had an in-situ soil in it’s densest possible state, then the top side of the equation and bottom side of the equation would be the same, so the result would be 1, and the Dr would be 100%. This is the reason why, this value is used all the time, in earthwork specifications. 

Finally, wet materials are hard to move with any equipment mentioned below, and therefore, inclement weather involving many rainy days, can slow down or even interrupt earthwork operations considerably.

In the next post of this series, we will discuss “Earthwork Equipment”

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