Foundations
Another thing we need to know in construction is how to calculate foundations. When building a foundation we start by digging out soil and need to calculate its total volume.
There are many forms of soil and based on their strength we can categorise them starting from rock formation to soft clay. Sometimes houses are even built on wetland. Between all these types of soil the foundation needs to be built to last. Therefor the softer the soil the costlier it is to build the foundation. Of course it is not cheap to build on rock formations either because there you need to start soil blasting or use other expensive methods of breaking the rocks.
Depending on the type of soil their natural collapse angle is an important indicator. For example on rocky soil it can be vertical at 90°. On quicksand it can vary as running water takes some soil with it. On regular sand it varies also, but can be around 30°.
When using containers filled with bulk materials (cement, flour, grain, etc.) in order to make sure we can get all of it out of the container we must take into consideration the collapsing angle on the outer sides of the container. This is especially important when building very large containers – otherwise problems with getting the materials out can arise.
When talking about bunkers it is a science on its own – different materials can act differently. Humidity, friction etc. also play a role. When collecting bulk materials into large piles the natural collapse angle must be considered.
In construction it is enough to know the natural collapse angle of the soil we plan to build upon. The image below shows the shape of the base in case of a rectangular shaped foundation.
In a construction drawing the natural collapse angle is shown either in degrees or ratios.
If however we want to calculate the volume of soil excavations in building the foundation, in case of rectangular foundation the cavity is in form of a frustum shaped geometrical body – this makes it possible to perform calculations.
To calculate the volume V, the following formula can be used:
A different formula can also be used, but its result will not be so exact:
Example
Lets look how those two formulas can be used, given the following values:
Height h = 1,4 m
Excavation bottom width b1=6m
Excavation bottom length l1=8m
And the excavation side measurement:
Width of the bank side b=8,8 m (depending on the collapse angle 1:1 or 45°, 6+1,4+1,4=8,8 )
Length of the bank side l=10,8m (depending on the collapse angle 1:1 or 45°, 8+1,4+1,4=10,8 )
Option 1
Option 2
The calculation shows a difference of 1,04 m3, which is not a huge error given large volume, but it is always recommended to do the proper calculations in order to get the exact solution.