Two Peg Test
- Establish 2 points approximately 50 metres apart on level ground as
shown below. Set the level half way between the 2 points.
- Take the 2 staff readings. In our example an error will exists (line of sight does not coincide with line of collimation).
Figure 2
- Move the level as close as possible to one of the peg. (In the case
above 'Peg A').
Take the 2 staff readings again. - If the difference in height is the same the level is okay. If not, as shown in the example above, the instrument needs to be serviced.
[ top of page ] Grid leveling is used for site investigation, for drawing contour lines and for the easy calculation of volumes. Figure 3
[ top of page ] Volume calculation from spot heights - Grid leveling
Isometric view of a building site 20 × 20 m
must
be defined to calculate the volume of the truncated prism A, B, C, etc.
The volume of a grid element (A, B, C etc). is the area of the grid element
multiplied by the average oft the four corner heights. To calculate the
volume correctly each prism is to be considered on its own.
Figure 4 below shows the site in isometric view. As can be seen the horizontal
plane (green rectangle) at RL = 12.900 lies between the RL = 10.000 and RL = 15.831.
If a house is placed on this level then cut (blue area) equals the fill (green area). However, if the FGL (finished ground level) is at RL 10.00
then all soil of the site need to be removed and if RL 15.831
soil must be transported to the site.
Figure 4 The two grid elements [ top of page ] Rectangular Base Method
As can be seen prism F is surrounded by other prisms and each corner must be counted four times.
The corners of the prism R
on the other hand must be counted one (corner), two (at the boundaries) and four (internal corner) as shown in Figure 4.
If you consider the whole lot (20 m x 20 m) and take an average of all the grid points (25 RL's) the volume quantity would be incorrect. Instead of calculate 16 single prism we could record a total of 64 points (RL's) with the number occurring at each intersecting grid point as shown in Figure 4. Each corner RL occurs 1 time, all other RL's on the boundary 2 times and all internal RL's 4 times. A MS-Excel program can quickly do the work for you. See below for additional information and a complete calculation example is shown in Table 2.
Triangular
Base Method
Figure 6
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MS - Excel Volume calculation
The work of getting the average of the spot levels can be simplified by the use of a suitable table as illustrated below: Step 1 Sum up the column 5 & 6 and find the mean height (MH) by dividing the sum of the levels by the sum of the number of common points.
Step 2 Find the difference between the mean height (MH) and the proposed finish ground level (FGL). a) the difference can be positive (+ve) or negative (-ve). b) if the mean height is greater (+ve) than the finish ground level (FGL) then it is a cut. c) if the mean height is smaller (-ve) than the finish ground level (FGL) then it is a fill . MH
< FGL = FILL
In the isometric view the finish ground level is: FGL = 12.900 [ top of page ] Contour lines
Contour lines show the vertical dimension (the third dimension) of the ground on site plans. The vertical distance separating contour lines gives an indication of the steepness of the slopes. A few simple rules for contour lines will be helpful in interpreting the vertical dimension of a building site. Steep slopes are represented by closely spaced contour lines. Figure
7
a) is the quickest method of plotting the contours. Estimate by visual inspection the position of a contour between two adjacent spot levels. Method a) We use similar triangles to to find the intersection of the contour lines on the level grid. For example the difference between RL 10.541 (grid point 21) and RL 11.687 (grid point 16) is 1.146 metres. The difference
between contour line 11.000 and RL 10.541 is
0.459. This figure will be used to calculate the intersection of
the 11.000 m contour line. As the increment
for contour lines is 0.500 m we add 0.500 + 0.459 = 0.959
to find the 11.500 contour line intersection.
0.459 is now used to find the distance and 0.959d1
for the 11.000 and d2 for the 11.500
contour lines.
Using similar triangles: Using the above equation the actual calculation for the contour lines 11.000 m and 11.500 m is:
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Assignment (Volumes and contour lines)
The opposite figure shows a building site. 1) For this site draw all contour lines at 1 metre interval. The distance
on the grid lines must be calculated using the formula for similar triangles.
2) Find the reduced level to establish a finish ground level (FGL)
by utilising the cut and fill method (cut equals fill) 3) How much soil is required if the RL of the building pad (FGL)
is to be 16.300. Calculate the volume. Figure 8
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