1. THE MASS DIAGRAM “MASS
HAUL DIAGRAM”(MHD)
Mass-haul diagrams are dawn to
calculate the volume of cutting and
filling in a job and to estimate the
amount of fill to be imported and the
haulage of earth from cutting to filling.
2. Mass-haul Diagram-cont-
The earth mass diagram is a
continuous graphical display of
cumulative cut and fill volume plotted
as ordinate versus station along the
centerline as abscissas.
3. Mass-haul Diagram-cont-
MHD is plotted above or below the
center-line profile so that both (MHD
&LP) can be used to analyze
earthworks operation
Just like in plotting LP, the abscissas
are plotted on the same scale as
plan, whereas ordinates are plotted at
large scale as possible, to
accommodate the range in
cumulative cuts and fills
4. It is necessary to understand the
following terminology to study
mass-haul diagrams.
haul: Refers to the volume of
material multiplied by the distance
moved, expressed in “station meters”
Station meter (stn m): Is 1m3 of
material moved 100m, thus 20m3
moved 2000m is haul of
20x2000/100=400stnm
Fee haul :The distance for which no
extra charge is imposed.
5. It is necessary to understand the
following terminology to study mass-
haul diagrams-cont-
Haul distance: The distance from
the face of the excavation to the
point where the earth is deposited
Average haul distance: The
distance from the centre of gravity
(CG) of the cutting to the CG of the
filling.
Borrow:The earth obtained from
outside sources such as borrow pits.
6. It is necessary to understand the
following terminology to study mass-
haul diagrams-cont-
Waste is the material excavated from
cuts but not used for the embankment
fills.
Limit of economic haul (LEH) is the
maximum haul distance. When this limit
is reached it is more economical to
waste and borrow material.
Bulking/swelling:The increase in
volume when the earth is compacted
from its original volume.
7. Bulking and shrinkage
Shrinkage: The reduction in volume when the
earth is compacted from its original in situ
volume.
When materials (e.g. sand) are excavated,
they tends to be loose. That is, 1m3 of
excavated sand will not produce 1m3 of fill
when compaction is applied (Shrinkage).
Whereas 1m3 of excavated rocks will give
/occupy large volume of fill than in situ( in
place)… Bulking/swelling.
8. Bulking and shrinkage
NB: i. Swelling /bulking of up to
30% (some say 40%) is possible
with excavated rocks.
ii. Shrinkage can be up to 11% for
sandy soil.(i.e. 11% less than in situ
sandy soil)
9. Bulking and shrinkage
When using materials which have
uniform shrinkage or swell factors;
compensation is accomplished by :
i. increasing (multiply by factor
greater than one (shrinkage) or
ii. Decreasing by multiplying by a
factor less than one
(swelling/bulking) the cut and fill
volumes.
10. Bulking and shrinkage
Example
a.If excavated material (soil) shrink
by 20% when compacted. What will
be required cut to produce 100m3
fill?
b. If the shrinkage factor is 20%,
What will be the amount of measured
cut to fill 80m3?
c. What will be the corrected volume
If 100m3 swell by 30% ?
11. USES OF MHD
A mass-haul diagram is used in
conjunction with the longitudinal
section of a road or railway line,it is
used to compare the economy of
various methods of earth work
distribution in route (e.g. road &
railway) construction.
12. USES OF MHD-cont
MHD-can be used to find:
The distance over which the cut volume
and fill volume balance
The quantity of earth to be moved and
the direction of movement
Areas requiring borrowing of materials
and the amount involved
Areas where earth has to be thrown
away and the amount involved
13. USES OF MHD-cont
The most economical movement
for the excavated earth
The best policy to adopt to obtain the
most economic use of plant
The best use of plant for the
distances over which volumes of cut
and fill are to be moved
14. We illustrate this principle
with an example.
Example: The data in the Table give
the areas of cutting or filling between
the chainages indicated. Draw a mass-
haul diagram and determine the amount
of earth to be borrowed for the
maximum haul distance.
16. Example:
Solution The longitudinal section is
shown in Fig.(a). this diagram shows
the chainages along the x-axis and
the areas of cutting and filling along
the y-axis. Cutting is considered
positive and filling is considered
negative.
17. Equipments used in Levelling
We calculate the volumes of cutting and
filling from the average end-area
method. These have been calculated
and listed in Table below.
18.
19. The mass-haul diagram:
The mass-haul diagram is plotted in
Fig(b). This diagram is plotted with
chainages along the x-axis and
cumulative volumes along the y-
axis.
20.
21. The following characteristics of the
mass-haul diagram are evident from
the graph plotted in this example.
A positive slope of the mass-haul diagram (as
in part AD) indicates excavation and a negative
slope (as in part DB) indicates filling or
embankment.
The y-coordinate at any point of the curve
gives the net volume (volume of cutting –
volume of filling).
The maximum point on the curve (D) indicates
the end of the excavation and the minimum
point (C) indicates the end of the
embankment.
22. The following characteristics of the
mass-haul diagram are evident from
the graph plotted in this example-ct-
When the curve crosses the x-axis, as at point
B, this shows that the excavation and filling are
balanced up to this point. AB is thus known as
the balancing line.
Any other horizontal line is also a balancing
line, such as EF, when starting from E.
The length of the balancing line is the
maximum haul distance when starting from
A.EF is the maximum haul distance when
starting E.
23. The following characteristics of the
mass-haul diagram are evident from
the graph plotted in this example-ct-
The area bound by the curve and the
balancing line is known as the haul
and is equal to volume x distance.
The minimum haul distance is
obtained when the algebraic sum of
the areas cut off by the balancing line
is a minimum.
24. The mass-haul diagram:
In this particular example, over the
distance selected, there is an excess
of filling, requiring earth to be
borrowed.
By computing the area under the
curve, it is possible to calculate the
haulage requirements (number of
vehicles of a particular capacity
required) and the haulage distances.
25. The mass-haul diagram:
One of the uses to which survey data is
put is for calculating volumes of
earthwork, reservoirs, etc. Volumes
can be calculated from cross
sections, contour maps, and spot
level.
