F.L.sd B sd

d

sd B sd

s:1s:1

N.S.L.

F.L.

ds:1s:1

X-Section in Banking/Filling

X-Section in Cutting

sd B sd

N.S.L.

F.L.

s:1

s:1

X-Section in Cut & Fill

N.S.L.

N.S.L.

F.L.Rise, s:1 Fall, s:1

L-Section in Banking/Filling

N.S.L.

F.L. Rise, s:1Fall, s:1

L-Section in Cutting

N.S.L.

F.L.

Rise, s:1

Fall, s:1

L-Section in Cut & Fill

Rise, s:1

Longitudinal Sectioning

Cross Sectioning

PLAN VIEW

(a) Mid-Sectional Area Method

F.L. N.S.L.

(m) (m) (m) (m) (m) (m)300 - d1 - -330 30 d2 (d1+d2)/2

360 30 d3 (d2+d3)/2

(b) Mean-Sectional Area Method

F.L. N.S.L.

(m) (m) (m) (m) (m)

-

(c) Prismoidal Formula Method

(m) (m) (m) (m)

- d1 - - - -

d2 (d1+d2)/2

d3 (d2+d3)/2

Area of Side Sloping Surface

Sloping Breadth Total Area of Side Slopes

(m) (m) (m) (m) (m)- - - -

Total =

Station/R.D.

Length b/w

stations, L

Height/Depth,d

Mean Height/Depth(dm)

Central Area, Ac(B*dm)

(m2)

Station/R.D.

Length b/w

stations, L

Height/Depth, d

Central Area, Ac

(Bd)

Triangular Area, At

(sd2)

(m2) (m2)

Station/R.D.

Length b/w

stations, L

Height/Depth, d

Mean Depth, dm

Central Area, AcB*dm

d12 d2

2

(m2) (m2) (m2)

Station/R.D.

Length b/w

stations, L

Height/Depth,

d

MeanHeight/Depth

dm dm*(√s2+1) 2*L*d*(√s2+1)

(m2)

Total X-Area, A (Ac+At)

Cutting FillingArea of Mid-Section:

- - - -=

=

Total = Quantity =

Mean X-Area, Am

Cutting Filling

A1 - - - Mean-Sectional Area:

A2 (A1+A2)/2

A3 (A2+A3)/2

Total =

Quantity =

Cutting Filling

Quantity or Volume =

- - - - -

=

Total = =

Total Area of Side Slopes

-

Total =

Triangular Area, At(s.dm2)

Earthwork(A*L)

(m2) (m2) (m3) (m3)

Total X-Area, A (Ac+At)

Earthwork(A*L)

(m2) (m2) (m3) (m3)

d1d2Triangular Area, Ats*{(d1

2+d22+d1d2)/3}

Total Area, A(Ac+At)

EarthworkA*L

(m2) (m2) (m2) (m3) (m3)

2*L*d*(√s2+1)

(m2)

Area of rectangular portion + area of two triangular portions

(Sectional area of central portion + sectional area of side slope portions) * Length

Bdm+1/2sdm2+1/2sdm2

Bdm+sdm2

L*(Bdm+sdm2)

A=(A1+A2)/2

A1= Bd1+sd12, A2=Bd2+sd2

2

L*(A1+A2)/2

L/6 (A1+A2+4Am)

{B(d1+d2)/2 + s(d12+d2

2+d1d2)/3}*L

Design Problem-1Calculate the quantity of earthwork for 200m length for a portion of a road in an uniform ground, the heights of banksat the two ends being 1.00m and 1.60m. The formation width is 10m and side slopes 2:1 (H:V). Assume that there is no transverse slope.

Design Problem-2Reduced level (R.L.) of ground along the centre line of a proposed road at 30m interval are given below.The formation level (F.L.) at R.D. of 300m is 107.0m and the road is in downward gradient of 1 in 150 upto R.D. of 420m and then the gradient changes to 1 in 100 downward. Formation width of the road is 10m and side slopes of banking are 2:1 (H:V).

R.D. (m) 300 330 360 390 420 450 480

R.L. of NSL (m) 105.0 105.6 105.44 105.9 105.42 104.3 105.0

R.L. of F.L. (m) 107.0Fall, 1 in 150 Fall, 1 in 100

Design Problem-3Estimate the quantities of earthwork for a portion of road for 400m lengthfrom the following data. Formation width is 10m. Side slopes are 2:1 and 1.5:1 in banking and cutting, respectively.

Station Distance (m)

25 1000 51.0 52.026 1040 50.9

Fall, 1 in 200

27 1080 50.528 1120 50.829 1160 50.630 1200 50.731 1240 51.232 1280 51.433 1320 51.334 1360 51.035 1400 50.6

i) Draw longitudinal section of the road and a typical cross section. Also, determine the quantity of earthwork involved.ii) For estimation of turfing on side slopes, find out the area of side slopes as well.

R.L. of N.S.L.(m)

R.L. of F.L.(m)

Design Problem-2R.D. (m)

Calculate the quantity of earthwork for 200m length for a portion of a road in an uniform ground, the heights of banks R.L. of NSL (m)at the two ends being 1.00m and 1.60m. The formation width is 10m and side slopes 2:1 (H:V). R.L. of F.L. (m)

Height/Depth (m)

Reduced level (R.L.) of ground along the centre line of a proposed road at 30m interval are given below.The formation level (F.L.) at R.D. of 300m is 107.0m and the road is in downward gradient of 1 in 150 upto R.D. of 420m and then the gradient changes to 1 in 100 downward. Formation width of the road is 10m and side slopes of

510 540 570 600

104.1 104.62 104.0 103.3

Fall, 1 in 100

Estimate the quantities of earthwork for a portion of road for 400m lengthfrom the following data. Formation width is 10m. Side slopes are 2:1 and 1.5:1 in banking and cutting, respectively.

Draw longitudinal section of the road and a typical cross section. Also, determine the quantity of earthwork involved.

Design Problem-2300 330 360 390 420 450 480 510 540

105.0 105.6 105.44 105.9 105.42 104.3 105.0 104.1 104.62

107.0 106.8 106.6 106.4 106.2 105.9 105.6 105.3 105.0

2.0 1.2 1.2 0.5 0.8 1.6 0.6 1.2 0.4

107.0

106.0

105.0

104.0

103.0

Datum

F.L.

N.S.L.

F.L.sd 10m sd

d 2:12:1

X-Section in Banking/Filling

N.S.L.

Longitudinal Section

570 600

104.0 103.3

104.7 104.4

0.7 1.1

N.S.L.