Earthwork Calculations: Quantity Surveying PDF

Quantity Surveying / 4th Civil Dep./ Baghdad University Prof. Dr. Meervat Altaie CHAPTER 4: EARTH WORK CALCULATIONS 4.1 Introduction Generally all the Civil Engineering projects like roads, railways, earth dams, canal, buildings etc. involves the earth work. This earth wor...

Quantity Surveying / 4th Civil Dep./ Baghdad University Prof. Dr. Meervat Altaie CHAPTER 4: EARTH WORK CALCULATIONS 4.1 Introduction Generally all the Civil Engineering projects like roads, railways, earth dams, canal, buildings etc. involves the earth work. This earth work may be either earth excavation or earth filling or sometimes both will get according to the desired shape and level.Basically the volume of earthwork is computed from length, breadth, and depth of excavation or filling. The various methods of calculating the earth work quantities shall be discussed. Earthwork includes: 1. Excavation 2. Grading: Moving earth to change elevation 3. Temporary shoring 4. Back fill or fill: Adding earth to raise grade 5. Compaction: Increasing density 6. Disposal 4.2 Productivity Factors A. Job conditions ^ Material type ^ Water level and moisture content ^ Job size ^ Length of haul ^ Haul road condition (accessibility and load restrictions) B. Management conditions ^ Equipment conditions and maintenance practices ^ Skills of work force and management ^ Planning, supervision and coordination of work. Quantity Surveying / 4th Civil Dep./ Baghdad University Prof. Dr. Meervat Altaie 4.3 Units of Measure  Cubic Meter (bank, loose, or compacted) Bank (BCUM): Materials in its natural state before disturbance (in-place, in-situ) Loose (LCUM): Material that has been compacted or disturbed or loaded Compacted (CCM): Material after compaction Material after compaction  Volume Bank: VB ^ Bank cubic yards (BCUM) ^ Density B Lb /BCUM Loose: Vl ^ Loose cubic yards (LCM) ^ Density L Lb/LCUM Compacted: Vc ^ Compacted cubic yards (CCUM) ^ Density C LB/CCM 123 Quantity Surveying / 4th Civil Dep./ Baghdad University Prof. Dr. Meervat Altaie 4.4 EARTHWORK IN BUILDING FOUNDATION TRENCHES Excavations of a foundation trench of a building, having walls of different thicknesses (widths), gives rise to trenches of different breadths, and sometimes even of different depths. Necessary drawings – plan and sections at appropriate locations – coupled with clear, lucid imagination, enable a civil engineer to estimate the various items of a building, including earthwork in an excavation of foundations. The very first step, in order to get introduced into these seemingly intricate mensuration procedures, is to comprehend the drawings of a straight compound wall (Figure below ) – Shows details out such a plan for the given compound wall which is, say, 6.5 m long. the total depth of the excavated trench adds upto: 50 cm of plinth course (below the ground level) + (3 × 20) cm of the three courses of brickwork done in three steps + 30 cm of lime concrete (LC) = 140 m, a depth 124  Quantity Surveying / 4th Civil Dep./ Baghdad University Prof. Dr. Meervat Altaie that is more than the usual depth of foundation for a brick wall because of local soil conditions. Therefore, earthwork in excavation in foundation of the wall = Length (L) × Breadth (B) × Height (H) / or Depth (D) = 6.50 × 1.0 × 1.40 = 9.1 m3 Figure : Section of a Straight Compound Wall in a Brickwork Two methods of calculating earthwork in excavation, viz, Centre-line method, and Long-wall and Short-wall method. Example 1: Calculate earthwork in excavation (in foundations), and filling under the floor and foundation trenches (i.e. refilling after the masonry has been done). Tabulate the results in the form of a bill of quantities. 125 Quantity Surveying / 4th Civil Dep./ Baghdad University Prof. Dr. Meervat Altaie 126  Quantity Surveying / 4th Civil Dep./ Baghdad University Prof. Dr. Meervat Altaie 4.5 ESTIMATION OF EARTHWORK IN ROAD Generally all the Civil Engineering projects like roads, railways, earth dams, canal bunds, buildings etc. involves the earth work.This earth work may be either earth excavation or earth filling or Some times both will get according to the desired shape and level. Basically the volume of earthwork is computed from length, breadth, and depth of excavation or filling. In this section the various methods of calculating the earth work in road quantities shall be discussed. It is measured in cubic meters without any allowance for an increase in bulk. The volume of earthwork shall be calculated by multiplying the length, breadth, and depth or height measured from the ground from which soil has been taken out. 127 Quantity Surveying / 4th Civil Dep./ Baghdad University Prof. Dr. Meervat Altaie 4.5.1 Case1: volume of earth work in banking or in cutting having "No longitudinal slope" V = (bd+2x * 1/2x * ndx d)L V = (bd+nd2 )L 4.5.2 Case 2: volume of earth work in banking or in cutting having "longitudinal slope" When the ground is in longitudinal slope or the formation has uniform gradient for a length the earth work may be calculated by the following methods. 1. By Mid Section or Mid ordinate method. 128  Quantity Surveying / 4th Civil Dep./ Baghdad University Prof. Dr. Meervat Altaie Where d1, d2 = depth of banks at two ends Mid ordinate (or) Average depth (dm ) = (d1 +d2)/2 Area of mid section (Am) = (bdm + ndm 2) volume of earth work (vm) = A x L = (bdm + ndm 2) ×L 2) Trepezoidal formula: (for two sections) In this method also called mean sectional area method Let A1 &A2 be two areas at two ends. A1= (bd1 + nd12 ), A2 = (bd2 +nd22 ) Am = A1 +A2 Volume of earth work (v) = Am ×L 3) Trapezoidal formula for a series of c/s areas at equal intervals. Let A1 ,A2 ,A3.......An are the cross sectional areas along L.S of Road 'L" is the distance between two cross sections The volume of earth work=length /2 [(sum of first and last areas) +2(remaing Areas) ] V= L/2[( A1+An )+2(A2 +A3 +..... + An−1 ) v = L [ (A1+An)/2 + A3 + A4 + A5 +...... An-1] 4) Prismoidal formula for a series of cross sectional areas at equal intervals. Note : This method is adopted when there is odd number of cross sections. Volume of earth work= length/ 3(Sum of first and last areas)+4(even areas)+2(odd Areas)] V= L /3[( A1 + An ) +4(A2 +A4 +A6 +..... +An−1 ) + 2(A3 +A5 +......+ An−2 )] 129 Quantity Surveying / 4th Civil Dep./ Baghdad University Prof. Dr. Meervat Altaie Example2: Find the volume of earth work in embankment of length 12m. Top width is 5.5m and depth is 2.5m the side slopes ara 1½:1 Sol : Top width b=5.5m V = (5.5 ×2.5+1.5×2.52 )12 = 77.5m3 Example 3 : The depths at two ends of an embankment of road of length 70m are 2m and 2.5m. The formation width and side slopes are 8m and 2:1 respectively. Estimate the Quantity of earth work by a) Mid Sectional Area b) Mean sectional Area method. Solution: a) b=8m, d1=2m, d2=2.5m, L=70m, n=2 Mean depth dm = d1+d2 = 2+2.5 =2.25m Mid sectional Area = Am = bdm+ndm2 = (8*2.25+2*2.252 )2=28.125m2 Volume of earth work (V)= Am* L = 28.125*70=1968.75m3. b) Area of c/s at one end A1 = bd1 +nd12 = 8*2+2*22 =24m Area of C/s at other end A2=bd2+nd22 =8*2.5+2*2.52 =32.5m2 Mean Sectional Area (Am) = A1 +A2 = 24 +32.5 =28.25m Volume of earth work (V)= Am*L=28.25*70=1977.5m3. Example 4 : The following width of road embank ment is 10m. The side slopes are 2:1 The depth along the centre line road at 50m intervals are 1.25, 1.10, 1.50, 1.20, 1.0,1.10, 1.15m calculate the Quantity of earth work by a) Mid sectional rule b) Trepezoidal rule c) Prismoidal rule Solution: a) Mid Sectional rule : b=10m, n=2. Depth d= 2.5m 130 Quantity Surveying / 4th Civil Dep./ Baghdad University Prof. Dr. Meervat Altaie b) Trepezoidal rule A= bd +nd2 A1 = bd1+nd12 = 10* 1.25+2* 1.252= 15.625 m2 A2 = bd2+nd22 = 10* 1.10+2* 1.102 =13.42m2 A3 = 10*1.15+2*1.152 = 14.145m2 A4 = 10* 1.2+2*1.22 =14.88m2 A5=10* 1.0+2*12 =12.0m2 , A6 = 10 * 1.1 +2*1.12 = 13.42m2 A7 = 10*1.15+2*1.152= 14.145 m2 Volume of earth work by Trepezoidal rule V= L/2[( A1+A7 )+2(A2 +A3 +A4+A5+A6 ) V = 50/2*[(15.625 +14.145)+2 (13.42 +14.145 +14.818 +12.0 = 4137.50 m c) By Prismoidal rule v = L/3 [ (A1 +An ) + 4(even Areas) +2(Odd Areas)] V = L/3 [(A1 +A7 ) + 4(A 2 + A4 + A6 ) + 2(A3 + A5 )] V= 60/3 [(15.625 +14.145) + 4(13.42 +14.88 +13.42) + 2(14.145 +12)] = 4149 m3 131  Quantity Surveying / 4th Civil Dep./ Baghdad University Prof. Dr. Meervat Altaie Example 5: Estimate the Quantity of earth work for a portion of road from the following data The formation level at Chainage 0 is 8.0 and having falling gradient of 1 in 100. The top width is 12m and side slopes 1½ horizontal to 1 vertical assuming the transverse direction is in level calculate the quantity of earth work Take 1 chain = 20m by using trepezoidol & Prismoidol formula. Solution : - b=12m n=5 1)Trepezoidal formula : V= L/2[( A1+A9 )+2(A2 +A3 +A4+A5+A6 +A7 +A8 ) V= 20 /2 [(6.375+3.09)+2(1.215 +1.215 +1.837 +4.38 +0.63 +1.215 +1.837 +1.2150] = 365.53m3 132 Quantity Surveying / 4th Civil Dep./ Baghdad University Prof. Dr. Meervat Altaie 2) Prismoidal formula : v = L/3 [( A + A ) + 4(even areas) + 2(Odd areas) V= 20/3( A1 + A10 ) + 4(A2 + A4 + A6 + A8 ) +2(A3 + A5 +A7 + A9 ) V=20/ 3 [(6.375+3.09)+4( 1.215+1.837+0.63+1.837)+2(1.215+4.38+1.815+1.215)] V = 317.27 m Example 6: The road has the following data The formation level at chainage zero is 22.0 and having a rising gradient of 1 in100 the top width is 12.0m and side slopes are1½ :1 Assuming the transverse direction is in level. calculate the quantity of earth work by a) Trepezoidalformula b) Prismoldal formula Solution: 133 Quantity Surveying / 4th Civil Dep./ Baghdad University Prof. Dr. Meervat Altaie a) Trepezoidal formula: Vol of earth work in embankment V= L/2[( A1+A7 )+2(A2 +A3 +A4+A5+A6 ) V= 20 /2 [(19.74 + 2.460+2(16.56 +12.01+6.375 +1.215 +1.215) = 969.5 m3 b)Prismoidal formula V = L/3 [( A1+An)+4(even Areas ) +2(Odd Areas) ] V = 20/3 [ (19.74+2.46)+4(16.56+6.325+1.2+5)+2(12.01+1.215)] = 968.33m3 Example 7:From the above problem if the formation level at 0th chainage in 20m. Calculate the volume of earth work by using the formulas? 134 Quantity Surveying / 4th Civil Dep./ Baghdad University Prof. Dr. Meervat Altaie a) Trepezoidal formula: Vol.of earth work in cutting V= L/2[( A1+An )+2(A2 +A3 +..... + An−1 ) V=20/2 [(7.74+26.46 )+2(10.56+15.015+21.375+28.215+28.215) = 2409.6 m3 b) Prismoidal formulae : V= L /3[( A1 + An ) + 4(even areas) + 2(Odd areas) ] V=20/3 ( A 1 + A 7 ) + 4 ( A 2 + A 4 + A 6 ) + 2 ( A 3 + A 5 )] V = 20/3 [ (7.74+26.46) + 4( 10.56+21.375+28.215) + 2(15.015+28.215)] V = 2408.4 m3 135 Quantity Surveying / 4th Civil Dep./ Baghdad University Prof. Dr. Meervat Altaie Example 8 :From the same above problem if the gradient is in 100 falling calculate the quantity of earth work by using the formulas a) Trepezoidal formula: Vol.of earth work in cutting V= L/2[( A1+An )+2(A2 +A3 +..... + An−1 ) V=20/2 [97.74+76.860 +2(16.56+28.215+43.335+60.375+69.615)] = 5208 m3 b) Prismoidal formulae : V= L /3[( A1 + An ) + 4(even areas) + 2(Odd areas) ] V=20/3 ( A 1 + A 7 ) + 4 ( A 2 + A 4 + A 6 ) + 2 ( A 3 + A 5 )] 136 Quantity Surveying / 4th Civil Dep./ Baghdad University Prof. Dr. Meervat Altaie V = 20/3 [ [ (7.74+76.86) + 4( 16.56+43.335+69.615) + 2(28.215+60.375)] V = 5198.8 m Example 9: From the problem 7.5 if the gradient is 1 in 100 raising up to 40th chainage and 1 in 100 falling ragient from 40th Chainage to 120th chainage. Calculate the vol of earth work by using the formulas. 20− = 0.1 0.7 0.7 = 2-0.1 0.7 +0.1 = 2 0.8 = 2 = 2.5 137 Quantity Surveying / 4th Civil Dep./ Baghdad University Prof. Dr. Meervat Altaie  volume of earth work in embankment here the intervals are not equal so we have to take the seperate volumes from oth chainage to 60th chainage and 60th chainage to 62.5 chainage = Vol (0 - 60) + vol(60 - 62.5)  By Tripezoidal formula 20 2.5 = [(19.74 +1.215)+2((16.56 +12.01)]+ [(1.215 +0.00)] 2 2 = 782.46m3  By Prismoidal 20 2.5 = [(19.74 +1.215)+4×16.56 + 2 ×12.01)]+ [(1.215 +0.00)] 3 3 == 742.44 m3  Vol of earth work in cutting Volume (v) = vol (62.5-80)+Vol (80-120)  By Tripezoidal formula 17.5 20 = (0 +9.135 )++ [(9.135 +19.74) ++15.015 , = 668.98m3 2 2  By Prismoidal 17.5 20 = (0 +9.135 )++ [(9.135 +19.74) +4×15.015] , = 646.18 m3 3 2 138 Quantity Surveying / 4th Civil Dep./ Baghdad University Prof. Dr. Meervat Altaie H. W 1) State the following formulae with usual notation a)Prismoidal formula b)Trepezoidal formula 1. For an embankment 90m long of uniform gradient when the height of bank is 2.4m at one end and 1.8m at the other end the width of embankment at top is 8m and its side slopes 2 vertical to 1 Horizontal calculate the quantity of earth work by a) Mid Sectional area method b) Mean sectional area method. 2. Find the earthwork in embankment between 5/2km to 5/5km of the proposed road whose c/s is given below. 2) The road has the following data The Formation level at chinage zero is 28 and having the rising gradient of 1 in 100 the top width is 10m and the side slopes are 1½ horizontal to 1 vertical Assuming transverse slope is level calculate the volume of earth 3) The reduced level of ground along the centre line of a proposed road from chaiage 0 to 6 are given below. The formation level at '0' chainage is 10.00 andtheroadisindownwardgradientof1in100formationwidthofroad is 10m and side slopes are 2:1 for both banking and cutting. Length of chain is 20m calculate the quantity of earth work required by a) Trepezoidal ruled)Prismoidalrule. 139