Quantity Survey & Estimation – Lecture # 11

Quantity Survey & Estimation – Lecture # 11

Table of Content

    • Estimating Earthwork
    • Estimation of Excavation for Roads in Plains
    • Estimation of Surface Drains

[su_divider top=”yes” text=”Go to the top” style=”default” divider_color=”#FD8B00″ link_color=”#FD8B00″ size=”4″ margin=”15″]

Quantity Survey & Estimation – Lecture # 11 – PDF

[wonderplugin_pdf src=”https://mytrustworth.com/wp-content/uploads/2019/06/Quantity-Survey-_-Estimation-Lecture-11-12.pdf” width=”100%” height=”550px” style=”border:0;”]

Download Quantity Survey & Estimation (Lecture # 11)

[su_divider top=”yes” text=”Go to the top” style=”default” divider_color=”#FD8B00″ link_color=”#FD8B00″ size=”4″ margin=”15″]

Quantity Survey & Estimation – Lecture # 11 – Excerpt

Quantity Survey & Estimation

Course Instructor

Engr. Shad Muhammad

Lecturer, Department of Civil Engineering

Qurtuba University of Science & IT, D. I. Khan.

Review of Lecture # 10

Estimating in Construction Industry

Types of Estimating

Contents of Lecture # 11 & 12

Estimating Earthwork

Estimation of Excavation for Roads in Plains

Estimation of Surface Drains

Estimating Earthwork

Calculating the quantities of earth that must be excavated is considered to be one of the most difficult aspects of the estimator’s task.

Calculating the excavation for the project often involves a great deal of work. The number of cubic yards to excavate is sometimes easy enough to compute, but calculating the cost for this portion of the work is difficult because of the various hidden items that may affect the cost.

These wp-wp-includess such variables as the type of soil, the required slope of the bank in the excavated area, whether bracing or sheet piling will be required, and whether groundwater will be encountered and pumping will be required.

Earthwork- Specifications

The estimator must carefully check the specifications to see exactly what is wp-wp-includessd in the excavation. Several questions demand answers:

i.What is the extent of work covered?

ii.What happens to the excess excavated material?

iii.Can it be left on the site or must it be removed?

iv.If the excess must be removed, how far must it be hauled?

v.Who does the clearing and grubbing? Who removes trees?

vi.Must the topsoil be stockpiled for future use? Where?

vii.Who is responsible for any trenching required for the electrical and mechanical trades?

If the owner is using separate contracts, it is important that the estimator understand exactly what work each contractor is performing.

If the general contractor is the sole contractor, that person becomes responsible for addressing all of the coordination issues.

Earthwork- Soil

One of the first items the estimator must consider is the type of soil that will be encountered at the site. The estimator may begin by investigating the soil borings shown on the drawings or wp-wp-includessd in the specifications.

Because of such notes and because the specifications for some projects provide no soil information, it is a common practice for the estimator to investigate the soil conditions when visiting the site.

Bringing a long-handled shovel or a post-hole digger will allow the estimator to personally check the soil and then record all observations in the project notebook.

Earthwork- Soil

Earthwork- Soil

Earthwork- Soil

Earthwork- Soil

Earthwork- Soil

Earthwork- Soil

Earthwork- Soil

Calculating- Excavation

Excavation is measured by the cubic yard for the quantity takeoff (27cf =1cy).

Before excavation, when the soil is in an undisturbed condition, it weighs about 100 pounds per cf; rock weighs about 150 pounds per cf, while normal weight concrete weighs 145 pounds per cf.

The site plan is the key drawing for determining earthwork requirements and is typically scaled in feet and decimals of a foot. There is usually no reason to change to units of feet and inches; however, at times they must be changed to decimals. Remember that when estimating quantities, the computations need not be worked out to an exact answer.


Swell & Compaction

Material in its natural state is referred to as bank materials and is measured in bank cubic yards (bcy).

When bank materials are excavated, the earth and rocks are disturbed and begin to swell. This expansion causes the soil to assume a larger volume; this expansion represents the amount of swell and is generally expressed as a percentage gained above the original volume. Uncompacted excavated materials are referred to as loose materials and are measured in loose cubic yards (lcy).

When loose materials are placed and compacted (as fill) on a project, it will be compressed into a smaller volume than when it was loose, and with the exception of solid rock it will occupy less volume than in its bank condition. This reduction in volume is referred to as shrinkage. Shrinkage is expressed as a percentage of the undisturbed original or bank volume. Materials that have been placed and compacted are referred to as compacted materials and are measured in compacted cubic yards (ccy).

Bank, loose, and compacted cubic yards are used to designate which volume we are talking about.

Unit of Measure

Cubic Yard (bank, loose, or compacted)

Earthwork Volume

Bank Volume: VB

Bank Cubic Yards (BCY) 

Density ‘B’ = Lb/BCY

Loose Volume: VL

Loose Cubic Yards (LCY)

Density ‘L’ = Lb/LCY

Compacted Volume: VC

Compacted Cubic Yards (CCY) 

Density ‘C’ = Lb/CCY

Earthwork Volume


A soil increases in volume when it is excavated.

Swell (%)   = (Bank Density/ Loose Density – 1)*100

Load Factor   = (Loose Density/ Bank Density)

Bank Volume   = Loose Volume x Load Factor

Earthwork Volume


  A soil decreases in volume when it is compacted.

Shrinkage (%)   = (1 – Bank Density / Compacted Density) x 100

Shrinkage Factor   = 1 – (Shrinkage/100)

Compacted Volume   = Bank Volume x Shrinkage Factor

Material Volume Characteristics

Typical Soil Volume Conversion Factors

Estimating Earth Work for Trenches and Foundation

Approximate Angle of Repose For Sloping Sides of Excavation

Swell & Compaction

A table of common swell and shrinkage factors for various types of soils. When possible, tests should be performed to determine the actual swell and shrinkage for the material.

Determine- Swell & Haul

Determine- Shrinkage & Haul


Equipment used for earthwork wp-wp-includesss trenching machines, bulldozers, power shovels, scrapers, front-end loaders, backhoes, and clamshells.

Each piece of equipment has its use; and as the estimator does the takeoff, the appropriate equipment for each phase of the excavation must be selected.

If material must be hauled some distance, either as the excavated material hauled out or the fill material hauled in, equipment such as trucks or tractor-pulled wagons may be required.


Equipment used wp-wp-includesss trenching machines, bulldozers, power shovels, scrapers, front-end loaders, backhoes, and clamshells.


Equipment used wp-wp-includesss trenching machines, bulldozers, power shovels, scrapers, front-end loaders, backhoes, and clamshells.


Equipment used wp-wp-includesss trenching machines, bulldozers, power shovels, self-propelled scrapers, front-end loaders, backhoes, and clamshells.


Equipment used wp-wp-includesss trenching machines, bulldozers, power shovels, scrapers, front-end loaders, backhoes, and clamshells.


Equipment used wp-wp-includesss trenching machines, bulldozers, power shovels, scrapers, front-end loaders, backhoes, and clamshells.


Equipment used wp-wp-includesss trenching machines, bulldozers, power shovels, scrapers, front-end loaders, backhoes, and clamshells.

Equipment Capacity (cy per hour)


The front-end loader is frequently used for excavating basements and can load directly into the trucks to haul the excavated material away.

A bulldozer and a front-end loader are often used in shallow excavations, provided the soil excavated is spread out near the excavation area.

If the equipment must travel over 100 feet in one direction, it will probably be more economical to select other types of equipment.

The backhoe is used for digging trenches for strip footings and utilities and for excavating individual pier footings, manholes, catch basins, and septic tanks. The excavated material is placed alongside the excavation.

For large projects, a trenching machine may be economically used for footing and utility trenches.

A power shovel is used in large excavations as an economical method of excavating and loading the trucks quickly and efficiently.

On large-sized grading projects, tractor hauled and self-propelled scrapers are used for the cutting and filling requirements.

Excavation-New Site Grade & Rough Grading

Virtually every project requires a certain amount of earthwork. It generally requires cutting and filling to reshape the grade.

Cutting consists of bringing the ground to a lower level by removing earth.

Filling is bringing soil in to build the land to a higher elevation.

Regardless of the type of form used, it is essential that the cut and fill quantities be kept separate to allow the estimator to see whether the available cut material can be used for fill.

In addition, the estimator needs these quantities to estimate the amount of effort required to convert the cut material into the fill material. For example, if the cut material is to be used for the fill material, it must be hauled to where it will be used and then compacted. This requires decisions concerning what type of hauling equipment will be used and the need for compaction equipment and their associated operators. In addition, because of shrinkage, one cubic yard of cut is not equal to one cubic yard of fill.

Estimating Earthwork

The primary drawing for site excavation is the site plan. This drawing typically shows contour lines and spot elevations, and locates all site improvements.

Contour lines connect points of equal elevation. Typically, contour lines are in one-foot increments and are based upon some benchmark, which is a permanent point of known elevation. Most commonly, the existing elevations are shown with dashed contour lines while the proposed new elevations are denoted with solid lines.

Estimating Earthwork

Spot elevations detail an exact elevation of a point or object on the site.

Because the contour lines are typically shown in one-foot increments, the elevation of any point between those lines must be estimated.

Through the use of spot elevations, the designer increases the accuracy of the site drawings.

For example, the top of a grate elevation on a catch basin may be denoted on the drawing as elevation 104.3´. Because that elevation is critical for the drainage of the parking lot, it is specified as an exact dimension.

Cross-Section Method

The cross-section method entails dividing the site into a grid and then determining the cut or fill for each of the grids.

The size of the grid should be a function of the site, the required changes, and the required level of accuracy.

If the changes in elevation are substantial, the grid should be small. The smaller the grid, the more accurate the quantity takeoff.

In Figure-A (next slide), the site was divided into a 50-foot grid in both directions.

Each line on the grid should be given a number or letter designation.

If the horizontal lines are numeric, the vertical lines would be alphabetic. The opposite is also true.

By using this type of labeling convention, points on the site plan can be easily found and referenced.

In addition to this numbering system, it is also helpful to number each resulting grid square.

The next step is to determine the approximate current and planned elevation for each grid line intersection. Once these are noted, the cut and fill elevation changes can also be noted.

Cross-Section Method

Cross-Section Method

Because contour lines rarely cross the grid intersections, it is necessary to estimate the current and proposed elevations at each of the grid intersection points.

If the proposed elevation is greater than the current elevation, fill will be required. Conversely, if the planned elevation is less than the current elevation, cutting will be needed.

Once all of the grids have been laid out with existing and proposed elevations and cut or fill, examine them to see which grids contain both cut and fill. This is done by checking the corners of the individual grid boxes.

Cross-Section Method

For the squares that contain only cut or fill, the changes in elevation are averaged and then multiplied by the grid area to determine the required volume of cut or fill. Those quantities are then entered in the appropriate column on the cut and fill worksheets.

Example: Fill Volume

Using grid 13 (Figure-A) as an example, determine the fill quantity.

Example: Cut Volume

Using grid 40 (Figure A) as an example, determine the cut quantity.

Example: Cut & Fill in the Same Grade

Grid 10 (Figure A) is an example of a square that contains both cut and fill.

Along line 2, somewhere between lines C and D, there is a point where there is no change in elevation. This point is found first by determining the total change in elevation and by dividing that amount by the distance between the points; second, determine the change in elevation per foot of run.

Total change in elevation (C–D) = 0.3’ + 0.7’ = 1.0’ change in elevation

Change in elevation per foot of run (C–D) = 1.0’/50’ = 0.02’ per foot of run

Example: Cut & Fill in the Same Grade

Because the elevation change is 0.02 foot per foot of run, the estimator can determine how many feet must be moved along that line until there has been a 0.3-foot change in elevation.

Distance from C2 = 0.3’/0.02’ per foot of run = 15’

This means that as one moves from point C2 toward point D2 at 15 feet past point C2, there is the theoretical point of no change in elevation, or the transition point between the cut and the fill. Because the same thing occurs along line 3 between points C3 and D3, the same calculations are required.

Total change in elevation (C–D) = 0.4’ + 0.3’ = 0.7’ change in elevation

Change in elevation per foot of run (C–D) = 0.7’/50’ = 0.014’ per foot of run

Example: Cut & Fill in the Same Grade

Grid 10 can be divided into two distinct grids: one for cut and one for fill.

The next step is to determine the area of the cut and fill portions. The most simple is to divide the areas into rectangles and/or triangles.

Example: Cut & Fill in the Same Grade

Example: Cut & Fill

Occasionally when the grid is divided, a portion of the grid will be neither cut nor fill. Grid 3 is an example of such an occurrence. Figure A is an excerpt from the site plan. In that grid, the change from fill to cut occurs on line 2 between C and D.

Example: Cut & Fill

Figure shows the dimensions and proportions between cut, fill, and the unchanged area of grid 3. The remaining 1,250 sf theoretically have no cut or fill.

Example: Cut & Fill

Example: Cut & Fill

Estimating Earthwork

When a specific grid contains both cut and fill, that grid needs to be divided into grids that contain only cut, only fill, or no change. These dividing lines occur along theoretical lines that have neither cut nor fill. These lines of no change in elevation are found by locating the grid sides that contain both cut and fill.

Earthwork wp-wp-includesss:


2.Grading: Moving earth to change elevation

3.Temporary shoring

4.Back fill or fill: Adding earth to raise grade

5.Compaction: Increasing density


Productivity Factors

  1. Job Conditions

Material type

Water level and moisture content

Job size

Length of haul

Haul road condition (accessibility and load restrictions)

  1. Management Conditions

Equipment conditions and maintenance practices

Skills of work force and management

Planning, supervision and coordination of work.

Job Efficiency Factors for Earthmoving Operations

Calculating Earthwork Quantities

  1. Contour Line/ Grid Method

Used for parking lots and site “leveling”

Grid size from 10’x10’ to 50’x50’

The greater the terrain variance the smaller the grid.

1.Determine by visual study of the site drawing if the net total will be an import (more fill required than cut) an export (less fill required than cut) or a blend (cut and fill about equal) 


2.Determine the pattern of calculation points or grid size.


3.Determine elevations at each calculation location, the corners of each grid.


4.Calculate the cubic yards of cut or fill required in each grid cell. 


5.Add the individual Grid Cell quantities together to arrive at the total cut, total fill volume and the import or volume export yardage required for the job.

  1. Contour Line/ Grid Method
  2. Contour Line/ Grid Method


  Grade the entire site to grade 90’

Quick Method

  Assume one grid

  Existing Level   =90.50

  Proposed Level   =90.00

  Cut       =0.50

  Total Cut  =   = 833 CY

  1. Contour Line/ Grid Method

Road Estimating (Earthwork)

Cross-section of earthwork of road in banking or in cutting is usually in the form of trapezium, and the quantity of earthwork may be calculated by:

Quantity or Volume of Earthwork = Sectional Area * Length

Sectional Area = Area of central rectangular portion + Area of two-side triangular portion

  =B*d + 2(1/2 sd * d) = Bd + sd2

S:1 is the ratio of side slopes as Horizontal: Vertical.

For 1 vertical, horizontal is s, for ‘d’ vertical, horizontal is sd.

Quantity = (Bd + sd2)*L

Road Estimating (Earthwork)

When the ground is in a longitudinal slope, the height of bank or the depth of cutting will be different at the two ends of the section, and mean height or depth may be taken for ‘d’ and sectional area at mid-section is taken out for mean height.

Sectional area at the two ends may be calculated and mean of 2 sectional area is taken out.

Sectional area at the mid-section or the mean sectional area multiplied by the length gives the quantity.

Mean Height = (d1+d2)/2

For different kinds of soils as sandy, clayey, rocky, etc. are estimated separately as the rates vary.

Road Estimating (Earthwork)

Lead: Horizontal distance travelled by the earth to be moved for banking or dumping.

Lift: Vertical distance travelled by the earthwork after excavating.

Road Estimating (Earthwork)

For the calculation of earthwork in a road longitudinal section & cross-section of the ground are taken and the formation line is fixed.

The formation line is fixed in consideration of flood level, gradient, height of the bank, depth of cutting, etc.

In plain areas, road is usually in banking, but if the road is in cutting for some length & in banking for some other length, the excavated earth from the cutting portion should be utilized for the banking portion.

But for estimating of earthwork, this point of utilizing excavated earth from cutting in certain length in banking of the adjacent length may not be taken into account to avoid complicacy.

In hilly areas, road is usually both in banking & in cutting & the excavated earth from cutting is utilized for banking within economical limits.

Road Estimating (Earthwork)

From the L-section & Formation Line, the height of bank & depth of cutting are calculated.

The difference of Reduced Level of ground and Reduced Level of formation line gives the height of bank or depth of cutting.

For plain areas, the ground is considered as level across, that is there is no cross-slope. The earthwork is calculated by parts of the length in between 2 consecutive stations or L-section & continued until the whole length is covered.

For longitudinal section R.L of ground is usually taken by leveling instrument at every 30 m apart along the center line of the road.

When the ground is fairly even, the levels may be taken at 40 to 50 m apart or even up to 100 m apart.

In uneven ground or hilly areas the R.L of ground may be taken at 20 m or more or less depending on the nature of the ground.

Road Estimating (Earthwork)

Estimate of road is prepared kilometer wise.

It is better if the distance apart of L-section is such that it is multiple to make the kilometer.

Longitudinal section is usually plotted with a horizontal scale of 1 cm = 10 m to 1 cm = 30 m.

Vertical scale of 1 cm = 1 m to 1 cm = 5 m.

Method 1: Mid-Sectional Area Method

The quantity of earthwork maybe calculated by the various methods of mensuration, out of which 3 are discussed here:

Method 1: Mid-Sectional Area Method

Quantity = Area of Mid-Section * Length.

Let d1 and d2 be the height of bank at two ends portion of embankment, L the length of the section, B the formation width and S:1 (H:V) the side slope, then;

Area of mid-section = Area of rectangular portion + Area of 2 triangular portions

=Bdm+1/2sdm2+1/2sdm2 = Bdm + sdm2

Quantity of earthwork = (Bdm + sdm2) * L

The quantity of earthwork may be calculated as;

Method 1: Mid-Sectional Area Method

Area of Side Sloping Surface:

The area of sides which may require turfing or pitching, may be found by multiplying the mean sloping breadth by the length.

The mean sloping breadth = sqrt (sd2+d2) = sqrt (52+1), where d = Mean ‘d’

Area of both side slopes = 2*L*d sqrt(s2+1)

In tabulated form;

Method 2: Mean-Sectional Area Method

Quantity = Mean Sectional Area * Length

Sectional area at one end A1 = Bd1+sd12

Sectional area at the other end A2 = Bd2 + sd2

  d1 and d2 are the heights or depth at the two ends.

The mean sectional area A = (A1+A2)/2

Quantity (Q) = Mean Sectional Area * Length

In tabulated form;

Method 3: Prismodial Formula Method

Quantity = L/6 (A1+A2+4Am)

Where A1 & A2 are the cross-sectional areas at the two ends of a portion of embankment of the road of length L, & Am is the mid-sectional area.

  Let, d1 & d2 be the heights of banks at the 2 ends, and dm be the mean height at the mid-section, B be the formation width & S:1 be the side slope.

Cross-sectional area at one end A1 = Bd1+sd12

Cross-sectional area at the other end A2 = Bd2 + sd2

Cross-sectional area at the Middle 

dm = (d1+d2)/2

Am = (Bd2 + sd2)

Quantity = L/6 (A1+A2+4Am) = [B*(d1+d2)/2+s((d12+d22+2d1d2)/3)]*L

Quantity (Q) = Sec. Area of central portion + Sec. area of side slope portions] * Length


Earthwork calculated by the Prismodial Formula (Method 3) is more accurate than calculated by the Method#1 & Method#2 but they will differ by less than 1%.

As the earthwork is a cheap item, Method 1 or Method # 2 is generally used as it is simple & entails less labour, but where rates are high & greater accuracy is required, Prismodial Formula may be used.

It may be noted that all the 3 Methods can be used for embankment as well as for cutting.

Cross-sectional figures for banking if inverted give cross-sections for cutting.

To distinguish cutting and banking, the cutting is indicated by – sign. (minus sign)


Reduced Level (R.L) of ground along the center line of a proposed road from chainage 10 to chainage 20 are given below. The formation level at the 10th chainage is 107 and the road is in downward gradient of 1 in 150 up to the chainage 14 and then the gradient changes to 1 in 100 downward. Formation width of road is 10 m and side slope of banking are 2:1 (H:V). Length of the chain is 30 m.

1.Draw longitudinal section of the road and a typical cross-section and prepare an estimate of earthwork at the rate of Rs. 275% m3.

2.Also find the area of the side slopes and the cost of turfing the side slopes at the rate of Rs. 60 % m2.


Surface Drains

These are open drains provided for conveying water from kitchens, bathrooms, and rain water to main sewers.

These are usually provided at sides of the road and along the boundary line of building.

The drains should not be laid under the buildings.

For efficient draining the surface drains should have certain qualities, such as should be laid in such a gradient to develop self-cleaning velocity, should be reasonably free board at the top, joint should be smooth finished, easy curves, inner surface should be smooth, cheap in construction & maintenance.

There are various types of surface drains as U-Shaped, V-Shaped, etc.

Surface Drains (Example)

Prepare an estimate of a surface drain for 10-meter length from the drawing given below.

Surface Drains (Example)

Surface Drains (Example)

[su_divider top=”yes” text=”Go to the top” style=”default” divider_color=”#FD8B00″ link_color=”#FD8B00″ size=”4″ margin=”15″]

Share this: