The document discusses excavation processes and calculations. It provides the formula to calculate the area of a trapezoid as Area = 1/2 * h * (a + b), where h is the height and a and b are the parallel sides. It then applies this formula to calculate the volume of materials excavated from trenches with sloping sides, which take on a trapezoidal shape. Converting the dimensions from mm to m, the formula can also be used to find the volume and weight of brickwork in walls.

1. Aims : After this session is over you will be able to: Apply analytical methods to the management and production of construction, civil engineering or building services installation processes and operations Objectives: To be able to Determine amounts of materials removed from excavations and the amounts of equipment required Compare the effectiveness and efficiency of solutions to construction situations .

2. Why is excavation important ? The first considerations when excavating must be ….

3. First - Excavation Hazards… The greatest risk… Cave-ins Other hazards include:.. Asphyxiation due to lack of… oxygen Inhalation of… toxic materials Moving machinery can cause… a collapse Accidental severing of… utility lines Fire

4. Injury and Death Excavating is one of the most hazardous construction operations Most accidents occur in trenches 5-15 feet deep There is usually no warning before a cave-in

5. Definitions Excavation – a man-made cut, cavity, trench, or depression formed by earth removal. Trench – a narrow excavation. The depth is greater than the width, but not wider than 15 feet. Shield - a structure able to withstand a cave-in and protect employees Shoring - a structure that supports the sides of an excavation and protects against cave-ins Sloping - a technique that employs a specific angle of incline on the sides of the excavation. The angle varies based on assessment of impacting site factors.

6. Summary The greatest risk in an excavation is a cave-in. Employees can be protected through sloping, shielding, and shoring the excavation. A competent person is responsible to inspect the excavation. Other excavation hazards include water accumulation, oxygen deficiency, toxic fumes, falls, and mobile equipment.

7. Steps to be followed during substructure construction Step 1 - Green field site This is the starting point for the excavation, the first stage is to remove the topsoil and state whether it is being kept or removed from site. The topsoil is excavated in isolation, as it is valuable. Where shall we dump the topsoil ?

8. Step 2 - Removal of top soil Topsoil is measured per metre squared as the depth to be excavated is given in the item description in the Bill of Quantities.

9. Step 3 Trench excavation This is the first use for the centre line measurement, which is multiplied by the breadth and depth of the trench to give the volume of material to be excavated

10. Step 4 Earthwork Support Support to the sides of the excavation is required to prevent collapse . Note that two depths are required, one for the outer side of the trench and one for the inner side of the trench.

11. Step 5 Concrete Foundations The centre line is again used in this item. The quantity of concrete required is measured by volume and Centre Line x Breadth x Depth is calculated

12. Step 6 Brickwork walling Brickwork walling in substructure billing is measured to the DPC level. The centre line is used but will need adjustment if the wall thickness changes between inner and outer leafs i.e. half brick and one brick thick.

13. Step 7 Backfill to trench Backfill is measured in two stages; the first is the quantity at either side of the brick walling by subtracting from the excavated material quantity the material for concrete foundations and brickwork. The second is at the outer leaf top soil level, a new centre line can be calculated for the backfill at this area.

14. For any excavation with sloping sides is there an easy way to calculate the perhaps thousands of tonnes of materials which needs to be removed … Trenches with sloping sides are trapezoidal in shape… Then we need to calculate the area of a trapezium… Lets see how we calculate the area of a …

15. The Area Of A Tra p ezium. A Trapezium is any closed shape which has two sides that are parallel and two sides that are not parallel.

16. The formula to calculate the area of a trapezium like the red one shown, is in the yellow box below it.Write the formula down : Area = ½ h ( a + b ) Get a pen and paper and lets try a few… a b h

17. What Goes In The Box ? To find the area of the shapes below Use the formula : 165cm 2 19.85m 2 (to 2 d.p) Area = ½ h ( a + b ) (1) 20cm 13cm 10cm 2.7m 5.4m 4.9m (2)

18. Example 1 Calculate the area of the trapezium below : Solution ( Using the formula). Area = ½ h ( a + b ) a = 16 b =11 h = 13 Area = ½ x 13 x ( 16 + 11 ) Area = ½ x 13 x 27 Area = 175.5cm 2 16cm 11cm 13cm

19. Now for the practical use of the Trapezium formula Now Use the trapezium formula to calculate the volume of the material excavated on the following page. Note something happens to the material when it is excavated…This can have an impact on the cost of transporting it. OK lets go,analyse the text on the next page and set your work out methodically….

22. Tutors note 1

23. clue-State Clue change Tutors note 3

24. Tutors note 4

25. Now for another practical use of the Trapezium formula Now Use the trapezium formula to calculate the volume of the wall on the following page. Then calculate the weight of the brickwork. Hint:- The dimensions shown are in mm…first divide all dimensions by 1000 to get your units in metres.