1. Quantity Calculation Calculation models Copyright 2006 © Nicolai Green Hansen

2. Quantity Calculation The quantity or the soil calculation is a statement of the soil masses that should be: Digged up Digged up Moved Moved Removed Removed Built-in Built-in Copyright 2006 © Nicolai Green Hansen

3. Quantity Calculation The quantities are used in the project design for: To create balance between removed and build-in quantities To create balance between removed and build-in quantities The basis for the tender for the relation between owner and contractor The basis for the tender for the relation between owner and contractor Regulation of the tender price (in case the real quantities are different in relation to the invitation for bids) Regulation of the tender price (in case the real quantities are different in relation to the invitation for bids) Copyright 2006 © Nicolai Green Hansen

4. Quantity Calculation The quantities are used in the project design for: Planning of the price calculation, including mashine calculation (size and working capacity) Planning of the price calculation, including mashine calculation (size and working capacity) Ressource controlling. The right ressources at the right times Ressource controlling. The right ressources at the right times During the working process to control that the Under arbejdets udførelse at kontrollere at der omsættes de mængder der skal During the working process to control that the Under arbejdets udførelse at kontrollere at der omsættes de mængder der skal Copyright 2006 © Nicolai Green Hansen

5. Quantity Calculation The quantities are used in the project design for: Calculation basis between contractor and the contract worker teams Calculation basis between contractor and the contract worker teams Bill demands for down payment from owner to contractor Bill demands for down payment from owner to contractor Copyright 2006 © Nicolai Green Hansen

6. Quantity Calculation Following mathematicals methods are shown: The prism method The prism method The ramp formula The ramp formula The square grid method The square grid method Copyright 2006 © Nicolai Green Hansen Truncated pyramid Truncated pyramid

7. Quantity Calculation The prism method Copyright 2006 © Nicolai Green Hansen Section in excavation area New road in terrain If equivalent sections with distance ”a” is inserted the total volume are:

8. Quantity Calculation The prism method ”F” means the surface area Ill. with figure: a= 5m F 1 =10 m 2 F 2 =12 m 2 F 3 =16 m 2 F 4 =14 m 2 F 5 =9 m 2 Ill. with figure: V = (10/2+12+16+14+9/2)x5 V = 258 m 3 Copyright 2006 © Nicolai Green Hansen

9. Quantity Calculation The ramp formula There is some confusion when a gradient of a slope is stated. Copyright 2006 © Nicolai Green Hansen An easy mnemonic rule is to think in fractions. 1:2 means therefore ”1 above 2” or converted 0,5. ”everything belowe 1 is not steep”

10. Quantity Calculation The ramp formula Is used among other things for determination of soil quantities in relation to up- and down ramps in building excavations. Copyright 2006 © Nicolai Green Hansen

11. Quantity Calculation Ramp formula Ill. with figure: m = 2 (the gradient of the ramp) n = 1 (the gradient of the slope of the platform) n 1 = 1 (the gradient of the slope of the ramp) a = 3 m (the width of the ramp) h = 4 m (the hight of the platform) Copyright 2006 © Nicolai Green Hansen

12. Quantity Calculation Ramp formula Ill. with figure: Copyright 2006 © Nicolai Green Hansen V = 35 m 3

13. Quantity Calculation The square grid method Copyright 2006 © Nicolai Green Hansen Should a bigger area be reprofiled the known square grid method from the plane topographical levelling is used. Originally terrain New terrain

14. Quantity Calculation The square grid method Copyright 2006 © Nicolai Green Hansen Princip: A square grid with the side lenght of ”a” is inserted. In the corner points the high difference between the originally terrain and the new terrain are readed. h is calculated negative for back filling and positive for excavation soil. Originally terrain New terrain

15. Quantity Calculation The square grid method Copyright 2006 © Nicolai Green Hansen The volume of the soil for each grid can then be determinated by: Ill. with figure: a = 5 m (sidelængden på nettet) h 1 = 2,5 m h 2 = 1,8 m h 3 = 1,0 m h 4 = 1,4 m

16. Quantity Calculation The square grid method Copyright 2006 © Nicolai Green Hansen Ill. with figure: V = 5 2 x((2,5+1,8+1,0+1,4)/4) V = 42 m 3

17. Quantity Calculation Truncated pyramid Copyright 2006 © Nicolai Green Hansen Ill. with figure: Depth of excavation: h = 3 m Top area G = 200 m 2 Bottom area g = 100 m 2