Quantity Calculation models Copyright 2006 Nicolai Green Hansen

Quantity Calculation models Copyright 2006 © Nicolai Green Hansen

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

Quantity Calculation The quantities are used in the project design for: • To create balance between removed and build-in quantities • 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) Copyright 2006 © Nicolai Green Hansen

Quantity Calculation The quantities are used in the project design for: • Planning of the price calculation, including mashine calculation (size and working capacity) • 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 skal Copyright 2006 © Nicolai Green Hansen

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

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

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

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

Quantity Calculation The ramp formula There is some confusion when a gradient of a slope is stated. 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” Copyright 2006 © Nicolai Green Hansen

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

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

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

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

Quantity Calculation The square grid method 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 Copyright 2006 © Nicolai Green Hansen

Quantity Calculation The square grid method 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 Copyright 2006 © Nicolai Green Hansen

Quantity Calculation The square grid method Ill. with figure: V = 52 x((2, 5+1, 8+1, 0+1, 4)/4) V = 42 m 3 Copyright 2006 © Nicolai Green Hansen

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