The bulldozer shown in the Figure below is fitted with a blade, 1.1 m high and 5

Question

The bulldozer shown in the Figure below is fitted with a blade, 1.1 m high and 5 m wide. What weight must the bulldozer be such that it can push the sand forward (to the right, as shown) without the tracks slipping on the underlying sand (with a Factor of Safety of 1.3)? Assumptions: The friction angle (delta) between the bulldozer tracks and the sand is equal to 0.6 times phi. The "side friction" (front and back sides between the block of sand that is being moved, and the sand on either side of the blade that stays behind) can be ignored. Do this calculation for the following two cases: (i). The sand is dry, with a dry unit weight gamma_d = 17 kN/m^3, and friction angle phi = 35 degree. (642.7 kN = 65.5 ton) (ii). The sand to the right of the vertical dashed line is saturated, with a saturated unit weight gamma_sat = 20 kN/m^3 and friction angle phi = 359. (480.5 kN = 49.0 ton)

Explanation / Answer

According to Rankines Theory

For the bullodzer to be able to push the sand forward, the weight of the bullodzer must be greater than the pressure acting on the bulldozer due to soil.

The pressure acting on the soil can be computed using the relation.

The bulldozer blade acts as a gravity retaining wall, which will retain the soil usingit's self weight.

The applicable check in this case would be check for overturning.

FOS = MR/MO

where FOS = 1.3

MR = Resisting Moment

MO = Overturning Moment

MO = Pa = 0.5*ka x y x h*h*h/3

where ka = 1-sin(phi)/1+sin(phi)

phi = angle of internal friction

y = density of soil (kn/m3)

h = height (m)

Pa = pressure acting per unit area

The values given are

phi = 35 degrees

h = 1.1m

MR = W*h/3

Putting values in equation

Case B1

1.3*W*1.1/3 = 0.5 * 0.63 * 17*1.1*1.1*1.1/3

Solving we get W = 642kN

Case B2

Density, y' = (20-10)kN/3

Water Density,Yw = 10kN/m3

Using the same relation, we get equation as

1.3*W*1.1/3 = 0.5 * 0.63 * (20-10)*1.1*1.1*1.1/3

We get the value as W = 480kN

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