Solved: The amount of pressure required to sink a large, heavy object in a soft

Chapter 10, Problem 10

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The amount of pressure required to sink a large, heavy object in a soft homogeneous soil that lies above a hard base soil can be predicted by the amount of pressure required to sink smaller objects in the same soil. Specifically, the amount of pressure p required to sink a circular plate ofradius r a distance d in the soft soil, where the hard base soil lies a distance D > d below the surface, can be approximated by an equation ofthe form p = kie^ + k3r, where ki, 2, and 3 are constants, with kj > 0, depending on d and the consistency of the soil but not on the radius ofthe plate. (See [Bek], pp. 89-94.) a. Find the values ofAq, k2, and Aq if we assume that a plate ofradius 1 in. requires a pressure of 10 lb/in.2 to sink 1 ftin a muddy field, a plate ofradius 2 in. requires a pressure of 12 lb/in.2 to sink I ft, and a plate of radius 3 in. requires a pressure of 15 lb/in.2 to sink this distance (assuming that the mud is more than 1 ft deep). b. Use your calculations from part (a) to predict the minimal size of circular plate that would be required to sustain a load of 500 lb on this field with sinkage of less than 1 ft.