A cylindrical specimen of dry sand with a minimum and maximum void ratio (emin and emax) of 0.5 and 0.8 respectively has a relative density of 45%. If the specimen is compacted such that the relative density is 60%, what will be the decrease in height of the sample if the initial height was 15cm? Assume that the specimen diameter remains constant such that any volume change occurs only as a change in height.

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Calculation of Settlement

The vertical displacement of the structural foundation due to the loading from the superstructure is known as settlement. It is due to the reduction of air voids present in the soil. The amount of vertical displacement depends on the bearing capacity of the soil on which the foundation is laid. The effect of the settlement depends on the magnitude of settlement, uniformity, and the structural design of the structure. The maximum allowable settlement for residential and office buildings should be less than 18 mm, for industrial buildings, it is 38 mm and for commercial buildings, it is 25 mm.