Soil Mechanics and Foundation
A tri-axial shear test is preferred to direct shear test, because

Precise measurement of pore pressure and change in volume during test, is not possible
It can be performed under all three drainage conditions with complete control
None of these
Stress distribution on the failure plane, is non uniform

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Soil Mechanics and Foundation
Coefficient of compressibility is

constant for any type of soil
different for different types of soils but same for a soil under different states of consolidation
independent of type of soil but depends on the stress history of soil
different for different types of soils and also different for a soil under different states of consolidation

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