As suggested by Lars Forssblad (1981), the three main actions of compaction are static pressure, impact force and vibration. Different compactors contain one or more modes of these actions. For example, vibratory tampers perform mainly by the principle of impact while vibratory rollers work with principle of static pressure and vibration.

For sandy soils, vibration is adequate for normal compaction because the action of

vibration sets the soil particles in motion and friction forces between soil particles are virtually demolished. During this vibration motion, the soil particles rearrange themselves to develop a dense state.

For normal soils, it is necessary to combine the action of vibration together with static pressure to breakdown the cohesion forces between soil particles in order to allow for better compaction. The static pressure of vibratory machines is adopted to exert a shearing force to eliminate the cohesion in clayey soils

In sandy soil, vibration is enough for compaction because sandy soil has no structure or weak structure. On the other hand, clayey soils are well structured and need to break these structures for compaction. Wetting and puddling of clayey soil and then drying make the soil compact.

Both the answers above are enough to understand the compaction process of cay vs sandy soil.

Good discussion. In addition to that,  I would like to add that the degree of compaction depends upon the nature of clay minerals, type of exchangeable cations, amount of energy applied, water content and extent of manipulation of the soil. Dry soils cannot be compacted to high densities due to in-compressible nature of soil particles and high internal friction. An increase in moisture content decreases cohesion between the particles and internal friction, and facilitates compaction.With increase in soil moisture, compaction increases to maximum and then decreases with further increase in soil water. A compacted layer is commonly found just below the usually tilled layer of soil. Compaction of coarse-textured soils is sometimes desirable for better seed germination and efficient utilization of water and nutrients.

Thanks all 

Basically, compaction is a resultant effect of both magnitude of externally applied mechanical load and internal resistance of soil particles to deformation. Compaction can therefore be perceived as "settlement or consolidation". Once the pore water pressure (pw) will have dissipated as a function of time (t) during load application, the effective stress (sigma s) in the soil will gradually increase with subsequent change (reduction) in volume. The soil becomes compacted. Sand and clay soils naturally react differently to external loads. Because sand soils have low or hardly any pore water pressure, disspitation and hence effective stress (sigma s) is zero or very low and so compaction is correspondingly low. On the contrary in a clayey soil and by similar applied external load, dissipation will be gradual (note: porosity) and with equally increasing effective stress. The clayey soil then settles or consolidates, compaction is said to have occured.. The rate of (un)consolidation is a function of pore water pressure dissipation UU, DC=f(pw) can either be undrained or drained, we speak of UU or DC respectively.

thanks David