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136tamper head. On the other hand, the groups of aggregate piers also featured construction of asingle aggregate pier, however compaction of which was completed via cone tamper head.Therefore, neglecting the effect of small deviations in properties of matrix soil betweendifferent test beds, and having the same pier construction methods to be utilized, the obtainedstiffness results for aggregate piers compacted via cone and truncated cone tampers werecompared in Table 35.Table 35: Comparison measurements for single aggregate piers at different testingstages compacted via cone and truncated cone beveled headsStg.#Test StagePier typeLength(mm)σ at δ top = 2mm (kPa)σ at δ top = 5mm (kPa)σ at δ top = 10mm (kPa)12Various BeveledHead TestsVarious Pier MixTests3 Group TestsAggregate Pier –Truncated ConeAggregate Pier -ConeAggregate Pier –Truncated ConeAggregate Pier -ConeStiffness ratio for truncated vs. cone betweenaggregate piers at stages 2 and 3Legend:k - stiffness modulus (kPa/mm)δ top - deflection at the top of the pier (mm)δ tell-tale - deflection at the bottom of the pier (mm)σ – stiffness of the pier (kPa)305 299 N/A N/A610 548 N/A N/A305 375 N/A N/A610 590 N/A N/A305 443 774 1,044610 494 789 1,028305 908 1,418 1,806610 1,083 1,841 2,065305 51 45 42610 54 57 50Conversions:1 m = 3.3 ft1 mm = 0.0394 in1 kPa = 0.145 psi1 kg/m 3 = 0.0624 pcfThe obtained results for the aggregate pier stiffness parameters for the cone and truncatedcone constructed piers at stages two and three respectively were further analyzed wherecomparison between stiffness results was expressed through percent difference calculation:Equation 20: Stiffness ratio for cone and truncated cone compacted aggregate piersstiffness ratio = σ truncated cone / σ cone (Equation 20)