Looking first for Vertical
Displacement under the centre of the applied loading (Δ) and then
solving for the modulus of elasticity (E), with certain
assumptions:
Δ = 2 (p )(a) (1
μ2) / E
Where p = contact
pressure, a = the radius of applied circle of loading, E = the modulus of elasticity and μ = Poissons
ratio. Assuming Poissons ratio is 0.5, then:
Δ = 1.5 (p )(a )
/ E
For a rigid plate (i.e. Clegg Hammer) rather than a flexible
plate then:
Δ = 1.18 (p ) (a
) / E
Calculating p from force
(Clegg Hammer Mass x Acceleration due to gravity) and the acceleration (deceleration,
Gm, i.e. value as measured by the Clegg Hammer times 10), where the Clegg Hammer radius
(in metres) and drop-height (in metres)
factor into it, and applying an additional factor of 0.6
for converting square wave used in maths to ½ sin wave type shape as observed
on actual impacts on compacted soils using a CRO and solving
now for E (in Pascals), this becomes:
E = (1.18)
(9.81) (0.6) (Gm ) (Gm) (Hammer Mass ) / π (Hammer
Radius) (Drop-Height)