I am analysing a 6-pile group under lateral loading and would like to include the contribution due to the base interface friction resistance of the cap (if we exclude any contribution from the cap base interface friction, the calculated pile group deflection is about 35mm under a lateral load of 11000kN). Since the bottom of the cap was cast in place on a sandy surface (with a friction angle of 30deg), as a first approximation, I have estimated the resistance contributed by base friction (Fb) as W*tan(delta), where W is the weight of the cap and delta is the friction angle between the concrete and the soil. The reinforced concrete cap is 12m (length), 8.4m (width), 2.1m (height). If delta is taken as 25deg, this would give a maximum frictional force (Fb) of about 2400kN.
I would like to get some comments or input on how to calculate the load-displacement curve associated with the development of interface friction on the sandy surface and, in particular, the amount of lateral movement needed to fully develop the maximum frictional force of 2400kN.
An important aspect, which you need to consider is future settlements below the cap. If the sand is loose, future settlements (e.g. from vibrations) may reduce the contact stress. If the sand is dense, you could probably use the adhesion factor similar to that used for shaft friction of concretet piles.
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