I'm new here and have read thru the posts on elastomeric bearing pads. What methods are used to fasten the bearing pad to a concrete bridge seat? Also, would it be appropriate to partially restrain the sides of the elastomeric pad to influence the shape factor S ?

An adhesion product appropriate for bonding to concrete is all that is specified in some cases.  This is the case for abutments and piers where the ends of the girders are cast in concrete diaphragms.  In open applications, the elastormeric pad is bonded with the same product but the overall bearing assembly is prohibited from moving in certain directions by use of sole plates and anchor bolts.

As for enhancing the shape factor, some bearing configuations probably do take this into account.  For example on multi-rotational bearings where the upper assembly sits in a lower assembly on a elastomer unit the unit is usually contained within some type of ring that prevents translation of the upper assembly and confines the lower elastomer unit as well.

It is broadly recommended that you do not attempt to bond bearing pads in place.
The technique can be difficult due to the use of anti ozonants in the rubberr compound, and if the ' adhesive ' fails, the co-efficient of friction reduces and thus the bearing can more easily slip out.
If you restrain by confining part of the rubber thickness, then the permitted shear deformation is reduced.
An exact answer would be governed by the overall thickness of the ' bearing ' pad you nominate.
So far as the other answer is concerned, a POT BEARING requires totally different ' restraiint ' compared to a bearing pad.

The shape factor is best effected by adding or removing shims. In this way you can better modify stiffness. External restraint to limit bulge is not the best approach. I would expect cutting action on the rubber surface which would probably be detrimental to bearing operation and life.

In Virginia, the DOT construction specifications require a gritty material to be bonded to the mating surfaces to increase the friction force between the pad and the structure.  I would expect this technique to be used in other states as well.

I would be surprised if the coefficient of friction between a pad and a mating surface of concrete or steel were less than 0.5.  I would expect it to be close to 1 when the grit is applied.

Incidently, check your anchor bolts carefully when you use elastomeric bearings.