The project is design & build there was discrepancy between the actual status & geotechnical report, shall the contractor claim or do it on his cost?

it depends on who executes the site investigation campagin and if it is under the contractor laibility ! 

if it is not under the contractor laibility, then he shall claim.

the Contractor shall claim

The contractor shall do it on his cost, because the geotechnical report shows the characteristic of soils and rocks of the construction´s site before the construction work. The Geotechnical report is the fundamental data for the foundations design, if there was discrepancy is for change on the design work or construction work.

The contractor can't make claim for the additional cost incurred in the process of reworking the foundation design because its a design and build project. The contractor should have engaged a  competent geotechnical specialist to ensure a detailed and accurate geotechnical investigation was carried out.