In such cases tunnel boring using TBMs is not preferred as the TBM itself causes high vibrations. You could use the jacked box method or the sequential excavation method (also called the new Austrian technique) as these two cause no vibrations. However please note that the sequential excavation method is not suitable within ground waters or weak soils.
The pile foundation is generally going deep into the ground and its stability may not be disturbed if New Austrian Tunneling Method (NATM) is adopted.However, this method is generally applicable in the soil strata. In case of rock, it may not work properly.