In this paper, we propose and discuss the applicability of the compressive sensing (CS) for the measurement and analysis of the ground-borne vibrations induced by pile driving. With this motivation, we consider two types of the most common pile driving techniques; i) impact pile driving and ii) vibratory pile driving. We show that ground-borne vibration parameters like longitudinal velocity (LV), transverse velocity (TV), vertical velocity (VV), force and inertia can be efficiently sensed by the CS for both of the two driving types mentioned above, since majority of these parameter's time series are sparse either in time or frequency domain. We show that time series of these parameters can be reconstructed using a far fewer number of samples than the classical Shannon's theorem states. Thus, when the CS technique is utilized, measurement times and hardware storage requirements of vibration sensing systems can be significantly reduced. Additionally, when the CS is used, such parameters can be exactly reconstructed even in the presence of missing data. CS based proposed in this paper can also be extended to measure and analyze other types of vibration data in soil dynamics and more generally to other vibration types encountered in engineering.