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The massive machine-type communication has been one of the most representative services for future wireless networks. It aims to support massive connectivity of user equipments (UEs) which sporadically transmit packets with small size. In this work, we assume the number of UEs grows linearly and unboundedly with blocklength and each UE has an individual codebook. Among all UEs, an unknown subset of UEs are active and transmit a fixed number of data bits to a base station over a shared-spectrum radio link. Under these settings, we derive the achievability and converse bounds on the minimum energy-per-bit for reliable random access over quasi-static fading channels with and without channel state information (CSI) at the receiver. These bounds provide energy-efficiency guidance for new schemes suited for massive random access. Simulation results indicate that the orthogonalization scheme TDMA is energy-inefficient for large values of UE density $μ$. Besides, the multi-user interference can be perfectly cancelled when $μ$ is below a critical threshold. In the case of no-CSI, the energy-per-bit for random access is only a bit more than that with the knowledge UE activity.