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UAVs are capable of improving the performance of next generation wireless systems. Specifically, UAVs can be exploited as aerial base-stations (UAV-BS) for supporting legitimate ground users in remote uncovered areas or in environments temporarily requiring high capacity. However, their communication performance is prone to both channel estimation errors and potential eavesdropping. Hence, we investigate the effective secrecy throughput of the UAV-aided uplink, in which rate-splitting multiple access (RSMA) is employed by each legitimate user for secure transmission under the scenario of massive access. To maximize the effective network secrecy throughput in the uplink, the transmission rate vs. power allocation relationship is formulated as a max-min optimization problem, relying on realistic imperfect CSI of both the legitimate users and of the potential eavesdroppers (Eves). We then propose a novel transformation of the associated probabilistic constraints for decoupling the variables, so that our design problem can be solved by alternatively activating the related block coordinate decent programming. In the model considered, each user transmits a superposition of two messages to a UAV-BS, each having different transmit power and the UAV-BS uses a SIC technique to decode the received messages. Given the non-convexity of the problem, it is decoupled into a pair of sub-problems. In particular, we derive a closed form expression for the optimal rate-splitting fraction of each user. Then, given the optimal rate-splitting fraction of each user, the ε-constrainted transmit power of each user is calculated by harnessing SPCA programming.