Logical phi-bits, classical analogs of qubits, are nonlinear modes arising in externally driven coupled finite-length acoustic waveguides. Logical phi-bits exhibit geometric phases that, by tuning the driving conditions, can be exploited to realize quantum-like operations in classical acoustic systems. In this work, we model the dynamics of phi-bits using a nonlinear three-chain mass-spring system to investigate the possible origins of the behavior of the phi-bit geometric phase observed in physical experiments. The model accounts for nonlinearity, dissipation, and boundary constraints. We examine how driving frequencies and nonlinear spring interactions shape phi-bit behaviors. Nonlinearities up to the fifth order significantly influence the geometric phase, with higher-order terms revealing interdependencies that expand the range of observable phenomena. Dissipation results in phi-bits states with complex amplitudes and may play a critical role in determining the behavior of the geometric phase. Finally, the effect of boundary conditions at the ends of the finite waveguides is also reported. This work contributes to the broader understanding of the complex behavior of the phi-bit geometric phase and more generally of acoustic analogues of quantum systems.