Accurate modeling of the time-dependent behavior of geomaterials is of great importance in a number of engineering structures interacting with soft, highly compressible clay layers or with organic clays and peats. In this work, a uniaxial constitutive model, based on Perzyna's overstress theory and directly extendible to multiaxial stress conditions, is formulated and validated. The proposed constitutive approach essentially has three innovative aspects. The first concerns the implementation of two viscoplastic mechanisms within Perzyna's theory in order to distinguish between short-term (quasi-instantaneous) and long-term plastic responses. Similarly, elastic response is simulated by combining an instantaneous and a long-term viscous deformation mechanism. The second innovative aspect concerns the use of a bespoke logarithmic law for viscous effects, which has never been used before to simulate delayed soil behavior (as far as the authors are aware). The third concerns the model's extensive validation by simulating a number of different laboratory test results, including conventional and unconventional oedometer tests with small and large load increments/decrements and wide and narrow loading/unloading cycles, constant rates of stress and strain tests, and oedometer tests performed in a Rowe consolidation cell with measurement of pore pressure dissipation.