This paper introduces a novel high-cycle accumulation model for sand, referred to as the NHCA model. While many empirical formulas for deformation accumulation rates (such as stress or density dependence) remain consistent with the HCA model proposed in 2005 (referred to as the OHCA), the NHCA model brings essential novelty through the definition of strain amplitude and the cycle counting method. The definition of strain amplitude is rooted in kinematic hardening principles, commonly found in multi-surface plasticity models. Notably, for polychromatic cycles (comprising oscillations with different frequencies), the amplitude lacked clear definition within the OHCA framework. This paper specifically explores the ovality and polarization of strain loops, as well as stochastic and polychromatic multiaxial cycles, as key points of interest. Additionally, experimental results and model calibration procedures are presented to support the NHCA model.