The high-cycle accumulation (HCA) model proposed by Niemunis et al. (2005) predicts permanent deformations in non-cohesive soils due to many cycles (N>10³) with relatively small amplitudes (ε^ampl<10^-3, so-called high- or polycyclic loading). This paper demonstrates the applicability of the HCA model to different sands. For this purpose, approximately 200 triaxial tests with 10⁵ cycles each have been performed on eight different quartz sands with mean grain sizes in the range of 0.15 mm≤d₅₀≤4.4 mm and coefficients of uniformity in the range of 1.3≤U_c≤4.5. For each sand, test series with a variation of stress amplitude, initial relative density, average mean pressure p^av and average stress ratio η^av=q^av/p^av have been conducted. The influence of the grain size distribution curve on the rate of strain accumulation is discussed. A comparison of the measured data with predictions made by the HCA model (with different material constants) is given. Correlations of the material constants with index or granulometric properties are discussed. The correlations may be useful for a simplified procedure to determine a set of material constants.