The analytical expression for the effective radius of curvature R of partially coherent Hermite-Gaussian (H-G) array beams propagating through atmospheric turbulence is derived, which is general and can be reduced to several typical cases. It is shown that turbulence results in a decrease of R. For the superposition of the intensity R is less sensitive to turbulence than that for the superposition of the cross-spectral density function. In free space, R of Gaussian Schell-model array beams and Gaussian array beams is larger than that of partially coherent H-G array beams, but it is more affected by turbulence. In free space, R of a single partially coherent H-G beam is smaller than that of the partially coherent H-G array beam, but it is less affected by turbulence. For the superposition of the intensity, the R of fully coherent H-G array beams is larger than that of partially coherent H-G array beams, but it is more affected by turbulence. In general, R is more sensitive to turbulence, if R is larger in free space. Therefore, the R of laser beams with larger R in free space will become smaller than the R of those with smaller R in free space after a certain propagation distance in turbulence.