Propagation of a coherent light beam through a random medium generates speckle patterns, in which some information of media and object is hidden. Speckles produced by particles smaller than wavelength are studied thoroughly, yet it is also essential to investigate speckles produced by larger particles. In this paper, the spatial intensity correlations of transmitted speckle patterns generated by large particles are studied theoretically and experimentally. A semi-empirical expression of spatial intensity correlation function of speckle patterns is derived based on Bethe-Salpeter equation, taking particle size and concentration into account. After performing experiments with various particle sizes and concentrations, we fit the theoretical expression to experimental results and determine the introduced parameters. We analyze the variation of spatial intensity correlation function with particle size and concentration. Theoretical analyses and experimental results given in this paper have potential applications in coherent imaging through random and disordered media.