Haversian remodeling is known to result in improved resistance to compressive fracture in healthy cortical bone. Here, we examine the individual roles of the mean porosity, structure of the network of pores and remodeled bone matrix properties in the fracture behavior of Haversian bone. The detailed structure of porosity network is obtained both pre- and post-testing of dry cubical bone samples using micro-Computed Tomography. Based on the periodicity in the features of porosity along tangential direction, we develop a two dimensional porosity-based random spring network model for Haversian bone. The model is shown to capture well the macroscopic response and reproduce the avalanche statistics similar to recently reported experiments on porcine bone. The predictions suggest that at the millimeter scale, the remodeled bone matrix of Haversian bone is less stiff but tougher than that of plexiform/primary bone.