The multiphysiochemical transport in electroosmosis of dilute electrolyte solutions (<1mM) through microporous media with granular random structures has been modeled in this work by our numerical framework consisting of three steps. First, the three-dimensional microstructures of porous media are reproduced by a random generation-growth method. Then the effects of chemical adsorption and electrical dissociation at the solid-liquid interfaces are considered to determine the electrical boundary conditions, which vary with the ionic concentration, the pH, and the temperature. Finally the nonlinear governing equations for the electrokinetic transport are solved by a highly efficient lattice Poisson-Boltzmann algorithm. The simulation results indicate that the electroosmotic permeability through the granular microporous media increases monotonically with the porosity, the ionic concentration, the pH and the environmental temperature. When the surface electric potential is higher than 50 mV, the permeability increases with the electric potential exponentially. The electroosmotic permeability increases with the pH exponentially, but with the temperature linearly. The present modeling results may improve our understanding of hydrodynamic and electrokinetic transport in geophysical systems, and help guide the design of porous electrodes in micro energy systems.