The state, county, or city authority having responsibility for the reconstruction or improvement of any public highway may, subject to prescribed conditions and limitations, authorize vehicles employed in such highway reconstruction or improvement to exceed the gross weight limitations contained in RCW 46.44.041 and 46.44.042 without a special permit or additional fees as prescribed by chapter 46.44 RCW, but only while operating within the boundaries of project limits as defined in the public works contract or plans.