The invention relates to a phased rubber composition and tire tread thereof intended for heavy duty service such as for example a truck tire. The phased rubber composition is comprised of the product of blending a first rubber phase comprised of cis 1,4-polybutadiene rubber and reinforcing filler comprised of rubber reinforcing carbon black and a second rubber phase comprised of natural cis 1,4-polyisoprene rubber and reinforcing filler comprised of precipitated silica.