To provide a construction method capable of surely forming an ice plug inside piping, applicable to large-diameter piping, and capable of converting the residual tensile stress applied to a part near a tip of a crack to the residual compressive stress.

In a construction method for forming a residual compressive stress region near a tip of a crack by enlarging the diameter of vertically arranged piping having a fine crack which does not pass through the inner surface, a fluid inside the piping is eliminated to form a gaseous environment, and a heat insulating material and a refrigerant container are provided near the crack of the piping. After previously cooling a vertically lower part of the crack of the piping to a freezing point or less, water is supplied from a vertically upper part along the pipe wall in the inner surface of the piping to form the ice plug. Gathering of water to the vertically upper part of the crack is confirmed, and the vertically upper part of the crack is cooled. With this procedure, a region sealed with water by the ice plug is formed near the crack inside the piping. Thereafter, as ice is formed in that region, diameter of the piping near the crack is enlarged by expansion of the volume upon change from water to ice. In such a manner, a residual compressive stress region is formed near the tip of the crack.