Extent of riprap layer with different stone sizes around rectangular bridge piers with or without an attached collar

In the present study, the extent of riprap layer with different sizes around bridge piers is investigated. rectangular pier with or without an attached protective collar aligned with the ow and skewed at different angles are tested. the optimal configurations of riprap extent for each pier condition with different sizes are determined. experiments showed that in case of aligned rectangular pier without a collar only 8% of the area around the pier is critical and the remaining 92% area can be protected with about 60% smaller riprap stones. as the skew angle of the pier increases up to 20°, the critical area increases up to 23% of the riprap extent. in case of protected pier with collar, the collar prevents the critical region around the pier in aligned and 5° skewed pier. however, by increasing the ow attack angle up to 20°, only a small area up to 30% in the riprap extent around the collar is critical and the remaining area can be placed with 40% smaller riprap size. finally, the design algorithm for riprap extent with different sizes is presented.