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Additional file 1.

Source: https://erdc-library.erdc.dren.mil/jspui/ A two-dimensional model study of a proposed reef breakwater for protection of the existing, damage-prone, rubble-mound breakwater at Burns Waterway Harbor was conducted. Sufficient 1:36-scale undistorted flume tests were conducted such that an optimum submerged reef could be selected. Specifically, it was desired to quantify performance (stability/transmission response) in terms of structure height and width, location relative to the existing breakwater, and stone size and gradation. Seven improvement plans were considered. All significantly improved stability of the existing breakwater and reduced transmitted wave heights to some extent. Test results for the various improvement plans showed that all structures tested were successful in reducing 7- and 9-sec, 5-ft incident waves to heights of 1 ft or less behind the existing breakwater. Also, as desired, wave heights of about 15 ft or less were observed behind the reef for 11.6-sec, 19-ft incident waves, thus eliminating most damage to the existing breakwater. Five-ton armor stone was completely stable at crest elevations of -10 and -20 ft low-water datum. Increasing the toe-to-toe spacing of the reef from the existing breakwater from 75 to 100 ft slightly improved stability of the existing structure and slightly increased lransmission.

Source: https://erdc-library.erdc.dren.mil/jspui/ High sea waves tend to appear in groups rather than individually. Because of the nature of wave grouping, it appears that it may be an important influence on the stability of rubble-mound structures. The research documented in this report was conducted to obtain a better understanding of the effects of wave grouping on the stability of stone armor when used on breakwater trunks. Results of this study show stability to be influenced by wave period, spectral width, and wave grouping intensity. Levels of wave grouping tested herein are achievable at some, but not all, prototype locations; therefore, results should be applied on a case-by-case basis.

Source: https://erdc-library.erdc.dren.mil/jspui/ The objective of this study was to investigate, via a two-dimensional (2-D) coastal model, alternate designs for the proposed revetment. Tests were conducted at a geometrically undistorted scale of 1:24, model to prototype. Based on test results, it was concluded that: a. Four- to six-ton armor stone is stable for the maximum wave heights that can be expected to occur for 8-and 10-sec waves at still-water levels (swl's) of +4.0 to +14.0 ft mean low tide (mlt) with assumed scour depths of -3.6 and -8.6 ft mit. b. Stability of the original concrete blocks, which were 6.0 ft by 5.5 ft by 2.5 ft and had 0 percent porosity, was only marginally acceptable for the maximum wave heights that can be expected to occur for 8- and lO-sec waves at swl's of +4.0 to +14.0 ft mit with an assumed scour depth of -3.6 ft mit. c. Several modified block plans were tested and it was determined that the optimum block size was 5.75 ft by 5.75 ft by 2.5 ft. These blocks, weighing 6 tons and having a porosity of 4 percent, should prove stable for the maximum wave heights that can be expected to occur for 8- to lO-sec waves at swl's of +4.0 to +14.0 ft mit with an assumed scour depth of -lO ft mit.

Source: https://erdc-library.erdc.dren.mil/jspui/ The purpose of this investigation was to obtain a better understanding of why significant variations in the stability coefficient occur. Specifically, it was hoped that functional relationships could be developed between the stability coefficient and such variables as wave height, wave period, and water depth. These functional relationships would then be used as input to an improved procedure for obtaining minimum armor unit weights required for hydraulic stability. Also, it was hoped that a link could be developed between breaking and nonbreaking wave test results. Based on results of model tests described herein, in which tetrapod, tribar, dolos, and stone armor are used on breakwater trunks and heads, it is concluded that test results are very significant in that they show tetrapod, tribar, dolos, and stone stability to be dependent on the combined effects of wave height, wave period, and water depth with minimum stability occurring at the lower values of d/L and higher values of H/d , i.e., longer wave periods in shallower water. An improved procedure for determining minimum armor unit weights was developed.

Source: https://erdc-library.erdc.dren.mil/jspui/ The purpose of the model investigation reported herein was to obtain design information for stone and dolos armor used on breakwater trunks and subjected to selected spectral wave conditions. More specifically, it was desired to determine the required weight of individual armor units (with given specific weights) needed for stability as a function of armor type, wave height and period, and sea-side slope of the breakwater. Based on test results, it was concluded that: -a. Stability of both armor types is influenced by wave height, wave period, breakwater slope, and, to a lesser extent, water depth. -b. A new energy based stability number which correlates strongly with the relative depth was developed, -c. Stone stability was more strongly influenced by changes in breakwater slope than was dolos stability. -d. Dolos test results showed more variability, i.e., were less repeatable than the stone stability tests.

Source: https://erdc-library.erdc.dren.mil/jspui/ The purpose of the investigation herein was to obtain design information for stone and dolos armor used on breakwater heads and subjected to nonbreaking waves. More specifically, it was desired to determine the minimum weight of individual armor units (with given specific weights) required for stability as a function of: (a.) Type of armor unit. (b.) Sea-side slope of the structure. (c.) Angle of wave attack. (d.) Wave period. (e.) Wave height. Based on tests and results described herein, in which stone and dolos armor are used on conical breakwater heads and subjected to nonbreaking waves with angles of wave attack of 0, 45, 90, and 135 deg, it is concluded that: (a.) The longer wave periods (2.00 and 2.75 sec) generally produce the lower stabilities. (b.) Angles of wave attack of 45 and 90 deg are the most critical. (c.) Flattening the slope from 1V on 1.5H to 1V on 2H does not improve stability of the stone armor.

Source: https://erdc-library.erdc.dren.mil/jspui/ The purpose of the model investigation reported herein was to investigate the suitability of articulated concrete mattresses (ACM's) for use at Lake Okeechobee, FL. Due to the absence of significant experience in applying this method of slope protection in a wave environment and the lack of appropriate design criteria, it was decided to investigate the stability response of the ACM's via a large-scale, two-dimensional coastal model. Based on tests conducted, it was concluded that for one layer of ACM's: -a. The maximum stable wave height is 3 ft if the mat is secured by top anchors only. -b. An addition of three rows of anchors near the still water level ( swl) and two rows of the anchors provides stability for up to 4-ft waves. -c. Anchors would be required between every other block and every other row from the water surface to the toe in order to achieve stability for the 5- and 6-ft waves. -d. Five- and eight-hundred-pound toe stones proved to be stable for 3- and 4-ft waves, respectively. -e. Additional toe stone reduces the maximum runup by about 0.5 ft. For two layers of ACM's it was concluded that: ~. The maximum stable wave height is 4 ft if the mats are secured by top anchors only. Q. With the toe stabilized by anchors or stone, localized lifting of the mats in the vicinity of the swl can be expected for 5- and 6-ft waves. £. Construction of a 3-ft-deep toe trench will significantly improve stability of the toe stone; however, stones loosened by the higher wave heights have the potential to roll upslope and downslope and may damage the mats. -d. An additional single layer of mats on the overbank will reduce maximum runup by about 1 ft. -e. Bedding stone movement can be expected for wave heights in excess of 4 ft. -f. Erosion of the sand embankment will be initiated by 2-ft waves if a bedding or filtering medium is not provided. For three layers of ACM's, it was concluded that ACM's are completely stable for 2-, 3-, and 4-ft waves. However, minor lifting of the toe can be expected for the 5- and 6-ft waves if toe anchors are not used.