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ERDC/ CHL CHETN III 64 June 2002 ( revised) Damage Development on Stone Armored Breakwaters and Revetments by Jeffery A. Melby PURPOSE: This Coastal and Hydraulics Engineering Technical Note ( CHETN) provides a method to calculate damage progression on a rubble mound breakwater, revetment, or jetty trunk armor layer. The methods apply to uniform sized armor stone ( 0.75W50 ≤ W50 ≤ 1.25W50, W50 = median weight of armor stone) as well as riprap ( 0.125W50 ≤ W50 ≤ 4W50) exposed to depth limited wave conditions. The equations discussed herein are primarily intended to be used as part of a life cycle analysis, to predict the damage for a series of storms throughout the lifetime of the structure. This life cycle analysis including damage prediction allows engineers to balance initial cost with expected maintenance costs in order to reduce the overall cost of the structure. The equations are intended to provide a tool for accurate damage estimates in order to reduce the possibility of unexpected maintenance costs. INTRODUCTION: Rubble mound breakwater, revetment, and jetty projects require accurate damage prediction as part of life cycle analyses. But few studies have been conducted to determine damage progression on stone armor layers for variable wave conditions over the life of a structure. Previous armor stability lab studies were intended to determine damage for the peak of a design storm. As such, most previous laboratory studies were begun with an undamaged structure and damage measured for a single design wave condition ( e. g., Hudson 1959; Van der Meer 1988). The empirical equations derived from these studies were valid for determining initial damage but not for damage progression through several storm events. Damage actually occurs as a result of a sequence of storms of varying severity and with varying water levels. This CHETN provides equations that allow the prediction of rubble mound deterioration with time. These relations are supplemented by predictive equations for the uncertainty or variability of damage for more accurate estimation of reliability or, conversely, probability of failure. Within this technical note, damage is defined in terms of the average normalized cross sectional eroded area of armor on the slope. Damage is defined up to the point that the underlayer is exposed through a hole the size of a nominal armor stone diameter Dn50 = ( M50/ ρa) 1/ 3, where M50 is the median mass of armor stone and ρa is the armor stone density. The condition where the underlayer is exposed defines failure of the armor layer because rapid destruction of the structure often occurs after this point. The damaged profile is described in terms of the engineering parameters maximum eroded depth, minimum remaining cover depth, and maximum cross shore length of the eroded region. Relations for these profile descriptors are given in terms of the mean damage. Further, relations describing the alongshore variability of damage and the profile descriptors are provided to support reliability or uncertainty analyses. These relations apply for single storms and for storm sequences given depth limited normally incident waves. The relations and supporting studies are described in a series of publications on damage ( Melby 1999; Melby and Kobayashi 1998a, 1998b, 1999). ERDC/ CHL CHETN III 64 June 2002 ( revised) DAMAGE DESCRIPTION: The Shore Protection Manual ( 1984) provides damage as a function of the marginal wave height exceeding the zero damage wave height. The Shore Protection Manual damage D% was defined as the normalized eroded volume in the active region, extending from the middle of the breakwater crest down to one wave height below the still water level. This design information is based on laboratory tests limited to monochromatic nonbreaking waves impinging on long structure slopes. The background reports provide little insight and no data. Broderick and Ahrens ( 1982) provided a definition of damage that was not a function of cross sectional geometry. They defined damage to an armor layer by the normalized eroded cross sectional area 250enASD= ( 1) where Ae = measured eroded cross sectional area ( Figures 1 and 2) Dn50 = nominal armor stone diameter Figure 1. Damaged section parameters 2 ERDC/ CHL CHETN III 64 June 2002 ( revised) hc h υ wc ta armor layer Ae Figure 2. Rubble mound structure cross section This damage formulation was popularized by van der Meer ( 1988). Melby and Kobayashi ( 1998a) utilized S as a general damage description and further defined the eroded profile using several engineering parameters: the maximum eroded depth E = de/ Dn50, the minimum remaining cover depth C = dc/ Dn50, and the maximum cross shore length of the eroded region L = le/ Dn50. These damaged section descriptors are shown in Figure 1. A typical structure cross section is shown in Figure 2. The maximum eroded depth and minimum remaining cover depth may not occur at the same location along a structure because of the variability of the armor layer thickness. PREDICTIVE RELATIONS: Melby and Kobayashi ( 1998a) conducted a series of experiments measuring the erosion of a stone armor layer for varying wave and water level conditions. The structure profile was measured repeatedly throughout the test at up to 32 sections alongshore. The 32 profiles were used to obtain mean damage and mean damaged profile as well as the alongshore variability of damage and the profile. The empirical equation proposed by Melby and Kobayashi ( 1998a) for predicting the temporal progression of mean eroded area as a function of time domain wave statistics is 50.250.2510.25() ()() 0.025() () snnnmnNStttfortttT+−≤≤ n n St=+ ( 2) where S( t) and S( tn) are predicted and known mean eroded areas at times t and tn, respectively, with t > tn. Ns = Hs / ( ΔDn50) is the stability number based on the average of the highest one third wave heights from a zero upcrossing analysis, Δ = Sr  1 where Sr is the armor stone specific gravity, and Tm is the mean period. The wave parameters are defined 5Hs seaward of the structure toe, which is the travel distance of large breaking waves. Equation 2 provides a means to compute damage over a sequence of N events, each of relatively constant wave conditions, where each event is defined over a time period from tn to tn+ 1, 1 ≤ n ≤ N. 3 ERDC/ CHL CHETN III 64 June 2002 ( revised) A similar equation relating mean damage to spectral wave characteristics was given by Melby and Kobayashi as 50.250.2510.25() ()() 0.022() () monnnpnNStttfortttT+−≤≤ n n St=+ ( 3) where Nmo = Hmo / ( ΔDn50), Hmo = 4( mo) 1/ 2, mo is the zero moment of the incident wave spectrum, and Tp is the spectral peak period. The empirical coefficients in Equations 2 and 3 will be primarily a function of structure slope, wave period, beach slope, and structure permeability. These equations have been verified for the following range of laboratory conditions: Structure slope, tan α: 1V: 2H Significant wave height, Hs: 5.05 cm – 15.80 cm Toe depth, h: 11.9 – 15.8 cm Mean wave period, Tm: 1.23 s – 1.80 s Iribarren parameter: tan α/( Hs/ Lom) 0.5: 2.08 – 4.17 Beach slope: 1V: 20H Structure crest height, hc: 30.5 cm Stone density, ρa: 2.66 g/ cm3 Armor stone gradations: 0.75M50 < M50 < 1.25M50, D85/ D15 = 1.25 and 0.125M50 < M50 < 4M50, D85/ D15 = 1.53 Filter layer: ( M50) armor/( M50) filter = 25, ( Dn50) armor/( Dn50) filter = 2.9 The deepwater wavelength computed from the mean period is Lom = gTm2/ 2π, where g is the acceleration of gravity. Equations 2 and 3 are plotted in Figure 3, where S( t) is plotted as a function of number of waves, Nw. Here Nw = t/ Tm. In Figure 3, the measured mean eroded area plus and minus one standard deviation are plotted. These data are from one very long series of six different storms with two water levels. Equations 2 and 3 should be conservative for most applications because they are based on severely breaking waves, a relatively steep beach slope, and a relatively impermeable core. Deviations from the range of tested conditions are likely to produce different empirical coefficients in Equations 2 and 3. Caution should be exercised in applications of these equations outside of the range of conditions tested. The mean parameters S, E, C, and L and the standard deviations σS, σE, σC, σL were used to describe the tendencies, variabilities, and ranges of damage and the damaged profile. All measured values from all measured series were in the following ranges Damage: 2.7()/ 3SSSσ−<−< ( 4) Eroded depth: 2.7()/ 2.7EEEσ−<−< ( 5) Cover depth: 2.7()/ 2.8CCCσ−<−< ( 6) 4 ERDC/ CHL CHETN III 64 June 2002 ( revised) Figure 3. Mean damage as a function of number of waves at mean period These ranges allow the lower and upper limits of the damaged profile descriptors to be estimated. In order to reduce the number of parameters for design, Melby and Kobayashi ( 1998a) expressed the key profile parameters as a function of the mean damage as follows: 0.650.5SSσ= ( 7) 0.50.46ES= ( 8) 0.1oCCS=− ( 9) 0.54.4LS= ( 10) Using Equations 4 and 7 with 13= S, corresponding to localized failure in the series shown in Figure 3, σS = 2.65 and 6 < S < 21. This illustrates the large alongshore variability of damage at failure for alongshore uniform waves. EXAMPLE: A single storm example is provided to show how parameters are used in the equations. A traditional rubble mound breakwater is to be constructed in seawater so that the longitudinal axis of the structure is parallel to the wave crests. The significant wave height used for design is 5 ERDC/ CHL CHETN III 64 June 2002 ( revised) determined to be depth limited from a shoaling/ refraction/ diffraction study. The design wave height is calculated at a distance of 5Hs seaward from the structure toe. Given design values: Significant wave height: Hs = 2.07 m ( 6.8 ft) Specific gravity of seawater: S = 1.0256 Specific gravity of armor stone: Sr = 2.65 Specific weight of armor stone: γr = 2.66x104 N/ m3 ( 169.6 lb/ ft3) Density of armor stone: ρr = 2.72 t/ m3 ( 5.27 slug/ ft3) Mean wave period: Tm = 10.8 s Structure seaward slope: tan α = 0.5 Median stone size: W50 = 1,311 kg ( 2,889 lbs) Stone gradation: 0.75W50 < W50 < 1.25W50 Storm duration: 4 hr = 14,400 s ( 1,333 waves at Tm) Armor layer thickness: 2Dn50 Calculations: 1/ 31/ 31/ 350505031.3110.784m2.72 t/ mnrrWMtDγρ ==== 502.07m1.60( 2.651) 0.784mssnHND=== Δ− Damage due to a single storm would be computed using Equation 2 as 50.250.250.2550.250.25() ()() 0.025() () 1.6000.025( 14,400s) 1.58( 10.8s) snnnmnNStStttT=+− =+= This damage level indicates that, for the single 4 hr storm, there would be an eroded area of about 1.6 median sized stones removed from a typical cross section. This is minimal damage and would not affect the integrity of the structure. Assuming uniform wave height alongshore, the alongshore variability, given as the standard deviation, of damage would be given by Equation 7. 0.650.650.50.5( 1.58) 0.67SSσ=== And the alongshore range of damage would be given by Equation 4 as 2.7( 0.67) 1.583.0( 0.67) 1.58003.61SSS−+≤≤+ ≤≤ ≥ 6 ERDC/ CHL CHETN III 64 June 2002 ( revised) So the range of damage along the shore is quite large but still represents only minimal damage to the structure. The damaged armor layer profile shape can be analyzed in a similar fashion. The initial layer thickness is 5022( 0.784m) 1.57mrntD=== Then the means of the maximum eroded depth, minimum remaining cover depth, and maximum eroded cross shore length, respectively, would be given by Equations 9, 10, and 11 as follows: 0.50.50.460.46( 1.58) 0.58ES=== 0.11.570.1( 1.58) 1.41oCCS=−=−= 0.50.54.44.4( 1.58) 5.5LS== = The mean dimensional eroded depth is de = Ē Dn50 = 0.58( 0.784 m) = 0.45 m. The mean dimensional minimum remaining cover depth is dc = CDn50 = 1.40( 0.784 m) = 1.11 m, so there is significant cover over the underlayer. Note that the initial thickness of the armor layer is not uniform; so the maximum eroded depth may not occur in the same location as the location of minimum remaining cover. In addition, the sum of Eand Cmay not be equal to oCfor the same reason. The mean of the maximum eroded length or cross shore eroded hole is le = 4.34 m. This stone size was very well suited for this application if this was a design level storm. If a storm of Nw = 5,000 waves were to strike the structure, then t = 5,000( 10.8 s) = 54,000 s. This represents a storm of a very long duration of 15 hr. The mean damage would increase to 50.250.251.60() 00.025( 54,000s) 2.20( 10.8s) St=+= This damage level is still quite acceptable for most situations. CONCLUSIONS: This CHETN provides a method for computing damage on a rubble mound breakwater, revetment, or jetty trunk section stone armor layer that is exposed to depth limited breaking waves. The methods are useful in determining the expected life of new or damaged structures and in developing life cycle analyses. The empirical equations should be conservative for most applications, but care should be exercised when applying outside of the tested conditions, as described in this technical note. ADDITIONAL INFORMATION: The author would like to thank Dr. Shamsul Chowdhury for valuable technical assistance with editing this document. This CHETN was produced with funding from the Navigation Systems R& D Program within the Prediction and Prevention of 7 ERDC/ CHL CHETN III 64 June 2002 ( revised) 8 Breakwater Deterioration Work Unit. The Principal Investigator for the work unit was Dr. Jeffrey A. Melby. Questions about this CHETN can be addressed to him at ( 601 634 2062 or e mail jeffrey. a. melby@ erdc. usace. army. mil). This CHETN should be referenced as follows: Melby, J. A. ( 2001). “ Damage development on stone armored breakwaters and revetments,” ERDC/ CHL CHETN III 64, U. S. Army Engineer Research and Development Center, Vicksburg, MS. http:// chl. wes. army. mil/ library/ publications/ chetn REFERENCES Broderick, L., and Ahrens, J. P. ( 1982). “ Rip rap stability scale effects,” Technical Paper 82 3, U. S. Army Engineer Waterways Experiment Station, Vicksburg, MS. Hudson, R. Y. ( 1959). “ Laboratory investigation of rubble mound breakwaters,” J. Wtrwy. and Harb. Div., 85( WW3), 93 121, ASCE, Reston, VA. Melby, J. A. ( 1999). “ Damage progression on rubble mound breakwaters,” TR CHL 99 17, U. S. Army Engineer Research and Development Center, Vicksburg, MS, Ph. D. diss., University of Delaware, Newark, DE. Melby, J. A., and Kobayashi, N. ( 1998a). “ Progression and variability of damage on rubble mound breakwaters,” J. Wtrwy., Port, Coast., and Oc., Engrg., 124( 6), 286 294, ASCE, Reston, VA. ______ . ( 1998b). “ Damage progression on breakwaters,” Proc., 26th Coast. Engrg. Conf., V 2, ASCE, Reston, VA, 1884 1897. ______ . ( 1999). “ Damage progression and variability on breakwater trunks,” Coastal Structures ’ 99, Balkema/ Rotterdam, 309 316. Shore protection manual. ( 1984). 4th ed., 2 Vol, U. S. Army Engineer Waterways Experiment Station, U. S. Government Printing Office, Washington, DC. Van der Meer, J. ( 1988). “ Rock slopes and gravel beaches under wave attack,” Ph. D. diss., Delft Hydraulics Communication No. 396, Delft Hydrulics Laboratory, Emmeloord, The Netherlands.
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Title  Damage development on stonearmored breakwaters and revetments 
Subject  BreakwatersProtectionMathematical models.; Rubble mound breakwatersProtectionMathematical models.; Shore protectionMathematical models. 
Description  Revised.; "June 2002."; Includes bibliographical references (p. 8). 
Creator  Melby, Jeffrey A. 
Publisher  U.S. Army Engineer Research and Development Center 
Contributors  Engineer Research and Development Center (U.S.); Coastal and Hydraulics Laboratory (U.S. Army Engineer Waterways Experiment Station) 
Type  Text 
Language  eng 
Relation  Also available via the Internet.; http://chl.erdc.usace.army.mil/library/publications/chetn/pdf/chetniii64.pdf; http://worldcat.org/oclc/404291849/viewonline 
DateIssued  2002 
FormatExtent  8 p. : digital PDF file, ill., chart, plan : 286.57 kb. 
RelationRequires  Mode of access: World Wide Web. 
RelationIs Part Of  ERDC/CHL CHETN ; III64; Technical note (Coastal and Hydraulics Engineering) ; III64. 
Transcript  ERDC/ CHL CHETN III 64 June 2002 ( revised) Damage Development on Stone Armored Breakwaters and Revetments by Jeffery A. Melby PURPOSE: This Coastal and Hydraulics Engineering Technical Note ( CHETN) provides a method to calculate damage progression on a rubble mound breakwater, revetment, or jetty trunk armor layer. The methods apply to uniform sized armor stone ( 0.75W50 ≤ W50 ≤ 1.25W50, W50 = median weight of armor stone) as well as riprap ( 0.125W50 ≤ W50 ≤ 4W50) exposed to depth limited wave conditions. The equations discussed herein are primarily intended to be used as part of a life cycle analysis, to predict the damage for a series of storms throughout the lifetime of the structure. This life cycle analysis including damage prediction allows engineers to balance initial cost with expected maintenance costs in order to reduce the overall cost of the structure. The equations are intended to provide a tool for accurate damage estimates in order to reduce the possibility of unexpected maintenance costs. INTRODUCTION: Rubble mound breakwater, revetment, and jetty projects require accurate damage prediction as part of life cycle analyses. But few studies have been conducted to determine damage progression on stone armor layers for variable wave conditions over the life of a structure. Previous armor stability lab studies were intended to determine damage for the peak of a design storm. As such, most previous laboratory studies were begun with an undamaged structure and damage measured for a single design wave condition ( e. g., Hudson 1959; Van der Meer 1988). The empirical equations derived from these studies were valid for determining initial damage but not for damage progression through several storm events. Damage actually occurs as a result of a sequence of storms of varying severity and with varying water levels. This CHETN provides equations that allow the prediction of rubble mound deterioration with time. These relations are supplemented by predictive equations for the uncertainty or variability of damage for more accurate estimation of reliability or, conversely, probability of failure. Within this technical note, damage is defined in terms of the average normalized cross sectional eroded area of armor on the slope. Damage is defined up to the point that the underlayer is exposed through a hole the size of a nominal armor stone diameter Dn50 = ( M50/ ρa) 1/ 3, where M50 is the median mass of armor stone and ρa is the armor stone density. The condition where the underlayer is exposed defines failure of the armor layer because rapid destruction of the structure often occurs after this point. The damaged profile is described in terms of the engineering parameters maximum eroded depth, minimum remaining cover depth, and maximum cross shore length of the eroded region. Relations for these profile descriptors are given in terms of the mean damage. Further, relations describing the alongshore variability of damage and the profile descriptors are provided to support reliability or uncertainty analyses. These relations apply for single storms and for storm sequences given depth limited normally incident waves. The relations and supporting studies are described in a series of publications on damage ( Melby 1999; Melby and Kobayashi 1998a, 1998b, 1999). ERDC/ CHL CHETN III 64 June 2002 ( revised) DAMAGE DESCRIPTION: The Shore Protection Manual ( 1984) provides damage as a function of the marginal wave height exceeding the zero damage wave height. The Shore Protection Manual damage D% was defined as the normalized eroded volume in the active region, extending from the middle of the breakwater crest down to one wave height below the still water level. This design information is based on laboratory tests limited to monochromatic nonbreaking waves impinging on long structure slopes. The background reports provide little insight and no data. Broderick and Ahrens ( 1982) provided a definition of damage that was not a function of cross sectional geometry. They defined damage to an armor layer by the normalized eroded cross sectional area 250enASD= ( 1) where Ae = measured eroded cross sectional area ( Figures 1 and 2) Dn50 = nominal armor stone diameter Figure 1. Damaged section parameters 2 ERDC/ CHL CHETN III 64 June 2002 ( revised) hc h υ wc ta armor layer Ae Figure 2. Rubble mound structure cross section This damage formulation was popularized by van der Meer ( 1988). Melby and Kobayashi ( 1998a) utilized S as a general damage description and further defined the eroded profile using several engineering parameters: the maximum eroded depth E = de/ Dn50, the minimum remaining cover depth C = dc/ Dn50, and the maximum cross shore length of the eroded region L = le/ Dn50. These damaged section descriptors are shown in Figure 1. A typical structure cross section is shown in Figure 2. The maximum eroded depth and minimum remaining cover depth may not occur at the same location along a structure because of the variability of the armor layer thickness. PREDICTIVE RELATIONS: Melby and Kobayashi ( 1998a) conducted a series of experiments measuring the erosion of a stone armor layer for varying wave and water level conditions. The structure profile was measured repeatedly throughout the test at up to 32 sections alongshore. The 32 profiles were used to obtain mean damage and mean damaged profile as well as the alongshore variability of damage and the profile. The empirical equation proposed by Melby and Kobayashi ( 1998a) for predicting the temporal progression of mean eroded area as a function of time domain wave statistics is 50.250.2510.25() ()() 0.025() () snnnmnNStttfortttT+−≤≤ n n St=+ ( 2) where S( t) and S( tn) are predicted and known mean eroded areas at times t and tn, respectively, with t > tn. Ns = Hs / ( ΔDn50) is the stability number based on the average of the highest one third wave heights from a zero upcrossing analysis, Δ = Sr  1 where Sr is the armor stone specific gravity, and Tm is the mean period. The wave parameters are defined 5Hs seaward of the structure toe, which is the travel distance of large breaking waves. Equation 2 provides a means to compute damage over a sequence of N events, each of relatively constant wave conditions, where each event is defined over a time period from tn to tn+ 1, 1 ≤ n ≤ N. 3 ERDC/ CHL CHETN III 64 June 2002 ( revised) A similar equation relating mean damage to spectral wave characteristics was given by Melby and Kobayashi as 50.250.2510.25() ()() 0.022() () monnnpnNStttfortttT+−≤≤ n n St=+ ( 3) where Nmo = Hmo / ( ΔDn50), Hmo = 4( mo) 1/ 2, mo is the zero moment of the incident wave spectrum, and Tp is the spectral peak period. The empirical coefficients in Equations 2 and 3 will be primarily a function of structure slope, wave period, beach slope, and structure permeability. These equations have been verified for the following range of laboratory conditions: Structure slope, tan α: 1V: 2H Significant wave height, Hs: 5.05 cm – 15.80 cm Toe depth, h: 11.9 – 15.8 cm Mean wave period, Tm: 1.23 s – 1.80 s Iribarren parameter: tan α/( Hs/ Lom) 0.5: 2.08 – 4.17 Beach slope: 1V: 20H Structure crest height, hc: 30.5 cm Stone density, ρa: 2.66 g/ cm3 Armor stone gradations: 0.75M50 < M50 < 1.25M50, D85/ D15 = 1.25 and 0.125M50 < M50 < 4M50, D85/ D15 = 1.53 Filter layer: ( M50) armor/( M50) filter = 25, ( Dn50) armor/( Dn50) filter = 2.9 The deepwater wavelength computed from the mean period is Lom = gTm2/ 2π, where g is the acceleration of gravity. Equations 2 and 3 are plotted in Figure 3, where S( t) is plotted as a function of number of waves, Nw. Here Nw = t/ Tm. In Figure 3, the measured mean eroded area plus and minus one standard deviation are plotted. These data are from one very long series of six different storms with two water levels. Equations 2 and 3 should be conservative for most applications because they are based on severely breaking waves, a relatively steep beach slope, and a relatively impermeable core. Deviations from the range of tested conditions are likely to produce different empirical coefficients in Equations 2 and 3. Caution should be exercised in applications of these equations outside of the range of conditions tested. The mean parameters S, E, C, and L and the standard deviations σS, σE, σC, σL were used to describe the tendencies, variabilities, and ranges of damage and the damaged profile. All measured values from all measured series were in the following ranges Damage: 2.7()/ 3SSSσ−<−< ( 4) Eroded depth: 2.7()/ 2.7EEEσ−<−< ( 5) Cover depth: 2.7()/ 2.8CCCσ−<−< ( 6) 4 ERDC/ CHL CHETN III 64 June 2002 ( revised) Figure 3. Mean damage as a function of number of waves at mean period These ranges allow the lower and upper limits of the damaged profile descriptors to be estimated. In order to reduce the number of parameters for design, Melby and Kobayashi ( 1998a) expressed the key profile parameters as a function of the mean damage as follows: 0.650.5SSσ= ( 7) 0.50.46ES= ( 8) 0.1oCCS=− ( 9) 0.54.4LS= ( 10) Using Equations 4 and 7 with 13= S, corresponding to localized failure in the series shown in Figure 3, σS = 2.65 and 6 < S < 21. This illustrates the large alongshore variability of damage at failure for alongshore uniform waves. EXAMPLE: A single storm example is provided to show how parameters are used in the equations. A traditional rubble mound breakwater is to be constructed in seawater so that the longitudinal axis of the structure is parallel to the wave crests. The significant wave height used for design is 5 ERDC/ CHL CHETN III 64 June 2002 ( revised) determined to be depth limited from a shoaling/ refraction/ diffraction study. The design wave height is calculated at a distance of 5Hs seaward from the structure toe. Given design values: Significant wave height: Hs = 2.07 m ( 6.8 ft) Specific gravity of seawater: S = 1.0256 Specific gravity of armor stone: Sr = 2.65 Specific weight of armor stone: γr = 2.66x104 N/ m3 ( 169.6 lb/ ft3) Density of armor stone: ρr = 2.72 t/ m3 ( 5.27 slug/ ft3) Mean wave period: Tm = 10.8 s Structure seaward slope: tan α = 0.5 Median stone size: W50 = 1,311 kg ( 2,889 lbs) Stone gradation: 0.75W50 < W50 < 1.25W50 Storm duration: 4 hr = 14,400 s ( 1,333 waves at Tm) Armor layer thickness: 2Dn50 Calculations: 1/ 31/ 31/ 350505031.3110.784m2.72 t/ mnrrWMtDγρ ==== 502.07m1.60( 2.651) 0.784mssnHND=== Δ− Damage due to a single storm would be computed using Equation 2 as 50.250.250.2550.250.25() ()() 0.025() () 1.6000.025( 14,400s) 1.58( 10.8s) snnnmnNStStttT=+− =+= This damage level indicates that, for the single 4 hr storm, there would be an eroded area of about 1.6 median sized stones removed from a typical cross section. This is minimal damage and would not affect the integrity of the structure. Assuming uniform wave height alongshore, the alongshore variability, given as the standard deviation, of damage would be given by Equation 7. 0.650.650.50.5( 1.58) 0.67SSσ=== And the alongshore range of damage would be given by Equation 4 as 2.7( 0.67) 1.583.0( 0.67) 1.58003.61SSS−+≤≤+ ≤≤ ≥ 6 ERDC/ CHL CHETN III 64 June 2002 ( revised) So the range of damage along the shore is quite large but still represents only minimal damage to the structure. The damaged armor layer profile shape can be analyzed in a similar fashion. The initial layer thickness is 5022( 0.784m) 1.57mrntD=== Then the means of the maximum eroded depth, minimum remaining cover depth, and maximum eroded cross shore length, respectively, would be given by Equations 9, 10, and 11 as follows: 0.50.50.460.46( 1.58) 0.58ES=== 0.11.570.1( 1.58) 1.41oCCS=−=−= 0.50.54.44.4( 1.58) 5.5LS== = The mean dimensional eroded depth is de = Ē Dn50 = 0.58( 0.784 m) = 0.45 m. The mean dimensional minimum remaining cover depth is dc = CDn50 = 1.40( 0.784 m) = 1.11 m, so there is significant cover over the underlayer. Note that the initial thickness of the armor layer is not uniform; so the maximum eroded depth may not occur in the same location as the location of minimum remaining cover. In addition, the sum of Eand Cmay not be equal to oCfor the same reason. The mean of the maximum eroded length or cross shore eroded hole is le = 4.34 m. This stone size was very well suited for this application if this was a design level storm. If a storm of Nw = 5,000 waves were to strike the structure, then t = 5,000( 10.8 s) = 54,000 s. This represents a storm of a very long duration of 15 hr. The mean damage would increase to 50.250.251.60() 00.025( 54,000s) 2.20( 10.8s) St=+= This damage level is still quite acceptable for most situations. CONCLUSIONS: This CHETN provides a method for computing damage on a rubble mound breakwater, revetment, or jetty trunk section stone armor layer that is exposed to depth limited breaking waves. The methods are useful in determining the expected life of new or damaged structures and in developing life cycle analyses. The empirical equations should be conservative for most applications, but care should be exercised when applying outside of the tested conditions, as described in this technical note. ADDITIONAL INFORMATION: The author would like to thank Dr. Shamsul Chowdhury for valuable technical assistance with editing this document. This CHETN was produced with funding from the Navigation Systems R& D Program within the Prediction and Prevention of 7 ERDC/ CHL CHETN III 64 June 2002 ( revised) 8 Breakwater Deterioration Work Unit. The Principal Investigator for the work unit was Dr. Jeffrey A. Melby. Questions about this CHETN can be addressed to him at ( 601 634 2062 or e mail jeffrey. a. melby@ erdc. usace. army. mil). This CHETN should be referenced as follows: Melby, J. A. ( 2001). “ Damage development on stone armored breakwaters and revetments,” ERDC/ CHL CHETN III 64, U. S. Army Engineer Research and Development Center, Vicksburg, MS. http:// chl. wes. army. mil/ library/ publications/ chetn REFERENCES Broderick, L., and Ahrens, J. P. ( 1982). “ Rip rap stability scale effects,” Technical Paper 82 3, U. S. Army Engineer Waterways Experiment Station, Vicksburg, MS. Hudson, R. Y. ( 1959). “ Laboratory investigation of rubble mound breakwaters,” J. Wtrwy. and Harb. Div., 85( WW3), 93 121, ASCE, Reston, VA. Melby, J. A. ( 1999). “ Damage progression on rubble mound breakwaters,” TR CHL 99 17, U. S. Army Engineer Research and Development Center, Vicksburg, MS, Ph. D. diss., University of Delaware, Newark, DE. Melby, J. A., and Kobayashi, N. ( 1998a). “ Progression and variability of damage on rubble mound breakwaters,” J. Wtrwy., Port, Coast., and Oc., Engrg., 124( 6), 286 294, ASCE, Reston, VA. ______ . ( 1998b). “ Damage progression on breakwaters,” Proc., 26th Coast. Engrg. Conf., V 2, ASCE, Reston, VA, 1884 1897. ______ . ( 1999). “ Damage progression and variability on breakwater trunks,” Coastal Structures ’ 99, Balkema/ Rotterdam, 309 316. Shore protection manual. ( 1984). 4th ed., 2 Vol, U. S. Army Engineer Waterways Experiment Station, U. S. Government Printing Office, Washington, DC. Van der Meer, J. ( 1988). “ Rock slopes and gravel beaches under wave attack,” Ph. D. diss., Delft Hydraulics Communication No. 396, Delft Hydrulics Laboratory, Emmeloord, The Netherlands. 
OCLC number  404291849 



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