AD-41M3" 31PUOINOTE UPPER LIMIT OF IRREOULUR MAY! RUNUP ON 1/1RIPRAP(U) COASTM. SI NEER INOCRESEARCH CENTER VICKS8IRIMs J P ESE l NAY SO CERC-TR-09-5UNCLRSIFIEDF/0G 13/10S W

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[I]C FILE COP' ,-

TECHNICAL REPORT CERC-88-5

U A APPROXIMATE UPPER LIMIT OF IRREGULARWAVE RUNUP ON RIPRAP

___ by(John P. Ahrens, Martha S. Heimbaugh

Coastal Engineering Research Center

DEPARTMENT OF THE ARMY,,Waterways Experiment Station, Corps of Engineers

PO Box 631, Vicksburg, Mississippi 39180-0631

DTICELECTE "-

JU 1 31988,,

May 1988 -.-1Final Report

Approved For Public Release; Distribution Unlimited

Prepared for US Army Engineer District, Detroit

PO Box 1027, Detroit, Michigan 48231-1027 .

and ,-

US Army Engineer District, Jacksonville ,PO Box 4970, Jacksonville, Florida 32232-0019

= ___l

Destroy this report when no longer needed. Do not returnit to the originator.

The findings in this report are not to be construed as an officialDepartment of the Army position unless so designated

by other authorized documents.

The contents of this report are not to be used foradvertising, publication, or promotional purposes.Citation of trade names does not constitute an %...

official endorsement or approval of the use ofsuch commercial products. -*'." .

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Technical Report CERC-88-5

6a NAME OF PERFORMING ORGANIZATION 6b OFFICE SYMBOL 7a NAME OF MONITORING ORGANIZATIONUSAEWES Coastal (if applicable) %.

Engineering Research r WESCW %

6c. AD3RESS (City, State. and ZIPCode) 7b ADDRESS (Cty, State, and ZIP Code) 0PO Box 631.,_-

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See reverse.

11 TITLE (Include Security Classification)

Approximate Upper Limit of Irregular Wave Runup on Riprap

12 PERSONAL AUTHOR(S)Ahrens, John P.; Heimbaugh, Martha S. S

13a TYPE OF REPORT 1b TIME COVERED 14 DATE OF REPORT (Year, Month, Day) 15 PAGE COUNT

Final report FROM TO May 1988 3316 SUPPLEMENTARY NOTATIONAvailable from National Technical Information Service, 5285 Port Royal Road, Springfield,

VA 22161.17 COSATI CODES 18 SUBJECT TERMS (Continue on reverse if necessary and identify by block number) % '%

FIELD GROUP SUB-GROUP- -- "rregular waves I Riprap, 0Prediction method Runup :Revetments

19 ABSTR T (Continue on reverse if necessary and identify by block number)

This report describes methods to calculate the approximate upper limit of runup on N Irriprap revetments caused by irregular wave action. A formula to predict the maximum runupis developed from one laboratory study and compared to data from a second study. Theformula is found to fit the data of both studies quite well. A slightly improved versionof the formula is then developed by combining the data from both studies. The improvedformula has little or no systematic error associated with structure slope, water depth, orwave conditions and is easy to use. Errors between predicted and observed elevations ofthe maximum runup had a root mean square value of approximately 12 percent. %

20 DSTR[BUTION AVAiLABILITY OF ABSTRACT 1I ABSTRACT SECURITY CLASS,FICATION %* ".tINCLASIF Fr I 'NLIMITED C-1 SAMP As Rpr C] DT'C USERS Unclassified "

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Unclassified

;I . %", .. , r .,., . ,C_ ., .-. -, . .-... r .- .. .. _... .. ...-.. .; , ,. " .v ".2 ,.,,".j..- .:¢ -; "'f WJ '- ;. "' .' ,' .'%f %" %:.,

UnclaspifiledSECURITY CLASSIFICAgIO OF THIS PAGE

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US Army Engineer District, Detroit; and

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P0 Box 1027Detroit, MI 48231-1027 and

P0 Box 4970Jacksonville, FL 32232-0019

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PREFACE

Summarized herein are important findings obtained from unpublished model

studies conducted by the Coastal Engineering Research Center (CERC) for the US

Army Engineer District, Detroit (NCE), and the US Army Engineer District,

Jacksonville (SAJ).

This report was prepared at the US Army Engineer Waterways Experiment

Station (WES). The data were compiled and analyzed by Mr. John P. Ahrens,

Oceanographer, and Ms. Martha S. Heimbaugh, Civil Engineer, both of CERC. The

data were collected by Messrs. Martin Titus and Louis Meyerly and Ms. Karen

Zirkel, Civil Engineering Technicians, CERC.

General supervision was provided by Dr. James R. Houston, Chief, CERC,

Mr. Charles C. Calhoun, Jr., Assistant Chief, CERC, Dr. Charles L. Vincent,

Program Manager, CERC, and Mr. C. E. Chatham, Jr., Chief, Wave Dynamics

Division, CERC.

COL Dwayne G. Lee, CE, was Commander and Director of WES during the 0

preparation and publication of this report. Dr. Robert W. Whalin was -'

Technical Director.

Accession For /. ..

NTIS GRA&I •DTIC TAB.

Unannounced El'e _

S. , ,,,,

Justfic- .

o.

stribution/SAvalability Codes

Distr Seialo/

Avail aror

1 Iis Specia

.. ... ,'. <',i

CONTENTS

Page

PREFACE ................................................................. 1

PART I: INTRODUCTION ................................................. 3

PART II: SOURCES OF DATA, TEST SETUPS, AND TEST CONDITIONS ............ 4..1

PART III: ANALYSIS OF DATA AND DEVELOPMENT OF RUNUP FORMULAS ........... 9

PART IV: SUMMIARY ...................................................... 24

PART V: CONCLUSIONS AND RECOMMENDATIONS .............................. 26 0

REFERENCES .............................................................. 27

APPENDIX A: SUMMARY OF JACKSONVILLE AND DETROIT DISTRICTTEST CONDITIONS ........................................... Al

20

. . . . . . . . ... . . . .. . . .. . . J

0_-

APPROXIMATE UPPER LIMIT OF IRREGULAR WAVE RUNUP ON RIPRAP

PART I: INTRODUCTION

I. In many locations riprap is the preferred type of shore protection

against wave attack. The two reasons for this are the low cost and nigh dura-

bility of stone, and the effectiveness of randomly placed stone, because of

its roughness and porosity, in dissipating wave energy and attenuating runup.

Because of these reasons, riprap has been the most studied type of revetment, --

and its performance is well documented.

2. Runup is one of the most important factors affecting the design of

revetments exposed to wave action. Generally, riprap revetments are designed

so that little or no runup exceeds the top of the protection. Because of the--

inherent complexity of natural wave trains and the interaction of incident

waves and the return flow of previous runup on a rough, porous slope, it is

difficult to predict the upper limit of wave uprush on riprap. This report

summarizes the most important results from two unpublished studies, and pre-

sents formulas to calculate the approximate limit of wave runup. Both studies

included laboratory tests of riprap exposed to irregular wave action. The

formulas can be used to compute the elevation to which protection needs to be S

extended to prevent exceedance by runup or to estimate the potential severity

of wave overtopping.

e

PART II: SOURCES OF DATA, TEST SETUPS, AND A.

TEST CONDITIONS

3. The sources of data for this report came from model studies conducted S

primarily for two US Army Corps of Engineer Districts, Detroit (NCE) and

Jacksonville (SAJ).

4. Model studies conducted for NCE were to investigate wave runup on

riprap-protected dredge disposal dikes in the Great Lakes. The scope of this S

study was expanded to include an unusually wide range of water depths at the

toe of the structure ds , zero-moment wave heights Hmo , and period of peak

energy density of the incident wave spectrum Tp By expanding the scope of

this study beyond the immediate problems occurring on the Great Lakes, the

opportunity to develop a general wave-runup prediction method was provided. A

summary of test conditions for both the NCE and SAJ studies is given in

Table 1, and data collected on both studies are tabulated in Appendix A.

Table 1

Summary of Test Conditions

Armor .Unit

Number 0Embankment ds Hmo P 50 Weight f

Study Slope cm cm cm g/cm Tests

NCE 1 on 2 11.9-38.5 4.9-17.5 1.02-4.74 189 2.65 40

SAJ 1 on 3 19.0-23.8 3.0-10.5 1.39-1.46 63.3-67.0 2.55 21

SAJ 1 on 4 19.0-23.8 3.2-10.3 1.39-1.49 56.9 2.55 8

5. A 1- on 2- (1 vertical:2 horizontal) structural slope was used in the

NCE study. Plywood roughened with glued on pea gravel was used as the sup- S

porting slope and simulated the impermeable core of the dike. This slope was

covered with a filter layer of Sioux Quartzite 5.5 cm thick. The range of

weight for this stone was from 6 to 41 g with a median weight of 18 g. Riprap

armor stone was placed by hand on top of the filter layer. Armor stones were

composed of Kimmswick Limestone with a range of weight from 144 to 233 g with 11 0..

a median weight of 189 g. The armor layer was 10 cm thick. Figure 1 shows aprofile view of the model structure, and Figure 2 shows a plan view of the

test setup. S

"4

'r rI

'77 .7.

150 -

PL YWOOD SUPPORT SLOPE ~lWITH PEA-GRA VEL ROUGHNESS

TOP OFARMORDIKE CROSS SECTIONTOP OFARMORDIMENSIONS IN MODEL UNITS

AND FIL TER LA YERS SCALE 1: 16, MODEL TO PROTOTYPEFOR MODEL TESTS

100 0a C

C-9'

RANGE OF'ft WATER LEVELS

50 C ' 1. ds 38.5

HORIZONTAL CONCRETE PLATFORM

PL YWOOD MA TTRESSWITH PEA G RAVEL CONCRETE]

01 1FRONTING 1 ON 15-')

9 8 7STATIONS, M

Figure 1. Profile view of structure tested during NCE studyJ

.GRAVEL WAVE ABSORBER BEACH WA VE TANK WA LL-

AUXILARY TEST CHANNEL LEGEND*WAVE GAGE

a RUNUP OBSERVER .

j-TOE OF ABSORBERGRAVEL WAVE ABSORBER BEACH.. ~ BEC

ETRITOST1 ON 15 FRONTING SLOPE 110 0.6M9> TRAINING WALLSMODE LDE

GVEWV * 3.75 M 290M '19 MTO WA VEGENERA TOR

ABSORBER BEACH *:*:::-*.;......

A VETA NKWA L L

9 8 7 6 5 4 3 2 1 0

WAVE TANK STATIONS. M

Figure 2. Plan view of test setup for NCE study

0

6. The model was constructed at a nominal 1:16 (model:prototype) undis- ,p.

torted Froude scale. The influence of scale effects at this large a scale was

considered to be small. To further reduce the possibility of scale effects,

the stone used in the filter layer was double the size required for geometri- S

cal similitude. Use of somewhat larger filter stones helps establish the :., .

proper flow-regime in the model filter layer when the revetment is exposed to

wave action; see Broderick and Ahrens (1982). Large-sized filter stone and a

1:16 scale were used in both the NCE and the SAJ studies to minimize the in- S

fluence of scale effects.

7. Tests for this study and the SAJ study were conducted in a 61-cm-wide

channel within the Coastal Engineering Research Center's (CERC's) 1.2- by 4.6-

by 42.7-m wave tank. Wave conditions were measured offshore by using three 0

parallel wire-resistance wave gages. Incident and reflected wave spectra were % be

resolved using the method of Goda and Suzuki (1976). Figure 2 shows a plan %

view of the wave tank setup for this study. Details relating to spectral wave

generation and the analysis of wave conditions in this wave tank are given by 0

Seelig (1980).

8. Maximum wave runup elevations were obtained by visual observations

made by an experienced observer, and quantified by using a point gage. The

observer stood immediately adjacent to the structure in a wave absorber chan- S

nel as shown in Figure 2. The duration of the runup observation was 256 sec, (0

corresponding to the data acquisition system's sampling interval for the wave

gages to obtain the wave information. The observer tried to measure the ex-

treme excursion of "green" water near the middle of the structure. Observa-

tions were not intended to measurc the upper limit of spray or splash. Prior

to using visual observations, some effort had been expended in trying to use

various types of continuous wave gages positioned just above the armor sur-

face, but runup elevations that were measured by the wave gages proved to be 0

unreliable. After some initial observations and discussion, two experienced

observers could obtain maximum runup elevations to within about a difference

of 3 percent or less of each other. Additional information about the NCE

study is given in Ahrens and Seelig (1980). 99. The SAJ study was conducted to investigate the stability of and wave

runup on riprap to be used to protect Herbert Hoover Dike on Lake Okeechobee,

Fiorida. Two structural slopes wcre tested during this study, 1 on 4 and 1 on

3. Figure 3 shows a profile view of the 1-on-4 slope tested. Figure 4 shows

6 %

V ~pp cJ'-$ '. -

PROTOTYPE DISTANCE FROM TOE OF DIKE. M55 50 45 40 35 30 25 20 15 10 5 0

2.0 NOTE VERTICAL DISTORTIONON10600

105

UNPROTECTED DIKEgoz ROUGHNESS ADDED 04z

HIGH WATER LEVEL =5.3 M 0 30 20 &~0_Zz

45LOW WATER LEVE L z4,6M A,0

< CONCRETE SLOPE> 30 ON 712

CONCRETE PLATFOHM;;. STEEL TOE0

CLAKE BOTTOM---. At

£0 2 5 20 1 5 1.0 0.5 0

MODEL, M

Figure 3. Profile view of the 1 on 4 structure tested during SAJ study

PROTOTYPE DISTANCE FROM TOE OF DIKE. M -

328 246 164 04

-0.368

0.O30 '

7z

-0.24o6

4 50

0.124

...... - 0.06

2 0

24 0 24.2 244 24.6 24.8 250 25.2 254 PLAB STATION. M

Figure 14. Profile view of cut and fill used to construct a 1 on 3dike embankment slope for SAJ study

%s

x" R 1:6

the cut and fill strategy used to construct a l-on-3, riprap-protected slope .Q%"-

on the embankment. Figure 5 shows a profile view of the 1-on-3 slope tested

and the location of the wave gages. Figure 6 shows a plan view of the test

setup. .

10. Since the armor stone planned to protect the dike was marine lime-

stone to be quarried in Florida, this type of stone was used in the model

tests. This stone has a density of 2.55 g/cm3 . The armor stone had a median ,6

weight which ranged from about 57 to 67 g during the course of the study (see

Table 1). Filter stone had a median weight of about 12 g and a layer thick-

ness of 2.5 cm. Additional details relating to test procedures and setup are

given in Ahrens and Zirkle (1982).

WAVE1o5 GAGES "

< 5 RIPRAP SECTION 1-1STI LL-WATER ELEVATION =5. 3 M 7'

'

4 45

_0I ON 12SLOPE CONCRETEPLATFORM

5S

836 24 72 0 12 24 36 48 60

PROTOTYPE DISTANCE FROM TOE OF DIKE, M

Figure 5. Profile view of 1-on-3, riprap-protected slopeand offshore wave gages

WALL OF WAVE TANK- "

GRAVEL ABSORBER BEACH TO WAVEGENERATOR, ig.29M

0.61 M

GRAVEL ABSORBER BEACH TALLSN

SRCUE0 00 0.61M

GRAVEL AB :SORBER BEACH WALL OF WAVE TANK-~

1 11 13 12 1 i 10 9 8 7 6 5 4 3 2 1 0

MODEL DISTANCE, M

0 DENOTES W5AVE GAGE LOCATION

Figure 6. Plan view of SAJ test setup

.

8

'".•-A

PART III: ANALYSIS OF DATA AND DEVELOPMENT 1OF RUNUP FORMULAS

11. The biggest difficulty with analyzing the data from the NCE study

was making accurate estimates of the zero-moment wave height Hm at the toe

of the structure. In the NCE study the wave heights were measured offshore in If N

a water depth 25 cm greater than at the toe of the structure. Due to shoaling

and breaking, a wide range of offshore wave conditions can yield the same

zero-moment wave height in shallow water. Therefore, the offshore wave height

is not as useful as the wave height at the toe of the riprap structure. The

wave conditions near the structure correlate well with the runup and often can

be estimated accurately by depth-limited considerations. Originally in the

NCE study the wave heights at the toe were estimated by using the method of

Goda (1975) which accounts for shoaling and breaking of irregular waves.

However, after scrutinizing the information generated by Goda's model, it was 'observed that for some situations the method yielded values of Hmo/ds

greater than 0.8 which is higher than has been observed in any of CERC's wave

tank calibration tests. Because of this limitation, it was decided to try and

develop another method to estimate Hmo at the toe of the structure.

12. Several methods were tested to account for the wave shoaling and

breaking between the offshore gages and the toe of the structure. The method

that worked best was a hybrid method which combined linear-wave shoaling with %-%

the relation given by Hughes (1984) as I P.%

[H [HH .mo°m ( 1) .7-.

whereL = Airy wave length calculated at those depths for the period of

peak energy density Tp I-

I and 0 inshore and offshore water depths, respectively

From wave-tank calibration tests it has been found that the approximate

limiting value for the zero-moment wave height is given by

o = 0.10 tanh (2) ml

... .." ,. .. . -,.. -, .-. ,

,, , , ", -.,,.,. ., ". -. " ".',.'..',.' ..'.... - ',.',."...;., .-, .... - ','-, ', - ", "-.'-', .- ,, , .' ." ';. ,- ... ,, - -- , -, - "-...'p"I ,- ,.

* -a - - -- -- - -.. Ka~~.-p .

where d is the water depth at or near the structure toe. The procedure

used to calculate the zero-moment wave height at the toe of the structure was

to calculate the value by using both linear shoaling and Equation 1 and then

taking the average of the two estimates. If the average exceeded the maximum S

value suggested by Equation 2, then that limiting value was used.

13. The ability of the above procedure to estimate Hmo in shallow

water is demonstrated in Figure 7 using wave-tank calibration data collected

170_ -

16

12 %

2

EI 10PERFECT CORRELA TION

_ 9 AND PREDICTION LINE

8 h0 .,

0 7

>6

5

4

3

2

0 2 4 6 8 10 12 14 16 18

OBSERVED, HMn, CM

Figure 7. Predicted versus observed Hmo for tank calibration data

prior to a study of wave overtopping of a seawall (Ahrens, Heimbaugh, and

Davidson 1986). This calibration data included a wide range of wave periods 0

and an extensive amount of wave shoaling and breaking for many conditions .

between the offshore wave gages and an inshore gage located in front of a wave -a

absorber beach. For the calibration data shown in Figure 7, the offshore

water depth ranged from 61.9 to 66.2 cm; the inshore water depth ranged from 422.9 to 27.2 cm; the offshore Hmo ranged from 1.6 to 21.5 cm; the inshore

Hmo ranged from 1.5 to 16.4 cm; and the period of peak energy density ranged

from 1.75 to 3.00 sec. The hybrid method given above appears to work well for

CERC calibration data because linear shoaling tends to overestimate inshore

10

.p I V V V %0 d 1%I V V V $1:

Hmo while Equation 1 tends to underestimate inshore Hmo , and Equation 2

provides a logical limiting value on Hmo . Based on the success of the

hybrid model in predicting known data, the model was applied to the NCE study

to estimate Hmo at the toe of the structure. Subsequent analysis of pre- 0

dicted and observed maximum runup elevations suggests that the hybrid method

makes good estimates of Hmo in shallow water.

14. The wide range of water depths tested in the NCE study had been

included partly to investigate the influence of water depth on wave runup. S

This concern is strongly reflected in the discussion of wave runup in the -.

Shore Protection Manual (1984). From previous studies it was known that runup

would be strongly influenced by the surf condition on the structures (Ahrens

and McCartney 1975), but it also seemed logical that the maximum runup would _

be dependent on the shape of the wave-height distribution and nonlinear

effects. The last two influences would be very dependent on the water depth

at the toe of the structure and the wave periods. To investigate the influ-

ence of surf characteristics on runup, the surf parameter for irregular waves .

is defined as

_ tan e3

where

tan e = tangent of the angle 0 between the structure slope andthe horizontal

Lo: gT2/27 = the deep-water wave length-0

g = the acceleration of gravity

When a runup model was formulated using the surf parameter, it was found to

contain some systematic errors which could be related to the relative wave •

height Hmo/ds . However, when a surf parameter was defined by using the

local wave length, a model could be formulated which did not include

systematic errors related to the relative wave height. The modified surf

parameter L is defined

t I/2 (4) ',.

(%0

L11

where

Lp = the Airy wave length calculated by using the water depth at the toeof the structure

ds : =the period of peak energy density, Tp

Runup is computed using the formula

Rmax aS (5)

H - 1.0 + bS

where

Rmax = elevation of maximum wave runup

S = surf parameter defined by either Equation 3 or 4 depending on 0the prediction method selected

a and b = dimensionless runup coefficients determined by regressionanalysis

Equation 5 has a form which is especially convenient and logical for predict-

ing wave runup on rough porous slopes as shown by Ahrens and McCartney (1975),

and, subsequently, by Seelig (1980) and US Army Corps of Engineers (1985). For ,-34

the NCE data, using the modified surf parameter defined by Equation 4, the

coefficients in Equation 5 were found to be a = 1.062 and b = 0.153 •

15. By using the coefficients given above, Equation 5 does a good job of

predicting Rmax for both the NCE and SAJ studies. Figure 8 shows the

predicted values of Rmax versus the observed values of Rmax by using dif-

ferent symbols to identify the two studies. The good fit to the NCE data is _

gratifying considering the problem related to estimating the Hm at the toe

of the structure. The good fit to the SAJ data is somewhat surprising consid-

ering that the thickness of the armor layer for the SAJ test was considerably

thinner than the armor layer used in the NCE tests. In addition, the struc- 0

tural slopes tested for SAJ were 1 on 3 and 1 on 4 compared with a slope of

I on 2 for the NCE tests. These findings indicate that the maximum runup may

not be too sensitive to the armor-layer thickness, and that the surf parameter

properly accounts for differences in the structural slopes. It should also be

recalled that the runup coefficients were obtained from the NCE study so that

the SAJ data provide a rather severe test for the runup model's predictive

ability.

16. By lumping the data from the two studies together, somewhat better

12

40 -DE

35 - -

o 20 -

PERFECT CORRELA TION'5*

0AND PREDICTION LINE

S25

o 2W

EIx a ohN ad A tde

1-

C) V.'10 '4 ,

aan b n caSAJ STUDY

0 10 20 30 40

Rma OBSERVED, CM

Figure 8. Rma predicted, using coefficients from NCE data, versus

kmax observed, both NCE and SAJ studies

a and b runup coefficients can be determined. By using regression analysis

on the combined data set, the improved coefficients are a = 1.154 and

b 0.202 . A new scatter plot comparing predicted and observed values was ...

prepared with the above coefficients, and Equation 5 was used to calculate the

predicted values of maximum runup. The new scatter plot (see Figure 9) shows

that the change in the runup coefficients caused very little change over the

scatter plot shown in Figure 8. Even though there was little change in the 0

scatter plot, the limiting value for R/Hmo dropped from 6.9 to 5.7; the

limiting value for Equation 5 is given by the ratio of a to b .

17. To investigate systematic error in predicting the maximum runup and

to identify possible ways to improve the prediction method based on the modi- @

fied surf parameter L , a series of error plots was made. In these plots,

the percent error %E in predicting the maximum runup is defined as

13 ,

22

. . . . - , i , . - -. .. ,% .,. . - .,= . . , . - , ,.) . . .d ? - .i' p' " s ." - .

WWLIJl&"%- l~..)"*k 777 .7 K T7 -7 -. 1- 7.17-.

40 t.

i ~35--I

PERFECT CORRELA TION 030 - AND PREDICTION LINE

S25 -c)a

O 20

r 15 --. J%

10

LEGEND~NCE STUDY

5 SAJ STUDYTaL

000 I 'j. "'

0 10 20 30 40

R,., OBSERVED, CM

Figure 9. Rmax predicted, using coefficients from both NCE and SAJ data,versus Rmax observed for NCE and SAJ data

(R ma) - (R a)o_ 0 (6)

00

where the subscripts p and o indicate predicted and observed, respec- ',

tively. The percent error is plotted versus ,L ds/Lp , Hmo/Lp

Hmo/ds , r(bar)/d 5 0 , and II, and cot 0 in Figute 10a, b, c, d, e, f, g,

and h, respectively, where r is the average armor-layer thickness and II

is Goda's (1983) nonlinear parameter defined for irregular waves %

HmoLHP (7) ,

tan h

The larger the value of II , the more nonlinear the waves with

14

HII-' mo- for deep-water conditions

and P

H L2iI_.. mop Ursell's parameter for shallow-water wave conditions

(2nd5)

Figure 10 shows little or no systematic error for the prediction method based

on Lp " Figure 10 also shows that the percent error ranges from -33 to

+44 percent, but that for most tests the error is within about ±10 percent.

18. Approximately 25 percent of the tests had a percent error greater

than ±10 percent. Because of this, it may be useful in some critical or life-

threatening situations to use a value of Rmax greater than the expected 0

value produced by Equation 5 when using the recommended coefficients. Fig-

ure 11 shows how the percent error which has been normalized by the standard

deviation of the data set a seems to have the shape of a normal distribu-

tion. To test this hypothesis, namely, that the percent error has a normal 0

distribution, a Kolmogorov-Smirnov (K&S) test was performed. This test is

used to determine whether or not the data deviate a statistically significant

amount from the assumed normal distribution model (Cornell and Benjamin 1970).

19. The K&S test indicates that the normal distribution for error should S

be accepted at the 20-percent significance level. A 20-percent level is a

more severe criterion than a 10-percent level as it indicates there is a

20-percent chance of rejecting a model which is in fact true, a Type I error.

The 20-percent significance level is the most severe criterion commonly tabu- •

lated for the K&S tests. Recognizing that errors have a normal distribution

provides an easy way to give more conservative estimates of Rmax than is

provided by a regression equation. Generally, about half the errors are above

the regression curve and about half are below, so the curve represents a 50 S

percent exceedance level. In Figure 12 a more cons.ervative trend is shown

above the regression curve. The conservative curve was generated by increas-

ing the runup regression coefficient a by two standard deviations of the

percent error, i.e.,

ac (conservative a) : a (1 + 2a) : 1.143 (1.0 + 2 x 0.1286) 1.437

The value of the runup coefficient b remains the same, i.e., b : 0.202

15

50 %

40 F , ,,I

4 0 % ,

3 0 U 0

00a:0

0

0 10

==o 6 m

• LEGEND 1

-30 NCE STUDYSAJ STUDY

23 4 tv

SURF PAR AM ETER US IN G, Lp ++

a. Percent error Rma versus surf parameter using Lp40 -5

2 30 ST D

40 w

50

20 -

.10 a NC TD

00 1U5 U

.116

IUk ..

V ~ IEE, **-. E-m

m m ,0.t

:• =U

_ . , .. .U

-20 + .>:,

I10 m I I'

LEGENDD11F ARM SF0, I"

b. Percent error Rma versus standard surf parameter,

Figure 10. Percent error in predicting Rmax (Sheet 1 of' 4) 0

50 I I I I

40

30 U

z

0

0 U'4 U

• LEGEND

•NCE STUDYow. ,0 SAJ STUDY

o 0 * * I I I-',

-40

0.02 0.04 006 0.08 0.10 0.12 0.14 0.16 0.18 0.20 %

RELATIVE DEPTH. ds/Lv ..

c. Percent error R,, versus relative depth, d /L

ax s p %r J.

5...,,.-T

40 ,:..

30a

10 •

SO I I . ,

40a

%.

: %,30

o2 . _ a' . •,.. ;

10 so

Uo • ., :: 0

• ,.GENO- -..... ,-20

LEGEND-30 M NCE STUDY

* C SAJ STUDY 0

-40 I II

001 002 003 004 0.05 0.06 007

WAVE STEEPNESS. Hro/LP

d. Percent error Rma versus steepness, Hmo/Lp %

Figure 10. (Sheet 2 of 4)

17

50 1,+",+

10 I I ,. ..

40 .

• :, 0.,.:

300

-20

U %

+d ,o4.b.10 a-~20o " - 1'" -"-..-

LEGEND-30 - Y - STUDY

0.1 02 0.3 0.4 0.5 0.6 07 +RELATIVE WAVE HEIGHT. Hmo/ds

e. Percent error R max versus wave height, H mo/d s ' "

- * U .;+

-20

20

LEGENDD <,;'

30 * NEESTUDY

-- 30 u SAJ *U SA, STUD.Y

I I I I

. Percent error Rmax versus w-aver hihtss H ar/50Id.-

00

h0

30 U

1E

-4

0 .9

-- MO L Y THICKNSS, ( /d.-

Pecn ero R essaro-ae tikesrbr/-20

50U

00 0 0 I1 01 1 1 3 2

40 , 4

30-

-20.

LEGEND .,

30 NCE STUDY0

• • SAJ STUDY

%-.

0 0 4 028 1,2 1 6 2.0 2 4 2 8 3 2

GODA'S NONLINEAR PARAMETER. II % P

9. Perent error Rax versus Godas nonlinear parameter, II

20

10 0

o 0

U U

EGEN

-30 ,-N

S E ST D

3 SAJ STUDY

04 08 12 1 .4 25 21/

GOA ONIER AAET• ,'.4

h.Percent error Rma versus strunonliea slpct a I

n ;.. ..

Figure~~4' 10 Set f4

19 %

iz

-3 I NC T Y

U m * SASTD

2 3 NCE STUD

Fiur 1. Shet4 f )

STRUCTRE SLOE CUT :,,,Js: ' ,4 ( (- , ,'*- -, * *. , ,-%"- .- . ., .. ) ".v ... , . .v.., .. 4...'--, *'.

-- ---------

09 \J

06

P6

04 NORMAL tIsrRIBurIoNT CURVE

02 LEGEND

04

NORMALIZED ERCLNT ERROR

Figure 11. Normal distribution curve for model datap

CONSERVATV REND-,

2 -.00,

LEGENDEXPECTED VALUES U0686 )~

%

MODIFIED 3,RF PARAMETER

Figure 12. Expected value and more conservative trendcurves for model

* P

20

..........

It can be seen in Figure 12 that the new conservative runup curve provides a

envelope for the observed data. The conservative curve would be expected to

exceed about 97.7 percent of the data. An exceedance level of 97.7 percent is

obtained from a standard normal distribution table for a value two standard S

deviations greater than the mean. Figure 12 helps confirm the method of'%. . % .'

choosing an envelope curve by showing only one observed value above the con-

servative curve. This is approximately what would be expected for a normal

distribution with a sample size of 69. Other curves used to predict maximum S

runup could be constructed which would be more or less conservative than the

example just provided. The degree of conservatism would be evaluated on the %

basis of the risk posed by waves overtopping the revetment.

20. Since the standard surf parameter has been frequently used to pre-

dict wave runup, it is useful to provide a prediction formula based on that .s.

method to allow comparison to earlier studies. Using Equation 3 to define the

surf parameter in Equation 5, the runup coefficients were determined for the

combined NCE and SAJ data sets as a = 1.022 and b = 0.247 . Figure 13

shows the predicted and observed values of Rmax/Hmo versus the standard surf

parameter. It can be seen that the predicted values follow the trend of the

observed data very well. Using the same method to evaluate errors as was used

%

PLUNGING REG ION I(LARGE NAVES SURGING REGION *

PLUNGE DIRECTL Y TRANSITION (SURGING OR STANDING WA VES I%ON RIPRAP, REGION AGAINST STRUCTURE,

1..

I (AND

Figure 13. Comparison of the prediction of Rmax using ,

21

, " " ,- " - ,!- •, ' A " -" ' " !a - ..- . .

[- . 5 5 . - - - - - . - .. -

for the Equation 4 model, it was found that there were no systematic errors %.d,

associated with the model which used the standard surf parameter. Figure 14

shows that the standarized percent errors for this model also seem to have a

normal distribution. Performing the K&S test once again showed that these

data were also normal at the 20-percent significance level and thus, could be

assumed to have a normal distribution. Figure 15 shows the more conservative

curve which could be expected to envelop 97.7 percent of the data and repre-

sents an increase of two standard deviations over the expected mean curve.

The coefficients for this conservative curve are a = 1.285 and b = 0.247'

Once again, this curve is only one of many more conservative curves that could

be constructed depending upon the design situation. Using the runup coeffi-

cients with the standard surf parameter would be an easy way to estimate Rmax

using a small calculator. The more accurate model would require the calcula-

tion of L for use in the modified surf parameter which would be morep

difficult than calculating the deep-water wave length for the standard surf

parameter.

% "

I f NORMAt D OSTRB1I~T/O

.'-. ."s

CURVE

,,>

LEGEND

SING

.'2 -,2

Figure 14. Normal distribution curve for model data

22

P,, , ,. III,% , , . . . . ... .. ,,...

3.5 p.

3 0 -T R E N D - - ,

25 -

2.0~ ~~ ~ ~ -0-XETDVLE

CONSERVATIVEN

1 5

00

~ 2.0

E or

771..

PART IV: SUMMARY

21. All the equations presented within this report were developed from

two unpublished laboratory studies. These equations provide an easy way to 0

calculate the Riax of irregular waves on riprap-protected embankments.

Table 2 summarizes the important information about two runup equations which

Table 2

Summarized Information for Maximum Runup Formula, Equation 5

Surf a ,StandardWave Parameter Deviation of

Formula Length Used in Runup Variance PercentCategory Used Equation 5 Coefficients Explained Error

Recommended Lp tL (Equation 4) a = 1.154 R2 0.843 12.3

b =0.202

20Alternative Lo (Equation 3) a = 1.022 R 0.817 12.9

b =0.247

represent the most accurate existing method to determine the approximate upper 0

limit of wave uprush on a riprap revetment. The two equations are presented

as a recommended method and an alternate method to compute Rmax . The recom-

mended method has little or no systematic error such as might be associated

with the influence of water depth or nonlinear effects and is slightly more •

accurate than the alternate method. The alternative method is easier to cal-

culate and can serve as a "rule of thumb" estimate. In Table 2 the runup co-

efficients are to be used in the general runup equation (Equation 5) by using

either the standard or modified surf parameter as noted. A method was devel-

oped which provides a reasonable way to make the predicted values of Rmax

more conservative. It was found that the errors in predicting Rmax have a

normal distribution, and this fact was used to adjust the runup coefficient

a so that any predetermined exceedance level for Rmax could be achieved.

For example, by increasing the coefficient a by two standard deviations of

the percent error gives Rmax predictions which would be expected to exceed

97.7 percent of the observed values of Rmax * This technique produces a

logical envelope for the data. Table 2 lists the standard deviation a of

24

Y"." " ' :

the percent error which was used in this method and the correlation squared - .

which is the variance explained by the regression equation used to predict ,r

l "S

w. "w

SA-

S

* %-

** ",..

S. '.'p

1%

PART V: CONCLUSIONS AND RECOMMENDATIONS

22. Visual observations of the maximum runup of irregular waves on rip-

rap give reliable values of the maximum elevation of wave uprush. For the two S

studies considered the time interval of observation was 256 sec. It is diffi-

cult for an observer to maintain adequate concentration on the runup process

for intervals longer than 256 sec. This interval provides between 100 and ke

250 runup events at the wave periods tested. Future tests will consider using 0

photogrametric methods to measure irregular wave runup on riprap to increase

the time interval of observation and to obtain the entire runup distribution !

rather than just the maximum value.

23. The runup equations presented appear to be the best available to es- 0

timate the approximate upper limit of irregular wave uprush on riprap revet-

ments. Further tests are planned which should produce improved methods to

determine the runup characteristics of irregular waves on rough and porous

slopes.

"- %

26S

714

NS

REFERENCES

Ahrens, J. P., and McCartney, B. L. 1975 (Jun). "Wave Period Effect on theStability of Riprap," Proceedings Civil Engineering in the Oceans III,American Society of Civil Engineers, Newark, Delaware, pp 1019-1034.

Ahrens, J. P., and Seelig, W. N. (May) 1980. "Wave Runup on a RiprapProtected Dike," unpublished report to the Detroit District, Detroit, %Michigan.

Ahrens, J. P., and Zirkle, K. P. (Jun) 1982. "Riprap Stability Model Tests,"unpublished report to the Jacksonville District, Jacksonville, Florida.

Ahrens, J. P., Heimbaugh, M. S., and Davidson, D. D. 1986. "Irregular WaveOvertopping of Seawall/Revetment Configurations, Roughans Point, Massa-chusetts," Technical Report CERC-86-7, US Army Engineer Waterways ExperimentStation, Vicksburg, Mississippi.

Broderick, L. L., and Ahrens, J. P. 1982 (Aug). "Riprap Stability Scale -Effects," Technical Report CERC-82-3, Ft. Belvoir, Virginia.

Cornell, C. A., and Benjamin, J. R. 1970. Probability, Statistics, and ODecision for Civil Engineers, McGraw-Hill, New York.

Goda, Y. 1975. "Irregular Wave Deformation in the Surf Zone," CoastalEngineering in Japan, Vol 18, pp 13-26.

Goda, Y. 1983 (Sep). "A Unified Nonlinearity Parameter of Water Waves,"Report of the Port and Harbor Research Institute, Vol 22, No. 3, pP 3-30,Yokosuka, Japan.

Goda, Y., and Suzuki, Y. 1976. "Estimation of Incident and Reflected Wavesin Random Wave Experiments," Procceedings of the Fifteenth InternationalConference on Coastal Engineering, Hawaii.

Hughes, S. A. 1984 (Dec). "The TMA Shallow-Water Spectrum Description andApplication," Technical Report CERC-84-7, US Army Engineer WaterwaysExperiment Station, Vicksburg, Mississippi.

Seelig, W. N. 1980 (Jun). "Two-dim .nsional Tests of Wave Transmission andReflection Characteristics of Laboratory Breakwaters," Technical ReportCERC-80-1, US Army Engineer Waterways Experiment Station, Vicksburg,Mississippi.

Shore Protection Manual. 1984. 4th ed. 2 vols, US Army Engineer WaterwaysExperiment Station, Vicksburg, Miss.Coastal Engineering Research Center, US S

Government Printing Office, Wahington, DC.

US Army Corps of Engineers. 1985 (Dec). "Estimating Irregular Wave RunupHeights on Rough Slopes, Computer Program: Wavrunup (MACE-14)," CERC CETN-I- _"'37, US Army Engineer Waterways Experiment Station, Vicksburg, Mississippi.

27

Se4

*** %

.., I~~ P . ~ 1U'~.'*~~' ;$' ' UUS- U& .

kk

'. . J,.p

0.

0

APPENDIX A

SUMMARY OF JACKSONVILLE AND DETROIT DISTRICT TEST CONDITIONS "'%.

I%

-p

•Si

-- sp .+. . iP ip i¢ +- .r w ,w w ," -.w+ o- , "+ + r " " +- . .- l+ ,."+, . ,," .- - .- i{" " +' ,+.. ° ... . - - % o o+ - oi i" .

+r~ , .... +• -+-. .. , ', .. . .. _,+".. . . . .. ,- ++,,-- . . ... ... ..

Table Al m-V.eo

Summary of Jacksonville (SAJ) and Detroit District (NCE) Test Conditions

offshore wave offshore inshore estimate inshore offshore W614. a reor r or Bedlan filter typical typill

degth perio4 Moo depth inshore ae structur frontion armor ut ldyer tigqht StoRn filter doeoloc. diam. armorgot

Tp ds lImo leotth Rit o slop sopf .#lob meight thickness filter unpt layer armor filter ribar-

study Test Lp cot Cot 656 1r ribar) stoe ejfht thickness stone stone over

dusign NO. Co SIC cm c. ce co co theta alpha qr qrlco3 ce Iqr qrIC03 ce Ce co (153

Detroit 1 36.111 2.753 5.177 11.911 4,945 294,171 11.392 2.3 15.0 17,16 2.65 IN." 111.1 2.63 5.51 4.13 1.89 2.42

Detroit 3.11 1.333 6.797 11.101 6.394 139.919 9.392 2.1 13.10 87.14 2.65 13.1 16.3 2.63 5.31 4.13 1.19 2.42Derot U.",1 1.:21 .7.48 ll.111 1.41 161.704 1. 58 2.tO 11.00 :97:: 1.13 1.1 19. 1 2.5 1514 .13 1 17 2-.12

Detroit 4 36.01 3.621 10.214 11.911 7.544 41.311 24.413 2.36 13.36 187.N 2.63 13.36 ILK 2.63 ..11 4.13 1.9 2.42

Detroit 36 .111 2.332 4.336 11.901 7.334 213.119 14.897 2.36 13.0 187.1 126 11.36 11.6 2.63 5.31 4.13 1. 2.42Detroit 6 34.1 .694 13.171 11.931 7.232 176.742 2.433 2.33 13.36 i7.3 2.63 13.38 18.36 2.65 5.53 4.13 1.9 2.42

Detroit 7 43.5N 3.262 5.251 21.511 5.3 459.122 12.402 2.1 15.36 187.11 2.65 13.0 18.0 2.65 5.38 4.13 1.69 2.42

Detroit 45.50 1.62 7.424 20.510 6.797 132.112 12.192 2.11 15.0 187.01 2.62 13.11 16.36 2.65 5.3S 4.13 1.69 2.42Detroit 9 43.383 1.371 7.761 23.386 7.232 213.219 13.386 2.36 13.36 117.36 2.63 16.36 16.36 2.63 3.38 4.13 1.69 2.42Detroit 13 43.310 1.534 9.13N 21.386 6.644 267.36 17.793 2.36 13.36 167.36 2.63 14.36 16.6 2.63 3.3 I 4.13 1.6N 2.42Detroit 11 43.388 3.37 9.656 28.581 9.564 491.3 28.38 2.36 15.0 197.36 2.63 11.6 18. 2.63 3.58 4.13 1.69 2.42Detroit 12 4M.3 2.32 1 5.710 21.54 10.239 279.32 17.22 2.19 15.31 197.11 2.63 11.3 16.0 2.65 5.5 4.13 1.69 2.42Detroit 13 533 2.632 13.402 2I.3 12.274 273.342 22.448 2.08 13.36 167.36 2.63 16.70 : 6. 2.63 3.51 4.13 1.61 2.42Detroit 14 45.510 1.684 11.777 20.510 11.891 227.174 22.293 2.11 13.3 197.08 2.63 1.6 16.: 2.63 5.38 4.13 1.89 2.42Detroit 13 3.5111 3.232 3.747 21.511 3.331 233426 16.497 2.11 I3.M 187.36 2.65 11.36 18.36 2.63 5.58 4.13 1.09 2.42

Detroit 16 33.381 1.143 3.269 28.381 7.638 163.363 14.387 2.33 13.36 167.36 2.63 13.36 16.36 2.63 3.38 4.13 1.39 2.42Detroit 17 3.301 1.368 12.877 29.51 11.413 243.684 19.93 2.06 13.11 187.31 2.63 13.36 19.96 2.65 5.58 4.13 1.09 2.42Detroit 1 53.381 1.541 13.1 4 20.511 14.331 387.721 33.393 2.11 13.36 167.11 7.65 11.3 16.36 2.6 5.58 4.13 1.89 2.42Detroit 14 53.581 1.62 17.77 28.591 13.631 231.62 26.14 2.3 13.36 107.36 2.65 11.8 18.3 2.65 5.5 4.13 1.8 2.42Detroit 23 53.31 2.17 14.632 29.511 14.114 347.337 26.433 2.36 15.30 107.11 2.63 1.36 19.89 2.63 5.58 4.13 1.89 2.42Detroit 21 53.511 4.740 12.687 28.501 12.339 73.372 33.395 2.30 15.0 187.36 2.63 1.3 19.14 2.63 3.5 4.13 1.69 2.42Detroit 22 53.581 3.203 17.737 29.511 15.421 24.679 26.194 2.1 13.36 187.18 2.65 11.0 18.3 2.63 5.5 4.13 1.89 2.42Detroit 23 53.251 3.122 3.926 33.2 1 .743 34.93 19.19 2.3 15.36 187.N6 2.63 1.36 16.36 2.65 3.51 4.13 1."9 2.42Detroit 24 538.299 .243 3.133 33.29 7.649 1971.63 13.612 2.16 13.06 167.11 2.63 1.10 16.30 2.63 5.51 4.13 1.69 2.42Detroit 2 538.2 0 1.33 7 1.331 33.2 0 .779 25.39 17.697 2.36 13.30 187.36 2.63 11.0 10.36 2.63 5.51 4.13 1.61 2.42Detroit 26 50.299 2.17 14.77 33.29 14.374 373.335 2.7 4 2.3 13.36 187.36 2.63 1.3 18.0 2.63 5.58 4.13 1.19 2.42Detroit 27 38.299 1.623 16.419 33.299 17.486 267.762 31.364 2.11 13.11 187.11 2.65 I6.M 19.1 2.63 3.38 4.17 1.09 2.62 1Detroit 25 38.294 3.241 1.763 33.299 9.436 372.3 27.794 2.36 15.3 187.11 2.635 1.M 18.3 2.65 5.58 4.13 1.89 2.42Detroit 29 50.299 4.746 13.373 33.29 14.234 347.677 37.796 2.1 15.36 107.96 2.65 1.10 18.88 2.63 3.58 4.13 1.81 2.42Detroit 27 50.29 2.1 1I.419 33.291 18.742 311.041 27.794 2.11 13.1 107.11 2.63 11.10 1.6 2.63 3.3 4.13 1.89 2.42Detroit 31 63.8 .733 6.23982. 33.2" 9.4 72316.442 17.62 2.33 15.11 187.1 2.63 JI.3 18.3 2.63 3.58 4.13 1.89 2.42Detroit 32 63.56 1.241 4.226 33.211 1.704 22.26 17.212 2.18 15.0 187.10 2.65 1.M 18.36 2.65 3.31 4.13 1.89 2.42Detroit 33 4.2" 2.19 8.88 39.3 7.763 28.49 13.1 6 2.271..9 187.5 2.63 13.36 12.9J 2.63 3.65 4,13 1.69 2.42 0Detroit 34 63.514 1.16 4.671 38.511 9.249 323.417 23.43 2.1 13.30 167.0 2.65 11.30 16.36 2.65 5.58 4.13 1.69 2.42 ' % .'-

Detroit 32 63.35H 1.34 12.946 30.51 12.281 239.032 22.81 2.33 13.36 187.N0 2.65 11.36 18.36 2.63 5.33 4.13 1.69 2.42 r "p.Detroit 36 63.56 4.74 14.381 38.56 14.831 963.331 33.96 2.83 1.N 187.11 2.63 11.0 16.3 2.63 5.5 4.13 1.69 2.42

Detroit 37 63.3WM 1.620 14.931 38.511 1.211 23.441 24.68 2.33 13.3 0 67.11 2.63 11.0 16.11 2.63 3.51 4.13 1.69 2.42Detroit 38 63.3 2.813 5 .92 38.3SI 9.721 26.574 22.18 2.11 13.N 187.18 2.65 11.36 19.06 2.65 3.58 4.13 1.81 2.42Detroit 39 34.11 1.062 6.63 11. 1 . 01 91.13 9.611 2.16 15.0 187.N 2.65 1.M 18.3 2.63 5.38 4.13 1.89 2.42Detroit 43 34.51 3.461 1.93 11.4 1 7.323 371.434 19.11 2.11 15.36 167.N 2.65 11.14 1.3 2.63 5.33 4.13 1.31 2.42

DrJ 3 34.312 1.49 44 23.662 7.44 213.16 9.611 4.11 6 36.1.1 2.65 .24 11.63 2.65 2.51 2.92 1.64 1.1Det 4 oi.12 1.446 .6 23.812 3.386 232.66 3.363 4.11 56.11 2.33 3.24 11.81 2.63 2.35 2.82 1.64 1.1354J 3 43.112 1.42 N6 23.812 6.153 199.736 .81 4.11 48 36.11 2.55 3.24 11.61 2,65 2.58 2.82 1.64 1.13 .SAJ 9 41.312 1.4N NA 23.612 3.181 212.61 5.585 4.10 N6 56.11 2.55 3.24 11.68 2.63 2.51 2.62 1.64 1.13 .SAJ 1 44.112 1.49 4A 1.82 l6.2153 177.70 19.497 4.31 38 56.1 2.5 3.34 11.63 2.65 2.5 2.82 1.64 1.21 6%. .

SAJ 11 44.051 1.420 M6 19.13 9.431 11.411 11.366 4.36 08 56.11 2.53 3.32 11.6# 2.65 2.50 2.82 1.64 1.18

SAJ 12 44.353 1.420 46 19.150 9.115 101.3M 8.392 4.36 %A 36.1N 2.3 3.13 11.61 2.63 2.5 2.62 1.64 111

Ski 03 44.158 1.470 94 19.358 6.311 181.41 7.211 4.0 M3 56.91 2.55 3.19 11.64 ?63 2.51 2.02 1.64 1.11SAJ 23 46.112 1.458 PA 23.812 1.123 214.70 13.516 26 0 66.6 t 3 4.43 11.66 2.63 2.5 2.96 L.64 1-'i

SM 26 41.112 1.4611 M 23.112 6.431 213.91 9.792 3.36 A 66. I 33 4.14 11.64 2.63 2.31 2.96 1.64 1.41SJ 27 4.112 1.421 U 23.112 3.143 I9.736 7.116 3.11 6 M . 2.55 4.11 11.61 2.63 2.51 2.96 1.64 1.9

SAJ 31 40.112 1.421 34 23.612 8.1 196,1 13.212 3.6 M 66.I

2.53 4.14 11161 2.63 2.51 2.94 1.64 1.37

SAJ 31 44.153 1.411 MA 19.150 11.382 181.331 12.71M 3.11 9 A 64.31 2.53 3.13 11.68 2.65 2.33 2.94 1.64 1.17SM 32 44.10 1.3911 MA 19.151 9.639 177.436 11 3.31 N 64.I 2.5 3.16 11.68 2.65 2.58 2.94 1.64 1.I

18J 33 44.58 1.460 U 19.154 9.325 186.3M 11.392 3.11 N0 64.63 2.3 3.14 11.68 2.63 2.51 2.94 1.64 1,17

56J 34 44.15 1.411 04 19.15 6.211 111.318 9.611 3IN MA 64.86 .55 2.85 11,6 2.63 2.31 2.94 1.64 1,97

SJ 35 44.5 1.68 MA 19.158 2.991 1664.8 3.611 3.33 "4 64.91 2.55 3.17 11.68 2.63 2.5 2.94 1.64 1.38

S4J 36 44.358 1.391 MA 19.11 11.516 177.73N 13.297 3.10 NA 64.0 2.55 3.21 11.68 2.65 2.31 2.94 1.64 1.14

SJ 37 44.13 1.421 Is 19.151 9.544 11.111 12.112 2.31 4A 64.81 2.55 3.0 11.61 2.65 2.31 2.94 1.64 1.12 ,

SJ so 44.138 1. 4 4 be 19.158 .192 178.136 11.697 3.11 %A 64.U 2.53 3.12 11.64 2.63 2.31 2.94 1.64 1.36 .1

SAJ 43 4.812 1.461 MA 23.612 9.668 217.1N 13.36 2.33 NA 64.38 :. 2.67 11.6h 2.63 2.31 2.94 1,64 1.41

S8J 44 49.912 1.141 4A 23.812 6.496 212.614 11.101 3.36 %A 64.54 2.23 2.63 11.68 2.63 2.31 2.94 1.0 1.91S*3 45 49.812 1 440 M6 23.012 3.124 213.36N 6.196 3.11 %A 64.58 2.55 2.54 11.61 2.63 2.51 2.94 1.64 3.96333 46 44.339 1.440 00 19.131 10.344 103.411 12.992 2.33 4A 63.38 2.55 3.11 116. 2.63 2.3 2.92 1.64 1.16 i ,'

S4J 47 44.151 1.468 44 1N,11 M .611 187.611 12.592 3. 6 A 4 JI ".33 2.94 11.68 2.63 2.31 2,92 1.64 2.31SM 43 44.058 1.411 36 19.350 8.113 171.618 11.611 3.30 Me 63.31 2.3 2.74 11.68 2.63 2.50 2.92 1.64 1.94

SM 49 44.338 1.440 4, 19.3, 6.134 114.31 3.192 3.33 04 63.3 . 2.33 11.8 2.63 2.33 2.92 1.64 ,.3756 1 38 44.050 1.431 VA 19.151 4.611 1112.11 7.296 3.I V 63.31 2.3 2.71 11.68 2.63 2.33 2.92 1.64 1.93 " ' 1

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