Coastal and Hydraulics Laboratory

CONCRETE ARMOR UNIT DESIGN

Jeffrey A. Melby, Ph.D.

Email: melbyj@wes.army.mil

CONCRETE ARMOR UNIT DESIGN

Contents

Based on CEM Chapter VI-5-2 (f) and VI-5-2 (h)

· INTRODUCTION· STABILITY OF VARIOUS SHAPES· CONCRETE ARMOR UNIT STRUCTURAL

RESPONSE· EXAMPLES

CONCRETE ARMOR UNIT SHAPES

CONCRETE ARMOR UNIT SHAPES

· Thousands of shapes· Many different applications· Most shapes have been patented and trademarked· Most basic shapes are in patents of 1950’s and 1960’s

TRIBARS AT KAHULUI, MAUI, HAWAII

PATTERN-PLACED TRIBAR

SANTA CRUZ, CALIFORNIA900 28 t QUADRIPODS

CUBES AT GIJON, SPAIN

Repair in 1995 of 90 t with 120 t concrete cubes!

Ringer crane is permanent fixture

CORE-LOC AT CHICAGO RIVER BAFFLE

ROUNDHEAD CONSTRUCTION

HUMBOLDT JETTIES, CALIFORNIA

HUMBOLDT JETTY HEAD

Khaboura, Omanoffshore U-shaped breakwater

MANASQUAN, NEW JERSEY

CORE-LOC FORM IN SOUTH AFRICA

CORE-LOC CASTING

KHABOURA, OMAN CASTING

ARMOR SELECTION CRITERIA

· Consider purpose of armor· Hydraulic stability· Structural capacity, materials· Engineering performance vs cost

� Volumetric efficiency� Ease of construction

ARMOR COMPARISON

· Stability and structural strength

· Cost of materials Total volume of concrete, reinforcing steel, and formsAdequate reinforcing steel will double the cost of materialsForm cost will be 10% - 100% of concrete cost

· Handling costsProportional to number of unitsA higher order function of armor size

ARMOR LAYER LAYOUT AND OPTIMIZATION

N = Number of armor unitsA = Surface area on slope

= Packing density coefficientV = Volume of individual armor unitW = Armor unit weightρ = Armor specific weightn = Number of thicknessesk = Layer coefficientr = Total armor layer thicknessVT = Total volume for N unitsP = Armor layer porosity

NA

V 2/3 where V W and nk (1 P/100)

VT NV r nk Dn where Dn V 1/3

ARMOR LAYER LAYOUT AND OPTIMIZATION

CAU VOLUME COMPARISON

00.5

11.5

22.5

33.5

4

core-

locac

cropo

dedo

los tribar

tetrap

odcu

bes

stone

Vr

Vrr

[(KD)r (cot )r]1/3

VOLUME OPTIMIZATION

· N/( A) = V(-2/3)

· VT/( A) = V1/3

· So the total number of units can decrease much faster than the total volume increases as the armor size increases

· If equipment is constant, then it may be more economical to go with larger units

0.00

0.50

1.00

1.50

2.00

2.50

3.00

0 2 4 6 8 10 12

Volume

NumberVolumeN/( A) = V(-2/3)

VT/( A) = V1/3

CONCRETE ARMOR UNIT PHYSICAL MODELING

· Damage definitions· Stability Studies· Strength Analyses

DAMAGE DEFINITIONS

· COUNTING METHOD� Appropriate for small amounts of damage (CAU’s)� ‘No movement’ is lower limit� Armor units rocking (important for dolosse)� Individual units displaced� D = number displaced / total number in active region� Nod = number displaced / total number in strip Dn wide

DAMAGE CLASSIFICATION

· CONCRETE ARMOR UNITS� INITIAL DAMAGE: Dolosse D = 0-2%, Core-Loc and Accropode

D = 0-1%, All shapes Nod = 0� INTERMEDIATE DAMAGE: Core-Loc and Accropode D = 1-5%� FAILURE: Dolosse D 15%, Core-Loc and Accropode D

10%, Cube Nod = 2, Tetrapod Nod=1.5, Accropode Nod=0.5

LESSER ANTILLES

CAU STABILITY FORMULAE

· Many different equations with various parameters· Different criteria used to judge stability· Best to check with Hudson equation· Use 4 KD 16· Larger KD is dangerous because of noninterlocked

condition, which is nearly impossible to avoid

· Also, armor layers are easily damaged during construction and nearly impossible to repair to original condition

NsHs

Dn

(6.7N 0.4od /N 0.3

z 1.0)s 0.1m

STABILITY OF CONCRETE CUBES

· Dn = Cube length· Nod = Number of units displaced within a strip Dn In

width · Valid for non-breaking irregular head-on waves · Two layers of randomly placed cubes · 3 < m < 6· Or see table for KD· Note very few stability experiments

STABILITY OF TETRAPODS

NsHs

Dn

(3.75N0.5od /N 0.25

z 0.85)s 0.2m

· Based on few tests· See table for KD

NsHs

Dn

2.32(Nod /N0.5z )0.2 1.33

TRADITIONAL TRAPEZOIDAL MULTILAYER STRUCTURE

RUBBLE MOUND FRONTING CAISSON STRUCTURE

STABILITY OF DOLOSSE

· Many equations

· Use Hudson with KD = 8 for no rocking with breaking waves

· Good performance in USA except for Crescent city and Cleveland

DOLOS SHAPES

r = 0.44 r = 0.38 r = 0.32

r = B/C

STABILITY CORE-LOC

· Extensive physical model tests with irregular waves yielded no repeatable instability

· Regular severely plunging breaker tests yielded KD = 16 for no-damage limit

· Variety of severe 3-D physical model tests yielded KD = 13 for heads

· Unit is licensed by 6 firms worldwide including Baird and Associates, Sogreah, and Tetra (formerly Nippon Tetrapod)

LIMITATIONS OF MOST GENERALIZED CAU PHYSICAL MODEL STUDIES

· Model studies did not include scaled strength - model units don’t break

· So damage above very low percentages is not in similitude

· Also toe is typically fixed which prevents sliding and limits damage in model

· Concrete armor may be less stable under oblique wave attack and armor is nearly always less stable at transitions

· Concrete armor design must be very conservative for these reasons and site specific physical modeling must address these details

STRUCTURAL STRENGTH OF CAU

· Specifications should always indicate the required flexural tensile strength

· Slender units have higher tensile stresses than bulky units but bulky units can have higher heat-of-hydration cracking

· Magnitude of impact stresses is much higher than other stresses - for example, any size dolos dropped from approximately one foot on a stiff surface will break

CAU STRUCTURAL DESIGN

· Several structural formulations for dolosse

· Core-locs were shown by Melby and Turk (1994) to have stresses approximately 60% those of dolosse under equivalent impact and static loadings

· Table VI-5-42 lists allowable impact speeds for placement

FATIGUE IN CAU

· Definition - the decrease in material strength due to repeated loading

· Typically loads due to waves are not high enough to cause fatigue that is significant

· The reduction in strength due to fatigue is offset by the long-term increase in strength. The increase in strength is typically about 50% over the first 5 years

· Impact fatigue is not an issue because we assume rocking units will break in our design

STRENGTH ENHANCEMENTS

· Change armor shape to increase section modulus and decrease moment arm

· Increase material strength

· Reinforce� Fibers� Rebar� Post-tension

STRUCTURAL STRENGTH OF CAU

· Typically unreinforced units -tensile strength of concrete is 10% of its compressive strength

· Light reinforcement used in Corps dolosse yields 15% to 20% increase in flexural tensile strength (rebar and fibers) and no increase in torsional strength (longitudinal rebar only, no hoops)

· High strength concrete can be brittle and relatively weak under impact loading

CRESCENT CITY, CALIFORNIA

CRESCENT CITY 42 t DOLOSSE

CRESCENT CITY, CALIFORNIA

· 1970 DESIGN� H=35', = 156pcf, cot = 2, W = 84,000lb => KD = 13.4� High strength

+ 1100 - 1300 psi Flexural tensile+ 400 - 600 psi Splitting tensile+ 7000 - 9000 psi Compressive

� Breakage ~ 75 %

· 1985 DESIGN� Similar except cot = 5 to 6, => KD = 4.5 to 5.4� Similar strength with added metal fibers

+ 1000 - 1500 psi Flexural tensile + 300 - 660 psi Splitting tensile+ 7700 - 1100 psi Compressive

� Breakage ~ 3%

LESSER ANTILLES

LESSER ANTILLES

LESSER ANTILLES

· Design armor chosen based on Hdesign = 17’ = 0.78 * hb=> 10 t units used

· Also based on form availability of 6 t and 10 t· Should have used Hdesign = 26’ = 1.2 * hb => 30 t· Design wave determined offshore which was

conservative for Atlantic hurricane· Units placed at light packing densities· Units placed with vertical fluke seaward· No money saved using existing forms!

EFFECT OF 1:8 SLOPE

Table 1. Crude Design Wave Height at Structure Toe For Revetment For Various ReturnPeriods with Associated Dolos Size for 5 Percent Breakage and Estimated Breakage for 6t Dolosse

ReturnPeriod

Yr

ToeDepth +StormSurge

ft

WavePeriod

Tpsec

WaveHeightAt 200’

HmoFt

BreakerHeightIndex

ShoalingCoeff

Ks

DesignWaveHeight

Hft

DolosSize forKD=16B=5%

t

Breakagefor 6 t

DolosseB%

1 17.3 10.0 15.0 1.12 1.10 16.9 5 22 17.6 10.5 18.5 1.10 1.12 19.3 7 35 18.3 11.5 23.0 1.09 1.15 19.9 8 410 18.8 12.0 26.5 1.07 1.16 20.1 8 520 19.2 13.0 30.0 1.08 1.20 20.6 9 1250 19.8 13.5 34.2 1.07 1.21 21.1 10 13100 20.0 14.0 38.0 1.07 1.23 21.3 10 19

Table 3. Crude Design Wave Height at 5Hs Seaward of the Shoreline ForRevetment ForVarious Return Periods with Associated Dolos Size for 5 Percent Breakage andEstimated Breakage for 6 t Dolosse

ReturnPeriod

Yr

ToeDepth +StormSurge

ft

WavePeriod

Tpsec

WaveHeightAt 200’

HmoFt

BreakerHeightIndex

ShoalingCoeff

Ks

DesignWaveHeight

Hft

DolosSize forKD=16B=5%

t

Breakagefor 6 t

DolosseB%

1 17.3 10.0 15.0 1.12 1.03 15.8 4 22 17.6 10.5 18.5 1.10 1.03 19.7 8 55 18.3 11.5 23.0 1.09 1.04 25.2 16 75

10 18.8 12.0 26.5 1.07 1.04 29.4 25 10020 19.2 13.0 30.0 1.08 1.06 34.3 39 10050 19.8 13.5 34.2 1.07 1.05 39.1 59 100

100 20.0 14.0 38.0 1.07 1.06 43.7 82 100

LESSER ANTILLES

· Alternative: High Density Aggregate· S=2.00, double cost of aggregate

Table 4Comparison of Armor CostsArmor RepairOption

ArmorWeight

ton

NumberRequired

Cost ofArmor

$M

Cost ofForms

$M

TotalMaterialCost$M

1. Normal density 5 cy dolosse 10 1300 1.43 0.25 1.68

7.9 700 0.31 02. HDA 5 cy and 3 cy dolosse 13.8 860 1.31 0 1.623a. Normal Density Core-Loc 18 1065 2.35 0.35 2.703b. HDA Core-Loc 6 1770 1.40 0.30 1.70

VATIA STONE

Coastal and Hydraulics Laboratory

CONCRETE ARMOR UNIT CONCLUSIONS

· Concrete armor is typically economical when there is no stone or the stone size is large

· Concrete armor design requires higher design reliability, but concrete armor units are usually stable for a wider range of wave heights