Stone DesignStone Design

Material in this section is drawn primarily from NEH 654 TS 14C and 14KMaterial in this section is drawn primarily from NEH 654 TS 14C and 14K

Jon FrippNDCSMC

Ft. Worth, TX

Rock Design

• Uses of rock

• Sizing methods

• Examples

Why use rock?

High stress areasHigh riskEmergency situations

•Quick response•Ecological Implications?•Geomorphic Implications?

Why use rock?

Result: Static channel boundary.Is this what is needed?

Photo from Meg Jonas

Photo from Jim Ludlam

May be part of Streambank Soil Bioengineering

USACE WES Rip Rap test facility

How Big?What Gradation?What Shape?What Density?What Quality?

What do we need to know?

If we are going to use rock – we need to do it right

Size

Answer: The particle size for which 50% of the sample is finer.

What is D50?

How big does the rock need to be?

Stone Sizing

FF = Force of flowing water

FD = Drag force

FL = Lift force

FW = Submerged weight

FC = Contact or interlock force

Empirical methods were developed for specific applications.

Stone Sizing

Bottom Line: Match the rock sizing method with the intended use.

High vs. Low Energy

Mild slope - Low Energy

Steep Slope - High EnergyNote: there are exceptions

Parallel flow – low energy

Impinging flow – high energyNote: there are exceptions

What variables do the equations account for?

•Usually stone size is the dependent variable•Is it part of a defined gradation?

•Independent variables can include:•Velocity•Depth•Energy slope•Bed slope•Side slope•Rock shape•Rock density•Others?

•Are those important?

USGS

44.201.050

Vd Arizona field data where riprap performed without damage.

d50 is median stone size (inches)V is channel velocity (fps)

Report 108 – (1970)

4/50 eRSd Developed for roadside drainage channels.

d50 is median stone size (inches)Se is energy slope (ft/ft)R is hydraulic radius (ft)

LANE’S Far West States Method

USACOE - Maynord52

1

5

30

.

DgK

V.

WS

WDTCvCsCSFd

dm = Stone size (ft); m percent finer by weight

D water depth in feetCs Stability Coefficient Z=2 or flatter C=0.30Cs = Stability coefficient (0.3 for angular rock, 0.375 for rounded rock)Cv = Velocity distribution coefficient (1.0 for straight channels or inside of bends, calculate for outside of bends)CT = Thickness coefficient (use 1.0 for 1 D100 or 1.5 D50, whichever is greater))

USACE WES Rip Rap test facility

For slopes < 2%

USACOE

R= center-line bend radius W = water surface width

)log(2.0283.1 WRCv

2

2

1 sin

sin1 K

rockangular for degrees) 40 (typically repose of angle

horizontalrock with of angle

USACOE – Boulder Design

)1(

)(18

SG

Sdepthd f

d = Minimum stone size (ft) depth = channel depthSf = channel friction slope SG = specific gravity of the stone

EMRRP-SR-11

Abt Rock Design

23.535.1 43.056.050 SqD

D50 is median stone size (inches)S channel slope in (ft/ft)q is unit discharge (ft3/ft)

Slopes: 2% to 20%

Rock design for spillways or loose rock grade controlSteven R. Abt, and Terry L. Johnson (1991)

529.05.150 923.112 qSD

0.02 < S < 0.1 For Slopes between 2% and 10%

ARS Rock Chutes

0.10<S<0.40

529.058.050 233.012 qSD

D50 is median stone size (inches)S channel slope ft/ftq is unit discharge (ft3/ft)

For Slopes between 10% and 40%

K. M. Robinson, C. E. Rice, and K. C. Kadavy (1998)

Rock Chute Design Spreadsheet

Given:GS = 2.65, Unit wt of stone 165.36 lb/ft3

Bottom Width = 40 ftn = 0.045Slope = 0.06 ft/ftDepth = 3.5 ft

Find:Appropriate rock size

Velocity = 16.7 ft/sQ = 2,340 ft3/sCritical Depth = 4.7 ft

Maynord D50 = 1.9 ftLane’s FWS D50 = 3.2 ftAbt and Johnson D50 = 1.3 ftARS rock chute D50 = 1.1 ft

Not appropriate for givens

Example Problem

Given:GS = 2.6Bend Radius = 350 ftChannel width = 50 ft Side slope = 2:1Slope = 0.01 ft/ftDepth = 5 ft

Find:Appropriate rock size using Lane’s FWS technique

Example Problem

Use graph in back of handout

Stone Sizing – Final Thoughts•Use a rock sizing method appropriate for your application

•Use several methods and look for convergence•But do not expect exact convergence

•Use a factor of safety appropriate for your situation

•Assess significant threats to life and property

•Size may need to be larger than what the equations indicate as sufficient to resist flows

•To resist ice and debris•For habitat enhancement•For aesthetic purposes•To reduce vandalism and theft

Questions?