!!

EcoHydraulic,Engineering,Homework,5,Engineered(Log(Jam(Design(

Coral(West((Feburary(11,(2015(!

PROBLEM,STATEMENT(! Opal!Creek!Ancient!Forest!Center!is!facing!lateral!erosion!on!a!steep!stream!

bank!toe.!!It!is!desirable!to!build!an!engineered!log!jam!(ELJ)!structure!to!prevent!

further!lateral!erosion.!!Seven!locally!sourced!Doug!Fir!trees!will!be!used!at!no!cost!

to!build!the!structure.!!The!logs!will!be!an!average!35!feet!in!length!with!root!wads!

intact.!It!is!requested!by!the!property!owner!that!the!bank!be!protected!up!to!the!25!

RYI.!!!

! The!method!for!designing!an!EJL!incorporates!a!factor!of!safety!(FOS)!of!at!

least!2.0!for!all!calculations.!!The!factor!of!safety!in!this!instance!is!high!due!to!the!

unpredictable!and!complex!nature!of!the!structure!and!its!surroundings.!!It!is!

imperative!for!the!owner!to!use!a!high!FOS,!regardless!of!extra!cost.!!Catastrophic!

failure!can!cause!flooding!and!other!high!costs!to!the!owner.!The!buoyancy!FOS!will!

affect!the!size!and!number!of!boulders!used!to!stabilize!the!structure!against!the!

force!of!buoyancy.!!The!sliding!FOS!is!the!determining!factor!for!calculating!the!

effective!obstructed!area!by!the!ELJ.!!The!Froude!number!is!utilized!to!estimate!

scour!depths,!which!are!important!for!creek!fauna!habitat!but!can!also!cause!failure!

in!the!structure.!

! Using!the!ELJ!Calculator!and!Rock!Density!Cost!Spreadsheets!

recommendations!were!provided.!!It!is!recommended!that!there!be!three!base,!two!

stacked,!and!two!top!members!of!the!ELJ.!!There!are!more!logs!as!base!members!are!

recommended!to!keep!more!of!the!structure!in!contact!with!the!bed!in!order!to!

promote!scour!and!pool!formation.!!!

In!order!to!keep!the!structure!stabilized!fourRfoot!boulders!are!suggested!

with!a!total!of!25!boulders!evenly!distributed!throughout!the!structure.!!These!

recommendations!provide!a!buoyancy!FOS!of!2.0!with!a!cost!of!$1,380!for!the!

boulders.!!Utilizing!the!Sliding!FOS!spreadsheet,!the!effective!waterway!area!

obstructed!by!the!EJL!was!calculated!to!get!a!FOS!above!2.0.!!This!area!was!

calculated!to!be!138Rft2.!!!

Last,!the!Froude!number!was!used!to!estimate!scour!depths!caused!by!the!

ELJ.!It!was!calculated!that!for!Froude!numbers!0.3!and!1.2,!the!scour!depths!were!of!

considerable!concern!and!action!should!be!taken!to!decrease!these!values.!!!

!

Example!of!ELJ:!

!a) Recommendations!for!base,!stacked,!and!top!members!(Buoyancy!FOS!Sheet):!

o Log!Characteristics:!

! Root!Wad!Diameter!=!5’!

! Root!Wad!Length!=!2.5’!

! Proportion!of!Voids!=!20%!

! Stem!Diameter!=!2.8’!

! Average!Length!=!35’!

o I!recommend!3!key!“base”!members,!2!stacked!“middle”!members,!and!2!top!

members.!!The!factor!of!safety!can!be!used!as!a!design!criterion!to!ensure!

that!the!logjam!will!not!float!and!be!sufficient!against!the!force!of!buoyancy.!

More!logs!as!base!members!are!recommended!to!keep!more!of!the!structure!

in!contact!with!the!bed!in!order!to!promote!scour!and!pool!formation.!

b) Boulder!size!and!number!recommendation!(Buoyancy!FOS!Sheet!&!Rock!Density!Cost!Sheet):!

o I!recommend!boulders!4!feet!in!size.!!According!to!the!table!below,!2!foot!

boulders!would!be!less!expensive,!however,!due!to!the!vast!amount!of!

boulders!needed!to!provide!a!factor!of!safety!of!2!and!the!likelihood!of!

boulders!shifting!due!to!forces!such!as!buoyancy!and!sliding,!one!should!

consider!a!larger!boulder.!!With!the!fourRfoot!boulder,!I!recommend!that!13!

be!submerged!and!12!be!above!water.!!Balancing!the!boulders!throughout!

the!structure!should!create!stability!in!the!case!of!a!flood!or!other!fast!

changes!in!flow.!!

!

!

!

!

!

!

!

!

!

Boulder Size (ft) Cost ($)

1 $1,372.50 2 $1,345.50 3 $1,398.00 4 $1,382.50 5 $1,402.70 6 $1,492.00 7 $1,481.00 8 $1,768.40 9 $1,888.50

10 $1,727.00 o !

c) !Effective!obstructed!(by!ELJ)!area!recommendation!(Sliding!FOS!Sheet):!o Simple!estimation!of!effective!waterway!area!obstructed!by!ELJ:!

3 2.8!!" ∗ 35!!" = 295!!"!!o This!is!a!rough!estimation,!not!taking!into!effect!unique!root!wad!shape,!

changing!tree!diameter,!and!the!fact!that!some!layers!of!the!logjam!would!be!

perpendicular!against!flow.!!With!this!estimated!area!obstructed,!the!factor!

of!safety!for!sliding!is!1.2.!!

o If!we!were!to!calculate!the!estimated!area!obstructed!with!the!middle!tree!

layer!being!perpendicular!to!flow:!

! Bottom!Layer:!

3(2.8!!") ∗ 2.8!!" = 24!!"!!! Middle!Layer:!

2.8!!" ∗ !35!!" = 98!!"!!! Top!Layer:!

2(2.8!!") ∗ 2.8!!" = 16!!"!!! Total:!138!ft2!

! Factor!of!Safety!=!3.0!

d) Froude!Number!Calculations!and!Scour!Depth:!o Fr!=!0.3!!

! Scour!Depth!=!19!feet!

o Fr!=!1.2!

! Scour!Depth!29!feet!

o These!scour!depths!are!of!considerable!concern!considering!that!they!are!

both!deeper!than!the!ELJ!is!tall.!!The!Froude!number!is!velocity!over!the!

wave!celerity.!At!values!above!one,!the!flow!is!considered!to!be!supercritical!

with!a!fast!rapid!flow.!!While,!values!below!one!are!considered!to!be!

subcritical!with!a!slower,!tranquil!flow.!Rapid!supercritical!flow!is!going!to!

hug!the!stream!bank!and!create!considerably!more!scour!than!a!slower!flow.!

The!denominator!of!the!Froude!number!has!the!value!of!hydraulic!depth.!!As!

depth!increases,!the!Froude!number!decreases!and!becomes!a!more!

desirable!value.!!If!possible,!I!recommend!considering!constructing!a!ELJ!in!a!

deeper!part!of!the!river!so!scour!will!not!be!such!a!large!issue.!!!

KEY "BASE" MEMBERSNumber of Logs with Rootwads NL = 3Specific Gravity of Large Wood SL = 0.50 specific gravityAverage Rootwad Diameter DRW = 5 feet Wood Volume = 255 cubic feet per memberAverage Rootwad Length LRW = 2.5 feetProportion of Voids in Rootwad p = 0.2 decimal %Tree Stem Average Diameter DTS = 2.8 feetTree Stem Average Length LTS = 35 feet FBL = 23,843 pounds

STACKED "MIDDLE" MEMBERSNumber of Logs with Rootwads NL = 2Specific Gravity of Large Wood SL = 0.50Average Rootwad Diameter DRW = 5 feet Wood Volume = 255 cubic feet per memberAverage Rootwad Length LRW = 2.5 feetProportion of Voids in Rootwad p = 0.2 decimal %Tree Stem Average Diameter DTS = 2.8 feetTree Stem Average Length LTS = 35 feet FBL = 15,896 pounds

TOP MEMBERSNumber of Logs with Rootwads NL = 2Specific Gravity of Large Wood SL = 0.50Average Rootwad Diameter DRW = 5 feet Wood Volume = 255 cubic feet per memberAverage Rootwad Length LRW = 2.5 feetProportion of Voids in Rootwad p = 0.2 decimal %Tree Stem Average Diameter DTS = 2.8 feetTree Stem Average Length LTS = 35 feet FBL = 15,896 pounds

BOULDER BALLASTSpecific Gravity of Boulders SS = 2.65

equivalent Diameter of Boulder DB = 4.0 feetNumber of Boulders Submerged NB = 13

Number of Boulders above water level NBU = 12 W' = 3,450 (pounds) effective weight per submerged boulderW = 5,541 (pounds) weight per boulder

Total Effective Weight for all Boulders = 111,339 pounds

FACTOR OF SAFETY: BUOYANCY

FSB = 2.0

Buoyancy Calculations for Engineered Log Jam Spreadsheet developed by Scott Wright, P.E. - NRCS Oregon - revision 1.2

Methodology based on a physics approach and information adapted from D'aoust & Millar (2000). The designer should attain a minimum factor of safety of 2.0 for the ELJ and the ELJ should act as a fully connected structure.

A simplified approach is used to estimate buoyancy where the logs and ballast boulders in the log jam are fully submerged. In addition, the log jam and boulders act as a composite structure and are assumed fully connected. Water velocity inside the log jam is highly turbulent and near zero, therefore vertical uplift forces are assumed negligible.A minimum factor of safety against buoyancy should be 1.5 with an ideal F.O.S. greater than 2.0.

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Douglas-fir, intermediate

Douglas-fir, intermediate

Douglas-fir, intermediate

Rock Unit Weight 165.0 lb/ft^3Water Unit Weight 62.4 lb/ft^4

Rock Specific Gravity 2.7

Size (ft) 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0Volume 0.5 4.2 14.1 33.5 65.4 113.0 179.5 267.9 381.5 523.3

Weight lbs 86.4 690.8 2331.5 5526.4 10793.8 18651.6 29618.1 44211.2 62949.2 86350.0Weight ton 0.0 0.3 1.2 2.8 5.4 9.3 14.8 22.1 31.5 43.2

Cost/ton 20.0Cost/rock 0.9 6.9 23.3 55.3 107.9 186.5 296.2 442.1 629.5 863.5

60 3 ft. 1398.930 5 ft 3238.1

4637.0

Cross-sectional area from HEC-RAS output, upstream of ELJ A = 1840 sq. ft.Effective waterway area obstructed by ELJ AELJ = 138 sq. ft.

Drag Coeff. CD = 1.3Max Stream Velocity at ELJ V = 8.00 fps

Type of streambed sediment GravelФ = 35 degrees

APPARENT DRAG COEFFICIENT

CDapp = 1.52

FD = 13016 pounds

Friction Factor of Logs on streambed f = 0.70 tangent of internal angle of streambed material

FF = ( W' - FBL - FLB ) f = 39,005 pounds

FSS = 3.0

FACTOR OF SAFETY: SLIDING

Horizontal Drag Force on ELJ

Sliding Calculations for Engineered Log Jams Ballasted by Boulders

Spreadsheet developed by Scott Wright, P.E. - NRCS Oregon - revision 1.0

Horizontal Streambed Friction Resistance on ELJ

Calculations make several simplifying assumptions including 1) no resistance from burial of ELJ elements, 2) ELJ isa solid structure, 3) frictional resistance is based on streambed material and normal force, and 4) ELJ is fully submerged.

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D =−

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!!!

EcoHydraulic,Engineering,Stable!Channel!Design!

Coral!West!Feburary!19,!2015!

!

PROBLEM,STATEMENT!The!city!of!Corvallis!is!in!need!of!a!bypass!channel!to!divert!dangerous!

flood!flows!around!the!city.!The!channel!is!going!to!be!on!a!slope!of!0.012.!!The!median!bed=material!size!is!given!to!be!55mm!(D50)!with!a!Manning’s!n!of!0.03.!!The!flow!rate!is!known!to!be!35!m3/s.!!! Two!approaches!were!taken!to!estimate!two!different!channel!dimensions.!!The!first!approach!utilizes!the!USBR!tractive!force!figure!to!identify!the!critical!shear!stress!for!the!given!D50!grain!size.!Using!the!shear!stress!equation,!the!depth!was!found.!!Width!of!the!channel!was!calculated!using!the!Manning’s!Equation.!!! The!second!approach!applied!the!Hjulstrom!Diagram!to!identify!the!velocity!in!order!to!avoid!erosion!and!sedimentation.!!The!velocity!is!then!used!in!the!Manning’s!Equation!to!find!the!second!channel!dimensions.!!! The!USBR!tractive!force!figure!yields!a!critical!shear!stress!of!4!kg/m2.!!The!shear!stress!diagram!yields!a!depth!of!0.3!meters.!!Utilizing!the!Manning’s!equation!give!a!width!of!12.4!meters.!!The!velocity!with!these!dimensions!is!about!9.4!m/s.!!According!to!the!Hjulstrom!Diagram,!this!velocity!will!most!likely!have!erosion!of!particles!from!bed.!!! Using!the!Hjulstrom!Diagram,!the!optimal!velocity!is!around!3.5!m/s.!!The!resultant!estimated!diameter!of!the!channel!has!a!width!of!7.2m!and!a!depth!of!1.4m.!These!results!will!avoid!issues!pertaining!to!erosion!and!deposition!in!the!bed.!!However,!the!depth!may!have!issues!because!of!the!high!resulting!shear!stress.!! Risks!of!erosion!and!deposition!in!a!flood!bypass!are!severe!and!should!be!avoided.!Both!erosion!and!deposition!can!cause!failure!by!changing!the!boundary!conditions.!Erosion!can!cause!unraveling!of!the!channel!and!a!factor!of!safety!should!be!built!into!the!procedure.!!One!possible!way!to!avoid!erosion!is!to!line!the!channel!with!grass.!!!! It!is!suggested!that!the!City!of!Corvallis!utilize!the!dimensions!found!with!the!Hjustrom!Diagram.!!The!channel!should!be!lined!with!a!suitable!grass!to!prevent!erosion!and!a!factor!of!safety!should!be!utilized!to!ensure!the!shear!stress!would!not!cause!failure!to!the!channel.!!

Considering!a!rectangular!channel:!

!!Critical!Shear!Stress!Approach!

1) Critical!Shear!Stress!for!given!grain!size=!4500!g/m2!(0.0098N/g)!=!44!N/m2!

!

2) Calculate!y!using!! = !"#,!! = !!" =

(!!"!!)(!.!!!! )

(!"#$ !!!)(!.!"#)

= !0.3!!"#"$%!!!

a. Where:!!!(Shear!Stress)!=!4!kg/m2!!

!!(Water!Density)!=!9810!N/m3!S!(Slope)!=!0.012!

!3) Calculate!Width:!!

!Manning’s!Equation:!

! = !" = !! ∗ !!! ∗ !

!!

! !

! ∗ !!! = ! ∗ !

!!!

= 9.6!

given!values:!

! = 35!!

! !! = 0.012!! = 0.03!! = 0.3!!!

!! = ! ∗ !!! = !

!" =! ∗ !! + 2!!

0.3b ∗ ( 0.3!! + 0.6)

!/! = 9.6!∴ b = !12.4!meters!

!!Therefore,!according!to!USBR!tractive!force!figure!the!critical!shear!stress!is!!4Vkg/m2.!!Utilizing!Manning’s!equation!the!resultant!dimensions!of!the!channel!is!0.3!meters!deep!and!12.4!meters!wide.!!!!!!!!!

!!!!!!!

Critical!Velocity!Approach!!4) Critical!Velocity!is!between!2!and!5!m/s!according!to!this!Hjulstrom!Diagram!

(~3.5!m/s).!!

!5) Calculating!Width!

a. Manning’s!equation!!

! = ! !!!!!

!!

! !

!!!!!!

!!= !! = 3.5 ∗ 0.03

0. 012!!

!!≅ 1!!

Q = VA!

A = QV =

35!!s

3.5!!= 10!!!

R = ! !!" =10!!

!" = 1!WP = 10m!

!One!possible!area!of!the!channel!is!a!width!of!7.2!m!and!a!depth!of!1.4!m.!!!!!

EcoHydraulic,Engineering,Comparing*Discharge*Estimates*

Coral*West*Febuaray*26,*2015*

!

PROBLEM,STATEMENT*! The!discharge!on!Oak!Creek!needs!to!be!established!for!management!purposes.!!Three!techniques!will!be!used!to!find!the!most!reliable!value!in!cubic!feet!per!second!(cfs).!!The!first!technique!is!directly!measuring!velocity!using!a!current!meter.!!This!method!is!commonly!used!within!the!USGS!and!will!provide!data!for!the!second!technique,!which!is!using!an!empirical!formula!known!as!Manning’s!Equation.!!The!third!technique!utilizes!rating!curves!established!over!30!years!of!recorded!stage!measurements.!!!! Using!a!Price!AA!meter!is!a!tool!to!find!current!data!on!a!river.!!The!process!involves!going!out!to!the!river,!and!collecting!data!in!small!sections.!!The!data!is!then!manipulated!to!find!total!discharge.!!The!area!collected!from!the!field!is!then!used!to!find!the!wetted!perimeter.!!The!wetted!perimeter,!slope,!and!Manning’s!n!of!the!river!is!then!used!to!calculate!discharge!with!Manning’s!Equation.!!Data!from!rating!curve!is!established!over!time!to!record!a!relationship!between!stage!and!corresponding!discharge!in!the!river.!!!! The!results!from!the!three!techniques!are!listed!in!the!table:!

Technique*

Discharge*

(cfs)*

Price*AA*

meter* 20*

Manning's*

Equation* 20*

Rating*

Curves* 18*

Mean* 19.33333333*

Standard*

Deviation* 1.15*

!! The!Price!AA!meter!and!Manning’s!Equation!seem!to!be!the!most!reliable!methods.!!They!are!empirical!and!based!on!current!data!of!the!stream.!!I!believe!that!the!rating!curve!method!is!the!least!reliable!because!the!stageNdischarge!relationship!could!change!over!time!due!to!erosion!and!deposition!of!sediment.!!!!!

point*

distance*

from*left*

edge*of*

water*(ft)*

Depth*from*

water*

surface*(ft)*

Area*(ft2)*

C*(number*

of*clicks*per*

60*seconds)*

Velocity*(ft/s)*discharge*

(ft3/s)*

1* 9.2* 1.2* 1.44* 4* 0.164786667* 0.2372928*

2* 10.4* 1.3* 1.56* 9* 0.34852* 0.5436912*

3* 11.6* 1.3* 1.56* 5* 0.201533333* 0.314392*

4* 12.8* 1.4* 1.68* 18* 0.67924* 1.1411232*

5* 14* 1.7* 2.04* 52* 1.928626667* 3.9343984*

6* 15.2* 1.7* 2.04* 54* 2.00212* 4.0843248*

7* 16.4* 2* 2.4* 50* 1.855133333* 4.45232*

8* 17.6* 2.1* 2.52* 33* 1.23044* 3.1007088*

9* 18.6* 2.3* 2.3* 26* 0.973213333* 2.238390667*

10* 20.5* 0.3* 0.57* 0* 0.0178* 0.010146*

* * * * *

Total*

Discharge* 20.05678787*

!*Areas!shaded!in!grey!are!calculated,!all!other!values!are!measured.!!

!XNaxis!is!depth!in!feet!!Example!Calculations:!!Area:!

! = !"#$%&'(!!"#$!!"#$!!"#!!!"!!"#$% ∗ !!"#ℎ!!"#$!!"#$%!!"#$%&'!!! = 10.4− 9.2 !" ∗ 1.2!" = 1.44!"!!

!Velocity:!

! = 2.2048 ∗ !"#$%&!!"!!"#!$%!!"#!!"#$%& + 0.0178!

0!

0.5!

1!

1.5!

2!

2.5!

distance!from!left!edge!of!water!(ft)! 9.2! 10.4! 11.6! 12.8! 14! 15.2! 16.4! 17.6! 18.6! 20.5!

River&Cross&Section&

!! = 2.2048 ∗ 960 + 0.0178 = 0.35 !"! !Discharge:!

! = !"#$ ∗ !"#$%&'(!!! = 1.44!"! ∗ 0.43852 !"! = 0.54 !"

!

! !!Manning’s!Equation!!

!!!!Average*

Depth*(ft)* 1.53*

Width*(ft)* 20.5*

Total*Area*

(ft)* 18.11*

P*(ft)* 23.56*

S* 0.001*

n* 0.035*

R*(ft)* 0.77*

Q*(ft^3/s)* 20.5*

!Rating!Curves!!

o For!Z>0.85’:!!Q(cfs)!=4.2902(Z^!1.6965)!o For!Z<0.85’:!!Q(cfs)!=7.1228(Z^1.7513)!

Using!the!deepest!part!of!the!channel,!Z!=!1.7!ft!!

! !"# = !4.2902 2.3!"!.!"!# = 18.37 !"!

! !!