1. !
!
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.!!!
!

2. 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.!!
!
!
!
!
!
!
!

3. !
!
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!

4. 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.!!!

5. KEY "BASE" MEMBERS
Number of Logs with Rootwads NL = 3
Specific Gravity of Large Wood SL = 0.50 specific gravity
Average Rootwad Diameter DRW = 5 feet Wood Volume = 255 cubic feet per member
Average Rootwad Length LRW = 2.5 feet
Proportion of Voids in Rootwad p = 0.2 decimal %
Tree Stem Average Diameter DTS = 2.8 feet
Tree Stem Average Length LTS = 35 feet FBL = 23,843 pounds
STACKED "MIDDLE" MEMBERS
Number of Logs with Rootwads NL = 2
Specific Gravity of Large Wood SL = 0.50
Average Rootwad Diameter DRW = 5 feet Wood Volume = 255 cubic feet per member
Average Rootwad Length LRW = 2.5 feet
Proportion of Voids in Rootwad p = 0.2 decimal %
Tree Stem Average Diameter DTS = 2.8 feet
Tree Stem Average Length LTS = 35 feet FBL = 15,896 pounds
TOP MEMBERS
Number of Logs with Rootwads NL = 2
Specific Gravity of Large Wood SL = 0.50
Average Rootwad Diameter DRW = 5 feet Wood Volume = 255 cubic feet per member
Average Rootwad Length LRW = 2.5 feet
Proportion of Voids in Rootwad p = 0.2 decimal %
Tree Stem Average Diameter DTS = 2.8 feet
Tree Stem Average Length LTS = 35 feet FBL = 15,896 pounds
BOULDER BALLAST
Specific Gravity of Boulders SS = 2.65
equivalent Diameter of Boulder DB = 4.0 feet
Number of Boulders Submerged NB = 13
Number of Boulders above water level NBU = 12 W' = 3,450 (pounds) effective weight per submerged boulder
W = 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.
LLw
RWRWTSTS
BL NSgp
LDLD
F ⋅−⋅##
$
%
&&
'
(
−⋅+= )1()1(
44
22
ρ
ππ
)1(
6
3
−⋅=# Sw
B
Sg
D
W ρ
π
∑
∑ "+
=
BL
B
F
WW
FS
)(
LLw
RWRWTSTS
BL NSgp
LDLD
F ⋅−⋅##
$
%
&&
'
(
−⋅+= )1()1(
44
22
ρ
ππ
LLw
RWRWTSTS
BL NSgp
LDLD
F ⋅−⋅##
$
%
&&
'
(
−⋅+= )1()1(
44
22
ρ
ππ
Douglas-fir, intermediate
Douglas-fir, intermediate
Douglas-fir, intermediate

6. Rock Unit Weight 165.0 lb/ft^3
Water 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 10.0
Volume 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 86350.0
Weight ton 0.0 0.3 1.2 2.8 5.4 9.3 14.8 22.1 31.5 43.2
Cost/ton 20.0
Cost/rock 0.9 6.9 23.3 55.3 107.9 186.5 296.2 442.1 629.5 863.5
60 3 ft. 1398.9
30 5 ft 3238.1
4637.0

7. 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 = 1.3
Max Stream Velocity at ELJ V = 8.00 fps
Type of streambed sediment Gravel
Ф = 35 degrees
APPARENT DRAG COEFFICIENT
CD
app
= 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 is
a solid structure, 3) frictional resistance is based on streambed material and normal force, and 4) ELJ is fully submerged.
wELJ
app
DD
V
ACF ρ⋅⋅⋅=
2
2
∑
∑=
DB
F
S
F
F
FS
A
A
Bwhere
B
C
C ELJDapp
D =
−
= 2
)1(

8. !
!
!
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.!!

9. 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!!"#"$%!
!
!

10. 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!!4V
kg/m2
.!!Utilizing!Manning’s!equation!the!resultant!dimensions!of!the!channel!is!
0.3!meters!deep!and!12.4!meters!wide.!!!
!
!
!
!
!
!
!
!
!
!
!
!
!

11. 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 =
Q
V
=
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.!!
!
!
!

12. 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.!!
!
!
!

13. 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&

14. !! = 2.2048 ∗
9
60
+ 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
!"!
!
!
!