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THE—$5

 

 

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PLACE IN RETURN BOX to remove this checkout from your record.
To AVOID FINES return on or before date due.
MAY BE RECALLED with earlier due date if requested.

DATE DUE m DATE DUE

3/01 c:/CIRCIDIIODuO.pfi5-p. 15

 

A Design of a Revetment Ball

for Erosion Control on Red Cedar River

A Thesis Submitted to
The Faculty of
RICHIGAN STATE COLLEGE
of

AGRICULTURE AND APPLIED SCIEKCE

by

J 0 H01 gate
hh-

Candidate for the Degree of

Bachelor of Science

June 1948

CN/

6/“ [W
C?"

TABLE 9;; CONTENTS

I Introduction
A. Discussion of problem
B. Preposed Measure to Alleviate Condtion
II Design or Cantilever Retaining Wall
A. Data and Assumptions for Design
B. Determination of Economical Dimensions
0. Investigation of Forces during High.Water
D. Design of Heel Slab
E. Design or Toe Slab
F. Design of Stem
l. Shear 8c Moment
2. Cutting off Steel Rods
G. Temperature Steel
H. Design or Piles
I. Drainage Weepholes
III Construction Estimate
A. Current Unit Prices
B. Quantities of Materials Estimate
c. -Cost Estimate

IV Situation Plan, Profiles, Detail Drawing a Bill of.
Materials (available in.pocket)

v Bibliography

2.06054:

I Introduction

This thesis is concerned with the protection of an
embankment against erosion by current. A problem frequently
met in engineering, bank erosion often has destructive ef-
fects on abuting land and structures.

A case, in point, is that treated in this paper. In
1934, a highway bridge was built over the Red Cedar hiver on
Kalamazoo Road between Lansing and East Lansing. The out-
line of the banks of the river, adjacent to the bridge, was
as shown in the situation plan at the end of this report.
During the ensuing fourteen years to 1948, the northwest
bank has been subjected to erosive action by the current.
This so-called "scouring" has changed the location of that
bank, as noted in the map.

The significance of this condition has been recognized
by local authorities. Further scouring of the bank can re-
sult in subsequent exposure of the foundation piles support-
ing abutment "A". This exposure is most likely to occur
when the summer low water level is less than Elev. 819.0
and the soil has been washed away under the abutment. Tim-
ber piles are most subject to decay at the water line where
they become alternately wet and dry, while the portion of a
pile, which remains continuously immersed in water, does not
decay and lasts practically forever.

This situation warrants the designing and building of a
structure to resist further erosive action. A retaining wall

has been selected as the design problem herein.

Enclosed are photographs from various angles showing
the present appearance of the site for the preposed re-

taining wall.

Photo No. l - Scour begins at this part or bank
Photo No. 2 - Erosion oocuring on west bank
Photo No. 3 - Additional view showing scouring
action
Photo No. 4 - Bridge adjacent to site of re-

taining wall

 

 

 

 

II Design of Cantilever Retaining Wall
A. Data and Assumptions for Design

Data:

 

Cantilever Retaining Wall
Surcharge: none
Impact (Vibration): none
Earth: We = 100 pcf

e = 0°

¢ ‘ 53° 40' = angle of internal
friction

Foundation pressure = 5000 psf (assumed maximum)

Specifications: (assumed)

 

wt. of Gene. = 150 pcf
f'c = 2000 psi n = 15
fc = 800 psi

v = 40 psi

u = 100 psi

fs = 18,000 psi

 

Design Constants: R = Egg = 159
J = 7/8
Coef. of friction between base & earth ' .40

I

        
 

/\‘- “/z/x /// \ ~ ~/./__, \. -

i

    

it we 1

B. Determination of Economical Dimensions

Pressure on base

 

C - cos 9 (nos 9 - c032 9 - cos? M)
(cos 0 + cosg’e - cosd C)

1-sin : 1-.554 = .287
l+sin 1+.554

p - th - .287X100Xl6 - 459 psg
459 x 16 = 5680 lb.
.__7;____

I.

 

 

 

 

 

 

 

 

AZ
///\\—‘~—// \\\///c~~/,/ ’ *
till
1 I It?“ ML; ”
W; l
"+3 $0" HIV 2L6.
hi .l/re/ 1”, 75¢] ""
_, xaza' :4

Check for trial width:
M - 5680 x 5.55 = 5/45 x 16 x 100
third pt. x (2/5b _ S/Bb)
- 19040- 12005 (2/55 - 5/8b )
19640-. 80052 - 450b2 - 550132
b2 = 56.1 b a 7.5 let b - 10'

Base pressures: Moments about too:

wl - 1.5x10xlx150 = 2250 lb. x 5.0 - 11,250 lb. ft.
W2 - lxl4.5xlxl50 - 2170 " x 5.0 - 6,520 " "
W3 - %x%xl4.5xlx150= 545 " x 3.67- 1,994 " "
W4 - §x§x14.5xlx100- 562 " x 5.85- 1.386 " "
W5 - 6xlxl4.5xlx100- 8700 " x 7.00- 60,900 " "

Wtot - 14,025 lb. 82,050 lb. ft.

Dist. from toe to Wtot : 82050 I 5.86 ft.

 

14025
I
........ .___5_§_3£_ 3.1. 40 1.40-.86- .74
5°35 14025 5.86 - 5.00 . .86

Eccentricity . .74 ft. ( mug-01. m 1/5 base 1: .60 - 1.67)
Since this design with base width equal to 10 ft. shows

a distance of .95 ft (1.67 - .74) between the extremity
of the middle third and the point where the resultant

load cuts the base, it was decided to take a smaller value
for 'b' in order to obtain a more economical design. It is
generally agreed that the optimum situation for economical
design occurs when the resultant cuts the base of the wall
at the extremity of the middle third.

Let b a 7.50 ft.
Iz"

///\\\”’\,\.\/” \ 5s

 

El. 320 Wafer

 

 

 

 

 

. " /
E 3660 M [are
a"
35-4" 255'
‘ W ’5 [L6 ’
Base Pressures: laments about toe:
'1 - 5.5214.sa:100 - 5075 15 x 5.75 . 29200 lb.tt.
I2 . 7.53: 1.51150 I 1690 H x 5.75 s 5340 u u
w; = 1/211/2x14.51100 - 562 x 5.65 . 1566 a "
'4 - l/2:l/2:tl4.51150 - 544 x 5.67 a 1997 a "
W5 :- 1:14.52150 I 2170: 5.00 - 6500 n '

Wtot- 9841 lb. 45425 lb ft

O
9 O
4 .u .
.l
0 C C

Dist. from too to Wtot s fl I 4.62 ft.
9841

3 .-
- 369° 3; s 2.00 ft. 4.62 - 3.75 - .87“.
5.35 9841

 

 

ROCCntricity'. 2.00 ' e87 . 1.15 ft.

(Allowable e 1.25)

B”. n.5,”. . g . .2. 1' so , 9841 ._.., 9841x1.15:5.75x12
A f 7.5' ' 117 gr...

1' I 1510 t 1185 = 2495 psf at toe
£23 psf at heel

'tot X mom. amm
E x 5.33

 

Factor of safety for overturning I

 

S.P. = 984114 62 3 45423
“#368015.“ W 8 2.32 (Allowable I 2.00)

Factor of Safety for Sliding =Ifiz_____0°°to___or_m__,,o,.t.,1.o,n,
s

8.1". i m = 1.07 (Anchorage not required since
3680 the soil 1- low in bearing
capacity and piles will be
driven)

Sometime during the spring, the Red Cedar River can be
counted on to reach flood levels and overflow its banks. Be-
cause of this, the forces acting will be analysed herein.

As shown in the following sketch, the earth pressure of
water pressure tend to cancel each other and consequently the
resultant force cuts the base closer to the center than at
low water. Therefore, the base pressure is less at the toe
than before.

The picture is also improved for shear along face a-b.
The bending moment on the stem could possibly be changed an

appreciable amount, however.

.1

0. Investigation of Forces during High Water

noments about face a-b I 5680 x 5.55 - 2000 (9.17)
'3 540ft1b' 650011111).

6 = v = 1680 = 4.00 in.
55' W
assume d t 12" at this
a - I 8 540 - 1.981s point
RB 133
As - s - 6500 I .054 in.2

mm

This area of steel will be taken carg of by temp. steel
spaced 5'-0" c/c i” 0 'I .20 in.

 

 

f/lfé bag #6 r

 

 

 

 

///(\\WA~- /,, \.\\//, ‘
Ear'ffl “-14." 85—0"Jeaa’
JL_
15-13680 '
[—21

 

D. Design of Heel Slab

W.
5'07: 1 :m

9 pa). L__1
MT 64* ..
a’ u
14% Watt) (Hf
’ 5’:

we r- 1.5 x 5.5 x 150 - 787.5 I 786

 

 

 

 

31 i 125 x 3.5 3 457.5 ' 438
32- 1110:}:5.5- 1940
laments about a-b:
4-5075 (1.75) + 788 (1.75) - 4:58 (1.75) - 1940 (1.17)=0
10250 - 767 - 2270 8 7,215 3 I a-b.

Bending causes tension in top fibers of heel slab.
VI5075+788-458-1940I54851b.

d'V'MBS ”5531:;
53'; W
Z I 5.5
d I n I 7213 2575 775
‘35 1'59 6 51.9
2 I 1110 psf
d I 7.20 in. I minim "d'
In this case assume 6. I 15 in. with 5 in. cover.
Check for allowable shear:

v I V I 3485 I 22.1 psi
WW

Steel Design for Heel Slab:

A, I I I 7215 x 12 I .566 in.2 reqd. per 12 in.
' s

Usez-i'dbarsI .401ng32
12 I 6" spacing c/c '
1

Check for Bond Stress: £0 3 5.14 in.

l3 V ' 3485 384.5 281 (100 0.1:.
£033 .

_ Therefore, special anchorage not required.
L = fs 9 3' 16000:.5 = 22,5 inches.

 

 

Iii"- x
’ I
.l '
_.'______ L
I 37" ‘T’T‘ I

 

 

/
J.
z

.. I
d "' {"2 ”—5 ”6/; 1499/ Qflflf:

- a

-'~

E. Design of Toe Slab

 

 

 

 

 

 

 

,6“ z I 2.5
2575 7'5.
x25
a; z I 795 per
2500
F‘J‘
z
w = 1.5 x 150 x 5.5 = 788 1b. as . 125 x 2.5 = 515 15.
R4 = 795 x 1 x 2.5 - 990 15. 35 - 1582 x 2.5 - 5950 15.

Moments about face 8-8:
-788 x 1.25 + 515 z 1.25 + 5950 x 1.25 3+ 990 x 1.67 = 6000 ft.l'

4350 + 1650
Shear I v I 4465 lb. Assume too 18" thick 0: d I 15"

v V = 4465 I 28.5 psi
53'! 1253778215

861 I6000
532' 125: 26.7

As I. I I 6000 z l2 3 .505 in.2 req'd. per foot.
s , .

Use 2}" 0 bars = .40 in.2 Bottom
at 6" spacing 0/6

Check for Bond Stress:

u 3 V 3 4465 = 108 psi
zofla e

L 3 st 3 18000 1|} 3 22.5 inches.
In x

Fe D0819. of at“

 

I/I\~s~/,,~~I// 9 Ill 7",”

14'4“

H

E-_3olo l6 —-

43,1 L: AMI,”
‘ . .
2’2

P‘thI .287‘:100:14.5-416

 

 

 

 

 

3 I 416 x 14.5 I 5010 lb.
-—T-.--

3h.” : 3°10 Ibo

d I 7 I 5010 I 7.17 inches
v """'""

d 8 I 8 14540 - 104e5 = 1002 ‘m0‘
3'5 15!
mt d . 15 in.

lake stem 12 in. at top
a 18 in. at bottom

7 a 28.7h2
F 1'"
Y: ' 14e2 he

Steel required at Junction of stem 6: base:

AsII =174 500 =.756 in.2
rm Imam-776515

‘x'figihzh;

xx - 28.7h5
"T"
8 4.2g3

Use a: 42 bars gives .75 in.2 per 12 inches

\NNQ gmxh. \b\0\\\§0b \5 0.0\ sexekNx oukhmth.
/ Z 3

/ / /

0'0

40

'20

{+16’Q‘IOII| (It I .V

w
W
I.
x.
as.
,6
W ?

0

 

.s-‘fl,

‘I..

'o. isle-v

on

{It

 

12 = 4 inch spacing
1 u
L I st = 18000:.5 = 22.5 inches embeMent
u 2
Investigation of shear a moment at third points:
7, = 14.55 h2 u, . 4.78 113

Where 7; a u, I shear a moment at any section “11"
dist. from top of wall

2214.5 8 9.67 11.- h v, a 14.55 x 9.672- 1540 lb.

I, - 4.76 53 a 4.78 x 9.673- 4520 ft.1b.

 

d-v 21540 =5.19 in.
#35 251778512

6 = 1 8 4320 . 3101 g 5058 1110 OeKe actual

5 "1'3! 'd' I 15"

As a n 8 4520112 - 255 114.2 '

153': mm ’
h s 14.5 a 4.85 ft. 73 = 14.55 x 4.852 = 555 lb.
T

a, = 4.78 x 4.85‘5 = 545 £5.15.

4

837 ~555 =.7981n.
"5'5 M
d I I I 545 = 5.92 I 1.98 or 2 inches
5 1'35
As s 545212 . .0577 15.2
W

0. Temperature Steel:
.0025 (ave.) x concrete x-section area

.0025 x 12 x 15 = .450 15.2

i¢@9"c/c . “£812”c/c
Use Front + . Back I .46 in.2

To support horis. steel in front of tom: Use i“ 5 bars 8 She"
Longitudnal bars in base: Use 4}“ 5 bars - 18" c/c

I

E. Design of Piles

Although data concerning soundings was not avail-
able for this design, helpful information was contributed by
Mr. W. C. Gunn, Civil Engineer. Mr. Gunn was the construc-
tion engineer for the bridge Job and consequently is familiar
with the supporting characteristics of the soil. Considering
the soil pressure developed at the toe, of the wall in.this
idesign, he advised the addition.of timber piling to assure
ample support.

The problem of spacing and size of piles was taken.up
with.Prof. C. A. Miller, Dept. of Civil Engineering. His
reference to a graphical method of determining this spacing
was greatly appreciated along with.his other helpful assis-
tance on the design of the wall.

Use 15 feet long piles, measuring 12 inches at butt and
tapering down to 9 inches at the tip. These piles can be
rated at 15 tons in this soil according to Mr. Gunn.

The graphical method for determining spacing is shown
on the following page. Since the theoretical center-line of
the piles on the toe side is only 1 foot from.the toe, the
piles will be moved.in another 6 inches. This will fulfill
the required.minimum distance of 18 inches from pile center-
line to edge of concrete. The second line of piles at 4

feet from the toe will be moved a corresponding distance.

\nhOQ hKhthxxflx 005%

U
26
e
m
5
M
/a
d
e
m
4a
+4
0

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i

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6/fi A65

 

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1
, .
, .
.I..
Q
\
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.
I
4.:

5
' \ . ~r
.- .- ._\\ '-
I‘.-.—~- I 0! ego—oh-..
- b

 

0' ”I ’
r.’ r
. 'f- '
l /
I l/
f
. . 1
/
o / '
e. f
I
| 1‘
e /
‘ I
4 / _
or .
." .
at
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t '
i
0 . .
I
g V
' . .
I
llo - --e e - o .
v. A
l
1-“ 1 A A A 1

 

Calculation of load transfered to each pile:

1.

[WI

I | ' 116’

W F 7%-
U l 32-0" I- IE
sr

 

 

 

 

 

 

 

 

Load er ile 8 2 '
uth 2%- fg. W I 2e3 x 4e5 ' 22,100 lbe

longitudnal
spacing. Load per pile equals approx. 11 tons.
Allowable pile capacity 3 16 tons.

Drainage We epholes

The drainage problem for this retaining wall is
somewhat different from the ordinary. Since the usual
location or weepholes near the bottom of the stem is,
in this case. below the river bed, the outlet will be
placed at a higher elevation (820 ft.). Above this
point bankrun grave]. is to be filled ~in as a filter-
ing medium for catching silt and other foreign matter
which would tend to clog the drains.

The weepholes are to be constructed by building
6" x 6" boxes integrally with the‘stem forms. This
technique is desirable because scrap lumber can be
used for the boxes and the work need not be complica-

ted by a possible difference in tile lengths and wall
thickness.

III Construction Estimate
A. Current Unit Prices
In the construction field,‘unit prices fluctuate
due to many varying conditions. Therefore, it is often
difficult to predict at a glance how much a certain struc-
ture will cost to build.

For this problem, the writer consulted with an.engineer
connected with a local contracting firm to get a typical
picture of the current prices in this area. The co-Opera-
tion of Mr. Dave Cole of the Reniger Construction Company
was greatly appreciated in connection with this matter.

The following unit prices will be used herewith;

Excavation
‘Power excavate - 80¢/yd.
Backfill - 25¢/yd.
Concrete

Materials: 25001b. - 5 sack concrete - $8.70/yd. deliver-
ed (ready mix)

Labor: Footing concrete - $2.00/yd.
Wall concrete - $3.50/yd.
Forms: Footings - Material - 15¢/sq.rt.
Labor - 25¢/sq.ft.
Walls - Material - 58¢/sq.ft.
Labor - 50¢/sq.ft.
Const. Joint - 50¢/lin.ft.

Reinforcing,Stee1

Material: Deformed, intermediate grade, billet steel
will be used.

Material Fabricated - $125/ton (this figure in-
cludes accessories such as
tie wire, beam chairs a
Spacers.)
Placing Steel - $50.00/ton
Carborundum Rub (surface finish)
Material - fi/sqd‘t.
Labor - 30¢/sq.ft.
Overhead - 10%
Includes: supervision, timekeeping, layout, expedit-

ing, sheds, workmen's compensation, social
security.

£9222. - a

M - 10% for a Job of this type and size.

B. Quantitie of Materials Estimate

Concrete : Footing -' Vol. = 28 x 7.5 x 370.7 x 1/27 a 240 cuoydso
Deduct cylinders gr pile heads:

Vol. of one cyl. = 11’th 3 .785 x l x lO I .655
z . cuefte

.655 cu.ft./cy1.x166 cyl. ' 108.5 cu.ft.
108e5 = 4.0 cu.yds.

240 - 4 8 256 cu.zds. ' conchol.in footing
StOm " V01. . 1 J’ 1.5 x 14e51370e731/27 8 249 cuqu.
T
Total Concrete Yardage 8 256 l» 249 I 485 cu.yds.
Steel : Footing steel top - i" 5 bars 5:.» rods 6 6" c/c
2 x 370 = 740 rods 740 x 5.17 i- 3820 lin.ft.
Footing steel bottom - i“ C bars 4'-2" rods @ 6" c/c
2 x 5‘70 x 4.17- 5080 lin.ft.

Footing steel longitudnal - 7%" 0 rods, entire length
- of wall
'7 x 5'70 8 2590 lin.ft.
Dowel steel - i” 57 bars - 4"«0'l - 4" c/c
5x570x43444011n.ft.
Stem steel - i“ W bars - ’7'-0" - 8" c/c
1.5 x 370 x 7 = 5880 lin.ft.
Temp. steel horis. - i" 0 bars
15 x 5'70 + 19 x 3'70 II 12,580 lin.ft.
Temp. steel vert. - 4}" 0 bars - 14'-6" - 5'-0" #0
14.5 x 125 rods 8 1780 lin.ft.
W: 8520 lin.ft. of i” ‘9’ bars
25850 lin.ft. or g" 0 bars
r ¢’/ bars weigh .850 lb/lin.ft.
i” 9! ' " .555 lb/lin.ft.
Total it. = 5520 x .350 + 25,550 x .668 . 25,020 15.
I 11.50 tons
Excavation: Slope trench 60° with horizontal
Volume of excavation I! agrxm I 2440 cu.yd.

 

Cost Estimate

Power Excavate - 2440 cu. yds. x .80¢/cu.yd.

Backfill - 1450 cu.yds. x .25¢/cu.yd.
Forms:Footing:

Materials - 15¢/sq.ft. x 570 ft. x g x 2

Labor - 25¢/sq.ft. x 5‘70 1: g x 2
Porms:Stem:
Materials - 58¢]sq.ft. 3.14.5 x 370 3.2
Labor - 50¢/sq.ft. x 14.5 x 5'70 x 2
Footing Concrete:
Materials - 256 cu.yd. x.8.70/cu.yd.
' delivered
Labor " 236 Gueyde : 3.00/cu.yd.
Stem Concrete: ‘
Materials - 249 cu.yd. x 8.70/cu.yd
delivered
Labor " 236 011.30. x sew/Weyde
Construction Joints:

One joint every 40 ft. = 92 Joints

3 3 1950.00

22 lin.ft./Joint x 92 Joints x 50¢/11n.ft.=

Reinforcing Steel:
laterials - 11.5 tons x $125/t0n
Labor (placing) - 11.5 tons x $50/ton

Carborundum Rub: upper art. of front sur-
face of stem will be rubbed for appear-
anOOe

laterials: - 8 x 570 x fi/aqxt.
Labor - 8.x 370 x 50¢/sq.ft.
Piling: 166 piles x $60/pile (driving i
materials)
TOte
Contractor's overhead I 10%

Contractor's profit 1' 81

362.00

259.00
452.00

4080.00
5570.00

2050.00
472.00

2170.00
872.00

1010.00

1440.00
575.00

14.80
888.00

9950.00

5189.48
2810:00

85 37894.28

V Bibliography

Urqhart. 9.15.1.1 Engineering Handbook.

Sutherland, 3., 8: Reese, R. C. Reinforced Concrete DesiE.
Pickels, Geo. W., Drainage g3 ELM-Control Engineering.
Underwood, 0., Standard Construction Methods.

Eshbach, O. 17., Handboog 2; Engineering Fundamentalg.

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