AD-173 16 LIFE-CYCLE NRLYSIS OF CORRODING SHEET PILE STRUCTURES

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*~ U"'R--R"US Anny Corpof EngineersConstruction Engieenng TECHNICAL REPORT M-86/12Research Laboratory September 1986

AD-A173 016

Life-Cycle Analysis of Corroding Sheet PileStructures for a Lock and Dam

byFrank W. Kearney

"his report documents research conducted at the ThomasJ. O'Brien Lock and Dam on the Ilinois Waterway inChicago to assess its structural condition, provide a strue.tural quality.vs.-time prognosis, and develop an appropriatecorrosion mitigation program. Although there is an abun-dance of design information for steel sheet pile structuraldesign, Including a program in the Corps of Engineers'computer-aided structural engineering (CASE) library, these 'pprograms are for new construction and do not consider theconsequences of corrosion damage. To realistically deter.mine the structural quality of the O'Brien Lock and todevelop a credible projection of its usable life, a specializedanalysis had to be developed for this particular structure;however, the analysis had to be general enough for use inother similar structures throughout the Corps.

Detailed field and laboratory analyses indicated thatthere is a large safety factor In the structure and that 0.25in. of corrosion can be tolerated anywhere without cata.

2" strophic results. However, corrosion that exceeds 0.25 in.0 L in highly stressed areas could cause catastrophic results.

C, lThe extreme value of corrosion calculated for the lockand dam is 0.0024 in. per year, which means that 83 yearsof corrosion must occur to achieve the 0.25 in. value.

It was found that cathodic protection could be used .ELEUTEl Uccessfully at this structure to prevent additional corrosiondamage. A deep well anode system is ideally suited for this OCT 16 Mproject.

B

Approved for public release; distribution unlimited. "

10 16 13 0 '

-C--7K- k 77 -71

UNCLASSIFIEDS5gCURIrY CLASSIFICATION OF THIS PAGE (3w. Dee. Entered)A

REPORT DOCUMENTATION PAGE RE CIMPTIO u RMs|. REPORT NUMBER 2. GOVT A NO 3. IENT'S CATALOG NUMBER

CERL-TR-M-86/12 1 ..

4. TITLE ( ,d Su ,ie) S. TYPE OF REPORT A PERIOD COVERED

LIFE-CYCLE ANALYSIS OF CORRODING SHEET PILE

STRUCTURES FOR A 1,01K AND DAM ___6. PERFORMING ORG. REPORT NUMBER

. UTOR() 6. CONTRACT OR GRANT NUMBER(*)

Frank W. Kearney

4. PERFORMING ORGANIZATION NAME AND ADDRESS 10. PROGRAM ELEMENT. PROJECT, TASK .'AREA & WORK UNIT NUMBERSU.S. Army Construction Engr Research Laboratory :KL. ;P.O. Box 4005 '

Champaign, IL 61820-1305 "',.,.;,

11. CONTROLLING OFFICE NAME AND ADDRESS 12. REPORT DATESeptember 1986

13. NUMBER OF PAGES119

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SCHEDULE 1

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Approved for public release; distribution unlimited.

-- % % h. ,* 17. DISTRIBUTION STATEMENT (of the ab.Irect entered In Block 20. If different from Report)

Copies are available from the National Technical Information Service

Springfield, VA 22161

IS. KEY WORDS (Continue anr' aim.. old. It necesary and Identify by block number) Iq~epe

Thomas ,J. O'Brien Lock and Dam %

corrosion *~vlocks (waterways) :'"oe,daln -

IS AMACT (tit sieeie o ffn.efs dfdily l black nuw)

This report documents research conducted at the Thomas J. O'Brien Lock and Damon the Illinois Waterway in Chicago to assess its structural condition, provide a structural

* quality-vs.-time prognosis, and develop an appropriate corrosion mitigation program.Although there is an abundance of design information for steel sheet pile structuraldesign, including a program in the Corps or Engineers' computer-aided structuralengineering (CASE) library, these programs are for new construction and do not considerthe consequences of corrosion damage. To realistically determine the structural quality

(cont'd,

13UITNCLASS IF I "El)SECURITY CLASSIFICATION Of THiS PAGE (When .Date Entered)

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BLOCK 20. (Cont'd)

of the O'Brien Lock and to develop a credible projection of its usable life, a specializedanalysis had to be developed for this particular structure; however, the analysis had to begeneral enough for use in other similar structures throughout the Corps.

Detailed field and laboratory analyses indicated that there is a large safety factorin the structure and that 0.25 in. of corrosion can be tolerated anywhere withoutcatastrophic results. However, corrosion that exceeds 0.25 in. in highly stressed areascould cause catastrophic results.

The extreme value of corrosion calculated for the lock and dam is 0.0024 in. peryear, which means that 83 years of corrosion must occur to achieve the 0.25 in. value.

It was found that cathodic protection could be used successfully at this structure toprevent additional corrosion damage. A deep well anode system is ideally suited for thisproject.

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FORPWORD

This research was conducted for the U.S. Army Corps of Engineers' ChicagoDistrict under Intra-Army Order 79-16, dated December 1978. The work was performedby the Engineering and Materials Division (EM), U.S. Army Construction Engineering

Research Laboratory (USA-CERL). The Chicago District Technical Monitor was Mr. I.Juzenas, NCC-DS.

Dr. R. Quattrone is Chief of USA-CERL-EM. COL Norman C. Hintz is Commanderand Director of USA-CERL, and Dr. L. R. Shaffer is Technical Director.

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CONTENTS

Page

DD FORM 1473 1FOREWORD 3LIST OF TABLES AND FIGURES 6

INTRODUCTION .................................................... 9BackgroundObjectiveApproach

2 FIELD TESTS AND RESULTS .................... ....... 11 .

3 LABORATORY TESTS AND RESULTS ................................ 49

4 STRUCTURAL ANALYSIS OVERVIEW ............................... 56

5 INTERLOCK FAILURE MODE ANALYSIS .............................. 58Variation of Interlock Strength with CorrosionNumerical Calculations of Strengths of Corroded Sheet Piles

6 ANALYSIS OF THE LOCK WALLS AND DAM ........................... 65Probable Modes of FailureShear in a Cross WallHoop Tension in a Cell of the Land WallHoop Tension in River Wall Cells and Dam Cells

7 ANALYSIS OF THE GUIDE WALLS .................................. 73Configuration of Walls and Tie Back SystemsPressure on the WallBeam Analysis of the Guide WallCrumpling of the Sheet PilesFailure of the Wale or the Tie RodCorrosion Failure Limits for the Upstream Guide WallCorrosion Failure Limits for the Downstream Guide Wall

8 CORROSION MECHANISMS AND MITIGATION ...................... 86Uniform AttackConcentration Cell CorrosionPitting CorrosionInterlock Crevice CorrosionMitigation

66

9 DEEP WELL ANODE SYSTEMS FOR CORROSION PROTECTIONOF O'BRIEN LOCK AND DAM ............. ....... ........ 89

Replaceable Deep Anode ConceptSystem Components and Their FunctionsInstallation PracticesSystem AdvantagesSubsurface Strata-O'Brien Lock and DamProposed Deep Well Anode Groundbed

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CONTENTS (Cont'd)

Page

10 CONCLUSIONS AND RECOMMENDATIONS ............................. 96

REFERENCES 98

APPENDIX A: Corrosion Principles and Cathodic Protection 99APPENDIX B: Nondestructive Evaluation Procedures-Polarization

Measurements, Ultrasonic Testing 111APPENDIX C: Notations 115

DISTRIBUTION

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TABLES

Number Page

1 Soil Resistivity Measurements--O'Brien Lock and Dam 20

2 Ultrasonic Thickness Measurements 26

3 Pit Depth and Area of Depth Measurements 31

4 Tensile Specimens--Uncorroded Lock Wall 51

5 Spectrographic Analysis of Test Pile 51

6 Spectrographic Analysis of Tubercles 52

7 Lock Wall Specimen Pitting Summary 53

8 O'Brien Water Samples From Lock Wall Cell Interior 55 '

9 Stress Required to Separate Claws of S-28 Sheet Piles 64

Al Classification of Electrolyte Resistivity 106

FIGURES

1 Four Locations of Test Piles 13

2 Pulling Test Piles 14

3 Corrosion Pattern Test Pile No. 1 15

4 Corrosion Pattern Test Pile No. 2 16

5 Corrosion Pattern Test Pile No. 3 17

6 Corrosion Pattern Test Pile No. 4 18

7 Soil Resistivity Test Locations 19

Polarization Corrosion Rate Monitor 19

9 O'Brien Lock and Dam (Ip=0.11A; IQ=0.15A; and Ic=0.064). 21

10 O'Brien Lock and Dam (Ip=0.93A; I-=0.67A; and 1c=0.39). 22

11 Lock Wall Waterside 23 -". .• -v

12 Dewatered Lock 24

13 Tubercle 24

6

Figures (Contkl)

Number Page

14 Ultrasound Testing Gauge 25 .-

15 Pit Depth Gauge 25

16 Tensile Testing 49

17 Typical Plot of Interlock Tensile Tests 50

18 Corroded Sheet Piles 57 kV

19 Uncorroded Sheet Piles 57

20 Exaggerated Illustration of Tensile Yielding of the Shanks 59

21 Combined Tension and Bending of a Ductile Bar 60 S."

22 Trace of Sheet Piles Interlock 62

23 Cellular Cofferdam 66• .- J

24 Cross Section of Land Wall of Lock 67

25 Segment of a Cofferdam Represented as an I-Beam 70 .

26 Stress in an Element of a Web of a Cross Wall 70

27 Cross Section of River Wall 72

28 Horizontal Section of Sheet Piling of Guide Wall 75

29 Guide Wall 75

30 Concentration Cell Corrosion 88 , A-

31 Deep Anode Cathodic Protection System 91

Al Electrochemical Reactions During Corrosion of Zinc InAir-Free Hydrochloric Acid 100

A2 Relationship of Potential to Net Current 103

A3 Variation of Potential in a Low-Resistance Electrolyte 104

A4 Variation of Potential in a High-Resistance Electrolyte 104 -.

A5 Impressed-Current Cathodic Protection 105

A6 Sacrificial-Anode Cathodic Protection 105 " AW

7. "

7 • .'".'. '.d,',.

Figures (Cont'd)

Number Page

A7 Typical Electrolyte Tank for Model Studies 108

A8 Field Mapping in Electrolyte Tank 108

A9 Electric Field Plot: Single Button Anode Energized 109

A10 Small Anode: Shadowing 109

All Shadowing: Plate at 45 Degrees 110 r.

A12 Shadowing: Plate at 90 Degrees 110 .

B1 Straight Beam Inspection Techniques Used in Scanning aTee Weld 113 C4.

B2 Angle Beam Inspection Technique Used in Scanning a Tee Weld 113 %

B3 A-Scan Presentation on Cathode Ray Tube 114

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LIFE-CYCLE ANALYSIS OF CORRODING SHEETPILE STRUCTURES FOR A LOCK AND DAM .*NI

1 INTRODUCTION

Background 1 '

In late 1977, the U.S. Army Corps of Engineers' Chicago District conducted apartial dewatering and inspection of the Thomas J. O'Brien Lock and Dam on the IllinoisWaterway in Chicago.I The inspection revealed excessive corrosion and severe pitting.This observation came at about the same time that the full extent of the corrosiondamage to the Lockport Lock and Dam (36 miles down the waterway from O'Brien) wasrecognized. The Chicago District asked the U.S. Army Construction EngineeringResearch Laboratory (USA-CERL) to analyze the corrosion damage, including its causesand extent, and to recommend remedial measures. . ,

The lock walls, guide walls, and dam all have a sheet pile structural system. -Although there is an abundance of design information for steel sheet pile structuraldesign, including a program in the Corps of Engineers' computer-aided structuralengineering (CASE) library, these programs are for new construction and do not considerthe consequences of corrosion damage. To realistically determine the structural qualityof the O'Brien Lock and to develop a credible projection of its usable life, a specializedanalysis had to be developed for this particular structure; however, the analysis had to begeneral enough for use in other similar structures throughout the Corps. '. ..

Objective

The objectives of this study were to assess the present structural condition of theO'Brien Lock and Dam, delineate a structural quality-vs.-time prognosis based onpredicted corrosion rates, and to develop the most appropriate corrosion mitigationprogram.

Approach

Carrying out these objectives required three major efforts: (1) establishing thepresent condition of the structure and appurtenances, (2) quantifying the ambient .corrosion environment, and (3) developing a projection of structural performance.

Evaluation of Site Corrosion Characteristics

The nature and extent of existing corrosion damage were examined and correlated ___with environmental history. Three elements were involved:

1. Field survey data analysis

'Thomas J. O'Brien Lock and Controlling Works, Periodic Inspection Report No. 3 (U.S.Army Corps of Engineers, December 1978). ,

9 ~

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2. Inspection and analysis of test piles

3. Corrosion environmental history determination.

In-Situ Corrosion Rate Measurements

The variation in corrosion conditions was determined by installing a continuouscorrosion monitoring system and measuring polarization current over several months. -

Cathodic Protection System Development

This activity involved developing a comprehensive cathodic protection corrosionmitigation system, including design of cathodic protection for the land side of lock wallsand guide walls, and design of cathodic protection for the water side of the lock walls,guide walls, and dam. Appendix A contains information on corrosion principles and -Lcathodic protection.

In addition, a structural analysis of the lock walls, guide walls, and dam wasconducted. This was a two-phase effort consisting of analytical studies and in-situtests. Based on the results of the site corrosion characteristics investigation, the presentstructural condition was assessed and a structural quality-vs.-time prognosis delineated. . •This included the following activities: ,,-

1. Determining the life-cycle of the lock and guide walls and of the anchor systems

2. Determining the structural integrity of the lock and guide walls in their presentstate of deterioration relative to original design requirements. '-v %

The in-situ measurements and tests, together with the laboratory testing, wereconducted simultaneously with the analytical work, and extremely close interaction wasmaintained. As the analytical work progressed, the need for additional field data wasnoted, and elements of the ongoing analysis were used to determine the most appropriatetest locations and procedures. . ,

During the field investigation phase, there was only one dewatering (in November '.1979); therefore, it was necessary to rely heavily on in-situ nondestructive evaluation .techniques (see Appendix B) for most of the field measurements, particularly the .polarization techniques. This investigation marked the first time that the Corps ofEngineers used a continuous and instantaneous corrosion rate measurement system. Thissystem was used to determine if there were any cyclical changes in the corrosivity ofwater flowing in the lock. .-

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2 FIELD TEST AND RESULTS .1L

In assessing the condition of a structure with corrosion damage, some type ofmeasurement is usually made to determine the metal loss. The loss is then divided by thetime it takes for this loss to occur; the resultant value is an average corrosion rate, -.---usually in milli-inches per year. To project life expectancy, this corrosion rate is used todetermine the specific time when the metal loss will reach the point that it renders thestructure unusable. In the case of the O'Brien Lock and Dam, such a simplified approach., .could not be used, because the ambient corrosive conditions were changing during the le%,

structure's 20-year existence, with a resultant variation in corrosion rate from year to* year. On the water side of the structure, the water quality changed as environmental

protection procedures were implemented; on the land side, runoff of water from landfilloperations near the project caused a variable electrolyte. It was therefore necessary touse innovative evaluation techniques to determine the corrosion mechanisms and theirimpact on various parts of the structure.

Fortunately, during construction, a series of H-beam piles had been placed adjacentto the lock structure; these piles were to be pulled out at 20-year intervals to indicatethe amount of corrosion damage. Figure 1 shows the location of the test piles, labeled 1through 4. These test piles were invaluable since they gave the corrosion indications forthe various depths for the backfill pattern used. Figure 2 shows the pile extractionprocess conducted in June 1978. The test piles were taken to USA-CERL for evaluation;the analysis used was identical to that used in a previous study. 2 Figures 3 through 6show the pattern of corrosion corresponding to various depths and backfill types. Asexpected, the corrosion pits are very severe in the region of coarse gravel backfill due toa crevice-type corrosion between the web and large stones. Analysis of this corrosionpattern served as valuable guidance for the ultrasonic measurements of the lock walls -during the dewatering inspection in November 1979.

Soil resistivity is another parameter affecting the corrosion rate on the land side of .. .-the structure. Several measurements were made adjacent to the lock wall and the guidewalls, as shown in Figure 7. Table 1 gives soil resistivity measurements. The extremevariation in soil resistivities was attributed to the nonuniformity of the backfill. The low

values of resistivity obtained at points 5, 6, and 7 and at points 17, 18, and 19 werecaused by septic tank effluent residue. These resistivity values, coupled with the landfilldrainage water, indicate a severe corrosion problem..

Although water samples were taken to determine the corrosivity of the waterwaywater, results of these samples would not indicate any cyclic variation in waterconductivity that might occur throughout the year due to increased barge traffic, heavywater runoff, etc. To determine if this might be occurring, USA-CERL installed a uniquecontinuous and instantaneous recording corrosion rate instrument. This device providesan indirect corrosion current reading or corrosion rate measurement by taking advantage ' ",.of the fact that there is a measurable relationship between the direct corrosion currentand the effect of an externally applied current on a metal surface. The sensing probeassembly is shown in Figure 8. The three electrodes at the tip of the probe have thesame carbon steel composition as the O'Brien structure's sheet piling. Analysis of dataobtained over about I year indicated no extreme variations in the water's corrosivity.

2A. Kumar, R. Lampo, and F. Kearney, Cathodic Protection of Civil Works Structures,Technical Report M-276/ADA080057 (U.S. Army Construction Engineering ResearchLaboratory [USA-CERLI, 1979).

..............................-. "2~. . . . . .. . . * .-..-... ,11.. . U * .* .*+"* "-""*"-

To assist In cathodic protection, design polarization, current requirement, and IRdrop tests were performed; these design curves are given in Figures 9, 10, and 11. USA-CERL Technical Report M-275 provides an extensive discussion of these types ofmeasurements.

3

In November 1979, the lock chamber was completely dewatered for the first time. , %There had been a partial dewatering in 1977, which was when it was determined that acorrosion problem existed. Figure 12 shows the dewatered lock. Besides the variouscorrosion products and contaminant buildup, there were numerous corrosion tubercles.Figure 13 is a close-up shot of a corrosion tubercle; Chapter 9 discusses how this type ofcorrosion forms. To ascertain what corrosive factors had affected the structure over thepast 20 years, several tubercles were dissected and the laminations studied; results areprovided on pp 49-55.

After the various corrosion formations had been analyzed, the entire lock wallsurface was sandblasted to provide a clean metal surface for ultrasonic thicknessmeasurements. These measurements were made with a state-of-the-art portable --electronic system (Figure 14). To systematize the measurement pattern, the coffer cell ,..numbers assigned in the construction drawings were used. Measurements were madestarting at 1 ft from the top of the cell and continuing down to the bottom point at 13 ftbelow the top of the cell. Table 2 provides the thickness measurements. Overall valueswere: thickness--0.348 in.; standard deviation 0.008 in.*

To establish the pitting factor for the lock wall, a pit depth gauge was used (see .Figure 15). Table 3 gives the pit depth and area. No statistical analysis can be used tosimplify the interpretation of these data; rather, it requires a tedious point-by-point .'evaluation to determine the seriousness of this pitting corrosion. Essentially, a "worstcase" analysis is used; that is, the deepest pit measured on the water side is coupled withthe deepest pit measured on the test piles representing the land-side corrosion of thelock wall; this value represents the maximum web thickness deterioration. After thesemeasurements were taken, suspect areas were re-examined; no incipient perforationswere detected.

.

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.. 4.-.'-3 F. Kearney, Corrosion of Steel Pilings in Seawater: Buzzards Bay-1975-1978, Interim "IReport M-275/ADA078626 (USA-CERL, 1979). .. ' ,.

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Figure 8. Polarization corrosion rate monitor.

19

.A5 *NONV. *~.5

Table 1

Soil Resistivity Measurements-OBrien Lock and Damrnle(12-14 June 1979)

Position(100-f t

Intervals) 5 ft 10 ft 15 ft Location Comments

1 45,002 55,535 9,4792 4,213 3,830 3,4473 5,457 3,830 2,8724 3,159 2,872 2,870 ~ k.5 3,351 2,298 1,9536 4,596 2,872 1,7237 4,787 2,489 2,2408 10,532 18,192 10,915

*9 143,625 157,030 120,645 Opposite Gate Recess10 172,350 178,095 129,262 Opposite Gate Recess .11 1,436 689 718 Along Fence12 13,405 17,235 9,19213 5,074 3,830 2,29814 47,875 53,620 40,215 '"15 25,852 45,960 43,087-16 4,213 5,170 1,723 Opposite Metal Pile17 7,085 6,511 6,60618 7,660 6,128 6,606 __19 4,787 3,447 3,73420 2,393 1,340 1,062 Opposite Brick Building

*21 230,040 185,755 163,732 End of Sheet Piling%22 191,500 134,050 86,175%23 210,650 180,010 109,155

%' %~16%& F

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.002 .4

.0011.200 0 -. 200 -400 -600 -800 -1.000 -1.2

VOLTAGE .-

Figure 9. O'Brien Lock and Dam (I .= .11A; I 0.15A; and 1e 0.064). S.

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Flgur, 10. O~rien lock and Dam (p = 0.93A; IQ 0.67A; and I = 0.39).

22

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Table 2

Ultrasonic Thickness Measurements

Pile No. 1 2 3 4 5 6 7 8 9 10

1 ft .368 .352 .350 .353 .358 .353 .362 .348 .342 .3562 ft .347 .364 .346 .355 .350 .357 .347 .348 .353 .3513 ft .330 .351 .353 .363 .360 .362 .350 .341 .353 .3584 ft .353 .327 .348 .353 .358 .349 .354 .359 .353 .3515 ft .330 .352 .335 .353 .355 .347 .342 .352 .348 .3416 ft .360 .347 .354 .348 .355 .340 .342 .344 .352 .3297 ft .355 .354 .353 .360 .357 .353 .344 .343 .362 .3398 ft .350 .333 .358 .346 .345 .330 .343 .336 .351 .353 A9 ft .333 .370 .355 .335 .354 .338 .350 .346 .350 .349 .

10 ft .356 .357 .363 .354 .348 .337 .340 .346 .350 .33511 ft .349 .345 .352 .354 .344 .336 .347 .342 .345 .34012 ft .367 .360 .345 .355 .345 .346 .339 .351 .349 .34113 ft .367 .358 .347 .333 .363 .342 .346 .354 .341 .350

X* .351 .3515 .3506 .3509 .3532 .3453 .3466 .3469 .3499 .3456SD** .013 .012 .0068 .0086 .0062 .0092 .0063 .0060 .0054 .0087

Pile No. 11 12 13 14 15 16 17 18 19 20

1 ft .360 .356 .352 .359 .353 .2 ft .353 .356 .337 .349 .3483 ft .346 .335 .3524 ft .350 .346 .3475 ft .342 .348 .351

A

6 ft .353 .327 .3467 ft .340 .354 .347 .348 .347 .-8 ft .347 .346 .341 .344 .352"-9 ft .344 .342 .342

10 ft .339 .348 .34711 ft .342 .347 .33912 ft .334 .348 .347 .347 .349 .351 .354 .347 .352 .34613 ft .352 .353 .354 .350 .352 .347 .346 .352 .347 .352 .

X .3463 .3466 .3463 .3495 .3505 .3490 .350 .3495 .3495 .3496

SD .0071 .0082 .0079 .0050 .0021 .0028 .0056 .0035 .0035 .0030

= mean.**SD = standard deviation.

S.. .-. _,

26

aafl .-. M.-

-PFI %,- N-. -Vrv r.ArjL

Table 2 (Cont'd) ..-

Pile No. 21 22 23 24 25 26 27 28 29 30

1 ft .346 .340 .357 .353 .363 .351 .358 .3512 ft .347 .349 .346 .344 .351 .351 .355 .351

.00 "

3 ft4 ft5 ft6 ft7 ft .352 .339 .351 .344 .345 .345 .340 .338 .358 .3408 ft .348 .340 .347 .353 .349 .347 .350 .349 .346 .3579 ft

10 ft11 ft12 ft .340 .345 .346 .355 .349 .348 .351 .349 .348 .34513 ft Not .346 .342 .349 .340 .347 .347 .351 .351 .351 ,. .

Blasted

X .3466 .3431 .3481 .3496 .3495 .3467 .347 .3481 .3526 .3491SD .0043 .0040 .0051 .0048 .0076 .0012 .0049 .0050 .0051 .0058

Pile No. 31 32 33 34 35 36 37 38 39 40

1 ft .353 * .355 * * .357 .3582 ft .350 * .348 * * .354 .3473 ft4 ft5 ft6 ft7 ft .345 * .347 .347 .339 .353 .3478 ft .345 .345 .344 .352 .345 .348 .342 ,.9 ft

10 ftli ft12 ft .347 .348 .356 .350 * .352 .35013 ft .340 .350 .342 .350 * .348 .355 .".-

.3466 .3476 .3486 .3497 .342 .352 .3498SD .0045 .0025 .0057 .0020 .0042 .0035 .0058 .. ,,_

• = Too rough.

*'0

* 27

% % e

Table 2 (Cont'd) z

Pile No. 41 42 43 44 45 46 47 48 49 50

ft * * * * * * * * *2 ft ***4 ft

5 ft6 ft .7 ft .340 * * * .361

8 ft * * * * .352 .359 * .361 .3519 fft

* l0oft11ift-12 ft .350 .360 .346 .366 .348 .354 .349 .342 .344 -13 ft .347 .348 .330 .358 .343 .347 .351 .354 .342

.3485 .354 .338 .362 .3457 .3533 .3500 .348 .3495SD .0021 .0084 .0133 .0056 .0053 .0060 .0014 .0084 .0085

Pile No. 51 52 53 54 55 56 57 58 59 60

1ift .359 * .352 * * * * * *2 ft .348 * .350 * * * * .349 * *3 ft

5 ft

6 ft7 ft .359 .357 * .363 * .345 .340 .348 * .3548 ft .351 .361 * .349 * .339 .363 .349 * .3509 ft

10 ft11 ft-.- .,

12 ft .362 .355 .348 .343 * .361 .363 * .334 .34813 ft .339 .333 .347 .347 .341 .357 .363 * .343 .350

X .353 .3515 .3492 .3505 .341 .3505 .3572 .3486 .3385 .3505SD .0086 .1258 .0022 .0086 0 .1024 .0115 .0005 .0063 .0025

* = Too rough.

, .,.. ..

J. % .0

%e %I t28

.':. ,,, . ,., ., -,..,.,,..... .,.,.._-.'_,,._, -T,.':',' ". '3' , ' .' .: .. ,'.'....'.. ,'..,. .. . ... .NON.

I 1 ] t-l/ l "i "i ". 1 . % % l / %/ ! /=.I - I , I .m - - . . .i- I II"I .- - -. .- l -

Table 2 (Cont'd) A',p .- "o%'

Pile No. 61 62 63 64 65 66 67 68 69 70

I ft * * * * * * .347 * * *, 2 ft * * * * * * .351 * * *3 ft J4 ft 05 ft6 ft r9.7 ft * * .355 .363 * .350 .346 .353 .351 *8 ft * * .357 .364 .347 .351 .344 .354 .343 *9 ft

lo ft11 ft12 ft * .352 .336 .339 .359 .351 .330 .351 .355 .345 'A13 ft * .340 .345 .346 .354 .346 .346 .342 .349 .355

x .346 .3482 .353 .3533 .3495 .344 .350 .3495 .350 % -6,% -SD .0084 .0097 .0124 .0060 .0023 .0072 .0054 .005 .0070

% 7

Pile No. 71 72 73 74 75 76 77 78 79 80

1 ft .347 * * * * * * *

2 ft .351 * * * * * * * * *3 ft -

4 ft5 ft6 ft .7 ft .352 .355 .333 * .349 * .337 * * .3538 ft .346 * .338 * .348 * .356 * * .3479 ft

10 f tlift" "

12 ft .354 .346 .327 .348 * .346 .344 .333 .347 *13 ft .353 353 .342 .335 .347 .351 .339 .342 .358 .344

X .3505 .3513 .335 .3415 .348 .3485 .344 .3375 .3525 .348SD .0032 .0047 .0064 .0091 .001 .0035 .0085 .0063 .0077 .0045

• = Too rough.

• .. *

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r. , % ',, - .,, .. % . . '. . . .' ' -. .- ' . . , -. , " " " - - .- .. .- . . .- .- ,,. ..- .: :- .. -.. .-

Table 2 (Cont'd)

Pile No. 81 82 83 84 85 86 87 88 89 90

I ft .356 * * * * * *2 ft * * * .358 * * *3 ft4 ft5 ft6 ft7 ft * .352 * .353 * .344 .354

8 ft * .349 * .351 * .348 .3489 ft

l0oft11 ft12 ft .348 .351 .355 .354 .348 * .35013 ft .351 .351 .348 .348 .347 .344 .347

X .3516 .3507 .3515 .3528 .3475 .3453 .3497SD .0040 .0012 .0049 .0037 .0007 .0023 .0030

4 _ _ -_

• = Too rough. .

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3 LABORATORY TESTS AND RESULTS

To complement the field tests, several types of tests were performed in the 00

laboratory. The tests were designed to measure material properties, such as tensile andinterlock strength, compare the strength of corroded and uncorroded components, assess

the structure's integrity, and provide constant values for use in later analysis. Thetesting was done on specimens obtained during the field testing. Figures 16 and 17 andTables 4 through 8 provide results of the laboratory tests.

.

-. . -.

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Figure 16. Tensile testing.5 ..:, .. . .

5.'.-"-

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50 ..

Table 4 %

Tensile Specimens-Uncorroded Lock Wall 4

Specimen Initial Area (in.2 ) Yield (psi) Ultimate (PSI)-

A .251 x .503 = .1264 43,547 74,443B .251 x .503 = .1263 44,338 74,426

.504 x .3755= .1893 43,547 74,443 ._

2 .504 x .375 = .1890 44,339 74,4263 .504 x .377 = .1900 43,684 73,1584 .504 x .376 = .1895 40,633 72,296

.- 4 ,.-.. ,

Table 5 0

Spectrographic Analysis of Test Pile

Sample Number: 3 "-'

Carbon 0.36%'"-'"-?

Manganese 0.82

Phosphorus 0.006

Sulfur 0.021 "

Silicon 0.06

Nickel 0.01

Chromium 0.04

Molybdenum

Table 6

Spectrographic Analysis of Tubercles*

Sample Number: 1

CO3 3.45%

NO 3 0.12

SO4 1.44

Chlorides Present

Qualitative Spectrochemical Analysis and Concentrational eachEstimates of Detected Constituents

Iron Major Constituent .. '..Silicon 0.3 - 3% ..-. 2Aluminum 0.05 - .5 .,,.Zinc 0.03 - .3 ..Magnesium, Calcium 0.02 -. 2 each ASodium, Manganese 0.01 -. 1 eachTitanium 0.003 - .03 %" dl eLead 0.002 - .02-., .'-,

Molybdenum, Zirconium, Tin 0.001 - .01 eachCopper, Nickel 0.0003 - .003 each

Chromium 0.0002 - .002 ,:.

Vanadium, Cobalt 0.0001 - .001 eachAsh 73.25

Sample Number: 2

CO 3 4.80% -'

NO 3 0.13

S04 1.98 *'

Chlorides Present .

Qualitative Spectrochemical Analysis and ConcentrationalEstimates of Detected Constituents

Identical to No. 1 except for:

' Sodium 0.02- .2%

Ash 52.12

*Analysis is based on the recovered ash.

52 1,st "%%A

Table 7

LokWall Specimn Pitting Summary

(Specimen Plate Size--8 x 11 in.)A• . .\-" ,, "

Cell Sample No. 2

Average thickness 0.349 in. (14 data points around edge; ultrasound testing in samelocations.)

Depth Number Total Area Average Area

.030 4 1.7875 .4468

.035 5 .4375 .0875

.040 6 .5625 .0937

.045 1 .0625 .0625 "

.050 2 .4375 .2187

.055 1 .125 .125 ..065 1 .250 .250.085 1 .125 .125 '. -

"- Cell Sample No. 17

Average thickness: 0.340 (10 data points) .'. .'

Depth Number Total Area Average Area

.030 2 .375 .1875

.035 4 1.250 .312-,

.040 2 .375 .1875

.045 6 1.500 .250.000 .000 .000.110 1 .375 .375 . , ... "

Cell Sample No. 34

Average thickness: 0.3398 (16 data points)

Depth Number Total Area Average Area

.030 17 4.7187 .2775

.035 4 .625 .156 . • *

.040 6 2.125 .354

.045 2 .375 .1875 -

.000 - .000 .000

.100 1 .0625 .0625

53 % %

-. , ., . , -= .- , _ - ,. . - . , .- , - - , . , . , . , _ ,, . , . - ",r5. 5.",",-5.5." P . "" "

'' ." : % "'""* """

" """ "" "' " -- ' -. = '. '"

% " " ""e'". "' .r%. ,, e "." " 4"" " . . .

", " " , , % . .' . , ." . , . , . . '. " % . ' " . ' " . ' ; " . . ,- , ' .. '. ' ." ' '. " '-, - . '. ' .• , , , . ", , - ' ," , ,, .' .# % ,

77

Table 7 (Cont'd).

Cell Sample No. 35

Average thickness: 0.3365 (16 data points)

Depth Number Total Area Average Area

.030 19 3.999 .210

.035 5 .875 .0175

.040 13 1.575 .121

.045 4 .500 .125

.050 21 2.1874 .104 ..055 2 .125 .0625.060 12 1.3125 .109.065 1 .0625 .0625.070 12 .8279 .0689.075 2 .0625 .0312.080 1 .0625 .0625.085 1 .0625 .0625.000 -. 000 .000.100 1 .0625 .0625

* Cell Sample No. 60

Average thickness: 0.340 (10 data points)

Depth Number Total Area Average Area

.030 6 1.875 .312

.035 6 .0937 .0156d.045 1 .500 .500 .

.050 3 .750 .250

.060 2 .375 .1875.000.000 .000

.090 1 .375 .375

V %

S'S.

544

.... ~y-

Table 8

O'Brien Water Samples From Lock Wall Cellinterior (19 November 1979)

Chloride Samples 12/13/79

Sample No. Chloride Content(Cell No.) Mole Equivalent/Liter

Ave

6 67 6 ,6

41 5 55 ' .-;'

% 10 r23 10 10. -,9

102 10 10

10 -. ~~ .- _-,57 5 5 ""J.":-

6 "

57 2nd Sample 5 55

6 2nd Sample 6 66

'-:"-N ... ".

. v

" " %-%ii

4.........

e..... 4 J % %4J* %4 %* %~~ %~~ ( ~ d J * ***-

4 STRUCTURAL ANALYSIS OVERVIEWThe purpose of the structural analyses provided in Chapters 5, 6, and 7 was to

estimate how long the sheet pile structural systems of the lock walls, guide walls, and

dam would function satisfactorily without major repairs, and to provide a basis fordeveloping a corrosion mitigation procedure. The life of a lock and dam depends on the .corrosion rates in critical areas of the structure, but the stress analysis concentrates onminimum allowable thicknesses of sheet piles. The life of a sheet pile is the time it takesfor corrosion to reduce the pile's thickness to its minimum allowable value.

Although pitting is harmful, it is not easily accounted for mathematically, exceptby statistical estimates of how much the pits reduce the mean thicknesses. Small,isolated, reduced sections in the sheet piling are not dangerous; also, corrosion reducesthicknesses rather uniformly. For example, Figure 18 is a profile of two interlocked testspecimens cut from a test pile that had been underground for 21 years. Rust on thespecimens was sand-blasted off. Corrosion had reduced the web thickness by about 33percent, but this was an extreme case. The claws of the specimens are bent because .?they were pulled apart in laboratory testing. Figure 19 shows a specimen that ispractically uncorroded; it had been embedded in clay near the bottom of a test pile for '.' . "21 years. %

The analyses given in Chapters 5, 6, and 7 are based on assumptions that render thestresses on the piles statically determinant. The factor, C, by which the hydrostaticpressure of the soil is to be multiplied to provide the pressure on a sheet-pile wall is notwell established. Rankine' derived the formula:*

C = tan2(450 ) [Eq 1

where e is the angle of friction of the soil. A formula of Coulomb5 sometimes is ,.*...recommended in preference to Rankine's formula, because it involves an additionalparameter--the friction of the soil on the wall. Terzaghi6 suggested that e = 340 forgravel, but argued that determination of C is a matter of engineering judgment. For thisanalysis, the value C = 0.45 is used, in conformity with Coulomb. If Eq 1 is roughlycorrect, the value C = 0.45 is quite conservative.

The density of the fill at O'Brien Lock and Dam is not exactly the same as the.*

density of the clay subsoil. Also, the variable C for the fill need not be the same as that %of the subsoil. However, due to the uncertainty in the value of C, these differences areignored.

All elevations except these quoted from referenced reports were measured fromv the bottom of the relevant sheet piles. ....

4S. Timoshenko and S. Woinowsky-Krieger, Theory of Plates and Shells, 2nd ed.(McGraw-Hill, 1959).

*Appendix C summarizes and defines the variables of all equations provided in this Ireport.5D. W. Taylor, Fundamentals of Soil Mechanics (John Wiley and Sons, 1948).6 K. Terzaghi, "Stability and Stiffness of Cellular Cofferdams," Trans. ASCE, Paper 2253(September 1944), pp 1083-1202. ~/

56

or d. . .e -f . . .. . . . .I? .-f

m.," ",- ",. = , -- ",,- .. ._,.t. .--. ",Y. " . r ... ")' ' .e .. #. . / .,,,Z ," , , "". . . "."' -# .- " . '.-,''k . " ".. .%.,-i p , ,/t; je'forP e, "dt' "% fe , ;, " . #;,'./-,,t ,q'" e ",',_" !""•" "e. ._ '.". - , •e,', "• .",. ,0 ,1 .*-.'J• ' , .. ,, '' -. .. . ." I e .•" ".,p .',,. ", ."

% %. %

PROFILE OFCORRODED S-28SHEET PILESPiles hod been buried in a dompenvironment for 21 years

4%

Figure 18. Corroded sheet piles.

S. e

* ..,.,p .,, ....-

PROFILE OF

UNCORRODED S-28SHEET PILESPiles had been buried deeply in S

* clay for 21 years

Figure 19. Uncorroded sheet piles.

. .% %%

5 INTERLOCK FAILURE MODE ANALYSIS

Variation of Interlock Strength With Corrosion

. Hoop tension in the walls of a cellular cofferdam may damage the sheet piling,either by rupturing the webs or by pulling the claws apart. The hoop tension required torupture the webs is to ,

U

Figure 19 is a profile of two interlocked segments of sheet piles with littleapparent damage, although this specimen had been buried deeply in clay for 21 years. Apossible eventual mode of failure would be simultaneous tensile rupture of the shanks of % e%the two bulbs. Before such a failure could occur, there would be considerable elongation % %.%of the shanks, as illustrated by Figure 20. It is apparent that the load, Nu , per inchrequired to cause this type of failure is

Nu = 2tlO [Eq 2JU

If the shank thickness, t., is reduced greatly by corrosion, this type of failure mayoccur. Certainly, Nu = 0 if t I = 0. Usually, however, the shanks must bend before theclaws part. Bending of the shanks causes the bulbs to pull on the hooks, and the hooksmust also bend before the claws part. This behavior was illustrated in Figure 18.

The shanks and the hooks are subjected to combined tension and bending. Beforeshanks and hooks analysis, combined tension and bending of a ductile rectangular bar of -thickness t and width w should be considered. The bar is subjected to a tension N and abending moment M. Then N w is the load per inch of width, and M is the bendingmoment per inch of width. Consequently, the dimension of Nw istF L

- I and thedimension of M is iF]. With the usual assumption that plane eross sections remainplane, the axiar strain e is a linear function of the transverse coordinate x, that is,

yc= ax + b, ""Y -K;.

as illustrated by Figure 21. Consequently, the distribution of stress a on the crosssection is identical in form to the stress-strain curve of the material (Figure 21). Thetension N and the bending moment M are determined by

t/2 t/24' N = J" a dx, M = - J" xo dx [Eq 3]

-t/2 t/2

The stress-strain relationship is represented by

a = f(c ) = f(ax+b) " :.

If the function f is given, the integrals in Eq 3 can be evaluated, and then a and b can be _______* expressed algebraically in terms of M and N. Then the abscissa c of the point of zero

stress and strain can be determined by the equation• .~ o',t,, .

E£ = ac+b =0 [Eq 4t1

In general, c depends on M and N.

* 58

.16 P.

y:

•... . ,, ' , *% o

. %

.,,. , .. -

k.-.-. .. .,. -- -,',-: -

I ;":-.p... .

IFigure 2O. Exaggerated illustration of tensile yieding of the shanks. -, :

a .- I

.'- a.. - °° .... / .*;* * . * ' - %' % =%.a.a o' . *.d. . . • ' .. % .. * / -% . \.$ - -o... .. S.. . . %% a-" : - . ''* ", ' "."d P "- '. ' .. "" ' . • .'

mill-

dO'*U

GE8

.4 *

-.

OJ'f

.........

Flwe21 omind esin ndbndngofadut~ br

60p

i1 N

The limiting case is reached if all the material is stressed to the ultimate valueof o . Then the stress distribution is as indicated by the dashed line in Figure 21, and afull plastic hinge is said to exist. For this case, it is seen from Figure 21 that

N - (i c) a + (it - c) a=0 [Eq 512 U 2

This equation reduces to:

N - 2 co = 0. [Eq 61

Also, equilibrium of moments about points 0 requires that

1 0 (1t + c) 2 la (1t - 2 0N c + M (-[- Eq 712u 2 2 )=

or 12 2

Ntc +M- a (- +c2) =0 [Eq 81u 4

Elimination of c from Eqs 6 and 7 yields

2 tN2 (Eq 91U a a _

Equation 9 is to be applied to the shanks and hooks of an interlock. 9

When a claw is under tension, the right-hand bulb exerts a force, N2 , on the left-hand bulb. If the claw deforms symmetrically, this force acts along the center line ofthe webs, as illustrated by Figure 22. The left-hand hook exerts a downward force, N1 ,on the left-hand bulb. The total tension in the shank of the left-hand bulb is N1 + N2 .The bending moment in the shank of the left-hand bulb is "

M = N e - Nle [Eq 1012 2 11 0

When a fully plastic hinge develops in the shank of the left-hand bulb, Eqs 9 and 10 showthat

(N + N2)2- 2 -1 24(Ne 2-Ne I t (IEq 11]

From Figure 22, the bending moment in the left-hand hook is Nle 3 . Consequently,by Eq 9, a fully plastic hinge develops in the left-hand hook when

4N e = t20 - 1 [Eq 121 .... ,.1 3 2 u a

Eq 12 yields

2N = 2eo (-1 [1 + 4 2 [Eq 13]

3

~61

.416l~~ .. ~ ".1 .

,.=# . , . ,- -. " % , - " " % -. % %' " " '* . . . ' " - p . = . ," ,. .- .,, , .

Nc

N2

t2t

N N

.'." -,, -L ,

Figure 22. Trace Of sheet piles interlock. :,-;::

62 "- , ...N N * . -%Z:'

, % N

., ,'

',V '.-,"'''' ""'-''",; .- , ,:- ..,.".",'-"""-- .,, w ,"-",",",', , J . , :.'.'.." " .• ., .,"•

Eqs 11 and 13 determine N1 and N2 . Generally, N2 > N1 , since the shanks bendoutward. It is convenient to write Eq 11 as follows:

1 N2 eo4N (e +e)a ta 0E 4(NNI + N2 + 4(NI + N2)e2u -4 e 1 e2u - 1 u 2U=04

Figure 22 shows that the total tension carried by a claw is

N = 2N1 + N2 [Eq 151

Both N1 and N2 are directly proportional to a % %2 UThe distances e and e are not known exactly. In view of this uncertainty, it is

reasonable to assume-that eI : e2 . Since ev + e3 is the distance between th centerlinesof the shank and the hook, e3 is then determined. Corrosion does not affect theeccentricities e 1 , e 2 , e 3 , but it reduces the thicknesses tI and t 2 , as well as the web -O..thickness t. It is assumed that t, and t 2 are reduced by the same amount, e.

Numerical Calculations of Strengths of Corroded Sheet Piles

Piles in the land wall, the river wall, and the dam are made of U.S. Steel No. S-28.The initial web thickness is t = 0.375 in. Figure 22 is a tracing of an interlock of S-28 -. -piles. Initially, the shank thickness is t, = 0.35 in., and the hook thickness is t 2 = 0.50 in.,as determined by measurements of uncorroded specimens. After uniform corrosion,

d these thicknesses are reduced to

t = 0.375-c, t1 = 0.35 -c, t = 0.50 -e * "'

where E is the reduction of the thicknesses caused by corrosion. Also, by measurementsof the specimens,

eF = e2 = 0.48 in., e3 = 0.56 in.

For the following computations, a is taken to be 60,000 lb/sq in., although this value .,'.may be low.

With these numbers, Eq 13 determines N 1. Then Eq 14 is a quadratic equation that

determines N1 + N. Finally, N is determined by Eq 15. This value of Nu is supersededby the value given'y Eq 2, if Wt is lower. In turn, both of these values are supersededby to , if It is the lowest value. However, according to the present calculations, S-28 %. .piles Fail because the claws part, rather than because of shank fracture or web fracture,unless the corrosion is extremely severe.

Table 9 presents computed stresses Nu (lb/in.) required to pull the claws apart. VIN I,These values are less than the web-rupture stress to or the shank-rupture stress 2t cu. ;a ..A graph of the data in Table 9 is roughly a straight ine. Although Table 9 was computed r 0with a = 60,000 lb/sq in., the stresses Nu corresponding to any other value of a can becomputed by proportioning the values in Table 9 directly as a

sl .'

63 ~~*'

.1.. J. .

,%' It% '

Table 9

Stress Required To Separate Claws of S-28 Sheet Piles

cy 60,000 lb/sq in.) .

S(i n.) NU (lb/in.)

0 211200.01 20320

0.06 164800.07 157500.08 179000.09 143300.106 16480p0.02 120300.11 12960 4

0.17 123000.18 81660

0.215 0610

0.22 660

0.24 6560

0:25 5160

0.26 473

64'

r.7t

% %

• % . 4'

6 ANALYSIS OF THE LOCK WALLS AND DAM

Probable Modes of Failure

The lock walls and dam are cellular cofferdams formed from interlocked S-28 sheetpiles driven into clay and hard glacial till. Figure 23 shows a plan view of a lock wall. 16Where a cross wall joins the cylindrical walls, there is a Y-shaped pile; the other sheet.piles are flat. The cells are filled with gravel. . .

A cellular cofferdam may fail in several ways. One type of failure is generalheaving or tilting of the whole structure. However, this is not a hazard at the O'BrienDam, since heaving has not occurred in the past, and the tendency for heaving is notaggravated by corrosion.

Terzaghi 7 regarded sliding in the interlocks of the cross walls as a potential type offailure. Corrosion actually mitigates this problem, since it tends to prevent slipping in - --the sheet-pile interlocks. Since slipping has not already damaged the cofferdams, it isunlikely that it will do so in the future. However, it is possible that the webs in the crosswalls will become so corroded that they will rupture in shear.

The cell walls carry considerable horizontal tension due to the pressure of the fill -and the water in the cells. If corrosion proceeds too far, this tension will cause the cells 4to burst. Since hoop tension is transmitted to the Y-piles at the junctions between thecylindrical walls and the cross walls, horizontal tension develops in the cross walls. .., ..

For studies of general stability of cellular cofferdams, the actual structure often is .replaced by a box structuring with rectangular cells, as indicated by the dashed lines inFigure 23. For cofferdams with conventional proportions, the width b' of a rectangularcell is taken to be 0.9b, where b is the outside width of the cofferdam.

Figure 24 is a cross section of the lock's land wall. The 4-ft elevation is theassumed height of the surface of pore water in the backfill. The elevation -4 ft* is the. -height of the surface of the pool in the lock chamber.

Shear in a Cross Wall

The land wall of the lock carries greater shear than the river wall due to the ". ' .

pressure of the backfill. The greatest shear occurs at the bottom of the lock chamber.From Figure 24, the net pressure, p, tending to overturn the land wall is

S x) , x > sP Cy(H - s) + (C y + y ) (s - x), h < x < s [Eq 16]

P Cy(H - s) + (C y + y (s - x), d < x < h

'K. Terzaghi (1944).*4 ft below the top of the piles.

5.

N..%'. % ~ .

65 1p A

V .p w. -

C...

%* %

h 7l =7-42

I

%%,V%

474

* LI - El.V +41

E1.=-55' 1.5,I

E. b .-4'

,,-9.,.--.

h*

Figure ~ ~ ~ ~ ~ ~ ~ ~ ~~J J4. Crs eto fln alo ok --e

.Id 9 . .

EU. -35 _______

L b 28.39' =VI

Figure 24. Cross section of land wall of lock.

67

9,9.. -* " ~ %Il N. %9** -. 9.,::4 ---- %A 9 ?Z

The total shear in a cross wall at the bottom of the chamber isH

F = L f p dxd

Consequently,

F = CyL(H - s)(s - d) + (C y' + y )L(s -d)2

2W

y L(h d) 2 + Cy'(H - s)2 L [Eq 171

From Figure 24, the following values are obtained for the land wall: H = 504 in.,s = 468 in., h = 372 in., d = 198 in. From U.S. Army Corps of Engineers information, 8 L =

. 316 in. For fresh water, y = 0.0361 lb/cu in. Also, y = 0.0723 lb/cu in, y' = 0.0376lb/cu in., and C = 0.45. 9 Wir h these numbers, Eq 17 yields F = 544,600 lb. .

It is not correct to assume that all the shear, F, is carried by the cross wall, since _41some of it is carried by the fill in the cells.' 0 However, lacking any reliable theory toestimate how much of the shear is carried by the fill, it is assumed that all of it is I.

carried by the cross wall. A segment of the cofferdam lying between the middle planes ,. '.'V.of adjacent cells is similar to a big I-beam (Figure 25). The segments of the cylindricalwalls from the flanges of the beam and the cross wall forms the web. For I-beams with ',%heavy flanges, the shearing stress is nearly constant on a cross section of the web.Consequently, since b = 28.39 ft (see Figure 24), the shear flow (lb/in.) in the cross wallat x = d is

S = F/b = 544,600/307 = 17,741 lb/in.

"his is the maximum shear flow expected in the cross wall under normal operating li- f"7'xconditions for the lock.

When the lock is dewatered, the shearing force in the cross wall is higher. Then h =d, and Eq 17 yields F = 717,000 lb. Hence, for the dewatered condition, S = F/bl =

717,000/307 = 2335 lb/in.

At a Y-pile junction, half of the shear flow, S, passes into each of the contractingcylindrical walls. Consequently, the shear flow in the cross wall is twice that in eithercylindrical wall at the junction.

Hoop Tension in a Cell of the Land Wall

The hoop tension in a cylindrical wall is determined by the membrane theory ofshells: z _ -.- z,"

N = Rq(x) [Eq 18]

where q(x) denotes the difference between the internal and external pressures on the

cylindrical wall.

8 Plans for the Construction of Calumet River Lock and Controlling Works (Chicago ,. .District, U.S. Army Corps of Engineers, November 1957).

9 Analysis of Calumet Sag Navigation Project-Lock (M.J.M., August 1956).0 K. Terzaghi.

68

____% %_ % h-_

By statics, the horizontal tension transmitted to a cross wall at its junction with V'N %.rlthe cylindrical walls is

T = 2Ncosa [Eq 19]

where a is half the angle between legs of the Y-pile. For the O'Brien Lock, a = 600.Consequently, T = N; i.e., the horizontal tension in a cross wall at its junction in thecylindrical walls is equal to the hoop tension in the cylindrical walls.

There is no danger of bursting the cylindrical shells on the land side of the land

wall, since the sheet piles there are completely buried. For the chamber side, the J

pressure q(x) in the range x > d is the same as the function p(x) defined by Eq 16.Consequently, for the cylindrical walls on the chamber side of the land wall, Eq 18 yields %

.. %41%

N(x) = R[Cy(H - s) + (Cy' + y )(s - x)], h < x < s [Eq 20]

N(x) = R[Cy(H - s) + (Cy' + yw)(s - x) - y (h - x), d < x < h .-

Eq 20 applies only up to X = 402 in., which is the top of the piles. The largest hoop

tension occurs at the bottom of the chamber (i.e., at x = d). Consequently, the maximumhoop tension in the land wall is .- -

N = R[Cy(H - s) + (Cy' + y )(s - d) - y (h - d)] [Eq 2 11max W W.

For the land wall, R = 316 in. As in the preceding computations, H = 504 in., s =468 in., h = 372 in., d = 198 in., y = 0.0361 lb/cu in., y = 0.0723 lb/cu in., y" = 0.0376lb/cu in., C = 0.45. With these values, Eq 21 yields N = 2909 lb/in. This is the 4maximum tension transmitted by the claws of the sheetpies under normal operatingconditions. For the dewatered condition, h = d, and Nm = 4894 lb/in. The value s = 468in. is somewhat arbitrary. After heavy precipitation, me fill might be saturated to the

top; in this case, s = H. Then, for the normal operating condition, N = 3142 lb/in., .and for the dewatered condition, Nmax = 5127 lb/in. It is apparent thatze height, s, ofthe surface of the pore water in the fill is quite influential.

An element of the web of a cross wall near the junction with the Y-pile is subjected

to shear S and tension N, as illustrated by Figure 26. By the Mohr circle, the maximum e.

shear in the cross wall is

S (S 2 + IN 2 ) 112 [Eq 221 . ..,max 2 max

For the normal operating condition, S = 1774 lb/in, and Nmax = 2909 lb/in. Consequently, ::; ',.

S a 2294 lb/in. For the dewatered condition, S = 2335 lb/in. and N = 4894 b/in.max ar ntesne maxThen Smax = 3382 lb/in. These results are on the high side, since shear carried by the fill

in a cell has been neglected. However, they indicate that the point of highest stress in

the lock wall is in a cross wall near its junction with the cylindrical walls on the chamberside of the land wall, and at the elevation of the bottom of the chamber. %

The ultimate shearing stress of the steel is probably greater than 30,000 lb/sq in.

The maximum shear in a cross wall is that for the dewatered condition (in this case, 3382lb/in). Accordingly, the minimum allowable thickness of a web in the cross wall is

t 3,382 = 0.1 in.30,000

69

V~-Z ... ..- .-... ,

' ' q.= ' %• ' " ","q.4,; . ' I_, I " ',l'*,df,',",.,. =-,''""e- -""I-, .'"e l,,'"# '" ." ","° - *°., ', %e

', .

% % Z

0I

Fi gre 25. ement of a cofferdam represented

as an I-beam. iNN

Jv~

-.

. .'

Figure 26. Stress In an element of a web of a cross

wall. ,'- '

I

4.4 *~ P

4......

70- " - -"

N%- -- l

Figue 25 Sementof coferdm reresntedas n I-eam

%

Since the initial thickness is 0.375 in., severe corrosion can develop before the crosswalls are in danger of failure.

The maximum tension in the claws of the sheet piles has been determined to beabout 5100 lb/in. Table 9 showed that the reduction, c, of thickness due to corrosionmay be 0.25 in. before there is danger of pulling the claws apart.

Hoop Tension in River Wall Cells and Dam Cells _-¢

Figure 27 is a cross section of the river wall. It shows that H = 504 in., h = 372 in.,s = 456 in., and d = 252 in. on the river side, and that d = 198 in. on the chamber side.Also, for the river wall, R 244 in. The maximum hoop tension occurs at the bottom of ethe lock chamber, at x = d = 198 in. Consequently, Eq 21 again applies, yielding

Nmax = 2186 lb/in.

There is no appreciable transverse shear in a cross wall of the river wall. Consequently,under normal operating conditions, N = 2186 lb/in, is the maximum principal stressboth in the cross wall and in the cylindrical walls on the chamber side of the river wall.For the dewatered condition, h = d, and Eq 21 yields

Nmax = 3719 lb/in, for the dewatered condition.

Eq 21 also applies for the river side of the river wall, with d = 252 in. The chamber sideof the river wall is stressed somewhat more than the river side.

The dam is similar to the river wall. Data for the dam a

L = R =201.5 in., H =312 in., d= 138 in.

If thef elevation of the wtrsurface downstream from the dam is -4 ft sfor thedownstream guide wall, h is 198 in. If, as for the river wall, the surface of the pore

water in the cells is taken to be 4 ft below the top of the piles, s = 264 in. Then, by Eq21, N = 1220 lb/in. in the dam. This is the hoop tension in the downstream side of thedam arate level of the bottom of the river. It is also the horizontal tension in the cross ,wall at that point.

4%

N ff7-

,- .. ,, 4,. 1

'Plans for the Construction of Calumet River Lock and Controlling Works. ,%

% %- =r=% % "

A." -", - ...

x=H

-- El. +7'.

- S 4voH4 -- El. +3'

El. -4' -4' -L--"I-I I IhI '.--- '_ _

IIIIChamberxzd iiiiiSide

El. -14' SIde

x=d E.-18.5'River I .,Side

, II-II-------El. -35 .

b=276" -I

Figure 27. Cross section of river waL.

72

7 ANALYSIS OF THE GUIDE WALLS

Configuration of Walls and Tie Back Systems

A guide wall is essentially a corrugated plate formed by interlocking z-shaped sheetpiles driven into clay and glacial till. Figure 28 shows a plan view of the wall. A cappingplate on top of the piles with a lip on one side is attached to the top of the piles by short, -pieces of welded-on rolled angles. A wale consisting of two rolled channels back-to-back, several yards below the pile cap (Figures 28 and 29) is connected by buried tie rodsto a buried sheet-pile wall located at some distance behind the guide wall. The tie rodsare several yards apart. There are 8- x 12-in. wooden fenders bolted to the guide wall.These fenders tend to strengthen the wall, but high localized stresses in the sheet pilingmay occur when barges or boats bump into them. Only stresses caused by earth pressureand water pressure on the walls are considered in the following analysis. The fenders are _disregarded.

%

Pressure on the Wall %

The corrugated guide wall is regarded as a flat orthotropic plate. Rectangularcoordinates (x,y) are set up in the plane of the plate, such that the y-axis coincides withthe bottom edge of the wall, and the x-axis is directed vertically upward. One bay of thewall between successive tie rods is considered. The tie rods are attached to the wale at •y= 0 and y = L. The bottom of the river adjacent to the wall lies at x = d; the level ofthe water in the river is at x = h; the wale lies at x = a, and the top of the wall lies atH. The backfill is saturated with water to the level x = s (Figure 29). Although thebackfill does not rise quite to the top of the wall, it is close to it. As a conservativeestimate, the level of the top of the backfill is taken to be x = H. 4

Below the level of the river bottom, the soil pressures on the two sides of the sheetpilings are generally unequal. The wall deflects, and, where it is embedded in the

subsoil, .k,

the passive soil pressure acts at any given point on one side of the wall, and the activesoil pressure acts at the adjacent point on the other side.' 2 It is reasonable to assume '-. Jdthat the deflection has a constant sign everywhere on a horizontal line along the wall.Thus, the net pressure, q, that the backfill, the water, and the subsoil exert on the walldepends only on the vertical coordinate x; it does not depend on y.

Since the piles penetrate deeply into the subsoil, there is no appreciable horizontal 6%,movement at the foot of a pile. Consequently, the deflection is believed to have aconstant sign over the entire wall (i.e., everywhere the deflection has the same sense [is .. ',.-.

-.

consistent in direction]). The net pressure q is the algebraic sum of the pressures on thefront and back sides of the wall. Consequently, as Figure 29 indicates, the pressure isgiven by the following equations:

q = Cy(H - x), x > s [Eq 231

q Cy(H - s) + (C ' + y) (s - x), h < x < s

q CyH s) + (Cy' + y )(S X) -y (h x), d < x < hw w

2K. Terzaghi. " .'.

73 U .

J-- MAPA

-q = Cy(H - s) + (Cy + y) (s- x) - W (h- x) - y (d- x), x < d '

in which C is the coefficient of active earth pressure and C is the coefficient of passive 'earth pressure. Eq 23 complies with the condition that q(x) is continuous in the entirerange 0 < x >H.

Beam Analysis of the Guide Wall

The guide wall will carry little horizontal tension, since such tension would flatten , . ..the corrugations. The equilibrium equations for plates'" then indicate that all themembrane stresses (N., N , Nxv) are small. Also, the bending moment M is practicallyzero because the interloc~cs in the piles act like hinges. Furthermore, (he transverseshear Q on any vertical section is small because the webs in the sheet piles are thin. Itmay beyconcluded from the equilibrium equations for moments in a plate' 4 that the .twisting moment M is small. The significant reactions are consequently the bending .moment M and the%ear Q on a horizontal section. For brevity, Mx is denoted simplybyM. %.-

In view of these simplifications, a vertical strip of the guide wall of unit width actslike a uniform beam carrying the lateral load q(x). At the top, the beam carries a ,concentrated reaction, F2 , from the capping plate (Figure 2). There is no bendingmoment at the top, if torsional stiffness of the capping plate is neglected (i.e., M = 0 at x .-. ": H). At the point x = a, the beam carries a concentrated force, Fl, from the wa e. .Since F, and F9 are forces per unit width in the y-direction, their dimension is [F L]Likewise, since M is a bending moment per unit width, its dimension is [F].

Since any vertical strip of the wall is in equilibrium, and since there is no shear atthe bottom of a sheet pile.

HF1 +F 2 = q(x) dx [Eq 241

0 -Eqs 23 and 24 yield

2(F )C ,+ s-y'd2(+ F2) = Cy(H2 - s2) + (Cy + y) 2 - h

2 - 2 [Eq 251 ..

Also, moments must balance about the axis of the wale. Since there is no shear orbending moment at the foot of a pile, this condition yields -.-

H-F(H - a) + J (x - a)q(x) dx= 0 [Eq 26]

20 0Eqs 23 and 26 yield -

Cy(H 3 s - (CyX + XY)s3 + y h3 + C'"d3 + 3Cya(H2 s 2 ) [Eq271W W~~2 2 2 . .

+ 3(Cy' + y )as - 3y ah2 - 3Cy'ad 2 + 6F2(H - a) = 0

Eq 27 shows that F 2 does not depend on y. Consequently, Eq 25 shows that F, also doesnot depend on y.

1'S. Timoshenko and S. Woinowsky-Krieger.14.S. Timoshenko and S. Woinowsky-Krieger.

74' .. .

-,'

I hiS..4 0

ii Wale

,, it,

. Figure 28. Horizontal section of sheet piling guide wall.

* "+0

Tieh

Rodd

I'g

= I~l II

IXWI

~~~~Figure 28. HoiotlscinGfsepln uide wall.

75

LI P % %=" % %' + *.. ,,'. , . . . % % % ",_ ._._*..+_-_'.% . +.%_ "= + +_'. o=--..0 +.* , ., e . % % ." "e %

'% - , % %

The tension, P, in a tie rod must balance the forces on one bay of the wall. Since %there is no shear in the wale or the pile cap at y = 0 or y = L, ..

H L HP = f f q(x) dx dy = L f q(x) dx [Eq28]

00 0Consequently, by Eq 24,

P (F 1 + F 2 )L [Eq 29]

Eqs 25 and 29 determine P.

Treating a unit vertical strip of the guide wall as a beam, the data in Figure 29gives

HM = F2 (H - x) - f (u - x)q(u)du, x > a [Eq 30]

x HM = F1 (a - x) + F2(H - x) -

f (u - x)q(u)du, x < aX

where u is a variable of integration. With Eq 23, the integrals in Eq 30 can beevaluated. Thus,

M = F2 (h - x) - Cy(H -x) , in x > s [Eq-31

1 3 1 3M F (h - x) - (Cy" + YW - Cy)(s - x) y(H - x)2 6 w S

in a ' x < s ,.D- -

M F(a -x) + F(H - x) -(Cy' + y-Cy)(s -x) 312 6

- Cy(H - x) 3 , in h < x < a 3

%

M F (a - x) + F2(H - x) -!(Cy + y - Cy)(s - x)

1 3 13-IY (H -x) +-ly (hb-x), in d x

With Eq 25, this yields ., v-

2[ -(Cy + Y - Cy)s - CyH + y W h + Cy'd] -Eq 321x=[ Eq 3 2] -- - -

The value of x given by Eq 32 is to be substituted into the last of Eq 31 to yield Mmax' ,

Eqs 25 and 27 determined F and F2 , if C and C are known. However, C, inparticular, is hard to estimate. If the capping plate is eliminated, F2 = 0. The cappingplate imposes less restraint on the sheet piles than the wale, since it is not connected , .directly to the tie rods; consequently, it may undergo appreciable deflection at the , -stations of the tie rods. Using the assumption F2 = 0, Eq 27 determines the valueof C that is statically consistent with the value of C. Eq 25 then determines F1 .

Crumpling of the Sheet Piles

The bending moment, M, given by Eq 31, causes compression and tension stresses inthe sheet piling, which are defined by the well-known beam equation. - -

M c [Eq 33]

It is unlikely that this stress will rupture the piles, even though corrosion is severe, sincelocal buckling, called "crumpling" or "crippling," will occur on the compression side .before rupture occurs on the tension side. .

On the basis of the effective-modulus theory, there is a method' 5 for simul- '-taneously plotting buckling curves for plates and columns. With column data only, itpermits compression buckling stresses for plates with various edge conditions to beestimated, when these stresses exceed the material's compression proportional limit. " ; .This method may be used to compute the crumpling stress of the compression side of thesheet piling. %

Beedle et al., 1 have given extensive data for structural steel columns. Theirresults show that the well-known parabolic approximation is quite accurate for mild steelcolumns; i.e.,

L E 1/2S a 1- ] ---- -(2-) [Eq34]cr y 42 CE 2 7Q'/C- a

o -- C 2 g p 2) % __ I 2;,".,..e " -

acr E (L 2) -L > (2 _)-1/2 .

where L/o is the slenderness ratio of the column, a is the compression yield stress, andC is the end fixity factor; i.e., L/ C is the redu4d length. The second part of Eq 34,which applies for sufficiently large L/p, is the Euler formula. .' .9

15 H. L. Langhaar, "Buckling of Aluminum-Alloy Columns and Plates," Jour. Aere. Sci., -Vol 10, No. 7 (July 1943), pp 218-222.

16 L. S. Beedle, T. V. Galambos, and L. Tall, Column Strength of Constructional Steels,

77 ...'........., ,,

%',',L . '.

• %. % -' "" ... -- .- .. .- %, - ... . ,,.-... -- ...-..- .-.- -. , - .- .:. --.v .--. -.- -. ..:. ...... ; -- .:

By the method described in Langhaar, 1 7 Eq 34 is modified to cover inelasticbuckling of axially compressed plates. The abscissa L/p-C-of the column curve ismerely replaced by w/t v-, where w is the width of the plate, t is the thickness of the b-,V--plate, and K is the edge fixity factor. Accordingly, the crumpling stress of the steelpiling (modulus of rupture) is

2(1 - _ __) w < E )1/2 %'...€

0 -(1_ w E2 / [Eq 35]

cr=K E (4 !L)2, .. >c4 y ,

W YFor hat-type stringers,1 8 w is interpreted to be the width of the hat between the ..centroids of the cross sections of the filleted areas. This interpretation will also be usedfor the sheet piles (Figure 28). The value of K is questionable, but for axially compressedsquare tubes with rounded edges, the value K = 6.25 conforms well with experimental -data.1 9 No doubt, the sheet piling will carry a greater stress than a uniformlycompressed square tube with width w and thickness t, since the sloping walls in the sheet " "piling tend to support the highly stressed flanges. However, the value of X (the elevationof surface of pore water in the fill) is not very important, and the value K = 6.25 is usedin the following computations.

Due to corrosion of the sheet piling, the thickness, t, gradually diminishes withtime. Eq 35 determines the crumpling stress, and hence, the maximum bending moment, ".M, corresponding to any given thickness, t. After some time, the thickness of a sheetpile at a critical section is reduced by an amount, e, due to corrosion; i.e., the thicknessat that time is t - e, where tQ is the initial thickness. Then the mean moment ofinertia of the pile, per unit width in the y-direction, is

I = I - kE [Eq 36]

where I0 is the initial value of the moment of inertia, and k is a constant determined by . -

the shape of the cross section. The value of e at which the pile will crumple isdetermined by equating the bending stress Me/l to the stress a in Eq 35. Thus, with 0 IK 6.25,

2a wI 0 - y [Eq 37]0 25E(t 0 2

This equation may be written as follows:

0O MCK 2 [Eq 381o w

Ka(l Y 2

25 ( t0 - -"

Fritz Lab. Reprint No. 177 (U.S. Steel Co.).''H. L. Langhaar.18 H. L. Langhaar. , . .19 L. S. Beedle, T. V. Galambos, and L. Tall.

'*~ :~..z-z. -.. -.

Eq 38 is to be solved for c. A first approximation is '- ;

10 Mc C.kk ci ~[Eq 391

Y ; }Y

The value m may be substituted into the right side of Eq 38 to provide a secondapproximatidn, c . Then E may be substituted into the right side of Eq 38 to provide athird approximation, E3 , a~d so on. Instead of Eq 39, any starting value e based onengineering judgment may be used.

! = 0.20 in. is a reasonable working value; however, in regions of low ormoderafe stress, this number could be greatly exceeded. To translate the numberEaH = 0.20 in. into projected years of service requires detailed knowledge of thecorrosion rates at critical places in the lock. Measurements taken during dewatering ofthe lock chamber in 1979 indicated that the mean thickness of the webs of sheet piles in O_the cofferdam is 0.348 in. Initially, the thickness of these webs was nominally 0.375 in. "The reduction occurred over 21 years. (The standard deviation of the measurements was _.0.008 in.)

The probability that a normally distributed random variable will lie within onestandard deviation of the mean is 0.682; the probability that it will lie within twostandard deviations of the mean is 0.954, and the probability that it will lie within threestandard deviations of the mean is 0.997. Consequently, on the basis of the cited,- "measurements, there should be very few places where the web thickness is less than0.324 in. (which is three standard deviations from the mean). Accordingly, a likely upperbound for the present amount of corrosion of the lock wall is

c = 0.375 - 0.324 = 0.051 in.

Since this reduction is considered to have occurred over 21 years, an extreme value of-" the corrosion rate is then

= 0.051/21 = 0.0024 in. per year

Consequently, the time required for the allowable amount of corrosion (c = 0.20 in.)to be reached is a.l.

0.20/0.0024 83 years

This period began when the lock opened (1958). Accordingly, the webs of the sheet piles '. .in the lock walls should serve until 2041. This is also true for the claws of the interlocksin the cofferdam walls, if the shanks and hooks in the claws corrode at the same rate as .the webs. However, crevice corrosion rates for parts of the claws are not as well known lotas those of the webs. Thus, more data about the corrosion rates of the claws aredesirable.

79

% .0 r, J, -% ...

%-. ,-,.-,.-..-._.-,.f...-._..,,. ,5 :. ......- , - s. .. ....... ...-. ... .. -. J-r.r.r~rr.

Failure of the Wale or a Tie Rod "..

A possible mode of failure is a tension rupture of a tie rod, as given by Eqs 25 and .. _.29. V

The wale can fail in several ways. Lateral buckling might be a mode of failure, but "- .-such a collapse is unlikely because of the resistance provided by the sheet piling and thebackf ill. 4

A shear failure of a channel's web is another p