Drilled shaft bridge foundation design parameters and procedures for bearing in SGC soils

              Drilled Shaft Bridge
Foundation Design Parameters
and Procedures for Bearing
in SGC Soils
Final Report 493
April 2011
Arizona Department of Transportation
Research Center
The contents of this report reflect the views of the authors who are responsible for the
facts and the accuracy of the data presented herein. The contents do not necessarily
reflect the official views or policies of the Arizona Department of Transportation or the
Federal Highway Administration. This report does not constitute a standard,
specification, or regulation. Trade or manufacturers’ names which may appear herein are
cited only because they are considered essential to the objectives of the report. The U.S.
Government and the State of Arizona do not endorse products or manufacturers.
Research Center reports are available on the Arizona Department of Transportation’s
internet site.
1. Report No.
FHWA-AZ-06-493
2. Government Accession No. 3. Recipient's Catalog No.
4. Title and Subtitle 5. Report Date
April, 2006
FINAL REPORT FOR PROJECT NO. KR00 1870TRN
Drilled Shaft Bridge Foundation Design Parameters and
Procedures for Bearing in SGC Soils
6. Performing Organization Code
7. Author
William N. Houston, Abdalla M. Harraz, Kenneth D. Walsh.,
Sandra L. Houston, and Courtland Perry
8. Performing Organization Report No.
9. Performing Organization Name and Address
ARIZONA STATE UNIVERSITY
10. Work Unit No.
1711 S. RURAL ROAD
TEMPE, ARIZONA 85287
11. Contract or Grant No.
SPR-493 SPR-PL-1(57) 493
12. Sponsoring Agency Name and Address
ARIZONA DEPARTMENT OF TRANSPORTATION
206 S. 17TH AVENUE
13.Type of Report & Period Covered
FINAL REPORT
PHOENIX, ARIZONA 85007 14. Sponsoring Agency Code
15. Supplementary Notes
Prepared in cooperation with the U.S. Department of Transportation, Federal Highway
Administration
16. Abstract
This report provides a simplified method to be used for evaluating the skin friction and tip resistance of
axially loaded drilled shafts. A summary of literature and current practice was completed and then a
comprehensive set of field and laboratory tests was performed. Several soil samples were collected
from different sites from Arizona and surrounding states. Large scale direct shear apparatus was
developed and used to determine the friction between soil and concrete. Finite element analyses were
conducted on several prototype cases to determine effect of soil parameters such as dilation on the skin
friction values. A step-by-step simplified approach was introduced to determine the skin and tip
resistance of drilled shaft foundations in gravelly soils. An example application was presented to guide
users in utilizing the simplified approach.
17. Key Words
Drilled Shaft, Drilled Shaft Capacity, Axial
loads, Skin Friction, End Bearing, Drilled
Shafts Design Models, Dilation,
Compressibility.
18. Distribution Statement 23. Registrant's Seal
19. Security Classification
Unclassified
20. Security Classification
Unclassified
21. No. of Pages
123
22. Price
SI* (MODERN METRIC) CONVERSION FACTORS
APPROXIMATE CONVERSIONS TO SI UNITS APPROXIMATE CONVERSIONS FROM SI UNITS
Symbol When You Know Multiply By To Find Symbol Symbol When You Know Multiply By To Find Symbol
LENGTH LENGTH
in inches 25.4 millimeters mm mm millimeters 0.039 inches in
ft feet 0.305 meters m m meters 3.28 feet ft
yd yards 0.914 meters m m meters 1.09 yards yd
mi miles 1.61 kilometers km km kilometers 0.621 miles mi
AREA AREA
in2 square inches 645.2 square millimeters mm2 mm2 Square millimeters 0.0016 square inches in2
ft2 square feet 0.093 square meters m2 m2 Square meters 10.764 square feet ft2
yd2 square yards 0.836 square meters m2 m2 Square meters 1.195 square yards yd2
ac acres 0.405 hectares ha ha hectares 2.47 acres ac
mi2 square miles 2.59 square kilometers km2 km2 Square kilometers 0.386 square miles mi2
VOLUME VOLUME
fl oz fluid ounces 29.57 milliliters mL mL milliliters 0.034 fluid ounces fl oz
gal gallons 3.785 liters L L liters 0.264 gallons gal
ft3 cubic feet 0.028 cubic meters m3 m3 Cubic meters 35.315 cubic feet ft3
yd3 cubic yards 0.765 cubic meters m3 m3 Cubic meters 1.308 cubic yards yd3
NOTE: Volumes greater than 1000L shall be shown in m3.
MASS MASS
oz ounces 28.35 grams g g grams 0.035 ounces oz
lb pounds 0.454 kilograms kg kg kilograms 2.205 pounds lb
T short tons (2000lb) 0.907 megagrams
(or “metric ton”)
mg
(or “t”)
mg megagrams
(or “metric ton”)
1.102 short tons (2000lb) T
TEMPERATURE (exact) TEMPERATURE (exact)
ºF Fahrenheit
temperature
5(F-32)/9
or (F-32)/1.8
Celsius temperature ºC ºC Celsius temperature 1.8C + 32 Fahrenheit
temperature
ºF
ILLUMINATION ILLUMINATION
fc foot candles 10.76 lux lx lx lux 0.0929 foot-candles fc
fl foot-Lamberts 3.426 candela/m2 cd/m2 cd/m2 candela/m2 0.2919 foot-Lamberts fl
FORCE AND PRESSURE OR STRESS FORCE AND PRESSURE OR STRESS
lbf poundforce 4.45 newtons N N newtons 0.225 poundforce lbf
lbf/in2 poundforce per
square inch
6.89 kilopascals kPa kPa kilopascals 0.145 poundforce per
square inch
lbf/in2
SI is the symbol for the International System of Units. Appropriate rounding should be made to comply with Section 4 of ASTM E380
TABLE OF CONTENTS
INTRODUCTION............................................................................................................. 1
SUMMARY OF LITERATURE AND CURRENT PRACTICE................................. 3
SUMMARY OF HISTORIC USE............................................................................................ 3
ANALYTICAL APPROACHES.............................................................................................. 8
Introduction ................................................................................................................. 8
Tomlinson 2001 ........................................................................................................... 8
Meyerhoff 1976.......................................................................................................... 10
Reese and O'Neill 1989 (AASHTO METHOD)......................................................... 10
Kulhawy 1989............................................................................................................ 10
Rollins, Clayton, Mikesell, and Blaise 1997.............................................................. 13
COMPARISON OF ACTUAL SKIN FRICTION FACTORS TO PREDICTED
FOR DRILLED SHAFT IN GRANULAR SOIL ........................................................ 15
INTRODUCTION............................................................................................................... 15
LOAD TESTS................................................................................................................... 15
VALUES OF FS DERIVED FROM DIRECT FIELD MEASUREMENTS ..................................... 16
PREDICTED VALUES OF FS .............................................................................................. 16
RESULTS........................................................................................................................ 17
DILATION ....................................................................................................................... 30
REPORT ON PRELIMINARY FINITE ELEMENT ANALYSES OF TWO CASE
HISTORY STUDIES OF AXIALLY LOADED DRILLED SHAFTS...................... 33
INTRODUCTION............................................................................................................... 33
CHARACTERISTICS OF THE SGC SOILS ........................................................................... 33
AXIAL COMPRESSION LOADING ON DRILLED SHAFTS.................................................... 33
Soil Profile................................................................................................................. 34
Pile Configuration ..................................................................................................... 34
Finite Element Analysis............................................................................................. 34
Effect of Dilation Angle.............................................................................................. 37
Best Fit Indicator....................................................................................................... 38
Selection of Best Set of Parameters for SGC............................................................. 39
UPLIFT LOADING ON DRILLED SHAFT TEST ................................................................... 39
Soil Profile................................................................................................................. 39
Pile Configuration ..................................................................................................... 40
Finite Element Analysis............................................................................................. 40
CONCLUSIONS FROM STUDY OF LITERATURE AND CURRENT PRACTICE......................... 43
DEVELOPMENT OF WORK PLAN FOR COMPLETION OF THE PROJECT
AND ASSESSMENT OF PROGNOSIS FOR SUCCESS........................................... 45
DATA GAPS .................................................................................................................... 45
WORK PLAN OVERVIEW................................................................................................. 46
PROGNOSIS FOR SUCCESS .............................................................................................. 48
FIELD TESTING........................................................................................................................53
IN-SITU DENSITY........................................................................................................................53
LAB TESTING ............................................................................................................................59
GRAIN SIZE DISTRIBUTION..........................................................................................................59
LARGE SCALE SHEAR TESTING ...................................................................................................68
Testing Procedure ..................................................................................................................69
Direct Shear Lab Test Program .............................................................................................74
Test Results............................................................................................................................75
MODELING OF THE DATA ...........................................................................................................85
K VALUES FROM THE DIRECT SHEAR TEST ................................................................................87
NUMERICAL ANALYSES........................................................................................................89
FINITE ELEMENT MODEL.............................................................................................................89
Analysis..................................................................................................................................90
POINT OF THE MOUNTAIN EAST SITE .........................................................................................92
K-DEPTH-% GRAVEL MODEL .....................................................................................................95
RECOMMENDED DESIGN PROCEDURES FOR DRILLED SHAFTS
IN GRAVELLY MATERIALS ......................................................................................99
COMPARISON OF THE ULTIMATE TIP RESISTANCE BY EQUATION 7 USING BEREZANTSEV
BEARING CAPACITY FACTORS WITH THE MEASURED TIP RESISTANCE FOR THE
BECKWITH AND BEDENKOP TEST ON SALT RIVER SGC...........................................................102
EXAMPLE DRILLED SHAFT DESIGN, USING
THE RECOMMENDED PROCEDURE.....................................................................105
CONCLUSIONS.......................................................................................................................109
REFERENCES..........................................................................................................................111
LIST OF FIGURES
FIGURE 1: RELATIONSHIP BETWEEN SPT N-VALUES AND ANGLE
OF SHEARING RESISTANCE [TOMLINSON, 2001] .......................................................... 9
FIGURE 2: END-BEARING CAPACITY FACTORS [HANSEN, 1961;BEREZANTSEV,1961] .................... 9
FIGURE 3. PREDICTED VS. ACTUAL FS VALUES, ALL METHODS..................................................... 17
FIGURE 4. PREDICTED VS. ACTUAL FS VALUES, TOMLINSON AND KULHAWY ............................... 18
FIGURE 5. PREDICTED VS. ACTUAL FS VALUES, MEYERHOFF........................................................ 18
FIGURE 6. PREDICTED VS. ACTUAL FS VALUES, REESE & O’NEILL ............................................... 19
FIGURE 7. PREDICTED VS. ACTUAL FS VALUES, ROLLINS ET AL. ................................................... 19
FIGURE 8. P VS. A VALUES, TOMLINSON AND KULHAWY, BY SOIL TYPE...................................... 20
FIGURE 9. P VS. A VALUES, MEYERHOFF, BY SOIL TYPE .............................................................. 20
FIGURE 10. P VS. A VALUES, REESE AND O’NEILL, BY SOIL TYPE ............................................... 21
FIGURE 11. P VS. A VALUES, ROLLINS ET AL., BY SOIL TYPE........................................................ 21
FIGURE 12. P VS. A VALUES, TOMLINSON AND KULHAWY, BY TEST TYPE................................... 22
FIGURE 13. P VS. A VALUES, MEYERHOFF, BY TEST TYPE............................................................ 22
FIGURE 14. P VS. A VALUES, REESE AND O’NEILL, BY TEST TYPE............................................... 23
FIGURE 15. P VS. A VALUES, ROLLINS ET AL., BY TEST TYPE....................................................... 30
FIGURE 16. AVERAGE P/A VS. % GRAVEL, ALL METHODS EXCEPT ROLLINS ET AL...................... 24
FIGURE 17. AVERAGE P/A VS. % GRAVEL, ROLLINS ET AL........................................................... 25
FIGURE 18. AVERAGE P/A VS. DEPTH TO MID-LAYER, ALL METHODS EXCEPT ROLLINS ET AL. .. 26
FIGURE 19. AVERAGE P/A VS. DEPTH TO MID-LAYER, ROLLINS ET AL......................................... 26
FIGURE 20. AVERAGE P/A VS. TEST TYPE, ALL METHODS EXCEPT ROLLINS ET AL. ..................... 27
FIGURE 21. AVERAGE P/A VS. TEST TYPE, ROLLINS ET AL. .......................................................... 27
FIGURE 22. K VS. % GRAVEL ........................................................................................................ 28
FIGURE 23. KPS VS. % GRAVEL ...................................................................................................... 29
FIGURE 24. K VS. DEPTH TO MID-LAYER...................................................................................... 29
FIGURE 25. K PS VS. DEPTH TO MID-LAYER ................................................................................. 30
FIGURE 26: TYPICAL GRAIN SIZE DISTRIBUTION OF SGC SOIL..................................................... 32
FIGURE 27: PILE CONFIGURATION ................................................................................................. 34
FIGURE 28: DRUCKER-PRAGER MODEL. ........................................................................................ 35
FIGURE 29: FIELD LOAD-DEFLECTION CURVE............................................................................... 35
FIGURE 30: EFFECT OF SOIL MODULUS, E, ON THE LOAD DEFLECTION CURVE. ............................. 36
FIGURE 31: EFFECT OF SOIL ANGLE OF INTERNAL FRICTION, Ø,
ON THE LOAD DEFLECTION CURVE............................................................................ 36
FIGURE 32: EFFECT OF SOIL DILATION ANGLE ON RESULTS.......................................................... 37
FIGURE 33: SET OF TRIALS OF MATCH FIELD LOAD-DEFLECTION CURVE. .................................... 37
FIGURE 34: R2 VALUES FOR DIFFERENT SETS OF Ø AND Ψ............................................................. 38
FIGURE 35: CURVE OF MAXIMUM R2 VALUES, FOR ψ VS φ. .......................................................... 38
FIGURE 36: GRAIN SIZE DISTRIBUTION FOR THE SOIL AT UTAH SITE.............................................. 39
FIGURE 37: PILE CONFIGURATION ................................................................................................. 40
FIGURE 38: LOAD DEFLECTION CURVE FOR THE UPLIFT TEST....................................................... 41
FIGURE 39: EFFECT OF SOIL MODULUS, E ON LOAD DEFLECTION CURVE. .................................... 41
FIGURE 40: EFFECT OF COEFFICIENT OF FRICTION BETWEEN PILE AND SOIL, F. ............................ 42
FIGURE 41: EFFECT OF COEFFICIENT OF FRICTION, F, ON LOAD DEFLECTION CURVE.................... 42
FIGURE 42: BEST FIT FOR THE UPLIFT LOAD TEST......................................................................... 43
FIGURE 43: K VS DEPTH FOR DIFFERENT GRAVEL CONTENT ......................................................... 49
FIGURE 44: GRAVEL CONTENT VS. UNIT WEIGHT,  -APPROXIMATE RELATIONSHIP .................... 49
FIGURE 45: GRAVEL CONTENT VS. φ` VALUE-APPROXIMATE RELATIONSHIP................................ 50
FIGURE 46: MEASURED VS. PREDICTED FOR A NEW EMPIRICAL MODEL ....................................... 51
FIGURE 47: HOLE IS EXCAVATED USING THE BACKHOE. ............................................................... 54
FIGURE 48: THE MATERIAL IS DUMPED (COLLECTED) IN A LOADER TO BE WEIGHED.................... 54
FIGURE 49: THE HOLE IS LINED WITH A PLASTIC SHEET................................................................. 55
FIGURE 50: THE WATER TANK USED TO FILL THE HOLE............................................................... 55
FIGURE 51: HOLE FILLED WITH WATER......................................................................................... 56
FIGURE 52: COLLECTED SAMPLES ................................................................................................. 56
FIGURE 53: GRAIN SIZE DISTRIBUTION FOR MATERIAL # 1, 91ST AVENUE (AZ1)......................... 60
FIGURE 54: GRAIN SIZE DISTRIBUTION FOR MATERIAL # 2, 91ST AVENUE (AZ2)......................... 60
FIGURE 55: GRAIN SIZE DISTRIBUTION FOR MATERIAL # 3, 91ST AVENUE (AZ3)......................... 60
FIGURE 56: GRAIN SIZE DISTRIBUTION FOR MATERIAL # 4, 51ST AVENUE (AZ1)......................... 61
FIGURE 57: GRAIN SIZE DISTRIBUTION FOR MATERIAL # 5, 51ST AVENUE (AZ2)......................... 61
FIGURE 58: GRAIN SIZE DISTRIBUTION FOR MATERIAL # 6, 51ST AVENUE (AZ3)......................... 61
FIGURE 59: GRAIN SIZE DISTRIBUTION FOR MATERIAL # 7, MAPLETON (UT1)............................. 62
FIGURE 60: GRAIN SIZE DISTRIBUTION FOR MATERIAL # 8, MAPLETON (UT2)............................. 62
FIGURE 61: GRAIN SIZE DISTRIBUTION FOR MATERIAL # 9,
POINT OF THE MOUNTAIN EAST (UT1). ..................................................................... 62
FIGURE 62: GRAIN SIZE DISTRIBUTION FOR MATERIAL # 10,
POINT OF THE MOUNTAIN EAST (UT2). ..................................................................... 63
FIGURE 63: GRAIN SIZE DISTRIBUTION FOR MATERIAL # 11,
POINT OF THE MOUNTAIN WEST (UT1). .................................................................... 63
FIGURE 64: GRAIN SIZE DISTRIBUTION FOR MATERIAL # 12,
POINT OF THE MOUNTAIN WEST (UT2). .................................................................... 63
FIGURE 65: GRAIN SIZE DISTRIBUTION FOR MATERIAL # 13, GARCIA RIVER (CA1)..................... 64
FIGURE 66: GRAIN SIZE DISTRIBUTION FOR MATERIAL # 14, GUALALA RIVER (CA2).................. 64
FIGURE 67: GRAIN SIZE DISTRIBUTION FOR MATERIAL # 15, REDWOOD CREEK (CA3). ............... 64
FIGURE 68: GRAIN SIZE DISTRIBUTION FOR MATERIAL # 16, NAVARRO RIVER (CA4). ................ 65
FIGURE 69: GRAIN SIZE DISTRIBUTION FOR MATERIAL # 17, COLUMBIA RIVER (OR1). ............... 65
FIGURE 70: GRAIN SIZE DISTRIBUTION FOR MATERIAL # 18, ROGUE RIVER (OR2). ..................... 66
FIGURE 71: GRAIN SIZE DISTRIBUTION FOR ALL MATERIALS........................................................ 66
FIGURE 72: MEASURED d
w
γ
γ
VALUES VERSUS PREDICTED ............................................................ 68
FIGURE 73: LARGE SCALE SHEAR BOX.......................................................................................... 69
FIGURE 74: MATERIAL IS MIXED DRY FIRST AND THEN WETTED. ................................................... 71
FIGURE 75: COMPACTING MATERIAL IN LAYERS........................................................................... 71
FIGURE 76: A COVER PLATE USED TO MAKE SURE MATERIAL IS FLUSH TO BOX TOP.................. 72
FIGURE 77: MATERIAL IS REMOVED FROM THE UPPER HALF OF THE BOX. ...................................... 72
FIGURE 78: POURING CONCRETE INTO THE BOX............................................................................. 73
FIGURE 79: LOAD DEFLECTION CURVE FOR MATERIAL #1. ........................................................... 75
FIGURE 80: LOAD DEFLECTION CURVE FOR MATERIAL #3. ........................................................... 76
FIGURE 81: LOAD DEFLECTION CURVE FOR MATERIAL #7. ........................................................... 76
FIGURE 82: LOAD DEFLECTION CURVE FOR MATERIAL #9. ........................................................... 77
FIGURE 83: LOAD DEFLECTION CURVE FOR MATERIAL #16. ......................................................... 77
FIGURE 84: LOAD DEFLECTION CURVE FOR MATERIAL #17. ......................................................... 78
FIGURE 85: SHEAR STRENGTH ENVELOPE FOR MATERIAL #1. ....................................................... 78
FIGURE 86: SHEAR STRENGTH ENVELOPE FOR MATERIAL #3. ....................................................... 79
FIGURE 87: SHEAR STRENGTH ENVELOPE FOR MATERIAL #7. ....................................................... 79
FIGURE 88: SHEAR STRENGTH ENVELOPE FOR MATERIAL #9. ....................................................... 80
FIGURE 89: SHEAR STRENGTH ENVELOPE FOR MATERIAL #16. ..................................................... 80
FIGURE 90: SHEAR STRENGTH ENVELOPE FOR MATERIAL #17. ..................................................... 81
FIGURE 91: SUMMARY OF THE SHEAR STRENGTH ENVELOPES FOR ALL CHOSEN MATERIALS....... 81
FIGURE 92: HORIZONTAL DEFORMATION VERSUS VERTICAL DEFORMATION FOR MATERIAL #1. . 82
FIGURE 93: HORIZONTAL DEFORMATION VERSUS VERTICAL DEFORMATION FOR MATERIAL #3. . 82
FIGURE 94: HORIZONTAL DEFORMATION VERSUS VERTICAL DEFORMATION FOR MATERIAL #7. . 83
FIGURE 95: HORIZONTAL DEFORMATION VERSUS VERTICAL DEFORMATION FOR MATERIAL #9. . 83
FIGURE 96: HORIZONTAL DEFORMATION VERSUS VERTICAL DEFORMATION FOR MATERIAL #16. 84
FIGURE 97: HORIZONTAL DEFORMATION VERSUS VERTICAL DEFORMATION FOR MATERIAL #17. 84
FIGURE 98: MEASURED Ψ VALUES VERSUS PREDICTED................................................................ 86
FIGURE 99: MEASURED VERSUS PREDICTED δ VALUES................................................................. 86
FIGURE 100: HALF SYMMETRY OF SHAFT AND SOIL DISCRETIZATION MESH................................88
FIGURE 101: P-Δ CURVES WITH DIFFERENT FINITE ELEMENT TRIALS FOR
15 FT SHAFT AT MAPLETON....................................................................................... 91
FIGURE 102: P-Δ CURVES WITH DIFFERENT FINITE ELEMENT TRIALS FOR
10 FT SHAFT AT MAPLETON....................................................................................... 91
FIGURE 103:P-Δ CURVES WITH DIFFERENT FINITE ELEMENT TRIALS FOR
5 FT SHAFT AT MAPLETON......................................................................................... 92
FIGURE 104:P-Δ CURVES WITH DIFFERENT FINITE ELEMENT TRIALS FOR 5 FT SHAFT
AT PT. EAST ............................................................................................................... 94
FIGURE 105: P-Δ CURVES WITH DIFFERENT FINITE ELEMENT TRIALS FOR 10 FT SHAFT AT
PT. EAST .................................................................................................................... 94
FIGURE 106: P-Δ CURVES WITH DIFFERENT FINITE ELEMENT TRIALS FOR 15 FT SHAFT
AT PT. EAST ............................................................................................................... 95
FIGURE 107: P-Δ CURVES WITH DIFFERENT FINITE ELEMENT TRIALS FOR 20 FT SHAFT
AT PT. EAST ............................................................................................................... 95
FIGURE 108: K-VALUE VERSUS DEPTH (FROM FINAL ELEMENT AND DIRECT SHEAR).................. 96
FIGURE 109: COMPARISON BETWEEN DIFFERENT METHODS USED TO REPRESENT
K-VERSUS-%GRAVEL ................................................................................................ 97
LIST OF TABLES
TABLE 1: LEGEND FOR PLAN DESCRIPTION AND SUMMARY............................................................ 4
TABLE 2: ζ TERMS ....................................................................................................................... 11
TABLE 3: TYPICAL ED VALUES ...................................................................................................... 12
TABLE 4: β VALUES...................................................................................................................... 13
TABLE 5: LOAD TESTS .................................................................................................................. 15
TABLE 6: RIVER BEDS AND GRAVEL PIT SITES .............................................................................. 53
TABLE 7: MOIST IN-SITU DENSITY ................................................................................................ 57
TABLE 8: NATURAL WATER CONTENT .......................................................................................... 59
TABLE 9: VARIOUS PARAMETERS OF THE GRAIN SIZE DISTRIBUTION FOR ALL MATERIALS.......... 67
TABLE 10: PROPERTIES OF THE CHOSEN SIX MATERIALS TO BE TESTED
IN LARGE SCALE SHEAR BOX .................................................................................... 74
TABLE 11: LARGE SCALE SHEAR BOX TEST MATRIX .................................................................... 74
TABLE 12: SUMMARY OF THE LARGE SCALE SHEAR BOX TEST RESULTS...................................... 85
TABLE 13: FINITE ELEMENT TRIALS FOR 15FT SHAFT AT MAPLETON............................................ 90
TABLE 14: FINITE ELEMENT TRIALS FOR 10FT SHAFT AT MAPLETON............................................ 90
TABLE 15: FINITE ELEMENT TRIALS FOR 5FT SHAFT AT MAPLETON.............................................. 90
TABLE 16: FINITE ELEMENT TRIALS FOR 5FT SHAFT AT POINT OF THE MOUNTAIN EAST .............. 92
TABLE 17: FINITE ELEMENT TRIALS FOR 10FT SHAFT AT POINT OF THE MOUNTAIN EAST ............ 93
TABLE 18: FINITE ELEMENT TRIALS FOR 15FT SHAFT AT POINT OF THE MOUNTAIN EAST ............ 93
TABLE 19: FINITE ELEMENT TRIALS FOR 20FT SHAFT AT POINT OF THE MOUNTAIN EAST ............ 93
TABLE 20: FACTOR OF SAFETY VS. DEFLECTION FOR DRILLED SHAFT SKIN FRICTION................ 100
TABLE 21: FACTOR OF SAFETY VS. DEFLECTION FOR DRILLED SHAFT TIP RESISTANCE.............. 100
TABLE 22: RESULTS FROM STEPS 1 AND 2 – EXAMPLE DESIGN ................................................... 105
TABLE 23: RESULTS FROM STEPS 3, 4, AND 5 – EXAMPLE DESIGN............................................... 105
TABLE 24: RESULTS FROM STEPS 6, 7, AND 8 – EXAMPLE DESIGN............................................... 106
TABLE 25: COMPARISON OF QTOTAL (DESIGN) AND Q APPLIED BY THE SUPERSTRUCTURE
AND INDICATED ACTIONS ........................................................................................ 107
ACKNOWLEDGMENTS
The authors wish to thank Christ Dimitroplos and all ADOT personnel and consultants
associated with this project for their support, patience, and perseverance in seeing this project
through. Financial support for the completion of this project was requested and received from the
Federal Highway Administration and this support is also gratefully acknowledged. We would
also like to thank Kyle Rollins for his encouragement and assistance in gaining access to certain
sites for testing and sampling and his discussions with us on the research project.
1
INTRODUCTION
Drilled shafts are used extensively by the Arizona Department of Transportation (ADOT) for
foundation support of transportation structures. Drilled shafts have become the preferred deep
foundation element in the state because soil conditions are usually unfavorable to driven piles,
scour depths on the ephemeral river channels are quite large, and there is increased confidence in
the bearing layer afforded by the drilled shaft construction process. These foundations are
typically designed using American Association of State Highway and Transportation Officials
(AASHTO) guidelines and local experience.
Coarse granular materials are commonly found in the high energy riverine environments of the
Arizona deserts. Variously described as river-run, sand-gravel-cobbles, or SGC, these materials
are encountered frequently at bridge foundation elements because of their proximity to the water
courses. Typically dense and containing particles as large as boulder-sized materials, SGC is
usually sub-rounded due to transport and the larger particles are very hard. The material is
frequently clean and uncemented in the upper portions of the deposit but contains low- to
moderate-plasticity fines and/or light cementation which generates some apparent cohesion
below a depth of 20 to 30 feet.
Extremely difficult to characterize, the material is impossible to sample and test. Lack of
cohesion makes the sampling process difficult for any soil but the large particle sizes of SGC
compound the problem dramatically. Particle sizes in excess of 12 inches or more may be found,
requiring samples with a minimum diameter of 40 inches. Even if samples could be obtained,
conventional lab equipment is not designed to handle the large size.
Two approaches are generally adopted in geotechnical practice when sampling and testing of the
material is not possible: 1) field testing and 2) extrapolation of test data and relationships for
finer grained cohesionless material. Field tests involve an extremely large volume of soil and are
best conducted on a drilled shaft of a size used in practice. Due to the very large capacities
developed in SGC soils, testing of this kind is difficult and expensive to perform. ADOT has
conducted some field testing on deep foundations with the most relevant in SGC soils — that
reported by Beckwith and Bedenkop (1973)—providing information only on tip resistance.
Extrapolation of test data and relationships for finer grained cohesionless material is the method
used somewhat exclusively in the past design practice in Arizona. Extrapolation is not trivial and
requires an excellent model that takes into account a variety of parameters. Most of the models
employed in the past have not properly accounted for the differences in grain size and density
between finer grained soils and SGC, especially as it relates to dilatancy. The most common
approach has been a direct utilization of the results for finer grained materials (such as those
outlined in the AASHTO standard as discussed by Reese and O’Neill 1989) without any
accounting at all for changes in grain size and density. This approach is very conservative, as
will be demonstrated subsequently.
To examine these issues an ADOT research project was initiated in 2000 (SPR-493, Bridge
Foundation Design Parameters and Procedures for Bearing in SGC Soil). This project's purpose
was to consider possible modifications to the existing procedures for use in gravelly materials.
The modifications would likely take the form of a set of recommendations for gravelly soils such
2
as SGC soils. New design procedures would need to be appropriate for a wide range of
gradations of gravelly materials. A potentially measurable property of the soil in place (such as
gradation) was to be related to the recommended values.
Following an exhaustive literature study, a mechanistic model was to be developed and
calibrated that predicts axial behavior. Full-scale load tests already reported in the literature that
are representative of the soil conditions, loading geometry, and boundary conditions which
ADOT typically encounters were to be used to calibrate the model.
This report presents the results of all efforts to date on SPR-493. It includes a summary of
literature and current practice, a summary of historic use, analytical approaches currently used,
data gaps, and reports on finite element analyses performed, field and lab testing results,
development of models and design methodology, and presentation of an example design of a
drilled shaft in gravelly material.
3
SUMMARY OF LITERATURE AND CURRENT PRACTICE
An exhaustive search of the literature found nineteen articles, three Federal Highway Admin-istration
(FHWA) reports, and one report prepared for ADOT that involved load tests on drilled
shafts in coarse granular material. At a majority of the sites reported in these studies only strata
of gravelly material were encountered. Typically, the shafts were instrumented and load transfer
curves given. From these load transfer curves the average unit side resistance on the shaft over the depth
of the gravelly strata could be calculated. The amount of information given on the strata was generally
limited to Standard Penetration Test (SPT) N-values, Unified Soil Classification System (USCS)
classifications, and general boring log descriptions. Additional information including results of
Cone Penetration Tests (CPT), Pressure-Meter Tests (PMT) and grain-size distributions (GSD)
were given only in a small number of cases. Ideally, densities and strength parameters also
would have been provided, but these data were rare.
Summary of Historic Use
The purpose of this section is to display how drilled shafts are used in axial load applications in
Arizona, specifically with regards to shaft geometry, group geometry, and soil conditions. Table
1 following includes first a legend for use with the inventory list provided as the continuation of
Table 1.
4
Table 1: Legend For Plan Description and Summary
Label Description
Project Number The original ADOT project number for the
structure.
Project Name The ADOT name designation for the
structure.
Route-Mile Post The route name (i.e. I10, I17, etc.) and the
mile post marking at which the structure
exists.
Arrangement “Staggered” or “In Line” designates the
arrangement of the pile group. Staggered
groups are in an offset row formation and
in-line groups are in straight lines. The
“R#:#” identifies the number of piles in
each row. R1 being row number 1 and R2
being row number 2, and the number of
piles in each row following respectively.
Location Locations are identified by station number
as per the ADOT As Built drawings for
each structure. Station numbers can be
found on the structure plans “Foundation
Details’ sheet.
Diameter Identifies the diameter of the piles in each
group in inches.
Length Identifies the lengths of each of the piles in
feet.
Normalized Spacing Actual distance center to center of piles in
the group divided by the pile diameter.
Normalized Spacing Row to Row Distance between rows of piles divided by
the pile diameter. (would be smaller than
above for staggered piles)
Depth at Top of Cap Identifies the depth of the pile at top of cap
in feet – positive numbers designating
subsurface.
Date Designed and Date Built Identifies the date of design and the date of
construction for the structures.
Soil Characterization Generalized from borings logs listed on
plans.
5
Proj. Num. Proj. Name Rte
Mile
Post
Arr. Loc. Dia. Lth Norm
Spcg
Norm
Spcg
Row
to
Row
Depth
at Top
of
Cap
Date
Des.
Date
Built
Soil Char.
RAM-600-
3-514
Washington
St. Pier-1
SR143-
2.07
InLine1x
4
130+08 60 39 4.7 5 1989 1993 Silty sand to Sand & Gravel
with cement to sand & Gravel
Conglomerate@30ft
RAM-600-
3-514
Washington
St. Pier-2
SR143-
2.07
InLine1x
4
130+98 60 22 4.7 5 1989 1993 Silty sand to Sand & Gravel
with cement to sand & Gravel
Conglomerate@30ft
RAM-600-
3-514
Washington
St. Pier-3
SR143-
2.07
InLine1x
4
131+77 60 22 4.7 5 1989 1993 Silty sand to Sand & Gravel
with cement to sand & Gravel
Conglomerate@30ft
RAM-600-
3-514
Washington
St. Pier-4
SR143-
2.07
InLine1x
4
132+50.5 60 33 4.7 5 1989 1993 Silty sand to Sand & Gravel
with cement to sand & Gravel
Conglomerate@30ft
RAM-600-
3-514
Washington
St. Pier-5
SR143-
2.07
InLine1x
4
133+23 60 21 4.7 5 1989 1993 Silty Sand to 20’ Gravel &
sand & Weathered Granite
RAM-600-
5-511
Mill Ave.
Viaduct Pier
1
SL202-
6.335
In Line
1x6
190+81.25 72 84 4.6
(North
Side),
6.25
(South
Side)
6.25 1989 1993 Sand to Gravelly Sand, Sandy
ravelly Clay @ 20’, Clayey
Sand 30��
RAM-600-
5-511
Mill Ave.
Viaduct Pier
2
SL202-
6.335
In Line
1x6
192+22.75 72 61 6.1 6.25 1989 1993 Sand to Gravelly Sand, Sandy
Gravelly Clay @ 20’, Clayey
Sand @ 30’
6
RAM-600-
5-511
Mill Ave.
Viaduct Pier
3
SL202-
6.335
In Line
1x6
193+64.25 72 60 5.2
(North
Side),
5.8
(South
Side)
6.25 1989 1993 Sand to Gravelly Sand, Sandy
Gravelly Clay @ 20’, Clayey
Sand @ 30’
RAM-600-
5-511
Mill Ave.
Viaduct Pier
4
SL202-
6.335
In Line
1x6
195+23.75 72 95 4.82
(North
Side),
5.5
(South
Side)
6.25 1989 1993 Sand to Gravelly Sand, Sandy
Gravelly Clay @ 20’, Clayey
Sand @ 30’
RAM-600-
5-511
Mill Ave.
Viaduct Pier
5
SL202-
6.335
In Line
1x6
196+83.25 72 11
4
4.8
(North
Side),
5.3
(South
Side)
6.25 1989 1993 Sand to Gravelly Sand, Sandy
Gravelly Clay @ 20`, Clayey
Sand @ 30`
RAM-600-
5-511
Mill Ave.
Viaduct Pier
6
SL202-
6.335
In Line
1x6
198+42.75 72 11
8
4.86
(North
Side),
5.0
(South
Side)
6.25 1989 1993 Sand to Gravelly Sand, Sandy
Gravelly Clay @ 20`, Clayey
Sand @ 30`
RAM-600-
5-506
Ramp N-E
(piers 4-8)
I10-
147.25
4
IN Line
2x2
vary 36 (32
-
75)
3.33 4 1988 1993 Sand Silt to 22` to sandy
Gravelly Clay with 5` layers
RBM-600-
0-504
35th Ave. SR-
101L-
22.19
In Line
1x3+1x2
+1x3
20+00 36 40.
25
3 3 4.5 1990 1994 Sandy Gravel and cobbles to
30` and Gravel and cobbles
7
RBM-600-
0-502
Skunk
Creek
Bridge,
Piers 1, 2, 3
SR417-
213.49
In Line
1x5
746+19.0,
747+40.0,
748+61.0
60 73 4.5 5 1986 1990
RAM-600-
0523
Ramp S-E,
Pier 1
SL101-
2
In Line
1x3+1x2
+1x3
36 30 3 3 1989
RAM-600-
0523
Ramp S-E,
Pier 2
SL101-
2
In Line
1x3+1x2
+1x3
36 62 3 3 1989
RAM-600-
0523
Ramp S-E,
Pier 3,4,5
SL101-
2
In Line
3x4
36 62 3 3 1989
RAM-600-
0523
Ramp W-N,
Pier 1
SL101-
2
In Line
2x3
27+88.52 36 3 3 5 1990
RAM-600-
0523
Ramp W-N,
Pier 2
SL101-
2
In Line
2x5
33+76.52 36 3 3 5 1990
8
Analytical Approaches
Introduction
All methods for determining the axial capacity of drilled shafts are based upon the
general equation:
Qult = Qp +Qs −W (1)
where Qult is the ultimate axial capacity of the shaft, Qp is the bearing capacity
component of the shaft and is contributed by the tip, Qs is the side resistance component
of the shaft and is contributed by side friction, and W is the weight of the shaft. It is
generally agreed that the weight of the shaft is approximately equal to the weight of the
soil displaced during drilling. Therefore, the W term is often neglected leaving:
ult p s Q = Q +Q (2)
The components Qp and Qs are calculated by the following two equations:
p p p Q = q A (3)
s s s Q = f A (4)
where qp is the base resistance per unit area, Ap is the cross-sectional area of the tip, fs is
the shaft resistance per unit area, and As is the surface area of the sides of the shaft in
contact with the soil. For differing layers of soils, Qs consists of contributions from each
layer.
The methods that follow are focused on determining qp and fs for cohesionless granular
soils. The methods are presented in their most updated form.
Tomlinson 2001
The unit skin resistance is calculated by Tomlinson (2001):
tan sf = Kσ ′ δ ≤ 110 [kN/m2] (5)
where σ ′ equals the average effective overburden pressure over the depth of a soil
layer, K is a coefficient of horizontal soil stress, and δ is the soil-pile friction interface
angle obtained from laboratory shear box tests. For drilled shafts in coarse soils, K
equals 0.7 to 1.0 times K0 with the higher value corresponding to good construction
technique. The coefficient of earth pressure at rest, K0, is the ratio between the
horizontal and the vertical effective stresses, and is found from the following equation:
0 (1 sin ) K OCR φ′
= − (6)
where φ′
is the effective angle of shearing resistance in a soil and OCR is the over-consolidation
ratio. The over-consolidation ratio is the ratio of the maximum previous
vertical effective overburden pressure to the existing vertical effective overburden
pressure. The value of φ′
is usually considered to be the same as the φ found using
Standard Penetration Tests (SPT) N-values. The relationship between SPT and φ as
established by Peck et al. (1967, p.310) and provided by Tomlinson is shown in Figure 1.
9
Figure 1: Relationship Between SPT N-Values and Angle of Shearing Resistance
[Tomlinson 2001]
Tomlinson recommends that the φ value be assumed representative of loose conditions
when considering drilled shafts. However, when the shafts are drilled and constructed
using bentonite slurry, the φ value should correspond to undisturbed conditions.
The unit base resistance is calculated by:
qp =σ ′Nq (7)
where q N is a bearing capacity factor and is found using a chart that includes
recommendations from both Hansen (1961) and Berezantsev (1961) (Figure 2). The φ
value is also found from SPT tests and should correspond to loose conditions for dry
constructed drilled shafts and undisturbed conditions for shafts constructed under
bentonite slurry.
Figure 2: End-Bearing Capacity Factors (Hansen 1961; Berezantsev 1961)
10
Meyerhoff 1976
Meyerhoff gives the unit side resistance as:
100 s
f = N tons per square foot ( tsf) (8)
where N is the average SPT N-value, not corrected for overburden pressure.
The unit base resistance can be calculated as:
1.2 p corr q = N tsf (9)
where Ncorr is the SPT N-value corrected for effective overburden pressure. The value of
Ncorr is referenced from Peck et al. (1967: 310) and standardizes N-values to the N-value
at an effective overburden pressure of 1 tsf (Reese and O'Neill 1989). It is found by
multiplying the field N-value by a correction factor CN:
10
0.77log 20 N C
σ
=
′ (10)
where σ′ is the vertical effective stress in tsf.
Reese and O'Neill 1989 (AASHTO METHOD)
The unit side resistance for a given layer is given by Reese and O’Neill and adopted by
AASHTO as:
s f = βσ ′ (11)
where β is equivalent to K tanδ in equation (5) and is given by the function
β =1.5−0.135z0.5; 0.25 ≤ β ≤1.20, (12)
σ ′ is the vertical effective stress at the middle of a layer, and z is the depth to the middle
of a layer in feet (Reese and O’Neill 1989; AASHTO 1998).
The unit base resistance is given by the following formula:
0.60 pq = N tsf ≤ 45 tsf (13)
where N is the uncorrected N-value from the SPT test within a distance of 2Bb below the
tip of the shaft. Bb is the diameter of the base of the shaft.
Kulhawy 1989
The unit side resistance is found using the general equation:
tan sf = Kσ ′ δ (14)
where δ can be expressed as a function of φ′
. The ratio / δ φ′
is a function of
construction technique and for good construction techniques equals 1. For poor slurry
construction techniques where sufficient care was not taken to ensure that all of the slurry
was expelled from the hole or the slurry was mixed together with and infiltrated the sides
of the hole, / δ φ′
is reduced to 0.8 or lower (Kulhawy 1989).
As with Tomlinson, K is a function of K0, the original in-situ coefficient of horizontal
earth pressure. Kulhawy recommends that K0 can be found from the following:
11
0 ( ) (1 sin )
max max
1 sin 3 1
4
K OCR OCR
OCR OCR φ φ − ′
⎡ ⎛ ⎞⎤ = − ′ ⎢ + ⎜ − ⎟⎥
⎢⎣ ⎝ ⎠⎥⎦
(15)
Where OCRmax is the maximum over-consolidation ratio experienced by the soil profile
of interest. If the OCRmax is unknown, or the current OCR is equal to the OCRmax, the
above equation simplifies to the following by setting OCRmax equal to OCR:
( ) sin '
0 1 sin K OCR φ φ′
= − (16)
The value of K can now be found using the ratio K/K0. With good construction technique
and prompt concreting, for both dry and slurry construction, K/K0 approaches 1. For poor
slurry technique K/K0 reduces to 2/3.
The unit base resistance is given by:
0.3 p r q qs qd qr q BN N γ γ = γ ′ ζ +σ ′ ζ ζ ζ (17)
where B is the diameter of the shaft, γ ′ is the average effective unit weight from depths
D to D + B, where D is the depth to the tip of the shaft, σ ′ is the vertical effective stress
at depth D, Nq is found from:
tan2 45 ( tan )
q 2 N e⎛ φ ′ ⎞ π φ ′
= ⎜ + ⎟
⎝ ⎠
􀁄􄐬 , (18)
Nγ is equal to
2( 1)tan q N N γ φ′
= − , (19)
and the ζ terms are found from Table 2.
Table 2: ζ Terms (Kulhawy 1991)
Modification Symbol Value
Shape qs ζ 1 tan φ′
+
Depth qd ζ ( )1 2 tan 1 sin 2 tan 1
180
D
B
π
φ φ − ′ ′ ⎡⎛ ⎞ ⎛ ⎞⎤ + − ⎢⎜ ⎟ ⎜ ⎟⎥ ⎣⎝ ⎠ ⎝ ⎠⎦
qr ζ { ( )( ) ( ) } 3.8tan 3.07sin log10 2 / 1 sin 1 Irr e ⎡⎣− φ ′⎤⎦+⎣⎡ φ ′ + φ ′ ⎦⎤ ≤
Rigidity
γ r ζ qr ζ
Irr is the reduced rigidity index and is found from the rigidity index, Ir. Ir is determined
from:
tan
d
r
avg
I G
σ φ
=
′ ′ (20)
12
where avg σ ′ is the average vertical effective stress from depths D to D + B and Gd is the
drained shear modulus. From elastic theory Gd is equal to:
1 / (1 )
2 d d d G = E +ν (21)
where Ed is the drained Young's modulus and d ν is the drained Poisson's ratio. Typical
ranges of Ed are given in Table 3.
Table 3: Typical Ed Values (Kulhawy 1991)
Drained Young's Modulus, Ed
Sand Consistency tons/ft2 MN/m2
Loose 50-200 5-20
Medium 200-500 20-50
Dense 500-1000 50-100
The drained Poisson's ratio can be found from:
0.1 0.3 d rel ν φ′
= + (22)
where rel φ′
is given by:
25
rel 45 25
φ
φ
′ − ′ =
−
􀁄􄐀
􀁄􄐀 􀁄􄐠 (23)
with limits of 0 and 1.
The rigidity index can now be found by:
1
r
rr
r
I I
I
=
+ Δ
(24)
where Δ is given by:
0.005(1 ) avg
rel
a p
σ
φ
⎛ ′ ⎞
Δ = − ′ ⎜ ⎟ ⎜ ⎟
⎝ ⎠
(25)
where pa is the atmospheric pressure in the appropriate stress units and avg
a p
σ ′
is limited to
10.
Irr must then be compared to the critical rigidity index, Irc which is found from:
2.85cot 45
0.5 2 rcI e
φ′
⎡ ⎛ ⎞⎤
⎢ ⎜ − ⎟⎥
= ⎣ ⎝ ⎠⎦
􀁄􄐠
(26)
If Irr is greater than Irc the soil behaves as a rigid-plastic material and 1 qr γ r ζ =ζ = . When
Irr is less than Irc the r ζ factors are determined from Table 2.
13
Rollins, Clayton, Mikesell, and Blaise 1997
Rollins et al. (1997) expanded on Reese and O'Neill's 1989 (and AASHTO's) method by
suggesting β factors for gravelly soils (Table 4).
Table 4: β values (Rollins, et al. 1997)
Percentage Gravel β
Less than 25% β =1.5−0.135z0.5; 0.25 ≤ β ≤1.20
Between 25% and 50% β = 2.0 − 0.0615z0.75 with 0.25 ≤ β ≤1.8
Greater than 50% β = 3.4e−0.0265z with 0.25 ≤ β ≤ 3.0
z is the depth to the center of the layer. Their results were based upon uplift tests and no
qp factor was studied.
14
15
COMPARISON OF ACTUAL SKIN FRICTION FACTORS TO PREDICTED
FOR DRILLED SHAFT IN GRANULAR SOIL
Introduction
Drilled shafts are used in many civil engineering projects including bridges, retaining
walls, offshore structures, and tanks. Advantages of drilled shafts include that they can be
drilled to different depths in many kinds of materials and can be designed and constructed
with different diameters. Predictive equations have been available for determining the
contribution of skin friction to the drilled shaft axial load carrying capacity for a number
of years. Many load tests have been performed in clays and sands. These load test results
have served to create and validate the equations used. Only a limited number of load
tests have been performed in the past on granular materials with high gravel content. It is
presumed that the skin friction factors of gravelly soils would be higher than those for
pure sands, because of the increased dilatancy of gravels prior to failure. As the use of
drilled shafts increases, more data from gravelly soils becomes available from load tests
to determine how well the current predictive equations work. This section of the report
focuses on skin friction factors arising from drilled shafts in granular materials with a
gravel content higher than zero. By back-analyzing the results from load tests, one can
determine the actual skin friction factors for drilled shafts in granular soils. These skin
friction factors were compared with the various predictive equations currently employed
for design purposes. The results show that the predictive equations are extremely
conservative for predicting the skin friction factor in gravelly soil conditions.
Load Tests
An extensive literature review was undertaken to find articles on drilled shaft load tests in
granular materials. The load tests and articles are identified in Table 5.
Table 5: Load Tests
Load Test Location Source Number of Shafts Tested
Takasaki Japan Fujioka and Yamada (1994) 2
Osaka Bay, Japan Matsui (1993) 1
Chalkis, Greece Frank et al. (1991) 1
Utah Bridge F-489 Price et al. (1992) 1
Utah Bridge F-438 Price et al. (1992) 1
Albuquerque: Alameda
Blvd. Chua and Aspar (1993) 1
Caliente, Nevada Konstantinidis et al. (1987) 2
Baker, California Konstantinidis et al. (1987) 2
Cupertino, California Baker (1993) 1
Oahu, Hawaii Rollins et al. (1997) 2
Southern California Tucker (1987) 16
Utah Rollins et al. (1997) 26
16
In all, 56 separate shafts were evaluated. Some shafts had more than one layer
instrumented allowing for more than one fs evaluation for that shaft. Many of the load
tests were identified in Rollins et al. (1997).
Values of fs Derived From Direct Field Measurements
The method used to obtain fs values depended on the type of field test performed. For
typical instrumented axial compression tests, the load-transfer curves generated by the
author were used. For gravel layers, the loads in the shaft at the upper and lower
boundaries of the gravel layer (as derived from strain gage data) were read from the
curves provided by the author of each paper or report. The difference between these two
loads was divided by the surface area of the shaft element. The outermost load-transfer
curve, which corresponds to the highest load applied to the top of the shaft, was used.
The ultimate load for uplift tests was determined by using the equation for a hyperbola:
Q
a b
Δ
=
+ Δ
(27)
where Q is the load in the shaft and Δ is the displacement. Dividing the numerator and
denominator of the right side of the equation by Δ gives:
Q 1 a b
=
+
Δ
(28)
The limit of Q as Δ approaches ∞ is 1
b
. Determining Q and Δ from the load
displacement curve at 95% and 70% of the highest Q achieved (during the load test)
gives two equations with two unknowns, a and b, which are then easily solved for. Qult is
then determined as 1
b
. Dividing Qult by the surface area of the shaft in contact with the
soils gives fs.
The fs values from Tucker’s article on Southern California Edison (SCE) drilled shafts
were used in this report (Tucker 1988). His data were based upon uplift tests; fs values
were determined using normalized curves that he had generated. These curves
normalized the displacement and load achieved in the field to a load corresponding to one
inch of displacement. Further information on his curves is given in his article.
Predicted Values of Fs
The input values for use with the predictive equations were typically given by the authors
who performed the load tests and/or reported the results. In cases where input data were
incomplete, the missing values were estimated, based on data that were given, as a part of
the present study. For the input values that depend upon construction technique it was
assumed that the construction technique was good. This is likely to be a valid assumption
because shafts that are constructed for load tests are generally given more attention
during the construction phase. In all cases the over-consolidation ratio (OCR) was
assumed to be 1. In other words, the current effective stress is the highest effective stress
that the soil has ever experienced. SPT N-values were provided in almost every test. The
angle of internal friction was estimated using a correlation between N and φ′
provided by
17
Peck (1967) for the majority of cases where it was not provided. The angle of soil-pile
interface was assumed to be equal to the angle of internal friction for all cases. Unit
weights of the soils were estimated based on soil descriptions and the vertical effective
stress was calculated using the typical procedure. The percentage of gravel was
estimated using the soil descriptions and Rollins et al. (1997). It was not difficult in
general to learn whether the soil was a sand, sandy gravel, or gravel.
Results
The results are presented in the charts that follow. Figure 3 displays predicted versus
actual fs for all of the predictive methods. Due to the assumptions made on the over-consolidation
ratio, Tomlinson’s and Kulhawy’s methods yield the same results. Figure
4, Figure 5, Figure 6, and Figure 7 display the fs comparisons for each method with
Tomlinson’s and Kulhawy’s shown on the same figure.
Predicted vs. Actual fs Values
0
2
4
6
8
10
0 5 10
Actual [tsf]
Predicted [tsf]
Tomlinson and
Kulhawy
Meyerhoff
Reese & O'Neill
Rollins et al.
Figure 3. Predicted vs. Actual fs values, All Methods
18
Predicted vs. Actual fs Values
Tomlinson and Kulhawy
0
2
4
6
8
10
0 5 10
Actual [tsf]
Predicted [tsf]
Tomlinson and
Kulhawy
Figure 4. Predicted vs. Actual fs Values, Tomlinson and Kulhawy
Predicted vs. Actual fs Values
Meyerhoff
0
2
4
6
8
10
0 5 10
Actual [tsf]
Predicted [tsf]
Meyerhoff
Figure 5. Predicted vs. Actual fs Values, Meyerhoff
19
Predicted vs. Actual fs Values Reese
& O'Neill
0
5
10
0 5 10
Actual [tsf]
Predicted [tsf]
Reese & O'Neill
Figure 6. Predicted vs. Actual fs Values, Reese and O’Neill
Predicted vs. Actual fs Values Rollins
et al.
0 2 4 6 8
10
0 5 10
Actual [tsf]
Predicted [tsf]
Rollins et al.
Figure 7. Predicted vs. Actual fs Values, Rollins et al. (1997)
20
There is a lot of scatter on the plots. In every case as the actual value of fs increases, the
likelihood of a correct prediction decreases. The Rollins et al. (1997) method appears to
offer the best correlation. To determine if a particular soil type is less likely to be
accurately predicted than another, Figure 8, Figure 9, Figure 10, and Figure 11
differentiate between sands, sands w/gravels, and gravels.
Predicted vs. Actual fs Values
Tomlinson and Kulhawy
0
2
4
6
8
10
0 5 10
Actual [tsf]
Predicted [tsf]
Sand
Sand/Gravel
Gravel
Figure 8. Predicted vs. Actual Values, Tomlinson and Kulhawy, by Soil Type
Predicted vs. Actual fs Values
Meyerhoff
0
2
4
6
8
10
0 5 10
Actual [tsf]
Predicted [tsf]
Sand
Sand/Gravel
Gravel
Figure 9. Predicted vs. Actual Values, Meyerhoff, by Soil Type
21
Predicted vs. Actual fs Values Reese
& O'Neill
0
2
4
6
8
10
0 5 10
Actual [tsf]
Predicted [tsf]
Sand
Sand/Gravel
Gravel
Figure 10. Predicted vs. Actual Values, Reese and O’Neill, by Soil Type
Predicted vs. Actual fs Values Rollins
et al.
0
2
4
6
8
10
0 5 10
Actual [tsf]
Predicted [tsf]
Sand
Sand/Gravel
Gravel
Figure 11. Predicted vs. Actual Values, Rollins et al., by Soil Type
22
Gravels are the least likely to have fs accurately predicted. This is true for all methods. It
appears that the modifications Rollins et al. make to the Reese and O’Neill method is sound
for sand with gravel and still conservative for gravels. The Tomlinson and Kulhawy methods
grossly under-predict all soil types while the Meyerhoff method offers a degree of
predictability similar to Reese and O’Neill’s.
There are three possible methods for testing the axial capacity of drilled shafts: Uplift,
Osterberg, and Compression. Figure 12, Figure 13, Figure 14, and Figure 15 differentiate
between the testing methods to determine if they have any influence on the results.
Predicted vs. Actual fs Values Tomlinson
and Kulhawy
0 2 4 6 8
10
0 5 10
Actual [tsf]
Predicted [tsf]
Uplift
Osterberg
Compression
Figure 12. Predicted vs. Actual Values, Tomlinson and Kulhawy, by Test Type
Predicted vs. Actual fs Values
Meyerhoff
0
2
4
6
8
10
0 5 10
Actual [tsf]
Predicted [tsf]
Uplift
Osterberg
Compression
Figure 13. Predicted vs. Actual Values, Meyerhoff, by Test Type
23
Predicted vs. Actual fs Values Reese &
O'Neill
0
2
4
6
8
10
0 5 10
Actual [tsf]
Predicted [tsf]
Uplift
Osterberg
Compression
Figure 14. Predicted vs. Actual Values, Reese and O’Neill, by Test Type
Predicted vs. Actual fs Values Rollins
et al.
0
2
4
6
8
10
0 5 10
Actual [tsf]
Predicted [tsf]
Uplift
Osterberg
Compression
Figure 15. Predicted vs. Actual Values, Rollins et al., by Test Type
24
The compression tests had the highest actual values of fs. Uplift tests had the lowest fs
values while Osterberg tests fell in the middle. This is an interesting result and could
imply that the test method does influence actual capacity determination.
From the preceding graphs, it is obvious that the Rollins et al. (1997) method provides the
best approximation of fs. The following graphs will examine the Tomlinson, Kulhawy,
Meyerhoff, and Reese and O’Neill methods as one group and the Rollins et al. method as
a second group. The first two figures, Figure 16 and Figure 17, take the predicted value
of fs divided by the actual value of fs for the two groups described above, and compare
the average to the percentage of gravel. The percentage of gravel represents the three soil
types: sands, sands with gravel, and gravel. Because the percent of gravel associated
with each computed value of skin friction was unknown, it was necessary to estimate
these values from the soil descriptions corresponding to sands, sand with gravel and
gravels. The values assigned were 20, 40, and 55 percent gravel, respectively. The
uncertainty in the gravel percentages has no doubt contributed to the scatter in the
computed values of the ratio of predicted to actual skin friction, P/A, and it is believed
that the scatter would have been much less if the gravel percentage values had been
measured and made available. However, the procedure adopted was essentially the only
method available for approximately assessing the influence of gravel content on the skin
friction. The point represents the average value of P/A and the line represents one
standard deviation above and below the average P/A.
Average P/A vs. % Gravel All Methods sans Rollins et
al.
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
20 40 55
% Gravel
Average Predicted/Actual
Figure 16. Average P/A vs. Percent Gravel, All Methods except Rollins et al.
25
Average P/A vs. % Gravel Rollins et al.
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
20 40 55
% Gravel
Average Predicted/Actual
Figure 17. Average P/A vs. Percent Gravel, Rollins et al.
Figure 16 displays the trend of decreasing predictability as the percentage of gravel
increases for the first group of predictive methods. The actual value of fs for gravelly
soils is under-predicted by an average of over 300%. For the Rollins method, Figure 17,
the average values of P/A are much closer to 1 for the different soil types. Note that in
the case of sands, which is the Reese and O’Neill method, the average P/A is very close
to 1.
26
Figure 18 and Figure 19 examine the same groupings but this time versus depth to mid-layer.
The depth to mid-layer was grouped into three depth intervals: 0-10 ft, 10-30 ft, and 30+ ft.
Average P/A vs. Depth to Mid-Layer All Methods
sans Rollins et al.
0.0
0.2
0.4
0.6
0.8
1.0
0-10 10-30 30+
Depth to Mid Layer
Average Predicted/Actual
Figure 18. Average P/A vs. Depth to Mid-Layer, All Methods except Rollins et al.
Average P/A vs. Depth to Mid-Layer Rollins et al.
0.0
0.5
1.0
1.5
2.0
2.5
0-10 10-30 30+
Depth to Mid Layer
Average Predicted/Actual
Figure 19. Average P/A vs. Depth to Mid-Layer, Rollins et al.
For the first group, correlation between average P/A and depth to mid-layer is poor. The
Rollins et al. group is better and the average values of P/A for depths greater than 10 ft
are over-predicted.
27
Figure 20 and Figure 21 examine the same groups with respect to test type.
Average P/A vs. Test Type All Methods sans
Rollins et al.
0.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
Compression Osterberg Uplift
Test Type
Average Predicted/Actual
Figure 20. Average P/A vs. Test Type, All Methods except Rollins et al.
Average P/A vs. Test Type Rollins et al.
0.00
0.50
1.00
1.50
2.00
2.50
Compression Osterberg Uplift
Test Type
Average Predicted/Actual
Figure 21. Average P/A vs. Test Type, Rollins et al.
Both figures display the same trend with the Rollins et al. method offset higher than the
other group.
28
The next series of plots examines what the K value (from equation 14) would need to be
to make the predicted value of fs match the actual value of fs. The vertical effective stress
is determined from the soil profile while δ is set equal to φ . The value of φ is
determined in one of two ways. The first is from SPT correlation as given by Peck et al.
(1967: 310). The second method converts the φ found from the SPT correlation to a
plane strain φ, or ps f,  . The relationship between φ and ps φ is:
sin φps = tan φ (29)
Equation 29 is based on two assumptions: (1) the values of φ from the SPT correlation
are more or less direct shear values, and (2) in the direct shear test the horizontal plane is
not the “failure” plane but rather the point at the top of the corresponding Mohr’s circle.
Setting fs equal to the actual value of fs, K is easily solved for. In Figure 22 the back-calculated
K is based on φ . In Figure 23 the back-calculated K is based on φ ps and is
denoted Kps. In figures 22 and 23, the back-calculated K values are plotted against the
percentage of gravel or soil type.
K vs. % Gravel
0.0
2.0
4.0
6.0
8.0
10.0
12.0
20 40 55
% Gravel
K
Figure 22. K vs. Percent Gravel
29
K ps vs. % Gravel
0.0
1.0
2.0
3.0
4.0
5.0
6.0
20 40 55
% Gravel
K ps
Figure 23. Kps vs. Percent Gravel
In both cases, the required K value increases as gravel content increases. Using ps φ
reduced the required K value for all cases by roughly half. Figure 24 and Figure 25
examine the required K values versus the depth to mid-layer.
K vs. Depth to Mid-Layer
0.0
2.0
4.0
6.0
8.0
10.0
12.0
0-10 10-30 30+
Depth to Mid-Layer
K
Figure 24. K vs. Depth to Mid-Layer
30
K ps vs. Depth to Mid-Layer
0.0
1.0
2.0
3.0
4.0
5.0
6.0
0-10 10-30 30+
Depth to Mid-Layer
K ps
Figure 25. K ps vs. Depth to Mid-Layer
The preceding figures show that the required K decreases with depth. In fact, using ps φ
the required K at depths greater than 30 ft is 1.
Dilation
The results presented above show that dilatancy is a key issue in the skin friction of
drilled shafts. Dilatancy is a term for shear induced volume change. When shear stress is
applied to an element, its volume can decrease, increase, or stay the same. When it is
lightly confined and initially dense, it tends to expand and is said to be dilatant. If it is
heavily confined and initially loose, then it tends to increase in density and is said to be
contractive. Therefore, whether or not it tends to dilate during shear and by how much
depends on how dense the material is initially and how heavily confined it is.
When a drilled shaft is loaded axially and starts to move downward relative to the soil, a
shear surface is established along the surface of the shaft or in the vicinity of the outer
surface of the shaft. It is in this region that dilation primarily occurs. The amount of
movement required for particles moving in and near the shaft surface depends on the
effective particle size and roughness of the shaft. The larger the particle size and the
rougher the shaft the more outward and downward movement is required to develop the
shear resistance. If a shaft were axially loaded and forced downward 2 inches, and the
particles around the shaft were of size up to about 2 inches, then particles around the
shaft would be forced to move radially outward a distance up to about 2 inches, due to the
dilatory effect, which depends on the particle size. This outward movement tendency
could be accommodated in one of two ways (or a combination of both). First, and
perhaps most importantly, outward movement of particles due to dilation is more or less
equivalent to cavity expansion and would be accomplished by an increase in radial
31
normal stress as the particles are forced outward. If the material surrounding the shaft
were of very low compressibility and densification could not be accommodated, then the
ground surface would heave slightly to accommodate the dilation. In most cases it is
expected that dilation is accommodated by both densification and heaving of the ground
surface.
The results of this study support the assertion of dilative behavior. The amount of
dilation and corresponding increase in radial stress is expected to increase with the
amount of gravel present in the soil, and the size of the gravel particles. With an increase
in radial stress the skin friction capacity of the drilled shaft is expected to increase. The
results clearly verified this phenomenon. As the depth increases, the confining pressure
increases and the outward particle movement is accommodated by local densification
around the shaft. Under these conditions the relative increase in radial stress is minimal
and the K values tend to approach about 1.
32
Figure 26: Typical Grain Size Distribution of SGC Soil
33
REPORT ON PRELIMINARY FINITE ELEMENT ANALYSES OF TWO CASE
HISTORY STUDIES OF AXIALLY LOADED DRILLED SHAFTS
Introduction
There are very few case histories in the literature which provide detailed information,
including full gradation curves, on large-scale axial loading of drilled shafts in very
coarse grained materials. Two such case histories have been identified and are presented
next. To enhance the usefulness of the load-deflection data, a series of parametric finite
element analyses was also performed.
A high percentage of Phoenix and the Salt River Valley area is underlain by very coarse
granular deposits consisting of mixtures of sand, gravel, and cobbles (SGC soil). This
section of the report presents results of finite element analysis for two axially loaded
concrete drilled shafts founded in SGC soils. The main objective of this study is to
determine a set of properties—soil angle of internal friction, φ; soil dilation angle, ψ;
coefficient of friction between soil and pile, f; coefficient of at-rest lateral earth pressure,
K; and soil modulus of elasticity, E—that best represent the SGC soils in the field.
Finite element analysis using ABAQUS Version 5.8 has been performed with the goal of
matching the load-deflection curves of these two tests by iterating with different sets of
soil parameters.
Characteristics of the SGC Soils
SGC soils predominate in the heavily populated areas of central and southern Arizona.
These soils were deposited by high-energy discharges of the Salt River and other
drainages. SGC soils consist mainly of sand, gravel, and cobbles with a small amount of
silt and are generally classified as GP in the Unified Soil Classification System. These
soils generally contain particles up to about 12 inches and occasionally contain scattered
boulders exceeding 24 inches. SGC soil also contains a very high percentage of quartz,
chert, and other very hard particles. This is typically reflected by very high wear on
drilling tools used in both foundation drilling and exploratory drilling into the deposit.
These types of soils are too coarse to enable the evaluation of relative density or
compressibility by conventional penetration tests and laboratory methods. Their coarse
nature also makes it extremely difficult and costly to obtain in-situ densities. The ranges
in gradation of typical SGC samples are shown in Figure 26.
Axial Compression Loading on Drilled Shafts
An axial load test was reporteded in May, 1973, as a part of research project no. HPR-1-
10(122), “An Investigation of the Load Carrying Capacity of Drilled Cast-in-Place
Concrete Piles Bearing on Coarse Granular Soils and Cemented Alluvial Fan Deposits,”
prepared by George H. Beckwith and Dale V. Bedenkop (1973) for the Arizona Highway
Department. The load tests were devised such that only the bearing capacity of the soil
would be analyzed for both belled and normal shafts. The finite element analysis which
follows examines only the load test on a normal shaft without a bell as reported by
Beckwith and Bedenkop (1973).
34
Soil Profile
The soil profile for the first test consisted of roughly 7 feet of uncemented or weakly
cemented silty clays and sandy clays underlain by moderate to strong lime-cemented clayey
sands and sandy clays to a depth of 11 to 13.50 feet. Beneath this is a layer of moderately
cemented clayey gravels; the SGC was first encountered between 14.5 to 16 feet, and it
extended downward more than 20 feet according to Beckwith and Bedenkop (1973). The
SGC layer is uncemented and relatively uniform except for a clean, fine to medium sand
encountered at between 17.5 to 19 feet. In general, soil moisture contents were very low
throughout the extent of the borings.
Pile Configuration
The reinforced concrete shaft had an average diameter of 2.50 feet and was 17.83 feet long.
The top of the shaft was about 6 inches above the ground surface as shown in Figure 27. The
side of the shaft was separated from the soil by a sonotube such that the test was strictly a
measure of end-bearing capacity (frictionless shaft).
Figure 27: Pile Configuration
Finite Element Analysis
A finite element model was created using the ABAQUS Finite Element Program. The shaft
was treated as a linear elastic material with modulus of elasticity, E, equal to 7.0×108 pounds
per square foot, and Poisson’s Ratio (υ) 0.30. The unit weight of the concrete is assumed to
be 150 pounds per cubic foot. The soil is treated as an elastic fully-plastic material as repre-sented
by the Drucker-Prager Model shown in Figure 28. The unit weight of the soil is
assumed to be 125 pcf with a Poisson’s Ratio of 0.40. Sliding elements were installed
between the shaft and the soil and have a coefficient of friction equal to zero to represent a
frictionless shaft. A parametric study was done to study the effect of the soil internal angle
of friction (φ), soil dilation angle (ψ), and soil modulus of elasticity (E), and to select opti-mum
values. An associated flow rule was assumed first, such that the soil angle of internal
friction equals the dilation angle. The field load-deflection curve is shown in Figure 29.
Figure 30 shows the effect of soil modulus of elasticity (E) on the load deflection curve of
30``
6``
17`-10``
Sonotube
35
the axially loaded pier. The effect of the internal friction angle on the final load deflection
curve is shown in Figure 31.
C
φ
τ
σ
φ
ψ
dεpl
Figure 28: Drucker-Prager Model.
0
100
200
300
400
500
600
700
800
900
1000
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
Displacement (in)
Load (Tons)
Figure 29: Field Load-Deflection Curve.
36
0
100
200
300
400
500
600
700
800
900
1000
1100
1200
1300
1400
1500
0 0.5 1 1.5 2 2.5
Displacement (in)
Load (Tons)
Test
E=0.4e7 psf
E=1.25e7 psf
E=2e7 psf
φ=36
Ψ=36
Figure 30: Effect of Soil Modulus, E, on the Load Deflection Curve.
Figure 31: Effect of Soil Angle of Internal Friction, ø, on the Load Deflection Curve
0
100
200
300
400
500
600
700
800
900
1000
1100
1200
0 0.5 1 1.5 2 2.5
Displacement (in)
Load (Tons)
Test
φ=30
φ=35
φ=37.5
φ=36
E=1.25e7 psf
Ψ=36
37
Effect of Dilation Angle
Of course, the higher the dilation angle (ψ), the more the soil dilates. The ψ value should
be less than or equal to the soil angle of internal friction (φ). A parametric study was
performed to study the effect of dilation angle on the load deflection curve for the axially
loaded drilled shaft. As an example of one of these sets of iterations, Figure 32 shows the
effect of the dilation angle on the deflection curve for φ = 36o. Both φ and ψ were
changed in such a way as to match the field load deflection curve as closely as possible.
Figure 33 shows a summary of these trials and their comparison with the field test.
0
100
200
300
400
500
600
700
800
900
1000
1100
1200
0 0.5 1 1.5 2 2.5
Displacement (in)
Load (Tons)
Test
ψ=36
ψ=30
ψ=40
E=1.25e7 psf
φ=36
Figure 32: Effect of Soil Dilation Angle on Results.
0
100
200
300
400
500
600
700
800
900
1000
1100
1200
0 0.5 1 1.5 2 2.5
Displacement (in)
Load (Tons)
Test
φ=36, ψ=36
φ=33, ψ=40
φ=39, ψ=30
φ=37.5, ψ=30
φ=34.5, ψ=40
φ=40, ψ=25
φ=45, ψ=10
φ=45, ψ=20
φ=45, ψ=18
Figure 33: Set of Trials of Match Field Load-Deflection curve.
38
Best Fit Indicator
The R2 value has been calculated using the Least Squares Method to correlate to the best
fit of these results to the real field test. Figure 34 shows the R2 values for the different
sets of finite element runs. Figure 35 shows the line representing the highest R2 values.
0
5
10
15
20
25
30
35
40
45
30 32.5 35 37.5 40 42.5 45 47.5
Soil Angle of Internal Friction, φ
Soil Dilation Angle, ψ
0.929 0.985
0.984
0.948 0.978 0.965
0.983
0.98
0.982
0.979
Figure 34: R2 Values for Different Sets of ø and Ψ
y = 549.44e-0.0765x
R2 = 0.9896
0
5
10
15
20
25
30
35
40
45
30 32.5 35 37.5 40 42.5 45 47.5
Soil Angle of Interanl Friction, φ Dilation Angle, ψ
Figure 35: Curve of Maximum R2 Values, for ψ vs φ.
39
Selection of Best Set of Parameters for SGC
Based on the comparisons shown in figures 30 through 35 it was concluded that the best
set of soil parameters for matching the field load-deflection curve for SGC is φ = 36o, for
ψ = 36o, and E = 1.25 X 107 psf. These values are associated with a unit weight of the
soil of 125 pcf and Poisson’s ratio of 0.40.
Uplift Loading on Drilled Shaft Test
This test was reported in January, 1997, in Drilled Shaft Side Friction in Gravelly Soils,
by Kyle M. Rollins, Robert J. Clayton, Rodney C. Mikesell, and Bradford C. Blaise for
the Utah Department of Transportation (UT-97.02) (Rollins et al. 1997). The main
objective of this test was to evaluate the side friction between the shaft and the soil
generated by applying an uplift load on the shaft. This study is one of a very small
number where sufficient data is available for back analysis.
Soil Profile
“A general description of the subsurface materials is as follows: from the ground surface
to a depth of 12 feet -very dense coarse to fine gravel with cobbles; from 12 feet to the
maximum depth of exploration (15 ft) - medium density sand. Percent gravel for the site
ranges from 68% in the gravely materials to 2% in the silty sand. … Maximum particle
size is 4 inches and ground water was encountered at 12.6 ft in the 15-foot shaft boring”
(Rollins et al. 1997: 45). The grain size distribution for the soil at this site is shown in
Figure 36. Additional specifics are given in Rollins et al (1997).
Figure 36: Grain size Distribution for the soil at Utah site.
40
Pile Configuration
The reinforced concrete pile had an average diameter of 2.00 feet and is 12.60 feet long
as shown in Figure 37.
12.6`
24``
Very Dense Gravel with
Brown to Dark Tan
Sand and Cobbles
% Gravel=56 to 65%
Figure 37: Pile Configuration
Finite Element Analysis
A finite element model was created using the ABAQUS Finite Element Program. The
pile was treated like the last case study as a linear elastic material with modulus of
elasticity, E, equal to 7.0×108 psf, and a Poisson’s Ratio, υ, of 0.30. The unit weight of
the concrete is assumed to be 150 pcf. The soil is also treated as an elastic fully plastic
material represented by the Drucker-Prager Model as shown in Figure 28. The unit
weight of the soil is assumed to be 125 pcf with a Poisson’s Ratio of 0.40. Friction
elements were installed between the shaft and the soil. A parametric study was done to
study the effect of the soil internal angle of friction (φ), soil dilation angle (ψ), coefficient
of friction between soil and pile (f), and soil modulus of elasticity (E). The field load-deflection
curve for the uplift load test is shown in Figure 38.
Figure 39 shows the effect of soil modulus of elasticity, E, on the load deflection curve
created by ABAQUS. The effect of the coefficient of friction between soil and pile, f, on
the final load deflection curve is shown in Figure 40.
Figure 41 shows the effect of the coefficient of at-rest lateral earth pressure, k, on the
load deflection curve. From the above analysis, Figure 42 shows the best set of soil
parameters for matching the field load-deflection curve. These parameters are: φ =42°,
ψ=42°, E=2.25×106 psf, k=2.8, and f=1.0.
The results of both sets of finite element analyses are expected to be useful in subsequent
phases of the research project.
41
0
25
50
75
100
125
150
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2
Displacement (in)
Load (Kips)
Figure 38: Load Deflection Curve for the Uplift Test.
0
25
50
75
100
125
150
175
200
0 0.1 0.2 0.3
Displacement (in)
Load (Kips)
Test
E=1.6e6 psf
E=2.25e6 psf
E=3.0e6 psf
φ=42
K=2.8
f=1.0
Ψ =42
Figure 39: Effect of Soil Modulus, E on Load Deflection Curve.
42
0
25
50
75
100
125
150
175
200
0 0.1 0.2 0.3
Displacement (in)
Load (Kips)
Test
f=0.70
f=1.0
f=1.50
φ=42
E=2.25x106 psf
K=2.8
Ψ=42
Figure 40: Effect of Coefficient of Friction between Pile and Soil, f.
0
25
50
75
100
125
150
175
200
0 0.1 0.2 0.3
Displacement (in)
Load (Kips)
Test
k=2.5
k=2.8
k=3.0
φ=42
E=2.25x106 psf
f=1.0
Ψ=42
Figure 41: Effect of Coefficient of Friction, f, on Load Deflection Curve.
43
0
25
50
75
100
125
150
175
200
0 0.1 0.2 0.3
Displacement (in)
Load (Kips)
Test
k=2.8, f=1, E=1.1e5
Figure 42: Best Fit for the Uplift Load Test.
Conclusions from Study of Literature and Current Practice
None of the predictive methods for fine-grained material reported on herein work
well for medium to high gravel content. All are extremely conservative at high drilled
shaft capacity. Rollins et al. begins to address the issue but it would appear that a method
specifically developed for gravelly soils is needed. It is relevant to note that the major
source of error in these predictive methods from the literature is apparently the “K,”
which is the ratio of horizontal normal stress to vertical normal stress. With the exception
of the Rollins et al. (1997). procedure, essentially all the methods limit the K value to
about 0.8. By contrast, Figures 16 through 25 show that the actual K ranges on average
from about 1.5 to nearly 6, with the highest values being associated with shallow depth
and high gravel content. Both conditions are associated with large radially-outward
movements due to dilation. Even though the Rollins procedure produces more or less
unbiased estimates of skin friction at low values of skin friction, the procedure greatly
underestimates capacity when the skin friction is high.
As one studies each of these procedures, it typically appears that each author is
focused on assessing the K value just before the drilled shaft is constructed. No evidence
exists that consideration was given to the buildup of K due to dilational behavior. In
most instances it appears that the models were developed for smooth-wall driven shafts in
fine-grained materials where dilational behavior was not an issue. It may well have not
been the intention of the authors that their models be applied to gravelly materials.
44
45
DEVELOPMENT OF WORK PLAN FOR COMPLETION OF THE PROJECT
AND ASSESSMENT OF PROGNOSIS FOR SUCCESS
Data Gaps
The impetus for SPR-493 came from ADOT and its consultants, who recognized the
dearth of data on the drilled shaft capacity in very coarse materials with grain sizes up to
that of SGC. They expressed concern that available design models from the literature for
fine-grained materials that are in use today are far too conservative when used for very
coarse-grained gravelly and cobbly materials and perhaps too conservative even for fine-grained
materials in some cases. This report shows this concern is well justified.
Given that the primary objective of SPR-493 was to develop a model for predicting the
capacity of single and groups of drilled shafts in gravelly materials, including coarse
gravels, it follows that potential data gaps would correspond to the data needed to
develop and then to use the predictive model.
A rather thorough literature review of methodologies for evaluating skin friction for
drilled shafts has been conducted and the results of this review were reported in the
“Summary of Literature and current Practice” section. These methodologies from the
literature were combined with the experiences of the SPR-493 research team to develop a
consensus on the most important parameters which influence the drilled shaft capacity
and the form of a predictive model that would be practical for practitioners to use. This
investigative process resulted in the conclusion that the most important parameters are:
1. Shear strength parameters of the material, φ′ (and c′ if material has significant
cohesion).
2. Density of the material.
3. Dilational behavior of the material (specifically the amount of radially outward
movement of particles which must occur to accommodate an increment of
downward movement of the shaft).
4. Compressibility of the material as a function of effective stress state.
5. The grain size distribution (GSD) of the material.
Several of the above factors are interrelated; i.e., they are not independent. It is
immediately obvious that even a modestly accurate evaluation of the above factors is not
practical for practitioners engaged in routine design of drilled shafts. Therefore, the
overall success of this research project requires that the above parameters be expressed as
simple functions of one or two material index properties, so that evaluation of drilled
shaft capacity can be easily accomplished. At this point in the research program it was
tentatively concluded that only one index property would be required: the grain size
distribution (GSD). It is believed that the other four parameters can be correlated, with
satisfactory accuracy, with GSD. This is because we were persuaded that density could
be related to GSD and the other parameters could then be related to density and/or GSD.
Because these correlations between GSD and the other 4 factors listed above had not yet
been developed, this was an important first task in the next phase of this research.
Correlations between grain size distribution (GSD), and each of the four factors:
46
1. c′ and φ′
2. Density
3. Dilational behavior
4. Compressibility
obviously required that GSD be paired with each of these four factors so that correlations
could be developed. The sources of data include (a) the literature, (b) the results of field
in-situ density measurements and field sampling, and (c) the results of a lab test program
performed at ASU as a part of SPR-493. The lab test program is described further under
the heading “Lab Testing,” but here it is noted that it involves large scale direct shear
tests on concrete/granular material interfaces. Each direct shear test series provides data
on the relationships between GSD and φ′, dilational behavior, and compressibility. The
relationship between GSD and density is derived from data obtained from the literature
and from data gathered during visits to the field for sampling at gravelly material sites.
In summary, the missing data needed to complete the SPR-493 study and develop a new
model which can be used to predict drilled shaft capacity in gravelly materials are:
Pairs of values of GSD and
a) c′, φ′
b) Density
c) Dilational behavior
d) Compressibility
Work Plan Overview
This work plan entails field site investigations, laboratory testing, and analytical work
including finite element simulations. It is aimed at development of a model for predicting
drilled shaft axial load capacity in gravelly materials. Although some of the analyses
conducted as a part of model development are rather sophisticated, the model finally
developed is simple to use and employs input which is readily ascertained by
practitioners. Because some background on the work plan was presented under the
section “Data Gaps,” the tasks to be completed will be described very briefly.
Task 1- Site Visits for Sample Retrieval
A wide variety of sites were visited to obtain data sets which relate GSD to material
density. A second objective was to obtain samples for laboratory testing. Activities at
each of these site visits included backhoe excavation to obtain representative samples and
measure density. These pairs of values of GSD and density were used to develop a
correlation between GSD and density.
Task 2- Laboratory Test Program
The purpose of the laboratory test program was to generate data which can be used to
relate GSD to:
1. c′, φ′
2. Dilational behavior
3. Compressibility
47
The test apparatus and testing technique used are comprised of a large-scale (about 12 in
square) direct shear apparatus which was used to measure compressibility, dilational
response, and shearing resistance of concrete/material interfaces. This apparatus was
designed and constructed at ASU. These tests were performed on a series of materials
representing the full spectrum of gravelly materials. The percent gravel ranged from very
small up to reasonably close to 100%. The materials included both well-graded and
relatively uniform GSDs. The percent fines was typically less than 5.
Each test series, for a material with a given GSD, included the following major steps:
1. Preparation/compaction to the density most typical of this GSD for naturally
deposited materials in the field (using the correlations developed in Task 1).
2. Excavation/removal of half of the material—to be replaced with quickset
concrete—while minimizing disturbance to the remaining material.
3. Casting of the concrete half of the test specimen, with the concrete being
pressurized to a level typical of field placement conditions. This boundary
condition is imposed to simulate as closely as possible the penetration into
gravelly materials by the most liquid fractions of the concrete, which occurs in
the field.
4. Application of confining pressure with measurement of compressibility of the
gravelly material.
5. Shear to failure, with measurement of dilational response and measurement of
shear resistance leading to c′ and φ′.
Task 3- Analysis and Model Development
This task was necessarily iterative. The basic form of the predictive model used for skin
friction, fs, and tip resistance, qtip, was
fs = c′ + σ′v K tan φ′ (30)
where
• c′ and φ′ are effective stress strength parameters
• vσ′ is the effective normal stress
• K is the ratio of horizontal normal stress to vertical normal stress
qtip = f(c′, φ′, compressibility, dilational response)
The above forms of the predictive model were used during the conduct of the research.
After completion of the research the practitioner/user will use greatly simplified
predictive equations as follows:
( ) s 1 f = f GSD,depth (31)
( ) tip 2 q = f GSD, depth (32)
48
Thus the ultimate users of the model will need only grain size distribution (GSD) data as
a material property as input. With only GSD data, the user can utilize a detailed step-by-step
procedure for drilled shaft design, to arrive at a final design.
The analyses under Task 3 proceeded somewhat as follows. The results from Tasks 1 and
2 were input to a Finite Element Model (FEM) which was used to predict the response of
the drilled shaft to load. The FEM input parameters were adjusted to optimize agreement
between prediction and measured results for as many as practical of the drilled shafts pre-sented
under the section “Comparison of Actual Skin Friction Factors to Predicted for Drilled
Shaft in Granular Soil.” The lateral stress ratio “K” was be evaluated from the FEM at all
load levels. These finite element iterations were be used to develop the functions f1 and f2
cited above. At the end of the model development process we have a model that:
1. Is theoretically sound
2. Is overall consistent with available field drilled shaft test data
3. Can be used with only GSD data as input
4. Does not suffer from the ultra-conservatism exhibited by existing models.
Task 4- Development of a Design Methodology
A design methodology was developed for the design of drilled shafts in gravelly
materials. The methodology includes a detailed design example.
Prognosis For Success
It would, perhaps, be expected that the research team would be optimistic about the
outcome of this effort even before the last half of the research work was completed.
However, there were good reasons for this optimism. First, the approach proposed is
fundamentally sound. The experimental and analytical phases were directed at identifying
and evaluating fundamental material response parameters that are directly related to
drilled shaft load capacity.
To further illustrate the cause for optimism, the research team constructed a crude
empirical model, based strictly on the data gathered under the “Summary of Literature
and Current Practice.” This empirical model was constructed by combining the data in
Figures 22 and 24 into one graph, using iterative adjustment to obtain smooth curves. The
resulting combination is shown in Figure 43. The K value is the ratio of the horizontal to
vertical stress as defined earlier. Likewise, the available database was used to very
approximately relate density and φ′ value to percent gravel, P+4. These correlations shown
in Figure 44 and Figure 45 are very approximate for several reasons, in particular the fact
that P+4 was not typically reported in connection with the field drilled shaft test and had
to be estimated from boring log material descriptions. These estimates contributed
significantly to the scatter in the final results.
49
0
2
4
6
8
10
12
0 10 20 30 40 50 60
Depth (ft)
K
55% = Percent Gravel = P+4
40%
20%
Figure 43: K vs Depth for different Gravel Content
105
110
115
120
125
130
20 25 30 35 40 45 50 55
% Gravel
γ (pcf)
Figure 44: Gravel Content vs. Unit Weight, γ-Approximate Relationship
50
32
33
34
35
36
37
38
39
20 25 30 35 40 45 50 55
% Gravel
φ`
Figure 45: Gravel Content vs. φ` Value-Approximate Relationship
The values from Figure 43 through Figure 45 were used together with the estimated P+4
values and knowledge of the depth to estimate skin friction, fs by:
fs = σ′v K tan φ′ (33)
These values of fs were then compared with the measured fs values to obtain Figure 46.
Comparison of Figure 46 with Figure 3 shows that even this crude empirical model with
all of its inherent approximations gives better agreement than any of the models found in
the literature. The scatter in Figure 46 is still excessive and needs improvement; however,
this was the starting point for the completion of the project. After the GSD and density at
field locations are measured , the lab test results are received, and the analytical studies
are completed, it would be quite reasonable to expect that a predictive model could be
generated that exhibits much less scatter than that shown in Figure 46.
51
0
2
4
6
8
10
0 2 4 6 8 10
Measured (tsf)
Predicted (tsf)
Figure 46: Measured vs. Predicted for a New Empirical Model
The results presented up to this point present the findings from the survey of literature
and current practice, the analyses of these literature findings, a report on preliminary
finite element analyses of two axially-loaded drilled shafts, a work plan for completion of
the project, and an assessment of the prognosis for success, together with a preliminary
empirical model for K vs percent gravel and depth. The sections which follow present
the results from newer work by the research team on field testing, laboratory work,
finite element analyses, and development of a design model and design methodology.
52
53
FIELD TESTING
Different river beds and gravel pits were visited to measure in-situ density and to collect some
granular material samples for further lab testing. Eleven sites were visited in four different
states: Arizona, Utah, California, and Oregon. A total of eighteen in-situ density tests were
conducted.
Table 6 shows the different sites and the number of in-situ density tests conducted at each site.
Table 6: River Beds and Gravel Pit Sites
Site Number of in-situ
density tests
Agua Fria River at 91st Avenue, Phoenix, AZ 3
Salt River at 51st Avenue, Phoenix, AZ 3
Gravel pit at Mapleton, Provo, UT 2
Gravel pit at Point of the Mountain East, Provo, UT 2
Gravel pit at Point of the Mountain West, Provo, UT 2
Garcia River near Highway One, Manchester, CA 1
Gualala River near Highway One, Gualala, CA 1
Redwood Creek and US101, CA 1
Navarro River on Highway 128, Albion, CA 1
Columbia River at Tomahawk Island, Portland, OR 1
Rogue River at Griffin Park, OR 1
Total 18
In-Situ Density
In most of the field in-situ density tests, a backhoe was used to excavate a very
substantial amount of the granular material and this material was weighed using large
scales available on site. A plastic sheet was used to line the hole. A large water tank was
used to fill the hole with water. The weights of the water tank before and after the hole
was filled with water were determined. The edges of the holes were often not perfectly
level, which caused the water to reach one edge of the hole before the others, so
additional measurements were taken in these cases to evaluate the remaining volume
using a measuring tape. The difference in water weights as well as the calculated
additional volume represents the volume of the hole. The moist density of the granular
material was calculated using the following equation.
= W
V
γ (34)
where γ is the natural moist unit weight of the material, W is the weight of the material
excavated from the hole including moisture, and V is the volume of the hole and can be
calculated by:
−
= b a +
w
V W W Calculated AdditionalVolume
γ
(35)
where Wb is the weight of water tank before filling the hole, and Wa is the weight of the
water tank after filling the hole, and γw is the water unit weight (9.81 kN/m3). Figures 47
54
through 52 show photographs taken in the field illustrating the various tasks required for
measuring the in-situ density.
Figure 47: Hole is Excavated Using the Backhoe.
Figure 48: The Material is Dumped (collected) in a Loader to be Weighed.
55
Figure 49: The hole is lined with a Plastic Sheet.
Figure 50: The Water Tank Used to Fill the Hole.
56
Figure 51: Hole Filled with Water.
Figure 52: Collected Samples
57
The material samples collected from the field were sealed as shown in Figure 52 to
maintain the natural water content of each . Table 7 shows the moist in-situ density for
each site. The moist in-situ density varied from a minimum value 104.6 pcf for the test at
Columbia River, OR, to a maximum value of 148.5 pcf for the second test at 51st Avenue,
Phoenix, AZ and the test at Rogue River, OR.
Table 7: Moist In-Situ Density
Test No. Site Moist In-Situ Density (pcf)
1 91st Avenue (1) (AZ) 107.8
2 91st Avenue (2) (AZ) 139.9
3 91st Avenue (3) (AZ) 135.9
4 51st Avenue (1) (AZ) 144.1
5 51st Avenue (2) (AZ) 148.5
6 51st Avenue (3) (AZ) 135.0
7 Mapleton (1) (UT) 141.8
8 Mapleton (2) (UT) 144.0
9 Point of the Mountain East (1) (UT) 109.0
10 Point of the Mountain East (2) (UT) 112.0
11 Point of the Mountain West (1) (UT) 114.4
12 Point of the Mountain West (2) (UT) 109.8
13 Garcia River (CA1) 125.6
14 Gualala River (CA2) 116.3
15 Redwood Creek (CA3) 142.4
16 Navarro River (CA4) 120.2
17 Columbia River (OR1) 104.6
18 Rogue River (OR2) 148.5
58
59
LAB TESTING
The lab testing can be divided into two main categories: first, grain size distribution and
moisture content and second, large scale direct shear testing.
Grain Size Distribution
The material samples collected from the field were dried in an oven to measure the water
content of each material. The water content for each test is shown in Table 8. The natural
water content varied from 0.99% at Redwood Creek, CA to 7.31% at Columbia River, OR.
The dry material was sieved using large sieve shakers. The sieves ranged from 2 inches in
size (5 cm) down to sieve #200 (0.074 mm). Occasionally it was necessary to measure a
few very large particles manually. Figures 53 through 70 show the grain size distributions
for the eighteen different material samples collected from the field. Figure 71 shows the
grain size distribution curves for all materials on the same plot. The percentage of gravel
varied from a minimum of 0% to a maximum of 82.1% as given in Table 9. The
percentage passing the # 200 sieve varied from 0.13% for Redwood Creek, CA, to a
maximum value of 5.05% for 51st Avenue, Phoenix, AZ.
Table 8: Natural Water Content
Material No. Site Water Content (%)
1 91st Avenue (1) 4.58
2 91st Avenue (2) 2.75
3 91st Avenue (3) 5.51
4 51st Avenue (1) 0.83
5 51st Avenue (2) 2.51
6 51st Avenue (3) 2.73
7 Mapleton (1) 2.74
8 Mapleton (2) 2.77
9 Point of the Mountain East (1) 2.14
10 Point of the Mountain East (2) 3.77
11 Point of the Mountain West (1) 2.90
12 Point of the Mountain West (2) 2.60
13 Garcia River (CA1) 2.15
14 Gualala River (CA2) 3.07
15 Redwood Creek (CA3) 0.99
16 Navarro River (CA4) 1.36
17 Columbia River (OR1) 7.31
18 Rogue River (OR2) 2.97
60
0
10
20
30
40
50
60
70
80
90
100
0.001 0.01 0.1 1 10 100
Sieve Size (in)
Passing (%)
Figure 53: Grain Size Distribution for Material #1, 91st Avenue (1).
0
10
20
30
40
50
60
70
80
90
100
0.001 0.01 0.1 1 10 100
Sieve Size (in)
Passing (%)
Figure 54: Grain Size Distribution for Material #2, 91st Avenue (2).
0
10
20
30
40
50
60
70
80
90
100
0.001 0.01 0.1 1 10 100
Sieve Size (in)
Passing (%)
Figure 55: Grain Size Distribution for Material #3, 91st Avenue (3).
61
0
10
20
30
40
50
60
70
80
90
100
0.001 0.01 0.1 1 10 100
Sieve Size (in)
Passing (%)
Figure 56: Grain Size Distribution for Material #4, 51st Avenue (1).
0
10
20
30
40
50
60
70
80
90
100
0.001 0.01 0.1 1 10 100
Sieve Size (in)
Passing (%)
Figure 57: Grain Size Distribution for Material #5, 51st Avenue (2).
0
10
20
30
40
50
60
70
80
90
100
0.001 0.01 0.1 1 10 100
Sieve Size (in)
Passing (%)
Figure 58: Grain Size Distribution for Material #6, 51st Avenue (3).
62
0
10
20
30
40
50
60
70
80
90
100
0.001 0.01 0.1 1 10 100
Sieve Size (in)
Passing (%)
Figure 59: Grain Size Distribution for Material #7, Mapleton (1).
0
10
20
30
40
50
60
70
80
90
100
0.001 0.01 0.1 1 10 100
Sieve Size (in)
Passing (%)
Figure 60: Grain Size Distribution for Material #8, Mapleton (2).
0
10
20
30
40
50
60
70
80
90
100
0.001 0.01 0.1 1 10 100
Sieve Size (in)
Passing (%)
Figure 61: Grain Size Distribution for Material #9, Point of the Mountain East (1).
63
0
10
20
30
40
50
60
70
80
90
100
0.001 0.01 0.1 1 10 100
Sieve Size (in)
Passing (%)
Figure 62: Grain Size Distribution for Material #10, Point of the Mountain East (2).
0
10
20
30
40
50
60
70
80
90
100
0.001 0.01 0.1 1 10 100
Sieve Size (in)
Passing (%)
Figure 63: Grain Size Distribution for Material #11, Point of the Mountain West (1).
0
10
20
30
40
50
60
70
80
90
100
0.001 0.01 0.1 1 10 100
Sieve Size (in)
Passing (%)
Figure 64: Grain Size Distribution for Material #12, Point of the Mountain West (2).
64
0
10
20
30
40
50
60
70
80
90
100
0.001 0.01 0.1 1 10 100
Sieve Size (in)
Passing (%)
Figure 65: Grain Size Distribution for Material #13, Garcia River (CA1).
0
10
20
30
40
50
60
70
80
90
100
0.001 0.01 0.1 1 10 100
Sieve Size (in)
Passing (%)
Figure 66: Grain Size Distribution for Material #14, Gualala River (CA2).
0
10
20
30
40
50
60
70
80
90
100
0.001 0.01 0.1 1 10 100
Sieve Size (in)
Passing (%)
Figure 67: Grain Size Distribution for Material #15, Redwood Creek (CA3).
65
0
10
20
30
40
50
60
70
80
90
100
0.001 0.01 0.1 1 10 100
Sieve Size (in)
Passing (%)
Figure 68: Grain Size Distribution for Material #16, Navarro River (CA4).
0
10
20
30
40
50
60
70
80
90
100
0.001 0.01 0.1 1 10 100
Sieve Size (in)
Passing (%)
Figure 69: Grain Size Distribution for Material #17, Columbia River (OR1).
66
Figure 70: Grain Size Distribution for Material #18, Rogue River (OR2).
0
10
20
30
40
50
60
70
80
90
100
0.001 0.01 0.1 1 10 100
Sieve Size (in)
Passing (%)
Test1 Test 2 Test 3 Test 4 Test 5 Test 6
Test 7 Test 8 Test 9 Test 10 Test 11 Test 12
Test 13 Test 14 Test 15 Test 16 Test 17 Test 18
Figure 71: Grain Size Distribution for All Materials.
0
10
20
30
40
50
60
70
80
90
100
0.001 0.01 0.1 1 10 100
Sieve Size (in)
Passing (%)
67
The primary gradation parameters, D10 up to D100, from each grain size distribution were
determined and are shown in Table 9. The D10 values ranged from 0.004 in. for the first
test at 91st Avenue, Phoenix, AZ, to a maximum value of 0.05 in. for the third test at 51st
Avenue, Phoenix, AZ. However, D100 varied from 10 in. for the second test for the mate-rial
at 91st Avenue, AZ, to a minimum of 0.25 in. for the material at Columbia River, OR.
Table 9: Various parameters of the Grain Size Distribution for All Samples.
Material No. D10 D20 D30 D40 D50 D60 D70 D80 D90 D100 P200 % Gravel
1 0.004 0.006 0.008 0.012 0.015 0.026 0.053 0.081 0.524 4 5.05 17.05
2 0.009 0.026 0.062 0.226 0.501 1.168 2.405 5.502 9.138 10 4 59.1
3 0.015 0.037 0.058 0.085 0.217 0.319 0.463 0.866 1.423 5 1.657 47.46
4 0.028 0.063 0.292 0.645 1.061 1.502 2.098 2.828 5.162 7 0.57 71.66
5 0.030 0.057 0.132 0.368 0.856 1.337 1.910 2.632 4.923 8 0.608 64.74
6 0.053 0.313 0.640 0.897 1.140 1.385 1.714 2.175 2.780 6 0.202 82.1
7 0.021 0.065 0.282 0.476 0.717 0.989 1.374 1.951 2.657 8 0.848 72.1
8 0.006 0.015 0.206 0.393 0.637 0.941 1.311 1.783 2.384 3 1.67 69.3
9 0.010 0.019 0.035 0.051 0.068 0.116 0.228 0.348 1.274 7 1.56 28.02
10 0.007 0.013 0.025 0.047 0.069 0.196 0.337 0.642 1.504 3 2.88 37.47
11 0.077 0.014 0.026 0.040 0.054 0.068 0.101 0.194 0.303 2 3.677 13.96
12 0.009 0.015 0.024 0.036 0.048 0.060 0.072 0.119 0.216 1.5 1.613 6.44
13 0.020 0.036 0.053 0.319 0.442 0.621 0.836 1.140 1.524 3 1.23 67.16
14 0.030 0.049 0.068 0.104 0.162 0.220 0.284 0.357 0.574 3 0.366 34.7
15 0.033 0.062 0.134 0.277 0.486 0.822 1.200 1.682 2.549 5 0.134 61.72
16 0.013 0.045 0.088 0.139 0.190 0.241 0.357 0.068 0.498 2 0.74 38.1
17 0.007 0.009 0.011 0.013 0.015 0.021 0.037 0.053 0.069 0.25 1.07 0
18 0.044 0.210 0.593 1.042 1.468 1.880 2.261 2.631 3.000 6 0.642 78.97
All “D” are in inches.
A model for correlation between in-situ density and grain size distribution parameters of
the granular material was developed using trial and error. The grain size distribution
parameters D90/D10 and D50 were found to be the best parameters for a good correlation
with the in-situ density. It was found that in-situ dry unit weight normalized to the unit
weight of water could be correlated to the grain size distribution parameters as follows:
( )
0.033
90 0.1343
50 50
10
d 0.662 1.474 ,
w
D D where D is in inches
D
γ
γ
⎛ ⎞
= ⎜ ⎟ +
⎝ ⎠
(36)
( )
0.033
90 0.1343
50 50
10
d 0.662 0.9546 ,
w
D D where D is in millimeters
D
γ
γ
⎛ ⎞
= ⎜ ⎟ +
⎝ ⎠
(37)
where γd is the in-situ dry unit weight and γw is the water unit weight (62.4 pcf or 9.81
kN/m3). The parameters D90, D50, and D10 are the particle sizes corresponding to 90, 50,
and 10 percent passing, respectively. The d
w
γ
γ ratios measured from the field work were
68
compared to the d
w
γ
γ
ratios predicted from our model (equation 36) and the comparison is
shown in Figure 72. The predicted values from the model are adequately close to the
measured ones, which indicates that the developed model is satisfactory for predicting the
in-situ dry density for stream deposited granular materials from gradation data.
1.4
1.5
1.6
1.7
1.8
1.9
2.0
2.1
2.2
2.3
2.4
1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4
Predicted (γd/γw)
Measured (γd/γw)
R2 = 0.90
Figure 72: Measured d
w
γ
γ
Values Versus Predicted
Large Scale Shear Testing
A large scale shear box (1ftx1ftx1ft) was designed and built to test granular material (up
to 2 inches particle size). Figure 73 shows a photograph of this device. The axial load
(confining stress) was applied using four self-bottled hydraulic jacks, each of which has a
4 ton capacity. The lateral load (shear stress) was applied using two self-bottled hydraulic
jacks, each of which has a 4 ton capacity. The shear load is applied on the upper half only
while the lower half of the box is restrained using spacers placed between the box and the
frame. The six jacks are connected to pressure gauges to read out the pressure. They were
calibrated using load cells. The lateral deformation is measured using two dial gauges and
the vertical deformation (compression or dilation) is measured using four dial gauges
distributed to the corners of the box. The confining pressure jacks sit on steel bearings to
minimize the friction between the jacks and the box.
69
Figure 73: Large Scale Shear Box
Testing Procedure
1. A certain amount of material remaining on each sieve was extracted to ensure that
the gradation of each test specimen precisely matched the grain size distribution
curve of each material. As shown in Figure 74, each layer of each test specimen
was mixed dry in four different mixes and each compacted to the proper density.
2. An amount of water was added to each mix to match the water content in the field
as shown in Figure 74.
3. The material was compacted in four layers; each layer being 3 inches thick, as
shown in Figure 75.
4. A cover plate was used to push the top layer flush with the box edges as shown in
Figure 76. This step ensures that the material is not over- or under-compacted and
brings the density more or less precisely to the target value.
70
5. The box was flipped 90° to another side and half of the material was excavated as
shown in Figure 77. The gravel particles are almost never equidimensional. The
longest dimension tends to be horizontal in the field. Therefore, in the field, the
orientation of the particles is usually perpendicular to the axis of the drilled shaft.
By flipping the box the gravel particles were oriented to be perpendicular to the
concrete face, to be subsequently placed. Thus, to the extent possible, the
“structure” of the gravel test specimen was matched to the expected field
configuration.
6. Concrete was mixed using high cement content and an accelerator was used to
make it set up quickly and have a high strength. The upper half of the box was
coated with Vaseline to make sure that the concrete would not stick to the steel
plates and also to make it easy to extract the concrete block after the test. The
concrete was then poured into the box as shown in Figure 78. Air pressure equal
to the estimated overburden pressure was applied to the concrete face to represent
the overburden pressure of the concrete at the depth of interest as shown in Figure
78.
7. After about two days, the concrete was adequately set up and the test specimen
was ready to be sheared. The box was lifted such that the concrete side was in the
bottom half and the material side was in the upper half. The winch shown in
Figure 73 was used to facilitate lifting and turning the filled shear box, which was
quite heavy.
8. The upper steel plate (the one in contact with the material) was replaced by the
plate which carries the steel bearings and the four hydraulic jacks and which
applies normal pressure.
9. The upper half of the box was then jacked up relative to the lower half to reduce
the friction between them. All six dial gauges (4 for axial deformations and 2 for
lateral deformation) were then installed. Initial readings were taken for all gauges.
10. The confining pressure was first increased to a pressure equal to the overburden
pressure of concrete corresponding to the depth (section) under consideration.
Next the confining pressure was adjusted to the target value (which could depend
on the anticipated K value, which of course depends on depth and percentage of
gravel).
11. The compressibility of the material was then determined from the increment(s) in
confining pressure described in previous steps.
12. This confining pressure was kept constant while applying the shear load. It was
generally necessary to adjust the confining pressure jacks to keep the pressure
constant, especially when dilation was large.
71
(a) Material is mixed dry (b) Water is added and mixed wet
Figure 74: Material is mixed dry first and then wetted.
(a) Material is poured into the box (b) Compacting material layer
(c) Compacting material layer (d) Measuring layer thickness
Figure 75: Compacting Material in Layers.
72
(a) Cover Plate into place. (b) Cover plate makes material flush
with box top.
Figure 76: A Cover Plate Used to Make Sure Material is Flush to Box Top.
Figure 77: Material is removed from the upper half of the box.
73
(a) Box Upper Half is Coated with Vaseline
(b) Concrete Poured from Mixer
(c) Concrete Poured into the Box
(d) Compacting Concrete
(e) Leveling Concrete
(f) Applying Air Pressure to Concrete
Figure 78: Pouring Concrete into the box.
74
Direct Shear Lab Test Program
Six materials (out of the available eighteen) were chosen to be tested in the large scale
direct shear box. They were chosen to cover a good range of percentage gravel and in-situ
density. Table 10 shows these materials with their different configurations. The test
matrix for all six materials is shown in Table 11. Each material was tested under three
different confining pressures, and compressibility was measured. The shear stress versus
lateral deformation was determined. The dilation response for each material was
measured, as a function of gravel percentage and confining pressure.
Table 10: Properties of the Chosen Six Materials to be
Tested in Large Scale Shear Box
Material
No. γd (pcf) D10 D50 D90 D90/D10 P200 % Gravel
1 103.1 0.004 0.015 0.524 134.957 5.05 17.05
3 128.8 0.015 0.217 1.423 92.2132 1.657 47.46
7 138.0 0.021 0.717 2.657 126.524 0.848 72.1
9 106.7 0.099 0.068 1.274 12.8664 1.56 28.02
16 118.6 0.013 0.190 0.498 37.1493 0.74 38.1
17 97.5 0.007 0.015 0.069 10.0477 1.07 0
Table11: Large Scale Shear Box Test Matrix
Material
No.
Confining Pressure (psf)
1
1185
2824
4345
3
1185
4345
7442
7
1185
4345
7442
9
1185
1934
4345
16
1185
2824
4345
17
418
1185
4345
75
Test Results
Six materials were chosen from the complete set as representative of the full range of
gradation and grain size distribution. These six were tested with large scale direct shear.
All 18 grain size distribution curves are shown in Figures 53-57.
Three different confining pressures, σ, were chosen for each material type as shown in
Table 11. The load, P, versus lateral deformation, Δ, curves at three different confining
pressures, σ, for each soil type are shown in Figure 79 through Figure 84.
Figure 79: Load Deflection Curve for Material #1.
76
0
500
1000
1500
2000
2500
3000
3500
4000
4500
0 0.05 0.1 0.15 0.2 0.25 0.3
Lateral Deformation, Δ (in)
Lateral Load, P (lb)
= 1185 psf
=4345 psf
=7442 psf
σ
σ
σ
Figure 80: Load Deflection Curve for Material #3.
0
1000
2000
3000
4000
5000
6000
0 0.05 0.1 0.15 0.2 0.25 0.3
Lateral Deformation, Δ (in)
Lateral Load, P (lb)
= 1185 psf
=4345 psf
=7442 psf
σ
σ
σ
Figure 81: Load Deflection Curve for Material #7.
77
Figure 82: Load Deflection Curve for Material #9.
Figure 83: Load Deflection Curve for Material #16.
78
0
500
1000
1500
2000
2500
3000
0 0.05 0.1 0.15 0.2
Lateral Deformation, Δ (in)
Lateral Load, P (lb)
= 418 psf
=1185 psf
=4345 psf
σ
σ
σ
Figure 84: Load Deflection Curve for Material #17.
The shear strength envelope for each material tested is shown in Figure 85 through Figure
90. Figure 91 shows the summary of the shear envelops for the six tested materials.
0
500
1000
1500
2000
2500
0 1000 2000 3000 4000 5000
Confining pressure, σ (psf)
Shear Strength, τ (psf)
Figure 85: Shear Strength Envelope for Material #1.
79
0
500
1000
1500
2000
2500
3000
3500
4000
4500
0 1000 2000 3000 4000 5000
Confining pressure, σ (psf)
Shear Strength, τ (psf)
Figure 86: Shear Strength Envelope for Material #3.
0
1000
2000
3000
4000
5000
6000
7000
0 1000 2000 3000 4000 5000 6000 7000 8000
Confining pressure, σ (psf)
Shear Strength, τ (psf)
Figure 87: Shear Strength Envelope for Material #7.
80
0
500
1000
1500
2000
2500
3000
0 1000 2000 3000 4000 5000
Confining pressure, σ (psf)
Shear Strength, τ (psf)
Figure 88: Shear Strength Envelope for Material #9.
0
500
1000
1500
2000
2500
3000
3500
0 1000 2000 3000 4000 5000
Confining pressure, σ (psf) Shear Strength, τ (psf)
Figure 89: Shear Strength Envelope for Material #16.
81
0
500
1000
1500
2000
2500
0 1000 2000 3000 4000 5000
Confining pressure, σ (psf)
Shear Strength, τ (psf)
Figure 90: Shear Strength Envelope for Material #17.
0
1000
2000
3000
4000
5000
6000
7000
0 2000 4000 6000 8000
Confining pressure, σ (psf) Shear Strength, τ (psf)
soil-1
soil-3
soil-7
soil-9
soil-16
soil-17
Figure 91: Summary of the Shear Strength Envelopes for all Chosen Materials.
82
In figures 92-93, the lateral deformation was plotted against the vertical deformation
for each soil at three different confining pressures. The dilation angle can be calculated
as the average value of the arc-tan of the vertical deformation over the horizontal
deformation.
Figure 92: Horizontal Deformation versus Vertical Deformation for Material #1.
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
0.18
0 0.05 0.1 0.15 0.2 0.25 0.3
Lateral Deformation, Δ (in)
Vertical Deformation, δ (in)
=1185 psf
=4345 psf
=7442 psf
σ ψ = 27.9°
σ
σ
Figure 93: Horizontal Deformation versus Vertical Deformation for Material #3.
83
0.00
0.05
0.10
0.15
0.20
0 0.05 0.1 0.15 0.2 0.25 0.3
Lateral Deformation, Δ (in)
Vertical Deformation, δ (in)
=1185 psf
=4345 psf
=7442 psf
σ ψ = 31°
σ
σ
Figure 94: Horizontal Deformation versus Vertical Deformation for Material #7.
Figure 95: Horizontal Deformation versus Vertical Deformation for Material #9.
84
Figure 96: Horizontal Deformation versus Vertical Deformation for Material #16.
-0.01
0.00
0.01
0.02
0.03
0.04
0.05
0 0.05 0.1 0.15 0.2
Lateral Deformation, Δ (in)
Vertical Deformation, δ (in)
=418 psf
=1185 psf
=4345 psf
σ ψ = 3°
σ
σ
Figure 97: Horizontal Deformation versus Vertical Deformation for Material #17.
85
The shear strength parameters, soil angle of internal friction (φ), cohesion (c), soil
dilation angle (ψ), and angle of friction between soil and concrete (δ), were determined
from the previous shear strength envelopes. The cohesion parameter is the intercept of the
shear envelope with the vertical axis, and the friction angle is the inclination of the shear
envelope with horizontal. The soil angle of internal friction was assumed to be equal to
the soil-concrete friction angle. The soil dilation angle was calculated as the average
arctangent of the positive vertical movement to the lateral horizontal movement. Table
12 presents the shear strength parameters for all six chosen materials.
Table 12: Summary of the Large Scale Shear Box Test Results
Material
No.
Soil Angle of
Internal
Friction, φ (°)
Soil-Concrete
Angle of
Friction, δ (°)
Cohesion
(psf)
Soil dilation
Angle, ψ (°)
1 20 20 365 6.5
3 36 36 845 27.9
7 38 38 498 32
9 24 24 614 15.7
16 30 30 352 20
17 18 18 648 3
Note: The values actually measured in the direct shear tests were δ. When computations required φ,
it was conservatively assumed that φ = δ.
Modeling of the Data
The modeling objective here was to develop a correlation between grain size distribution
parameters and the soil dilation angle (ψ), and the soil-concrete friction angle (δ). After
several trials, correlations between these parameters were developed as follows:
( )
( )
0.0114
90 1.1
0.5
10 50
15.5 D 1.63 0.168 %G
D D
ψ
⎛ ⎞
= ⎜ ⎟ − +
⎝ ⎠
(38)
( )
( )
0.107
10 0.818
0.466 50
90 50
26.74 D 0.4376 0.715 %G , where D is in inches
D D
δ
⎛ ⎞
= ⎜ ⎟ − +
⎝ ⎠
(39)
and % G is the percentage of gravel in the material; D50 must be in inch units for
equations 38 and 39.
86
The values of soil dilation angle and soil/concrete friction angle measured from test
results versus the predicted values from the previous two equations are shown in Figure
98 and Figure 99. These figures show that these equations give good values for both soil
dilation and soil / concrete friction angles.
0.0
5.0
10.0
15.0
20.0
25.0
30.0
35.0
0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0
Measured Value (ψ)
Predicted Value (ψ)
R2 = 0.97
Figure 98: Measured Ψ Values Versus Predicted.
0.0
5.0
10.0
15.0
20.0
25.0
30.0
35.0
40.0
0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0
Measured Value (δ)
Predicted Value (δ)
R2 = 0.95
Figure 99: Measured Versus Predicted δ Values.
The results from field and laboratory tests presented in previous sections were helpful in
identifying soil properties for the numerical analyses performed subsequently.
87
K Values From The Direct Shear Test
Given that K is defined as the ratio of the horizontal normal stress to the vertical normal
stress it would appear on the surface that K cannot be measured from a direct shear test.
However, if it is assumed that the following conditions exist, then K can be measured if
the direct shear test progresses in increments, as it did for the tests done for this study.
1. Assume that the confining pressure initially applied represents the overburden
pressure at the particular depth being represented.
2. When the shear stress is increased, dilation ensues. However, for our tests this
dilation is essentially inhibited by the stiffness of the oil in the hydraulic jacks
applying the (normal) confining pressure. If it is assumed that the stiffness of the
oil is comparable to the stiffness of the gravel surrounding the drilled shaft
prototype, or at least sufficiently close in stiffness so as to have minor effect on
the results, then the maximum normal stress generated by the dilation tendency
divided by the initial value of the confining pressure would produce a K, similar
to that developed in the prototype.
This excess normal pressure must be bled off before a set of readings is taken
so the confining pressure returns to its initial value. It is noteworthy that if the
confining pressure had been maintained constant with a pressure regulator,
a servo device, or dead weights, this opportunity to infer a K value would
not have been afforded. Thus, in these tests, the confining stress was only
incrementally constant; that is, within the increment it did rise – in proportion
to the dilation. For these tests the K values were evaluated as described
above. K values for the last few increments (near failure) were averaged and
plotted in Figure 108, to be presented subsequently.
88
Soil Finite Elements
Infinite (continuous) Soil Elements
Shaft Elements
Y X
Z
FIGURE 100: HALF SYMMETRY OF SHAFT AND SOIL DISCRETIZATION
MESH
89
NUMERICAL ANALYSES
Several finite element analyses were conducted to help in developing the final model to
predict the skin friction values for drilled shaft foundations in gravelly soils. The finite
element program ABAQUS was used for these analyses. Two different sites were picked
where field test data on drilled shaft foundations in gravelly soils were available and also
where the research team had visited and did field and lab testing on samples of these
materials that had been returned to the laboratory. These two sites are Mapleton and Point
of the Mountain East. The drilled shaft field load tests were done in January, 1997, at
these two sites in Utah, as a part of research project UT-97.02, “Drilled Shaft Side
Friction in Gravelly Soils.” The main objective of their tests was to evaluate the side
friction between the shaft and the soil generated by applying an uplift load on the shaft.
For each site we prepared the data required for each finite element run. The data included
soil and shaft properties. The soil properties were: soil density (γ), soil angle of internal
friction (φ), soil modulus of elasticity (Es), soil dilation (Ψ), Poisson Ratio (ν), and soil
shaft friction angle (δ). The shaft parameters consist of shaft diameter (D), length (L),
and modulus of elasticity (Ec). For all analyses we assumed that the Poisson Ratio to be
0.4 for soil and 0.3 for concrete.
Equation 36 was used to predict the soil density (γ), and equations 37 and 38 to predict
the soil dilation angle (Ψ), and soil shaft friction angle (δ). All of these equations utilize
the soil grain size distributions which were available for each layer (different depths) in
Rollins et al. (1997).
Finite Element Model
Finite element analyses, using the program ABAQUS (1998), were performed on a 3-D
finite element model with 8-node elements. The boundary conditions include infinite
(continuous) elements to reduce the effect of stress concentrations. The mesh shown in
Figure 100 presents the results of several mesh refinement runs. In this mesh, the soil and
shaft were discretized. The model consists of one single shaft with the load applied at the
top of the shaft. The behavior of the reinforced concrete shaft was modeled as linear
elastic. The soil was modeled as an elastic-perfectly-plastic, Drucker-Prager-Type
material (Chen and Baladi, 1985), with volumetric dilation. Friction elements with a
coefficient of friction (f), were used to represent the interaction between the soil and the
shaft.
A general description of the subsurface materials is as follows: from the ground surface
to a depth of 12ft – very dense, coarse to fine gravel with cobbles; from 12ft to the
maximum depth of exploration (15ft) – medium dense silty sand. The percent gravel for
the site ranged from 68% in the gravelly material to 2% in the silty sand. Standard
penetration blow counts range from 88 blows per 12 inches in the gravels to 11 blows per
12 inches in the silty sand. The reinforced concrete shaft had an average diameter of 24
inches and was 12.5 feet long.
90
Analysis
As stated earlier, a finite element model was created using the ABAQUS Program
(1998). The shaft was treated as a linear elastic material with modulus of elasticity, E,
equal to 3.3×107 kPa. The unit weight of the concrete was assumed to be 23.5 kN/m3.
Friction elements were installed between the shaft and the soil. Several trials were
conducted to find a set of parameters which gives the best fit curve to the field load test.
Tables 13 through 15 show these trials for shafts 15ft, 10ft, and 5ft in length,
respectively. The best fit set of parameters is indicated in each table with an asterisk. The
trials listed in tables 13 – 15 are correspondingly plotted in figures 101 – 103.
Table 13: Finite Element Trials for 15ft Shaft at Mapleton
15 ft Shaft
Trial Soil Properties
Number C (kPa) φ F E (kPa) Ko Ψ
1 23.85 38 1.0 357000 0.85 34
2 23.85 38 1.0 857000 0.85 34
3 23.85 38 0.8 857000 0.85 34
4 23.85 33 0.8 2.5×106 0.85 30
5* 23.85 36 0.8 2.5×106 0.85 32
6 23.85 33 0.8 3.5×106 0.85 30
* Best fit parameters set
Table 14: Finite Element Trials for 10ft Shaft at Mapleton
10 ft Shaft
Trial Soil Properties
Number C (kPa) φ F E (kPa) Ko Ψ
1 23.85 37 0.8 2.5×106 0.85 33
2 23.85 36 0.8 2.5×106 0.85 32
3 23.85 35 0.8 2.5×106 0.85 31
4* 23.85 34 0.8 2.5×106 0.85 30
5 23.85 34 0.8 2.5×106 0.85 30
* Best fit parameters set
Table 15: Finite Element Trials for 5ft Shaft at Mapleton
5 ft Shaft
Trial Soil Properties
Number C (kPa) φ F E (kPa) Ko Ψ
1 23.85 34 0.8 2.5×106 0.85 32
2* 23.85 35 0.8 2.5×106 0.85 33
* Best fit parameters set
91
0
100
200
300
400
500
600
0.0 0.2 0.4 0.6 0.8 1.0
Axial Deformation, Δ (in)
Axial Load, P (Kips)
Field Curve trial-1
trial-2 trial-3
trial-4 trial-5
trial-6 trial-7
Best Fit
Figure 101: P-Δ Curves with Different Finite Element Trials
for 15 ft Shaft at Mapleton
0
20
40
60
80
100
120
140
160
180
0.00 0.05 0.10 0.15 0.20 0.25
Axial Deformation, Δ (in)
Axial Load, P (Kips)
Field Curve
trial-1
trial-2
trial-3
trial-4
Best Fit
Figure 102: P-Δ Curves with Different Finite Element Trials
for 10 ft Shaft at Mapleton
92
0
20
40
60
80
100
120
140
0.0 0.1 0.2 0.3 0.4 0.5
Axial Deformation, Δ (in)
Load, P (kips)
Field Curve
trial-1
trial-2
Best fit
Figure 103: P-Δ Curves with Different Finite Element Trials
for 5 ft Shaft at Mapleton
Point of the Mountain East Site
The subsurface materials generally are as follows: from the ground surface to a depth of
17ft – very dense, coarse to medium dense gravelly sand with silt; from 17ft to the
maximum depth of exploration (20ft) – a dense layer of sand was found in the 10 foot
shaft side, while a layer of dense fine gravel with sand and silt was found in the 5,15, and
20 foot shaft sites.. Percent gravel for the site ranges from 58% in the gravelly material to
4% in the sand with silt. Standard penetration blow counts range from 64 per 12 inches in
the gravels to 15 per 12 inches in the sand layers. The reinforced concrete shaft had an
average diameter of 24 inches and was 16.5 feet long.
Tables 16 through 19 show the results for sh