Calibration of Deterministic Parameters

Reassessment of Offshore Platforms in the Arabian Gulf

Hassan Zaghloul

DISSERTATION.COM

Boca Raton

Calibration of Deterministic Parameters: Reassessment of Offshore Platforms in the Arabian Gulf

Copyright © 2008 Hassan Zaghloul

All rights reserved. No part of this book may be reproduced or transmitted in any form or by any means,

electronic or mechanical, including photocopying, recording, or by any information storage and retrieval system, without written permission from the publisher.

Dissertation.com

Boca Raton, Florida USA • 2011

ISBN-10: 1-59942-397-9

ISBN-13: 978-1-59942-397-5

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DEDICATION

To the loving memory of my father

To my mother who had the arduous task of raising four children by herself after

the sudden death of my father

To my beloved wife Mine’ who endured my absences and supported my passion

for this research

To our sons Taha and Zaccaria who make our life beautiful

To all those who have contributed to this thesis

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ABSTRACT

The Arabian Gulf oil and gas production reserves have made it one of the world’s

strategic producers since early 1960s, with many of the existing platforms stretched

beyond their original design life. Advances in drilling technology and reservoir

assessments have extended the requirement for the service life of those existing

platforms even further. Extension of the life span of an existing platform requires

satisfactory reassessment of its various structural components, including piled

foundations.

The American Petroleum Institute Recommended Practice 2A (API RP2A) is

commonly used in the Arabian Gulf for reassessment of existing platforms. The

API guidelines have been developed for conditions in the Gulf of Mexico, the

waters off Alaska and the Pacific and Atlantic seaboards of the USA. However, the

Arabian Gulf conditions are fundamentally different to those encountered in US

waters. Hence, there is a need to develop guidelines for reassessment of existing

offshore structures to account for the specific conditions of the Arabian Gulf.

This thesis performs statistical analyses on databases collected during this research

from existing platforms to calibrate relevant load and resistance factors for the

required guidelines. The developed guidelines are based on established approaches

used in developing international codes and standards such as API RP2A-LRFD.

The outcome of this research revolves around the following three main issues:

1. Calibration of resistance factors for axial capacity of piles driven in the

carbonate soils

API RP2A (1993, 2000) does not quantify limiting soil parameters for piles driven

in carbonate soils and provides a single factor to predict the capacity of piled

foundations. This research identifies a set of limiting engineering parameters and

calibrates corresponding capacity reduction factors to predict axial capacity of

driven piles in the carbonate soils of the Arabian Gulf.

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Further, this thesis shows that the use of a single capacity reduction factor of 0.7, an

approach that is adopted in API RP2A-LRFD (1993), does not consider that axial

pile capacity in existing platforms is influenced by many parameters identified in

this research, including implied risk level, manning levels, variation in pile wall

thickness along its depth, soil composition, hammer type, installation method,

penetration ratio and the level of optimization in the original design. The

reassessment guidelines developed in this research recommends a set of capacity

reduction factors within a range of 0.4-1.0 to reflect the influence of the factors

discussed above.

2. Development of open area live loads (OALL) on offshore platforms

API RP2A-LRFD (1993) refers to ASCE Standard 7-05 to quantify live loads.

However, ASCE Standard 7-05 is only applicable to building structures and does

not quantify values for OALL on offshore platforms. This thesis reveals that, unlike

building structures, the magnitude of OALL on an offshore platform deck is not

independent of loading conditions.

OALL values on offshore platforms are rather affected by factors such as platform

size, safe working load (SWL) of materials handling equipment, expected life span

of the platform, deck location on the platform (upper deck versus other decks) and

the selected influence surface (pile, primary beams, secondary beams or topside

columns). This research investigates those factors and recommends a simplified

formula to calculate OALL. The proposed formula is a function of the SWL of the

material handling equipment which dominates the magnitude of the OALL.

Reassessment applications require a combination factor for OALL, which is a

function of the coefficient of variation (COV) of the mean lifetime maximum live

loads. This thesis proposes a combination factor of 1.5 on the basis that the COV =

10% to 20% of the mean lifetime maximum live loads on offshore platforms, which

is calculated in this research, is similar to the COV (14%) used to develop the live

load combination factor (1.5) in API RP2A-LRFD (1993).

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3. Effect of extreme storm conditions on the reliability of existing platforms in

the Arabian Gulf

In the process of calibrating pile resistance factors and development of OALL, this

research develops a set of statistical parameters for load and resistance factors. The

statistical parameters are used to perform reliability analysis on a selected platform

in the Arabian Gulf. The platform is selected such that the outcome of the reliability

analysis is applicable to other platforms in that region.

The outcome of the reliability analysis reveals that operating overload conditions

dominate the failure mechanism in the Arabian Gulf. The reliability analysis

resulted in an insignificant (10-71) probability of failure under extreme storm

conditions compared to the higher value (10-6) under operating overload conditions.

Such extreme values are only possible in a mathematical model and have little

physical meaning. Nevertheless, and despite lack of a physical meaning to such

extremely low failure probability value, it demonstrates that operating overload

dominates the failure mechanism in the Arabian Gulf. The extremely low

probability of failure is partly a result of no wave-in-deck as the wave heights are

lower than the deck at high return periods.

Consequently, reassessment of existing platforms in the Arabian Gulf would be

sufficiently addressed by considering operating overload conditions only. This

contrasts with Section ‘R’ of API RP2A (1993, 2000), which focuses on extreme

environmental conditions when performing reassessment.

The probabilities of failure considered in this research do not include errors and

omissions (controlled by quality assurance procedures) or material deterioration

(controlled by choice of materials, detailing, protective devices, and inspection and

repair procedures) or reliability-based maintenance.

Addressing operating overload conditions requires attending to two issues, namely

the capacity of piles driven in carbonate soils and OALL, which have been

addressed in this research. The operational overload situation is likely to occur

during shutdown condition or during drilling or work over activities where

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significant OALL are usually applied to platform decks. Such operational overload

can be managed by placing signs at various open areas on the platform nominating

the maximum load limits (kPa), introducing procedures that ensure that maximum

load limits are not exceeded during operation and management of human behavior

by reinforcing the importance of following the procedures.

The outcomes of this research are expected to have a profound influence on

reassessment of existing platforms in the Arabian Gulf.

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TABLE OF CONTENTS

CHAPTER 1. 1

INTRODUCTION ................................................................................................................................1

1.1. BACKGROUND 1 1.2. PROBLEM STATEMENT 3 1.3. METHODOLOGY 3 1.4. JUSTIFICATION OF THE RESEARCH 4 1.5. OUTLINE OF THE THESIS 7

CHAPTER 2. 8

RESEARCH ISSUES ............................................................................................................................8

2.1. INTRODUCTION 8 2.2. ROAD MAP 9 2.3. REASSESSMENT APPROACHES 9 2.3.1. Screening Level Check 10 2.3.2. Design Level Check 10 2.3.3. Structural Reliability Analysis Method 12 2.3.4. Probabilistic Approach 17 2.4. DEVELOPMENT APPROACH 18 2.5. SELECTION OF CALIBRATION CODE 18 2.5.1. Assessment of WSD 18 2.5.2. Assessment of LRFD 20 2.6. HISTORICAL BACKGROUND OF LRFD CODES 21 2.6.1. LRFD for Steel Building Structures 21 2.6.2. LRFD for Offshore Piled foundations 23 2.7. AXIAL PILE CAPACITY IN CARBONATE SOILS 27 2.7.1. Deposition History of Carbonate Soils in the Arabian Gulf 28 2.7.2. Characteristics of Carbonate Sediments 29 2.7.3. Installation Experience of Piles Driven in Carbonate Soils 31 2.7.4. Review of Loading Tests in Carbonate Soils 33 2.7.5. Sources of Difficulty in establishing Engineering Parameters 35 2.7.6. Approach used in Industry Practice 37

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2.8. OPEN AREA LIVE LOADS (OALL) 38 2.8.1. Background 38 2.8.2. Live Load Surveys for ASCE Standard 7-05 39 2.8.3. Probabilistic Model in ASCE Standard 40 2.8.4. Applicability of Probabilistic Model to Offshore Structures 41 2.8.5. Reduction Factors in ASCE Standard 42 2.9. CHARACTERIZATION OF THE CLIMATOLOGY IN THE ARABIAN GULF 43 2.10. SUMMARY 46 2.10.1. Code to be used in Calibration 46 2.10.2. Axial Pile Capacity in Carbonated Soils 46 2.10.3. Target Reliability Level 47 2.10.4. Open Area Live Load (OALL) 47 2.10.5. Dominant Failure Mechanism 47

CHAPTER 3. 60

METHODOLOGY ............................................................................................................................. 60

3.1. INTRODUCTION 60 3.2. OUTLINE OF THE METHODOLOGY 60 3.3. DATA COLLECTION AND GROUPING 62 3.3.1. Challenges 62 3.3.2. Sub-grouping the Data 62 3.4. STATISTICAL ANALYSIS 63 3.4.1. Distribution Type 63 3.4.2. Distribution Properties 64 3.5. APPLICATION OF RELIABILITY- BASED METHOD 66 3.5.1. Calculation of Probability of Failure 66 3.5.2. Bayesian Update 69 3.6. PREDICTION OF AXIAL PILE CAPACITY 72 3.7. CALIBRATION OF PILE RESISTANCE FACTORS 73 3.8. DERIVATION OF OPEN AREA LIVE LOADS (OALL) 76 3.8.1. Influence Surface Concept 76 3.8.2. Extreme Value Analysis 77 3.9. COMPUTER SOFTWARE PROGRAMS 78 3.9.1. Risk Analysis Software - @RISK 78

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3.9.2. APIPILE - Pile Capacity Spreadsheet 79 3.9.3. GRLWEAP-Wave Equation Analysis Program 79 3.9.4. Structural Analysis Computer Software (SACS) 80 3.9.5. Pile Driving Analyzer (PDA) 82 3.9.6. Case Pile Wave Analysis Program (CAPWAP) 83 3.10. SCOPE DELIMITATION AND KEY ASSUMPTIONS 85 3.11. JUSTIFICATION OF THE METHODOLOGY 86 3.11.1. Reliability-Based Method 86 3.11.2. Extent of the Database 86 3.11.3. Bayesian Updating 87 3.11.4. Wave Equation Analysis Method 87 3.11.5. Influence Surface Method 88 3.12. SUMMARY 89

CHAPTER 4. 102

CALIBRATION OF PILE RESISTANCE FACTORS .......................................................................102

4.1. INTRODUCTION 102 4.2. CALIBRATION MECHANICS OF AXIAL PILE RESISTANCE FACTORS 102 4.3. PILE INSTALLATION DATABASE 103 4.4. PREDICTED AXIAL PILE CAPACITY 105 4.4.1. Limiting Engineering Parameters 105 4.4.2. Input Data to APIPILE 108 4.4.3. Output from APIPILE 109 4.5. ACTUAL AXIAL PILE CAPACITY 109 4.5.1. Methodology 110 4.5.2. Input Data for Wave Equation Analysis 110 4.5.3. Short Term Axial Pile Capacity 115 4.5.4. Time Effect - Computing Setup Factors 116 4.5.5. Back-Analysis Procedure 120 4.5.6. Sensitivity Analysis of the Computed Actual Pile Capacity 126 4.6. STATISTICAL PARAMETERS OF BIAS FACTORS 127 4.6.1. Statistics of the Complete Database 128 4.6.2. Grouping by Installation Method 129 4.6.3. Grouping by Soil Type 131

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4.6.4. Grouping by Optimized Design 132 4.6.5. Grouping by Penetration Ratio 133 4.7. BENCHMARKING STATISTICS OF BIAS FACTOR 133 4.7.1. Bias Factors in API RP2A-LRFD (1993) 134 4.7.2. Bias in the Statistics of Bias Factors 135 4.8. BAYESIAN UPDATE OF BIAS FACTOR STATISTICS 138 4.8.1. “Prior” Distribution 138 4.8.2. “Likelihood” Distribution 139 4.8.3. “Posterior” Distribution 139 4.9. TARGET RELIABILITY INDEX 139 4.10. CALIBRATION OF RESISTANCE FACTORS 140 4.10.1. Target Reliability Levels 141 4.10.2. Soil Types 141 4.10.3. Installation Methods 142 4.10.4. Penetration Ratio 142 4.11. SUMMARY 143

CHAPTER 5. 202

CALIBRATION OF OPEN AREA LIVE LOADS............................................................................. 202

5.1. BACKGROUND 202 5.2. DEFINITIONS USED IN DEVELOPMENT OF OALL 203 5.3. CALIBRATION MECHANICS OF OALL 204 5.4. NATURE OF LIVE LOADS ON OFFSHORE PLATFORMS 204 5.5. EQUIPMENT LOAD DATABASE 206 5.6. SUBGROUPING THE EQUIPMENT DATABASE 207 5.6.1. Subgrouping by Platform Function 207 5.6.2. Subgrouping by Location on Platform 208 5.6.3. Subgrouping By Crane and Monorail SWL 208 5.7. STATISTICAL PARAMETERS OF EQUIPMENT WEIGHTS 209 5.7.1. On Lower Decks 209 5.7.2. On Upper Deck 210 5.7.3. Conclusion 210 5.8. CALCULATION OF MEAN LIFETIME MAXIMUM PILE LOAD 210 5.8.1. Extreme Axial Pile Load Using Normal Distribution 212

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5.8.2. Extreme Axial Pile Load using Lognormal Distribution 213 5.8.3. Minimum Separation Distance 215 5.10. BENCHMARKING THE STATISTICS OF OALL 219 5.11. SENSITIVITY ANALYSIS OF OALL PARAMETERS 220 5.11.1. Varying the Deck Area 220 5.11.2. Minimum Separation Distance 221 5.11.3. Varying the Crane Capacity 222 5.12. LIVE LOAD FACTORS 222 5.13. SUMMARY 224

CHAPTER 6. 248

DOMINANT FAILURE MECHANISM............................................................................................248

6.1. OBJECTIVE 248 6.2. PERFORMANCE MODEL 249 6.3. APPROACH 249 6.4. LOGIC OF PLATFORM SELECTION 249 6.5. MATHEMATICAL MODEL 251 6.5.1. Structural Modeling 251 6.5.2. Foundation Modeling 255 6.5.3. Loading Model 257 6.6. PUSHOVER ANALYSIS 258 6.6.1. Extreme Storm Conditions 259 6.6.2. Operating Overload Conditions 260 6.6.3. Analysis of the Results 261 6.7. LOAD AND RESISTANCE STATISTICS 262 6.7.1. Resistance Statistics 262 6.7.2. Dead Load Statistics 263 6.7.3. Live Load Statistics 263 6.7.4. Environmental Load Statistics 263 6.8. PROBABILITY OF FAILURE CALCULATIONS 265 6.8.1. Using Pushover Analysis Results 266 6.8.2. Validating Probability of Failure under Operating Overload Condition 269 6.9. CALIBRATION OF ENVIRONMENTAL PARTIAL LOAD FACTORS 274 6.10. SUMMARY 277

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CHAPTER 7. 307

CASE STUDY .................................................................................................................................. 307

7.1. BACKGROUND 307 7.2. DESCRIPTION OF THE PLATFORM 308 7.3. MATHEMATICAL MODEL 309 7.4. ANALYSIS OF THE RESULTS 310 7.5. SUMMARY 312

CHAPTER 8. 323

SUMMARY, CONCLUSIONS AND RECOMMENDATIONS ......................................................... 323

8.1. SUMMARY 323 8.2. METHODOLOGY 323 8.2.1. Open Area Live Load (OALL) 324 8.2.2. Axial Pile Capacity in Carbonate Soils 324 8.2.3. Dominant Failure Mechanism 325 8.3. CONCLUSIONS 326 8.3.1. Dominant Failure Mechanism in the Arabian Gulf 326 8.3.2. Applicability of Section ‘R’ to the Arabian Gulf Conditions 327 8.3.3. Specifications for OALL 327 8.3.4. Limiting Engineering Parameters of Carbonate Soils 328 8.3.5. Bias Factors of Axial Pile Capacity in the Arabian Gulf 329 8.3.6. Target Reliability Levels 330 8.3.7. Specifications for Axial Pile Capacity in Carbonate Soils 330 8.3.8. Modification to Deterministic Method for Reassessment 332 8.3.9. Limitations of API RP2A Prediction Model 333 8.3.10. Modeling Pile-Soil Interaction 334 8.4. RECOMMENDATIONS FOR FUTURE RESEARCH 334 8.4.1. Technical Issues 334 8.4.2. philosophical issues 336

BIBLIOGRAPHY ............................................................................................................................. 343

AUTHOR’S PUBLICATIONS ......................................................................................................... 389

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APPENDICES..................................................................................................................................390

APPENDIX A: EQUIPMENT DATABASE 391

APPENDIX B: PILED FOUNDATION DATABASE 392

APPENDIX C: SOIL PROFILE DATABASE 393

APPENDIX D: PREDICTED STATIC CAPACITY OF PILES IN THE DATABASE 394

APPENDIX E: “ACTUAL” PILE CAPACITY USING BACK ANALYSIS PROCEDURE DEVELOPED

IN THIS RESEARCH 395

APPENDIX F: COMMON STATISTICAL DISTRIBUTIONS USE IN THIS RESEARCH 396

APPENDIX G: STRUCTURAL RELIABILITY ANALYSIS (SRA) 397

APPENDIX H: PREDICTION METHODS FOR AXIAL PILE CAPACITY IN “NORMAL” SOILS 398

APPENDIX I: APIPILE MANUAL 399

APPENDIX J: SACS INPUT FILES AND EXTRACTS FROM SACS OUTPUT FILES 400

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ACKNOWLEDGMENTS

I owe an immense debt of gratitude to my supervisor, Professor Beverley Ronalds,

for her support from the formative stages of this thesis to its final draft. Her sound

advice, careful guidance and conscientious reviews of several drafts of this thesis

were invaluable as I travelled through the journey of this research.

I extend my appreciation to Dr. Geoff Cole and Dr. Manolis Fakas for providing

valuable suggestions during this research and to Dr. Mostafa Ismail for the

conscientious proof reading and making valuable suggestions to the last draft of this

thesis. Thanks to Dr. Krystyna Haq for reviewing an earlier draft of this thesis.

This acknowledgment must include all scholars and academics listed in the

Bibliography for providing the necessary background to this research. In particular,

the direct and indirect contribution of Professor Robert Bea to this research was

immensely useful and greatly appreciated. This also extends to Professor Bengt

Fellenius and Dr. Frank Rausche, who provided guidance at the start of this research

and offered software free of charge.

Last but not least, I appreciate the outstanding support from UWA library and

administration staff at the School of Oil and Gas Engineering.

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DEFINITIONS

Definitions adopted by researchers are often not uniform, so key and controversial

terms are defined in this section to establish positions taken in the research.

Fellenius (1999) recommended some of the following definitions adopted in this

research.

Term Definition

Allowable Load Maximum load that may be safely applied to a foundation unit under expected loading and soil conditions and determined as the Capacity divided by the Factor of Safety.

Applied (Service) Load Load actually applied to a foundation unit

Axial, Bearing, Shaft and Toe Capacity

Ultimate Resistance of the unit.

Blow count During pile driving, the blow count represents the count of blows for a specified penetration of the pile into the soil. Typically, the count of blows is measured for a pile driven one foot into the soil and the blow count is recorded in a pile driving record.

Capacity The maximum or ultimate soil resistance mobilized by a foundation unit. It is used as a stand-alone term and is synonymous with Ultimate Resistance.

Capacity, bearing The maximum or ultimate soil resistance mobilized by a foundation unit subjected to downward loading. It is the sum of the shaft resistance and the toe or ‘end bearing’ resistance.

Dynamic Monitoring The recording of strain and acceleration induced in a pile during driving and presentation of the data in terms of stress and transferred energy in the pile as well as of estimates of capacity.

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Term Definition

Factor of Safety The ratio of maximum available resistance or of the capacity to the code allowable stress or load.

Loading Test Refers to the situation of a test performed by loading a pile while Load Test is a test for finding out what load is applied to a pile.

Limit State A state that defines the boundary between a safe and unsafe situation

Penetration Resistance Effort required in advancing a pile. When quantified, it is either the number of blows required for the pile to penetrate a certain distance or the distance penetrated for a certain number of blows.

Pile Head The uppermost end of a Pile

Pile Impedance A material property of a pile cross-section determined as the product of the Young's modulus (E) and area (A) of the cross section divided by the wave speed (c).

Pile Point A special type of pile shoe.

Pile Shaft The portion of the pile between the pile head and the pile toe.

Pile Shoe A separate reinforcement attached to the pile toe of a pile to facilitate driving, to protect the lower end of the pile and/or to increase the toe resistance of the pile.

Pile Toe The lowermost end of a pile.

Pore Pressure Pressure in the water and gas present in the voids between the soil grains minus the atmospheric pressure.

Probability of failure This is an unfortunate choice of wording because it can be mistakenly treated as being synonymous with the actual rate of failure. The prefix “nominal” or “notional” is often applied to the probability of failure to emphasize its formal nature (CIRIA, 1977, Ellingwood et al., 1980, Melchers, 1999). An alternative would be to use the reliability index, β, which is mostly free of such connotation.

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Term Definition

Quantitative Risk Assessment (QRA)

Formal and systematic approach for identifying potentially hazardous events and estimating likelihood and consequences of accidents developing from these events to people, environment and resources.

Ultimate Load Capacity evaluated from the results of a static loading test.

Set Penetration for one blow, sometimes penetration for a series of blows.

Setup or Soil Setup Describes the effect of resistance increase with time after driving. This term is sometimes referred to as Soil Freeze but this term will not be used in this thesis as it has a different meaning for cold regions of the world.

Shaft Resistance Calculated as the integral over the embedded pile area of the unit skin friction value

Structural Analysis Refers to the technique of making stiffness or stress calculations while Structural Assessment includes the whole process of modeling the problem, analysis and interpretation of the results.

Structural Reliability Analysis (SRA)

SRA aims at determining the probability of failure of a Limit State that, in its basic form, attains an unsafe situation. In SRA, a Limit State is represented, again in its basic form, by a Limit State equation which attains a negative value for unsafe situations and a positive value for safe situations. The Limit State equation incorporates basic random variables defined by probability density functions through (a) statistical analysis of existing sample data and (b) by experience and theoretical considerations. The representation of real structural systems may involve a number of Limit States (such as buckling, yielding, fatigue or excessive deformation under various loading conditions), some of which may be represented by a number of different failure equations.

In this case, the analysis needs to incorporate statistical correlation effects between the basic random variables as well as between Limit State equations (a set of basic random variables only affect the outcome of different

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Limit State equations).

In this thesis, SRA is primarily concerned with calculating the probability of ultimate collapse of the total substructure due to extreme environmental storm loading. It does not treat all possible hazards to the structure from a QRA viewpoint.

Toe Resistance Soil resistance acting on the pile toe

Transferred Energy The energy transferred to the pile head and determined as the integral over time of the product of force, velocity, and pile impedance.

Wave Speed The speed of strain propagation in a pile.

Wave Trace A graphic representation against time of a force or velocity measurement.

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NOMENCLATURE

Symbol Definition

A Side surface area of pile or a factor to account for cyclic or static loading

BOR beginning of restrike

BS base shear

c Constant that accounts for the errors associated with simplification of the equation describing reliability of pile groups

C Wave speed in m/s

CAPWAP Case Pile Wave Analysis Program

COV Coefficient of variation

COVQ Coefficient of variation of load

COVQD Coefficients of variation for dead load (QD)

COVQL Coefficients of variation for live load (QL).

COVR Coefficient of variation of resistance

COVχ Coefficient of variation of system effect

COVζ Coefficient of variation of group efficiency

CS Soil type dominated by clayey soils overlain by sandy soils

CC Carbonate content

C(x,y) Influence coefficient

Cdb Hammer damping factor

d Mean water depth

D Diameter of a pile or hammer damping input value

Dn Nominal dead load

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Symbol Definition

DOE Department of Energy

d/gT2app Dimensionless relative depth

EOD End of driving

E(W) Mean of the equipment weights

Eh Hammer efficiency

Er Manufacturer rated hammer energy

ETR Energy transfer efficiency

F Unit skin friction capacity or total axial force on the column using influence surface diagram

F(x) A value used to approximate Cumulative Distribution Function at each value of x

FORM First order reliability method

fs,si Limit on unit friction value for a silica sand with a carbonate content (CC) of 20% or lower

fs,80 Limit on unit friction value applicable with carbonate content (CC) of 80% or greater

FOS Factor of safety

g Acceleration of gravity

H/gT2app Dimensionless wave steepness

H Wave height

HAT Highest astronomical tide

Hs Significant wave height

Hb Breaking wave height

Js Damping constant for skin friction

Jp Damping constant for end bearing

kram Hammer cushion or impact block or ram stiffness

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Symbol Definition

k Initial modulus of subgrade reaction in force per volume units

K Coefficient of lateral earth pressure

kN Kilo Newton = Unit of pressure measurement

L Length of a pile or wave length

LAT Lowest astronomical tide

Ln Nominal live load

LT Lifetime of T years

LRFD Load Resistance Factor Design

m Shape parameter for Weibull distribution

MHHW Mean higher high water

MHLW Mean higher low water

MLHW Mean lower high water

MLLW Mean lower low water

MN Mega Newton = 1000 * kN

MPa Mega Pascal

mram Ram mass

MSL Mean sea level

N Bearing capacity factor

OALL Open area live load

Pa Pascal

p-y curve Lateral soil resistance-deflection curve

( )BAP j Posterior distribution on A

( )jABP

Likelihood function of the data

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Symbol Definition

P(Aj) Prior distribution on A

psf or lb/ft2 Pounds per square foot

PH Horizontal load

PV Vertical load

pu Ultimate bearing capacity at depth X in units of force per unit length

Pf Probability of failure

Pf a Annual probability of failure

Pf L Probability of failure for a lifetime of L years

PDA Pile Driving Analyzer

q-z curve Relation between mobilized end bearing resistance & axial tip deflection

Q Load as described in reliability formulation

Qt Total capacity of a pile

Qs Skin friction capacity of a pile

QP End bearing capacity of a pile

Qi Nominal load effect

Qmean Mean load

q Unit end bearing capacity

Q80 Limit on end bearing applicable to carbonate content of 80% or higher

Qsi Limit on end bearing applicable to silica sand with a carbonate content of 20% or lower

R Resistance as described in reliability formulation

R2 Correlation coefficient value – a measure of correlation between two sets of data.

RP Return period

Rmean Mean resistance

Rm Measured value of resistance

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Symbol Definition

Rn Nominal resistance or predict nominal pile capacity using API RP2A

Sb Set per blow

su Undrained shear strength

SRD Soil resistance to driving

SRA Structural reliability analysis

SACS Structural analysis computer software

SC Soil type dominated by sandy soils overlain by clayey soils

SPT Standard penetration test

t Mobilized soil adhesion

tmax Unit skin friction capacity

t-z curve Axial load transfer relationship

Tapp Apparent wave period

Tp Peak period

Tz Mean zero-crossing period

V Current speed

W Wind Load

WSD Working Stress Design

Wn Nominal wind load

Wram Hammer ram weight

x and y Normalized spatial variables ranging from zero to one

X and Y Dimensions to define tributary area for a column or a pile

z Local pile deflection

αn Dispersion parameter

βT Target reliability index