PRACTICAL COURSE IN CONCRETE
CONTENTS INTRODUCTION AND READER’S GUIDE THE PROCESS OF CHLORIDE INGRESS TYPES OF CHLORIDE TRANSPORT IN CONCRETE EQUATIONS OF DI?USION FICK’S SECOND GENERAL LAW OF DI?USION FICK’S ?RST LAW OF DI?USION THE DI?ERENTIAL EQUATION OF DI?USION E?ECT OF CRACKS ON CHLORIDE INGRESS INITIAL AND BOUNDARY CONDITIONS THE COLLEPARDI MODEL THE LIGHTCON MODEL THE HETEK MODEL CHLORIDE BINDING CHLORIDE-LADEN ENVIRONMENTS SOURCES OF CHLORIDE SEAWATER CHLORIDE CONTAINING DE-ICING SALTS PVC ?RE INDUSTRIAL PROCESSES MARINE ENVIRONMENTS GOVERNING PARAMETERS OF MARINE STRUCTURES CONCRETE SUBMERGED IN SEAWATER VERSUS MARINE ATMOSPHERE ROAD ENVIRONMENTS PARAMETERS OF THE ROAD ENVIRONMENT ROAD TRA?C ZONES CORROSION CORROSION AND ITS CONSEQUENCES ANODES, CATHODES AND INCIPIENT ANODES CONTENTS CORROSION CURRENT AND CORROSION RATE THRESHOLD VALUE OF CHLORIDE IN CONCRETE CORROSION INHIBITORS E?ECTS OF INHIBITORS CORROSION TESTS WITH MIGRATING INHIBITORS FIELD TESTS INITIATION PERIOD OF TIME AND SERVICE LIFETIME CORROSION MULTI-PROBES DESIGN AGAINST CORROSION CLASS OF ENVIRONMENT AND METHOD OF SAFETY COMPOSITION OF THE CONCRETE STRUCTURAL DESIGN AND DESIGN OF REBAR COVER TEST METHODS ANALYSIS OF CHLORIDE CONTENT OF CONCRETE SOURCES OF UNCERTAINTIES EXPOSURE CONDITIONS IN ?ELD LABORATORY EXPOSURE CONDITIONS PREPARATION OF POWDER SAMPLES FOR ANALYSIS ANALYSIS OF CHLORIDE CONTENT CHLORIDE PRO?LES CHLORIDE PRO?LE OF CONCRETE EXPOSED TO SEAWATER DETERMINATION OF CHLORIDE PARAMETERS CHLORIDE PRO?LES FOR DI?USION DEVIATIONS FROM THE IDEAL SHAPE OTHER METHODS FOR THE DETERMINATION OF THE CHLORIDE PARAMETERS CHARACTERISTIC VALUE OF OBSERVATIONS EXAMINATION OF CONCRETE SAMPLING MAINTENANCE AND RENOVATION OF RC STRUCTURES REPAIR OF CORROSION WITH CORROSION INHIBITORS CHOICE OF CORROSION INHIBITOR FOR REPAIR OF RC STRUCTURES APPLICATION OF CORROSION INHIBITORS IN CONCRETE REPAIRS ELECTRO-CHEMICAL CHLORIDE REMOVAL CATHODIC PROTECTION SURFACE PROTECTION DESIGN OF CHLORIDE EXPOSED RC STRUCTURES SERVICE LIFE METHODS OF DESIGN DETERMINISTIC DESIGN STOCHASTIC DESIGN CONTENTS CONSTANT CHLORIDE DI?USIVITY PARAMETERS OF THE CHLORIDE PRO?LE CHLORIDE PRO?LE EQUATION OF A CHLORIDE PRO?LE THE ‘?RST YEAR CHLORIDE INGRESS’ FLUX OF CHLORIDES INTENSITY OF PENETRATING CHLORIDE DI?USION RATE OF CHLORIDE TYPES OF CHLORIDE PRO?LES ACHIEVED CHLORIDE PRO?LE POTENTIAL CHLORIDE PRO?LE CHLORIDE PARAMETERS DETERMINED BY APPROXIMATION TEST OF HETEROGENEITY METHOD OF SURFACE TANGENT THREE SETS OF OBSERVATION CHLORIDE PARAMETERS BY REGRESSION ANALYSIS NON-LINEAR CURVE-?TTING CHLORIDE INGRESS INTO PRISMATIC SPECIMENS CHLORIDE INGRESS INTO WALLS FROM OPPOSITE SIDES FICK’S SECOND LAW OF DI?USION CHLORIDE INGRESS INTO SPECIMENS HAVING SQUARE CROSS- SECTIONS CHLORIDE INGRESS FROM DE-ICING SALT CHLORIDE CONTENT OF CONCRETE SURFACE CHLORIDE PRO?LES OF DE-ICED CONCRETE OLD MARINE RC STRUCTURES FICK’S SECOND LAW FOR CONSTANT CHLORIDE DI?USIVITY CHLORIDE INGRESS INTO OLD CONCRETE INITIATION PERIOD DETERMINATION BY A CHLORIDE PRO?LE CORROSION DOMAIN (T, C)-DIAGRAM (T, D)-DIAGRAM SERVICE LIFETIME CORROSION MULTI-PROBE OBSERVATIONS FROM A CORROSION MULTI-PROBE ROUGH ESTIMATES BY CHLORIDE INDICATORS PROBABILISTIC ANALYSIS INTRODUCTION TO THE RELIABILITY INDEX CONTENTS THE MULTI-DIMENSIONAL PROBLEM GEOMETRICAL MEANING OF THE RELIABILITY INDEX PROBABILITY OF CORROSION CHARACTERISTIC INITIATION PERIOD OF TIME DETERMINATION OF THE CHARACTERISTIC VALUE BY MEANS OF A TABLE ERROR FUNCTION AND RELATED FUNCTIONS THE GAMMA FUNCTION DE?NITION AND EXTENSIONS SPECIAL VALUES IMPORTANT FORMULÆ THE RE?ECTION FORMULA THE DUPLICATION FORMULA GAUߒS MULTIPLICATION FORMULA POCHHAMMER’S SYMBOL AND RELATED SYMBOLS APPROXIMATION FORMULÆ STIRLING’S FORMULA THE ERROR FUNCTION AND RELATED FUNCTIONS SPECIAL VALUES OF ERFC(U) CONNECTION WITH FICK’S SECOND LAW SERIES EXPANSIONS OF ERFC(U) VARIANT OF TAYLOR’S FORMULA ESTIMATES APPROXIMATIONS INVERSE OF THE COMPLEMENTARY ERROR FUNCTION REPEATED INTEGRALS OF ERFC(U) EXTENSION OF FICK’S SECOND LAW SERIES EXPANSIONS FOR INERFC(U) THE ?P(U) FUNCTIONS DE?NITION AND MAIN THEOREM FICK’S SECOND LAW FOR ?P(U) H¨OLDER’S INEQUALITY AND RELATED RESULTS DI?ERENTIATION AND TAYLOR EXPANSION OF ?P(U) SERIES EXPANSION OF ?P(U) SOME ESTIMATES POLYNOMIAL APPROXIMATION OF ?P(U) GENERALIZED REPEATED INTEGRALS OF ?P(U) CONNECTION WITH HYPERGEOMETRIC FUNCTIONS? 3 3 10 THE ?P(U) FUNCTIONS BESSEL FUNCTIONS RECURRENCE FORMULÆ ZEROS OF J?(R) AND J?(R)Y?(?R) ?J?(?R)Y?(R) BESSEL FUNCTIONS FOR ? = N + 2, N ?N0 OTHER USEFUL FUNCTIONS THE FUNCTION H(?, ?) THE FUNCTION H1(?, ?) FICK’S SECOND LAW FOR CONSTANT DI?USION COE?CIENT THE GENERAL INITIAL/BOUNDARY VALUE PROBLEM EIGENFUNCTION EXPANSIONS HELMHOLTZ’S EQUATION CHANGE OF COORDINATES IN THE OPERATOR ?2 SEPARATION OF THE VARIABLES METHOD OF SOLUTION OF FICK’S SECOND LAW SUMMARY A CATALOGUE OF SOLUTIONS OF FICK’S 2ND LAW HALF-IN?NITE INTERVAL, 1 DIMENSION BOUNDED INTERVAL, 1 DIMENSION BOUNDED TWO-DIMENSIONAL INTERVAL BOUNDED THREE-DIMENSIONAL INTERVAL CIRCLE IN THE PLANE SECTOR OF A CIRCLE IN THE PLANE ANNULUS SECTOR OF AN ANNULUS FINITE CYLINDRICAL COLUMN 4 3 10 SECTOR OF A ?NITE CYLINDRICAL COLUMN 4 3 11 FINITE PIPE 4 3 12 SECTOR OF A ?NITE PIPE TIME-DEPENDENT CHLORIDE DI?USIVITY CONSTANT SURFACE CHLORIDE CONTENT LIGHTCON MODEL OF CHLORIDE INGRESS PROBLEM OF ESTIMATING THE CHLORIDE INGRESS INTO CONCRETE ASSUMPTIONS OF THE LIGHTCON MODEL MASS BALANCE OF CHLORIDE IN AN ELEMENT VOLUME OF CONCRETE ACHIEVED CHLORIDE DI?USION COE?CIENT BOUNDARY CONDITION GRAPHS OF CHLORIDE PRO?LES CHLORIDE INGRESS INTO CONCRETE INITIATION PERIOD OF TIME CORROSION MULTIPROBE OBSERVATIONS FROM A CORROSION MULTIPROBE CHLORIDE INGRESS INTO PRISMATIC RC COMPONENTS CONTENTS EQUATIONS OF THE PROBLEM STEP FUNCTION AS A BOUNDARY CONDITION CHLORIDE PRO?LES OF THE CONCRETE TIME-DEPENDENT SURFACE CHLORIDE CONTENT EXTENSION OF THE LIGHTCON MODEL THE HETEK MODEL OF CHLORIDE INGRESS INTO CONCRETE THE PROBLEM OF ESTIMATING THE CHLORIDE INGRESS INTO CONCRETE ASSUMPTIONS OF THE HETEK MODEL MASS BALANCE OF CHLORIDE IN A VOLUME ELEMENT OF CONCRETE PLOTTING THE CHLORIDE PRO?LES LINEARIZATION OF THE HETEK MODEL CHLORIDE CONTENT OF SURFACE HETEK MODEL BY APPROXIMATIONS APPROXIMATION OF THE ?P(U) FUNCTIONS METHOD OF INVERSE CORES METHOD OF TEST FORMULÆ FOR PARAMETERS OF CHLORIDE INGRESS CORROSION MULTIPROBE (MACROCELL TECHNIQUE) DESIGN OF CONCRETE COVER THE AGE PARAMETER, ? SURFACE CHLORIDE CONTENT AFTER 1 YEAR OF EXPOSURE, C1 SURFACE CHLORIDE CONTENT AFTER 100 YEARS OF EXPOSURE, C100 THE EXPONENT P THE FACTOR S1 THE THRESHOLD VALUE OF CHLORIDE IN CONCRETE, CCR NT BUILD 443 LOCATION-DEPENDENT CHLORIDE DI?USIVITY THE ONE-DIMENSIONAL CASE THE ISOTROPIC CASE IN HIGHER DIMENSIONS THE RECTANGULAR CASE THE UNIT CIRCLE SPECIAL TOPICS PREDICTION OF REINFORCEMENT CORROSION PRINCIPLE OF A CORROSION MACRO CELL MATHEMATICAL MODELS OF A CORROSION MULTI PROBE THE LIGHTCON MODEL FOR THE MULTI PROBE THE HETEK MODEL FOR THE MULTI PROBE COATING THE SEMI-IN?NITE COMPOSITE MEDIUM THE ?NITE COMPOSITE MEDIUM THE 2-COMPOSITE ?NITE MEDIUM THE 2-COMPOSITE ?NITE MEDIUM, EXAMPLES THE 3-COMPOSITE ?NITE MEDIUM SYMMETRIC 3-COMPOSITE MEDIA FURTHER DEVELOPMENTS TABLES TABLES OF ERFC(U) TABLES OF INV ERFC(U) TABLES OF ?P(U) TABLES OF INV ?P(U) TABLES OF ?P(U) TABLES OF INV ?P(U) TABLE OF H(X, T) TABLES OF H0(X, T)