Reliability-Based Design and Quality Control of Bored Piles

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Reliability-Based Design and Quality Control

of Bored Piles

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Reliability-Based Design and Quality Control

of Bored Piles

Proefschrift

ter verkrijging van de graad van doctor aan de Technische Universiteit Delft,

op gezag van de Rector Magnificus prof.ir. K.C.A.M. Luyben, voorzitter van het College voor Promoties,

in het openbaar te verdedigen

op woensdag 3 december 2014 om 10:00 uur

door

BACH Duong

Master of Engineering

National University of Civil Engineering geboren te Hanoi, Vietnam

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Dit proefschrift is goedgekeurd door de promotoren: Prof.drs.ir. J.K. Vrijling

Prof.dr.ir. P.H.A.J.M. van Gelder Samenstelling promotiecommissie:

Rector Magnificus voorzitter

Prof.drs.ir. J.K. Vrijling Technische Universiteit Delft, promotor Prof.dr.ir. P.H.A.J.M. van Gelder Technische Universiteit Delft, promotor Prof.dr. M.A. Hicks Technische Universiteit Delft

Prof.ir. T. Vellinga Technische Universiteit Delft Dr.ir. K.J. Bakker Technische Universiteit Delft

Dr. T.V. Cuong Vietnam Institute for Building Science and Technology Dr.ir. W.M.G. Courage TNO, the Netherlands

Prof.dr.ir. S.N. Jonkman Technische Universiteit Delft, reservelid

This research has been financially supported by the Ministry of Education and Training of Vietnam and Delft University of Technology.

Keywords: Bored piles, reliability-based design, quality control, resistance factor calibra-tion, set-up, Bayesian inference, Prob2B-Plaxis.

This thesis should be referred to as: Bach, D. (2014). Reliability-based design and quality control of bored piles. Ph.D. thesis, Delft University of Technology.

Cover layout by Tran Trong An

Cover image: Probability Density Functions of Load and Resistance Printed by Sieca Repro, Delft, the Netherlands

ISBN 978-94-6186-379-9

Copyright c 2014 byBACH Duong

All rights reserved. No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording or by any information storage and retrieval system, without written permission of the author.

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Summary

Bored piles are a type of deep foundations which have been and are being widely used in construction engineering such as high-rise buildings, bridges, jetties, and so on. Al-though bored piles have remarkable advantages over driven piles, the quality of bored piles is frequently affected by many causes of imperfection, which mainly come from the inadequate ground investigation and construction procedures. It can be said that design and quality control of bored piles are two closely related stages. A quality control proce-dure has to be clearly addressed in the design stage; and decision making in the design, for many cases, has to be based on the testing results of a quality control procedure. Therefore, two major objectives need to be solved in this thesis as: (1) Propose models to calibrate resistance factors for the Load and Resistance Factor Design (LRFD) approach and find a suitable model aiming to directly determine reliability of a bored pile consid-ering some types of defect that may occur in the bored pile. (2) Select a quality control method and evaluate its reliability when applied to bored piles.

The thesis consists of chapters, in each of which a new model is proposed, and then is applied for a specific case study. The logicality and succession of the theoretical issues between chapters are systematically presented.

In Chapter 2, a history of the development of design approaches is presented, including the Allowable Stress Design (ASD), the Limit State Design (LSD), and the Reliability-Based Design (RBD). Advantages and limitations of each design approach are discussed in detail. This chapter focuses on analyzing the LSD with the use of partial safety factors following the ultimate limit state. In which, the calibration of resistance factors under the framework of the LRFD is one of the main objectives of this thesis. The level II and level III reliability methods are used to calibrate these resistance factors.

In Chapter 3, the quality control approaches of bored piles are briefly introduced as an important part of the design and construction process. The post-construction tests com-prise planned and unplanned tests, in which planned tests are typically non-destructive test methods. Of these methods, the Cross-hole Sonic Logging (CSL) method, the most widely used method for testing the integrity of bored pile concrete, is chosen aiming to evaluate its reliability. The inspection probability, which is used as a measurement of re-liability for the CSL method, was formulated based on the encountered probability and the detection probability. For an assigned target inspection probability, the magnitude of a defect that can be detected is a function of the pile diameter and the number of ac-cess tubes arranged. A neac-cessary number of acac-cess tubes is recommended in this study. This finding is a good reference associated with design engineers and project managers

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Summary Summary in making decisions for the design of bored piles.

In Chapter 4, the calibration models of resistance factors, following the framework of the LRFD, are proposed and presented with respect to some technical aspects of bored piles. The calibrated resistance factors aim at achieving target reliability levels for a set of load factors that were already specified in the structure code. For a calibration procedure, the model uncertainty is considered and represented through the resistance bias factor. At first, calibration models of a common resistance factor using three reliability meth-ods are presented. The reliability methmeth-ods consist of the First Order Second Moment (FOSM) method, the First Order Reliability Method (FORM), and Monte Carlo Simula-tion (MCS). In this study, the calibraSimula-tion model using MCS is proposed, aiming to gain a more precise resistance factor and to reduce the calibration time. Sixteen calibration cases are considered; each calibration case is represented by a soil type, a prediction method, and a construction method. The resistance factors obtained from the proposed calibra-tion procedure have a good correlacalibra-tion with those from other calibracalibra-tion procedures that were officially accepted in practice. This confirms that the proposed calibration model is valid and applicable. One interesting finding is that the calibrated resistance factor strongly depends on the ratio of the coefficient of variation to the mean of the resistance bias factor with a linear relation. This is an important basis for calibrating the shaft and base resistance factors separately.

Next, a calibration procedure for separate shaft and base resistance factors is proposed, because the degrees of uncertainty of shaft and base resistances are different. The use of a common resistance factor as mentioned above clearly does not reflect this difference. In order to calibrate shaft and base resistance factors separately, the shaft and base resis-tance bias factors need to be determined. By the proposed calibration procedure, many couples of values for the shaft and base resistance factors would be derived; all of which satisfy the target reliability levels. Therefore, a ”correlation ratio” is proposed aiming to represent the correlation between uncertainty degrees of shaft and base resistance bias factors. To which, a unique couple of values for the shaft and base resistance factors is finally obtained. Through a case study at the site of the Los Angeles Memorial Coliseum (the US), using shaft and base resistance factors may lead to a more economical design than a design using a common resistance factor.

In Chapter 5, the increase of pile resistance with time, compared to the initial resistance, is usually referred to as ”set-up” effect. The initial resistance is also called the reference resistance; and the portion of increasing resistance with time is called the set-up resis-tance. Although the bored pile set-up effect is not as dramatic as the driven pile set-up effect, incorporating the set-up effect into the LRFD for bored piles is more or less nec-essary. By this incorporation, an economical design can also be gained. Therefore, a calibration procedure for the reference and set-up resistance factors is presented and ap-plied for a case study at the site of the new SR20 eastbound bridge in Florida (the US). Due to the compatibility in the calibration algorithm, the calibration procedure used for the set-up effect is completely the same as that for the shaft and base resistance factors. The calibration model of a common resistance factor as mentioned in Chapter 4 is nor-mally based on the initial empirical distributions of the resistance bias factor. In general, these distributions have been built up by a large amount of data collected from many

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Summary Summary different sites. Therefore, applying a common resistance factor, which is calibrated from the initial empirical distribution, for a specific site may not be completely consistent. Through the experimental outcomes of pile loading tests at a designed site, the Bayesian inference enables to reduce uncertainty with respect to the initial empirical distribution in terms of load test results within a site. To which, a posterior distribution of the resis-tance bias factor is then derived. A re-calibration process of a common resisresis-tance factor is subsequently carried out and an updating resistance factor is obtained. As a result, a more precise design using the updating resistance factor can be reached. The Bayesian inference is applied for a case study at the site of the 330 MW Uong Bi Extension No. 2 Thermal Power Plant in Quang Ninh province (Vietnam). The derived results and some comments are presented in Chapter 6.

It can be seen that, the LRFD uses the resistance factors that were obtained through the calibration process and satisfies the specified target reliability levels. This approach does not require the explicit use of the probabilistic description of random variables and there-fore it has been familiar to design engineers in terms of its simplicity. In current practice, however, clients and project managers are more and more interested in the reached re-liability level or the probability of failure of a pile foundation. Therefore, applying the RBD aiming to directly estimate reliability levels for a specific bored pile foundation is of interest.

In Chapter 7, the reliability of a single bored pile is directly determined by the use of a coupling calculation between the finite element package (Plaxis version 9.0) and the nu-merical probabilistic toolbox (Prob2B). The reliability is assessed, not only for an intact bored pile but also for a defect bored pile, by assuming different types and magnitudes of defect that may occur within the pile body. Two failure modes, the Geotechnical Fail-ure (GF) mode and the Structural FailFail-ure (SF) mode, are proposed in this study. The GF mode pertains to the geotechnical resistance of bored piles and the SF mode is re-lated to the compressive stress in bored pile concrete. Both modes are evaluated through reached reliability levels for bored piles that are subjected to a specified combination of loads from the superstructure. Based on which, the reliability of an axially loaded pile is comprehensively assessed. Through a case study at Pier T10 of the An Dong bridge in Ninh Thuan province (Vietnam), some findings and comments are presented in this chapter.

Finally, the conclusions and recommendations are stated in Chapter 8. Some models proposed in Chapters 4, 5, and 6 can be well applied for driven piles.

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Samenvatting

Boorpalen zijn diepe funderingen die veel en wijdverbreid in de bouwtechniek gebruikt worden, zoals bij hoogbouw, bruggen en steigers. Hoewel boorpalen een aanzienlijk voordeel hebben ten opzichte van geheide palen, wordt de kwaliteit van boorpalen vaak be¨ınvloed door velerlei oorzaken van onvolmaaktheid, voornamelijk als gevolg van on-toereikend grondonderzoek en de constructieprocedures. Ontwerp en kwaliteitscontrole van boorpalen zijn daarom twee nauw verwante fasen. Een kwaliteitscontroleprocedure moet in de ontwerpfase worden aangepakt; en besluitvorming in het ontwerp moet in veel gevallen worden gebaseerd op de testresultaten van een kwaliteitscontroleproce-dure.

Twee belangrijke doelstellingen worden in deze thesis opgelost: (1) Het voorstellen van modellen om de weerstandsfactoren voor de belasting en weerstand van de ”Load and Resistance Factor Design” (LRFD) benadering te kalibreren, en een geschikt model te vinden dat is gericht op de betrouwbaarheid van boorpalen, met inachtname van ver-schillende soorten defecten die zich in boorpalen kunnen voordoen. (2) Het selecteren van een methode voor kwaliteitscontrole, en het evalueren van de betrouwbaarheid van deze methode bij toepassing op boorpalen.

In ieder hoofdstuk in dit proefschrift wordt een nieuw model voorgesteld, hetgeen ver-volgens wordt toegepast op een specifieke case study. De opeenvolging van de theore-tische kwesties in de hoofdstukken wordt op die manier systematisch en logisch gepre-senteerd.

In hoofdstuk 2 wordt de geschiedenis van de ontwikkeling van ontwerpbenaderingen gepresenteerd, met inbegrip van ”Allowable Stress Design” (ASD), ”Limit State Design” (LSD), en ”Reliability-Based Design” (RBD). Voordelen en beperkingen van elke ont-werpbenadering worden in detail besproken. Dit hoofdstuk is vooral gericht op de ana-lyse van de LSD met gebruik van partiële veiligheidsfactoren volgens de ”Ultimate Li-mit State”. De kalibratie van weerstandsfactoren in het kader van de LRFD is één van de belangrijkste doelstellingen van dit proefschrift. Niveau II en niveau III betrouwbaar-heidsmethoden zijn gebruikt om deze weerstandsfactoren te kalibreren.

In hoofdstuk 3 worden diverse benaderingen van kwaliteitscontrole van boorpalen in het kort ge¨ıntroduceerd als een belangrijk onderdeel van het ontwerp en het bouwpro-ces. De testen na de bouw omvatten geplande en ongeplande proeven, waarin de ge-plande proeven typische, niet-destructieve testmethoden zijn. Van deze methodes is de ”Cross-hole Sonic Logging” (CSL) methode de meest gebruikte methode voor het testen

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Samenvatting Samenvatting van de integriteit van betonnen boorpalen. De betrouwbaarheid van deze methode is ge¨evalueerd. De inspectiekans, die wordt gebruikt als een maat voor de betrouwbaar-heid van de CSL methode, werd geformuleerd op basis van de kans op het stuiten op een defect en de kans op het daadwerkelijk detecteren van een defect, de detectiekans. Voor een bepaalde streefwaarde voor de inspectiekans is de omvang van een defect dat gedetecteerd kan worden een functie van de diameter van de paal en het aantal toegangs-buisjes. In deze studie wordt een noodzakelijk aantal toegangsbuizen aanbevolen. Deze bevinding is een goede referentie voor ingenieurs en projectmanagers die zich bezig hou-den met ontwerp en met het nemen van beslissingen voor het ontwerp van boorpalen. In hoofdstuk 4 worden de kalibratiemodellen van weerstandsfactoren volgens het kader van de LRFD voorgesteld en gepresenteerd met betrekking tot bepaalde technische as-pecten van boorpalen. De gekalibreerde weerstandsfactoren zijn gericht op het bereiken van streefwaarden van betrouwbaarheid voor een reeks belastingsfactoren die al in de constructiecode gespecificeerd zijn. Bij een kalibratieprocedure wordt de onzekerheid in het model beschouwd, en vertegenwoordigd door de weerstand-bias-factor.

Allereerst worden de kalibratiemodellen van een gemeenschappelijke weerstandsfactor met behulp van drie betrouwbaarheidsmethoden gepresenteerd. De betrouwbaarheids-methoden bestaan uit de ”First Order Second Moment” (FOSM) methode, de ”First Or-der Reliability Method” (FORM) en Monte Carlo Simulatie (MCS). In deze studie wordt het kalibratiemodel met behulp van MCS voorgesteld, met als doel een meer precieze weerstandsfactor te verkrijgen en om de tijdsduur van kalibratie te verminderen. Zes-tien studies van kalibratie worden beschouwd; ieder geval van kalibratie wordt ge-karakteriseerd door een bodemtype, een voorspellingsmethode en een bouwmethode. De weerstandsfactoren, die uit de voorgestelde kalibratieprocedure verkregen zijn, heb-ben een goede correlatie met die uit andere kalibratieprocedures, welke in de praktijk reeds officieel aanvaard zijn. Dit bevestigt dat het voorgestelde kalibratiemodel geldig en toepasbaar is. Een interessante bevinding is dat de gekalibreerde weerstandsfactor sterk afhangt van de verhouding tussen de variatieco¨effici¨ent en het gemiddelde van de weerstand-bias-factor, met een lineaire relatie. Dit is een belangrijke basis voor het afzonderlijk kalibreren van de schacht- en de puntweerstandsfactoren.

Vervolgens wordt een kalibratieprocedure voor afzonderlijke schacht- en puntweerstands-factoren voorgesteld, omdat de mate van onzekerheid van schacht- en puntweerstand verschillend is. Het gebruik van een gemeenschappelijke weerstandsfactor, zoals hierbo-ven genoemd, reflecteert dit verschil niet. Om de schacht- en puntweerstandsfactoren af-zonderlijk te kalibreren, moeten de schacht- en puntweerstands-bias-factoren worden be-paald. In de voorgestelde kalibratieprocedure worden vele paren van waarden voor de schacht- en puntweerstandsfactoren afgeleid; welke allen voldoen aan de betrouwbaar-heid van de streefwaarden. Een ”correlatieverhouding” wordt daarom voorgesteld, die de correlatie tussen onzekerheidswaarden van schacht- en puntweerstands-bias-factoren vertegenwoordigt. Tenslotte wordt een uniek paar waarden voor de schacht- en punt-weerstandsfactoren verkregen. Het gebruik van schacht en puntpunt-weerstandsfactoren lei-den voor een casestudy op het terrein van de Los Angeles Memorial Coliseum (V.S.) tot een economischer ontwerp dan een ontwerp met behulp van een gemeenschappelijke weerstandsfactor.

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Samenvatting Samenvatting In hoofdstuk 5 wordt het zogenaamde ”set-up”-effect beschouwd. Dit is de verhoging van de weerstand van de boorpaal in de tijd ten opzichte van de aanvankelijke weer-stand. De aanvankelijke weerstand wordt ook wel de referentieweerstand genoemd; en het gedeelte van de in de tijd toenemende weerstand wordt de ”set-up”-weerstand ge-noemd. Hoewel het ”set-up” effect bij boorpalen niet zo sterk is als bij geheide palen, is het meenemen van het ”set-up”-effect in de LRFD voor boorpalen min of meer een nood-zaak. Door dit effect mee te nemen, is het ook mogelijk om een economisch ontwerp te verkrijgen. Een kalibratieprocedure voor de referentie- en ”set-up”-weerstandsfactoren wordt vervolgens gepresenteerd en toegepast op een casestudy op de locatie van de nieuwe SR20 eastbound bridge in Florida (V.S.). Vanwege de compatibiliteit in het kali-bratie-algoritme is de kalibratieprocedure die gebruikt is voor het effect van de ”set-up” volledig hetzelfde als die voor de schacht- en puntweerstandsfactoren.

Het kalibratiemodel met een gemeenschappelijke weerstandsfactor, zoals vermeld in hoofdstuk 4, is gewoonlijk gebaseerd op de eerste empirische verdelingen van de weer-stands-bias-factor. In het algemeen zijn deze verdelingen opgebouwd door een grote hoeveelheid gegevens die verzameld zijn op vele verschillende plekken. Dus, het toe-passen van een gemeenschappelijke weerstandsfactor voor een bepaalde plek, die uit de eerste empirische verdeling is gekalibreerd, is mogelijk niet geheel consistent. Dankzij de experimentele resultaten van de belasting van boorpalen op een testlocatie, maakt Bay-esiaanse gevolgtrekking het mogelijk de onzekerheid met betrekking tot de eerste em-pirische verdeling in termen van de experimentele belastingsresultaten voor een locatie te verminderen. Naar aanleiding hiervan kan een verdeling van de weerstands-bias-factor achteraf afgeleid worden. Een herkalibratieproces van een gemeenschappelijke factor van weerstand wordt vervolgens uitgevoerd en een aangepaste weerstandsfactor wordt verkregen. Op deze wijze kan met behulp van de aangepaste weerstandsfactor een nauwkeuriger ontwerp worden verkregen. De Bayesiaanse gevolgtrekking is toe-gepast op een casestudy voor de locatie van de 330 MW Uong Bi uitbreiding van de tweede thermische krachtcentrale in de provincie Quang Ninh (Vietnam). De afgeleide resultaten en toepasselijke opmerkingen worden gepresenteerd in hoofdstuk 6.

Het blijkt dat, met het gebruik van de LRFD, de weerstandsfactoren die zijn verkregen in het kalibratieproces voldoen aan de opgegeven streefwaarden van betrouwbaarheid. Deze aanpak vereist geen expliciet gebruik van de probabilistische beschrijving van sto-chastische variabelen, en is door haar eenvoud een vertrouwde benadering geweest voor technische ontwerpers. Echter, in de huidige praktijk zijn klanten en projectmanagers steeds meer ge¨ınteresseerd in het te bereiken betrouwbaarheidsniveau of de waarschijn-lijkheid van falen van een paalfundering. Het is dus van belang om RBD toe te passen voor een directe schatting van de betrouwbaarheidsniveaus van een specifieke boorpaal-fundering.

In hoofdstuk 7 wordt de betrouwbaarheid van een enkele boorpaal rechtstreeks bepaald door het gebruik van een berekening, die de koppeling maakt tussen het eindige elemen-ten pakket (Plaxis versie 9.0) en het numerieke probabilistische gereedschap (Prob2B). De betrouwbaarheid is niet alleen voor een intacte boorpaal, maar ook voor een defecte boorpaal beoordeeld, door uit te gaan van verschillende typen en groottes van defecten die zich bij de boorpalen kunnen voordoen. Twee wijzen van falen, de Geotechnische

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Samenvatting Samenvatting faal (GF) modus en de Structurele faal (SF) modus, worden in deze studie voorgesteld. De GF modus heeft betrekking op de geotechnische weerstand van boorpalen en de SF modus is gerelateerd aan de drukspanning in betonnen boorpalen. Beide modi worden ge¨evalueerd via de bereikte betrouwbaarheidsniveaus voor boorpalen, die onderworpen worden aan een specifieke combinatie van belasting van de bovenbouw. Op basis hier-van wordt de betrouwbaarheid hier-van een axiaal belaste paal uitgebreid beoordeeld. Aan de hand van een casestudy bij Pier T10 van de brug van An Dong, in de provincie Ninh Thuan (Vietnam), worden de bevindingen en opmerkingen gepresenteerd.

De conclusies en aanbevelingen zijn tot slot vermeld in hoofdstuk 8. Sommige van de modellen, zoals voorgesteld in hoofdstukken 4, 5 en 6, kunnen ook zeer goed worden toegepast voor geheide palen.

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Chapter 1

Introduction

1.1 Background

1.1.1 Introduction to bored piles

The usual role of a deep foundation is to transfer vertical loads through weak, near-surface soils to rock or strong soil layers at a certain depth. There are many types of deep foundations, and a classification can be made in various ways. Several factors that can be used in classifying deep foundations are given below (O’Neill and Reese,1999):

• Materials: Steel; concrete-plain, reinforced, or pre-stressed; timber; or some combi-nation of these materials.

• Methods of transferring load to the soil or rock: Principally in end-bearing, princi-pally in skin friction, or in some combination of the two methods.

• Methods of installation: Impact hammers, vibratory hammers, drilling an open hole; or by use of some special method.

• Influence of installation on soil or rock: Displacement piles, such as a closed-ended steel pile pipe, that displace a large volume of soil as the piles are driven; or non-displacement piles, such as H-pile or open-ended steel piles, that displace a rela-tively small volume of soil during driving, or bored piles, which result in essen-tially no displacement of the soil or rock.

A bored pile is a deep foundation that is constructed by placing fluid concrete in an open drilled hole, which is typically from 1.0 to 2.5 m in diameter, and up to 60 m in length, but which can extend to depths of as much as 90 m or more in special cases (Brown et al.,2010). A reinforcing steel cage can be installed in the excavation, if desired, prior to placing the concrete. Bored piles are also referred to as drilled piers, caissons, cast-in-dry-hole piles, and drilled shafts (the United States). The bored pile, as constructed, mainly supports axial loads through a combination of shaft and base resistances. The

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1.1 Background Introduction

Figure 1.1: Scheme of a bored pile subjected to loads.

large diameter bored pile is also capable of providing substantial resistance to lateral and flexural loads as illustrated in Figure1.1.

The methods of bored pile construction, which normally use rotary drilling rigs, can be classified in three main categories: (1) The dry method, (2) the casing method, and (3) the slurry method. The ”mixed” method is given when two of those methods are applied the same time for a bored pile. The method of construction that is selected depends on the subsurface conditions at a site. Because elements of the bored pile design can depend on the method of construction; consideration of the construction method is a part of the design process.

The dry method is applicable to soil and rock that are above the groundwater level and that will not cave or slump when the hole is drilled to its full depth. A geomaterial that meets this requirement is a homogeneous, stiff clay. The dry method can sometimes be used for soils under the groundwater level if the soils are low in permeability and the hole is excavated and concreted quickly, so that only a small amount of water will seep into the hole during the time the excavation is open.

The casing method is applicable to sites where the caving or excessive soil or rock de-formation can occur when a bore hole is excavated. Sometimes, soils or rocks that are stable when they are cut but which will slough soon afterwards. In such a case, a cas-ing (a simple steel pipe) needs to be used to keep the bore hole stable. Another notable case, in which a casing can be used, is a clean sand layer below the groundwater level underlain by a layer of impermeable limestone, into which the bored pile will penetrate. Since the overlying sand layer is water bearing, it is necessary to seal the bottom of the casing into the limestone layer to prevent flow of water into the bore hole. Most casing is recovered as the concrete is being placed and is called as temporary casing. In special

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Introduction 1.1 Background cases, the casing which remains and becomes a permanent part of bored pile is called the permanent casing.

Figure 1.2 describes the principle construction steps of a bored pile under the slurry method. The steps consist of drilling a hole into the soil with slurry, placing a reinforcing steel cage, and placing concrete. The slurry is utilized to keep the bore hole stable for the entire depth of the excavation. The soil conditions for which the slurry is used could be any of the conditions described for the casing method. The slurry method can be a feasible option in a permeable, water bearing soil, if it is impossible to seal casing into a stratum of soil or rock with low permeability. It can also be used in very deep holes with a narrow construction space where casing is hardly used since the difficulty of handling a very long casing.

(a) Drilling with slurry

(c) Placing concrete (d) Completed bored pile (b) Placing reinforcing cage

Figure 1.2: Slurry method of construction (O’Neill and Reese,1999).

It is also noted that there are two types of drilled piles which differ from the bored pile: Micropiles and Continuous Flight Auger (CFA) piles.

Micropiles are drilled piles which are typically less than 0.3 m in diameter and con-structed using a high-strength steel rod or pipe which is considered as a hard core of the pile. These piles can even be drilled into hard rock and achieve very high axial resistance for a very small structural component. Micropiles are favored in conditions where the small size is an advantage, and where lightweight, mobile drilling equipment must be employed (Armour et al.,2000).

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1.1 Background Introduction CFA piles are typically 0.3 to 0.9 m in diameter. These piles are distinguished from bored piles in that the pile is formed by screwing the continuous auger or displacement tool into the ground and then grouting or concreting through the hollow center of the auger; thus there is not an open hole at any time during the construction process. Guidelines for the design and construction of this type of pile are provided byBrown et al.(2007). Bored piles can be installed in a variety of soil and rock profiles, and are most efficiently utilized where a strong bearing layer is present. When the pile toe is founded within or on rock, extremely large axial resistance can be achieved with a small footprint. Bored piles can also be installed into hard, scour-resistant soil and rock formations to be found below scourable soil in conditions where installation of driven piles might be impracti-cal or impossible. Bored piles have increasing uses for highway bridges in seismiimpracti-cally active areas because of the flexural strength of a large diameter column of reinforcing concrete. Furthermore, bored piles may be used as foundations for other applications such as jetties, high-rise buildings, retaining walls, etc.

The most significant limitations of bored piles are related to the sensitivity of the con-struction procedure, to ground conditions and to the influence of ground conditions on bored pile performance. A summary of advantages and limitations of bored piles com-pared to other types of deep foundation is addressed byBrown et al.(2010) in Table1.1.

Table 1.1: Advantages and limitations of bored piles

Advantage Limitation

. Easy construction in cohesive materials, even rock

. Construction is sensitive to groundwa-ter or difficult drilling conditions

. Suitable to a wide range of ground con-ditions

. Performance of the bored pile may be influenced by the construction procedure . Visual inspection of bearing stratum . No direct measurement of axial

resis-tance during installation . Possible to have extremely high axial

re-sistance

. Load testing of high axial resistance may be challenging and expensive

. Excellent strength in flexure . Structural integrity requires careful con-struction

. A single bored pile foundation without the need for a pile cap

. A single bored pile foundation lacks re-dundancy and must have a high degree of reliability

. Low noise and vibration and therefore well suited to use in urban areas and near existing structures

. Requires an experienced, capable con-structor

. Can penetrate below scour zone into sta-ble, scour-resistant formation

. May not be efficient in deep soft soils without suitable bearing formation . Can be easily adjusted to accommodate

variable conditions encountered in pro-duction

. Requires thorough site investigation with evaluation of conditions affecting construction

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Introduction 1.1 Background 1.1.2 Design approaches

The Allowable Stress Design (ASD), also called the Working Stress Design (WSD), has been used in civil engineering since the early 1800’s. Under the ASD, a design load, which consists of the actual forces applied to piles, has to be less than the resistance di-vided by a global Factor of Safety (FS). This approach has several shortcomings, the most significant of which is that it does not provide a consistent framework for incorporating the sources of uncertainty into the design. In fact, each component of the load and the resistance has a different level of variability and uncertainty.

In the 1950s, the demand for a more economical design of piles brought about the use of the Limit State Design (LSD). Two types of limit states are usually considered, Ultimate Limit States (ULS), and Serviceability Limit States (SLS). The ULS pertains to structural safety and involves structural collapse or, in relation to piles, the ultimate resistance of soils. The SLS pertains to conditions, such as excessive deformations and settlements or deterioration of the structure that would affect the performance of the structure under expected working loads. The format of the LSD involves the application of Partial Safety Factors (PSFs) to increase the loads (factored loads) and to decrease the resistance (fac-tored resistance). This approach represents a fundamental improvement over the global factor of safety in the ASD, because the partial safety factors are applied directly to the uncertain quantities of load and resistance.

The PSFs in the LSD are determined subjectively based on two criteria: (1) A larger PSF should be applied to a more uncertain quantity. (2) The PSFs should result in approxi-mately the same dimensions as those obtained from traditional practice. This approach did not satisfy one of the basic requirements of limit state design, because the occurrence of each limit state is sufficiently improbable (Brown et al.,2010).

During the past two decades, the next step in the advanced LSD methodology has been to apply reliability analysis to establish the PSFs, in order to account for the uncertainty and variability for loads and resistances. One of the advantages of this approach is that all components of the structure, including the foundations, can be designed to a uni-form level of safety. However, the LSD has developed differently in North America and in Europe, mainly in the manner for calculating factored resistance for the ULS. This problem will be further discussed in Chapter2. In North America, Japan, South Korea, Hong Kong China, and recently in Vietnam, the LSD based on the reliability analysis has increasingly been used with a new name as the Load and Resistance Factor Design (LRFD), in which the PSFs applied to loads are termed load factors and those applied to resistances are termed resistance factors. Here, each resistance factor is the product of a calibration study in which a Limit State Function (LSF) is evaluated to predict a specific component of resistance (e.g., shaft or base or both types of resistance) to a spec-ified target reliability level. These efforts have led to a number of design codes around the world: For highway structure foundations (e.g., Barker et al., 1991; Nowak, 1999;

Paikowsky et al.,2004), for transmission line structure foundations in the United States (Phoon et al.,1995; Phoon et al.,2003), the National Building Code in Canada (Becker,

1996), and the Geo-Code 21 in Japan (Honjo and Kusakabe,2002).

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1.1 Background Introduction being replaced by the PSFs. Therefore, there is some degree of compatibility between the LRFD and the ASD. However, the calibration processes are often invisible to design engi-neers, many assumptions and simplifications (e.g., probability distributions of loads and resistances) and model uncertainties adopted in the calibration processes are unknown to the designer. This situation can lead to potential misuse of the PSFs that are only valid for the assumptions and simplifications adopted in a certain calibration case. Design engineers have no flexibility in changing any of these assumptions or simplifications be-cause works of re-calibration are usually unfamiliar to them. In addition, the PSFs in the LRFD are calibrated for some specified target reliability levels. A change in required reliability levels will cause a designer considerable difficulty in finding or selecting suit-able PSFs. Therefore, in current practice, designers as well as clients are becoming more and more attracted to a new calculation procedure, called the Reliability-Based Design (RBD), aiming to directly estimate reliability levels for pile foundations. In the RBD, it is possible to accommodate specific needs of a particular project when considering param-eter uncertainties (e.g.,Orr and Breysse,2008;Wang et al.,2011) or model uncertainties (e.g.,Teixeira,2012).

1.1.3 Quality control approaches

Most bored piles are constructed routinely and without difficulty, and are sound struc-tural elements. However, unexpected defects in a completed bored pile can arise during the construction process through errors in handling of slurry, reinforcing steel cages, con-crete, casings, and other factors. Therefore, tests to evaluate the structural soundness, or ”integrity”, of completed bored piles are an important part of bored pile quality control. This is especially important where non-redundant piles are installed or where construc-tion procedures are employed in which visual inspecconstruc-tion of the concreting process is impossible, such as underwater or under slurry concrete placement.

From a management perspective, post-construction tests on completed bored piles can be placed into two categories (Brown et al.,2010):

• Planned tests that are included as a part of the quality control procedure.

• Unplanned tests that are performed as part of a forensic investigation in response to observations made by an inspector or constructor that indicates a defect might exist within a pile.

Planned tests for quality control typically are Non-Destructive Tests (NDT) and are rel-atively inexpensive; such tests are performed routinely on bored piles. Meanwhile, un-planned tests performed as part of a forensic investigation will normally be more time-consuming and expensive, and the result can be more ambiguous than those of properly performed and planned tests.

The most common NDT methods are the Cross-hole Sonic Logging (CSL) method, the Gamma-Gamma Logging (GGL) method, and the Sonic Echo (SE) method. Of these methods, the CSL method is currently the most widely used test for quality assurance of bored pile concrete. For this method, vertical access tubes are cast into the pile prior to

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Introduction 1.2 Problem outline concrete placement. The tubes are normally placed inside the reinforcing steel cage and must be filled with water to facilitate the transmission of high frequency compressional sonic waves between a transmitter probe and a receiver one, which are lowered the same time into each access tube. Acoustic signals are measured providing evaluation of con-crete quality between the tubes. This method has advantages that are relatively accurate and relatively low cost. The limitation of this method is that it is difficult to locate defects outside the line of sight between tubes. The physical description for this method will be presented in detail in Chapter3.

A frequent response to concerns about the integrity of a bored pile, usually as a result of a problem observed during placement of concrete and identified by the inspector, or as a result of significant anomalies detected from non-destructive tests, is to institute a pro-gram of drilling and/or coring. Core sampling provides a direct visual examination of concrete and the opportunity to conduct strength tests on production concrete. However, drilling and coring are time-consuming and expensive, and which fall into the category of unplanned tests.

1.2 Problem outline

1.2.1 Objective and scope

Through some features regarding the development history of the design models and the current quality control approaches for bored pile foundations as mentioned above, this study will focus on the objectives as follows:

1. Evaluating the reliability of the CSL method, the most widely used method, in testi-fying the concrete quality of bored piles.

2. Calibrating resistance factors for the design of bored pile foundations, which follows the framework of the LRFD. Resistance factor calibrations are conducted for differ-ent resistance prediction methods considering differdiffer-ent construction methods. The calibrated resistance factors have to meet specified target reliability indices.

3. Applying a model of the reliability-based design aiming to directly estimate the re-liability of bored pile foundations. Parameter uncertainties of soils are included in soil models. The reliability of bored pile is evaluated by considering the situations of pile with and without defects in light of geotechnical and structural failure modes proposed.

1.2.2 Research questions

In order to clarify the objectives of this study as stated above, the following questions have to be answered. The chapter number, in which the corresponding question is an-swered, is shown in brackets.

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1.3 Thesis outline Introduction • In order to evaluate the reliability of the CSL method, some terms are given, which are the encountered probability, the detection probability, and the inspection prob-ability. So, what are the encountered, detection, and inspection probabilities? How to determine the optimal number of access tubes for the CSL method? (Chapter 3) • Until now, resistance factors have usually been calibrated through some reliability

methods, which are the First Order Second Moment (FOSM) method and the First Order Reliability Method (FORM). A question given is: How is a common resis-tance factor calibrated following the LRFD through the Monte Carlo Simulation (MCS)? (Chapter 4)

• By the Monte Carlo Simulation (MCS), how are the shaft and base resistance factors calibrated separately? What is the correlation between them? (Chapter 4)

• The set-up effect is represented as the increase in resistance of piles with time. How is the set-up effect incorporated into the LRFD aiming to reach an economic design? (Chapter 5)

• For a specific site, based on the Bayesian inference, how do the pile loading test results affect the initial calibrated resistance factors? (Chapter 6)

• How will the reliability of a bored pile change when considering the influence of various types of defect? To evaluate this problem, a model of the reliability-based design is applied and the parameter uncertainties of soils are included in this model. (Chapter 7)

1.2.3 Study approach

Most of chapters of the thesis follow the modelling approach using the knowledge of probabilistic methods. For each proposed model there will be an accompanied case study aiming to apply the proposed model. The data sets of bored pile foundations used in case studies are collected from many sources, mainly from the United States and Vietnam, including superstructures such as highway bridges and buildings.

The validation of the models is quite difficult due to the lack of physical experiments as well as actual proofs of past projects. Therefore, the model results are compared to those of the models of other authors that are widely accepted, or those have been accepted into the current design standards.

This study is dedicated to axially loaded bored pile foundations under the ultimate limit state. Other types of loads following the serviceability limit state are not mentioned herein; they are beyond the scope of this study.

1.3 Thesis outline

The thesis is structured as follows. Chapter 2 provides an overview on the development history of design approaches for bored pile foundations and probabilistic methods used.

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Introduction 1.3 Thesis outline In Chapter 3, the quality control approaches for the bored pile concrete are introduced. The cross-hole sonic logging method is chosen as a study object in which, the concepts as ”encountered, detection, and inspection probabilities” are presented. Through these con-cepts, the reliability of the cross-hole sonic logging method will sufficiently be evaluated. Next, in Chapter 4, a model is used to calibrate a common resistance factor. In addition, a new model is proposed to calibrate shaft and base resistance factors separately aiming to reflect exactly the difference between shaft and base resistance uncertainties. Chapter 5 presents the set-up phenomenon of piles. A model is proposed aiming to incorporate the set-up into the LRFD. A procedure for the LRFD-based design with the set-up is presented and an economic design may be attained. The Bayesian inference is used in Chapter 6 to update resistance factors as some pile loading tests are conducted on a site. Based on this information, the use of the Bayesian inference will reduce uncertainty of the model that was initially used to calibrate resistance factors; then new values of re-sistance factors can be obtained through the re-calibration process. Chapter 7 describes a model of the reliability-based design which is used to directly determine reliability of bored pile foundations with and without defects. Also, parameter uncertainties of soils and the influence of types of defects on reliability of piles are discussed in this chapter. Finally, conclusions and recommendations from the present study are drawn in Chapter 8. A schematic outline of this thesis is depicted in Figure1.3.

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1.3 Thesis outline Introduction

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Chapter 2

Design approaches

2.1 Introduction

In this chapter the design approaches, as introduced in Chapter1, will be discussed in more detail. The methodology, the advantages and the limitations of each approach will be presented and the logical succession from approach to approach will be discussed. Tracking the history of approaches, we can recognize that the probabilistic method or the reliability method has played a very important role in developing and improving design approaches. Current knowledge on probabilistic theory is broad, thus this chapter does not intend to thoroughly represent entire concepts as well as methods in this theory, but to briefly introduce those concepts and methods directly related to the study.

The outline of this chapter is as follows: Section2.2introduces the concept ”uncertainty”, one of the most basic concepts of the probabilistic theory. The design approaches are systematically presented in Section 2.3. The reliability methods applied to the design approaches are described in Section 2.4. Finally, the chapter ends with conclusions in Section2.5.

2.2 Uncertainty

In van Gelder (2000), uncertainties in all aspects related to the civil engineering were comprehensively described, and can primarily be divided into two categories:

• Inherent uncertainties, which stem from variability in known (or observable) popu-lations and, therefore, represent randomness in samples. It is impossible to reduce inherent uncertainties.

• Epistemic uncertainties, which come from a basic lack of knowledge of fundamen-tal phenomena and which may change as knowledge increases.

From the two categories of uncertainties mentioned above,van Gelder(2000) proposed subdividing the inherent uncertainty and epistemic uncertainty into five types of

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un-2.2 Uncertainty Design approaches certainty: Inherent uncertainty in time and in space, parameter uncertainty, distribution type uncertainty and, subsequently, model uncertainty as shown in Figure2.1.

Figure 2.1: Types of uncertainty (van Gelder,2000).

Two types of uncertainty, which are parameter uncertainty and model uncertainty, are directly related to the contents of the thesis. They are briefly introduced below.

2.2.1 Parameter uncertainty

This uncertainty occurs when the parameters of a distribution are determined by a lim-ited number of data. The smaller the number of data, the larger the parameter uncer-tainty. A parameter of a distribution function is estimated from the data and is thus a random variable. The parameter uncertainty can be described by the distribution func-tion of the parameter (van Gelder,2000).

2.2.2 Model uncertainty

Many design models aiming to estimate the design factor, like loads and resistances, are imperfect. They can be imperfect, because the physical phenomena are not known or insufficiently considered, or some variables of lesser importance are omitted in the design model for purpose of simplicity in calculations.

To construct a framework in which model uncertainty can be determined in the environ-ment of parameter and observation uncertainties, the parameter, the observation, and the model uncertainties should be defined and their relationships need to be clarified (Zhang,2009). Let g(θ)denote a scalar prediction model to simulate the behaviour of

a system, where θ is a vector denoting uncertain parameters. Due to the presence of model uncertainty, g(θ)may not be the same as the actual system response, y. Therefore,

a model correction factor is used to model the effect of model uncertainty. The exact value of the model correction factor may be system-dependent; but it is reasonable to assume that the value of the model correction factor may follow a common probabilistic distribution. Thus the model correction factor is described as a random variable (Zhang,

2009).

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Design approaches 2.3 Design approaches

et al.,1994;Moss et al.,2006) or in a multiplicative way (e.g.,Ang and Tang,1990;Barker et al.,1991;Zhang et al.,2001;Paikowsky et al.,2004;Allen,2005;Abu-Farsakh and Yu,

2010). The additive model correction factor, ε, is defined as the difference between actual performance, y, and prediction model, g(θ):

y= g(θ) +ε (2.1)

and the multiplicative model correction factor, λ, is defined as:

y =λg(θ) (2.2)

Hereafter, the multiplicative model correction factor, λ, will be used throughout the study by a new name ”bias factor” aiming to be compatible with other works of authors that are cited in this study.

2.3 Design approaches

The primary objectives of engineering design are safety, serviceability, and economy. Safety and serviceability can be improved by increasing the safety margins or levels of safety in order to reduce the probability of failure. However, this will increase the cost of the structure. Consideration of overall economy in design involves balancing the increased cost against the potential losses (i.e., failure). Regardless of the design philos-ophy and approach used, the basic design criterion is that the capacity or resistance of the system must be greater than the demand or loads on the system for an acceptable or required level of safety. In equation format, the design criterion is given by:

Resistance (R) > Load e f f ects(Q) (2.3) The design approaches have not remained stagnant, but have changed over the years in response to a changing social environment, higher public awareness and expectations, and advancements in technology (Becker,1996). The comparison between the load ef-fects and resistance for an assessment of safety can be conducted in various ways, in-cluding the following: (1) A single global factor of safety as embodied in allowable stress design; (2) partial factors of safety as embodied in limit state design; and (3) reliability-based design.

2.3.1 Allowable stress design

The Allowable Stress Design (ASD), also called the Working Stress Design (WSD), has been the traditional design basis in civil engineering since it was first introduced in the early 1800’s. Under the ASD, an applied load, Qa, which consists of actual forces applied

to piles, has to be less than the ultimate resistance, Ru, divided by a global Factor of

Safety (FS):

Qa ≤

Ru

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2.3 Design approaches Design approaches A global factor of safety is used, which lumps all uncertainties associated with the de-sign process into a single value with no distinction made as to whether it is applied to resistance or to load effects. The assessment of the level of safety of the structure is made on the basis of global factors of safety, which were developed from previous experience with similar structures in similar environments or under similar conditions. The values of the FS selected for design reflect past experience and the consequence of failure. The higher the uncertainty, the larger the FS. Table2.1presents FS values used in the Standard Speci f ications f or Highway Bridges (AASHTO,1997) in conjunction with different levels of control in design analysis and during construction. Presumably, when a more reliable and consistent level of control is used, a smaller FS can be used, which leads to a more economical design.

Table 2.1: Factors of safety on ultimate axial geotechnical resistance based on level of construction control (AASHTO,

1997)

Basis for design Increasing design/construction

and control level control

Subsurface exploration √ √ √ √ √

Static calculation √ √ √ √ √

Dynamic formula √

Wave equation √ √ √ √

CAPWAP(*)analysis √ √

Static loading test √ √

FS 3.50 2.75 2.25 2.00 1.90

(*)_{CAse Pile Wave Analysis Program (}_{Rausche et al.}_,₁₉₈₅_).

In the ASD, both the load and resistance are generally considered to be deterministic and characterized in calculation by a single value. In Figure2.2(a), Eq. 2.4 implies that both load and resistance are well defined, each with a unique value. However, loads and resistances are dependent upon a number of variables. In reality, ranges in loads and resistances exist following certain frequency distribution diagrams as shown in Fig-ure2.2(b), which are called Probability Density Functions (PDF) of load and resistance, respectively. Thus, unique values do not exist for loads and resistances.

The probability density functions, as shown in Figure 2.2(b), can be assigned specific values, such as the mean of the distribution curves, Q and R, or nominal values, Qn

and Rn, to assist in characterizing the frequency diagrams. The design values do not

necessarily need to be taken as the mean values, although this is common geotechnical design practice. The design process may also involve overestimating the mean load ef-fects (i.e., Qn≥Q) and underestimating the mean resistance (i.e., Rn≤R) as presented in Becker(1996).

Two alternative definitions of the FS can be defined as follows: Mean FS= R

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Design approaches 2.3 Design approaches 0 1.0 (a) In ASD Load or resistance (Q,R) Probability of occurence 0 (b) In reality Load or resistance (Q,R) Frequency of occurence Safety margin = Safety margin = PDF of PDF of Qa Ru Q Qn Rn R Ru− Qa R − Q Q R

Figure 2.2: Definitions of load and resistance in ASD and in reality.

Nominal FS= Rn

Qn

(2.6) The values for FS as defined in Eqs. 2.5 and2.6 do not equal each other; the mean FS is larger than the nominal FS. The intersection of the Q and R curves, depicted by the shaded region in Figure2.2(b), represents a condition where, under some combinations of loads and resistances, the resistance is less than the load and failure can occur. This intersection indicates that a probability of failure exists for some combinations of loads and resistances. For given distributions of load and resistance, different values of FS can be calculated, meanwhile the actual level of safety or probability of failure remains the same. Therefore, the global FS in the ASD does not provide a consistent measure of the level of safety or probability of failure.

0

(a) Well−defined Q and R

Load or resistance (Q,R) Frequency of occurence 0 (b) Poorly−defined R Load or resistance (Q,R) Frequency of occurence 0 (c) Poorly−defined Q and R Load or resistance (Q,R) Frequency of occurence R Q R Q R Q Q R R Q Q R

Figure 2.3: Possible load and resistance distributions.

The shortcoming of the ASD is described in Figure2.3through consideration of the dis-tribution curves. Figure2.3(a) represents the case where the load and resistance are well defined and controlled. There is a relative low probability of failure as shown by the small overlap area of the Q and R distribution curves. The case, where the load is well defined, but the resistance is not, is illustrated in Figure2.3(b). In this case both the load

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2.3 Design approaches Design approaches and resistance are not well defined, as represented by the broad distribution curves as shown in Figure2.3(c). It can be seen that, although the value of Q and R are the same and, therefore, FS is the same for all three cases, the overlap area is much larger; respec-tively the probability of failure is much higher with respect to the second and third cases. It is noted that the overlap area denoted by the shaded area is not equal to the probability of failure; however, it is related to the probability of failure.

2.3.2 Limit state design

Limit states are defined as conditions under which a structure or its component members no longer perform their intended functions. Whenever a structure or part of a structure fails to satisfy one of its intended performance criteria, it is said to have reached a limit state (Becker,1996).

In the Limit State Design (LSD), two types of limit states are usually considered: Ultimate Limit States (ULS) and Serviceability Limit States (SLS).

The ULS pertains to structural safety and to defining components that are dangerous (Allen,1994); they involve the total or partial collapse of the structure, e.g., strength, ul-timate bearing capacity, overturning, sliding, and so on. The ULS conditions are usually checked using separate Partial Safety Factors (PSFs) on loads and resistances. Because of their relationship to safety, the ULS conditions have a low probability of occurrence for well-designed structures (Duncan et al.,1989).

The SLS represents conditions which affect the function or service requirements of the structure under expected service or working loads. The SLS includes conditions that may restrict the intended use of the structure such as deformation, cracking, excessive total or differential settlement, excessive vibrations, local damage, and deterioration. Deforma-tion or settlement of foundaDeforma-tions could also cause loss of serviceability in the building. The SLS may be viewed as those things that ”make life difficult” (Allen,1994). The SLS has a higher probability of occurrence than the ULS (Duncan et al.,1989).

Note that the SLS conditions are checked using unfactored loads and geotechnical prop-erties. A partial factor of one is used on all specified load effects and on the characteristic values of deformation and compressibility properties of soils, which are generally based on conservative mean values obtained from in situ or laboratory tests. In this sense, the methodology of calculation in connection with the SLS in the LSD is virtually identical to that of the ASD (Becker,1996).

In geotechnical design, a serviceability condition or settlement criterion frequently con-stitutes the primary limit state. The design would be based on specific SLS; the ULS would be checked subsequently. Regardless of the complexity of calculation, all limit states designs are carried out to satisfy the following criteria:

• The ULS:

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Design approaches 2.3 Design approaches • The SLS:

De f ormation≤ Tolerance de f ormation to remain serviceable (2.8)

Becker(1996) featured the development history of geotechnical limit states design as fol-lows: The first uses of limit state concepts in geotechnical engineering include the work of Coulomb in 1773 who, based on limit states consideration, derived the critical height of a vertical embankment in a cohesive soil. In 1857, Rankine established limit states of active and passive earth pressure. Therefore, limit state problems in soil mechanics such as theories of earth pressure and bearing capacity, stability of slopes, and seepage were already treated in the 18th and 19th centuries. In 1943, Terzaghi pointed out two principle groups of problems in geotechnical limit states, namely, stability problems and elasticity problems. The above two groups of problems coincide with the ULS and SLS, respectively, in the LSD.Taylor(1948) introduced partial safety factors for the cohesive and frictional components (i.e., c0and tanϕ0) of the shear strength of soil for the stability analysis of slopes. This approach was subsequently formalized byBrinch Hansen(1953,

1956) who established a philosophy of geotechnical design based on separately applying partial safety factors to loads and strength.

In this approach, the characteristic load effects are multiplied by their respective par-tial factors to obtain design loads, and the strength parameters are divided by their re-spective partial factors to arrive at the design strength parameters for the calculation of geotechnical resistance:

Design load =Characteristic load×Load f actor(γ) (2.9)

Design strength= Characteristic strength

Partial strength f actor(fc or fϕ)

(2.10) The values of the partial factors are summarized in Table 2.2. Meyerhof (1995) noted that the partial factors, fromBrinch Hansen (1953,1956) until Eurocode 7 (CEN,1992), were chosen to give the same design as the conventional ASD. Scrutinizing some partial factors in Eurocode 7 (CEN,2004), it can be seen that these values have undergone only minor changes during the past 50 years.

The use of the LSD with partial safety factors has developed differently in North America and in Europe, mainly in the manner of calculating factored resistances for the ULS. This problem is presented following (Becker,1996):

In the f actored strength (European) approach, partial factors are applied directly to only the strength parameters that contribute to overall resistance for each applicable limit state. In particular, specified partial factors are applied to the individual soil strength properties of angle internal friction (tanϕ0) and cohesion (c0) prior to using them in cal-culating design resistance. In the f actored resistance (North American) approach, an overall resistance factor is applied to the resistance for each applicable limit state. With this approach, the calculated ultimate resistance is firstly calculated using characteristic strength parameters (unfactored strength parameters); the calculated ultimate resistance is then multiplied by a single resistance factor to obtain the factored resistance for design.

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2.3 Design approaches Design approaches Table 2.2: Summary of partial factors for foundation design

Item Brinch Hansen DS 415 Eurocode 7 Eurocode 7

(1953) (1956) (DI 1965) (CEN 1992)(*) (CEN 2004)(*) Loads .Dead loads 1.0 1.0 1.0 1.1 (0.9) 1.1 (0.9) .Live loads 1.5 1.5 1.5 1.5 (0) 1.5 (0) Soil strength .Friction (tanϕ0) 1.25 1.2 1.25 1.25 1.25 .Cohesion (c0) Spread foundations - 1.7 1.75 1.4 - 1.6 1.0 - 1.4 Pile foundations - 2.0 2.0 1.4 - 1.6 1.0 - 1.5

Ultimate pile capacity

.Load tests - 1.6 1.6 1.7 - 2.4 1.0 - 1.4

(*)_{Values in parentheses indicate minimum factors for certain load combinations.}

A comparison of the European and North American approaches is shown in Figure2.4. For both approaches, the design (factored) resistance must be greater than or equal to the design (factored) load effects. The primary difference in the conceptualization lies in the resistance side. The load effects side is identical for both approaches; the characteristic load effects are multiplied by appropriate load factors to produce the design (factored) load effects for design as indicated in Eq. 2.9. However, different values of load factors are used in the two approaches.

Figure 2.4: Comparison of limit states design approaches for the ULS (Ovesen and Orr,

Reliability-Based Design and Quality Control of Bored Piles

Reliability-Based Design and Quality Control

of Bored Piles

Reliability-Based Design and Quality Control

of Bored Piles

Contents

Summary

Samenvatting

Chapter 1

Introduction

1.1

Background

1.2

Problem outline

1.3

Thesis outline

Chapter 2

Design approaches

2.1

Introduction

2.2

Uncertainty

2.3

Design approaches