- Email: [email protected]

Contents lists available at ScienceDirect

Composite Structures journal homepage: www.elsevier.com/locate/compstruct

Partial safety factors for CFRP-wrapped bridge piers: Model assessment and calibration Joan R. Casas ⇑, José L. Chambi Construction Engineering Department, Technical University of Catalonia – BARCELONATECH, C/Jordi Girona 1-3, Campus Nord, Mòdul C1, 08034 Barcelona, Spain

a r t i c l e

i n f o

Article history: Available online 1 August 2014 Keywords: Safety factor Carbon ﬁber composites Bridges Strengthening Model error Pier

a b s t r a c t Concerning the strengthening or seismic retroﬁtting of bridge piers, the use of ﬁber reinforced polymers (FRP) has increased as an element of conﬁnement of concrete due to its easy application and excellent mechanical and chemical properties. However, due to the lack of codes and standards and the lack of experience in the long term behavior, uncertainties exist in the calculation bases along the dimensioning of this reinforcement and more precisely in the partial coefﬁcients of safety to be adopted for the material properties. As a consequence, bridge engineers are reluctant to use composite materials in the strengthening of damaged bridge piers. To try to overcome this problem, this paper describes the methodology for a reliability-based calibration of the partial safety factors to be used for the conﬁned concrete in the design of strengthening to axial-bending forces using CFRP. The method requires the deﬁnition of a response model jointly with the statistical deﬁnition of the model error. This is discussed in the ﬁrst part of the paper. The reliability-based procedure is developed based on the design equation and the corresponding model. A simple set of partial safety factors is ﬁnally proposed and compared with those proposed in existing guidelines. Ó 2014 Elsevier Ltd. All rights reserved.

1. Introduction In recent years, the use of composite materials or ﬁber reinforced polymers (FRP) as a strengthening alternative of concrete elements in compression has increased due to their excellent mechanical and chemical properties. Many theoretical and experimental studies have shown that the lateral conﬁnement of columns mainly increases the strength and the ductility of concrete [1–6]. As the eventual failure of FRP conﬁned concrete is by rupture of the FRP jacket, the ultimate condition of the conﬁned concrete is often characterized by the compressive strength and ultimate axial deformation, which are closely related to the ultimate strain (or tensile strength) of the FRP. Despite the steady progress in the investigation and the improvement of these composites, there are still weaknesses on the application as reinforcement in concrete structures, although some guidelines for the reinforcement design and construction procedures concerning to this material are available [7–13]. One of the important gaps that slow the implementation of this type of reinforcement is the lack of objective safety criteria. Because of the relative novelty of this technology, a more complete understanding of the behavior ⇑ Corresponding author. Tel.: +34 934016513. E-mail address: [email protected] (J.R. Casas). http://dx.doi.org/10.1016/j.compstruct.2014.07.032 0263-8223/Ó 2014 Elsevier Ltd. All rights reserved.

of FRP-conﬁned pier elements and their failure mechanisms need to be gained before the wide spread adoption of this technology in engineering practice. As a minimum, the conﬁdence levels in the safety margins of existing and proposed design criteria should be ascertained. This would require an objective estimation of the biases implied in existing and recently proposed design criteria and an analysis of the variability of the error of the predicted ultimate loads. Hence, there is a need to develop methods and models to take into account the inherent uncertainty in the strengthening of axially loaded members with composite materials through a partial safety factor to apply in their dimensioning. The design process of a new concrete structure or the strengthening of an existing one should verify:

Rd P Sd

ð1Þ

Being Rd and Sd the design values of the resistance and actions respectively. When using a semi-probabilistic approach, the design values for a structural concrete element are calculated as:

Rd ¼ R Sd ¼

f ck f yk ;

ð2Þ

cc cs

n X

n X

i¼1

i¼1

cfi Ski ¼

cfi SðQ ki Þ

ð3Þ

268

J.R. Casas, J.L. Chambi / Composite Structures 118 (2014) 267–283

where: Ski = characteristic value of the action ‘‘i’’, due to load Qki; cﬁ = partial safety factor of action ‘‘i’’; fck = characteristic strength of concrete; cc = partial safety factor of concrete strength; fyk = characteristic strength of reinforcing/prestressing steel; cs = partial safety factor of steel strength. If the partial safety factors have been appropriately calibrated, then a required level of safety (deﬁned during the calibration process) is assured by veriﬁcation of Eq. (1). The codes and standards dealing with the design of new concrete structures provide appropriate values of the partial safety factors for concrete and steel. However, when dealing with the retroﬁt of an existing concrete column, to be strengthened through the conﬁnement of the concrete core with the addition of a CFRP jacket, the question arises about the suitability of using the same partial safety factor as used for the unconﬁned concrete. As the resisting mechanism of the conﬁned concrete differs from that in un-conﬁned concrete and other uncertainties (as the interaction between concrete and composite) may be present, it seems logical to use a different design value, obtained as: 0

f ccd ¼

0 f cc

ccc

ð4Þ

with: 0 f ccd design value of the strength of conﬁned concrete; 0 f cc characteristic/nominal value of conﬁned concrete strength; ccc partial safety factor of conﬁned concrete strength. Different models exist for the calculation of the nominal value of the conﬁned concrete. The question is: what should be the value of the partial safety factor ccc to use in the design equation to get a safe design? Some codes and recommendations deﬁne safety factors for the design of FRP-conﬁned RC columns. However, detailed probabilistic information to support the selected resistance factors is lacking and the safety factor is ﬁxed based on the experience and engineering judgment. The aim of the present study is to propose objective and appropriate reliability-based design equations with properly calibrated safety factors that can be used during the design of a strengthening using carbon ﬁber reinforced polymer (CFRP) wraps to enhance the capacity of piers of existing bridges subjected to combined axial/bending actions. One of the ﬁrst works related to the reliability in FRP-strengthened structures is due to Plevris et al. [14]. In this case, the investigated elements were beams strengthened in ﬂexure with CFRP laminates. The failure mode considered was the failure in bending. In the case of FRP-wrapped columns there are few studies on the subject of reliability evaluation [15–17]. Even less experiences are available dealing with the reliability-based calibration of safety factors for FRP-conﬁned concrete. In his study, Val [15] evaluated the reliability of FRP-conﬁned reinforced concrete circular columns and proposed a modiﬁcation of the strength reduction factor used in the ACI 318-99 for circular columns in compression with low eccentricity ratio. The reduction factor depends on the conﬁnement ratio. He assessed an overall resistance factor, rather than the partial material factors as shown in Eq. (2). The sensitivity analysis carried out by Val concludes that only 4 random variables have signiﬁcant inﬂuence on the column reliability: the compressive strength of unconﬁned concrete, the strength of conﬁned concrete (which in turn depends on the composite characteristics), the model error and the live load. Al-Tersawy et al. [17] conducted a study of the reliability of short RC columns strengthened using CFRP wraps and calibrated the strength reduction factors for the Egyptian Code of FRP

concrete. They show how the reduction factors depend on the steel ratio of reinforcement, mainly for low eccentricities. Zou and Hong [18] proposed a partial safety factor for concrete resistance for FRP-conﬁned columns in buildings designed according to the Canadian Code A23.3-04, based on a reliability-based calibration to achieve a 50 year target reliability index around 3.5. A relevant result of this study is that the reliability level of the FRP-conﬁned reinforced columns is almost insensitive to the reinforcement ratio. The ﬁnal objective of the present study is to propose appropriate reliability-based design equations with properly calibrated safety factors. The statistical analysis of the selected existing conﬁning models will provide the necessary input to calibrate appropriate safety factors that should be applied in conjunction with the selected models. In this way, future design codes could provide to design engineers the tools necessary to use FRP-wrapped concrete bridge piers strengthening schemes that would lead to uniform, consistent and economical safety levels. 2. Model assessment For an appropriate calibration, the ﬁrst step is to derive the most accurate design equations for the mechanical properties of the conﬁned concrete, based on the available theoretical models, jointly with the statistical characterization of the random variable ‘‘model error’’. This random variable is deﬁned as the ratio of the actual response to the response predicted by the model. The model error should be statistically characterized by deﬁning the type of random variable and its mean value (or bias ratio) and standard deviation (or coefﬁcient of variation). This is carried out in the present chapter. Later on, these equations and random variable will be applied to a set of bridge piers representative of a big population of existing bridges. Various models have been proposed to represent the stress– strain behavior of conﬁned concrete elements by FRP, subjected to compression, with circular and square sections. Ozbakkaloglu et al. [19] report a total of 88 models available. According to Lam and Teng [20], these models are classiﬁed into two main categories: design-oriented models and analysis-oriented models. In design models, the axial compressive strength, the ultimate strain and stress–strain behavior are determined using expressions explicitly obtained as the better approximation to the experimental data. They are generally deﬁned using simple closed-form expressions and are suitable for direct use in practical design. Analysis-oriented models allow to predict stress–strain diagrams implicitly by iterative numerical processes. They account for the interaction between the conﬁning material and the concrete core. A complete compilation of analysis-oriented models has been published by Jiang and Teng [21]. A complete summary of both design and analysis models is available in Ozbakkaloglu et al. [19]. From the available models, only design-oriented models are considered in this research. This is due to the ﬁnal objective, i.e., the calibration of safety factors to be used in the design. This decision is based on the following facts: 1. A calibration process requires a high-number of calculations and simulations to obtain the ultimate strength and strain of the conﬁned element. Therefore, simple and easy to apply models are required. This is accomplished by design-oriented models. 2. The safety factors are derived to be used in the design of the strengthening of existing structures and, hence, jointly with design-oriented models for the prediction of axial compressive strength and ultimate strain of conﬁned concrete. Therefore, it

J.R. Casas, J.L. Chambi / Composite Structures 118 (2014) 267–283

269

results more logical and accurate to calibrate those safety factors with design-oriented models. 2.1. Statistical appraisal of existing models As mentioned before, in [19], a complete review and assessment of stress–strain models was carried out. The model performances, established in terms of accuracy and consistency were quantiﬁed using four statistical indicators: the mean square error, the average absolute error, the linear trend slope and the standard deviation. The two statistical indicators used to establish overall model accuracy were the mean square error and average absolute error. However, none of the four indicators obtained are useful in the statistical deﬁnition of the model error. Because of that, and the fact that the data-base used for the study was not available, a new data base has been deﬁned in the present study. From the available conﬁnement models described in [19], some have been selected to check their accuracy when compared to existing experimental results. These models, which are design-oriented and cover a large spectrum of years, from 1988 to 2010, are the following: Mander et al. [22], Pilakoutas and Mortazavi [23], Toutanji [5], Spoelstra and Monti [24], Eid and Paultre [25], Teng, et al. [26], Wu and Zhou [27]. For the Spoelstra and Monti model, the design-oriented simpliﬁed version is used as described in [9]. A complete description of them as well as of the experimental data base with a total of 126 tests can be found in Chambi [28]. The experimental data is built up from 14 references, ranging from 1997 to 2009. All tests were carried out in cylindrical specimens conﬁned with carbon composites. The data base is shown in Appendix A. The items considered are the year, the CFRP properties as modulus of elasticity, number and thickness of layers, geometrical data, ultimate 0 strength (f co ) and strain (eco) of the non-conﬁned concrete and 0 strength (f cu ) and ultimate strain (ecu,exp) of conﬁned concrete. The hoop strain in the ﬁbre at failure (eh,rup) is also indicated. For few tests only, also the strain in the concrete in the transversal direction is displayed. f0 The random variables considered in the analysis are f 0cu;exp and ecu;exp ecu;mod ,

cu;mod

where ‘‘exp’’ refers to the experimental value and ‘‘mod’’ to

the value obtained from the model. It should be pointed out that the ultimate strain of the composite jacket obtained in the test, is generally lower than the ultimate strain of the material obtained from a tensile test. Lam and Teng [20], suggest that in the conﬁnement models, ej must be taken as the failure strain of the ring, eh,rup, measured in the FRP jacket and not as the ultimate strain of the FRP material, efrp, as done in several existing models. The realizations of the two random variables as obtained from the 126 tests are displayed in Figs. 1–7 for the strength, and in Figs. 8–12 for the strain. The models of Pilakoutas and Wu do not provide ultimate strain values.

0

0

Fig. 1. f cu;exp: =f cu;mod: vs test number. Model of Mander et al. [22].

0

0

Fig. 2. f cu;exp: =f cu;mod: vs test number. Model of Pilakoutas and Mortazavi [23].

0

0

Fig. 3. f cu;exp: =f cu;mod: vs test number. Model of Toutanji [5].

0

0

Fig. 4. f cu;exp: =f cu;mod: vs test number. Model of Spolestra and Monti (simpliﬁed) [24].

0

0

Fig. 5. f cu;exp: =f cu;mod: vs test number. Model of Eid and Paultre [25].

0

0

Fig. 6. f cu;exp: =f cu;mod: vs test number. Model of Teng et al. [26].

270

J.R. Casas, J.L. Chambi / Composite Structures 118 (2014) 267–283

0

0

Fig. 7. f cu;exp: =f cu;mod: vs test number. Model of Wu and Zhou [27].

Fig. 8. ecu,exp./ecu,mod. vs test number. Model of Mander et al. [22].

Fig. 12. ecu,exp./ecu,mod. vs test number. Model of Teng et al. [26].

In Table 1 are shown the mean, standard deviation and coefﬁcient of variation of the random variable model error in the prediction of maximum compressive strength (a) and ultimate strain (b) obtained with the models. From Figs. 1–12 and the values in Table 1, it may be concluded that the model which provides a better approximation is the one by Teng et al. [26], as it shows a mean value closer to 1 and the lowest coefﬁcient of variation for both strength and strain. Similar values are also obtained for the model of Eid and Paultre [25]. Therefore, Teng et al. model will be used for the safety factor’s calibration. This result agrees with the results reported in [19], where it is indicated that from the design-oriented models the top performing strength enhancement models were those proposed by Lam and Teng [20] whereas the best performing strain enhancement models were those proposed by Tamuzs et al. [29] and Teng et al. [26]. This model, with some modiﬁcation, has been adopted for design by the Concrete Society [11] and ACI [7]. f0 Further statistical analysis show that the random variables f 0cu;exp cu;mod

e

and e cu;exp , when the model values (denominator) are obtained with cu;mod

Fig. 9. ecu,exp./ecu,mod. vs test number. Model of Toutanji [5].

the Teng et al. model can be statistically described as Normal variables (see Figs. 13 and 14) with mean and standard deviation as indicated in Table 1. In fact, the values displayed in a Normal probability plot are quite close to a straight line, more for strength than for strain. 3. Calibration of partial-safety factors To start with the process of calibration and once the selection of the theoretical model and corresponding design equation are done, the next step is to deﬁne the range of possible structures/elements where the obtained safety factors will be of application. Therefore, the bridge and pier population is presented next. 3.1. Bridge population

Fig. 10. ecu,exp./ecu,mod. vs test number. Model of Spolestra and Monti [24].

Fig. 11. ecu,exp./ecu,mod. vs test number. Model of Eid and Paultre [25].

The bridge population where the calibration was performed is represented by continuous multi-span bridges (maximum spanlength 45 m) with circular concrete piers and a maximum height of 10 m. The piers may be composed of either one or two columns. This covers an important number of short and medium span prestressed/reinforced concrete bridges present in actual highways and railways. Therefore, a large amount of the concrete bridge population is taken into account. Also, conﬁnement by FRP in circular columns is more popular due to better conﬁnement than in rectangular shapes. For the selected span-length range, the most representative concrete cross-sections are precast girders plus upper slab and voided and un-voided slabs. Because in precast girders normally bents are used, providing a frame action in the transversal direction, the case of piers in concrete slabs is more critically as they act as independent elements. Therefore,

271

J.R. Casas, J.L. Chambi / Composite Structures 118 (2014) 267–283 Table 1 Mean value (lx), standard deviation (rx) and coefﬁcient of variation (COVx) for the conﬁnement models

lx rx COVx

Mander et al.

Pilakoutas

Toutanji

Spolestra

a

b

a

b

a

b

a

0.903 0.105 0.116

1.008 0.244 0.242

1.046 0.117 0.112

– – –

0.912 0.073 0.080

1.109 0.274 0.247

1.172 0.128 0.109

f 0cu;exp: f 0cu;mod:

e

¼ a; e cu;exp: ¼ b. cu;mod:

Eid and Paultre

Teng et al.

Wu and Zhou

b

a

b

a

b

a

b

1.105 0.384 0.348

1.022 0.082 0.080

0.920 0.215 0.234

1.083 0.080 0.074

0.910 0.212 0.233

1.150 0.138 0.120

– – –

the following representative bridges and piers have been analysed: 1- Post-tensioned concrete 3-span with massive slab. In the case of unique column per support-line, the column has a diameter of 1.0 m. The case of 2 columns corresponds to a diameter of 0.6 m (see Fig. 15). 2- Post-tensioned concrete 4-span with voided slab. The central pier (P-1) and the lateral piers (P-2) are of 1.10 m in diameter in the case of unique column and of 0.8 m in diameter for 2 columns (see Fig. 16).

0

0

0

0

Fig. 13. Normal probability plot of (f cu;exp: =f cu;mod: ; Zi).

Fig. 14. Normal probability plot of (f cu;exp: =f cu;mod: ; Zi).

The bridges are designed according to Eurocodes of actions and concrete [30,31]. They are continuous over piers and supported in piers and abutments by elastomeric bearing pads. Therefore, the axial force is the dominant action in the piers, due to the effect of self-weight, permanent loads and trafﬁc action. The axial force is accompanied by a bending moment due to the horizontal forces present at the top of the piers. These horizontal forces are caused by 3 main actions: (1) the long-term longitudinal displacement due to post-tensioning, creep, shrinkage and temperature variation along the year, (2) the braking forces in the longitudinal direction due to the vehicles in the deck and (3) the wind actions in the transversal direction. As a result of those actions, and taking into account the partial safety factors present in the Eurocode, the design value of the axial force (Nd) and the design value of the bending moment at the bottom of the pier (Md) were obtained, and the amount of longitudinal reinforcement was calculated at the ultimate limit state (ULS). In all cases, the most critical situation is due to the bending moment in the longitudinal direction. In Figs. 17–22 are shown the cross-section and steel reinforcement for both bridges with one or two columns per pier, and the corresponding interaction diagram (bending moment-axial force diagram) and the design point (Nd, Md). The interaction diagrams for

Fig. 15. Elevation and cross-section of 3-span prestressed concrete bridge (dimensions in m).

272

J.R. Casas, J.L. Chambi / Composite Structures 118 (2014) 267–283

Fig. 16. Elevation and cross-section of 4-span prestressed concrete bridge (dimensions in m).

Fig. 17. Interaction diagram: original and with loss of steel (3-span, massive slab, 1 column per support line).

Fig. 18. Interaction diagram: original and with loss of steel (3-span, massive slab, 2 columns per support line).

the original piers are obtained with the design values of the resistance of the materials (un-conﬁned concrete and reinforcing steel). The stress–strain diagram for the un-conﬁned concrete and reinforcing steel are those derived by Mander et al. [22] and Caltrans [32], respectively. The characteristic strength of the concrete is

25 MPa and for the reinforcing steel, the characteristic yielding point is 400 MPa. Apart of the original M–N diagrams, the diagrams corresponding to a loss of reinforcing steel area of around 60% are also plotted. In this case, the non-compliance with the safety conditions requires the strengthening by CFRP wrapping. The design of

J.R. Casas, J.L. Chambi / Composite Structures 118 (2014) 267–283

Fig. 19. Interaction diagram: original and with loss of steel (4-span, voided slab, Pier 1, 1column per support line).

Fig. 20. Interaction diagram: original and with loss of steel (4-span, voided slab, Pier 1, 2columns per support line).

Fig. 21. Interaction diagram: original and with loss of steel (4-span, voided slab, Pier 2, 1column per support line).

273

274

J.R. Casas, J.L. Chambi / Composite Structures 118 (2014) 267–283

Fig. 22. Interaction diagram: original and with loss of steel (4-span, voided slab, Pier 2, 2 columns per support line).

the required strengthening will serve as the basis for the calibration of the partial safety factors of conﬁned concrete. 3.2. Calibration The calibration process is done following the strengthening design of the damaged piers. To this end, the assumption is that because of a deterioration process, the piers loss a certain amount of the reinforcing steel. Therefore, the CFRP jacket is designed (the thickness of the CFRP) to restore to the pier a required level of safety (target level). When designing the amount of CFRP for repair, the main unknown is the partial safety factor to be applied to compressive strength of concrete (ccc), as it may differ from the one proposed in the design codes for conventional un-conﬁned reinforced concrete (cc). The design value of compressive strength of conﬁned concrete is expressed as: 0

0

f ccd ¼

f cc

ccc

ð5Þ

0

where f cc is the nominal strength of conﬁned concrete. According to the study carried out in chapter 2, the stress–strain relationship to be used for the conﬁned concrete is the one derived by Teng et al. [26]. The nominal strength of the conﬁned concrete may be evaluated as the nominal strength of the un-conﬁned concrete (fck) plus and additional part due to the lateral conﬁnement pressure (fl), represented by the value k, dependent of the conﬁnement model considered. 0

f cc ¼ ðf ck þ k f l Þ

ð6Þ

For the Teng et al. model, this equation is as follows in the case of always increasing stress–strain relationship (qK > 0.01): 0

f cc ¼ 1 þ 3:5ðqK 0:01Þqe fck 2EFRP t qK ¼ ðf ck =eco ÞD

qe ¼

eh;rup eco

ð7Þ

EFRP = elastic modulus of FRP along the circumferential direction; t = total thickness of FRP jacket; eh,rup = hoop rupture strain of the FRP jacket; D = diameter. It is worth mentioning that eh,rup is normally much lower than the ultimate strain of the composite alone. According to Pessiki et al. [33], an efﬁciency factor, ke, can be deﬁned as:

eh;rup ¼ ke efrp

ð10Þ

where efrp is the ultimate strain of the composite in the tension test of the composite. The value of ke depends on the type of FRP and a value of 0.586 has been recommended by Lam and Teng [20] for concrete conﬁned with carbon composites. To obtain ccc, it is here proposed to carry out a reliability-based calibration process for a feasible range of strengthening with CFRP in the previously deﬁned damaged concrete piers. To this end, a Limit State Function (LSF) is deﬁned, the uncertainty of the most representative variables is considered and, by simulation, the resistance and load are statistically deﬁned. The LSF is:

G ¼ XR XS

ð11Þ

qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ with X R ¼ ðNÞ2 þ ðM=DÞ2 being (N, M) couples of values of axial force and bending moment for which the section fails (N–M interacqﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ tion diagram), and X S ¼ ðND þ N L Þ2 þ ððML þ MID Þ=DÞ2

ND is the axial force at the bottom of the pier due to the dead loads (from both the pier and the deck), NL is the axial load due to trafﬁc, ML is the bending moment at the bottom of the pier due to braking of trafﬁc in the deck, and MID is the bending moment due to the imposed longitudinal displacements in the deck (due to creep, shrinkage, prestressing force and annual variation of temperature) that provoke an horizontal force at the top of the pier because of the stiffness of the elastomeric bearings. Note that the permanent loads do not produce bending moment in the

ð8Þ ð9Þ

where: fl = lateral conﬁning pressure due to the FRP jacket at failure because of the circumferential strain in the jacket; fck = characteristic compressive strength of non-conﬁned concrete; eco = longitudinal strain at the unconﬁned concrete strength;

Table 2 Basic random variables in the resistance. Variable

Bias

COV

Variable type

0 f cc

Nominal value

1.12

0.17

Log-Normal

36.29

ecu fy esu

0.89 1.09 1.28

0.34 0.11 0.13

Normal Log-Normal Log-Normal

0.0115 400 0.10

275

J.R. Casas, J.L. Chambi / Composite Structures 118 (2014) 267–283

pier as the boundary condition between deck and pier is simply supported. The resistance variable XR is based on the concept of M–N interaction diagrams. The M–N diagrams are obtained using sectional analysis procedures developed for conventional RC columns using the basic parameters of the materials (concrete and reinforcing steel). The sectional analysis used for unconﬁned concrete can be also used in the case of conﬁned concrete with FRP jackets, as demonstrated by the tests and the results presented in Bisby and Ranger [34]. The only difference for FRP-conﬁned concrete is that the stress–strain curve for the unconﬁned concrete is replaced by an FRP conﬁned stress–strain curve based on concentrically-loaded FRP-conﬁned concrete. It is shown in [34] how the Teng et al. [26] curve for concentrically-loaded concrete gives resistance predictions that are close to the experimental ones for a large range of load eccentricities. The random variables considered in the resistance of the pier 0 are: compressive strength (f cc ) and ultimate strain (ecu) of the conﬁned concrete, yielding strength (fy) and ultimate strain (esu) of the reinforcing steel. Their statistical deﬁnition is presented in Table 2. The unconﬁned concrete has a nominal strength of 25 MPa with a coefﬁcient of variation of 15%. The variability of the ultimate strain of unconﬁned concrete is taken as 25%. The elasticity modulus of the CFRP is 230 GPa with a ultimate strain of 1.5%. The efﬁciency coefﬁcient is 0.586. A modeling random variable (n), is also considered which takes into account the model error when estimating the strength of conﬁned-concrete via a particular model, and depends on the conﬁnement model adopted in the design. In this case, the adopted model is the one by Teng et al. [26] and therefore: 0

0

f cc ¼ f cc;mod: n

Fig. 24. Simulated data points of variable XR in normal probability paper (high eccentricity).

ð12Þ

The random variable n which represents the model error is normally distributed with mean and coefﬁcient of variation equal to 1.083 and 7.4% respectively. The same applies to the random variable representing the model error to derive ecu, but in this case the mean and COV are 0.91 and 23.3%. With the basic random variables as deﬁned in Table 2, a simulation process is carried out to statistically deﬁne the random variable XR. A latin-hypercube based simulation [35] is performed with 50 simulations. In each simulation a complete N–M interaction diagram is obtained, with a total of 50 curves, as presented

Fig. 25. Interaction diagrams obtained in the simulation and eccentricity corresponding to predominant compression.

Fig. 26. Simulated data points of variable XR in normal probability paper (low eccentricity).

Table 3 Random variables in the action side.

Fig. 23. Interaction diagrams obtained in the simulation and eccentricity corresponding to predominant bending (3-span, 1 column).

Variable

Bias

COV

VariableType

Nominal value

ND NL ML MID

1.05 0.73 0.73 1.0

0.10 0.20 0.20 0.10

Normal Gumbel Gumbel Normal

Drawings Eurocode Eurocode Design

in Fig. 23. The results in Fig. 23 correspond to the case of the 3-span bridge with only one column per pier. The design values of the axial force and bending moment in this case are Nd = 9908 kN

276

J.R. Casas, J.L. Chambi / Composite Structures 118 (2014) 267–283

Fig. 28. t (mm) vs ccc (3-span, massive slab, 2 column). Fig. 27. t (mm) vs ccc (3-span, massive slab, 1 column).

and Md = 2134 kN m. For clarity of the ﬁgure, only some of the 50 simulated curves are drawn. Also the interaction diagrams corresponding to the original pier (non-conﬁned concrete) and damaged pier are shown. The intersection of the 50 curves with the line from the origin to the design point (Nd, Md) gives a data set of 50 points. Drawing these points (XRi) in Normal probability paper, we obtain the results in Fig. 24. From Fig. 24, we can conclude that the random variable XR for this particular eccentricity (Md/Nd = 0.215 m), can be described by a Normal distribution with mean 19385 N and COV = 17%. The eccentricity corresponds to the case of high bending with low axial force. If we consider the case of low bending with higher axial force (see Fig. 25), the results in Fig. 26 are obtained. The case of high axial force corresponds to piers close to the point in the deck with zero longitudinal displacements because of long-term effects. Also in this case, a Normal distribution ﬁts well the data with a mean value of 28304 N and a COV = 17.5%. Therefore, in the range of possible solutions of strengthening considered in the present study and the feasible range of eccentricities for the bridge population covered, we can conclude that the variable XR may be characterized as Normal with a mean value depending on the thickness and mechanical properties of CFRP applied and a COV equal to 17%. The random variables present in XS are deﬁned in Table 3. These variables may be considered as uncorrelated because they are due to independent actions (permanent load, trafﬁc load, imposed displacements in longitudinal direction). Also the axial load and bending moment due to trafﬁc load can be assumed independent as they come from different origin of the trafﬁc action. One correspond to the weight of the vehicles in the deck, meanwhile the other is due to their braking effects on the pier. The nominal value for the dead load is calculated based on the dimensions of the elements and the density of reinforced concrete. The bias and COV are those normally assumed for concrete elements ‘‘cast in situ’’ [36]. The nominal value for the trafﬁc actions are the characteristic values of these actions according to Eurocode 1 [30], deﬁned as the percentile of 5% for a time period of 50 years. The coefﬁcient of variation for trafﬁc action is taken as 20% according to Sivakumar et al. [37]. The nominal value of the moment due to the imposed movements in the longitudinal direction due to prestressing, creep, temperature and shrinkage is evaluated for each bridge according to the nominal values for each of those actions taken from the Eurocode [30]. First, the elastomeric bearing pads are designed and then, the horizontal forces at the top of the piers obtained. Because of the symmetry in the bridges, the horizontal force due to

Fig. 29. t (mm) vs ccc (4-span, voided slab, pier P-1, 1 column).

Fig. 30. t (mm) vs ccc (4-span, voided slab, pier P-1, 2 column).

imposed movements at the top of pier P-2 in the bridge with 4 spans is equal to zero. Once the random variables XR, ND, NL, ML and MID in Eq. (11) are deﬁned, the reliability index b is calculated using FORM [36]. 4. Results To obtain a set of calibrated safety factors, different strengthening designs (different values of CFRP thickness) according to

277

J.R. Casas, J.L. Chambi / Composite Structures 118 (2014) 267–283

is considered according to the recommendations of Eid and Paultre [25] and Seible et al. [39] and the condition to have an always increasing shape of the stress–strain relationship (qk > 0.01). A summary of the results for target reliability index 3 and 3.5 are presented in Figs. 27–32. Taking into account the shape of the partial safety factor as a function of the CFRP thickness and the fact that the safety factors should be as simple as possible, the following values are proposed for a target reliability of 3.5:

ccc = 1.15 if tmin 6 t 6 2 mm ccc = 1.30 if t > 2 mm With the proposed values and following the standard design process, the repaired piers show the reliability indices as presented in Table 4, which are in the range of the target value. Fig. 31. t (mm) vs ccc (4-span, voided slab, pier P-2, 1 column).

5. Comparison with other guidelines The comparison of the partial safety factors obtained here with the safety factor provided in the ACI guide [7] is not possible because ACI proposes a global safety factor for the resistance of the element, and not partial safety factors to be applied to materials. For this reason, the comparison with the FIB recommendations [9] and the Canadian Code [13] are investigated. Because the partial safety factors in the FIB guide apply to the unconﬁned concrete and the FRP material and not directly to the conﬁned concrete only, as proposed here, the procedure is as follows: 1. Design of the CFRP strengthening of the bridge piers using the FIB guidelines. 2. Calculation of the reliability index for the designs according to FIB and the proposed method. 3. Calculation of an equivalent partial safety factor for FIB with the same safety format as that proposed in the present study.

Fig. 32. t (mm) vs ccc (4-span, voided slab, pier P-2, 2 columns).

According to [9], the safety format for conﬁned concrete strength is: Table 4 Reliability index of the piers designed with the proposed partial safety factors. Bridge and pier type

t (mm)

b

3 Spans, 1 column per pier

0.8 2.0

3.52 3.55

3 Spans, 2 column per pier

0.8 2.0

3.41 3.41

4 Spans, P-1, 1 column per pier

0.8 2.0

3.81 3.85

4 Spans, P-1, 2 column per pier

0.8 2.0

3.95 3.98

4 Spans, P-2, 1 column per pier

0.8 2.0

3.55 3.59

4 Spans, P-2, 2 column per pier

0.8 2.0

3.33 3.56

assumed values of ccc are obtained and the corresponding reliability indexes are calculated. The proposed value of ccc will be that resulting in a reliability index closer to the target value. Two target values are considered: b0 = 3 and 3.5 according to target values adopted in structural code calibration [38]. The overall results and M–N interaction diagrams for all cases studied with different thickness and values of ccc can be found in Chambi [28]. A minimum thickness of the composite of 0.8 mm

0

f cc;d ¼

f ck

cc

þk

fl

ð13Þ

cf

And according to the format proposed here: 0

f cc;d ¼

f ck þ kfl

ð14Þ

ccc

Table 5 Reliability index of the piers strengthened with the proposed partial safety factors and the safety factors from FIB [9]. Bridge and pier type

t (mm)

b

bFIB

3 Spans, 1 column per pier

0.8 2.0

3.52 3.55

2.98 3.28

3 Spans, 2 column per pier

0.8 2.0

3.41 3.41

2.86 3.14

4 Spans, P-1, 1 column per pier

0.8 2.0

3.81 3.85

3.25 3.58

4 Spans, P-1, 2 column per pier

0.8 2.0

3.95 3.98

3.42 3.72

4 Spans, P-2, 1 column per pier

0.8 2.0

3.55 3.59

3.01 3.32

4 Spans, P-2, 2 column per pier

0.8 2.0

3.33 3.56

2.79 3.05

278

J.R. Casas, J.L. Chambi / Composite Structures 118 (2014) 267–283 0

f cc;d design strength of conﬁned concrete; fck characteristic strength of non-conﬁned concrete; cc partial safety factor of non-conﬁned concrete (1.5 according to FIB [9]); k parameter depending on the conﬁnement model; fl lateral conﬁning pressure; cf partial safety factor of FRP (1.35 according to FIB [9]); ccc partial safety factor of conﬁned concrete (as proposed in this study). The values of the reliability factors for both designs are compared in Table 5 for 2 values of the thickness of FRP corresponding to the 2 ranges of values proposed. Comparing the values of the reliability index, we may conclude that the safety format from FIB, with a partial safety factor of 1.35 applied directly to the ﬁber tension and 1.5 applied to the concrete strength, is equivalent to a partial safety factor ccc = 1.48 applied to the strength of the conﬁned concrete. This value is higher than the values obtained in the calibration carried out in the present study, which means that designs according to FIB guide are overdesigned to get a target reliability index of 3.5. This, in turn, means that too much CFRP is used, delivering more expensive solutions. The difference may be explained by the fact that as seen from Eq. (13) the safety factor in the ﬁbre is the one corresponding to the strength obtained in a tensile test of the composite. Therefore, the effects on the safety of the wrapping operation and the interaction with the aggregates of the concrete are not taken into account. In any case, it becomes non-coherent to use a partial safety factor obtained in conditions much different to those where the application is carried out. In the case of the Canadian Code [13], a concrete resistance factor equal to 0.65 (ccc = 1/0.65 = 1.54) is proposed. However, in their study, Zou and Hong [18] concluded that the use of this value leads to the reliabilities of the designed FRP-conﬁned RC columns to be signiﬁcantly higher than the 50 years target reliability index of 3.0 that was used to select the factored design load in the National Building Code of Canada. As a result, they propose a resistance factor of 0.75 (ccc = 1/0.75 = 1.33) for a target reliability index of 3.5. This value, proposed for buildings, is similar to the one proposed here for bridges and therefore strengths the conclusions obtained in [18].

one may conclude that the variability in the resistance of the CFRP strengthened columns is similar to the variability of the conﬁned concrete compressive strength. This conﬁrms the fact that the compressive strength of concrete is the critical parameter in the resistance of eccentrically axially-loaded bridge piers for low and medium eccentricities. This covers the full range of potential column eccentricities present in the bridge population considered. 3. The calibration process has given the following results for the partial safety factor of conﬁned concrete, to be used in the sectional analysis to obtain the N–M interaction diagrams with a partial safety factor of 1.15 for the reinforcing steel:

ccc ¼ 1:15 if tmin 6 t 6 2 mm ccc ¼ 1:30 if t > 2 mm

4.

5.

6.

6. Conclusions From the study of the available conﬁnement models, a calculation of the partial safety factor to be used for conﬁned concrete with CFRP which takes into account the model error and other relevant uncertainties has been carried out. From the obtained results the following conclusions can be drawn: 1. The comparison of the available conﬁnement models with a data base of 126 tests has proven that a good ﬁt is obtained with the model of Teng et al. [26]. Therefore, this model is proposed as the basis of the design equation and for the reliability-based calibration of the corresponding partial safety factors of conﬁned concrete. The ‘‘model error’’ random variable to be used in the calibration process responds to a Normal distribution with a bias ratio equal to 1.08 and coefﬁcient of variation of 7.4% in the case of concrete strength, and bias ratio of 0.91 and coefﬁcient of variation of 23.3% in the case of ultimate strain. 2. Via a simulation process with the following random variables: compressive strength and ultimate strain of the conﬁned concrete, yield strength and ultimate strain of reinforcing steel,

7.

with t the thickness of the CFRP jacket. These are the values to be used in the design, jointly with the nominal value of the strength of CFRP conﬁned concrete obtained with the model of Teng et al. [26]. A comparison of the proposed safety factors with those presented in FIB [9], reveals that the last are quite over-conservative. In fact, the use in FIB of a partial safety factor cf = 1.35 applied to the stress in the CFRP, and a factor of cc = 1.5 for concrete, is roughly equivalent to a partial safety factor in the strength of the conﬁned concrete in the order of ccc = 1.48, which is clearly higher than the values obtained in the present study. The difference is due to the incoherence in the calculation format of the safety factor proposed by FIB which takes into account the behavior of the composite working alone, ignoring the wrapping effects and the interaction with the conﬁned concrete. The safety factors obtained in this study for strengthening of bridge piers are in accordance with those proposed in the Canadian Code for building structures. As mentioned, the calibrated safety factors include the model error. In the present study, the model error is included in the strength and strain of the conﬁned concrete, and not in the interaction diagram as proposed by other researchers [17,18,40]. The approach adopted here seems more accurate because takes into account that the test data used to calibrate this error model is based on test in concrete specimens without longitudinal reinforcement. The correct appraisal of an error model representative of the interaction diagram will need a calibration using reinforced concrete specimens tested in both compression and bending as well. The present approach has also practical advantages. In fact, in the case of a model error applied to the interaction diagram, the coefﬁcient of variation depends on the load eccentricity [40], and 3 major zones can be observed [17]. In our case, this distinction is not necessary. The values proposed herein are of application for the cases similar to those studied. However, the proposed methodology for calibration is complete general and may be applied to other conﬁnement models, other bridge systems and other pier types.

Acknowledgment The authors want to thank the Spanish Ministry of Education for the ﬁnancial support provided through Research Project BIA201016332.

Appendix A Data base of compression tests with CFRP conﬁned concrete (circular sections). Reference

Specimen

Layers

t Thickness [mm]

ECFRP (GPa)

Diameter D [mm]

Height H [mm]

Non conﬁned concrete 0 f co

[MPa]

Conﬁned concrete 0

eco (%)

et (%)

f cu [MPa]

ecu,exp. (%)

etcu (%)

eh,rup (%)

46.6 87.2 104.6

1.51 3.11 4.15

– – –

0.94 0.82 0.76

1 2 3

– – –

0.17 0.5 0.67

224.6 224.6 224.6

100 100 100

200 200 200

30.2 30.2 30.2

0.23 0.23 0.23

– – –

Toutanji [5]

C1 C5

2 2

0.22 0.33

230.5 372.8

76 76

305 305

30.93 30.93

0.19 0.19

0.18 0.18

95.02 94.01

2.45 1.55

– –

1.25 0.55

Demers and Naele [42]

D25-1 D25-2 D25-3 D25-4 D40-1 D40-2 D40-3 D40-4 U25-1 U25-2 U25-3 U25-4 U40-1 U40-2 U40-3 U40-4

– – – – – – – – – – – – – – – –

0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9

84 84 84 84 84 84 84 84 84 84 84 84 84 84 84 84

300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300

1200 1200 1200 1200 1200 1200 1200 1200 1200 1200 1200 1200 1200 1200 1200 1200

24.2 20.5 26.8 24 43.1 43.6 41.8 46.2 24.2 20.5 26.8 24 43.1 43.6 41.8 46.2

0.18 0.21 0.2 0.21 0.26 0.27 0.25 0.28 0.18 0.21 0.2 0.21 0.26 0.27 0.25 0.28

– – – – – – – – – – – – – – – –

33.4 31.3 37.1 38.8 51.1 55.7 52.1 44.8 32.2 36.6 35.8 37 50.1 52.3 54.8 53.6

0.67 0.77 0.7 0.91 0.54 0.59 0.49 0.76 0.38 0.99 0.66 0.98 0.55 0.38 0.42 0.56

– – – – – – – – – – – – – – – –

0.35 0.39 0.34 0.44 0.55 0.48 0.41 0.5 0.37 0.57 0.43 0.57 0.61 0.42 0.63 0.33

Matthys et al. [43]

10 11

– –

0.12 0.12

200 200

150 150

300 300

34.9 34.9

0.21 0.21

– –

44.3 42.2

0.85 0.72

– –

1.15 1.08

Rochette and Labossiere [44]

C100–C2

– – –

0.6 0.6 0.6

100 100 100

200 200 200

42 42 42

0.2 0.2 0.2

– – –

73.5 73.5 67.6

1.6 1.57 1.35

– – –

0.89 0.95 0.8

Xiao and Wu [45]

24 25 26 27 28 29 30 31 32 33 34 35

– – – – – – – – – – – –

0.38 0.38 0.38 0.76 0.76 0.76 1.14 1.14 0.38 0.38 0.38 0.76

152 152 152 152 152 152 152 152 152 152 152 152

305 305 305 305 305 305 305 305 305 305 305 305

33.7 33.7 33.7 33.7 33.7 33.7 33.7 33.7 43.8 43.8 43.8 43.8

0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

– – – – – – – – – – – –

47.9 49.7 49.4 64.6 75.2 71.8 82.9 95.4 54.8 52.1 48.7 84

1.2 1.4 1.24 1.65 2.25 2.16 2.45 3.03 0.98 0.47 0.37 1.57

– – – – – – – – – – – –

0.84 1.15 0.87 0.91 1 1 0.82 0.9 0.81 0.76 0.28 0.92

82.7 82.7 82.7 105 105 105 105 105 105 105 105 105 105 105 105

279

(continued on next page)

J.R. Casas, J.L. Chambi / Composite Structures 118 (2014) 267–283

Watanabe et al. [41]

280

Appendix A (continued) Reference

Specimen

Layers

t Thickness [mm]

ECFRP (GPa)

Diameter D [mm]

Height H [mm]

Non conﬁned concrete 0

Conﬁned concrete 0

f co [MPa]

eco (%)

et (%)

f cu [MPa]

ecu,exp. (%)

etcu (%)

eh,rup (%)

– – – – – – – – – – – – –

0.76 0.76 1.14 1.14 1.14 0.38 0.38 0.38 0.76 0.76 1.14 1.14 1.14

105 105 105 105 105 105 105 105 105 105 105 105 105

152 152 152 152 152 152 152 152 152 152 152 152 152

305 305 305 305 305 305 305 305 305 305 305 305 305

43.8 43.8 43.8 43.8 43.8 55.2 55.2 55.2 55.2 55.2 55.2 55.2 55.2

0.2 0.2 0.2 0.2 0.2 0.21938 0.21938 0.21938 0.21938 0.21938 0.21938 0.21938 0.21938

– – – – – – – – – – – – –

79.2 85 96.5 92.6 94 57.9 62.9 58.1 74.6 77.6 106.5 108 103.3

1.37 1.66 1.74 1.68 1.75 0.69 0.48 0.49 1.21 0.81 1.43 1.45 1.18

– – – – – – – – – – – – –

1 1.01 0.79 0.71 0.84 0.7 0.62 0.19 0.74 0.83 0.76 0.85 0.7

Dias da Silva et al. [46]

61 62 63

– – –

0.111 0.222 0.333

240 240 240

150 150 150

600 600 600

28.2 28.2 28.2

0.2 0.2 0.2

– – –

31.4 57.4 69.5

0.39 2.05 2.59

– – –

0.26 1.18 1.14

Shehata et al. [47]

75 76

– –

0.165 0.33

235 235

150 150

300 300

29.8 29.8

0.21 0.21

– –

57 72.1

1.23 1.74

– –

1.23 1.19

Aire et al. [48]

HF30

HF70

1 3 6 3 6 9 12

0.117 0.351 0.702 0.351 0.702 1.053 1.404

204.27 204.27 204.27 204.27 204.27 204.27 204.27

150 150 150 150 150 150 150

300 300 300 300 300 300 300

42 42 42 69 69 69 69

0.239 0.239 0.239 0.24 0.24 0.24 0.24

0.0635 0.0635 0.0635 0.0435 0.0435 0.0435 0.0435

0.92 2.116 3.162 0.776 1.634 2.281 2.387

0.884 0.927 1.05 0.821 1.03 1.137 0.85

0.884 0.927 1.05 0.821 1.03 1.137 0.85

Lam and Teng [49]

C1-1 C1-2 C1-3 C2-1 C2-2 C2-3 C3-1 C3-2 C3-3

1 1 1 2 2 2 3 3 3

0.165 0.165 0.165 0.33 0.33 0.33 0.495 0.495 0.495

250 250 250 250 250 250 250 250 250

152 152 152 152 152 152 152 152 152

305 305 305 305 305 305 305 305 305

35.9 35.9 35.9 35.9 35.9 35.9 34.3 34.3 34.3

0.203 0.203 0.203 0.203 0.203 0.203 0.188 0.188 0.188

– – – – – – – – –

50.4 47.2 53.2 68.7 69.9 71.6 82.6 90.4 97.3

1.273 1.106 1.292 1.683 1.962 1.85 2.046 2.413 2.516

– – – – – – – – –

1.147 0.969 0.981 0.988 1.001 0.949 0.799 0.884 0.968

Berthet et al. [50]

C20–C1

1 1 1 2 2 2 1

0.165 0.165 0.165 0.33 0.33 0.33 0.11

230 230 230 230 230 230 230

160 160 160 160 160 160 160

320 320 320 320 320 320 320

24.3 25.5 25.2 24.3 25.5 25.2 40.3

0.241 0.203 0.256 0.241 0.203 0.256 0.186

– – – – – – –

42.8 37.8 45.8 56.7 55.2 56.1 49.8

1.633 0.932 1.674 1.725 1.577 1.68 0.554

– – – – – – –

0.957 0.964 0.96 0.899 0.911 0.908 1.015

C20–C2

C40–C1

46 77 108 98 156 199 217

J.R. Casas, J.L. Chambi / Composite Structures 118 (2014) 267–283

36 37 38 39 40 41 42 43 44 45 46 47 48

Appendix A (continued) Reference

Specimen

C40–C1.5

C40–C2

C40–C4

C40–C12 C50–C2

C50–C4

t Thickness [mm]

ECFRP (GPa)

Diameter D [mm]

1 1 1.5 1.5 1.5 2 2 2 4 4 4 9 9 12 2 2 2 4 4 4

0.11 0.11 0.165 0.165 0.165 0.22 0.22 0.22 0.44 0.44 0.44 0.99 0.99 1.32 0.33 0.33 0.33 0.66 0.66 0.66

230 230 230 230 230 230 230 230 230 230 230 230 230 230 230 230 230 230 230 230

160 160 160 160 160 160 160 160 160 160 160 160 160 160 160 160 160 160 160 160

320 320 320 320 320 320 320 320 320 320 320 320 320 320 320 320 320 320 320 320

Height H [mm]

Non conﬁned concrete 0 f co

Conﬁned concrete 0

eco (%)

et (%)

f cu [MPa]

ecu,exp. (%)

etcu (%)

eh,rup (%)

39.3 40.6 40.3 39.3 40.6 40.3 39.3 40.6 40.3 39.3 40.6 40.3 39.3 40.3 51.4 52.7 51.8 51.4 52.7 51.8

0.211 0.204 0.186 0.211 0.204 0.186 0.211 0.204 0.186 0.211 0.204 0.186 0.211 0.186 0.248 0.201 0.231 0.248 0.201 0.231

– – – – – – – – – – – – – – – – – – – –

50.8 48.8 53.7 54.7 51.8 59.7 60.7 60.2 91.6 89.6 86.6 142.4 140.4 166.3 82.6 82.8 82.3 108.1 112 107.9

0.663 0.608 0.66 0.619 0.639 0.599 0.693 0.73 1.443 1.364 1.166 2.461 2.389 2.7 0.832 0.699 0.765 1.141 1.124 1.121

– – – – – – – – – – – – – – – – – – – –

0.952 1.203 0.88 0.853 1.042 0.788 0.83 0.809 0.924 0.967 0.885 0.989 1.002 0.999 0.934 0.865 0.891 0.667 0.871 0.882

0.9 1.21 1.11 1.91 2.08 1.25

– – – – – –

0.81 1.08 1.07 1.06 1.13 0.79

2.551 2.613 2.794 3.082 3.7 3.544 0.895 0.914 0.691 0.888 1.304 1.025 1.304 1.936 1.821

– – – – – – – – – – – – – – –

0.977 0.965 0.892 0.927 0.872 0.877 0.935 1.092 0.734 0.969 1.184 0.938 0.902 1.13 1.064

1.01

–

0.82

[MPa]

Lam et al. [51]

CI–M1 CI–M2 CI–M3 CII–M1 CII–M2 CII–M3

– – – – – –

0.165 0.165 0.165 0.33 0.33 0.33

250 250 250 247 247 247

152 152 152 152 152 152

305 305 305 305 305 305

41.1 41.1 41.1 38.9 38.9 38.9

0.256 0.256 0.256 0.25 0.25 0.25

– – – – – –

52.6 57 55.4 76.8 79.1 65.8

Jiang and Teng [21]

34 35 36 37 38 39 40 41 42 43 44 45 46 47 48

– – – – – – – – – – – – – – –

0.68 0.68 1.02 1.02 1.36 1.36 0.11 0.11 0.11 0.11 0.22 0.22 0.33 0.33 0.33

240.7 240.7 240.7 240.7 240.7 240.7 260 260 260 260 260 260 250.5 250.5 250.5

152 152 152 152 152 152 152 152 152 152 152 152 152 152 152

305 305 305 305 305 305 305 305 305 305 305 305 305 305 305

38 38 38 38 38 38 37.7 37.7 44.2 44.2 44.2 44.2 47.6 47.6 47.6

0.217 0.217 0.217 0.217 0.217 0.217 0.275 0.275 0.26 0.26 0.26 0.26 0.279 0.279 0.279

– – – – – – – – – – – – – – –

110.1 107.1 129 135.7 161.3 158.5 48.5 50.3 48.1 51.1 65.7 62.9 82.7 85.5 85.5

Eid et al. [52]

N1

1

0.381

78

152

300

32.1

0.21

–

39.71

281

(continued on next page)

J.R. Casas, J.L. Chambi / Composite Structures 118 (2014) 267–283

C40–C9

Layers

J.R. Casas, J.L. Chambi / Composite Structures 118 (2014) 267–283

Reference

Appendix A (continued)

0.95 0.88 0.84 1.2 1.27 – – – – – 1.9 2.29 0.68 1.2 1.6 57.58 74.24 59.8 80.04 99.84 – – – – – 0.21 0.2 0.24 0.24 0.24 32.1 33.6 48 48 48 300 300 300 300 300 152 152 152 152 152 78 78 78 78 78 0.762 1.143 0.381 0.762 1.143 2 3 1 2 3

ecu,exp. (%) 0

f cu [MPa]

eco (%) [MPa] 0 f co

References

N2 N3 M1 M2 M3

Specimen

Layers

t Thickness [mm]

ECFRP (GPa)

Diameter D [mm]

Height H [mm]

Non conﬁned concrete

et (%)

Conﬁned concrete

etcu (%)

eh,rup (%)

282

[1] Priestley M, Seible F, Fyfe E. Column seismic retroﬁt using ﬁberglass/epoxy jackets. In Proc. ﬁrst int. conf. on advanced composites materials in bridges and structures, CSCE, Sherbrocke, Quebec, Canada; 1992. p. 287–98. [2] Saadatmanesh H, Ehsani M, Li M. Strength and ductility of concrete columns externally reinforced with ﬁber composite strips. ACI Struct J 1994;91(4): 434–47. [3] Mirmiran A, Shahawy M. Behavior of concrete columns conﬁned by ﬁber composites. ASCE J Struct Eng 1997;123(5):583–90. [4] Karbhari V, Gao Y. Composite jacketed concrete under uniaxial compressionveriﬁcation of simple design equations. J Mater Civil Eng 1997;9(4):185–93. [5] Toutanji H. Stress–strain characteristics of concrete columns externally conﬁned with advanced ﬁber composite sheets. ACI Mater J 1999;96(3): 397–404. [6] Xiao Y, Wu H. Compressive behavior of concrete conﬁned by carbon ﬁber composite jackets. ASCE J Mater Civil Eng 2000;12(2):139–46. [7] ACI440.2R-08. Guide for the design and construction of externally bonded FRP systems for strengthening concrete structures. Farmington Hills, MI: American Concrete Institute; 2008. [8] CNR-DT 200/R1/2013. Guide for design and construction of externally bonded FRP systems for strengthening concrete structures. Rome: National Research Council; 2013. [9] FIB. Externally bonded FRP reinforcement for RC structures. FIB bulletin n. 14, Lausanne: Federation Internationale du Béton; 2001. [10] JSCE. Recommendations for upgrading of concrete structures with use of continuous ﬁbre sheets. Tokyo: Japan Society of Civil Engineers; 2001. [11] TR55. Design guidance for strengthening concrete structures using ﬁbre composite material. Technical Report no.55. 2nd ed. London: The Concrete Society; 2004. [12] FIB. Model Code 2010, ﬁnal draft, FIB bulletins 65 and 66, Lausanne: Federation Internationale du Béton; 2012. [13] CSA. CSA S806–12 Design and construction of building components with ﬁbrereinforced polymers. Toronto: Canadian Standards Association, 2nd ed.; 2012. [14] Plevris N, Triantaﬁllou TC, Veneziano D. Reliability of RC members strengthened with CFRP laminates. J Struct Eng 1995;121:1037–44. [15] Val DV. Reliability of ﬁber-reinforced polymer-conﬁned reinforced concrete columns. J Struct Eng 2003;129(8):1122–30. [16] Realfonzo R, Napoli A. Concrete conﬁned by FRP systems: conﬁnement efﬁciency and design strength models. Compos Part B: Eng 2011;42:736–55. [17] Al-Tersawy SH, Hodhod OA, Hefnawy AM. Reliability and code calibration of RC short columns conﬁned with CFRP wraps. In: Proceedings of FRPRCS8. Patras: University of Patras; 2007. [18] Zou Y, Hong HP. Reliability assessment of FRP-conﬁned concrete columns designed for buildings. Struct Infrastruct Eng 2011;7(3):243–58. [19] Ozbakkaloglu T, Lim JC, Vincent T. FRP-conﬁned concrete in circular sections: review and assessment of stress–strain models. Eng Struct 2013;49:1068–88. [20] Lam L, Teng JG. Design oriented stress–strain model for FRP-conﬁned concrete. Constr Build Mater 2003;17(6–7):471–89. [21] Jiang T, Teng JG. Analysis-oriented models for FRP-conﬁned concrete. Eng Struct 2007;29(11):2968–86. [22] Mander JB, Priestley MJN, Park R. Theoretical stress–strain model for conﬁned concrete. ASCE J Struct Eng 1988;114(8):1804–26. [23] Pilakoutas K, Mortazavi AA. Ductility through external conﬁnement of RC members with FRP. In: Non-metallic (FRP) reinforcement for concrete structures. Tokyo: Japan Concrete Institute; 1997. p. 225–32. [24] Spoelstra MR, Monti G. FRP-conﬁned concrete model. ASCE J Compos Constr 1999;3(3):143–50. [25] Eid R, Paultre P. Analytical model for FRP-conﬁned circular reinforced concrete columns. ASCE J Compos Constr 2008;12(5):541–52. [26] Teng JG, Jiang T, Lam L, Luo YZ. Reﬁnement of a design-oriented stress–strain model for FRP-conﬁned concrete. ASCE J Compos Constr 2009;13(4):269–78. [27] Wu YF, Zhou YW. Uniﬁed strength model based on Hoek–Brown failure criterion for circular and square concrete columns conﬁned by FRP. ASCE J Mater Civil Eng 2010;14(2):175–84. [28] Chambi JL. Caracterización estadística de los modelos de conﬁnamiento y determinación de coeﬁcientes parciales de seguridad para el refuerzo de pilas de puentes de hormigón mediante materiales compuestos (CFRP) [Ph.D. thesis] (in Spanish). Technical University of Catalonia-BARCELONATECH, 2012. [29] Tamuzs V, Tepfers R, Zile E, Ladnova O. Behavior of concrete cylinders conﬁned by a carbon composite III: deformability and the ultimate axial strain. Mech Compos Mater 2006;42(4):303–14. [30] CEN. Eurocode 1: Eurocode 1: actions on structures. ENV1991-1. Brussels: European Committee for Standardization; 1994. [31] CEN. Eurocode 2: design of concrete structures. ENV1992-1. Brussels: European Committee for Standarization; 1991. [32] CALTRANS. Seismic design criteria v1.6. California Department of Transportation; 2010. [33] Pessiki S, Harries KA, Kestner JT, Sause R, Ricles JM. Axial behavior of reinforced concrete columns conﬁned with FRP jackets. J Compos Constr ASCE 2001; 5(4):237–45. [34] Bisby L, Ranger M. Axial-ﬂexural interaction in circular FRP-conﬁned reinforced concrete columns. Constr Build Mater 2010;24:1672–81. [35] Florian A. An efﬁcient sampling scheme: updated latin hypercube sampling. Probab Eng Mech 1992;7:123–30.

J.R. Casas, J.L. Chambi / Composite Structures 118 (2014) 267–283 [36] Nowak AS, Collins KR. Reliability of structures. McGraw-Hill; 2000. [37] Sivakumar B, Ghosn M, Moses F. Protocols for collecting and using trafﬁc data in bridge design. NCHRP Project 12–76, Transportation Research Board, Washington, DC; 2009. [38] Casas JR, Wisniewski D. D4.4.1 background document: safety format and required safety levels. Background document D4.4.1 to SB-resistance (2007) ‘‘Guideline for load and resistance assessment of railway bridges’’. Sustainable Bridges Project. VI European Framework Program; 2007. [39] Seible F, Preistley N, Hegemier GA, Innamorato D. Seismic retroﬁt of RC columns with continuous carbon ﬁber jackets. J Compos Constr 1997;1(2):52–62. [40] Hong HP, Zhou W. Reliability evaluation of RC columns. J Struct Eng 1999;125(7):784–90. [41] Watanabe K, Nakamura H, Honda Y, Toyoshima M, Iso M, Fujimaki T, Kaneto, M, Shirai N. Conﬁnement effect of FRP sheet on strength and ductility of concrete cylinders under uniaxial compression. In Proceedings of the third international symposium – non-metallic (FRP) reinforcement for concrete structures, vol. 1. Sapporo; 1997. p. 233–40. [42] Demers M, Neale KW. Conﬁnement of reinforced concrete columns with ﬁbre reinforced composite sheets an experimental study. Can J Civil Eng 1999;26:226–41. [43] Matthys S, Taerwe L, Audenaert K. Tests on axially loaded concrete columns conﬁned by ﬁber reinforced polymer sheet wrapping. In: Dolan CW, Rizkalla SH, Nanni A, editors. Proc. fourth int. symp. on ﬁber reinforced polymer reinforcement for reinforced concrete structures, SP-188. Detroit: American Concrete Institute; 1999. p. 217–29.

283

[44] Rochette P, Labossière P. Axial testing of rectangular column models conﬁned with composites. J Compos Constr ASCE 2000;4(3):129–36. [45] Xiao Y, Wu H. Compressive behavior of concrete conﬁned by carbon ﬁber composite jackets. J Mater Civil Eng 2000;12(2):139–46. [46] Dias da Silva V, Santos JMC. Strengthening of axially loaded concrete cylinders by surface composites. In: Figueiras J, Juvandes L, Faria R, Marques AT, Ferreira A, Barros J, Appleton J, editors. Proceedings of the international conference on composites in constructions, Lisse. The Netherlands: A.A. Balkema Publishers; 2001. p. 257–62. [47] Shehata IAEM, Carneiro LAV, Shehata LCD. Strength of short concrete columns conﬁned with CFRP sheets. Mater Struct 2002;35(1):50–8. [48] Aire C, Gettu R, Casas JR, Marques S, Marques. Estudio experimental y modelo teórico del hormigón conﬁnado lateralmente con polímeros reforzados con ﬁbras (FRP). Mater Constr 2010;60(297):1–13. [49] Lam L, Teng JG. Ultimate condition of ﬁber reinforced polymer-conﬁned concrete. J Compos Constr 2004;8(6):539–48. [50] Berthet JF, Ferrier E, Hamelin P. Compressive behavior of concrete externally conﬁned by composite jackets. Part A: Experimental study. Constr Build Mater 2005;19(3):223–32. [51] Lam L, Teng JG, Cheng CH, Xiao Y. FRP-conﬁned concrete under axial cyclic compression. Cem Concr Compos 2006;28(10):949–58. [52] Eid R, Roy N, Paultre P. Normal- and high-strength concrete circular elements wrapped with FRP composites. J Compos Constr 2009;13(2):113–24.

Copyright © 2024 C.COEK.INFO. All rights reserved.