FIBRE REINFORCED CONCRETE PIPES: NEW DESIGNING TRENDS * ** * * Albert de la Fuente , Antonio Figueiredo , Antonio Aguado , Climent Molins and ** Renata Escariz *
DEC, Dep. Construction Eng., Univesitat Politècnica de Catalunya (UPC) C/ Jordi Girona Salgado 1-3, 08034, Barcelona, España e-mail:
[email protected];
[email protected];
[email protected]. web page: www.upc.edu **
University of São Paulo, Department of Civil Construction Engineering, Caixa Postal 61548. CEP 05424-970. São Paulo, Brazil. e-mail:
[email protected];
[email protected]. web page: www.poli.usp.br
Keywords: fibres, pipes, crushing test, numerical simulation, design. Summary: The main advantages related to the use of structural fibres as main reinforcement in concrete pipes is of widespread knowledge. However, in spite of the numerous experimental campaigns carried out and published in the scientific literature, their use has not been properly consolidated. Among those reasons, the most important one is the lack of a systematic method for its design. In this respect, the type and the amount of fibres for each internal diameter (Di) and required strength class has been traditionally determined by means of the crushing test. This is a reliable method, but not efficient from an economic point of view when it is used indirectly with designing purposes, since there exist several Di, thicknesses (e) and commercial strength classes. Therefore, it is evident that there is a need for a methodology that would enable the systematic design of fibre reinforced concrete pipes (FRCPs) for any Di and strength class. In this sense, several experimental campaigns and numerical models for the analysis of FRCPs were developed in conjunction by the Universitat Politècnica de Catalunya (UPC) and the Universidade de São Paulo (USP) in order to gain knowledge about the mechanical response of this element. The aim of this work is, on the one hand, to introduce the most relevant aspects regarding the mechanical response of FRCPs and its numerical simulation by the means the developed Model for the Analysis of Pipes (MAP). On the other hand, the suitability of the MAP for the design of this type of pipes is verified by contrasting the experimental results obtained from FRCPs with Di of 600 mm, 800 mm and 1000 mm. Finally, a new design methodology based on the use of the MAP is presented. All this aspects are expected to boost the use of fibres as the main reinforcement in concrete pipes.
1
INTRODUCTION
It is well-known that the addition of fibres in the concrete provides advantages from both the technical and the economic point of view. From the technical point of view, a substantial improvement of several mechanical properties of concrete is achieved [1], especially with the addition of metallic fibres [2]. The use of fibres also contribute economically, because allows to save up on the assembling operations related to conventional reinforcement and reducing labour force, equipment use, and associated risks [3]. FRCPs have already been considered as alternatives to unreinforced concrete pipes (UCPs) and steel bar reinforced concrete pipes (SBRCPs) in several experimental campaigns both in Brazil [4-5] and Spain [3]. However, their introduction in the market is under progress due to several factors such as: (1) the risk of damage when manipulating the pipes; (2) the lack of calculation methods for this type of material, and (3) the difficulty to overcome the inertia towards change [6]. Nonetheless, nowadays there are solutions for such problems: (1) polishing with emery powder to remove
imperfecctions and avvoid possible e injuries; (2 ) constitutive e equations to simulate m mechanical response of the fib bre reinforce ed concrete (FRC) ( subjeccted to tensiion [7-8], and d (3) it has bbeen verified d that the incorpora ation of fibre es improves the t response e of the pipe and leads to o a global redduction of costs [9]. Anoth her relevantt aspect related to FR RCPs techno ology is the lack of reecommendations and simplified d calculation n methods. Because B of tthis, the des sign of FRCP Ps is normallly carried ou ut by trial and erro or: trying outt several dos sages of fibrres (Cf) until finding an optimal o valuee of Cf that meet the requirem ments of the desired stren ngth class in n the crushin ng test (CT) (Figure ( 1). T This design procedure p is hardlyy operative and uneconom mical due to the variety of o internal dia ameters (Di),, values of e, strength classes and types of o fibres. Forr this reason n, it is neces ssary to dev velop analytiical and/or numerical n tools tha at would makke possible to o carry out th he optimal de esign and the verificationn of FRCPs, for which do not exxist any type e of design methodology m except testin ng procedure es.
Figure 1. Three ed ge bearing te est or crushing test. With the aim of studying the e viability of using fibre reinforced concrete (FR RC) in concre ete pipes (CPs), th he Universita at Politècnica a de Catalun nya (UPC) and a the Unive ersidade de São Paulo (USP), in conjuncttion with national companies within tthe sector off CP manufa acturers, havve carried ou ut several experime ental campaigns [10-11] and develop ped numerica al models forr the analysiss of CPs [12--14]. In thiss sense, the main goal of o this paper consist, firsttly, of introdu ucing the num merical tool Model M for the Anallysis of Pipe es (MAP) wh hich has bee en developed to assess the mechannical behavio our up to failure of FRCPs. Fo or this purpo ose, the mosst recent con nstitutive equ uations for thhe simulation n of FRC have been implemen nted. Secondly, it is provved that MA AP is an appropriate tooll to design steel s fibre ed concrete pipes p (SFRC CPs) up to 10 000 mm of Di. The suitability of the MA AP for this purpose is reinforce verified b by contrastin ng the experrimental resu ults obtained from SFRCPs with Di eequal to 600 mm, 800 mm and 1000 mm prresented in [10, [ 4 and 11 1], respective ely. Finally, itt is concludeed that the MAP could be syste ematically ussed to design their FRCP Ps avoiding the repetitiv vely use of tthe CT as an n indirect design m method, espe ecially for the e fibre conten nt determination.
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THE E CRUSHIN NG TEST IN N STEEL FI BRE REINFORCED CONCRETE C E PIPES
2.1 Tes st procedurre accordin ng to EN 19 916:2002 [1 15] The ttest is carried d out by mea ans the appliication of a lo ongitudinal lo oad uniformlly distributed d over the upper ge eneratrix of the t pipe, which leans on n two longitudinal strips (Figure ( 1). T The loading sequence s
2
throughout time used with SFRCPs is shown in Figure 2; what makes it different from that established for CPs and steel bar reinforced concrete pipes (SBRCPs) is the existence of an unloading-reloading process. Likewise, the pipe has to fulfil the following strength requirements: Maintaining the proof load (Fc) for a minute without undergoing damage noticeable at visual verification, that is, without reaching the cracking load (Fcr). Fc should be equal or higher than 67 % of the ultimate load (Fn) fixed for the required strength class. Leading the pipe to failure, obtaining a failure load (Fu) higher than Fn. When the load falls at least a 5 % of Fu, the pipe is totally unloaded and then reloaded, verifying that a minimum post-failure load (Fmin,pos) not lower than Fc is reached. Fmin,pos must be maintained for at least one minute.
F
(a)
Spreading beam
Di D O Supports
(b) F
Ridge e
Fu ≥ Fn Springline
Invert Fc ≥ 0,67Fn 1 min
1 min
t
F/2
F/2 2β
Figure 1. (a) Transversal section of the CP and (b) load pattern of the test procedure. This cyclic loading process aims at verifying if Cf and the type of fibres are suitable to guarantee the Fmin,pos load and, indirectly, if the fibre-concrete anchorage and the post-peak strength of the SFRC used are appropriate [4].Nevertheless, in previous experimental campaigns involving SFRCPs has been proved that the maximum values of the post-failure load (Fmax,pos) obtained by means continuous or cyclical tests do not show significant differences, therefore the first one can be adopted. Thanks to this, the implementation of the CT becomes easier and, consequently, CPs manufacturers will not perceive the use of fibres as an unnecessary difficulty.
2.2 Measuring procedure To guarantee a suitable accuracy of the results obtained during the required unloading-reloading process of the CT (see Figure 2b), it is necessary to use devices capable of an uninterrupted measurement of the vertical displacement at the ridge (v) (see Figure 2a). In the campaigns carried out, LVDTs were stuck to the inner face of the pipe ridge and fixed to the invert. The data recorded were downloaded to a computer and were processed in order to obtain the F–v curves for a
3
subsequent analysis. Additionally, in some specimens the crack width of the ridge (w) was measured for some values of F (see Figure 3). F
v w
Figure 3. Measurement of the crack width during the CT.
2.3 Analysis of the mechanical response of FRCPs The mechanical behaviour of a FRCPs subjected to the CT depends on its geometry (Di and e) as well as on the type and amount of fibres (Cf) used. In this respect, the responses recorded in the tests coincide with three different general patterns; regardless of whether the test is cyclical or continuous (see Figure 4). Finally, the integral response of a FRCP can be described in three stages, governed by the stress-strain state of the ridge and haunches sections [16]. Stage 1. Linear elastic behaviour of the whole element, which ends when the first crack appears at the ridge once the cracking load has been reached (Fr,cr). Its value depends on the geometry (Di and e) and on the flexural strength of the concrete matrix (fct,fl). Stage 2. When the first crack appears, the ridge section begins to work in cracking regime, whereas the rest of the sections maintain their linear response. Initially, the fibres bridging the crack begin to work gradually, thus there is an initial drop of F and a subsequent recovery. For the same pipe, the lower the Cf, the sharper the drop, and vice-versa. Stage 2 ends when the cracking load of the haunches is reached (Fs,cr). In this respect, if the Cf is low in comparison with the dimensions of the pipe (case A from Figure 4), Fs,cr will not reach the Fr,cr value, and it will be considered that the response is subcritical [17], coinciding Fr,cr with the Fu load of the system. On the other hand, in the case of moderate-high Cf, Fs,cr can be higher than Fr,cr, and thus the response will be supercritical (cases B and C from Figure 4). Stage 3. Just as in stage 2, when Fs,cr is reached, there is a snap-through that leads to the postfailure regime. At this stage, two different behaviours can be obtained depending on Cf: softening (cases A and B from Figure 4) if Cf is low or moderate, or hardening (case C from Figure 4) if Cf is high with regard to the dimensions of the pipe. Likewise, during this regime Fpos,max is reached; this is a value which must be assessed in SFRCP [15]. It must be noted that, in the case of FRCPs with hardening in the post-failure response, the Fmax,pos load is the highest one in all the test and, therefore, corresponds to the Fu load of the pipe.
4
F
Fr,cr = Fu Fs,cr = Fmax,pos
F F, r cr
Fs,cr = Fu F Fmax,pos
B
A
C
Cf,2
Cf,1
v
Fs,cr
Fmax,pos = Fu
Fr,cr Cf,3
v
Cf,1 < Cf,2 < Cf,3
v
Figure 4. Typical F-v patterns obtained in FRCPs during the CT.
3 NUMERICAL MODELLING OF THE CRUSHING TEST FOR FRCPs In this work, the Model for the Analysis of Pipes (MAP) is presented and used to deal with the numerical simulation of the mechanical response in the CT of the SFRCPs tested in the different experimental campaigns. It was developed on the basis of the hypotheses of structural behaviour introduced in [9] for the analysis of UCPs and SFRCs. The MAP simulates the global response of the pipe considering that the non-linear phenomena occur in two critical sections (ridge and haunches), whereas the rest of the pipe behaves linearly. This is a non-linear hinge model which can capture the three stages of behaviour previously described (Figure 4) by incorporating two hinges:
Stage 1 is simulated considering a linear behaviour throughout the whole element (Figure 5a). Stage 2 is simulated by imposing that the cracking in R activates the non-linear hinge in said section, whereas the rest of the element responds linearly (Figure 5b). Stage 3 is simulated by imposing that the cracking in S activates the second non-linear hinge, both hinges being linked by a circumference sector which behaves linearly (Figure 5c). a)
b)
F R
F MS
Rm
F C
R
MR
Rm
S
c)
F
Rm
Rm
o
S
S F MS
MR
MR
o
Rm
F MS
Rm
o
Figure 5. Structural model: (a) full linear regime, (b) linear regime with cracking in R and (c) also in S. The simulation of the mechanical behaviour of the sections (see Figure 6) was carried out by means of the numerical model called Analysis of Evolutionary Sections (AES) developed by the same authors of this work and presented in [18]. Regarding the simulation of the FRC mechanical response, the expression suggested in [19] was implemented in AES to deal with the simulation of the uniaxial compressive response of FRC. On the other hand, the simulation of its tensile behavior has been approached by means of the trilineal σc-εc model proposed in [7], because it has already been used in several numerical-experimental contrasting works [20-21], guaranteeing good results.
5
dAc
εc,sup
a)
χ
xn
εc(yc) yc
ys,i
M
εs,i
σs
εc,inf
N yG
As,i σc fcm
b)
σu Ecm 1 -25‰ σ3
ε2 ε1 2‰
σ2
3.5‰
εc
σ1
Figure 6. (a) Cross section discretization and (b) constitutive laws adopted to simulate the SFRC. The value of the crack width (w) is calculated considering that the crack surfaces rotate as a rigid body (see Figure 7), forming an angle, namely φ, between the crack faces. This angle is related to the sectional curvature χ by means of the length of the hinge lbc [22]. The value of lbc varies depending on the stress level of the section. In this sense, for this work, a constant value of e/2 for lbc has been adopted, following the recommendations in [22] for the analysis of SFRCPs. Non linear regime
Linear regime
σc(εc)
Linear regime e
sn
φ w lbc = e/2 Figure 7. Rigid body configuration adopted to simulate the non-linear hinge.
4 CONTRASTING THE MODEL MAP WITH THE EXPERIMENTAL VALUES With the aim of contrasting the MAP with experimental results obtained in specimens tested under real conditions, the data available from three different experimental campaigns which involved the
6
production and testing of SFRCPs with Di of 600 mm [10], of 800 mm [4] and of 1000 mm [11] by using different values of Cf are taken as reference. It has to be mentioned that in these experimental campaigns, the same type of fibres (length lf = 60 mm, diameter df = 0.75, Young modulus Ef = 210000 N/mm2 and a tensile strength ffu = 1100 N/mm2) were used as the unique reinforcement of the CPs. However, no characterization tests of the mechanical properties of the different SFRCs were carried out, except for the uniaxial compressive strength (fcm = 30 N/mm2). Fortunately, for this kind of fibres there are enough information in the literature to deal with the numerical simulation by means the model AES. In particular, the equations suggested in [23] were used to obtain the different values of the flexural residual strength of the SFRCs (fR,i) associated with each Cf. These equations were adjusted using the same type of fibres used in the production of the SFRCPs tested in the different campaigns. Therefore, on the basis of the estimated values of fR,i for each Cf, the σ-ε diagrams [7] were used to simulate the tensile response of the SFRC (see Figure 6b and Table 1). Table1. Values of σi (N/mm2) and εi (‰) used to define the constitutive equation of the tensioned FRC (see Fig. 6b) for each value of Cf. Cf (kg/m3) 10 20 30 40
σ1 3,572 3,572 3,572 3,572
ε1 0,112 0,112 0,112 0,112
σ2 0,741 1,166 1,592 2,017
ε2 0,212 0,212 0,212 0,212
σ3 0,564 0,888 1,212 1,536
ε3 25,000 25,000 25,000 25,000
The average values of Fu and Fmax,pos obtained in the tests and by using MAP are presented in Table 2, where ξ stands for the relative error of the numerical value with regard to the experimental one. Likewise, Table 2 details the type of behaviour obtained by the MAP for each pipe, taking into account the classification introduced in Figure 4. Table2. Experimental and numerical results for the SFRCPs analysed.
Di = 600 mm e = 72 mm
Di = 800 mm e = 92 mm
Di = 1000 mm e = 90 mm
Cf (kg/m3)
CODE
10 20 40 10 20 25 30 35 40 0 20 25 35
600/72-10 600/72-20 600/72-40 800/92-10 800/92-20 800/92-25 800/92-30 800/92-35 800/92-40 1000/90-0 1000/90-20 1000/90-25 1000/90-35
Fu (kN/m2)
Fmax,pos (kN/m2)
Exp. MAP ξ (%) Exp. MAP ξ (%) 56 60 69 76 87 92 92 97 95 52 56 59 64
48 14.3 52 13.3 66 4.3 75 1.9 82 5.7 88 4.3 91 1.1 96 1.0 100 -5.3 51 1.1 51 8.4 53 10.7 58 9.5
40 49 69 41 63 77 81 89 88 32 39 60
37 46 66 38 57 66 75 85 92 9 33 39 53
7.5 6.1 4.3 7.3 9.5 14.3 7.4 4.5 -4.5 -3.1 0.0 11.7
Type of Response B B C A B B B B B A B B B
The numerical simulations highlight that the mechanical response of the pipes in the CT from the series 600/72-10, 800/92-10, 1000/90-0 and 1000/90-20 (Di/e-Cf) correspond to a behaviour of the
7
type A from Figure 4 (Fr,cr = Fu). The remaining pipes show a type B behaviour (Fs,cr = Fu), except the pipes from the series 600/72-40 which show a type C behaviour. Further conclusions from the results shown in Table 2 are: The maximum value of ξ detected for Fu is 14.3% (600/72-10), whereas the minimum value is -5.3% (800/92-40), the average value being 5.4%. Consequently, the MAP tends to underestimate the Fu load of the system, possibly due to the fact that the values of fRi used in the numerical simulations for the different SFRCs lead to safe results. The maximum value of ξ obtained in Fmax,pos is 14.3% (800/92-25), and the minimum value is -4.5% (800/92-40). In this case, the average value of ξ is 5.2%, which leads to the conclusion that THE MAP also tends to underestimate the Fmax,pos load. Considering the low values of ξ obtained, it can be assumed that the correlation between the experimental and the numerical values is acceptable. Thus the MAP could be used for the design of SFRCPs as long as Di was equal or lower than 1000 mm.
5 NEW DESIGN METHODOLOGY BASED ON THE USE OF THE MAP The design of the reinforcement of a FRCP by means of the CT, fixing the geometry (Di and e) and the strength class, can be a time consuming and economically expensive process, depending on the experience of the manufacturers. If the same type of pipe has been already produced by the manufacturer, an initial value of Cf could be known, and consequently the process of trial and error requires less testing efforts. Nevertheless, in most cases the manufacturers do not have former experience, since the possible commercial combinations of Di, h and strength classes are numerous and, in consequence, a high number of tests could be necessary to guarantee an optimal value of Cf. Apart from all that, there is also the fact that, up to date, no national regulation has established values for Cf in SFRCPs. In order to improve this current framework, the MAP is proposed as a tool aiming at making it easier for the manufacturers to design these elements. The strategy consists in using the MAP to obtain a reliable initial value of Cf (by means of the Fu-Cf and Fmax,pos-Cf curves) for the Di, e, type of fibres and the target strength class. In this way, the initial uncertainty regarding the value of Cf is reduced and, therefore, so does the number of tests necessary to adjust its optimal value. As an example on how this process might be implemented (see Figure 8), the results obtained with the MAP for the pipes 600/72 (see Table 2) will be used to adjust the Fu-Cf and Fmax,pos-Cf curves which will provide the values of Cf necessary to reach the strength class C60 (Fc = 40 kN/m2 and Fn = 60 kN/m2) according to the EN 1916:2002 [15]. The results depicted in Figure 8 bring to the light that: The numerical values fit, showing R2 coefficients higher than 0.98 in both cases, with a linear tendency. This is due to the fact that the relations suggested in [23] for the assessment of fR,i are linear with respect to Cf and the uniaxial compression behaviour of concrete is also linear for the range of displacements v (lower than 10 mm) which has been fixed for the analysis. For a pipe with Di of 600 mm and e of 72 mm, 31 kg/m3 of fibres would be enough to reach the class C60. In this sense, this value is on the side of safety since the average test results (Table 2) showed that with only 20 kg/m3 of fibres, this class could be reached. Nonetheless, this value has a low reliability as the required value of Fn (60 kN/m2) is reached exactly, thus any variation of Cf with respect to the 20 kg/m3 used, might lead to values of Fu of the SFRCP lower than the strict 60 kN/m2 fixed in the EN 1916:2002. This systematic procedure presented for a SFRCP with Di of 600 mm and e of 72 mm could be carried out with SFRCPs with Di up to 1000 mm and with any e and strength class. However, if the designer used a different type of fibres from the ones used in this experimental campaign, the suitable
8
relations fRi-Cf should be adopted. Luckily, the great majority of the fibres suppliers have this data or, alternatively, these can be obtained by performing the prismatic beam tests [29-23].
80 Fu = 0,609Cf + 41 R² = 0,983
70 60 F (kN/m2)
Fmax,pos = 0,970Cf + 27 R² = 0,998
50
Di = 600 mm e = 72 mm
40 30 13 kg/m3
20 10
15
31 kg/m3 20
25 Cf
30
35
40
45
(kg/m3)
Figure 8. Fu-Cf and Fmax,pos-Cf curves for 600/72 SFRCP obtained by means the MAP. As an application, the Tables 3 and 4 gather the strength classes reached for different Cf, Di and values of e (Table 5) established in [15]. Tables 3 and 4. Strength classes for thickness (e) type B and C, respectively. Di (mm) 150 200 250 300 400 500 600 700 800 900 1000
3 Cf (kg/m )
Di (mm)
20 25 30 35 40 45 50 55 60
C135
150 200 250 300 400 500 600 700 800 900 1000
C180
C90
C60
Cf (kg/m3) 20 25 30 35 40 45 50 55 60
C180
C90
C135
It must be noticed, that a range of values for Cf [20 kg/m3 – 60 kg/m3] has been fixed. In this sense, the 20 kg/m3 respond to the fact that is necessary a minimum reinforcement to avoid the brittle failure as well as to guarantee the self-stability of the pipe in fresh state once the external mould is taken
9
away. Likewise, values of Cf over the 60 kg/m3 have been proven to lead to a non-competitive solution in comparison with the traditional steel bar reinforced concrete pipes.
e (mm)
Type B Type C
150 22 -
Table 5. Thickness e of the pipe for each Di. Di (mm) 200 250 300 400 500 600 700 29 32 50 59 67 75 84 69 78 86 94 102
800 92 111
900 100 119
100 109 128
6 CONCLUSIONS Accordingly to the results gathered in the Table 2, the MAP model simulates satisfactorily the mechanical response of SFRCPs subjected to the CT. In the case of the pipes analysed in this paper, the model tends to slightly underestimate their strength capacity compared with those obtained experimentally. Still, the average error for the Fu load and the Fmax,pos load is 5.4% and 5.2% respectively, and, in any case, on the side of safety. The Fu-Cf and Fmax,pos-Cf curves obtained by using MAP fit very well simple straight tendencies, thus simplifying the process of designing SFRCPs for a particular strength class. In this sense, an example on how to deduce a practical design tables for a specific type of fibres has been developed obtaining the following conclusions (see Tables 3 and 4): The maximum strength class C180 could be reached for SFRCPs type B with Di up to 400 mm without the need of any steel reinforcement cage and values of Cf ranging from 40 kg/m3 to 60 kg/m3, meanwhile in the case of pipes type C, the class C180 could be obtained with only a Cf of 20 kg/m3. Likewise, for this type of pipes, the whole reinforcement could be replaced by fibres even for Di of 700 mm. It is possible to reach the strength class C90 for pipes with Di up to 1000 mm type B. Alternatively, the class C135 could be accomplished for pipes with same Di provided a thickness type B was used. These results are interesting not only from a scientific point of view, but also from a technical point of view since the replacement of the whole steel reinforcement cage by a low or moderate Cf is an attractive strategy in comparison to the traditional systems (reduction of the production time, labour costs, risks associated with the manipulation of the steel cages, stocking areas, among others). Nowadays, more experimental campaigns involving FRCPs produced with different types of fibres (materials and geometry) are being conducted with the aim of contrasting the design model proposed here with a wider range of FRCPs.
7 ACKNOWLEDGEMENTS The authors of this document wish to show their gratitude for the economic support received through the Research Project BIA2010-17478: Construction processes by means of fiber reinforced concretes. Likewise, Prof. Antonio D. de Figueiredo wishes to thank the CAPES Coordenação de Aperfeiçoamento de Pessoal de Nível Superior for their support in awarding him the postdoctoral scholarship developed at the UPC, which made possible his participation in this research work. Finally, Renata C. Escariz is grateful to the Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) for their support in awarding her the postgraduate scholarship.
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