Flexural Strengthening of Two-Way RC Slabs with Textile-Reinforced Mortar: Experimental Investigation and Design Equations

Strengthening of existing concrete structures has become an urgent need in recent years as a result of aging and/or the necessity to comply with the requirements of modern design codes (i.e., Eurocodes). As the main objective of strengthening methods is to achieve sustainability and cost-effectiveness, the engineering community has progressively turned to the use of advanced structural materials. The introduction of textile-reinforced mortar (TRM) almost a decade ago (Triantafillou et al. 2006; Bournas et al. 2007) can be recognized as remarkable progress in the field of structural retrofitting.

TRM is a cement-based composite material that consists of high-strength fibers (i.e., carbon, glass, or basalt) in the form of textiles combined with inorganic matrices, such as cement-based mortars. The textiles that are used as reinforcement of the composite material typically comprise fiber rovings in two orthogonal directions. The same material can also be found in the literature with the acronyms TRC or FRCM (e.g., Brameshuber 2016; ACI 2013; Carloni et al. 2015). One of the characteristics of TRM is its advantages over fiber-reinforced polymers (a broadly used epoxy-based composite material), namely, low cost, resistance at high temperatures, compatibility with concrete and masonry substrates, ability to apply on wet surfaces, and low temperatures and air permeability.

A significant research effort has been made in the last few years toward the exploitation of the TRM strengthening technique in several cases of structural retrofitting. Experimental investigations on strengthening of reinforced concrete (RC) (e.g., Bournas et al. 2009; Bournas and Triantafillou 2011; D’ Ambrisi and Focacci 2011; Elsanadedy et al. 2013; Babaeidarabad et al. 2014; Koutas et al. 2014; Tzoura and Triantafillou 2014; Bournas et al. 2015; Loreto et al. 2015; Ombres 2015; Tetta et al. 2015, 2016) or masonry elements (Papanicolaou et al. 2007; Harajli et al. 2010; Babaeidarabad et al. 2013; Koutas et al. 2015a, b) have shown very promising results. Research on strengthening of RC slabs, though, has been rather limited (Jesse et al. 2008; Papanicolaou et al. 2009; Schladitz et al. 2012; Loreto et al. 2014), with most of the studies focusing on the flexural behavior of one-way slabs. The only study reported in the international literature on strengthening of two-way RC slabs with TRM is that of Papanicolaou et al. (2009) who tested four square slabs under concentrated load with three of them being retrofitted with carbon or glass TRM. Nevertheless, all slabs in the study of Papanicolaou et al. (2009) (including the unretrofitted one) failed in punching shear without developing a plastic collapse mechanism in flexure, and therefore TRM served for a punching shear capacity increase.

The use of TRM for increasing the flexural capacity of two-way RC slabs has not been investigated to date. This paper investigates for the first time the flexural strengthening of two-way RC slabs with externally bonded TRM. The parameters under investigation are the number of TRM layers, the strengthening configuration, the material of the textile fibers, and the presence of initial cracking. For this purpose, six large-scale slabs were experimentally tested, with the results being used to derive simple design equations. Details are provided in the following sections.

The responses of all slabs tested are presented in Fig. 6 in the form of load versus central deflection curves, whereas the final crack pattern of each slab is illustrated in Fig. 7. Table 2 also summarizes the main test results: the peak load, $P_{\text{max}}$; the midspan deflection corresponding to $P_{\text{max}}$; the observed failure mode; the flexural capacity increase from strengthening; the precracking (initial) stiffness, which is calculated from the force-midspan deflection curves as the tangent stiffness of the uncracked stage; the cracking load (approximate load level based on the observations during testing and the change in the slope of load-displacement curves); the postcracking stiffness, which is calculated from the force-central deflection curves as the tangent stiffness of the cracked state; and the load at the serviceability limit state (SLS). According to the Eurocode 2—Part 1 (CEN 2004), the SLS is reached when the midspan deflection becomes equal to $\ell /250$, where $\ell$ is the slab’s effective span (here this deflection is equal to 6 mm).

As designed, the control slab (CON) failed in flexure after yielding of the steel reinforcement and the development of significant plastic deformations. The first flexural cracks appeared at a load level of 40 kN, which resulted in a decrease in the stiffness as depicted by the slope change in Fig. 6. This was followed by steel yielding and further development of the cracks [Fig. 7(a)], accompanied by large deflections. As expected, all corners of the slab were progressively uplifted as a result of the significant twisting moments [Fig. 8(a)]. Ultimately, the control slab reached a maximum load of 95 kN. At that point the collapse mechanism of the slab involved the formation of an almost circular-shaped crack, which appeared at the top of the slab [marked red in Fig. 8(b)], as a result of moment redistribution at very large displacements.

Slab C1, which was strengthened with one carbon-fiber TRM layer, failed in a similar way (flexure-dominated behavior) but at a substantially higher load, equal to 207 kN, owing to the contribution of the TRM to the flexural resistance. The slab exhibited a stiffer behavior with respect to the control slab (42% increase in the precracking stiffness—see Table 2), and as indicated by the change in the slope of the load-displacement curve in Fig. 6, the cracking load was also increased, reaching 70 kN. The activation in tension of the fibers crossing the flexural cracks resulted in a significant increase of the postcracking flexural stiffness ($4.25\mathrm{kN}/\mathrm{mm}$) when compared to the CON slab ($1.0\mathrm{kN}/\mathrm{mm}$). The postcracking stiffness in Table 2 has been calculated as the slope between the cracking point and the ultimate load in the load-midspan deflection curves. Fig. 7(b) shows the crack pattern of the C1 slab, which comprises a few major cracks and several minor cracks on the face of the TRM. Failure of this specimen was progressive, as a result of the fibers’ partial rupture and slippage within the mortar layer across the major cracks that are visible in Fig. 7(b). After the flexural capacity was reached, the load gradually dropped and a circular-shaped crack appeared at the top of the slab as a part of the collapse mechanism at large displacements, similarly to the CON specimen.

Slab C2, which was strengthened with two carbon-fiber TRM layers, failed at an even higher load, equal to 291 kN, owing to the contribution of the additional carbon TRM layer. The cracking load for this specimen was 90 kN, whereas even higher precracking and postcracking stiffnesses (17.6 and $7.5\mathrm{kN}/\mathrm{mm}$, respectively) compared to C1 were recorded. Failure of this specimen was attributed to partial slippage of the fibers within the mortar across two cracks [Fig. 7(c)], followed by concrete punching shear [Fig. 8(c)]. The brittle nature of this failure mode resulted in a very abrupt load drop at levels slightly above the ultimate capacity of the CON slab (Fig. 6). The residual capacity was provided by both the steel reinforcement and the TRM layers through the development of a membrane resisting mechanism. The punching area at the top of the slab had a rectangular shape following the perimeter of all four load-application points, indicating that this failure might not have occurred if loading was uniformly distributed.

Slab C1_part, which was strengthened with the same amount of textile reinforcement with slab C1 but in a different configuration (Fig. 2), failed in flexure at an ultimate load of 178 kN. The initial stiffness of this specimen reached even higher levels ($24.1\mathrm{kN}/\mathrm{mm}$) compared to the slabs C1 and C2. The first cracks were developed at a load level of 75 kN, whereas the postcracking stiffness ($6.25\mathrm{kN}/\mathrm{mm}$) was very close to the average of the C1 and C2 slabs’ postcracking stiffness (Table 2). This specimen failed in flexure after yielding of the steel reinforcement and slippage of the textile fibers through the mortar, but with a different crack pattern at the face of TRM. As illustrated in Fig. 7(d), four major cracks were developed on the face of TRM at the overlapping region of the two strips. The fibers crossing these cracks were highly stressed and ultimately experienced partial rupture and slippage within the mortar, which led to a gradual drop of the load as shown in Fig. 6. The cracks that appeared on the face of the TRM composite did not appear at the location of the cracks developed at the concrete substrate, as revealed in the uncovered part of the slab in Fig. 4(e).

Slab G3, which was strengthened with three layers of glass-fiber TRM, failed in flexure after yielding of the steel reinforcement, at an ultimate load of 142 kN. The initial stiffness of this slab was high enough ($22.0\mathrm{kN}/\mathrm{mm}$), owing to the thickness of the mortar needed for the application of three layers. The load level at first crack was equal to 90 kN, whereas the postcracking stiffness ($4.05\mathrm{kN}/\mathrm{mm}$) was lower than all the other retrofitted slabs. As illustrated in Fig. 7(e), the crack pattern of slab G3 comprised only a few major cracks on the face of the TRM. The failure mode of this specimen is associated with the partial rupture and slippage of the glass fibers within the mortar along the developed cracks [Fig. 8(d)]. This failure mode was identical to that observed in slabs C1 and C1_part and similarly led to a gradual drop of the load.

Finally, specimen C3_cr, which was initially precracked and retrofitted with three layers of carbon-fiber TRM before testing, failed in flexure at a load equal to 302 kN. As shown in Fig. 6, the initial stiffness of this slab was much lower than the stiffness of the rest of the specimens, owing to the cracked state of the concrete. At a load level of 50 kN the stiffness was significantly increased, thus indicating the full activation of the strengthening layers in tension. At this stage, the bending stiffness of slab C3_cr was higher than the stiffness of slab C2 ($10.5\mathrm{kN}/\mathrm{mm}$) as a result of the third TRM layer. Failure was attributed to slippage of the textile fiber within the mortar mainly along the cracks shown in Fig. 7(f).

All slabs responded as designed and failed after yielding of the internal steel reinforcement because of the failure (slippage and/or partial fracture) of the externally bonded TRM reinforcement. The flexural capacity of the lightly reinforced concrete slabs was substantially increased by all strengthening schemes proposed in this study. In terms of the various parameters investigated in this experimental program, an examination of the results (Table 2) in terms of ultimate capacity, cracking load, precracking (initial) stiffness, postcracking stiffness, and resistance at the serviceability limit state (SLS) revealed the following information.

In an attempt to provide simple design equations for calculating the flexural moment of resistance per unit length of two-way slabs retrofitted with TRM, two steps were followed.

Initially, the experimental moment of resistance of the retrofitted slabs was derived after calibrating Eq. (1) to the results of the unretrofitted (CON) slabwhere $P_{\text{max}}$ = flexural load-bearing capacity; $k$ = load to moment calibration factor; and $m_R$ = flexural moment of resistance per unit length. Through the use of standard cross section analysis-based analytical modeling (Navier-Bernoulli hypothesis for plane cross sections) and the rectangular stress block approach for concrete in compression (without safety factors), the unretrofitted specimen (CON) yielded a value of $m_R=6.0\mathrm{kNm}/\mathrm{m}$. By substituting the ultimate load measured experimentally and the flexural moment of resistance per unit length calculated analytically for the unretrofitted specimen, Eq. (1) yielded a value of $k$ equal to 15.8. This calculated value of $k$ was then used in combination with the peak force of the strengthened specimens (Table 2) to determine the experimental flexural moment of resistance per unit length $m_{R,\exp }$ (second column of Table 3). Note that slab C3_cr was not included in this procedure because of its initial cracked situation.

This approximate approach for defining factor $k$ was deemed necessary because of the lack of reliable analytical models in the literature that correlate the moment of resistance (per unit length) to the applied load in two-way slabs. The value of the $k$ factor, which is commonly derived by applying the so-called yield line theory, is sensitive to the crack (or yield) pattern, which in turn depends on the slab’s aspect ratio, the loading and the support conditions. The equation proposed by Rankin and Long (1987) and used also by Ebead and Marzouk (2004) for calculating the flexural capacity of two-way slabs having a crack pattern quite similar to the one observed in this study yielded a value of $m_R$ equal to $11.2\mathrm{kNm}/\mathrm{m}$. This value underestimates the load-carrying capacity of the unretrofitted slab by 29% and hence it was not further considered for this study.

The effective tensile stress in the TRM reinforcement at flexural failure, $f_{te}$, was then calculated based on the $m_{R,\exp }$ values, using cross section analysis for the flexurally strengthened slabs, with the tensile force (per unit length), $F_t$, carried by the TRM layers being expressed by the Eq. (2)where $w_t/w_s$ = factor to account for the case where the TRM width ($w_t$) covers only a part of the slab width ($w_s$), like in the C1_part specimen.

The obtained TRM effective stress and concrete strain values at the ultimate limit state (failure of TRM) are reported in Table 3 as $f_{te,\exp }$ and ${ϵ}_{c,\exp }$, respectively. It is observed that in the case of full coverage of the slab’s tensile face with TRM, for textile reinforcement ratios, ${\rho }_t$, in the range of 0.095–0.19%, the TRM effective stress varies between 765 and 922 MPa for carbon TRM and is approximately 300 MPa for glass TRM. However, in the case of half coverage of the slab’s tensile face with carbon TRM in each direction, a much higher stress value of 1,305 MPa was obtained, indicating better fiber utilization when applied close to the region of maximum moments. The concrete strain values were close to 1% in both cases of coverage.

Based on the above findings and with the aim of eliminating the need for iterative calculations and cross section analysis, simple formulas for the calculation of the flexural moment of resistance of slabs retrofitted with TRM are proposed in this study. Following the suggestion of Ebead and Marzouk (2004) for the case of FRP retrofitted slabs, here the moment of resistance per unit length, $m_R$, can be calculated as the summary of the contribution of the steel reinforcement, $m_{Rs}$, and the TRM, $m_{Rt}$ [Eq. (3)]

The contribution of the steel reinforcement to the total moment of resistance can be approximately taken equal to the moment of resistance of the unretrofitted slab. Based on the recommendations of ACI 318-08 (ACI 2008), the following simple formula to calculate $m_{Rs}$ (in absence of compression reinforcement) is proposed:

The contribution of the textile reinforcement to the moment of resistance is calculated by Eq. (5)where $F_t$ is expressed by Eq. (2), and the neutral axis depth, $x$, is calculated via Eq. (6)

It is proposed in this study that the value of TRM effective stress ($f_{te}$) to be used in Eqs. (2) and (6) can be calculated from Eq. (7) for carbon-fiber TRM, whereas for glass fiber TRM a value of $f_{te}=300\mathrm{MPa}$ should be considered until more experimental data become available. Eq. (7) has been derived by fitting a power equation to the experimental results, considering the different reinforcement ratios of specimens C1, C2, and C1_part (Fig. 10). An upper limit for $f_{te}$ has been set to 1,300 MPa

The value of concrete compressive strain to be used in Eq. (6) is suggested to be ${ϵ}_c=0.001$ (based on the values of ${ϵ}_{c,\exp }$ in Table 3). A sensitivity analysis showed that the results are not very sensitive to this parameter. For example, by increasing ${ϵ}_c$ from 0.005 to 0.0035 (600% increase), $m_{Rt}$ decreases by 20%, whereas for more rational values of ${ϵ}_c$ in the range of $0.01\pm 0.005$ the $m_{Rt}$ values change from $-5.5\%$ to $+4.5\%$.

For design purposes it is recommended to use a design value of the TRM contribution to the moment of resistance, simply by using a design value for the effective stress, $f_{\text{ted}}$ (dashed curve in Fig. 10). This value is here suggested to be calculated as

By applying the proposed methodology [Eqs. (1)–(8)], the theoretical values of the flexural moment of resistance, $m_{R,\mathrm{theor}}$ (using $f_{te}$ values), as well as the design values, $m_{R,d}$ (using $f_{\text{ted}}$ values), were calculated for the retrofitted slabs tested in this study and are presented in Table 3 (except for the slab C1_cr). The results show very good agreement between the experimental and theoretical values of the flexural moment of resistance. The suggestions for the value of the effective stress that should be used in Eqs. (2) and (6) are based only on the results of this study and therefore should be treated carefully. A refined model should be developed when more experimental data will become available. After obtaining the flexural capacity of the retrofitted slabs, the design engineer should check that it does not exceed the punching shear capacity.

This paper presents an experimental investigation on the effectiveness of a novel material, namely textile-reinforced mortar (TRM), as a means of strengthening in flexure two-way RC slabs. The design of specimens allowed the investigation of a series of parameters including the number of TRM layers, the strengthening configuration, the type of fibers, and the role of initial cracking in the slab. In addition, design equations are suggested, based on the test results. The main conclusions are summarized in a rather qualitative manner as follows:

In view of the limited number of tests performed in this study, the above results as well as the design equations should be considered as rather preliminary. Future research should be directed toward providing a better understanding of parameters, including textile geometry, steel reinforcement ratio, and different slab dimensions, to investigate possible scale effects.

The authors wish to thank the students Joshua Spong, Sultan Alotaibi, Saad Raoof, and Zoi Tetta, the lab manager Mike Langford, the chief technician Nigel Rook and the technicians Gary Davies, Sam Cook, and Balbir Loyla, for their assistance in the experimental work. The research described in this paper has been financed by the University of Nottingham through the Dean of Engineering Prize, a scheme for pump priming support for early career academic staff.