Properties of fibre-reinforced self-compacting concrete subjected to prolonged mixing: an experimental and fuzzy logic investigation

Abstract

This article investigates the effect of prolonged mixing on the rheological properties and compressive strength of fibre-reinforced self-compacting concretes (FRSCCs). Twenty FRSCC mixes with five cementitious material contents (300, 350, 400, 450 and 500 kg/m³) and three types of fibres and dosages (polypropylene at 0.1%, steel at 1.0%, or synthetic at 1.0%) were first produced. The mixes were then subjected to four mixing intervals of 20 min each (total mixing time = 80 min). The rheological properties of the fresh FRSCC mixes were examined, and the corresponding compressive strength of the hardened FRSCCs was subsequently obtained. Overall, the results from slump flow, T50, V-funnel and L-box tests on fresh mixes, as well as the 28-day compressive strength on the hardened FRSCCs, were in line with previous results reported in the literature. The results show that all mixes lost their self-compacting properties after 80 min of mixing. It was also found that mixes with high cementitious material contents (500 kg/m³) and highest polypropylene fibre dosage were most affected by prolonged mixing, with average losses of 30% and 35% in rheological properties and compressive strength, respectively. Based on the test results, this study proposes a novel fuzzy logic approach to predict the slump loss and at 28-day compressive strength loss of FRSCCs subjected to prolonged mixing. This article contributes towards a better understanding of FRSCCs after prolonged mixing, which can help make informed decisions about their use in new and repaired concrete structures.

1 Introduction

1.1 Background

Self-compacting concrete (SCC) is widely used in structures where casting, compaction and vibration are problematic or challenging. Fibres are often added to SCC on site to produce fibre-reinforced self-compacting concrete (FRSCC) for applications such as tunnel linings, concrete road pavements or repair overlays. The fibres reduce the plastic shrinkage of fresh concrete [1] and increase the permeability and toughness of the hardened concrete [2], as well as fatigue resistance [3]. However, the presence of fibres can also reduce the workability and flowability of fresh FRSCC mixes [4]. As a result, the rheological properties of FRSCC are of particular interest to engineers and concrete technologists [5,6,7]. For instance, Güneyisi et al. [8] studied the fresh and rheological properties of glass FRSCC containing nanosilica and fly ash to optimise the fibre dosage. Alberti et al. [9] also proposed optimising the fibre dosage using blends of various types of fibres, including steel and polyolefin fibres. Algin et al. [10] studied the effects of chopped basalt fibres on the fresh and hardened properties of FRSCC and proposed optimum dosages and length of fibres. Lee et al. [11] examined the rheological properties and flow characteristics of self-compacting synthetic fibre-reinforced cementitious composites to quantify the effect of water-to-binder ratio and fibre dosage. All the above studies identified the need for further research into the fresh and hardened properties of FRSCC.

The strength and durability of concrete depend heavily on the rheological properties of the fresh mix. Very often, the degradation of rheological properties over time is measured by the ‘slump loss’ [12], which is linked to the loss of free water in ‘plastic’ concrete. Whilst the free water is mainly eliminated by the hydration of cement and evaporation [13], other technological aspects like the duration of mixing, transportation, delivery, placing, compacting and finishing of the concrete can also affect the slump loss [14]. To compensate for the expected loss of rheological properties, plasticisers and/or superplasticisers are often added to the concrete [15, 16]. Whilst this is a common practice, high amounts of additives can have detrimental effects on the rheological and mechanical properties of concrete [17,18,19]. The amount of superplasticiser used for this purpose depends on the specific properties of the cement and mix proportion of concrete [20,21,22], and thus it should be carefully chosen.

Delays and long distances between the concrete plant and construction site can sometimes prolong mixing time in a truck’s drum, which in turn stiffens the concrete due to a reduction in the free water contents. Such water reduction also reduces the flowability of concrete [23], as well as its workability and compressive strength [22]. Moreover, whilst current codes of practice [e.g. ASTM C94 [24]] indicate that the discharge of a concrete mix should be completed within 90 min after the start of mixing (or before the drum of the mixer has revolved 300 times), no equivalent guidelines exist for FRSCC and thus its rheological properties have to be examined on an ad-hoc basis. As this examination can be costly and time-consuming, there is a need to develop practical models to calculate the properties of FRSCCs after a potential prolonged mixing time. These models can help designers and concrete technologists make informed decisions about the suitability of such concretes for use in a structure.

In the last decades, numerous studies have applied soft computing methods to predict different properties of concrete, such as artificial neural networks [25,26,27,28,29,30,31], nature-inspired algorithms [32] and fuzzy logic systems [29,30,31,32,33,34,35,36]. For example, Silva et al. [37] successfully combined fuzzy logic and genetic algorithms to predict concrete shrinkage. Arslan et al. [38] used a rule-based Mamdani type fuzzy logic model to predict the bond behaviour of lightweight concrete. Najjar et al. [39] predicted the engineering properties of pre-placed aggregate concrete using fuzzy logic systems. They showed that the proposed model was a useful aid for the design of such mixes. Rashid et al [40] predicted the compressive strength of concrete containing green foundry sand by using fuzzy logic systems. Beycioglu et al. [41] developed a rule-based Mamdani type fuzzy logic model to predict the mechanical properties of blended cements at elevated temperatures. Among these above-mentioned mathematical methods, fuzzy systems have proven successful to calculate the fresh properties of fibre-reinforced concrete [42]. To date however, the application of fuzzy logic systems for calculating the fresh properties of FRSCC has not been examined.

1.2 Research gap

The existing literature has identified the need for a better understanding of the rheological properties of FRSCC and thus more research is necessary to address this knowledge gap. This is even more relevant in cases where FRSCC is subjected to prolonged mixing, which can often occur due to delays in discharge time. Whilst current codes of practice suggest discharge times for normal concrete mixes, no equivalent guidance exists for FRSCC. Moreover, to date, limited work exists on the use of soft computing methods to predict the rheological properties of FRSCC.

This article investigates the effect of prolonged mixing on the rheological properties and compressive strength of FRSCC. Twenty mixes with five cementitious materials contents (300, 350, 400, 450 and 500 kg/m³), and three types of fibres and fibre dosages (polypropylene at 0.1%, steel at 1% or synthetic at 1%) were produced. The mixes were then subjected to a prolonged mixing (up to 80 min) divided into four intervals of 20 min each. Tests performed after each interval included the slump flow, T50, V-funnel and L-box tests on fresh mixes, as well as the 28-day compressive strength on the hardened FRSCCs. Based on the test results and on a fuzzy system with a generalized Mamdani’s interference engine and four different t-norms (minimum, product, Lukasiewicz and Einstein product), this study also proposes a new approach to predict the slump flow loss and the 28-day compressive strength loss of FRSCCs subjected to prolonged mixing.

1.3 Research significance

FRSCCs are more used nowadays in new structural projects and building repairs. The experimental results from twenty mixes and three different types of fibres extensively used in construction (polypropylene, manufacture steel, and synthetic) provide new insights into the rheological and hardened properties of FRSCCs subjected to prolonged mixing. The methodology systematically investigates the properties of typical mixes currently used in the construction industry, and therefore the test results can serve as a benchmark for future studies in the field. The novel fuzzy system approach proposed in this study also extends the applicability of soft computing methods to the prediction of FRSCCs’ properties subjected to prolonged mixing, which has not neem investigated before. This study is part of a wider research effort that aims to investigate the use of different types of self-compacting concrete as repair overlays [43]. Ultimately, this article contributes towards a better understanding of the rheological and hardened properties of FRSCC after prolonged mixing, which can help engineers and concrete technologists make informed decisions about the suitability of such concretes for use in structures.

2 Experimental programme

2.1 Mix proportions and materials

Table 1 summarises the twenty mixes produced in this study. Five amounts of cementitious materials were considered: 300, 350, 400, 450 and 500 kg/m³. FRSCC mixes usually have more than 300 kg/m³ of cementitious materials so as to achieve the typical compressive strengths specified for most structural applications. Likewise, more than 500 kg/m³ of cementitious materials in a mix typically causes a very high hydration heat, which can cause early cracking. All mixes had fly ash at a 10% replacement level by weight of cement. In order to improve the rheological properties of FRSCC mixes produced in this study, limestone powder was used as a filler in the mixes. Such material is not used as a binder but due to its fineness and filling properties, it helps improve the rheological behaviour of self-compacting concretes. The mix design was carried out following the recommendations by EFNARC [44].

Table 1 Mix proportions of FRSCC mixes

The fine aggregate of all FRSCC mixes consisted of river sand with a maximum size of 3.0 mm, an apparent specific gravity of 2700 kg/m³, and a water absorption of 1.5%. Coarse aggregate with a maximum size of 12.5 mm was used. Cement type CEM II 42.5 was used. Normal tap water was used in all FRSCC mixes. The amount of superplasticiser in all mixes was equal to 1.2% of the weight of all cementitious materials. The coarse to fine aggregate ratio and water to powder (cement + fly ash) ratio were kept constant and equal to 1.17 and 0.36, respectively. Three types of fibres with optimised dosages in terms of mechanical properties and volume fractions as proposed in references [45, 46] were used: polypropylene at 0.1%, steel at 1.0%, and synthetic fibres at 1.0%. Figure 1 shows the fibres used in the FRSCC mixes, whereas Table 2 lists their corresponding physical and mechanical properties. Likewise, Table 3 summarises the physical properties and chemical composition of the cement and fly ash used in the mixes. The specific weight of the limestone powder was 2.7 g/cm³.

Fig. 1

Fibres used in FRSCC mixes a synthetic, b steel, and c polypropylene

Table 2 Properties of fibres used in FRSCC mixes

Table 3 Physical properties and chemical composition of cement and fly ash used in FRSCC mixes

In Table 1, the twenty FRSCC mixes are identified according to the amount of cementitious materials and type of fibres (PP = polypropylene, ST = steel, SYN = synthetic). Mixes P300, P350, P400, P450 and P500 were control mixes without fibres. The mixes were produced in laboratory conditions, and therefore the effect of wind on surface evaporation was controlled. The temperature ranged between 18 °C and 23 °C on the days of the tests.

2.2 Mixing procedure

All materials were initially mixed for 5 min to homogenise the mix. Following this initial mixing, slump flow (see Fig. 2a), T50 (Fig. 2b), V-funnel (Fig. 2c) and L-box (Fig. 2d) tests were conducted on all mixes. The results from these initial tests were considered as t = 0 min. The above tests were then repeated after t = 20, 40, 60, and 80 min of mixing in a pan mixer. This is in line with ASTM C94 [24] that indicates that mix discharges should be completed within 90 min in after initial mixing. It should be noted that the above tests were also carried out at t = 100 min, but these proved unreliable as all mixes lost their self-compacting properties after t = 80 min. The mixing speed was constant and set to 8.0 rpm. Cubic moulds of 150 mm were filled after each mixing interval (t = 0, 20, 40, 60, and 80 min) to determine the compressive strength (f_cm) at 28 days. All cubes were cured in water for those 28 days. The average compressive strength of each mix was obtained from three cubic specimens.

Fig. 2

Tests on FRSCC mixes a slump flow, b T50 time, c L-box, and d V-funnel

3 Results and analysis

3.1 Rheological tests

Table 4 summarises the rheological and mechanical properties of the FRSCC mixes. The most relevant results are discussed in the following sections.

Table 4 Rheological and mechanical properties of FRSCC mixes

3.1.1 Slump flow tests

As expected, the slump flow reduced with increasing mixing times. For example, the slump flow of mix P300 dropped by 4.6% at t = 20 min, and then 12.4% at t = 60 min. The results also indicate that higher cementitious material contents increased the paste contents and thus the mixes’ flowability. This in turn increased the slump flow results between t = 0 and t = 20 min. For instance, compared to P300PP, the slump flow of P500PP increased by 19.4% and 15.3% at t = 0 and t = 20 min, respectively. However, with increasing mixing time, mixes P450 and P500 had a more rapid loss of slump. For example, compared to P300SYN, the slump flow of mix P450SYN was 2.0% and 7.1% lower at t = 40 min and t = 60 min, respectively. This faster slump flow loss can be attributed to the fact that during the hydration process, an increase in temperature increases the evaporation of the free water in the mix. Therefore, the initial setting is faster, as it is the slump flow loss. The results from these tests are in line with those reported by Zayed and Almalki [22], who found that the diameter of the slump flow test decreased from 67 cm at t = 0 to 49 cm at t = 90 min in SCC mixes with a superplasticiser dosage of 1.5% of cement mass.

The results in Table 4 also indicate that the addition of fibres reduced the slump flow, in particular in the case of mixes with polypropylene fibres. The negative effect of the fibres also increased with the amount of cementitious materials. For example, compared to counterpart mixes without fibres and at t = 60 min, the slump flow reduction of mix P300ST was 7%, whereas such reduction was 11.2% for mix P450ST. Moreover, the fibres speeded up the loss of self-compacting properties at t = 60 min (instead of t = 80 min for mixes without fibres). This is more evident in mixes P500X (X = type of fibre), where the self-compacting properties were lost at t = 40 min only. It should be noted that, in this study, it is assumed that the mixes are self-compacting up to a slump flow of 500 mm. However, guidelines such as EFNARC [44] adopt a slump flow limit for SCC of 600 mm, whereas other guidelines (e.g. [47], [48] adopt a limit of 550 mm.

3.1.2 T50 tests

Overall, high amounts of cementitious materials resulted in higher T50 time. For example, T50 was 4.2 s for P300 at t = 0 min, whereas such value was 6.2 s for P400 (i.e. 37.5% higher). In all cases, the presence of fibres increased T50 time. For mixes P450X, the polypropylene fibres increased T50 by 7.3%. In general, the highest increments in T50 time corresponded to polypropylene fibres. Due to their small size and capillary properties, polypropylene fibres tend to bond better to the paste and aggregates, which in turn reduces the flowability of the FRSCC. Comparatively, Zayed and Almalki [22] reported that SCC mixes with a superplasticiser dosage of 1.5% of cement mass did not reach the 50 cm diameter mark after a mixing time t = 90 min.

3.1.3 V-funnel tests

The presence of the fibres, in general, increased the discharge time. For instance, at t = 0 min, the discharge time of P350PP increased by 18.2% compared to P350. The highest increase in discharge time was for mixes with steel fibres. This can be attributed to the larger size of the steel fibres. Indeed, as FRSCCs with steel fibres tried to leave the V-funnel outlet, it was observed that the path was partially blocked, and this reduced the speed of concrete discharge. It was also observed that, as the amount of cementitious materials and mixing time increased, mixes P450 and P500 lost their homogeneity and therefore their discharge time decreased (especially at t = 40 min). Overall, the results show that the discharge time increased with the mixing time. This is consistent with the V-funnel test results reported by Zayed and Almalki [22], who indicate that the discharge time after a mixing time t = 90 min was approximately twice the discharge time at t = 0.

3.1.4 L-box tests

Whilst the blockage ratio was 1.0 until t = 40 min for P300, P350 and P400, such ratio was reached just at t = 20 min for P450 and P500. Also, adding fibres to the mixes reduced the initial blockage ratio. Similar to the case of the V-funnel tests, the addition of fibres had more negative effects on the results. For example, the polypropylene, steel and synthetic fibres reduced the blockage ratio of P350X by 18.4%, 29.9% and 23.0% at t = 60 min, respectively. The results in Table 4 also show that an increase in the amount of cementitious materials had a minor effect on blockage ratio, except for mixes P500 where the blockage ratios tended to be smaller than those of P300. The above results coincide with previous findings [22] which indicate that the blockage ratio decreases with the increase in mixing time.

3.2 Compressive strength test results

Table 4 also lists the mean compressive strength f_cm of all mixes. The tests were conducted according to ASTM C39 [49]. The results show that a prolonged mixing time decreased consistently the value f_cm in all mixes. Among the mixes without fibres, mix P500 experienced the highest reduction in f_cm with increasing mixing time, whereas mixes P300 and 350 had the lowest reduction in f_cm. It is also shown that higher amounts of cementitious materials worsen the negative effect of mixing time on compressive strength. For instance, at t = 60 min, the f_cm of P300 dropped by 19.3%, whereas the f_cm of P450 dropped by 28.4%. Overall, the presence of steel and synthetic fibres had minor effects on f_cm over time. However, polypropylene fibres reduced f_cm over time more significantly. For example, for mixes P400X at t = 20 min, f_cm dropped by 8.9%, 4.8%, and 5.0% after polypropylene, steel, and synthetic fibres were added, respectively.

In general, the test results indicate that only mixes P300, P350, P400 and P450 (all without fibres) maintained their self-compacting properties up to t = 80 min. The largest loss in slump flow (of about 30%) was for mix P500PP. Not surprisingly, such mix also experienced the largest drop in f_cm (about 35%). The reason for this can be attributed the fact that all mixes had the same water to cementitious materials ratio. The higher the cementitious materials contents, the more water in the concrete. By increasing the mixing time in a mix with more cementitious materials, more water is lost and therefore higher losses were observed.

As the slump flow is deemed as an indicator of the rheological properties of FRSCC, Table 5 in Appendix A summarises the slump flow loss after each step. Based on the test results presented above, the following section proposes a fuzzy system to calculate the slump flow and 28-day compressive strength losses of FRSCCs.

4 Prediction of slump flow and compressive strength losses

The three variables found in this study to affect the rheological and mechanical properties of FRSCC (i.e. mixing time, powder content and type of fibres) are chosen here to predict the slump flow and compressive strength losses. It should be also mentioned that the data from mixes with 300, 400 and 500 kg/m³ cementitious materials contents were used to create the fuzzy system. Then the system was tested using the results from mixes with 350 and 450 kg/m³ of cementitious materials.

4.1 Background on generalized Mamdani’s fuzzy system

A three-step algorithm was used to design the fuzzy system. Suppose that $N$ input–output pairs $(x^{1} ,y^{1} )$,$(x^{2} ,y^{2} )$,…,$(x^{N} ,y^{N} )$ are given, where $x^{k} = (x_{1}^{k} ,...,x_{n}^{k} )$,$\forall k \in \{ 1,...,N\}$, i.e., ${\mathcal{X}}^{\mathcal{K}}\in U={U}_{1\times }{U}_{2\times \dots \times }{U}_{\mathcalligra{n}}\subseteq {\mathcal{R}}^{\mathcalligra{n}}$ and ${\gamma }^{\rm K}\epsilon V\subseteq \mathcal{R}$. The objective was to design a fuzzy system $f(x)$ based on $M$ input–output pairs (training phase), according to the following steps:

Step 1. Define fuzzy sets to cover the input and output spaces. For each $U_{j}$($j = 1,...,n$), $M$ fuzzy sets are defined $A_{j}^{l}$ ($l = 1,...,M$), which are required to be complete in $U_{j}$. This is, for any $x_{j} \in U_{j}$, an $A_{j}^{l}$ exists such that $\mu_{{A_{j}^{\,l} }} (x_{j} ) \ne 0$. For example, by defining $\mu_{{A_{j}^{\,l} }} (x_{j} )$ as a Gaussian membership function (Eq. (1)), it may be considered that $\sigma_{j}^{l} = \left| {\,\overline{x}_{\,j}^{\,(l + 1)} - \overline{x}_{\,j}^{\,l} \,} \right|/2$($l = 1,2,...,M$):

$$\mu_{{A_{\,j}^{\,l} }} (x_{j} ) = e^{{ - \,\,\left( {\frac{{x_{j} - \overline{x}_{\,j}^{\,l} }}{{\sigma_{j}^{l} }}} \right)^{2} }}$$

(1)

where $\overline{x}_{j}^{\,l}$ is the centre of the individual fuzzy set $A_{j}^{l}$; and $\sigma_{j}^{l} > 0$.

Step 2. Create the fuzzy rule base. In this step, the algorithm generates one rule from one input–output pair. Specifically, for each input–output pair $(x^{l} ,y^{l} ) = (x_{1}^{l} ,...,x_{n}^{l} ,y^{l} )$, $l = 1,2,...,M$, the algorithm obtains a fuzzy IF–THEN rule as follows:

$$Rule(l):\,\,IF\,(x_{1}^{l} \,\,is\,\,A_{1}^{\,l} )\,and\,(x_{2}^{l} \,\,is\,\,A_{2}^{\,l} )\,and\,...\,and\,(x_{n}^{l} \,\,is\,\,A_{n}^{\,l} ),\,THEN\,(y^{l} \,\,is\,\,B^{\,l} )$$

(2)

where $A_{i}^{\,l}$ and $B^{\,l}$($l = 1,2,...,M$) are fuzzy sets in ${U}_{i}\subseteq \mathcal{R}$ ($i = 1,2,...,n$); and$V\subseteq \mathcal{R}$. Moreover, $x = (x_{1} ,x_{2} ,...,x_{n} )^{T} \in U$ and $y \in V$ are the input and output variables of the fuzzy system, respectively, where$U={U}_{1\times }{U}_{2\times \dots \times }{U}_{\mathcalligra{n}}{\subseteq \mathcal{R}}^{\mathcalligra{n}}$. Fuzzy implications convert a fuzzy IF–THEN rule into a fuzzy relationship in the input–output product space $U \times V$.

Step 3. Construct the fuzzy system based on the fuzzy rule base. The algorithm then uses Eq. (3) to construct the fuzzy system based on the fuzzy rule base created in Step 2:

$$f(x) = \frac{{\sum\nolimits_{l = 1}^{M} {\overline{y}^{\,l} \,\,\varphi_{j = 1}^{n} (\mu_{{A_{j}^{\,l} }} (x_{j} ))} }}{{\sum\nolimits_{l = 1}^{M} {\,\varphi_{j = 1}^{n} (\mu_{{A_{j}^{\,l} }} (x_{j} ))} }}$$

(3)

where $\mathcal{x}\in U \subseteq {\mathcal{R}}^{n}$ is the input to the fuzzy system; and $\mathcal{F}\left(\mathcal{x}\right)\in V\subseteq \mathcal{R}$ is the output of the fuzzy system (desired approximator).

4.2 Proposed fuzzy system

To predict the slump flow and 28-day compressive strength losses, the fuzzy system (Eq. (3)) is applied along with a generalised Mamdani’s inference engine defined by the minimum t-norm $\varphi (x,y) = \min \{ x,y\}$, product t-norm $\varphi (x,y) = xy$, Lukasiewicz t-norm $\varphi (x,y) = \max \{ x + y - 1,0\}$ and Einstein product t-norm, as specified in Eq. (4):

$$\varphi (x,y) = \left\{ {\begin{array}{*{20}c} 0 & {x = y = 0} \\ {\frac{xy}{{2 - (x + y - xy)}}} & {otherwise} \\ \end{array} } \right.$$

(4)

Also, a singleton fuzzifier and a centre average defuzzifier are used based on Eq. (5) and Eq. (6), respectively. Gaussian membership functions are also defined for the inputs (i.e. mixing time, type of fibres and powder content), as shown in Fig. 3a–c.

$$\mu_{{A^{\prime}}} (t) = \left\{ {\begin{array}{*{20}c} 1 & {t = x} \\ 0 & {otherwise} \\ \end{array} } \right.$$

(5)

$$y^{*} = \frac{{\sum\nolimits_{l = 1}^{M} {\overline{y}^{l} \,w_{l} } }}{{\sum\nolimits_{l = 1}^{M} {w_{l} } }}$$

(6)

where $y^{*} \in U$; $\overline{y}^{\,l}$ is the centre of the $l$ ‘s individual output fuzzy set $\overline{B}^{\,l}$; and $w_{l}$ is its height.

Fig. 3

Membership functions for three inputs a mixing time, b type of fibre, and c powder content

Figures 4a–d and 5a–d compare, respectively, the slump flow loss and 28-day compressive strength loss calculated by each fuzzy method with the test results presented in Table 5. The results in Figs. 4a–d indicate that the proposed system and the t-norms predict accurately the slump flow loss, with the best results being for the minimum t-norm (R² = 0.96 in Fig. 4b). Likewise, Figs. 5a–d show that all t-norms give reasonable predictions of the 28-day compressive strength loss (R² = 0.83–0.86), with the best result being for the Einstein product t-norm giving R² = 0.86 (see Fig. 5d).

Fig. 4

Prediction of slump flow loss with proposed fuzzy logic inference system using different t-norms:a product t-norm, b minimum t-norm, c Lukasiewicz t-norm, and d Einstein product t-norm,

Fig. 5

Prediction of 28-day compressive strength loss with proposed fuzzy logic inference system with different t-norms: a product t-norm, b minimum t-norm, c Lukasiewicz t-norm, and d Einstein product t-norm

Based on linear regression, Eqs. (7) and (8) are also proposed here to predict slump flow loss (SFL) and 28-day compressive strength loss (CSL), respectively:

$$SFL \left(\mathrm{\%}\right)= -30.241+0.445\cdot MT+0.060\cdot PC+1.328\cdot TF$$

(7)

$$CSL \left(\mathrm{\%}\right)= -49.198+0.669 \cdot MT+0.087\cdot PC+2.542\cdot TF$$

(8)

where MT is the mixing time in minutes; PC is the powder content (cement + fly ash) in kg/m³; and TF is the type of fibre (TF = 1 for no fibres, TF = 2 for synthetic fibres, TF = 3 for steel fibres, and TF = 4 for polypropylene fibres).

Figure 6 compares the test results with the values SFL and CSL calculated by Eqs. (7) and (8), respectively. It is shown that the R² values given by Eqs. (7) and (8) are equal to 0.83 and 0.68, respectively. Therefore, the predictions given by the proposed fuzzy system are more accurate compared to the linear regression results for both slump flow and 28-day compressive strength losses. Moreover, the proposed fuzzy system can be extended to calculate the losses of other FRSCC mixes.

Fig. 6

Test results vs SFL and CSL values calculated by Eqs. (7) and (8)

Based on the results of this study, it is possible to conclude that the use of fuzzy systems with the generalised Mamdani’s inference engine defined by different t-norms is a suitable approach to predict the slump flow loss and 28-day compressive strength loss of FRSCCs due to prolonged mixing time. However, since only a few FRSCC mixes and three types of fibres were used in the training of the fuzzy system, more research is necessary to extend the application of the system to calculate the slump flow and 28-day compressive strength losses of other FRSCC mixes with other types of fibres.

5 Summary and conclusions

This article investigated the effect of prolonged mixing on the rheological properties and compressive strength of fibre-reinforced self-compacting concrete (FRSCC). Twenty mixes with five cementitious materials contents (300, 350, 400, 450 and 500 kg/m³), and three types of fibres and fibre dosages (polypropylene at 0.1%, steel at 1% or synthetic at 1%) were produced. The mixes were subjected to a prolonged mixing (80 min) divided into four intervals of 20 min each (t = 0, 20, 40, 60 and 80 min), after which rheological and 28-day compressive tests were performed. Bassed on the experimental results, a fuzzy system with a generalized Mamdani’s interference engine and four different t-norms (minimum, product, Lukasiewicz and Einstein product) was proposed to predict the slump flow loss and the 28-day compressive strength loss of FRSCCs subjected to prolonged mixing. Based on the results of this study, the following conclusions are drawn:

• All the original and FRSCC mixes lost their self-compacting properties after t = 80 min. Overall, the results from slump flow, T50, V-funnel and L-box tests on fresh mixes, as well as the 28-day compressive strength on the hardened FRSCCs, were in line with previous results reported in the literature.

• As the mixing time increased, the rheological properties of the mixes decreased. Mixes containing high amounts of cementitious materials (500 kg/m³) experienced the most severe loss of rheological properties after t = 40 min.

• In general, the addition of fibres in FRSCCs caused the mixes to lose their self-compacting ability one time interval (i.e. 20 min) earlier, compared to counterpart mixes without fibres.

• Among the three types of fibres examined in the FRSCC mixes, polypropylene fibres had the most negative effect on slump flow and T50 results. However, the highest losses in V-funnel and L-box results as well as in 28-day compressive strength were for mixes containing steel fibres.

• For the FRSCC mixes investigated in this article, the novel fuzzy system approach with a minimum and Einstein t-norms predicted more accurately the slump flow and compressive strength losses (R² = 0.96 and R² = 0.86, respectively) compared to other t-norm methods. Accordingly, fuzzy systems can be effectively used to predict the properties of FRSCCs after prolonged mixing, which can help engineers and concrete technologists make informed decisions about the suitability of such concretes for use in structures.

Appendix

Table 5 Slump flow (SF) loss and compressive strength (CS) loss of mixes