The affordability, resilience, and durability of concrete position it as a widely used construction material. While conventional concrete (CC) has limitations in meeting contemporary needs, collaborative efforts from 1997 to 2002 resulted in ultra-high-performance concrete (UHPC) [^1-2]. UHPC, with superior properties, is reinforced with microsteel fibers and defined by ACI 239R-18 as concrete with a minimum compressive strength of 150 MPa. Its microscopic structure and fiber reinforcement contribute to exceptional performance, with a focus on minimizing heterogeneity [^3-5]. UHPC employs various reactive powders and maintains a low water content for improved performance [^6,7]. Furthermore, UHPC is characterized by its low water content, which lessens the thickness of interfacial transition zones within the cement particles by confining cement particles in small spaces. The disadvantage of this technique is that it reduces the workability of the paste, which requires including superplasticizers in the paste [⁸]. This concrete is, therefore, objectively designed to exhibit improved ductility in addition to high compressive strength [⁹].

The popularity of UHPC is growing, evident in its increased applications in bridge construction for both highway and pedestrian use. It finds use in onshore and offshore infrastructures, with notable benefits in earthquake- or impact-prone regions. Recent studies highlight its application in post-stressed railway sleepers, aiming for cost-efficiency and durability. Field tests on prestressed precast UHPC pilings have also been conducted across various structures [^10-25].

Nevertheless, while UHPC boasts excellent mechanical performance, its high cost, attributed to expensive constituents and the excessive use of natural resources, hinders widespread adoption [^26-29]. To address environmental concerns, waste by-products have been incorporated as supplementary cementitious materials (SCMs) [^30-34]. Moreover, the lack of codified guidelines for material and structural designs poses challenges to the utilization of UHPC mixtures with these SCMs [³⁵].

Concrete's flowability, crucial for efficient construction, is defined as its ability to work without significant homogeneity loss [^36,37]. Assessing this property, often done through a slump cone test, determines how easily fresh concrete can be compacted, finished, and placed on-site without immediate segregation. Customized concrete mixes cater to specific construction types, and flowability is classified as high, medium, low, extremely low, or very low [³⁸]. In concrete technology, flowability is paramount, and advanced mix design procedures alone are insufficient for longevity if proper pouring and compaction are compromised. Hence, understanding factors influencing flowability is imperative.

In the context of UHPC, substituting typical reactive powders with alternative SCMs necessitates rigorous experimental validation to ensure effectiveness [⁶]. New mixture designs with fewer environmental impacts can alleviate barriers to UHPC popularity. However, mandatory lab experimentation is complex due to cost, duration, and labor intensity. Statistical modeling techniques offer a simplified approach to concrete mix design but face challenges with the large number of variables and complex relationships in UHPC, making traditional regression techniques less effective [^38-40].

Artificial Neural Networks (ANNs) have become prominent computational tools for modeling real-life problem-solving, offering insight into complex relationships between input and output data pairs [⁴¹]. Widely applied in civil engineering, ANNs demonstrate competence in solving intricate engineering problems related to traffic management, water resources engineering, structural health monitoring, structural classification, materials simulation, and concrete mix design [^6,42-47]. The scientific literature reflects a growing trend in using ANNs to forecast the mechanical properties of various cement-based materials [^44-47].

ANNs have also been utilized to predict the performance of UHPC through data-driven approaches but limited studies conducted mostly focused on strength forecasting [^48,49]. Despite the effectiveness of ANNs in ensuring prediction accuracy, their application to predict the flowability properties of UHPC, especially when incorporating multiple SCMs, remains a subject of inquiry and requires further exploration.

This research aims to create a model utilizing an ANN approach to simulate the UHPC flowability. Given the intricate composition and rheological behavior of UHPC, particularly in terms of fresh mix flowability, developing an efficient mix design is challenging. The study incorporates a Connection Weight Approach (CWA) into the ANN model, conducting a sensitivity analysis to elucidate the impact of mixture features on flowability. The significance of this work lies in its potential to streamline the UHPC mix design process by offering a reliable tool for predicting flowability properties. The developed ANN model could assist engineers and researchers in optimizing UHPC mixture composition, reducing waste, and improving production efficiency. The research methodology involved data collection on the flowability properties of UHPC mixtures, data preprocessing, construction of an ANN model using collected data and relevant mix design parameters, and rigorous assessment of model accuracy and reliability through statistical analyses and comparisons with a testing data subset.

Data preprocessing involves outliers’ detection and normalization. Outliers, defined as significant deviations from a dataset's general behavior, were identified using bivariate boxplots and Cook's distance [^49-51]. Further information on these procedures can be found in [^48,52-53]. At the end of this process, the database without outliers contained 793 observations.

For its part, data normalization is essential for training ANN regression models. It overcomes issues related to scale and distribution of input variables by bringing them to a common scale (0 to 1 in our case). Normalization ensures equal contribution of each feature to the learning process, prevents dominant features from overshadowing others, and enhances convergence, allowing the model to learn efficiently [⁴⁸].

Finally, the cleaned and normalized database was split into 80% for training and 20% for testing. Additionally, the training base was divided into four for k-fold validation. This rigorous approach enhances the reliability and robustness of the trained network, improving its generalization capability for more accurate regression predictions [^47,48].

The resilient backpropagation algorithm (RProp) was adopted to train the ANN [⁵⁵]. The RProp is similar to the conventional backpropagation algorithm, but it is considerably faster and does not require any free parameters (like learning rate). Additionally, it uses feed-forward neural networks to perform supervised batch learning, which has been widely adopted in deep learning applications. The principle of RProp is that the derivative size and step size should not negatively affect the weighting step. Therefore, the direction of the weight update is determined solely by the sign of the derivative. Fig. 3 illustrates the application of the RProp algorithm in the current research.

Figure 3 Source: The authors

The nonlinearity nature of the ANN is provided by the activation function known as log sigmoid. The method of this activation function has been well-documented in ANN applications in the concrete engineering field [^6,47,48].

To define the optimal hidden layer neurons, k-fold validation combined with the average root mean squared error (RMSE) is employed [Eq. (1)]. Here, k-fold validation involves dividing the dataset into k equally sized subsets, or "folds," and then training the neural network on k-1 folds while validating its performance on the leftover partition. This procedure is realized k times, with every partition utilized as the validation dataset once. The average RMSE, which measures the prediction error of the model, is calculated across all k folds [⁴⁸].

By varying the hidden layer’s number of neurons in the k-fold validation process, the performance of the ANN model is obtained for different configurations. The hidden layer’s number of neurons is varied over a range of values, and the configuration that results in the lowest average RMSE is selected as the optimal number of neurons. In this manner, the most effective neural network architecture is identified to achieve a balance between model complexity and prediction accuracy for the current concrete engineering problem [⁶].

The capability of the model to calculate the targeted response was evaluated based on four parameters: (i) the RMSE; (ii) the coefficient of determination [R ² , Eq. (2)]; (iii) the mean absolute error [MAPE, Eq. (3)], and (iv) the normalized mean bias error [NMBE, Eq. (4)].

Where,

n: the number of data points in the training and testing sets.

a _i : the targeted response.

: the predicted response.

: the mean of the targeted response.

A CWA is a method used to interpret and understand the internal workings of ANNs [⁵⁶], which are often called "black boxes" due to their complexity and non-linearity. This approach involves analyzing the weights assigned to the connections between neurons in the neural network. It is possible to gain insights into the relative importance of different input features or variables by examining the magnitude and direction of these weights. This approach is useful in interpreting and explaining the decision-making process of ANN used in the concrete investigation by recent research [^6,48,57]. Engineers and practitioners in the cementitious materials field will better understand the effect of concrete's components on its characteristics.

This study developed an ANN model with a unique one-hidden layer by employing the R statistical language and the neuralnet function. Sixteen different architectures were tested for each activation function, and 100 models were computed for each architecture to mitigate the effect of the connection's initial weight allocation. As a result, a total of 3,200 ANN approaches were established to forecast the slump flow of fresh UHPC utilizing the earlier mentioned 793 test result records. These networks consisted of an input layer containing the input nodes, a hidden layer of computational neurons, and an output layer. The input signals were grouped into two classes:

The volume ratio of UHPC-making ingredients: including cement (PC), silica fume (SF), fly ash (FA), ground granulated blast furnace slag (GGBFS), waste ground glass powder (GP), rice husk ash (RHA), fluid catalytic residue (FC3R), metakaolin (MK), limestone powder (LP), water (W), polycarboxylate-based high-range water reducer admixture (HRWR), quartz powder (QP), and total aggregate (A).

The VPD is not typically included in scientific articles but was estimated using the available data, particularly the mean particle size (d₅₀) and the mixture proportion. The calculation of VPD was based on the compressive packing model theory [^58-60]. Fig. 4 depicts the average RMSE obtained in the most favorable initial weight allocation versus the hidden layer’s number of neurons. It is evident that three neurons in the hidden layer of the ANN result in the minimum RMSE. Therefore, the ANN configuration shown in Fig. 5 was selected for implementation.

Figure 4 Source: The authors

Figure 5 Source: The authors

The performance of the ANN model was measured using the metrics listed in Table 1. Based on these results, it can be concluded that the ANN approach predicts UHPC slump flow reasonably well, with R² values of 0.97 and 0.91 for training and testing subsets, respectively. The regression plot shown in Fig. 6 also shows the good performance of the ANN model. Furthermore, the performance metrics on train and test data subsets are in the same order of magnitude, indicating proper implementation of the k-fold validation method [^6,47,48].

Table 1

Subset	RMSE	R2	MAPE	NMBE
Train	7.509	0.971	4.477%	-2.175%
Test	9.603	0.909	5.372%	-0.137%

Source: The authors.

Figure 6 Source: The authors

A summary of the findings obtained by the CWA is shown in Fig. 7. The results of the CWA analysis were consistent with expectations, indicating that water content (W) had the highest positive importance in predicting slump flow, followed by HRWR dosage. Other variables that positively influenced slump flow were those related to the water amount (WP, WB), demonstrating relative importance. The dosages of LP, FA, and GP also show a positive influence on the flowability of the mixture. A similar pattern of results was observed in previous studies in this area [^6,61].

Figure 7 Source: The authors

The significance of LP dosage in the improvement of UHPC rheological performance has been well-established in previous research. Yu, Spiesz, and Brouwers [⁶²] concluded that LP utilized as a partial substitution for C could significantly enhance the flowability of UHPC, emphasizing its importance as a supplementary material in UHPC production. Furthermore, recent studies [^63,64] have highlighted the positive impact of LP on the UHPC’s mechanical durability features, making it a promising addition to modern concrete technology. Additionally, LP has shown the ability to mitigate the cement-polycarboxylate incompatibility in UHPC, which poses a serious concern in the application of this excellent cementitious material [^65-67].

The fly ash, on the other hand, significantly affects the rheological properties of UHPC. Its particles’ spherical shape improves the concrete mixture's flowability, workability, and cohesion. It reduces internal friction, allowing for smoother movement of particles. This results in enhanced stability, reduced segregation, and improved overall rheological performance of UHPC [⁴⁸]. On the other hand, fly ash is still an ultra-fine powder that demands water in concrete. Therefore, the fly ash addition produces a limited positive effect as shown in Fig. 7.

The positive influence of GP on concrete can be attributed to its remarkably low water absorption characteristics [^7,30,68], which in turn improves the rheology of the concrete. Furthermore, the incorporation of GP in the mixture leads to an augment in alkaline concentration due to its high Na₂O concentration [^69,70]. Consequently, the liquid phase's higher alkalinity results in the paste's lower shear strength, contributing to increased flowability [^7,71,72]. Moreover, it is also relevant to glass particles having almost zero water absorption. Therefore, when partially replacing other components, the inclusion of GP provides more free water to contribute to the rheology properties of concrete [⁷⁰].

Moreover, MSA has a slightly positive influence on the rheological features of the fresh-state UHPC. In this sense, sand’s maximum size and gradation are critical factors influencing the rheological behavior of this high-performance cementitious composite. Typically, UHPC employs manufactured crushed and classified quartz as micro sand with an MSA value of 600 µm, which may necessitate an increase in binder proportion to ensure adequate flowability [⁷³]. This is due to the fact that smaller sand grains lead to a larger specific surface, requiring a higher amount of paste to achieve the desired workability. Consequently, when the sand volume is fixed, the utilization of sand with a larger maximum particle size can be considered to improve rheological performance and mitigate shear thickening behavior [^73,74]. Thus, the larger the particle size, the larger the slump flow of UHPC.

Continuing with the analysis of the CWA results, the following list of UHPC-making materials appears to have a positive but non-significant influence on the rheological features of the UHPC: GGBSF, QP, and VPD.

On the one hand, the collective findings of several recent studies shed light on the significant impact of GGBFS on the rheology and mechanical properties of concrete, supporting the results depicted in Fig. 7. Bature et al. [⁷⁵] conducted experiments revealing that the addition of GGBFS to concrete resulted in a notable reduction in its dynamic yield stress, leading to improved workability and pumpability. Gokce [⁷⁶] corroborated these findings, demonstrating that incorporating GGBS into self-compacting concrete notably enhanced its flow consistency. For its part, Torres et al. [⁷⁷] conducted a comprehensive study examining the impact of different superplasticizers on the reactive powder concrete’s workability and compressive strength when this SCM was incorporated. The results underscored the significant role of superplasticizer type and composition in influencing concrete spread, viscosity, and compressive performance. This effect was found to be far more significant than the GGBSF. Moreover, as per Zang et al. [⁷⁸], finer particles of slag with sizes up to 30 microns negatively influenced the rheology of concrete, while coarser particles with sizes between 30 and 45 microns had the opposite effect.

To sum up, the above paragraph highlights the findings from recent studies that collectively emphasize that the impact of GGBFS on the rheology of concrete is limited and depends upon its particle size more than chemical reactions [^75-79]. The latter supports the results observed in the CWA analysis.

For its part, QP is a constituent of a typical UHPC mixture proportion whose main objective is to contribute to obtaining the desired concrete packing density [^79,80]. Similarly, to what we will see occurs with VPD, the CWA analysis shows that this component has a positive effect but is of limited relevance to the UHPC’s slump flow value.

The case of the influence of the VPD on the UHPC’s rheological features can be a little bit controversial when comparing it to other typologies of concrete. The studies reviewed in the field of concrete engineering indicate that particle packing density plays a significant role in the rheological properties of concrete. Ghoddousiet al. [⁸¹] demonstrated in their work published in 2014 that exists an optimal packing density for self-consolidating concrete mixtures, which leads to improved velocity and rheological properties. In general, higher packing densities can result in mixtures that require less water, thereby reducing the amount of cement needed. For its part, Chateau [⁸²] provided an overview of the impact of particle properties on packing characteristics and presented predictive models for packing density in particle mixtures. Mehdipour & Khayat [⁸³] conducted a review on the influence of packing features of colloidal and non-colloidal particles on the rheo-physical properties of cementitious suspensions and concluded that the rheological features are mainly influenced by the relative solid packing fraction. Collectively, these studies suggest that optimizing particle packing density can enhance the concrete rheological features and potentially reduce the amount of cement required. However, in the case of UHPC, this situation is negatively compensated by the necessity of ultra-fine particles to obtain the high packing density values that reach values over 0.8 when conventional concrete’s around 0.6 [⁷⁰]. These ultra-fine particles, such as SF with an average particle size of about 0.15 microns, thereby augmenting drastically the specific surface of the mixture [^84,85]. This balance could be the explanation for why VPD appears to be positive but with non-relevant importance in the slump flow of UHPC, contrary to what happens in other concrete types.

The CWA analysis indicates the little adverse effect of aggregate (A) on UHPC’s workability. In this sense, Yang et al. [⁸⁶] found that the addition of angular manufactured sand, the typical aggregate utilized in UHPC, can negatively affect the flowability and volume stability of this special concrete. According to this research work, the incorporation of quartz angular micro sand might disturb the UHPC particle packing skeleton, leading to a deterioration of the slump flow values.

The next component to be commented on is cement (C), which, as expected, displays a negative influence on the UHPC slump flow. Portland cement clinker’s mineral composition, which includes C₃S, C₂S, C₃A, and C₄AF, is a significant factor that affects the workability of any type of fresh concrete. Gypsum is incorporated into the clinker to grind the cement, and each mineral composition reacts with water at different rates and requires different amounts of water. As such, the mineral composition can affect the cement paste’s rheological properties. Ions like SO₄ ^2-, OH^-, Na⁺, and K⁺ may be released into the water when cement comes into contact with water, which can influence the adsorption of the superplasticizer onto cement particles, thereby influencing cement paste rheological performance [⁸⁷]. The cement’s fineness also impacts the cement paste’s rheological performance since fine cement particles hydrate faster than coarser ones and require more water for a given flowability. Many researchers have extensively studied cement’s chemical and physical features, and the results indicate that an increase in cement dosage can reduce the flowability of fresh concrete [⁸⁸]. For instance, Hope et al. [88] found that cement with high Al₂O₃ or C₂S contents requires more water, while cement with high ignition loss, C₃S content, or high carbonate concentration demands less water for a given slump. Mork et al. [⁸⁹] noted that reducing the gypsum-to-hemihydrate ratio can decrease the yield stress of concrete for cement with high C₃A and alkalis content, but the effects were less pronounced for cement with lower C₃A and alkalis content. Dils et al. [⁹⁰] examined the impact of cement's chemical composition and refinement on the rheological properties of UHPC and discovered that cement with a high C₃A and specific surface, a high alkali content, and a low SO₃ content provided poor flowability.

For its part, Chen & Kwan [⁹¹] showed that an increase in cement dosage could decrease the fresh concrete’s workability, increasing the yield stress and apparent viscosity, particularly at higher water-to-cement ratios. At lower water content, the addition of superfine cement can improve the rheological properties of cement paste by filling the voids, increasing the packing density, and releasing the water between cement particles, leading to a thicker water film coating the particles in the cement paste. However, at higher water dosages, the addition of superfine cement may not have an obvious influence on the water film thickness due to the high specific surface area, which can increase plastic viscosity and yield stress [^87,91]. Hence, the aforementioned pieces of research support the obtained CWA results (Fig. 7).

Regarding the SF, which is UHPC’s most common SCM to enhance mechanical and durability properties. However, excessive dosage of SF can worsen the flowability of UHPC owing to the SF’s small particle size. SF particles are so fine that they augment the specific surface area of the mixture, leading to a greater demand for water and superplasticizers to maintain the required workability. The WB in UHPC is closely linked to the SF content because of the aforementioned reasons [28]. These explanations are in line with the findings presented in Fig. 7.

Incorporating metakaolin (MK) into the UHPC leads to a reduction in slump flow, as the replacement ratio of this SCM increases. This reduction in flowability can be attributed to the accelerating effect of MK on the hydration process, which is supported by the high pozzolanic activity index observed at the early ages of this concrete-making ingredient. Additionally, the high content of amorphous SiO₂ and Al₂O₃, as well as the porous non-spherical particles of MK contribute to the negative impact on workability [^92,93]. Moreover, these pieces of research also suggested that the chemical reaction of reactive SiO₂ and Al₂O₃ content of MK can generate enormous heat during the hydration process, which can worsen flowability. Therefore, it should be noted that previous studies have demonstrated that incorporating MK into concrete requires more water or superplasticizer to achieve the desired level of flowability [^94,95].

For its part, the incorporation of RHA in concrete results in a decrease in the slump flow value of UHPC, and this effect becomes more significant with an increase in the amount of RHA used (i.e., as the percentage of partial substitution of RHA increases, the factor A value decreases). The negative impact on the rheology of the concrete can be attributed to the non-spherical shape and porosity of RHA particles [⁴⁸]. The use of materials with higher surface area and water absorption reduces the availability of free water in UHPC. This lower free water content increases friction between the solid particles in the bulk paste, resulting in highly viscous concrete with a lower slump flow. Additionally, replacing cement with RHA by weight leads to a higher paste volume due to RHA's lower density, which reduces the amount of free water available. Therefore, incorporating RHA necessitates greater water and/or superplasticizer contents to achieve the desired workability, as previously reported by [^96-97].

Finally, the highest degree of importance is attributed to FC3R. This can be ascribed to the increased formation of ettringite with higher levels of FC3R substitution for C in the concrete, as evidenced in previous studies [^48,92], resulting in decreased flowability. Additionally, it has been demonstrated in several investigations that the incorporation of FC3R in concrete necessitates higher water content to achieve the desired workability [^48,92,93].