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Exploring temperature-resilient recycled aggregate concrete with waste rubber: An experimental and multi-objective optimization analysis

  • Yunchao Tang , Yufei Wang , Dongxiao Wu , Mengcheng Chen , Lan Pang , Junbo Sun EMAIL logo , Wanhui Feng EMAIL logo and Xiangyu Wang EMAIL logo
Published/Copyright: August 8, 2023
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REVIEWS ON ADVANCED MATERIALS SCIENCE
From the journal REVIEWS ON ADVANCED MATERIALS SCIENCE Volume 62 Issue 1

Abstract

For low-carbon sustainability, recycled rubber particles (RPs) and recycled aggregate (RA) could be used to make rubber-modified recycled aggregate concrete (RRAC). The characteristics (compressive strength and peak strain) of RRAC with various amounts of RA and RPs after heating at various temperatures were studied in this work. The results show that high temperatures significantly decreased the uniaxial compressive strength (UCS), whereas the addition of RA (e.g., 50%) and RPs (e.g., 5%) can mitigate the negative effect caused by high temperatures. The peak strain can also be improved by increasing the replacement ratios of RA and RP. Support vector regression (SVR) models were trained using a total of 120 groups of UCS and peak strain experimental datasets, and an SVR-based multi-objective optimization model was proposed. The excellent correlation coefficients (0.9772 for UCS and 0.9412 for peak strain) found to illustrate the remarkable accuracy of the SVR models. The Pareto fronts of a tri-objective mixture optimization design (UCS, strain, and cost) were successfully generated as the decision reference at varying temperature conditions. A sensitivity analysis was performed to rank the importance of the input variables where temperature was found as the most important one. In addition, the replacement ratio of RA is more important compared with that of the RP for both the UCS and strain datasets. Among the mechanical properties of concrete, compressive strength and peak strain are two key properties. This study provides guidance for the study of RRAC constitutive models under high temperatures.

Keywords: rubber-modified recycled aggregate; compressive strength; peak strain; machine learning; multi-objective optimization

1 Introduction

Nowadays, the demolition of buildings and transportation infrastructure, such as bridges and sidewalks, produces a large amount of construction waste [1,2,3,4]. The discarded Portland cement concrete can be crushed into small pieces, divided into different sizes, and reused as a new concrete aggregate. One type of aggregate is known as recycled aggregate (RA). Unlike ordinary concrete that uses entirely natural aggregate (NA), concrete made entirely or partially from RA is known as recycled aggregate concrete (RAC). However, RAs have some disadvantages, as the voids and microcracks of the old mortar cover the surface [5,6,7]. These defects weaken the mechanical properties of RAC. Recent research has proposed a series of environmentally friendly methods for recycling waste rubber tires in engineering projects [8,9,10]. One effective approach for treating waste tires is to use rubber particles (RPs) as a replacement material for fine aggregates in concrete. Studies have shown that the mechanical properties of rubber concrete and ordinary concrete differ. RPs can enhance the deformation capacity of concrete [11]. Therefore, some disadvantages of RAC, which is a soft material, can be overcome by using RPs as part of the fine aggregate, known as rubber-modified recycled aggregate concrete (RRAC) [12,13].

Fire is one of the most damaging environmental situations that may occur in a concrete structure [14,15,16]. Typically, fire generates a high-temperature differential in the concrete. The temperature differential in concrete results in chemical and physical processes such as dehydration of the cement slurry, aggregate breakdown, mass loss, deformation, and strength loss, all of which have a detrimental effect on the mechanical and thermal characteristics of the concrete. When concrete is subjected to extreme heat, its mechanical characteristics deteriorate. It begins to degrade at temperatures between 200 and 300°C and continues to degrade as the temperature increases, lowering the structure’s strength and stiffness. Aggregates usually account for 70% of the volume of concrete. Therefore, the thermal properties of concrete largely depend on the type of aggregate because the responses of different aggregates to high temperatures differ significantly. Many studies have reported that the difference between the mechanical properties of RAC and natural aggregate concrete (NAC) at ambient temperatures increases with the increase in the RA replacement rate, particularly at a replacement rate of above 50% [17,18,19].

Therefore, the particularity of RAs also leads to different thermal properties of RAC compared with NAC. Research has been conducted to evaluate the residual mechanical properties of RAC subjected to elevated temperatures, which showed that the old mortar attached to the RAs reduced the elastic modulus and compressive strength of the RAC. When the temperature exceeds 600°C, the effect of temperature on the degradation of RAC at 100% RA replacement rate is higher than that of NAC [20,21,22]. Therefore, it is necessary to develop a method to reduce the thermal degradation of RAC, particularly at a high RA replacement rate. Pliya et al. [23] found that the ease of spalling of NAC at high temperatures, which reflects the thermal strain of NAC, is greater than that of RAC.

Additionally, RRAC has attracted considerable attention due to the toughening impact of RPs on concrete [24,25,26]. RRAC is a sustainable material derived from debris that also possesses exceptional mechanical qualities. Compressive and flexural behaviors are feasible in structural engineering [27,28,29]. Liu et al. [12] found that RPs can effectively improve the fatigue performance of RAC. Chen et al. [30] investigated the deformation capacity of RRAC, which is higher than that of RAC. Previous studies investigated the thermomechanical properties of RRAC and discovered that adding RPs can help minimize RAC spalling [31,32,33]. This is because many interior pores assist in the discharge of internal steam via overflowing RPs following high-temperature heating.

Many specimens containing varying amounts of RPs and RA are usually prepared and tested to quantify the effects of RPs and RA on the mechanical properties of RRAC. However, this lab-based approach requires considerable time and effort for sample preparation and data analysis. Numerous high-tech technologies have emerged mainly due to the development of artificial intelligence [34,35,36,37,38,39]. Machine learning (ML) models with reliable prediction performance and generalization, such as random forest (RF), artificial neural network (ANN), and support vector regression (SVR) can be established based on existing experimental data [40,41,42,43]. SVR has been widely used for data mining due to its good noise resistance, reliable generalization performance, and quick training speed compared to other ML models, as reported by many experts [44,45,46]. It can solve linear or non-linear problems by mapping to the higher-dimensional space. Therefore, this study attempted to predict experimental data using an SVR model. However, the performance of SVR is highly dependent on hyperparameters. We used the beetle antennae search (BAS) algorithm to automatically tune the hyperparameters of SVR instead of conventional optimization strategies [47,48]. Furthermore, compared with other optimization algorithms, such as the genetic algorithm [19] and the firefly algorithm [49], BAS yields a higher adjustment efficiency [50].

Among the mechanical properties of concrete, the compressive strength and the strain corresponding to the peak stress (peak strain) are two key properties. The reason is that the constitutive model of concrete is related to these two factors, and high-strength concrete with high deformation ability is also one of the goals pursued by concrete materials. Therefore, the two primary characteristics of RRAC studied in this research are uniaxial compressive strength (UCS) and peak strain. Apart from ML predictions of the UCS and strain, a multi-objective optimization (MOO) model is proposed to optimize the mixture design using a metaheuristic algorithm [51,52]. MOO has been verified as a feasible approach for the material mixture design [19,53,54]. For instance, Zhang et al. [55] used a multi-objective particle swarm optimization technique to effectively optimize the strength, slump, and cost of plastic concrete. The single-objective optimization design is rarely considered because it does not meet complicated design requirements in practice. Therefore, by using the SVR-BAS-based MOO model (MOBAS-SVR), three objectives (i.e., UCS, peak strain, and cost) can be optimized simultaneously by introducing a Pareto front. The goal of this study is to optimize three parameters (UCS, peak strain, and cost) of RRAC concurrently utilizing MOBAS-SVR after heating at various temperatures. RRAC was used to produce 120 specimens with the provided goal values.

The rest of the article is organized as follows. Section 2 summarizes the RRAC’s general mix composition. Section 3 summarizes the approach for MOO, including data description, objective functions, hyperparameter tuning, and multi-objective and variable sensitivity analysis (SA). The experimental results are presented in Section 4. In Section 5, the modeling results based on the methods described in Section 3 are analyzed. The main conclusions drawn based on the findings of this study are presented in Section 6.

2 Materials and methods

2.1 Raw materials and mix proportions

In the experiments, Shijing Brand ordinary Portland cement was used. The nominal strengths of the cement were chosen to be P.O. 32.5R and P.O. 42.5R. Medium sand with particle sizes ranging from 0 to 5 mm, a fineness modulus of 2.52, and an apparent density of 2679 kg·m−3 were used. RAs were created from crushed concrete waste on a construction site in Shenzhen and treated by Shenzhen Lvfa Pengcheng Environmental Technology Co., Ltd. Specifically, the discarded concrete blocks and stone materials in construction and demolition wastes were crushed, washed, and screened to continuous grading. Before producing the concrete mixes, RAs were washed again and the saturated surface dryness conditions were ensured. The percentage of sediment content, elongated particles, and impurities were 0.88, 9.3, and 1.0, which were satisfied with the requirements of the codes. RAs were added to the RAC by replacing an equal amount of NA. Figure 1 depicts the grading curves of the NA and RA. All coarse aggregates were classified as Grade II aggregates. The particle size and apparent density of RPs were 0.86 mm (20-mesh size) and 1,020 kg·m−3, respectively. Running water was used in all experiments.

Figure 1 Gradation of NAs and RAs.
Figure 1

Gradation of NAs and RAs.

For the 42.5 MPa cement mixture, RA was used to replace 0, 25, 50, 75, and 100% of the volume of NA. RPs were used instead of 0, 5, 10, and 15% of the volume of sand. It was also necessary to use a polycarboxylic acid water-reducing admixture at a concentration of 3.88 kg·m−3. Because of the use of P.O. 32.5R cement, only 50% of the NA was replaced with RA, and no more than 0, 10, and 25% of the volume of sand were replaced with RPs when using P.O. 32.5R concrete. Comparing P.O. 42.5R and P.O. 32.5R, the water-to-cement ratios were comparable at 0.45 and 0.43 for both materials.

2.2 Experimental program and specimen preparation

After 24 h of specimen pouring, the molds were removed. The cylinder was then cured for 28 days at a constant temperature of 20 ± 2°C and a relative humidity of 95% under standard conditions (diameter and height of 150 and 300 mm, respectively). The high-temperature treatment was carried out in a box-type electric furnace with a temperature control accuracy of 1°C. The gap between the cylinder and the furnace wall was also maintained at or above 20 mm in order to ensure that the sample surface was heated consistently throughout the process. The thermal rate was fixed to 5°C·min‒1 [56]. The temperature was held constant for 60 min after achieving the desired temperature (T = 200, 300, 400, 500, or 600°C), and then the heating was turned off. Next, the specimen was removed from the furnace, cooled at room temperature, and prepared for a uniaxial compression test. In addition, each mix proportion had a group of unheated specimens (T = 25°C). The heating curve of the RRAC is shown in Figure 2.

Figure 2 Heating curves of RRAC.
Figure 2

Heating curves of RRAC.

2.3 Compression test setup

As illustrated in Figure 3, after heating the specimens, a gypsum-leveling layer was applied to the two end surfaces of each cylinder before compression in line with ASTM C617 [57]. Compression tests were conducted using a hydraulic servo universal testing machine in accordance with ASTM C39 [58] and C469 [59]. The loading speed was set at 0.18 mm·min−1 over the course of the test. To determine the longitudinal deformation of the cylinder, two linear variable differential transformers were employed in conjunction with each other. To capture the synchronous displacement and force data, a strain acquisition device with a 1 Hz acquisition frequency was also employed. The UCS and peak strain were then calculated by averaging three specimens from each group.

Figure 3 Sketch of the uniaxial compression test.
Figure 3

Sketch of the uniaxial compression test.

3 MOO methodology

Figure 4 depicts the flowchart for the MOO mixing design of RRAC utilizing MOBAS-SVR. To begin, two SVR models were trained to predict the UCS and peak strain values using the BAS method and fivefold cross-validation (CV). Second, an objective function of the mixture expanse was established to evaluate the cost of each group based on the unit price and density of the raw materials. Third, by applying an MOO function using the weighted sum approach, the UCS, peak strain, and cost were considered as objectives. Finally, non-dominated optimum solutions based on the Pareto front were developed.

Figure 4 Flowchart of the concrete optimization design based on the MOBAS-SVR system.
Figure 4

Flowchart of the concrete optimization design based on the MOBAS-SVR system.

3.1 Data description

The input datasets were constructed using the experimental findings of 120 sample groups. The water content, cement content, RA, NA, sand, RPs, water reducer (WR), cement grade (G), and temperature (T) are all input variables. UCS and peak strain of RRACs are output variables. Table 1 lists the variables and their associated minimum, maximum, median, and standard deviation.

Table 1

Statistical details of the input and output variables based on the UCS dataset

Variables Minimum Maximum Mean Median SD Variation coefficient
W (kg·m−3) 185 216 211.35 216 11.07 0.052
C (kg·m−3) 430 485 476.75 485 19.64 0.041
RA (kg·m−3) 0 1,194 651.50 618 316.28 0.485
NA (kg·m−3) 0 1,194 498.00 597 334.20 0.671
Sand (kg·m−3) 451 547 500.45 502 27.84 0.056
RPs (kg·m−3) 0 49 17.40 21 13.44 0.773
WR (kg·m−3) 0 3.88 3.30 3.88 1.39 0.420
G (MPa) 32.5 42.5 41.00 42.5 3.57 0.087
T (°C) 25 600 337.50 350 190.26 0.564
UCS (MPa) 4.2 58.75 35.38 35.09 12.58 0.355
Strain (%) 0.12 1.19 0.48 0.42 0.23 0.475

3.2 Objective function: BAS-SVR-based model

3.2.1 SVR

SVR is a classic implementation of support vector machines in regression problems, and it is also a common regression method. It can handle nonlinear problems by transforming data from the space where the sample is located to a high-dimensional space, which is realized using the kernel function [60]. The data are expressed in the form of ( x i , y i ), where x i is a feature vector with one dimension and y i is a regression value with scalar properties. The training dataset consists of n groups in the form of ( x i , y i ) as given in Eq. (1), and the regression function is expressed as given in Eq. (2):

(1) { ( x 1 , y 1 ) , ( x 2 , y 2 ) , … , ( x n , y n ) } ,

(2) f ( x ) = w ∙ φ ( x ) + β ,

where φ ( x ) is a mapping function, w is the weight vector, and β is the bias. The loss function is introduced to determine the degree of difference between f ( x i ) and y i , as formulated in the following equation:

(3) L ( x , y , f ) = | y i − f ( x i ) | e = 0 , | y i − f ( x i ) | < e , | y i − f ( x i ) | − e i , | y i − f ( x i ) | ≥ e ,

where e is the maximum tolerance error, indicating that the function will not be penalized if the training points are within the e-tube range. The problem is described as follows, with the least structural risk taken into account:

(4) R ( w ) = 1 2 ‖ w ‖ 2 + ∑ i = 1 n L ( x , y , f ) .

Slack variables ( δ i and δ i * ) are used to deal with infeasible constraints to increase tolerance for biased data. Eq. (4) is equivalent to the following convex optimization function:

min w , e , δ , δ * R ( w ) = 1 2 ‖ w ‖ 2 + C ∑ i = 1 n ( δ i + δ i * ) ,

(5) s . t . y i − w ⋅ φ ( x ) − β ≤ e + δ i , w ⋅ φ ( x ) + β − y i ≤ e + δ i , * δ i ≥ 0 , δ i * ≥ 0 ,

where C is the penalty parameter used to measure the degree of penalty for the dissimilarity between the regression curve and the e -tube sample.

Figure 5 depicts the basic principles of nonlinear SVR by combining images with text and formula labeling. Thereafter, the prime problem should be converted to a dual problem by adopting positive Lagrange multipliers ( α i , α i * , u i , u i * ) to allow multiple constraints. The dual function is given in Eq. (6):

(6) L ( w , β , δ , a , u ) = 1 2 ‖ w ‖ 2 + C ∑ i = 1 n ( δ i + δ i * ) − ∑ i = 1 n a i ( e + δ i − y i + w ⋅ φ ( x i ) + β ) − ∑ i = 1 n a i * ( e + δ i + y i − w ⋅ φ ( x i ) − β ) − ∑ i = 1 n ( u i δ i + u i * δ i * ) .

Figure 5 SVR machine [61].
Figure 5

SVR machine [61].

Eq. (7) [62] should satisfy the Karush–Kuhn–Tuck (KKT) conditions for both the dual and original points when the constraint equations are significantly at odds with one another and the target equation is differentiable. Optimal solutions meet the KKT criteria, which state that the product of the dual variable and a constraint is zero, which is expressed in Eq. (8):

(7) ∂ L ∂ w = w − ∑ i = 1 n ( a i − a i * ) φ ( x i ) = 0 , ∂ L ∂ β = ∑ i = 1 n ( a i − a i * ) = 0 , C − a i − u i = 0 , C − a i * − u i * = 0 ,

(8) a i ( e + δ i − y i + w ⋅ φ ( x i ) + β ) = 0 , a i * ( e + δ i + y i − w ⋅ φ ( x i ) − β ) = 0 , ( C − a i ) δ i = 0 , ( C − a i * ) δ i * = 0 .

Solving the above equations, the final Langrage dual problem is obtained as follows:

(9) max i − 1 2 ∑ i = 1 n ∑ j = 1 n ( a i − a i * ) ( a j − a j * ) x j T x j − e ∑ i = 1 n ( a i − a i * ) + ∑ i = 1 n y i ( a i − a i * ) s . t ∑ i = 1 n ( a i − a i * ) = 0 , a i , a i * ∈ [ 0 , C ] .

From Eq. (8), the weight factor w source is ∑ i = 1 n ( a i − a i * ) φ ( x i ) , and Eq. (10) gives the regression function:

(10) f ( x ) = ∑ i = 1 n ( a i − a i * ) φ ( x i ) x + β .

3.2.2 BAS

It is the goal of BAS, a meta-heuristic method, to discover the optimal hyperparameters for ML models. Like other bionic algorithms, it is based on the behavior of long-horned beetles [63]. Through its two antennae, a beetle can detect the concentration of odor and travel to the side with the highest concentration. In the BAS method, the variables x l and x r denote the left- and right-side antenna locations, respectively. The position of the antenna at the ith moment can be expressed as given in Eq. (11).

x l i = x i + d i b ,

(11) x r i = x i − d i b ,

where b is a randomly generated vector that represents the random moving direction of the beetle. The random function and dimension, rand and k, respectively, are introduced such that the vector b can be expressed as given in Eq. (12):

(12) b = rand ( k , 1 ) ‖ rand ( k , 1 ) ‖ .

The position vector of the beetle is expressed in Eq. (13), where the step size is δ and f ( x ) is the fitness function. In addition, the antenna step size and length can be updated according to the following equations. The pseudo-code of the BAS is shown in Figure 6:

(13) x i = x i − 1 + δ i b sign ( f ( x r i ) − f ( x l i ) ) ,

(14) d i = 0 . 95 d i − 1 + 0 . 01 ,

(15) δ i = 0 . 95 δ i − 1 .

Figure 6 Pseudocode for BAS.
Figure 6

Pseudocode for BAS.

3.3 Hyperparameter tuning

3.3.1 Cross-fold validation

There are two basic hyperparameters that need to be tuned in the SVR model: the Gaussian kernel parameter γ and the penalty coefficient c . A five-fold CV was adopted to avoid over-fitting problems and ensure full use of the dataset. The UCS dataset was randomly divided into two parts, namely the test dataset, which accounts for 30% of the total dataset, and the training dataset, which accounts for 70% of the total dataset. The same is true for the strain dataset. Subsequently, the training dataset was divided into five equal but non-overlapping folds, as shown in Figure 7 [64]. The BAS algorithm used four of the folds to tune the hyperparameters of the SVR model during the training process. The remaining fold was used as a verification fold to check the robustness of the model training. After the verification, the root mean square error (RMSE) was calculated. Cross-validation was performed five times using the above process. Subsequently, the best hyperparameters with the smallest RSME were assembled on the model and used to predict the UCS and strain.

Figure 7 Five-fold cross-validation.
Figure 7

Five-fold cross-validation.

3.3.2 Performance evaluation

Choosing appropriate evaluation indicators is key to comprehensively and accurately evaluating the performance of the model. In this study, the correlation coefficient (R), the mean absolute percentage error (MAPE), the mean absolute error (MAE), and RMSE were used as the evaluation indicators of the SVR model. These indicators are defined as follows [64]:

(16) R = ∑ i = 1 n ( y i * − y * ̅ ) ( y i − y ̅ ) ∑ i = 1 n ( y i * − y * ̅ ) 2 ∑ i = 1 n ( y i * − y ̅ ) 2 ,

(17) MAPE = 1 n ∑ i = 1 n y i * − y i y i ,

(18) MAE = 1 n ∑ i = 1 n | y i * − y i | ,

(19) RSME = 1 n ∑ i = 1 n ( y i * − y i ) 2 ,

where n is the data sample of n groups, y i * and y i are the predicted and actual results, respectively, and y * ̅ and y ̅ indicate the average of the predicted and actual results, respectively.

3.4 MOO

3.4.1 Objective function establishment

The BAS-SVR model was selected as the objective function for UCS and strain. The cost objective function involves polynomial calculations as

(20) Cost ( $· m − 3 ) = C C Q C + C W Q W + C RA Q RA + C NA Q NA + C s Q s + C RP Q RP + C WR Q WR .

In Eq. (20), Q C , Q W , Q RA , Q NA , Q s , Q RP , and Q WR are the quantities (kg·m−3) of cement, water, RA, NA, sand, RP, and WR, respectively. C is the unit price ($·kg−1) of each raw material of RRCA, which is summarized in Table 2.

Table 2

The unit cost of each variable of RRAC

Variables Notation Unit price ($·kg−1) Unit weight (kg·m−3)
OPC C C 0.057 3,000
Water C W 0.001 1,000
RA C RA 0.003 2,500
NA C NA 0.0065 2,700
Sand C S 0.009 2,600
RP C RP 0.27 1,300
WR C WRA 1.2 1,350
OPC strength G 0 0
Temperature T 0 0

3.4.2 Constraints

This research imposed limits on the MOO issue, including material range constraints, concrete volume constraints, and ratio constraints.

  1. Range constraints

    The data range can be set for the UCS and strain datasets of RRCA, as expressed in the following equation:

    (21) d i min ≤ d i ≤ d i max ,

    where d i min and d i max represent the minimum and maximum value of the i th variable, respectively.

  2. Volume constraints

    The amount of the solid should be equal to 1 m3, expressed as follows:

    (22) V m = Q C U C + Q W U W + Q RA U RA + Q NA U NA + Q s U s + Q RP U RP + Q WR U WR ,

    where U c , U w , U RA , U NA , U s , U RP , and U WR are the unit weights of OPC, water, RA, NA, sand, RP, and WR, respectively.

  3. Ratio constraints

To optimize the RRCA mixture, it is necessary to establish a correlation among dissimilar raw materials by determining the ratio constraints. The input variables that depend on the framework dataset are listed in Table 3.

Table 3

Constraints of RRCA input variables

Variables Expressions Lower bound Upper bound
NA C NA (kg·m−3) 0 1,194
Sand C s 488 536
RA ratio C RA / ( C RA + C NA ) 0.5 1
RP ratio C RP / ( C RP + C s ) 0 0.09

3.4.3 Construction of MOBAS–SVR

The MOBAS-SVR model was established based on the objective functions of UCS, strain, and cost, and the weighted summation method was applied. Finally, the objectives ( f k ) were combined to generate a single composite objective function ( F ), which is expressed as given in the following equation:

(23) F = ∑ k = 1 k w k f k , ∑ k = 1 k w k = 1 ,

where the weights are calculated as w k = p k K , k is a uniform distribution number, and p k is a random number from the uniform distribution, which is in the range of 0–1.

Therefore, the above function can be expressed as follows:

(24) F = w 1 · UCS + w 2 · strain + w 3 · cost ,

(25) ∑ k = 1 3 w k = 1 .

Because there are multiple objectives in the MOO problem that need to be optimized, the Pareto optimal front is proposed to provide a non-dominated solution, as detailed in the next paragraphs. This stipulates that the conditions of other objective functions cannot be enhanced without deteriorating the other functions [65].

If A is the set of feasible solutions and x * ∈ A is one of the Pareto optimal solutions, then there is no x ∈ A that satisfies

(26) f k ( x ) ≤ f k ( x * ) for k = 1 , 2 , 3 , … , t and

(27) f k ( x ) < f k ( x * ) for at least one k .

If for each x , f ( x * ) is greater than f ( x ) , then the Pareto optimal solution x * is realized. The set of Pareto optimal solutions define the Pareto front, as shown in Figure 8, which represents the set of non-dominated solutions. The BAS algorithm can be improved to the MOBAS-SVR model using the weight summation method to cope with the Pareto front of the MOO problem. The pseudo-code is shown in Figure 9.

Figure 8 Pareto line model with feasible points [65].
Figure 8

Pareto line model with feasible points [65].

Figure 9 Pseudocode of MOBAS-SVR.
Figure 9

Pseudocode of MOBAS-SVR.

3.4.4 Decision-making for MOO designs

As mentioned above, although the Pareto front can cope with the MOO problem, it cannot be used for decision-making because the final optimal mixing ratio cannot be obtained. Therefore, a multi-criteria decision technique is proposed, which is based on the technique for order preference by similarity to the ideal solution (TOPSIS). According to the Pareto front with ideal points (positive and negative), solutions that are close to the positive ideal point and far from the negative ideal point and are suitable for TOPSIS. The ideal point (positive) is the solution when the value of the composite function is maximized, whereas the ideal point (negative) is the solution when the value of the object function is minimized. Finally, the best solution is required to obtain the highest C i , as given in the following equations:

(28) d i + = ∑ j = 1 n ( F ij − F j ideal ) 2 ,

(29) d i − = ∑ j = 1 n ( F ij − F j non − ideal ) 2 ,

(30) C i = d i − d i + + d i − ,

where d i + and d i − are the positive and negative solutions, respectively, i and n are the i th Pareto point and the number of objectives, respectively, F j non - ideal is the non-ideal value, and F j ideal indicates the ideal value of the j th objective.

3.5 Variable importance measure

A method based on SA is proposed to investigate the relationship between the input and output more deeply and accurately. When the input value changes within its value range, it can reflect its effect on the recommended SVR output. The structure of the input and output variables must be determined. Next, all the input variables were evaluated, while the remaining variables were unchanged. SA can be divided into two forms: global and local analyses. The limitation of local SA is that it cannot be used to determine the uncertainty of the model. Global sensitivity analysis (GSA) can be used to evaluate input variables to improve them concurrently. Consequently, in this research, GSA was used to rank multiple variables. GSA modeling depicts the importance of variables in the form of bar graphs, with the lowest range being 0% and the highest being 100% [66]. The gradient metric used to estimate the change in the outcome of the output and the relative importance expression are given in the following equations [66]:

(31) g ε = ∑ j = 2 L | y ε , j ˆ − y ϵ , j − 1 ˆ | L − 1 ,

(32) R ε = g ε ∑ i = 1 I g i ,

where ε is the input variable to be studied, y ε , j ˆ is the sensitivity response indicator for x ε , j , and R ε is the relative importance of the variable.

4 Experimental results

The test data (UCS and peak strain) from the experimental work described in Section 2.3 are shown in Figure 10. A total of 120 datasets were collected from the experimental training works. The results show that the UCS was significantly weakened by temperature, as shown in Figure 10a. With an increase in the RA replacement rate, the residual UCS of RAC was higher than that of the UCS with a 0% RA replacement rate after high-temperature heating (P.O. 42.5R). Specifically, the maximum UCS can be observed for RRAC with a 50% RA replacement rate and 5% RP content, which only decreased by 11.43% (200°C), 21.20% (300°C), 30.96% (400°C), 38.47% (500°C), and 45.97% (600°C) compared with compression without heating. For RRAC with 0% RA replacement and 5% RP content, the decrease in UCS reached 36.92% (200°C), 39.96% (300°C), 43.02% (400°C), 52.47% (500°C), and 61.92% (600°C). The results were similar when cement with a grading of P.O. 32.5R was used. The decrease in the UCS of the specimens after heating was still smaller than that of the specimen with 0% RA replacement rate. The reason is that RAs with higher porosity can enhance UCS at high temperatures because the thermal expansion coefficient of RA is closer to that of mortar compared with NA [67]. This result is consistent with those obtained in previous studies [31,32].

Figure 10 Plots of the 120 experimental datasets used in this study: (a) UCS and (b) peak strain.
Figure 10

Plots of the 120 experimental datasets used in this study: (a) UCS and (b) peak strain.

The test results indicate that, on the one hand, the number of internal cracks increased after exposure to more than 400°C and the hydrates (such as C–S–H gels) in the concrete decomposed, resulting in an increase in the internal pressure and spalling at the surface of the specimens [31,32], as shown in Figure 11a. Finally, spalling significantly decreased the UCS of all the specimens. On the other hand, when the RP content is small, the presence of RPs inhibits the development of internal cracks in RRAC. However, with an increase in the RP content, many pores are formed due to rubber melting, leading to higher porosity in the sample, as shown in Figure 11b. Meanwhile, the internal structure becomes too loose, thereby decreasing the UCS. Therefore, in terms of the UCS, an excessive RA replacement rate and RP content are not recommended.

Figure 11 (a) Spalling on the surface of specimens at elevated temperatures. (b) Melted RPs escaping through pores.
Figure 11

(a) Spalling on the surface of specimens at elevated temperatures. (b) Melted RPs escaping through pores.

With an increase in the RA replacement rate at room temperature, the peak strain was higher than that of NAC owing to the higher porosity of Ras, as shown in Figure 10b, which is consistent with the results reported in previous studies on RAC tested at room temperature [17]. At elevated temperatures, the effect of the target temperature on the peak strain was obvious. For instance, for RRAC with a 50% RA replacement rate and 10% RP content, the peak strain increased by 27% (200°C), 59% (300°C), 95% (400°C), 177% (500°C), and 259% (600°C) compared with the results obtained at room temperature. Furthermore, the effect of the RP content on the peak strain of RRAC is larger than that of the RA replacement rate. Because RPs are a type of soft material, the deformation capacity of RRAC was effectively enhanced at room temperature, which is consistent with other results. Considering a target temperature of 600°C as an example, at RP contents of 5, 10, and 15%, the peak strain of RRAC (P.O. 42.5R, 100% RA replacement rate) increased by 1.5, 10.0, and 17.4%, respectively, compared with the values for the specimen without RPs. This is because after heating at this temperature, RPs and calcium hydroxide were completely decomposed, which increased the porosity and enhanced the deformation (peak strain) of the specimen at the same load. Because of the difference in the mechanical properties of RRAC and ordinary concrete at elevated temperatures, it is necessary to optimize the thermal properties of RRAC.

5 Modeling results

5.1 Hyperparameter tuning

As mentioned earlier, the hyperparameters ( γ and c ) of SVR were adjusted using the BAS algorithm combined with fivefold cross-validation to obtain the optimal fold with the smallest RMSE. The third fold achieved the minimum RMSE in the UCS dataset, and the first fold in the strain dataset achieved the minimum RMSE, as shown in Figure 12. Figure 13 shows the RMSE iteration situation for both UCS and strain datasets. For the UCS dataset, the RMSE curve required 49 iterations to converge, whereas the strain dataset required 11 iterations to converge. This demonstrates that the BAS algorithm smoothly sought out the optimal hyperparameters of SVR. The optimal hyperparameters c and γ of the SVR model are 245.0654 and 1.8891 for UCS prediction, and 55.6384 and 0.36419 for strain prediction, respectively.

Figure 12 Fivefold CV for tuning hyperparameters on the (a) UCS dataset and (b) strain dataset.
Figure 12

Fivefold CV for tuning hyperparameters on the (a) UCS dataset and (b) strain dataset.

Figure 13 Normalized RMSE versus iteration in the optimal fold for (a) UCS dataset and (b) strain dataset.
Figure 13

Normalized RMSE versus iteration in the optimal fold for (a) UCS dataset and (b) strain dataset.

5.2 Performance of BAS-SVR

Figure 14 illustrates the prediction performance of the trained SVR models for UCS and strain. The solid black line denotes a curve that fits perfectly. The closer a point is near this line, the less variance there is between expected and actual values. The majority of dots are clustered toward the diagonal, showing the model’s excellent prediction accuracy.

Figure 14 Actual versus predicted values for (a) UCS and (b) strain.
Figure 14

Actual versus predicted values for (a) UCS and (b) strain.

Table 4 lists the evaluation index values of UCS and strain including the RMSE, R, MAE, and MAPE. The R values for the UCS and strain datasets are 0.9772 and 0.9412, respectively, indicating a strong correlation between the predicted and actual results. Meanwhile, the RMSE, MAE, and MAPE values are low, indicating the low prediction error of the established BAS-SVR models. In addition, the RMSE and R values for the training set and test set are similar. This result indicates that there are no over-fitting or under-fitting problems. As a result, the SVR models with BAS-tuned hyperparameters demonstrated strong prediction ability for both the UCS and strain datasets.

Table 4

Evaluation of BAS-SVR for UCS and strain datasets

Test category Evaluation index
RMSE R MAE MAPE
UCS (SVR) 3.1232 MPa 0.9772 2.3040 MPa 0.0987
UCS (ANN) 2.6521 MPa 0.9751 1.8131 MPa 0.0620
UCS (RF) 3.8492 MPa 0.9672 2.9862 MPa 0.1250
Strain (SVR) 0.0857% 0.9412 0.0705% 0.1889
Strain (ANN) 0.0890% 0.0892 0.0560% 0.1680
Strain (RF) 0.0890% 0.0893 0.0580% 0.1530

To verify the accuracy of the established SVR model, the RF and ANN algorithms are also established as comparative models [40,41]. Table 4 also shows the specific evaluation indices, where SVR is observed to have the highest accuracy compared to RF and ANN. Figure 15 illustrates the integration of standard deviation, RMSE, and R-value in polar coordinates. The “actual” point represents the information of the raw data, and the closest position of the model to this point indicates the best prediction performance. Therefore, the SVR model is the most suitable for predicting UCS and strain in this study.

Figure 15 Taylor diagrams of RF, ANN, and SVR for predicting (a) UCS and (b) strain.
Figure 15

Taylor diagrams of RF, ANN, and SVR for predicting (a) UCS and (b) strain.

5.3 RRAC mixture optimization

The goal of this study is to minimize the cost and maximize the UCS and strain under given constraints. Figure 16 shows the Pareto front of MOBAS-SVR obtained at different temperatures (25, 200, 300, 400, 500, and 600°C). Tables 5 and 6 list the typical mixture design of four points (A, B, C, and D) corresponding to the conditions of the largest TOPSIS, highest UCS, maximum strain, and lowest cost, respectively. When a single UCS, strain, or cost is considered separately, points B, C, and D can be used as the optimal solution for single-objective optimization. Multiple goals can be effectively integrated to obtain a more suitable solution using the TOPSIS decision-making method.

Figure 16 Pareto front based on cost, UCS, and strain of RRAC at different temperatures: (a) T = 25°C, (b) T = 200°C, (c) T = 300°C, (d) T = 400°C, (e) T = 500°C, and (f) T = 600°C.
Figure 16

Pareto front based on cost, UCS, and strain of RRAC at different temperatures: (a) T = 25°C, (b) T = 200°C, (c) T = 300°C, (d) T = 400°C, (e) T = 500°C, and (f) T = 600°C.

Table 5

Mixture proportions of Pareto solutions (T = 25°C)

Mixture A (final point) B C D
W (kg·m−3) 214.7 215.7 208.7 208.4
C (kg·m−3) 476.6 465.5 485.0 448.7
G (MPa) 42.5 42.5 42.5 42.5
RA (kg·m−3) 96.1 606.2 45.2 994.2
NA (kg·m−3) 1023.2 481.6 1094.7 120.7
Sand (kg·m−3) 537.6 507.9 534.0 519.2
RPs (kg·m−3) 0.0 10.9 0.0 0.0
WR (kg·m−3) 3.3 3.4 0.0 0.0
UCS (MPa) 48.9 53.2 36.8 37.8
Strain (%) 0.47 0.19 0.49 0.42
Cost ($·m−3) 43.1 43.3 40.0 34.2
TOPSIS score 1.00 0.46 0.74 0.66
Table 6

Mixture proportions of Pareto solutions (T = 400°C)

Mixture A (final point) B C D
W (kg·m−3) 207.8 211.5 194.6 201.6
C (kg·m−3) 444.4 430.0 434.1 473.1
G (MPa) 42.5 42.5 42.5 42.5
RA (kg·m−3) 0.2 435.9 571.8 941.5
NA (kg·m−3) 1194.0 717.8 597.5 180.1
Sand (kg·m−3) 479.9 526.3 502.6 514.1
RPs (kg·m−3) 15.5 0.6 18.3 0.0
WR (kg·m−3) 2.5 2.7 0.0 0.0
UCS (MPa) 30.4 32.4 16.2 19.3
Strain (%) 0.70 0.55 0.71 0.63
Cost ($·m−3) 44.8 38.8 40.0 35.8
TOPSIS score 1.00 0.38 0.75 0.49

At room temperature (T = 25°C, Table 5), Point B maximizes UCS at 53.2 MPa but it yields a smaller strain (0.19%) than the other points. Conversely, Point C yields the largest strain of 0.49%; however, the UCS (36.8 MPa) at this point is smaller than any other Pareto point. In addition, Point D yields the minimum cost of 34.2$·m−3, with relatively low values of UCS (37.8 MPa) and strain (0.42%). Point A is considered the most suitable solution that achieved the best tradeoff between the UCS, strain, and cost because it has the highest TOPSIS score (1), UCS of 48.9 MPa, a strain of 0.47%, and cost of 43.1$·m−3. Similarly, the MOO mixture design can be evaluated at other temperatures. As the temperature increases, the compressive strength gradually decreases, whereas the peak strain increases, which is consistent with experimental results. In conclusion, the final choice is based on the decision- maker’s choice to achieve a tradeoff between these three objectives. Under the condition that no specific requirements are presented, the solution of comprehensive consideration (TOPSIS = 1) can be prioritized.

5.4 Variable importance analysis

An SA was performed to evaluate the importance of the input variables for the results presented in terms of the importance ratio, which reflects the estimated influence of variables on UCS and peak strain, as shown in Figure 17. The input variable that had the highest impact on UCS is temperature, accounting for 61.07%, followed by the RA ratio with an importance ratio of 25.91%, the RP ratio with an importance ratio of 10.71%, and the OPC grade with an importance ratio of 2.31%.

Figure 17 Evaluation of the importance of input variables for the UCS and peak strain of RRAC.
Figure 17

Evaluation of the importance of input variables for the UCS and peak strain of RRAC.

Among the input variables of strain, temperature had the highest influence on the result, accounting for 74.29%, followed by the RA ratio with an importance ratio of 12.65%, the RP ratio with an importance ratio of 9.55%, and the OPC grade with an importance ratio of 3.51%.

6 Conclusion

In this study, the UCS and peak strain of RRAC were investigated to evaluate the effects of RPs, RA, and temperature. A MOBAS-SVR model was successfully established based on the experimental outcomes, simultaneously optimizing three objectives and developing the corresponding mixture design at varying temperatures. A variable SA was also performed. The following conclusions are drawn based on the findings of this study:

  1. The UCS was weakened after exposure to high temperatures (more than 400℃). The combination of 50% RA and 5% RPs achieved the maximum UCS of RRAC compared with other combination ratios of RA and RPs. The peak strain is positively related to RA owing to its higher porosity than that of NA. Similarly, RPs increase the peak strain owing to their soft properties.

  2. The BAS algorithm successfully adjusted the hyperparameters of the SVR models on both the UCS and peak strain datasets. The R values were 0.9772 and 0.9412, respectively, indicating the relatively high accuracy of the established BAS-SVR models.

  3. The MOO problem was successfully addressed by introducing the MOBAS-SVR model, and the UCS, peak strain, and cost were optimized simultaneously. The Pareto fronts obtained in this study at varying temperatures provide valuable design solutions for decision-makers. The preferable non-dominated solution can be determined using the TOPSIS method.

  4. According to the variable SA, temperature is the dominant variable among all the input variables. In addition, the RA replacement ratio is more important compared with the RP replacement ratio for both the UCS and strain datasets.

To enhance the predictive accuracy and versatility of RRAC’s properties, future efforts will focus on broadening the dataset to include more input variables such as cement ingredient, aggregate grading, and RA or rubber category. Additionally, exploring advanced or updated ML and MOO models will be a priority for modeling RRAC’s properties.

Acknowledgments

The authors would like to acknowledge the China Postdoctoral Science Foundation, Natural Science Foundation of Guangxi Province, Guangdong Basic and Applied Basic Research Foundation, and the Guangxi Key Laboratory of Disaster Prevention and Engineering Safety for providing the financial resources to carry out the work.

  1. Funding information: This research was funded by the China Postdoctoral Science Foundation (2021M690765), Natural Science Foundation of Guangxi Province (2021GXNSFAA220045), Guangdong Basic and Applied Basic Research Foundation (2022A1515010008, 2023A1515010870), and the Systematic Project of Guangxi Key Laboratory of Disaster Prevention and Engineering Safety (2021ZDK007).

  2. Author contributions: All authors have accepted responsibility for the entire content of this manuscript and approved its submission.

  3. Conflict of interest: The authors state no conflict of interest.

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Received: 2023-04-28
Revised: 2023-06-26
Accepted: 2023-07-12
Published Online: 2023-08-08

© 2023 the author(s), published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.

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https://doi.org/10.1515/rams-2023-0347
Keywords for this article
rubber-modified recycled aggregate; compressive strength; peak strain; machine learning; multi-objective optimization
Creative Commons
BY 4.0

Articles in the same Issue

  1. Review Articles
  2. Progress in preparation and ablation resistance of ultra-high-temperature ceramics modified C/C composites for extreme environment
  3. Solar lighting systems applied in photocatalysis to treat pollutants – A review
  4. Technological advances in three-dimensional skin tissue engineering
  5. Hybrid magnesium matrix composites: A review of reinforcement philosophies, mechanical and tribological characteristics
  6. Application prospect of calcium peroxide nanoparticles in biomedical field
  7. Research progress on basalt fiber-based functionalized composites
  8. Evaluation of the properties and applications of FRP bars and anchors: A review
  9. A critical review on mechanical, durability, and microstructural properties of industrial by-product-based geopolymer composites
  10. Multifunctional engineered cementitious composites modified with nanomaterials and their applications: An overview
  11. Role of bioglass derivatives in tissue regeneration and repair: A review
  12. Research progress on properties of cement-based composites incorporating graphene oxide
  13. Properties of ultra-high performance concrete and conventional concrete with coal bottom ash as aggregate replacement and nanoadditives: A review
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  17. Wear properties of graphene-reinforced aluminium metal matrix composite: A review
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  78. Effect of molybdenum tailings aggregate on mechanical properties of engineered cementitious composites and stirrup-confined ECC stub columns
  79. Experimental study on the seismic performance of short shear walls comprising cold-formed steel and high-strength reinforced concrete with concealed bracing
  80. Failure criteria and microstructure evolution mechanism of the alkali–silica reaction of concrete
  81. Mechanical, fracture-deformation, and tribology behavior of fillers-reinforced sisal fiber composites for lightweight automotive applications
  82. UV aging behavior evolution characterization of HALS-modified asphalt based on micro-morphological features
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  88. Alkali-activated binder based on red mud with class F fly ash and ground granulated blast-furnace slag under ambient temperature
  89. Facile synthesis of g-C3N4 nanosheets for effective degradation of organic pollutants via ball milling
  90. DEM study on the loading rate effect of marble under different confining pressures
  91. Conductive and self-cleaning composite membranes from corn husk nanofiber embedded with inorganic fillers (TiO2, CaO, and eggshell) by sol–gel and casting processes for smart membrane applications
  92. Laser re-melting of modified multimodal Cr3C2–NiCr coatings by HVOF: Effect on the microstructure and anticorrosion properties
  93. Damage constitutive model of jointed rock mass considering structural features and load effect
  94. Thermosetting polymer composites: Manufacturing and properties study
  95. CSG compressive strength prediction based on LSTM and interpretable machine learning
  96. Axial compression behavior and stress–strain relationship of slurry-wrapping treatment recycled aggregate concrete-filled steel tube short columns
  97. Space-time evolution characteristics of loaded gas-bearing coal fractures based on industrial μCT
  98. Dual-biprism-based single-camera high-speed 3D-digital image correlation for deformation measurement on sandwich structures under low velocity impact
  99. Effects of cold deformation modes on microstructure uniformity and mechanical properties of large 2219 Al–Cu alloy rings
  100. Basalt fiber as natural reinforcement to improve the performance of ecological grouting slurry for the conservation of earthen sites
  101. Interaction of micro-fluid structure in a pressure-driven duct flow with a nearby placed current-carrying wire: A numerical investigation
  102. A simulation modeling methodology considering random multiple shots for shot peening process
  103. Optimization and characterization of composite modified asphalt with pyrolytic carbon black and chicken feather fiber
  104. Synthesis, characterization, and application of the novel nanomagnet adsorbent for the removal of Cr(vi) ions
  105. Multi-perspective structural integrity-based computational investigations on airframe of Gyrodyne-configured multi-rotor UAV through coupled CFD and FEA approaches for various lightweight sandwich composites and alloys
  106. Influence of PVA fibers on the durability of cementitious composites under the wet–heat–salt coupling environment
  107. Compressive behavior of BFRP-confined ceramsite concrete: An experimental study and stress–strain model
  108. Interval models for uncertainty analysis and degradation prediction of the mechanical properties of rubber
  109. Preparation of PVDF-HFP/CB/Ni nanocomposite films for piezoelectric energy harvesting
  110. Frost resistance and life prediction of recycled brick aggregate concrete with waste polypropylene fiber
  111. Synthetic leathers as a possible source of chemicals and odorous substances in indoor environment
  112. Mechanical properties of seawater volcanic scoria aggregate concrete-filled circular GFRP and stainless steel tubes under axial compression
  113. Effect of curved anchor impellers on power consumption and hydrodynamic parameters of yield stress fluids (Bingham–Papanastasiou model) in stirred tanks
  114. All-dielectric tunable zero-refractive index metamaterials based on phase change materials
  115. Influence of ultrasonication time on the various properties of alkaline-treated mango seed waste filler reinforced PVA biocomposite
  116. Research on key casting process of high-grade CNC machine tool bed nodular cast iron
  117. Latest research progress of SiCp/Al composite for electronic packaging
  118. Special Issue on 3D and 4D Printing of Advanced Functional Materials - Part I
  119. Molecular dynamics simulation on electrohydrodynamic atomization: Stable dripping mode by pre-load voltage
  120. Research progress of metal-based additive manufacturing in medical implants
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