Genetic programming to formulate viscoelastic behavior of modified asphalt binder

https://doi.org/10.1016/j.conbuildmat.2021.122954Get rights and content

Highlights

  • Three types of additives were used at three different dosages: crumb rubber, SBS, and PPA to modify bitumen.

  • Genetic programming based closed-form equations are developed for G* and δ of modified bitumens.

  • G* and δ of original bitumen, test temperature and frequency were considered as model inputs.

  • The performance of models were successfully verified using statistical indices and external data validation.

Abstract

The objective of this research was to develop prediction models for complex shear modulus (G*) and phase angle (δ) of bitumens modified with crumb rubber, styrene-butadiene styrene, and polyphosphoric acid at low and moderate temperatures. The experiments consisted of three different dosages of each modifier added to the original bitumen followed by measurement of G* and δ of the original and modified bitumen using the dynamic shear rheometer (DSR) test in frequency sweep mode (21 loading frequencies from 0.1 to 100 Hz) at seven test temperatures: −22, −16, −10, 0, 10, 16 and 22 °C. Having the experimental database, a robust genetic programming (GP) method was used to develop an individual prediction model for each modifier based on temperature, loading frequency, the G* and δ of the original bitumen, and the dosage of the modifier. Results showed that GP successfully developed accurate and meaningful expressions for calculating G* and δ of the modified bitumen as two main constitutive components of the viscoelastic behavior of bituminous composites. Then, a parametric study and sensitivity analysis were performed on the developed models to better understand the effect of variables on the trend of the models. The modifier dosage is the most effective input variable of the model and the amount of G* and δ of the original bitumen accurately reflect the effect of temperature and loading frequency on viscoelastic behavior of the modified bitumen, as they behave linearly at the considered test temperatures.

Introduction

Modification of original bitumen is a well-known method for improving its rheological and mechanical properties in order to meet the standard criteria and for increasing the life span of asphalt pavement. There are several additives used to enhance the low-, moderate-, and high-temperature performance of original bitumen, which can be selected based on climate conditions and dominant distress. Numerous previous publications investigated the effect of such additives on mechanical behavior, durability, and workability characteristics of original bitumen [1], [2], [3].

One of the major concerns regarding bitumen that is modified with different dosages of additives is precisely predicting its viscoelastic characteristics at the desired loading frequency, temperature, and additive concentration. Experimental and numerical modeling were used for this purpose, which assumed a simple thermo-rheological behavior of the original and modified bitumen. Although such an assumption can work for relating time and temperature based on the time–temperature superposition principle (TTSP), it is difficult for these equations to account for additive dosage. Therefore, prediction models such as GP can be used to intelligently predict the viscoelastic behavior of modified bitumen that has additional dosage and viscoelastic characteristics relative to the original bitumen.

GP, which in general is defined as a specialization of genetic algorithm (GA), is a powerful method for optimizing complex problems and uses computer-based programs instead of binary strings to solve problems [4]. GP has an inherent superiority over conventional mathematical and statistical approaches and black-box algorithms such as ANN, which is the ability of GP to produce explicit equations without using initial prediction models that present the relation between the involved parameters. This ability can be easily implemented in the practical design of modified asphalt binders. A recent extension of GP is gene expression programming (GEP), which was proposed by Ferreira [5]. Computer programs of different sizes and shapes are encoded in linear chromosomes of fixed length and comprise the GEP solutions. In order to predict the complex relationships between inputs and outputs of a data source, researchers presented methodologies for using GP to generate prediction formulae for engineering problems [6].

Gholampour et al. [7] applied the GEP technique on a large test database to develop formulae with a wide range of applicability for predicting the mechanical properties of recycled aggregate concrete. To predict the dynamic modulus, which is one of the most important mechanical property parameters of asphalt concrete, Liu et. al [8] explored two different GEP approach models for hot mix asphalt (HMA) and mixtures containing recycled asphalt shingles. The GEP approach was implemented in order to develop a prediction model of density and viscosity of bitumen [9]. Results of the presented model were compared with traditional empirical models in order to investigate its performance. To predict fracture energy of asphalt concrete specimens, Majidifard et al. used GEP and hybrid artificial neural network/simulated annealing (ANN/SA) by implementing an experimental database containing results of disk-shaped compact tension (DC(T)) tests. More recently, fatigue life prediction of hot mix asphalt (HMA) was formulated using GP [10]. Although several research works used artificial neural network models to predict the rheological and mechanical characteristics of modified bitumens with different types of additives [11], [12], [13], the GEP has not been used for relating the percentage of additive and other effective parameters to the desired properties of modified bitumen as a closed form equation. Since the mechanism of the effect that different additives have on original bitumen varies regarding the type of its interaction (physical/chemical), intrinsic properties of the original bitumen, and testing conditions, particular equations for each type of additive must be derived. It is well-known that the original and modified bitumen behave as viscoelastic materials in which their characteristics depend on time, temperature, and loading rate. Therefore, an appropriate simple closed form equation should include constitutive properties of the original bitumen, the percentage of additives, and testing conditions to predict the rheological and mechanical characteristics of modified bitumen.

In this study, three different prevalent types of additives were selected and were used to modify the original bitumen, which included crumb rubber, styrene–butadienestyrene (SBS), and polyphosphoric acid (PPA). Each modifier was added to the original bitumen at three different dosages: 10, 15, and 20 wt% for crumb rubber, 2, 4, and 6 wt% for SBS, and 0.5, 1, and 1.5 wt% for PPA. Then, two constitutive viscoelastic parameters (complex shear modulus (G*) and phase angle (δ)) were measured by performing a frequency sweep test at seven different test temperatures: –22, −16, −10, 0, 10, 16, and 22 °C. The purpose of this study is to use the GEP technique to predict G* and δ of modified bitumen based on these parameters measured for the original bitumen. Such a model will make it possible to find the optimum dosage of each additive in order to achieve the desired viscoelastic properties at low and moderate temperatures. In summary, Fig. 1 illustrates the flow of work in this study.

Section snippets

Experimental program

In this research, three common types of bitumen additives, including crumb rubber, styrene–butadienestyrene (SBS) and polyphosphoric acid (PPA), were used to enhance the rheological and mechanical characteristics of the original bitumen. First in this section, these modifiers are briefly introduced; then, sample preparation, the test method, and generated results are presented.

Gene expression programming (GEP)

Using GP, which was originally introduced as a useful prediction algorithm by Koza [24], the relationships between the involved parameters of a problem are predicted based on the principle of Darwinian natural selection. The commonly used mechanisms of genetic algorithm (GA) can also be utilized in GP; nevertheless, the solution representation is different. The result of GA is in the form of a fixed-length binary string; however, an evolving GP results in a computer code of prediction can be

Model development

In order to develop a GP prediction model for estimating the complex shear modulus (G*) and phase angle (δ) of modified asphalt bitumens, all of the effective input parameters that were part of the experimental program have to incorporated into the models. It is well-known that the original bitumen, as well as modified ones, behave like viscoelastic materials and their mechanical behavior depends on time (frequency of applied load) and temperature. The additive dosage used to modify the

Validity of the proposed models

As per the recommendation by Frank and Todeschini [28], a model can be safely acceptable if the ratio of the number of data sets to the number of input parameters is greater than five. Here, the mentioned ratio for CR, SBS, and PPA modified bitumen are 88, 88, and 80, respectively, which indicates the validity of the number of data. Moreover, for a valid model, it is necessary for the error value (e.g., RRMSE) to be at its minimum, and R to be higher than 0.8 [29]. In all of the selected

Parametric study and sensitivity analysis

A parametric study of the GEP models was conducted to examine the robustness of the prediction models for all three modified bitumens, and the response of each GEP model to its corresponding input parameters was investigated. The three-dimensional diagrams in Fig. 13, Fig. 14, Fig. 15 illustrate the general trend of the models against pairs of input predictors for the presented formulae for CR, SBS, and PPA modified bitumens. As can be seen in Fig. 13, Fig. 14, Fig. 15, the observed trends were

Summary and conclusion

GEP, which is a robust and natural development of traditional GP, was used to develop formulae that can be used to predict the complex shear modulus and phase angle of modified asphalt bitumen. The input data consisted of results of an experimental program conducted on three different additives, namely crumb rubber, SBS, and PPA. It is necessary to mention that all experiments were performed at a low strain amplitude (0.01%), and consequently, all derived equations are valid for the linear

Future research work

This research work presented a GEP model that can be used to predict complex shear modulus (G*) and phase angle (δ) as two constitutive parameters of bitumen modified with crumb rubber, SBS, and PPA, and three closed-form equations were derived for these additives. However, two main issues should be considered for future research works: 1) using original bitumens from different sources, and 2) running experiments under different test conditions. Original bitumens from different sources can be

CRediT authorship contribution statement

Alireza Sadat Hosseini: Conceptualization, Validation, Formal analysis, Writing - original draft, Visualization. Pouria Hajikarimi: Conceptualization, Investigation, Writing - original draft, Visualization. Mostafa Gandomi: Software, Formal analysis, Visualization. Fereidoon Moghadas Nejad: Methodology, Resources, Supervision. Amir H. Gandomi: Methodology, Software, Formal analysis, Writing - review & editing, Supervision.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

References (35)

  • A. Golbraikh et al.

    Beware of q2!

    J. Mol. Graph. Model.

    (2002)
  • A. Samieadel et al.

    Interplay between wax and polyphosphoric acid and its effect on bitumen thermomechanical properties

    Constr. Build. Mater.

    (2020)
  • K.B. Vural et al.

    Evaluation of Low-Temperature and Elastic Properties of Crumb Rubber– and SBS-Modified Bitumen and Mixtures

    J. Mater. Civ. Eng.

    (Feb. 2013)
  • A.H. Gandomi et al.

    Novel approach to strength modeling of concrete under triaxial compression

    J. Mater. Civ. Eng.

    (2012)
  • C. Ferreira, “Gene expression programming: a new adaptive algorithm for solving problems,” arXiv Prepr. cs/0102027,...
  • A.H. Gandomi et al.

    Handbook of genetic programming applications

    (2015)
  • J. Liu et al.

    Prediction models of mixtures’ dynamic modulus using gene expression programming

    Int. J. Pavement Eng.

    (Nov. 2017)
  • Cited by (15)

    • Development of shape memory polyurethane/SBS compositely modified asphalt and synergistic modification mechanism

      2023, Construction and Building Materials
      Citation Excerpt :

      Jasso et al. [19] discussed the impacts of SBS/sulfur on the mechanical and rheological properties of asphalt, and reported that the vulcanization of SBS in asphalt led to the formation of a stronger elastic network and enhanced rheological properties. Hosseini et al. [20] established the prediction models for complex shear modulus and phase angle of SBS, crumb rubber, and polyphosphoric acid modified asphalt. They pointed out that the modifier content was the most effective input variable of the model.

    View all citing articles on Scopus
    View full text