3C Tecnología. Glosas de innovación aplicadas a la pyme. ISSN: 2254 – 4143 Ed. 35 Vol. 9 N.º 3 Septiembre - Diciembre
47
MIX DESIGN WITH RESPONSE SURFACE METHODOLOGY TO
OPTIMIZE THE FLEXURAL STRENGTH OF CONCRETE
Freddy Lizardo Kaseng Solis
National University Federico Villarreal, Lima, (Perú).
E-mail: fkaseng@unfv.edu.pe ORCID: https://orcid.org/0000-0002-2878-9053
Luis Jimmy Clemente Condori
National University Federico Villarreal, Lima, (Perú).
E-mail: kelvin0296@yahoo.es ORCID: https://orcid.org/0000-0002-0250-4363
Ciro Rodriguez Rodriguez
National University Mayor de San Marcos, Lima, (Perú).
E-mail: crodriguezro@unmsm.edu.pe ORCID: https://orcid.org/0000-0003-2112-1349
Recepción:
14/05/2020
Aceptación:
08/07/2020
Publicación:
14/09/2020
Citación sugerida:
Kaseng, F.L., Clemente, L.J., y Rodriguez, C. (2020). Mix design with response surface methodology to optimize
the exural strength of concrete. 3C Tecnología. Glosas de innovación aplicadas a la pyme, 9(3), 47-57. https://doi.
org/10.17993/3ctecno/2020.v9n3e35.47-57
3C Tecnología. Glosas de innovación aplicadas a la pyme. ISSN: 2254 – 4143 Ed. 35 Vol. 9 N.º 3 Septiembre - Diciembre
48
https://doi.org/10.17993/3ctecno/2020.v9n3e35.47-57
ABSTRACT
This paper presents a technical proposal for the application of experimental designs in the construction
processes of civil works, specically in the manufacture of concrete for rigid pavements. Currently is
still does not apply these technological advances, or any application of research methods that allows
optimizing processes to more satisfactory levels, despite the advantages and benets they provide in
terms of achieving unexpected performance and signicant savings of component materials. The
experimental design model is a classic statistical model whose objective is to determine if the independent
factors inuence in a variable of interest in this case the modulus of breakage of the concrete or in
another important factor, during the bending test. The answer surface methodology is based on the
experimentation in three stages, the results achieved allow locating an optimal area where the adjusted
values lead to reduced consumption of them and expanding the strength of the concrete.
KEYWORDS
Concrete, Experimental method, Optimization, Resistance, Flexural strength, Rigid pavements.
3C Tecnología. Glosas de innovación aplicadas a la pyme. ISSN: 2254 – 4143 Ed. 35 Vol. 9 N.º 3 Septiembre - Diciembre
49
https://doi.org/10.17993/3ctecno/2020.v9n3e35.47-57
1. INTRODUCTION
The rigid pavements made based on concrete, present in their vast majority the presence of structural
and supercial ssures, these have become a problem regarding its functionality and the useful life in
terms of the level of service to the vehicles that circulate in these routes.
The reasons are many; among the most relevant we can name the mix design for concrete, the method
of making the “cloths”, the materials used, the quantity or proportion of the components, etc., the latter
is constitutes the objective of the investigation. It is observed that the method used at the present time are
the conventional ones that do not allow the necessary adjustments to be made to the materials and their
performance in order to achieve optimum levels in terms of dosage and as a product, greater resistance
to bending called the Break Module (MR).
The manufacturing method is frequently that of the American Concrete Institute (ACI), as the dosage
is very rigid and closed, it does not allow modications to be made to the components, such as cement,
aggregate, water, additives, etc. For this, it is necessary to resort to other methods that give the possibility
of manipulating these independent variables and with the hypothesis of reaching optimum levels of the
mechanical properties of the concrete. For this it is necessary to use the experimental designs (widely used
in other areas of engineering) that, based on a practical methodology and the use of logical reasoning,
it is possible to adjust both the quantity of materials and the resistance to exion even more optimal, is
possible use algortihms for calculations as Sánchez et al. (2020) and Soto et al. (2020).
Deterministic simulation models have the characteristic of being a technique for solving practical
problems (Levy et al., 2020), such as an overall change of variables over time. Experimental models
are an approximation to the real system. From the above, there is a need to repeat multiple simulation
runs, consequently, its use in an investigation should be planned as a series of experiments that lead to
signicant interpretations of the relationships of interest (Huapaya, Rodriguez & Esenarro, 2020).
3C Tecnología. Glosas de innovación aplicadas a la pyme. ISSN: 2254 – 4143 Ed. 35 Vol. 9 N.º 3 Septiembre - Diciembre
50
https://doi.org/10.17993/3ctecno/2020.v9n3e35.47-57
The response surface methodology (MSR) was used in this investigation. This modeling methodology
is a holistic approach that allows us to postulate the form of the objective function, update and limit the
values of the parameters, as well as explore and approach the region close to the optimal estimate.
2. METHOD
The Response Surface Methodology (MSR) is the tool used to achieve the proposed objectives, for which
reason it was necessary to experiment sequentially in the stages it comprises until the desired level of
improvement is found. In this case, after a rst experimental stage (selection of inuential variables) it
was necessary to move the experimental region (move from place) in a suitable direction, or to explore
the initial experimental region in more detail (see Figure 1). The way to do both is part of the so-called
Response Surface Methodology (MSR).
Figure 1. Basic actions of the MSR. Source: (Gutiérrez-Pulido & De la Vara, 2008).
3C Tecnología. Glosas de innovación aplicadas a la pyme. ISSN: 2254 – 4143 Ed. 35 Vol. 9 N.º 3 Septiembre - Diciembre
51
https://doi.org/10.17993/3ctecno/2020.v9n3e35.47-57
2.1. SIEVING OR CLASSIFICATION
In this rst optimization stage, we identify the controllable variables that can signicantly inuence the
process responses (ne aggregate, cement) and “eliminate” those that were not signicant for a good
economic orientation of the process, because it reduces the number of variables and Experimental tests
in the later stages of optimization (Figure 2). When controllable variables range from low to high, they
aect expected responses. For our case, we use the rst-order factorial design.
Figure 2. The sequence of the MSR. Source: (Montgomery & Runger, 1996).
2.2. ESCALATION
Having located the optimal region, and observing that it is still far from the initial experiments (sieving),
then was initiated the second stage called “scaling”, which consisted of successively climbing towards
the optimal region until reaching it (Figure 3), to achieve for this objective, we use the indirect method
of ascending slopes in two periods. The method of the steepest ascent is the one that allowed us to go to
the zone of the maximum increase of the response, according to formula (1).
3C Tecnología. Glosas de innovación aplicadas a la pyme. ISSN: 2254 – 4143 Ed. 35 Vol. 9 N.º 3 Septiembre - Diciembre
52
https://doi.org/10.17993/3ctecno/2020.v9n3e35.47-57
(1)
Figure 3. The sequence of the MSR. Source: (Montgomery & Runger, 1996).
2.3. FINAL OPTIMIZATION
When locating ourselves in the previous stages of the experimental region that contains the optimum, in
this region, the second-order eects were more signicant in absolute value than the rst-order eects;
this region is appropriately described by second-order mathematical models as shown in equation (2).
In this case, we use the hexagonal design of Figure 4. After closing the optimal region, in this stage, the
second-order eects are more signicant, for which we use the formula.
(2)
Y=b
0
+Σb
i
x
i
+Σb
ii
x
i
2
+Σ Σ b
ij
x
i
x
j
+ε
i=1 i=1 i=1 j=2
j
Response variable
Unknown parameters
Random error
3C Tecnología. Glosas de innovación aplicadas a la pyme. ISSN: 2254 – 4143 Ed. 35 Vol. 9 N.º 3 Septiembre - Diciembre
53
https://doi.org/10.17993/3ctecno/2020.v9n3e35.47-57
Figure 4. Hexagonal design structure with coded values.
3. RESULTS
The beam bending tests carried out at 4, 14, 21, and 28 days provide us with information on the modulus
of rupture. It is observed that the mean (41.37) of the module of the ten designs with variable factors
concerning the mean of the standard design (36.40) diers in 4.97, the design that grants the highest
resistance is the second (44.82) at 28 days of maturation. And for the pattern design, it has a dierence
of 8.42.
Table 1. Details of the control.
Beams 30x30x50 Patron
Date Empty 06/01/18 06/01/18 06/01/18 07/01/18 07/01/18 07/01/18 07/01/17 08/01/18 08/01/18 08/01/18 07/01/18 Mean
Breakdate Date 03/02/2018 03/02/2018 03/02/2018 04/02/2018 04/02/2018 04/02/2018 04/02/2017 05/02/2018 05/02/2018 05/02/2018 04/02/2018
READING (Kn / Cm²) 33.73 35.21 32.62 31.07 31.85 35.1 30.59 35.09 30.4 32.05 28.59 32.39
READING P (Kg / Cm²) 3439.45 3590.36 3326.26 3168.21 3247.74 3579.15 3119.26 3578.13 3099.89 3268.14 2915.32 3302.90
FREE LIGHT L (Cm) 45 45 45 45 45 45 45 45 45 45 45 45
AVERAGE WIDTH B (Cm) 15.30 15.40 15.20 15.40 15.50 15.40 15.30 15.50 15.40 15.30 15.60 15.39
AVERAGE HEIGHT D (Cm) 15.50 15.30 15.30 15.50 15.30 15.40 15.20 15.40 15.60 15.30 15.20 15.36
Edge Distance 29 27 17.5 24.8 26.7 24.9 17.7 20.1 29.4 25.5 28 24.6
Distance In middle Third 11.5 9.5 0 7.3 9.2 7.4 0.2 2.6 11.9 8 10.5 7.1
BREAKDOWN M(Kg / Cm²) 42.11 44.82 42.07 38.53 40.28 44.10 39.71 43.80 37.22 41.06 36.40 41.37
Source: authors’ own elaboration.
3C Tecnología. Glosas de innovación aplicadas a la pyme. ISSN: 2254 – 4143 Ed. 35 Vol. 9 N.º 3 Septiembre - Diciembre
54
https://doi.org/10.17993/3ctecno/2020.v9n3e35.47-57
The optimal conditions of the controllable, independent variables are Cement = 617.95 kg / m³ and the
ne aggregate = 1816.44 kg / m³, replacing these values obtained in the coded mathematical model, the
maximum strength of the concrete is obtained, which would reach 93%. By using the MINITAB version
16 software, we elaborated on the optimization graphs for the exural resistance of rigid pavement
concrete.
Figure 4. Optimized area for the controlled factors of strength to compressive. Source: authors’ own elaboration.
A curve system is observed in the graph, and due to the color distribution, the maximum eciency is
achieved with the maximum level of cement and with a standard level of ne aggregate (dark green
color).
Figure 5. The efciency of the optimization process regarding ne aggregate and cement. Source: authors’ own elaboration.
3C Tecnología. Glosas de innovación aplicadas a la pyme. ISSN: 2254 – 4143 Ed. 35 Vol. 9 N.º 3 Septiembre - Diciembre
55
https://doi.org/10.17993/3ctecno/2020.v9n3e35.47-57
In the quadratic eect spatial graph, the contour system is notorious, for the levels generated the
maximum eciency of the concrete resistance is achieved with the maximum levels of cement and the
standard level of ne aggregate.
4. CONCLUSIONS
The ranges considered concerning direct tensile strength with compressive strength for concretes made
with aggregates from the Mantaro river and Portland cement type I were considered between 201 kg /
cm² and 420 kg / cm² and are the ranges of the experiment that they allowed to expand the surface of
optimal levels, in terms of the volumes of the materials. Besides, the extension of the working ranges can
reduce the consumption of materials, achieving the same resistance that was initially reached.
The Response Surface Methodology is an extremely versatile technique that allows the use of dierent
experimental designs and statistical tools to solve system optimization problems and can be applied to the
optimization of a single response or the simultaneous optimization of several responses.
REFERENCES
Córdova, I. (2012). Proyecto de Investigación Cuantitativa. Editorial San Marcos, p. 77.
Gutiérrez-Pulido, H., & De la Vara, R. (2008). Análisis y Diseño de Experimentos (2ª ed.). McGraw-Hill.
Huapaya, H. D., Rodriguez, C., & Esenarro, D. (2020). Comparative analysis of supervised
machine learning algorithms for heart disease detection. 3C Tecnología. Glosas de innovación
aplicadas a la pyme. Edición Especial, Abril 2020, 233-247. http://doi.org/10.17993/3ctecno.2020.
specialissue5.233-247
3C Tecnología. Glosas de innovación aplicadas a la pyme. ISSN: 2254 – 4143 Ed. 35 Vol. 9 N.º 3 Septiembre - Diciembre
56
https://doi.org/10.17993/3ctecno/2020.v9n3e35.47-57
Levy, J., Pandey, B., Chowdhry, B., & Rodriguez, C. (2020). Prologue: Recent trends in computer
science and engineering (RTCSE). 3C Tecnología. Glosas de innovación aplicadas a la pyme. Edición
Especial, Abril 2020, 19-25. http://doi.org/10.17993/3ctecno.2020.specialissue5.19-25
Montgomery, D. C., & Runger, G. C. (1996). Probabilidad y estadística aplicadas a la ingeniería. McGraw-
Hill.
Rosental, M. M., & Iudin, P. F. (2008). Diccionario Filosóco. Editora Política. http://www.losoa.org/
urss/d1965.htm
Sabino, C. (1986). El proceso de investigación. Editorial Panapo, p. 53. http://paginas.ufm.edu/sabino/
ingles/book/proceso_investigacion.pdf
Sánchez, J., Vega, H., Guzmán, Y., Rodriguez, C., & Quinto, D. (2020). Data mart design to
improve the decision-making process of the after-sales service. Test Engineering and Management, 83,
15481–15494. http://www.testmagzine.biz/index.php/testmagzine/article/view/6539
Soto, B., Vega, H., Guzmán, Y., Rodriguez, C., & Quinto, D. (2020). Classication algorithm
based on machine learning to optimize athletes talent detection. Test Engineering and Management,
83, 13464–13471. https://testmagzine.biz/index.php/testmagzine/article/view/6067
Torre, C. (2004). Tecnología del concreto para ingenieros civiles. LEM-UNI, p. 74.
