Evolutionary strategies as applied to shear strain effects in reinforced concrete beams

doi:10.1016/j.asoc.2017.03.037

Applied Soft Computing

Volume 57, August 2017, Pages 164-176

https://doi.org/10.1016/j.asoc.2017.03.037 Get rights and content

Highlights

•
Evolutionary strategies are analyzed to solve a real and relevant problem.
•
The problem of shear strain effects in reinforced concrete beams is under study.
•
Inverse analysis assuming the so-called tension stiffening area is performed.
•
Several objective functions are proposed to fit better with experimental results.
•
Our results reveal CMA-ES obtains a robust a real fit for the targeted problem.

Abstract

The reinforced concrete beams is a structural member that is widely used in all types of building and civil constructions. These beams are subjected to different external loads that, above a critical value, may cause the collapse of the whole structure, having devastating consequences for civilians. Therefore, the a priori simulation of the internal forces developed within a reinforced concrete beam, when it is subjected to external loads, is mandatory to figure out its progressive structural response, to provide integrated risk assessment for a wide range of constructions such as buildings, bridges, etc. In this paper, we provide a simulation framework to estimate the behavior of reinforced concrete beams when they are subjected to external loads. Of particular interest to us is the simulation of the particularly damaging internal force, called Shear force. Several techniques are under study such as regression analysis, Little Genetic Algorithm (LGA) and Covariance Matrix Adaptation Evolution Strategy (CMA-ES), along with different objective functions (lineal, polynomial and rational functions) to provide a solution that satisfies both the physical and computational constraints of the targeted problem. These techniques are empirically optimized by using different parameters and genetic operators such as elitism, penalization for unfeasible individuals, crossing by one point or by linear combination of two individuals, mutation by gen or by individual. Numerical results reveal that CMA-ES algorithm together with a proper objective function, elitism and penalization allows predicting, under a relative error less than 5% (compared to experimental data taken from a tested beam), the shear response of a reinforced concrete beam in the stages near to the structural collapse.

Graphical abstract

An inverse analysis of the degradation of the bond between the concrete and the reinforcement, assuming the so-called tension stiffening area in the concrete as a function of the shear strain is performed. This problem is studied and analyzed using a preliminary least squares method and two evolutionary strategies in order to provide a solution that satisfies both the physical and computational constraints of the problem.

Introduction

The transmission of shear through the cracked web of a reinforced concrete beam is a complex phenomenon that has been the subject of several studies in the last decades [1], [2], [3]. The formulation of a mechanical model that determines the shear response curve of a reinforced concrete beam requires taking into account, for each level of stress, the inclination of the cracks in the web. Compression Field Theories (CFTs) [4], [5], [6] establish kinematic relationships between the inclination of these cracks and the strains in the reinforcement and the concrete. The experimental validation of CFTs [5], [6], [7] concluded that the consideration of the tension stiffening area prescribed by the international standards significantly underestimates the shear strength of the beam in the load stages near to the structural shear failure (high strains). Therefore, it is interesting to model the strength degradation, which the concrete experiences when the shear force increases, as a function of the member shear strain [6]. Previous works assume the tension stiffening area (denoted as A_c in Fig. 1) to be constant [6], [7], [8] which does not fit with the reality. Actually, Gil Martin et al. concluded in [6] that such area decreases as long as crack spacing decreases or the tensile strain increases.

In this paper, we analyze several strategies to perform an inverse analysis of the strain effects in the shear response of reinforced concrete beams to look for an optimal function (κ) that perfectly model the stiffening area (A_c). Fig. 1 summarizes the problem statement and the methodology we use to provide a novel solution to this relevant problem. Firstly, the adjustment of a strength degradation function is attempted by using standard regression through classical least square fitting method. The results of applying this technique show low correlation coefficients because of, among other reasons, the high non-linearity of the problem and the large number of variables involved. Therefore, more complex optimization techniques are required to deal with such challenging problem. We propose the use of evolutionary techniques as they are gaining increasing acceptance, and they are now used in a wide variety of application domains where the computational cost is not affordable by traditional machines [9]. In these disciplines, NP-complete problems; i.e., problems that cannot be targeted by exact resolution algorithm as its computational cost saves a polynomial relation to the size of the input, emerge very often. The task becomes even more difficult whenever the problem to solve has a high dimensionality by the presence of a large number of features or input variables like the problem targeted here. The major findings of this paper include the following:

1
An inverse analysis of the strain effects in the shear response of reinforced concrete beams is proposed to better estimate the shear strength of the beam in the load stages near to the structural shear failure.
2
A preliminary analysis of the physical problem is performed using regression techniques.
3
Two different genetic algorithms; the Little Genetic Algorithm (LGA) and the Covariance Matrix Adaptation Evolution Strategy (CMA-ES) are proposed using a polynomial approximation as degradation function of the tension stiffening area.
4
To improve the results obtained by our strategies, a new rational degradation function of the tension stiffening area is adjusted, obtaining up to 95% of adjustment compared to experimental data from a shear test of a reinforced concrete beam.

The rest of the paper is organized as follows. Section 2 shows a related work about the shear model considered in this work before introducing the strength degradation as a function of the shear strain. In Section 3 the equations of the physical problem under consideration are presented and the numerical complexity of the model to optimize is justified. Next, in Section 4 a preliminary analysis of the problem is shown using the least square fitting technique, before the two evolutionary approaches are described to solve this challenging problem (Section 5). Section 6 discusses the results obtained by the different computationally techniques targeted in this paper. Finally, Section 7 provides some conclusions and directions for future work, and in Appendix, Table 2 shows the characteristics of the specimens used for the different experiments performed along this paper.

Section snippets

Related work

In 1986 Vecchio and Collins developed an analytical model, the Modified Compression Field Theory (MCFT) [4], that predicted the full load-strain response of a reinforce concrete member subjected to shear, taking into account the equilibrium, compatibility and constitutive relationships of the involved materials; in particular, the stress–strain relationship for the steel was then assumed elastic-perfectly plastic, resulting in a elastic modulus constant up to the steel yield stress and then

Problem statement

When a reinforced concrete beam is subjected to external loads, these are equilibrated through a set of internal forces developed within the beam. Among these internal forces, one of them is particularly damaging, the so-called shear force. There are several methods to analyze the shear strength of a reinforced and prestressed concrete beam [16], [18], [19], [20]. Among them, there is a family of methods based on the Compression Field Theories (CFT) which not only predict the ultimate (failure)

Preliminary analysis: least square fitting

This section introduces a first approximation based on least square fitting to adjust the tension stiffening area based on κ parameter. In order to perform this technique, we use experimental information about 42 tested beams in shear provided by different authors, listed in Table 2. This information includes the ultimate shear (ν_u), the experimental stress in stirrups (σ_st,exp) at failure and the yield stress of the stirrups (f_y,t).

In analogous way to the analysis developed in Fig. 3, a set of

Evolutionary approaches to predict the evolution of the tension-stiffening area

This section introduces two different evolutionary algorithms to deal with the problem of shear strain effect on the above described tension-stiffening area; the Little Genetic Algorithm (LGA) and the Covariance Matrix Adaptation Evolution Strategy (CMA-ES). Firstly, we determine the objective function that models the degradation parameter (κ) to be optimized by our algorithms before we introduce them and show their application to this problem. Moreover, algorithmic parameters are also tuned to

Discussion

Throughout this paper, we have modeled the shear strength degradation of a reinforced concrete beam as a function of its shear strain. Three different techniques are proposed to perform this objective; they are: regression technique, the LGA technique and the CMA-ES technique. These techniques have been adapted in order to fulfill the problem requirements. In this section, the computational results obtained for these techniques are compared using a real scenario provided by the experimental

Conclusions and future work

The degradation effect of the concrete bonded to the steel in a reinforced concrete beam has been introduced in the steel constitutive model through the tension stiffening area. As a consequence, this area is not constant, but it changes due to the tendency of concrete to degrade as the external load increases. In this paper, we propose several strategies to perform an inverse analysis of the tension stiffening area in the context of the Compression Field Theories (CFTs).

First of all, a

Acknowledgements

This work is jointly supported by the Fundación Séneca (Agencia Regional de Ciencia y Tecnología, Región de Murcia) under grant 18946/JLI/13 and by the Spanish MINECO under grant TIN2016-78799-P (AEI/FEDER, UE). We also thank NVIDIA for hardware donation under GPU Educational Center 2014–2016 and Research Center 2015–2016. Finally, we thank the anonymous reviewers for their careful reading of our manuscript and their many insightful comments and suggestions.

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View full text

Evolutionary strategies as applied to shear strain effects in reinforced concrete beams

Highlights

Abstract

Graphical abstract

Introduction

Section snippets

Related work

Problem statement

Preliminary analysis: least square fitting

Evolutionary approaches to predict the evolution of the tension-stiffening area

Discussion

Conclusions and future work

Acknowledgements

Eng. Fail. Anal.

Constr. Build. Mater.

Eng. Struct.

Adv. Eng. Softw.

Eng. Struct.

Measurement

Eng. Struct.

Eng. Struct.

Shear strengthening of reinforced concrete T-beams under cyclic loading with TRM or FRP jackets

Mater. Struct.

Enhanced external progressive collapse mitigation scheme for RC structures

Int. J. Struct. Eng.

The modified compression-field theory for reinforced concrete elements subjected to shear

ACI J. Proc.

Constitutive laws of concrete in tension and reinforcing bars stiffened by concrete

ACI Struct. J.

Refinements to compression field theory, with application to wall-type structures

ACI Spec. Publ.

In-plane shear behaviour of thin low reinforced concrete panels for earthquake re-construction

Mater. Struct.

Handbook of Natural Computing

A simpler compression field theory for structural concrete

Stud. Ric. Politec. Milano Sc. Spec. Costr. Cem. Armato

Computing the refined compression field theory

Int. J. Concr. Struct. Mater.

Multi-objective optimization of reinforced cement concrete retaining wall

Indian Geotech. J.

A seismic optimization procedure for reinforced concrete framed buildings based on eigenfrequency optimization

Eng. Optim.

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Int. J. Concr. Struct. Mater.

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Hormigón armado y pretensado: concreto reforzado y preesforzado