Applied Computational Intelligence and Soft Computing

Volume 2017 (2017), Article ID 9897078, 11 pages

https://doi.org/10.1155/2017/9897078

## Modeling Punching Shear Capacity of Fiber-Reinforced Polymer Concrete Slabs: A Comparative Study of Instance-Based and Neural Network Learning

^{1}Institute of Research and Development, Faculty of Civil Engineering, Duy Tan University, K7/25 Quang Trung, Danang, Vietnam^{2}Faculty of Architecture, Duy Tan University, K7/25 Quang Trung, Danang, Vietnam^{3}International School, Duy Tan University, 254 Nguyen Van Linh, Danang 550000, Vietnam

Correspondence should be addressed to Nhat-Duc Hoang; nv.ude.utd@cudtahngnaoh

Received 1 December 2016; Revised 17 January 2017; Accepted 15 March 2017; Published 4 April 2017

Academic Editor: Lukasz Sadowski

Copyright © 2017 Nhat-Duc Hoang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

This study investigates an adaptive-weighted instanced-based learning, for the prediction of the ultimate punching shear capacity (UPSC) of fiber-reinforced polymer- (FRP-) reinforced slabs. The concept of the new method is to employ the Differential Evolution to construct an adaptive instance-based regression model. The performance of the proposed model is compared to those of Artificial Neural Network (ANN) and traditional formula-based methods. A dataset which contains the testing results of FRP-reinforced concrete slabs has been collected to establish and verify new approach. This study shows that the investigated instance-based regression model is capable of delivering the prediction result which is far more accurate than traditional formulas and very competitive with the black-box approach of ANN. Furthermore, the proposed adaptive-weighted instanced-based learning provides a means for quantifying the relevancy of each factor used for the prediction of UPSC of FRP-reinforced slabs.

#### 1. Introduction

In civil engineering, fiber-reinforced polymer (FRP) composites have been increasingly employed due to their strength and stiffness, good thermomechanical properties, capacity for resisting corrosion, low weight, and outstanding durability [1–4]. It is proper to note that corrosion of steel reinforcement is the major factor which influences the deterioration and shortens the service life of reinforced concrete structures [5–7]. Thus, the utilizations of FRP composites have created the condition for enhancing the productivity of construction process, meliorating the performance of concrete structures, reduction of maintenance budgets spent for infrastructure, and possible elongation of structure service lives [8, 9].

Steel-reinforced two-way flat slabs are popular structural systems that can simplify and accelerate on-site operations and facilitate flexible partitioning of space [10]. The two-way flat slabs are particularly efficient for constructing parking structures. Additionally, computing the slab’s resistance of shear stresses at supporting columns is a major concern in the design procedure of this structure [11]. Notably, the slab-supporting column connections have been shown to be vulnerable to high shear stresses and this might bring about brittle and sudden punching shear failures [10]. Especially when the steel reinforcements get corroded due to moisture and other hostile factors in the operational environment, punching shear failures may occur at these slab-column connections. Accordingly, these may lead to progressive collapse of the whole structure [12].

Due to such reasons, FRP bars are recently considered as effective substitutions to the traditional steel bars in concrete flat slabs [13]. Moreover, UPSC is critical factor which determines the design process of concrete slabs supported by columns. Thus, this problem is extensively studied in the literature [14]. As a consequence, various researches have been conducted to investigate the applicability of existing empirical approaches and modify them to predict the punching shear capacity of FRP-reinforced slabs [1, 10, 15, 16].

Recently, machine learning has been proved to provide a feasible alternative for modeling the punching shear capacity of FRP-reinforced slabs [6, 9, 15, 17]. The Artificial Neural Network (ANN) has been employed to predict the FRP-reinforced slab punching shear capacity [6]. The research shows that the predictive result produced by ANN is considerably more accurate than those computed by the empirical formulas. Despite the fact that ANN is a powerful method for modeling nonlinear systems [18, 19], the learning process of ANN suffers from certain challenges [20].

One major difficulty of ANN is that its model establishment stage is accomplished via a gradient descent (GD) algorithm. GD algorithm is known to be very complex and may contain many local minima [20]. Another disadvantage of the ANN approach lies in their knowledge representation [21]; the black-box nature of the method makes it difficult for structural engineers to comprehend how the ANN predicts the punching shear capacity of FRP-reinforced slabs. In addition, the ANN approach intrinsically provides no means of measuring the contribution of each input factors to the model performance.

This research aims at extending the body of knowledge by investigating a new learning alternative for modeling the punching shear capacity of FRP-reinforced slabs. The proposed approach is hybridization of an improved kernel regression and the Differential Evolution (DE) [22]. The research objective is to establish a prediction model with transparent structure, self-adaptive learning, and the capability to express the relevancy of input variables.

Notably, the kernel regression belongs to the class of instance-based regression, which is also called nonparametric regression. Nonparametric regression offers a flexible and effective way of approximating the regression function especially when the form of the regression function is inherently complex [23, 24]. The reason is that, in such circumstance, it can be difficult to construct a universal parametric model based on a limited amount of training samples. Since good performances of the nonparametric approach have been observed throughout the literature [21, 25–28], the nonparametric regression is worth being investigated in solving the problem of interest.

Furthermore, learning based on instances or examples is a common practice in construction engineering. Thus, an instance-based model for punching shear capacity of FRP-reinforced slabs can be easily perceived by practical engineers; this may facilitate the applicability of the new approach. The rest of the article is organized as follows. The second section introduces the research method. The third section describes the proposed hybrid instance-based learning, followed by the experimental results. The final section summarizes our research with several conclusions.

#### 2. Research Methodology

##### 2.1. A Review of Formulas for Estimating Punching Shear Capacity of FRP-Reinforced Slabs

The shear resistance of the concrete () is known to influence the punching shear capacity of two-way reinforced concrete flat slabs. acts over the area proportional to the length of a critical perimeter () multiplied by the effective depth of the section (). Currently, there is a critical need to investigate design equations and prediction models for determining the punching shear strength of concrete slabs reinforced with FRP composite bars. The reason is that existing design equations applied for FRP-reinforced concrete sections are originated from those previously applied for steel-reinforced counterparts with certain adjustments for considering the replacement of steel by FRP. The following section reviews formula-based methods for the prediction of UPSC of FRP-reinforced slabs; it is noted that the system of units for all equations is SI.

The American Concrete Institute (ACI) Code (ACI 318-11) introduces a design formula to account for the shear transfer in two-way steel-reinforced concrete slabs:where denotes the specified compressive strength of the concrete (MPa), represents the perimeter of the critical section for slabs and footings at a distance of away from the column face, and is the average flexural depth of the slab.

In addition, The British Standard (BS 8110-97) suggests a formula to attain the punching shear capacity for steel-reinforced slabs as shown below:where denotes the characteristic concrete cube compressive strength (N/mm^{2}), represents the steel reinforcement ratio, is the perimeter of the critical section for slabs and footings at a distance of 1.5*d*/2 away from the loaded area (mm), and represents the average flexural depth of the slab.

On the basis of experiments, El-Ghandour et al. [29] suggested a modification to the ACI’s equation by multiplying it by the term to account for the use of FRP bars as follows: where and are Young’s modulus of the FRP-reinforced slab and Young’s modulus of the steel reinforcement, respectively.

El-Ghandour et al. [30] modified the BS 8110-97’s design equation and suggested an alternative formula to obtain the shear strength of FRP-reinforced concrete slabs as follows:

Matthys and Taerwe [31] put forward an enhancement of the BS 8110-97 as follows:

Ospina et al. [32] introduced an improved version of the equation proposed by Matthys and Taerwe [31]; in this revision, the cube root of the modular ration is replaced by the square root. This design formula is shown as follows:

A design equation has been proposed by the subcommittee ACI440H [16] for calculation of steel-reinforced two-way concrete slabs. This equation has considered the influence of reinforcement stiffness to account for the shear transfer in two-way concrete slabs as follows:where is the perimeter of the critical section for slabs and footings at a distance of away. And is the cracked transformed section neutral axis depth (mm) and is calculated as follows:where is defined in the following equation:

In (9), it is noted that = / denotes modular ratio and is the concrete modulus of elasticity.

##### 2.2. The Collected Dataset of Punching Shear Tests

The dataset of FRP-reinforced concrete flat slab used in this study consists of 82 tests recorded in previous research works [6, 15, 33]. As the previous work of Vu and Hoang [17], the type of column section (), section area of column (), effective flexural depth of slab (), compressive strength of concrete (), Young’s modulus of the FRP-reinforced slab (), and reinforcement ratio () are considered as input factors that determine the ultimate punching capacity of the FRP-reinforced concrete flat slab. The shape of the column section includes three forms: square (), circle (), and rectangle (). In the dataset, the numbers of square, circle, and rectangle sections are 50, 13, and 19, respectively. The range of the punching capacity varies from 61 kN to 1600 kN. Table 1 shows the variables and their statistical descriptions. The whole dataset is provided in the Appendix.