Elsevier

Engineering Structures

Volume 274, 1 January 2023, 115173
Engineering Structures

Backbone model for reinforced concrete block shear wall components and systems using controlled multigene genetic programming

https://doi.org/10.1016/j.engstruct.2022.115173Get rights and content

Highlights

  • Factors affecting RCBSWs response were identified using variables selection procedures.

  • A simplified backbone curve for fully grouted RCBSWs was developed using MGGP.

  • The developed model predictions were validated at the component- and system-level.

  • The accuracy of the MGGP model was compared to that of existing models.

  • Sensitivity analyses were conducted to study the model variables’ influences on predictions.

Abstract

Reinforced concrete block shear walls (RCBSWs) have been used as an effective seismic force resisting system in low- and medium-rise buildings for many decades. However, attributed to their complex nonlinear behavior and the composite nature of their constituent materials, accurate prediction of their seismic performance, relying solely on mechanics, has been challenging. This study adopts multi-gene genetic programming (MGGP)— a class of bio-inspired artificial intelligence, to uncover the complexity of RCBSW behaviors and develop simplified procedures for predicting the full backbone curve of flexure-dominated RCBSWs under cyclic loading. A piecewise linear backbone curve was developed using five secant stiffness expressions associated with: cracking; yielding; 80% ultimate; ultimate; and 20% strength degradation (i.e., post-peak stage) derived through mechanics-controlled MGGP. Based on the experimental results of large-scale cyclically loaded fully-grouted RCBSWs, compiled from previously reported studies, a variable selection procedure was performed to identify the most influential variable subset governing wall behaviors. Subsequently, the MGGP stiffness expressions were trained and tested, and their accuracy was compared to that of existing models employing various statistical measures. In addition, the predictability of the developed backbone model was assessed at the system-level against experimental results of two two-story buildings available in the literature. This study demonstrates the power of the MGGP approach in addressing the complexity of the cyclic behavior of RCBSWs at both component- and system-level—offering an efficient prediction tool that can be adopted by relevant seismic design standards pertaining to RCBSW buildings.

Introduction

Considering the proliferation of low- and mid-rise buildings, the use of reinforced concrete block shear walls (RCBSWs) as a seismic force-resisting system has been undergoing extensive research. In the past, RCBSW buildings were constructed without adequate reinforcement detailing accounting for seismic demands [1], [2]. For example, field surveys following the aftermath of major seismic events, such as the 2010 Maule and the 2014 Iquique earthquakes, documented that a significant number of RCBSWs were severely damaged and/or have completely collapsed [2], [3], [4]. Subsequently, new design and prescriptive detailing requirements have been introduced by relevant design standards (e.g., ASCE/SEI 41-17 [5], CSA S304-14 [6], and TMS 402/602-16 [7]) to ensure adequate RCBSWs seismic performance. In parallel, extensive research studies have been performed to evaluate the seismic response of RCBSWs, which were found to be highly influenced by their shear-span ratios, the magnitude of the applied axial loads, and the horizontal and vertical reinforcement ratios [8], [9]. However, the complexity of RCBSWs as composite structural components (i.e., made up of different interacting nonlinear materials) challenges accurate prediction of their behavior under seismic loading. A few researchers attempted to address this issue by modeling the load-displacement backbone curve of RCBSWs under cyclic loading through analytical and empirical approaches.

Ashour and El-Dakhakhni [10] proposed a trilinear backbone curve for fully grouted RCBSWs using three secant stiffness expressions (Eqs. (1a), (1b), (1c)) for yielding (Ky), ultimate (Ku), and 20% strength degradation (K0.8u) (as shown in Fig. 1a). The backbone curve was developed based on the experimental results of four individual RCBSWs tested under lateral cyclic loads.Ky=1/hw33EmIe+1.2hwGmAe,Ku=0.6×Ky,K0.8u=0.2×KyGm=0.4Em,Ie=αIg,Ae=αAg,α=100fy+Pufm,AgΔy=QyKy,Δu=QuKu,Δ0.8u=Q0.8uK0.8uwhere, hw is the wall height, Ig is the wall gross moment of inertia, Ie is the wall effective moment of inertia, Ae is the wall effective area, Ag is the wall gross area, Em is the masonry elastic modulus, Gm is the masonry shear modulus, fm, is the masonry compressive strength, fy is the reinforcement yielding strength, Δy,Δu, and Δ0.8u are the displacements corresponding to yielding strength (Qy), ultimate strength (Qu), and 20% strength degradation (Q0.8u), respectively.

Later on, Ashour and Galal in 2017 [11], proposed a modification to Ky, Ku, and K0.8u (presented in Eqs. (2a), (2b)) originally developed by Ashour and El-Dakhakhni [10]. In addition, a new secant stiffness expression was introduced to the backbone curve defining the stiffness up to cracking (Kcr). Fig. 1b shows the quad-linear modified backbone curve that was developed by Ashour and Galal in 2017 [11] based on a dataset consisted of 25 RCBSWs.Kcr=Kg=1/hw33EmIg+1.2hwGmAg,KP=αKgKy=-0.00096KP2+0.89801KP,Ku=0.2875×Ky,K0.8u=0.5479×Ku

Ezzeldin et al. [12] also proposed a trilinear moment-rotation backbone model for RCBSWs (Fig. 1c) based on the ASCE/SEI 41-17 [5] originally developed for reinforced concrete (rather than concrete block) shear walls. The proposed model was validated at the system level against the results of eight RCBSWs with and without boundary elements. As shown in Fig. 1c, Ezzeldin et al. [12] model defined the elastic zone up to point B by the elastic rotation (θy), whereas parameter a and b were used to represent the plastic rotation up to the ultimate strength (θu) and failure (θr) at point C and E, respectively. The parameter c is also suggested to quantify the residual moment (Mr) at point D. In their study, Ezzeldin et al. [12] evaluated the yielding, ultimate, and residual strengths (Qy, Qu, and Qr, respectively) by dividing the corresponding moments by the wall heights, whereas the displacements at yield, ultimate, and residual strengths (Δy, Δu and Δr, respectively) are calculated according to Eqs. (3a), (3b), (3c).Δy=QyKy,Ky=αKgΔmax=Δy+ah-lpΔr=Δy+bh-lpwhere a = 0.006 rad, b = 0.015 rad, c = 60%, and lp is the plastic hinge length of the wall that was assumed to be 50% of the wall flexural depth but less than the wall height and less than 50% of the wall length, according to ASCE/SEI 41-17 [5].

The predictability of available backbone models is restricted by the limited number of RCBSW test results used in their development and validation (typically, a maximum of 25 walls). In addition, these models were produced employing basic mechanics, simplified regression analyses, without performing variables selection procedures to determine the key parameters controlling the seismic performance of RCBSWs. As a result, the methodologies adopted to develop current models may not facilitate uncovering the non-linear interactions between the influencing (input) parameters and their relationships with the resulting wall behavior (output). Understandably, available models were also not updated considering new datasets, that were not used in their original development—posing further challenges to these models’ generalizability. Subsequently, developing more efficient procedures to accurately predict the response of RCBSWs remains key to further improve seismic design.

Recently, several studies employed artificial intelligence techniques to interpret complex, multivariant behaviors in structural engineering due to their ability to capture nonlinear input-output relationships. Genetic programming is an artificial intelligence technique which follows Darwinian principles [13] to identify the near-optimal mathematical model relating the system input variables to the sought-after target (output) [14], [15]. In recent studies, genetic programming and its more powerful variant (i.e., multi-gene genetic programming (MGGP)) have been utilized to predict concrete creep [16], the shear strength of short rectangular reinforced concrete columns [17], the elastic shear buckling of tapered steel plate girders [18], the bond strength of composite bars in concrete [19], the degree of steel corrosion damage in reinforced concrete [20], the shear-strength of squat reinforced concrete walls with boundary elements [21], the shear strength of steel fibers reinforced concrete beams [22], [23].

The capabilities of MGGP were thus utilized in this study to develop the necessary expressions to generate the backbone curve of fully grouted RCBSWs. Following a variable selection procedure, the MGGP-based model was developed, trained, and tested using the results of 74 RCBSWs compiled from literature. The prediction performance of the developed MGGP-based backbone model was assessed at both the component- and system-levels and was also compared against existing available models. Finally, sensitivity analyses were conducted to provide further insights into the extents of the influences of each input parameter on the prediction performance of the developed MGGP model.

Section snippets

Research significance and organization

Developing accurate load-displacement backbone curves for cyclically loaded RCBSWs is key to define their various response characteristics such as initial stiffness, cracking, yielding and ultimate strengths, ductility, energy dissipation capacity, and post-peak behavior. MGGP was employed herein for two main reasons: (i) to capture the complex nonlinearity controlling the relationships between the different design parameters and the wall responses, and (ii) to produce explicit mathematical

Model architecture

Fig. 3 shows the proposed load-displacement backbone model, which was defined by five key points, as follows:

  • The first point refers to the cracking initiation. The cracking load (Qcr) is computed by enforcing equilibrium, assuming a fixed masonry flexure tensile strength of 0.65 MPa, as recommended by the CSA [6].

  • The second point refers to the initiation of yielding in the outermost reinforcement bar. The corresponding yielding load (Qy) is calculated using mechanics principles (i.e., force

Dataset description

The dataset utilized in the current study includes the design parameters and experimental backbone curves of 74 cyclically loaded RCBSWs collected from previous studies including: Eikanas (6 walls) [25], Priestley & Elder (2 walls) [26], Shing (11 walls) [27], Shedid et al. (6 walls) [28], Shedid et al. (2 walls) [29], Sherman (8 walls) [30], Hernandez (3 walls) [31], Siam et al. (4 walls) [32], Kapoi (8 walls) [33], and Ahmadi et al. (24 walls) [34]. It is worth noting that all walls

Variable selection

The inclusion of too many or too few input variables in a model usually leads to unnecessarily complexity or inaccurate prediction expressions. As such, the identification of the most relevant input variables is key to achieve efficient and elegant expressions for practicing engineers. Subsequently, in this study, the best subset selection procedure (BSS) was adopted to select the most influential subset of independent variables on the cyclic behavior of RCBSWs.

For k independent variables, the

Development of the MGGP backbone model

MGGP, through the MATLAB© toolbox GPTIPS [38], was employed to develop the identified five secant stiffness expressions, in a form of KiKg=fPAw.fm,ρv, where Ki refers to the Kcr, Ky, K0.8u, Ku, and K0.8u.

The dataset was divided into a training subset (70% of the total data set) and a testing subset (30% of the total data set) in a stratified manner, where both sets have similar statistical properties, as recommended by Ahangar-Asr et al. [39]. The training subset is first used to develop and

Component-level model performance assessment

The prediction performance of the developed MGGP-based backbone model was evaluated against that of existing backbone models that were specifically proposed for fully grouted RCBSWs. The trilinear backbone model proposed by Ashour and El-Dakhakhni [10], the quad-liner backbone model proposed by Ashour and Galal [11], and the trilinear backbone model proposed by Ezzeldin et al. [12] were used for comparison.

Fig. 11 shows the comparison between the experimental backbone models of 22 RCBSWs (i.e.,

System-level model performance assessment

Beyond component-level response predictions, the capability of the developed MGGP model in predicting the cyclic response of full RCBSW buildings (i.e., system-level) is assessed in this section. Two two-story RCBSW buildings constructed and tested by Heerema et al. [44], [45] (Building II) and Ashour and El-Dakhakhni [10] (Building III) were used for comparison. Both buildings were identical in terms of their RCBSWs’ geometry, materials, reinforcement, and distribution, whereas they differed

Sensitivity analyses

Further analysis was conducted in this section to examine the behavior of the prediction expressions to the different input parameters. Fig. 15 presents the relationship between the MGGP-based expressions (Kcr, Ky, K’0.8u, Ku, K0.8u) and the input parameters used in the modelling. These relationships were investigated by changing one parameter within its range, while the other parameters were set at their mean values. The results of the parametric analysis in Fig. 15 show that all wall design

Conclusions

The current paper employed multi-gene genetic programming (MGGP), a bio-inspired artificial intelligence technique, to efficiently develop a piecewise-linear backbone model for flexure-dominated fully-grouted reinforced concrete block shear walls (RCBSWs). An experimental dataset of 74 RCBSW was collected from previous studies and utilized to train and test the MGGP expressions employed to generate the wall response backbone. A variable selection procedure was performed on the collected dataset

CRediT authorship contribution statement

Hana Elgamel: Conceptualization, Data curation, Investigation, Methodology, Software, Formal analysis, Validation, Visualization, Writing – original draft. Mohamed K. Ismail: Conceptualization, Data curation, Investigation, Methodology, Software, Formal analysis, Validation, Visualization, Writing – review & editing, Supervision. Ahmed Ashour: Conceptualization, Data curation, Investigation, Formal analysis, Writing – review & editing, Supervision. Wael El-Dakhakhni: Conceptualization, Funding

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.

Acknowledgements

This research was facilitated with funding provided by the Natural Sciences and Engineering Research Council of Canada (NSERC), the Canadian Concrete Masonry Producers Association (CCMPA), and the Canada Masonry Design Centre (CMDC).

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