Application of artificial neural networks and multiple linear regression on local bond stress equation of UHPC and reinforcing steel bars

Abstract

We investigated the use of an Artificial Neural Network (ANN) to predict the Local Bond Stress (LBS) between Ultra-High-Performance Concrete (UHPC) and steel bars, in order to evaluate the accuracy of our LBS equation, proposed by Multiple Linear Regression (MLR). The experimental and numerical LBS results of specimens, based on RILEM standards and using pullout tests, were assessed by the ANN algorithm using the TensorFlow platform. For each specimen, steel bar diameters ([Formula: see text] of 12, 14, 16, 18, and 20, concrete compressive strength ([Formula: see text]), bond lengths ([Formula: see text]), and concrete covers ([Formula: see text]) of [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] were used as input parameters for our ANN. To obtain an accurate LBS equation, we first modified the existing formula, then used MLR to establish a new LBS equation. Finally, we applied ANN to verify our new proposed equation. The numerical pullout test values from ABAQUS and experimental results from our laboratory were compared with the proposed LBS equation and ANN algorithm results. The results confirmed that our LBS equation is logically accurate and that there is a strong agreement between the experimental, numerical, theoretical, and the predicted LBS values. Moreover, the ANN algorithm proved the precision of our proposed LBS equation.

Figure 1

Research structure.

Figure 2

Geometric dimensions of RILEM standard specimens.

Figure 3

Pullout test lab and specimen installation.

Figure 4

Non-linear model for stress–strain curve of concrete; compressive behavior.

Figure 5

Non-linear model for the stress–strain curve of concrete under tension.

Figure 6

Bond force and bond stress results from ABAQUS with different dimensions of elements, compared to the experimental results.

Figure 7

Specimen modeling in ABAQUS.

Figure 8

Bond stress results: numerical analysis vs. experimental analysis.

Figure 9

Linear relationship: $\frac{f_b}{u_{\mathit{test}}}$ vs. $\frac{c}{d_b}$.

Figure 10

Linear relationship between $u$ and $c$.

Figure 10

Linear relationship between $u$ and $c$.

Figure 11

Linear relationship between $u$ and $\sqrt{f_c^{\prime }}$.

Figure 12

Linear relationship between $u$ and $l$.

Figure 12

Linear relationship between $u$ and $l$.

Figure 13

Structure of an ANN neural network.

Figure 14

Activation function of neurons (f).

Figure 15

Loss function, MSE.

Figure 16

LBS equations and ANN accuracy.