Predict the Ultimate Moment Capacity of Reactive Powder Concrete Beams Exposed to Fire Flame Using Artificial Neural Network and Multiple Linear Regression Models

Abstract In this paper, the mathematical model has been used to predicting ultimate bending moment capacity of RPC and NSC beam specimens. From observed data and present experimental test results, Multi Linear Regression technique (RT) and Artificial Neural Network Multi Layers Perceptron (ANNMLP) models are proposed for predictions. The accuracy of the proposed equations was examined by comparison with similar existing equations and available experimental results. The models are built, trained and tested using 25 data sets. The data used in the models consists of four input parameters, which are the compressive strength , volume fraction of steel fibers , concrete cover , burning temperature level .A combined experimental and modeling study was taken to develop a database of the estimation ability of the effects of exposure to real fire flame on ultimate load capacity of RPC and NSC in addition to others (independent variables) to predict the dependent variable using IBM SPSS Statistics version 21 program. It is shown that ANN model with three neurons in hidden layer predicts the ultimate moment capacity of reinforced concrete beams before and after exposure to fire flame with high degree of accuracy, the moment capacities predicted by ANN are in line with the results provided by the ultimate moment capacity of experimental test .


I. INTRODUCTION
Reactive powder concrete (RPC) is the generic name for a class of cementitious composite materials developed by the technical division of Bouygues, laboratory in France in the early 1990's. It is characterized by extremely good physical properties, particularly strength and ductility [1]. RPC is a relatively new cement-based material composed of cement, ultra-fine reactive powder, and high-quality fine aggregate. Through elimination of the coarse aggregates and reducing the water-tocementitious material ratio, RPC has the unique properties of ultra-high compressive strength and excellent durability [2]. RPC is a new generation concrete developed through microstructure enhancement techniques for cementitious materials. As compared to ordinary cementbased materials, the primary improvements of RPC include the particle size homogeneity, porosity, and microstructures [3]. Nowadays, RPC is regarded as a promising material for special pre-stressed and precast concrete members, including those industrial and nuclear waste storage facilities.
More and more attention has been paid on the mechanical properties of RPC at room temperature [3], [4], but few studies have been conducted on the residual mechanical properties of RPC after elevated temperatures [5], [6].
Most of the previous studies indicated two important components (as key components) for the successful performance of the concrete in fire; the first deals with its essential properties as a construction material, and the second one deals with its functionality in a structure. Concrete was known to be non-combustible with slow rate of heat transfer [7].
Many researchers studied the effect of fire on ordinary concrete, reinforced concrete members on exposing such members to high temperatures in special ovens or fire flame. They worked on the strength and deformation properties at elevated temperatures. However, no works were done on the structural behavior of reactive powder concrete (RPC) beam specimens exposed to direct fire flame.

EXPERIMENTAL DETAILS Materials and Methods
Effective production of concrete mix is achieved by more stringent requirements on materials selecting, controlling and proportioning the entire ingredient.

Materials:
The RPC considered here is prepared by the following ingredients: ASTM Type I Portland cement produced in Iraq of (MASS) and taken from local markets, the used cement conforms to Iraqi standard [8]; natural sand (0-600μm with a specific gravity of 2.7),the results show that the grading and sulfate content are conformed to the requirements of [9]; a polycarbokylate-based superplasticizer (SP),complies with [10]; Densified micro-silica fume from BASF, Silica fume is produced in conformance with the [11]specifications and brass-coated steel micro-fibers, with a density of 7860 kg/m 3 , a length of 13mm, a diameter of 0.18mm and an l/d ratio of 72. The cross section of the fiber was circular. The chemical composition and physical properties of cement and silica fume used are presented in Tables I and II respectively.

III. CONCRETE MIXING PROCEDURE
The mixing procedure is an important thing to obtain the required workability and homogeneity. The RPC mix ratios are based on guidelines given in previous studies [12], [13]. The mixes are detailed in Table III. DETAILS OF BEAMS Thirty beam specimens with (100×100×1000mm) dimension. Each beam was reinforced with 48mm as longitudinal reinforcement, and 6mm bars were used for stirrups reinforcement at 100mm C/C as shown in Fig.1. All the beams, are tested under flexural moment. LOAD MEASUREMENT The load is applied in two points loading with 300mm spacing between these points as shown in Fig. 2, the test continues up to failure, using a hydraulic machine 150 KN capacity. Before loading,

VI.
BURNING TEMPERATURE AND TESTING METHODOLOGY After the curing procedure for the specimens, the burning procedure was applied. The specimens were burnt with direct fire flame at temperatures (150, 200, 300 and 400ºC) with a net of methane burners inside a brick stove.
The following steps explained the burning procedure:  Carrying concrete samples carefully into position by hand inside the stove to avoid unexpected external stresses.  The concrete specimen fair-faced toward the fire flame exposure to be able to observation the concrete spalling and cracking clearly and test the specimen in the same direction.  When the target temperature reached, two digital thermometers continuously measured the temperature; one of them was positioned in fire flame contact area, while the other was at the face of the specimen. Also three thermocouples were used to measure the temperature, two of them were positioned at 25mm and mid depth 50mm of the cross-section of reinforced NSC and RPC beams, another one was positioned at the longitudinal steel reinforcement layer of the beam, the holes made it during the concrete cast of specimen. The Fig. 3 depicts the burning process.  In addition, the temperature of concrete and steel reinforcement was measured at different depths by applying infrared ray thermometer from about approximately 2 meters from the concrete exposed to fire.  Test the concrete specimens after cooling to reach the room temperature around 25ºC.  Finally test the beams with two point loads In this study for cooling regime, the fire flame was switched off at the end of the exposure time. The samples were removed immediately after being extinguished and picked by using thermal gloves. All samples were cooled by foam spray fire extinguisher before testing. This process of cooling adopted in this work in order to simulate this problem to practical site conditions. See Fig. 4.
These test methods technology met various standards such as [14]. In this research, the exposure time is one hour and the temperature levels are 150, 200, 300 and 400 ºC.

Residual First Crack Load and Ultimate Load of Beams Exposed to Fire
It is very important for reinforced concrete beams as it makes concrete fail in flexure to prevent sudden collapse (yielding of steel reinforcement). According to experimental tests, it can clearly note that the values of ultimate load capacity decrease when the beams were exposed to burning temperature (200, 300 and 400ºC) for RPC and NSC reinforced beams, but the values of ultimate load capacity increase when the beams of RPC were exposed to burning temperature at 150ºC. The longitudinal reinforcement ratio may also have a significant effect on the first cracking load as well as on ultimate load, and the ratio of first cracking load to the ultimate load may decrease clearly with using longitudinal reinforcement ratio for RPC beam specimens before and after exposure to fire flame.
Two different concrete cover CC thickness used (15 and 30mm), and two percentages of micro steel fiber volume fraction used in this study (1% and 2%). In general, the increase of micro steel fiber volume fraction increased the ultimate load carrying capacity and the first crack load of the beam specimens for the same concrete cover. Increasing the micro steel fiber from 1.0 to 2.0% increased the ultimate load carrying capacity by (12.9, 11.1, 4.0, 4.8 and 19.0%) at burning temperatures (150, 200, 300 and 400ºC) respectively as shown in Fig. 5, and the first crack load decreased by (22.0, 14.4, 6.6 and 8.1%) at (25, 150, 200, 300ºC) respectively. This is normally explained by the efficiency of steel fibers in arresting the propagation and controlling the growth of the flexure and diagonal cracks within the beam when they cross them, and hence, steel fibers maintain the beam integrity throughout the post-cracking stages of behavior. The beam, hence could withstand greater loads and deflection before failure.
While for the same micro steel fiber volume fraction =2.0%, decrease of concrete cover CC increased the ultimate load carrying capacity and the first crack load of the beam specimens. Decreasing the CC from 30 to 15 increased the ultimate load carrying capacity by (12. To enhance the fire resistance of reinforced concrete members, the conventional design method in most publications including building Codes (ACI; BS;EuroCode; Joint, etc.), is to increase the concrete cover CC thickness of reinforced concrete members, as shown in Table IV.  When selecting the model for the multiple linear regression analysis another important consideration is the model fit. Adding independent variables to a multiple linear regression model will always increase its statistical validity, because it will always explain a bit more variance (typically expressed as R²).
Multiple linear regression analysis consists of more than just fitting a linear line through a cloud of data points. It consists of three stages: i. Analyzing the correlation and directionality of the data.
ii. Estimating the model, i.e., fitting the line. iii. Evaluating the validity and usefulness of the model.
There are three major uses for Multiple Linear Regression Analysis: 1-causal analysis, 2-forecasting an effect and 3-trend forecasting. Other than correlation analysis, which focuses on the strength of therelationship between two or more variables, regression analysis assumes a dependence or causal relationship between one or more independent and one dependent variable.
Developing multiple linear regressions model to use in the prediction of RPC and NSC beams ultimate moment capacity. Regression models can be classified as linear and non-linear models. To make a good prediction with non-linear regressionmodels, you have to possess preliminary information on the assumed degree of the model, therefore, is preferred the use of the linear regression model. The prediction multiple linear regression model (variables and coefficients) used is shown in

X. DEVELOPING ARTIFICIAL NEURAL NETWORKS (ANNS)
A number of factors influence the performance of the neural network, which can be described as the speed of learning and the generalization capacities of neural networks. In the following, several main factors are discussed in details. Fig. 7 depicts steps of developing in flow chart.

Training Algorithm
There are different optimization techniques to be used in the training of neural networks. They have a variety of computation and storage requirements, and no one is best suited to all locations. In the following, the outlines of the two training optimization techniques that are used for building the neural network are defined [16]: i. Steepest Descent with Momentum. ii. Resilient Back propagation.

Pre-processing and Post-processing of Data
Data scaling is another essential step for network training. The network can be more speedy and efficient if the input and target are scaled to fall in specific range. The training is preferred if the problem region is relatively narrow in some dimensions and elongated in others.

Initializing Weight Factor
Prior to training a neural network, initial values for the weights, between the nodes of the various layers must be set. Typically, the weight factors are initialized to small and random values by using either Random or Widrow-Hoff method. When the nodes are connected by a large weight value, the neural network might become paralyzed. This phenomenon occurs since, at the high output values corresponding to the high weight value, the derivative of the transfer function approaches zero, and accordingly the weight change approaches to zero. Thus, the training of neural networks approaches to a halt. For the present study the training of the neural network is carried out using 25 data sets divided into 70% for training, 15% for testing and 15% for validation. The data sets are presented in Table VIII

XI. DEVELOPMENT STAGES OF ARTIFICIAL NEURAL NETWORK MODEL AND OPTIMIZATION
In this study, the application of artificial neural networks model (ANN) developed to predict the ultimate moment capacity of RPC and NSC reinforced beams exposed to fire flame is investigated. An ANN model is built, trained, validated and tested using 25 data sets. The data used in the ANN model consists of 4 input parameters, which are the compressive strength of the concrete , volume fraction of micro steel fibers % , concrete cover (CC) and burning temperature level . The method of trial and error was carried out to define the configuration of ANN. In present study the network is trained with one hidden layer of 3 neurons. The network schematic is shown in Fig. 9. These parameters used in ANN model to predict the ultimate moment capacity of RPC and NSC reinforced beams with high degree of accuracy within the range of input parameters considered. The relative importance for the input parameters is shown in Fig. 10 Table IX.

ARTIFICIAL NEURAL NETWORK MODEL PERFORMANCE
The performance of ANN was evaluated by conducting four statistical analyses. The performance of the inference system was measured using Root Mean Square Error (RMSE), Mean Absolute Error (MAE), Absolute average deviation (AAD)% and the coefficient of determination (R 2 ). The model that minimized the error values and percentage (RMSE, MAE and AAD%) and maximized (R 2 ) is selected as the optimum network. These statistical parameters are used to compare the performance of the various methods (ANN and RT) as follows:  RMSE Root Mean Square Erroris given in equation (3).The lowest RMSE coefficient is recommended.  MAE the Mean Absolute Error, using equation (4).  AAD% Absolute Average Deviation is calculated to learn the accuracy of the models, using equation (5).  R 2 the coefficient of determination.The better model that R 2 achieves a maximum of less than 1, using equation (6).  Fig. 11 to 13 shows the comparison between the prediction of the ultimate moment capacity of the training and testing data with respect to the observed results. It is clear that the performance of the ANN is better than RT model. Fig. 11 and 12 show the models performance, it can be seen that ANN model results has exhibited better predictive performance and are closer to the observed results, and the moment capacity predicted by ANN are in line with results provided by experimental test. Fig.  13illustrate the ANN and RT models prediction residuals error. It can be seen that the RT errors are more scattered from the observed results, while the ANN errors are distributed close to zero axis. To show the superiority of proposed models, the RMSE, MAE, AAD% and R 2 values for ANN and RT models are presented in Table XI. The comparison of the results indicate that the ANN model has a high value of R 2 (0.9666) and a lower value of RMSE, MAE and AAD% (0.2337, 0.1572 and 2.2990) respectively, so that its performance is more accurate from RT model.