The compressive strength of concrete is one of most important mechanical parameters in the performance assessment of existing reinforced concrete structures. According to various international codes, core samples are drilled and tested to obtain the concrete compressive strengths. Non-destructive testing is an important alternative when destructive testing is not feasible without damaging the structure. The commonly used non-destructive testing (NDT) methods to estimate the

Existing reinforced concrete structures were built according to standards and materials quite different to those available today. The evaluation of structural performance when seismic zones are concerned requires procedures and methods able to cover lack of data about mechanical material properties and reinforcement detailing. The structural assessment is more relevant when structural strengthening is necessary to prevent failures due to earthquakes.

Procedures and methods, such as detailed inspections and tests on materials, are mandatory to establish the performance levels in recent seismic codes. Accordingly, assessment of the

Non-destructive testing (NDT) of materials and structures is a testing and analysis technique without causing damage to the structure, aiming at maintenance and diagnosis [

Fortunately, NDT can effectively supplement coring since the compressive strength can be cheaply evaluated throughout the whole structure. The procedure of NDT must be only used in conjunction with destructive testing according to both European and Italian Standards. Note that firstly steel reinforcements must be localized in order to perform properly a non-destructive test and/or destructive test method. To this end, a

The commonly used NDT methods to predict concrete compressive strength include the rebound hammer test and the ultrasonic pulse Velocity (V) test. Ultrasonic method is a form of NDT and characterization of materials and structures in civil, mechanical, aerospace, automotive engineering. Concerning concrete structures, note that “This test method covers the determination of the propagation velocity of longitudinal stress wave pulses through concrete. This test method does not apply to the propagation of other types of stress waves through concrete” as reported in [

The rebound hammer is a handheld instrument used for testing the quality of hardened concrete in an existing structure. The test device was developed in 1948 by Ernst Schmidt at the Swiss Federal Materials Testing and Experimental Institute in Zurich. The development of this “new” device originates from tests carried out to measure hardness of metals. For this reason, this test can be considered as an extension of the

Many calibration curves have been proposed in literature with wide dispersion around the original Schmidt curve. The large deviation of curves raised a crucial question of whether the rebound hammer is effective or not in estimating the concrete strength [

The questionable reliability of both methods can be partially contrasted by using them together. One of the most employed NDT combined methods in practice is the SonReb method, developed by RILEM Technical Committees 7 NDT and TC-43 CND [

The most used techniques to predict compressive concrete strength based on the SonReb measurements are computational modeling, artificial intelligence, and parametric multi-variable regression models. Computational modeling is based on the modeling of complex physical phenomena and thus is often not practical. Parametric multi-variable regression models, on the other hand, can be more easily implemented and used in practice for future applications, such as the reliability assessment of reinforcement concreste (RC) structures incorporating field data. Artificial intelligence including the

The aim of this paper is to verify the accuracy of ANN approach comparing the estimated compressive strength based on NDT measured parameters with the effective compressive strength based on destructive test results on cores drilled at adjacent locations. To this end, a relevant number of destructive tests and NDTs have been performed on many reinforced concrete structures [

ANN is an information processing system inspired by biological nervous system being constituted by many neurons connected in a complex network. The intelligent behavior arises from interactions among numerous interconnected neurons aggregated into layers, naming input layer, hidden layer and output layer. Some receive information from the external environment (i.e., input layer), some send responses in the environment (i.e., output layer), others communicate only with other units inside the network (i.e., hidden layer). In a standard neural network, signals travel from the input layer to the output layer along the hidden layer. Such systems learn from examples, generally without being programmed with any task-specific rules [

There are several types of ANN depending on the type of connections between the different layers, on the activation functions and learning algorithms. Depending on the type of connections between artificial neurons, Feed-Forward Network (FFN) (please provide the abbreviation) is the simplest and most used typology and is constituted by more than two layers of neurons. In other words, the input layer and output layer are bridged by one or more hidden layers. Each neuron is connected to all the neurons of the previous layer but has no connection with the neurons of its own layer and the signal propagates in a unidirectional way from input to output through the hidden layer. A schematic representation of a three-layer ANN is reported in

The fundamental building blocks of each neural networks, both biological and artificial, are represented by the neurons. These are an elementary information processing unit characterized by connections (synapses) able to transfer the signal (stimulus) into other neurons. Each neuron sums the weighted inputs emitting an

where x is the input of the neuron.

The values of synaptic weights represent the first unknown parameter to be determined. In order to minimize the total error of the network, a process of learning (or training) must be carried out. In the supervised learning process, the aim is the prediction of the output value for each valid input data, based only on a limited number of examples of correspondence.

From a mathematical point of view the learning process consists of finding a minimum of a function in a n-dimensional space. This function is given by the variation of the error based on the weights of the network.

The most effective and widespread technique used in the learning with more supervision is the backpropagation error algorithm, which minimizes the total error of the network through the modification of the weights of the connections. In order to search for a minimum, it is usually used the gradient descent technique.

For our purpose, a feed-forward network composed of 3 layers (input, output, hidden layers), with sigmoid logistic activation function and supervised learning with backpropagation error algorithm has been employed (

The effectiveness of the networks has been investigated as a function of the only variable parameter in their architecture: the number of neurons of the hidden layer. In order to understand the influence of the number of connections in a 3-layered feed-forward network with two non-destructive parameters (RI and V) input, nine ANNs were considered. The increment steps of the units in all the networks were established based on the efficiency-computational time ratio.

The principal data of all considered networks are reported in

RMSE |
|||
---|---|---|---|

2-5-1 | 1000 | 212 | 1.8438 |

2-10-1 | 2000 | 1063 | 1.1023 |

2-15-1 | 3000 | 1935 | 0.7393 |

2-20-1 | 5000 | 2109 | 0.7234 |

2-25-1 | 8000 | 3842 | 0.7650 |

2-30-1 | 8000 | 3953 | 0.3245 |

2-50-1 | 10000 | 6074 | 0.0001 |

2-70-1 | 200000 | 101626 | 0.0002 |

2-90-1 | 1000000 | 244198 | 0.0023 |

The

It is worth mentioning that _{ck} is the actual

where:

-_{core} is the strength of a core specimen.

-C_{H/D} is correction factor depending on the height/diameter ratio H/D, equal to 2 (1.5 + D/H).

-C_{dia} is correction factor depending on the diameter of core D, equal to 1.06, 1.00 and 0.98 for D equal to 50, 100 and 150 mm, respectively.

-C_{a} is correction factor depending on the presence of reinforcing bars, equal to 1 for no bars, and varying between 1.03 for small diameter bars and 1.13 for large diameter bars.

-C_{d} is correction factor depending on the damage due to drilling, equal to 1.20 for _{core} < 20 MPa and 1.10 for _{core} > 20 MPa.

The problem of conversion from cylinder to cube strength has been widely investigated in Indelicato et al. [

Nine different ANNs are considered to understand the influence of the number of units in a 3-layered feed-forward network with two non-destructive parameters RI and V as inputs.

To evaluate the accuracy of ANN approach, some of the estimated compressive strengths have been compared with the effective compressive strengths determined in DT on samples extracted in adjacent locations (

N. | _{c} |
RI | V |
|||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

1 | 10,00 | 34,72 | 2470 | 12,4045 | 12,5107 | 12,4807 | 12,3810 | 12,4806 | 10,1252 | 10,0000 | 10,0000 | 10,0003 |

2 | 12,60 | 38,89 | 2450 | 14,1812 | 15,7506 | 13,8110 | 12,4210 | 13,8110 | 13,6588 | 12,6000 | 12,6001 | 12,5998 |

3 | 17,50 | 36,39 | 2830 | 16,2242 | 16,6681 | 17,3358 | 16,1923 | 16,3358 | 17,4761 | 17,5000 | 17,4999 | 17,4992 |

4 | 17,80 | 31,90 | 3250 | 17,5759 | 17,8196 | 17,8132 | 17,8548 | 17,8116 | 17,8220 | 17,8000 | 17,7999 | 17,7999 |

5 | 18,50 | 37,22 | 2960 | 18,3682 | 18,4567 | 18,4685 | 18,4242 | 18,4769 | 18,4369 | 18,4998 | 18,4998 | 18,4989 |

6 | 18,70 | 38,83 | 2930 | 22,4640 | 19,5950 | 19,2881 | 19,1786 | 19,0493 | 19,0621 | 18,6998 | 18,6999 | 18,7034 |

7 | 18,90 | 34,61 | 3285 | 19,0821 | 18,8114 | 18,8407 | 18,7993 | 18,8590 | 18,8803 | 18,9001 | 18,8999 | 18,8991 |

8 | 20,60 | 39,34 | 3120 | 21,8318 | 21,1724 | 20,9882 | 21,1203 | 20,8386 | 20,9991 | 20,5999 | 20,6001 | 20,6003 |

9 | 23,25 | 39,78 | 3140 | 23,9773 | 22,9694 | 23,0516 | 22,8894 | 23,1242 | 22,9554 | 23,2501 | 23,2502 | 23,2474 |

10 | 25,60 | 36,84 | 3500 | 26,0369 | 25,6881 | 25,6579 | 25,6741 | 25,6392 | 25,5776 | 25,5998 | 25,5999 | 25,5985 |

11 | 27,80 | 39,00 | 2965 | 22,6131 | 26,7146 | 27,0905 | 27,2633 | 27,3822 | 27,3983 | 27,7998 | 27,7998 | 27,7933 |

12 | 29,30 | 41,44 | 3470 | 28,8481 | 29,2246 | 29,2521 | 29,3104 | 29,2810 | 29,3188 | 29,2999 | 29,3000 | 29,2980 |

13 | 32,16 | 38,39 | 3490 | 31,5879 | 32,0823 | 32,1095 | 32,0834 | 32,1253 | 32,1612 | 32,1602 | 32,1598 | 32,1582 |

14 | 36,80 | 45,45 | 3750 | 37,3258 | 37,0199 | 36,9461 | 36,8660 | 36,8773 | 36,8214 | 36,7998 | 36,7997 | 36,7981 |

15 | 54,10 | 47,28 | 3900 | 53,6062 | 53,8774 | 53,9513 | 54,0112 | 54,0136 | 54,0522 | 54,1001 | 54,1001 | 54,0981 |

16 | 56,60 | 47,33 | 4095 | 56,7532 | 56,6734 | 56,6491 | 56,6405 | 56,6284 | 56,6289 | 56,6001 | 56,6003 | 56,5981 |

RMSE [Mpa] | 1,8438 | 1,1023 | 0,7393 | 0,7234 | 0,7650 | 0,3245 | 0,0001 | 0,0002 | 0,0023 |

Based on the results of the present research, it can be observed that the neurons of the hidden layer constitute the data processing unit of the system more susceptible to error and their quantity can extremely influence the final output. Therefore, using too few neurons in the hidden layer gives rise to a phenomenon known as

On the contrary too large number of hidden neurons would encourage another critical phenomenon known as

It follows that Ann 2-50-1 can be considered the best performing for predicting the compressive concrete strength. The training and learning phases of this ANN with 50 neurons in the hidden layer are reported in

It is important to point out the better potential estimation of ANN present approach compared to parametric multi-variable regression approach [_{ck} values obtained during DT experimental campaign with respect to f_{c} values calculated according to the latter approach using the following different correlation formulations suggested by Giacchetti et al. [

According to the Standards of Tuscany Region _{c}

The comparative study of the above correlation formulas is shown in

In general, most of the models used to study the on-site concrete compressive strength consist of mathematical rules and expressions that try to capture relationship between NDT parameters and concrete mechanical characteristics. Generally, these mathematical models based on experimental data are presented in regression forms. However, since these regression methods have shown less accuracy in concrete strength predictions, in the recent years new techniques, such as ANN, have been employed to approximate this non-linear and complex problem.

The results obtained from the study indicate the excellent estimation potential of a multilayer feed-forward neural network trained with

Analyzing the results obtained for the neural networks characterized by two input parameters (i.e., RI and V value) it can be observed a significant improvement in the estimation of concrete compressive strength since for networks with 50 neurons into the hidden layer (RMSE = 0.00013 MPa, about 50000 times lower than that obtained with the regression formulas found in the literature).

Artificial Neural Network

Destructive Testing

Feed-Forward Network

Non-Destructive Testing

Rebound Index

Root Mean Squared error

Ultrasonic Pulse Velocity