INTRODUCTION
Artificial Intelligence (AI) mechanisms are more and more frequently applied to all sorts of civil engineering problems. New methods and algorithms which allow civil engineers to use these techniques in a different way on diverse problems are available or being made available. One AI techniques stands out over the rest: Artificial Neural Networks (ANN). Their most remarkable traits are their ability to learn, the possibility of generalization and their tolerance towards mistakes. These characteristics make their use viable and cost-efficient in any field in general, and in Structural Engineering in particular. The most extended construction material nowadays is concrete, mainly because of its high resistance and its adaptability to formwork during its fabrication process. Along this chapter we will find different applications of ANNs to structural concrete.
Artificial Neural Networks
Warren McCulloch and Walter Pitts are credited for the origin of Artificial Networks in the 1940s, since they were the first to design an artificial neuron (McCulloch & Pitts, 1943). They proposed the binary mode (active or inactive) neuron model with a fixed threshold which must be surpassed for it to change state. Some of the concepts they introduced still hold useful today.
Artificial Neural Networks intend to simulate the properties found in biological neural systems through mathematical models by the way of artificial mechanisms. A neuron is considered a formal element, or module, or basic network unit which receives information from other modules or the environment; it then integrates and computes this information to emit a single output which will be identically transmitted to subsequent multiple neurons (Wasserman, 1989).
The output of an artificial neuron is determined by its propagation or excitation, activation and transfer functions.
The propagation function is generally the summation of each input multiplied by the weight of its interconnection (net value):
The activation function modifies the latter, relating the neural input to the next activation state.
The transfer function is applied to the result of the activation function. It is used to bound the neuron’s output and is generally given by the interpretation intended for the output. Some of the most commonly used transfer functions are the sigmoid (to obtain values in the [0,1] interval) and the hyperbolic tangent (to obtain values in the [-1,1] interval).
Once each element in the process is defined, the type of network (network topology) to use must be designed. These can be divided in forward-feed networks, where information moves in one direction only (from input to output), and networks with partial or total feedback, where information can flow in any direction.
Finally, learning rules and training type must be defined. Learning rules are divided in supervised and non-supervised (Brown & Harris, 1994) (Lin & Lee, 1996) and within the latter, self-organizing learning and reinforcement learning (Hoskins & Himmelblau, 1992). The type of training will be determined by the type of learning chosen.
An Introduction to Concrete (Material and Structure)
Structural concrete is a construction material created from the mixture of cement, water, aggregates and additions or admixtures with diverse functions. The goal is to create a material with rock-like appearance, with sufficient compressive strength and the ability to adopt adequate structural shapes. Concrete is moldable during its preparation phase, once the components have mixed together go produce a fluid mass which conveniently occupies the cavities in a mould named formwork. After a few hours, concrete hardens thanks to the chemical hydration reaction experimented by cement, generating a paste which envelops the aggregates and gives the ensemble the appearance of an artificial rock somewhat similar to a conglomerate.
Hardened concrete offers good compressive strength, but very low tensile strength. This is why structures created with this material must be reinforced by use of steel rebars, configured by rods which are placed (before pouring the concrete) along the lines where calculation predicts the highest tensile stresses. Cracking, which reduces the durability of the structure, is thus hindered, and sufficient resistance is guaranteed with a very low probability of failure. The entirety formed by concrete and rebar is referred to as Structural Concrete (Shah, 1993).
Two phases thus characterize the evolution of concrete in time. In the first phase, concrete must be fluid enough to ensure ease of placement, and a time to initial set long enough to allow transportation from plant to worksite. Flowability depends basically on the type and quantity of the ingredients in the mixture. Special chemical admixtures (such as plasticizers and superplasticizers) guarantee flowability without grossly increasing the amount of water, whose ratio relative to the amount of cement (or water/cement ratio, w/c) is on reverse proportion to strength attained. The science of rheology deals with the study of the behavior of fresh concrete. A variety of tests can be used to determine flowability of fresh concrete, the most popular amongst them being the Abrams cone (Abrams, 1922) or slump cone test (Domone, 1998).
The second phase (and longest over time) is the hardened phase of concrete, which determines the behavior of the structure it gives shape to, from the point of view of serviceability (by imposing limitations on cracking and compliance) and resistance to failure (by imposing limitations on the minimal loads that can be resisted, as compared to the internal forces produced by external loading), always within the frame of sufficient durability for the service life foreseen.
The study of structural concrete from every point of view has been undertaken following many different optics. The experimental path has been very productive, generating along the past 50 years a database (with a tendency to scatter) which has been used to sanction studies carried along the second and third path that follow. The analytical path also constitutes a fundamental tool to approach concrete behavior, both from the material and structural point of view. Development of theoretical behavior models goes back to the early 20th century, and theoretical equations developed since have been corrected through testing (as mentioned above) before becoming a part of codes and specifications. This method of analysis has been reinforced with the development of numerical methods and computational systems, capable of solving a great number of simultaneous equations. In particular, the Finite Element Method (and other methods in the same family) and optimization techniques have brought a remarkable capacity to approximate behavior of structural concrete, having their results benchmarked in may applications by the aforementioned experimental testing.
Three basic lines of study are thus available. Being complementary between them, they have played a decisive role in the production of national and international codes and rules which guide or legislate the project, execution and maintenance of structural concrete works. Concrete is a complex material, which presents a number of problems for analytical study, and so is an adequate field for the development of analysis techniques based on neural networks (Gonzalez, Martinez and Carro, 2006)
Application of Artificial Neural Networks to problems in the field of structural concrete has unfolded in the past few years in two ways. On one hand, analytical and structural optimization systems faster than traditional (usually iterative) methods have been generated starting with expressions and calculation rules. On the other, the numerous databases created form the large amount oftests published in the scientific community have allowed for the development of very powerful ANN which have thrown light on various complex phenomena. In a few cases, specific designed codes have been improved through the use of these techniques; some examples follow.
Application of Artificial Neural Networks to Optimization Problems
Design of concrete structures is based on the determination of two basic parameters: member thickness (effective depth d, depth of a beam or slab section measured from the compression face to the centroid of reinforcement) and amount of reinforcement (established as the total area As of steel in a section, materialized as rebars, or the reinforcement ratio, the ratio between steel area and concrete area in the section). Calculation methods are iterative, since a large number of conditions must be verified in the structure, and the aforementioned parameters are fixed as a function of three basic conditions which are sequentially followed: structural safety, maximum ductility at failure and minimal cost. Design rules, expressed through equations, allow for a first solution which is corrected to meet all calculation scenarios, finally converging when the difference between input and output parameters are negligible.
In some cases it is possible to develop optimization algorithms, whose analytical formulation opens the way to the generation of a database. Hadi (Hadi, 2003) has performed this work for simply supported reinforced concrete beams, and the expressions obtained after the optimization process determine the parameters specified above, while simultaneously assigning the cost associated to the optimal solution (related to the cost of materials and formwork). With these expressions, Hadi develops a database with the following variables: applied flexural moment (M), compressive strength of concrete (f), steel strength (f), section width (b), section depth (h), and unit costs of concrete (C’), steel (C) and formwork (C).
Network parameters used are as follows. The number of training samples is 550; number of input layer neurons is 8; number of hidden layer neurons is 10; number of output layer neurons is 4; type of backpropagation is Levenberg-Marquardt backpropagation; activation function is sigmoidal function; learning rate; 0.01; number of epochs is 3000; sum-square error achieved is 0.08. The network had been tested with 50 samples and yielded the average error of 6.1%.
Hadi studies various factors when choosing network architecture and backpropagation algorithm type. When two layers of hidden neurons are used, precision is not improved while computation time is increased. The number of samples depends on the complexity of the problem and the number of input and output parameters. If a value is fixed for the input costs, there are no noticeable precision improvements between training the network with 200 or 1000 samples. When costs are introduced as input parameters, 100 samples are not enough to achieve convergence in training. Finally, the training algorithm is also checked, studying the range between pure backpropagation (too slow for training), backpropagation with momentum and with adaptive learning, backpropagation with Levenberg-Marquardt updating rule and fast learning backpropagation. The latter is finally retained since it requires less time to get the network to converge while providing very good results (Demuth, H. & Beale, M.,1995)
Application of Artificial Neural Networks to Prediction of Concrete Physical Parameters Measurable Through Testing: Concrete Strength and Consistency Other neural network applications are supported by large experimental databases, created through years of research, which allow for the prediction of phenomena with complex analytical formulation.
One of these cases is the determination of two basic concrete parameters: its workability when mixed, necessary for ease of placement in concrete, and its compressive strength once hardened, which is basic to the evaluation of the capacity of the structure. The variables that necessarily determine these two parameters are the components of concrete: amounts of cement, water, fine aggregate (sand), coarse aggregate (small gravel and large gravel), and other components such as pozzolanic additions (which bring soundness and delayed strength increase, especially in the case of fly ash and silica fume) and admixtures (which fluidify the fresh mixture allowing the use of reduced amounts of water). There are still no analytical or numerical models that faithfully predict fresh concrete consistency (related to flowability, and usually evaluated by the slump of a molded concrete cone) or compressive strength (determined by crushing of prismatic specimens in a press).
Ozta§ et al. (Ozta§, Pala, Ozbay, Kanca, ^aglar & Bati, 2006) have developed a neural network from 187 concrete mixes, for which all parameters are know, using 169 of them for training and 18, randomly selected, for verification. Database variables are sometimes taken as a ratio between them, since there is available knowledge about the dependency of slump and strength on such parameters. The established range for the 7 parameter set is shown in Table 1.
Network architecture, as determined by 7 input neurons and two hidden layers of 5 and 3 neurons respectively.
The back-propagation learning algorithm has been used in feed-forward two hidden-layers. The learning algorithm used in the study is scaled conjugate gradients algorithm (SCGA), activation function is sigmoidal function, and number of epochs is 10,000. The prediction capacity of the network is better in the “Compressive Strength” output (maximum error of 6%) than in the
Table 1. Input parameter range
| Input parameters | Minimum | Maximum |
| W/B (ratio, %)a | 18 | 45 |
| W (kg/m3)b | 140 | 165 |
| s/a (ratio, %)c | 35 | 52 |
| FA (ratio, %)d | 0 | 20 |
| AE (kg/m3)e | 0.036 | 0.078 |
| SF (ratio, %)f | 5 | 25 |
| SP (kg/m3)g | 1.89 | 36.5 |
(a) [Water]/[binder] ratio, considering binder as the lump sum of cement, fly ash and silica fume
(b) Amount of water
(c) [Amount of sand]/[Total aggregate (sand+small gravel+large gravel)]
(d) Percentage of cement substituted by fly ash
(e) Amount of air-entraining agent
(f) Percentage of cement substituted by silica fume
(g) Amount of superplasticizer
(a) [Water]/[binder] ratio, considering binder as the lump sum of cement, fly ash and silica fume
(b) Amount of water
(c) [Amount of sand]/[Total aggregate (sand+small gravel+large gravel)]
(d) Percentage of cement substituted by fly ash
(e) Amount of air-entraining agent
(f) Percentage of cement substituted by silica fume
(g) Amount of superplasticizer
“Slump” output (errors up to 25%). This is due to the fact that the relation between the chosen variables and strength is much stronger than in the case of slump, which is influenced by other non-contemplated variables (e. g. type and power of concrete mixer, mixing order of components, aggregate moisture) and the method for measurement of consistency, whose adequacy for the particular type of concrete used in the database is questioned by some authors.
Application of Artificial Neural Networks to the Development of Design Formulae and Codes
The last application presented in this paper is the response analysis to shear forces in concrete beams. These forces generate transverse tensile stresses in concrete beams which require placement of rebars perpendicular to the beam axis, known as hoops or ties. Analytical determination of failure load from the variables that intervene in this problem is very complex, and in general most of the formulae used today are based on experimental interpolations with no dimensional consistency. Cladera and Mari (Cladera & Mari, 2004) have studied the problem through laboratory testing, developing a neural network for the strength analysis of beams with no shear reinforcement. They rely on a database compiled by Bentz (Bentz, 2000) and Kuchma (Kuchma, 2002), where the variables are effective depth (d), beam width (b, though introduced as d/b), shear span (a/d, see Figure 1), longitudinal reinforcement ratio (pl = A/bd) and compressive strength of concrete (/). Of course, failure load is provided for each of the 177 tests found in the database. They use 147 tests to train the network and 30 for verification, on a one layer architecture with 10 hidden neurons and a retropropagation learning mechanism. The ranges for the variables are shown on Table 2. Almost 8000 iterations were required to attain best results.
Table 2 Input parameter ranges
| Parameter | Minimum | Maximum |
| d(mm) | 101.6 | 1090 |
| d/b | 0.37 | 7.17 |
| P (%) | 0.50 | 6.64 |
| fc(MPa) | 14.7 | 101.8 |
| a/d | 2.48 | 7.86 |
| vjm | 19.52 | 332.14 |
Figure 1. Span loading a ofa beam.
Table 3. Comparison between available codes and proposed equations for shear strength.
| Procedure | ACI 11-5 | ACI 11-3 | MC-90 | EC-2 | AASHTO | Eq.(7) | Eq.(8) |
| Average | 1.16 | 1.29 | 1.15 | 1.02 | 1.28 | 1.15 | 1.13 |
| Median | 1.15 | 1.25 | 1.16 | 0.99 | 1.25 | 1.14 | 1.12 |
| Standard deviation | 0.31 | 0.40 | 0.19 | 0.23 | 0.22 | 0.18 | 0.19 |
| CoV (%) | 26.89 | 31.21 | 16.57 | 22.03 | 16.80 | 15.73 | 16.42 |
| Minimum | 0.42 | 0.42 | 0.65 | 0.57 | 0.86 | 0.73 | 0.78 |
| Maximum | 2.14 | 2.47 | 1.78 | 1.78 | 2.14 | 1.69 | 1.85 |
The adjustment provided by training presents an average ratio V /V . of 0.99, and 1.02 in validation.
c test pred
The authors have effectively created a laboratory with a neural network, in which they “test” (within parameter range) new beams by changing exclusively one parameter each time. Finally, they come up with two alternative design formulae that improve noticeably any given formula developed up to that moment. Table 3 presents a comparison between those two expressions (named Eq. 7 and Eq. 8) and others found in a series of international codes.
CONCLUSION
• The field of structural concrete shows great potential for the application of neural networks. Successful approaches to optimization, prediction of complex physical parameters and design formulae development have been presented.
• The network topology used in most cases for structural concrete is forward-feed, multilayer with backpropagation, typically with one or two hidden layers. The most commonly used training algorithms are descent gradient with momentum and adaptive learning, and Levenberg-Marquardt.
• The biggest potential of ANNs is their capacity to generate virtual testing laboratories which substitute with precision expensive real laboratory tests within the proper range of values.A methodical “testing” program throws light on the influence of the different variables in complex phenomena at reduced cost.
• The field of structural concrete counts upon extensive databases, generated through the years, that can be analyzed with this technique. An effort should be made to compile and homogenize these databases to extract the maximum possible knowledge, which has great influence on structural safety.
KEY TERMS
Compression: Stress generated by pressing or squeezing.
Consistency: The relative mobility or ability of freshly mixed concrete or mortar to flow; the usual measurement for concrete is slump, equal to the subsidence measured to the nearest 1/4 in. (6 mm) of a molded specimen immediately after removal of the slump cone.
Ductility: That property of a material by virtue of which it may undergo large permanent deformation without rupture.
Formwork: Total system of support for freshly placed concrete including the mold or sheathing that contacts the concrete as well as supporting members, hardware, and necessary bracing; sometimes called shuttering in the UK.
Shear Span: Distance between a reaction and the nearest load point.
Structural Safety: Structural response stronger than the internal forces produced by external loading.
Tension: Stress generated by stretching.
