Electrical Current Flow Modeling Using Meshless Method in Homogeneous Concrete

Concrete is the most widely used construction material in the world for many decades. Old existing structures are deteriorated and needed inspection and repair. Electrical methods, which are inexpensive and easy to handle, are well known as non-destructive inspection methods. They can give information about the position, size, and orientation of inclusions like bar and fiber, condition of corrosion, state of humidity and probable corrosive ions, and the degree of cracking in concrete. Both alternate and direct currents (AC & DC) can be used in electrical resistance measurement (ERT). A major problem of the DC method is the measurement error produced by a polarization of the specimen. In AC methods the frequency should be kept as low as possible to avoid the inductance effects of long connecting cables and also the frequency has to be high enough to avoid electrode polarization effects. In ERT, electric current is injected through electrodes, and the voltage produced on the object surface is recorded using several electrode pairs. Then an estimate of the spatial distribution of conductivity is mapped (Karhunen et al., 2010).The finite element method (FEM) has been widely applied for the numerical solution of governing physical-based partial differential equation of electric current flow (Hou and Lynch, 2009). FEM needs a mesh in the solution domain or on its boundary which makes some difficulty in highly irregular and complex geometry. The meshless method is an alternative solution that was developed to establish a system of (linear) algebraic equations for the entire domain of the problem without creating pre-defined meshes. In this study meshless method is used due to the following advantages (Nourani and Babakhani, 2012): 1) It doesn’t require a domain and boundary meshing; 2) there is no need for integration in domain and boundary; 3) point location is the only variable in RBF functions which makes it suitable for high dimensional problems; 4) RBF is easy to code and implement. Among various types of meshless methods, multi-quadratic radial basis function formulation (MQ-RBF) is mostly utilized. One challenging issue related to the MQ-RBF method is the calibration of shape coefficient which is a case-sensitive parameter. This research proposed a Bayesian statistical theorem for the calibration of shape coefficient.