مدل‌سازی جریان الکتریکی با استفاده از روش عددی بدون شبکه در بتن همگن

نوع مقاله : مقاله کامل پژوهشی

نویسندگان

1 دانشکده مهندسی عمران، دانشگاه تبریز

2 دانشکده مهندسی عمران ، دانشگاه تبریز

چکیده

     تکنیک سنجش پتانسیل الکتریکی، توموگرافی (Tomography)، به‌عنوان یک روش غیرمخرب در ارزیابی خصوصیات کیفی و دوام بتن مطرح می ­باشد. در این مطالعه، روش عددی بدون شبکه برای حل معادلات دیفرانسیل شبیه ­ساز عبور جریان الکتریکی و توزیع پتانسیل الکتریکی در محیط دوبعدی بتن، توسعه داده شد. برای بهینه ­سازی ضریب شکل در مدل بدون شبکه از تکنیک احتمالاتی بیزی استفاده شد و به‌منظور بررسی روش پیشنهادی، مدل آزمایشگاهی ایجاد گردید. برای این منظور جریان مستقیم از طریق یک جفت الکترود متصل به نمونه تزریق و پتانسیل الکتریکی در 14 نقطه پیرامونی نمونه اندازه­ گیری شد. تعداد 35 آرایش جفت الکترود مختلف برای تزریق در بتن انتخاب شد و ضریب شکل بهینه برای تمامی آرایش ­ها محاسبه شد. برای ارزیابی توانایی مدل پیشنهادی، نتایج حاصل با نتایج مدل کامسول (Comsol) که از روش اجزاء محدود در حل مسائل جریان و پتانسیل الکتریکی بهره می­ برد، مقایسه شد. نتایج تحقیق نشان داد که کارایی روش عددی بدون شبکه نسبت به مدل کامسول 8 درصد بیشتر می­ باشد که این مسئله می­ تواند ناشی از عدم قطعیت خصوصیات فیزیکی بتن در شرایط واقعی بوده که از طریق بهینه کردن ضریب شکل در روش بدون شبکه لحاظ می­شود. همچنین نتایج نشان داده که بهترین حالت برای اندازه­ گیری پتانسیل الکتریکی، استفاده از آرایش جفت الکترودهای روبروی هم است.

کلیدواژه‌ها


عنوان مقاله [English]

Electrical Current Flow Modeling Using Meshless Method in Homogeneous Concrete

نویسندگان [English]

  • Nasser Taghizadieh 1
  • Saeid Movahedi 2
1 Faculty of Civil Engineering, University of Tabriz. Tabriz. Iran
2 Faculty of Civil Engineering, Tabriz University, Tabriz,. Iran
چکیده [English]

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.

کلیدواژه‌ها [English]

  • Concrete
  • Electrical Potential
  • Meshless method
  • Bayes’ Theorem
ASTM, Standard test method for sieve analysis of fine and coarse aggregates, 2006, ASTM C136-06.
ASTM, Standard specification for concrete aggregates, Appendix XI, Methods for evaluating potential reactivity of an aggregate. American Society for Testing and Materials, Annual Book of ASTM Standards, Concrete and Mineral Aggregates, 14, 1979.
ASTM, Standard specifcation for standard sand, ASTM C778, 2002.
Atluri SN, Kim HG, Cho JY, “A critical assessment of the truly meshless local Petrov-Galerkin (MLPG), and local boundary integral equation (LBIE) methods”, Computational mechanics, 1999, 24 (5), 348-372.
Chen W, Fu ZJ, Chen CS, “Recent advances in radial basis function collocation methods”, Heidelberg: Springer, 2014.
Cowles MK, “Applied Bayesian statistics: with R and Open BUGS examples (Vol. 98). Springer Science & Business Media, 2013.
Duarte CA, Oden JT, “An hp adaptive method using clouds”, Computer methods in applied mechanics and engineering, 1996, 139 (1-4), 237-262.
Golberg MA, Chen CS, Karur SR, “Improved multiquadric approximation for partial differential equations”, Engineering Analysis with boundary elements, 1996, 18 (1), 9-17.
Hallaji M, Pour-Ghaz M, “A new sensing skin for qualitative damage detection in concrete elements: Rapid difference imaging with electrical resistance tomography”, NDT & E International, 2014, 68, 13-21.
Hallaji M, Seppänen A, Pour-Ghaz M, “Electrical impedance tomography-based sensing skin for quantitative imaging of damage in concrete”, Smart Materials and Structures, 2014, 23 (8), 085001.
Hallaji M, Seppänen A, Pour-Ghaz M, “Electrical resistance tomography to monitor unsaturated moisture flow in cementitious materials”, Cement and Concrete Research, 2015, 69, 10-18.
Hansson ILH, Hansson CM, “Electrical resistivity measurements of Portland cement based materials”, Cement and Concrete Research, 1983, 13 (5), 675-683.
Hardy RL, “Multiquadric equations of topography and other irregular surfaces”, Journal of Geophysical Research, 1971, 76 (8), 1905-1915.
Hardy RL, “Theory and applications of the multiquadric-biharmonic method 20 years of discovery 1968-1988”, Computers & Mathematics with Applications, 1990, 19 (8-9), 163-208.
Hon YC, Chen W, “Boundary knot method for 2D and 3D Helmholtz and convection-diffusion problems under complicated geometry”, International Journal for Numerical Methods in Engineering, 2003, 56 (13), 1931-1948.
Hou TC, Lynch JP, “Electrical impedance tomographic methods for sensing strain fields and crack damage in cementitious structures”, Journal of Intelligent Material Systems and Structures, 2009, 20 (11), 1363-1379.
Hou TC, Lynch JP, “Electrical impedance tomographic methods for sensing strain fields and crack damage in cementitious structures”, Journal of Intelligent Material Systems and Structures, 2009, 20 (11), 1363-1379.
Kansa EJ, Carlson RE, “Improved accuracy of multiquadric interpolation using variable shape parameters”, Computers & Mathematics with Applications, 1992, 24 (12), 99-120.
Kansa EJ, “Multiquadrics- A scattered data approximation scheme with applications to computational fluid-dynamics-II solutions to parabolic, hyperbolic and elliptic partial differential equations”, Computers & Mathematics with Applications, 1990, 19 (8-9), 147-161.
Karhunen K, Seppänen A, Lehikoinen A, Blunt J, Kaipio JP, Monteiro PJ, “Electrical Resistance Tomography for Assessment of Cracks in Concrete”, ACI Materials Journal, 2010, 107 (5).
Karhunen K, Seppänen A, Lehikoinen A, Monteiro PJ, Kaipio JP, “Electrical resistance tomography imaging of concrete”, Cement and Concrete Research, 2010, 40 (1), 137-145.
Lataste JF, Sirieix C, Breysse D, Frappa M, “Electrical resistivity measurement applied to cracking assessment on reinforced concrete structures in civil engineering”, NDT & E International, 2003, 36 (6), 383-394.
Li J, Chen CS, Pepper D, Chen Y, “Mesh-free method for groundwater modeling”, WIT Transactions on Modelling and Simulation, 2002, 32.
Liu WK, Jun S, Zhang YF, “Reproducing kernel particle methods”, International Journal for Numerical Methods in Fluids, 1995, 20 (8‐9), 1081-1106.
Meenal M, Eldho TI, “Two-dimensional contaminant transport modeling using meshfree point collocation method (PCM)”, Engineering Analysis with Boundary Elements, 2012, 36 (4), 551-561.
Melsa JL, Cohn DL, “Decision and Estimation Theory”, 1978.
Nourani V, Babakhani A, “Integration of artificial neural networks with radial basis function interpolation in earthfill dam seepage modeling”, Journal of Computing in Civil Engineering, 2012, 27 (2), 183-195.
Nourani V, Mousavi S, “Spatiotemporal groundwater level modeling using hybrid artificial intelligence-meshless method”, Journal of Hydrology, 2016, 536, 10-25.
Nourani V, Mousavi S, Dabrowska D, Sadikoglu F, “Conjunction of radial basis function interpolator and artificial intelligence models for time-space modeling of contaminant transport in porous media”, Journal of Hydrology, 2017, 548, 569-587.
Ozyurt N, Mason TO, Shah SP, “Non-destructive monitoring of fiber orientation using AC-IS: An industrial-scale application”, Cement and concrete research, 2006, 36 (9), 1653-1660.
Telford WM, Telford WM, Geldart LP, Sheriff RE, Sheriff RE, “Applied geophysics (Vol. 1)”, Cambridge University Press, 1990.
Tihonov AN, “Solution of incorrectly formulated problems and the regularization method”, Soviet Math., 1963, 4, 1035-1038.
Wen S, Chung DDL, “Electrical-resistance-based damage self-sensing in carbon fiber reinforced cement”, Carbon, 2007, 45 (4), 710-716.
Woo LY, Kidner NJ, Wansom S, Mason TO, “Combined time domain reflectometry and AC-impedance spectroscopy of fiber-reinforced fresh-cement composites”, Cement and Concrete Research, 2007, 37 (1), 89-95.
Zhang J, Monteiro PJ, Morrison HF, “Noninvasive surface measurement of corrosion impedance of reinforcing bar in concrete-part 1: experimental results”, Materials Journal, 2001, 98 (2), 116-125.
Zhang J, Monteiro PJ, Morrison HF, “Noninvasive surface measurement of corrosion impedance of reinforcing bar in concrete-part 2: forward modeling”, Materials Journal, 2002, 99 (3), 242-249.
Zhang J, Monteiro PJ, Morrison HF, Mancio M, “Noninvasive surface measurement of corrosion impedance of reinforcing bar in concrete-part 3: effect of geometry and material properties, Materials Journal, 2004, 101 (4), 273-280.