The paper deals with numerical simulations of wave propagation in reinforced concrete for damage detection purposes. A novel formulation of a 3D spectral element was proposed. The reinforcement modelled as the truss spectral element was embedded in the 3D solid spectral finite element. Numerical simulations have been conducted on cuboid concrete specimens reinforced with two steel bars. Different degradation models were considered to study the real behaviour of bended beams.
 V. Srinivas, S. Sasmal, K. Ramanjaneyulu, and C. Antony Jeyasehar, “Influence of test conditions on modal characteristics of reinforced concrete structures under different damage scenarios”, Archives of Civil and Mechanical Engineering 13, 491‒505 (2013).
 V. Pérez-Gracia and F. García García, I. Rodriguez Abad, „GPR evaluation of the damage found in the reinforced concrete base of a block of flats: A case study”, NDT&E International 41, 341‒353 (2008).
 K. Ohno and M. Ohtsu, “Crack classification in concrete based on acoustic emission”, Construction and Building Materials 24, 2339‒2346 (2010).
 C.-C. Cheng, T.-M. Cheng, and C.-H. Chiang, “Defect detection of concrete structures using both infrared thermography and elastic waves”, Automation in Construction 18, 87‒92 (2008).
 D.G. Aggelis and T. Shiotani, “Repair evaluation of concrete cracks using surface and through-transmission wave measurements”, Cement & Concrete Composites 29, 700‒711 (2007).
 J. Hoła, Ł. Sadowski, and K. Schabowicz, „Nondestructive identification of delaminations in concrete floor toppings with acoustic methods”, Automation in Construction 20, 799‒807 (2011).
 Y. Yang, G. Cascante, and M.A. Polak, “Depth detection of surface-breathing crack in concrete plates using fundamental Lamb modes”, NDT&E International 42, 501‒512 (2009).
 J. Hoła, J. Bień, Ł. Sadowski, and K. Schabowicz, „Non-destructive and semi-destructive diagnostics of concrete structures in assessment of their durability”, Bulletin of the Polish Academy of Sciences Technical Sciences 63, 87‒96 (2015).
 A. Garbacz, “Application of stress based NDT methods for concrete repair bond quality control”, Bulletin of the Polish Academy of Sciences Technical Sciences 63, 77‒85 (2015).
 M. Rucka and K. Wilde, “Experimental study on ultrasonic monitoring of splitting failure in reinforced concrete”, Journal of Nondestructive Evaluation 32, 372‒383 (2013).
 M. Rucka and K. Wilde, “Ultrasound monitoring for evaluation of damage in reinforced concrete”, Bulletin of the Polish Academy of Sciences: Technical Sciences 63, 1‒11 (2015).
 B.S. Divsholi and Y. Yang, “Combined embedded and surface-bonded piezoelectric transducers for monitoring of concrete structures”, NDT&E International 65, 28‒34 (2014).
 F. Moradi-Marani, P. Rivard, C.-P. Lamarche, and S.A. Kodjo, “Evaluating the damage in reinforced concrete slabs under bending test with the energy of ultrasonic waves”, Construction and Building Materials 73, 663‒673 (2014).
 M. Rucka. “Experimental and numerical studies of guided wave damage detection in bars with structural discontinuities”, Archive of Applied Mechanics 80, 1371‒1390 (2010).
 M. Rucka. “Modelling of in-plane wave propagation in a plate using spectral element method and Kane-Mindlin theory with application to damage detection”, Archive of Applied Mechanics 81, 1877‒1888 (2011).
 T. Patera, “A spectral element method for fluid dynamics: laminar flow in a channel expansion”, Journal of Computational Physics 54, 468‒488 (1984).
 J. F. Semblat and J. J. Brioist, “Efficiency of higher order finite elements for the analysis of seismic wave propagation”, Journal of Sound and Vibration 231, 460‒467 (2000).
 D. Komatitsch, R. Martin, J. Tromp, M.A. Taylor, and B.A. Wingate, “Wave propagation in 2-D elastic media using a spectral element method with triangles and quadrangles”, Journal of Computational Acoustics 9, 703‒718 (2001).
 W. Ostachowicz, P. Kudela, M. Krawczuk, and A. Żak Guided Waves in Structures for SHM: The Time-Domain Spectral Element Method, Wiley, 2012.
 A. Żak, M. Krawczuk, and W. Ostachowicz, „Propagation of inplane wave in an isotropic panel with a crack”, Finite Elements in Analysis and Design 42, 929‒941 (2006).
 M. Rucka, W. Witkowski, J. Chróscielewski, and K. Wilde, “Damage detection of a T-shaped panel by wave propagation analysis in the plane stress”, Archives of Civil Engineering LVIII(1), 3‒24 (2012).
 J. Chróścielewski, M. Rucka, W. Witkowski, and K. Wilde, “Formulation of spectral truss element for guided waves damage detection in spatial steel trusses”, Archives of Civil Engineering LV(1), 43‒63 (2009).
 A. Żak, “A novel formulation of a spectral plate element for wave propagation in isotropic structures”, Finite Elements in Analysis and Design 45, 650‒658 (2009).
 Y. Liu, N. Hu, C. Yan, X. Peng, and B. Yan, “Construction of a Mindlin pseudospectral plate element and evaluating efficiency of the element”, Finite Elements in Analysis and Design 45, 538‒546 (2009).
 W. Witkowski, M. Rucka, J. Chróścielewski, and K. Wilde, “Wave propagation analysis in spatial frames using spectral Timoshenko beam elements in the context of damage detection”. Archives of Civil Engineering LV(3), 367‒402 (2009).
 A. Żak and M. Krawczuk, “Certain numerical issues of wave propagation modelling in rods by the Spectral Finite Element Method”, Finite Elements in Analysis and Design 47, 1036‒1046 (2011).
 L. Ge, X. Wang, and C. Jin, “Numerical modelling of PZT-induced Lamb wave-based crack detection in plate-like structures”, Wave Motion 51, 867‒885 (2014).
 H. Peng, Meng G., and F. Li, “Modeling of wave propagation in plate structures using three-dimensional spectral element method for damage detection”, Journal of Sound and Vibration 320, 942‒954 (2009).
 A. Żak, M. Krawczuk, Ł. Skarbek, and M. Palacz, “Numerical analysis of elastic wave propagation in unbounded structures”, Finite Elements in Analysis and Design 90, 1–10 (2014).
 D.M. Joglekar and M. Mitra, “Nonlinear analysis of flexural wave propagation through 1D waveguides with breathing crack”, Journal of Sound and Vibration 344, 242‒257 (2015).
 R. Sridhar, A. Chakraborty, and S. Gopalakrishnan, “Wave propagation analysis in anisotropic and inhomogeneous uncracked and cracked structures using pseudospectral finite element method”, International Journal of Solids and Structures 43, 4997‒5031 (2006).
 O.C. Zienkiewicz and R.L. Taylor, The Finite Element Method, Butterworth-Heinemann, 2000.
 T.J.R. Hughes, The Finite Element Method: linear static and dynamics finite element analysis, Dover Publications, Inc., New York, 2000.
 W. Witkowski, M. Rucka, J. Chróścielewski, and K. Wilde, “On some properties of 2D spectral finite elements in problems of wave propagation”, Finite Elements in Analysis and Design 55, 31‒41 (2012).
 M. Koizumi, “FGM activities in Japan”, Composites Part B 28B, 1‒4 (1997).
 J. Woo and S. A. Meguid, “Nonlinear analysis of functionally graded plates and shallow shells”, International Journal of Solids and Structures 38, 7409‒7421, (2001).