# Assessing Voided Reinforced Concrete by Numerical Modelling of Impact-Generated Rayleigh Waves
## 1 Introduction  
It is of general interest to develop non-destructive inspection techniques, especially in Europe, where the building stock is relatively old. For example, across Europe, 60% of the non-residential buildings were built before 1980. In the UK specifically, over 50% of the residential building stock was built before 1960, while less than 15% was built between 1991 and 2010 ([PERSON], et al., 2016) [1]. Consequently, the development of non-destructive testing (NDT) methods and equipment have been accelerated to address the urgent needfor either short-term or long-term inspections since NDT methods allow the inspection to be carried out without immobilising or damaging the structure ([PERSON], et al., 2014) [2], which makes them ideal for routine inspections. Among the many NDT methods developed, elastic wave-based methods have great potential in detecting surface and subsurface defects. Other NDT methods, such as X-ray radiography and tomography, have limited practicability due to health and safety issues ([PERSON], et al., 2018) [3]. Elastic wave-based methods are highly suitable for on-site inspections. Elastic waves are generated by an impact force striking onto a surface. Body waves (i.e., compression and shear waves) and surface waves (i.e., Rayleigh waves) are generated. Rayleigh waves (R-wave) make up the highest energy portion (67%) ([PERSON] and [PERSON], 1955) [4], which means that R-waves are easily excited and recorded at the surface. Also, an R-wave travels radially with a circular waveform. Compared to other waves (with spherical waveforms), the attenuation of the R-wave amplitude due to geometric spreading is much less than for body waves, making R-waves suitable for long-distance inspections ([PERSON], et al., 1998) [5]. Surface waves are also preferred when structural members with restricted access need to be inspected, as only one-side access is required for surface wave-based methods. The point-source/point-receiver pulse-echo technique was first proposed by [PERSON] et al. ([PERSON], et al., 1986) [6] for flaw detection in concrete. This innovation initiated the development of impact-echo methods ([PERSON] and [PERSON], 1992) [7]. At that time, only the detection of simple defects in concrete was demonstrated. Since then, many efforts have been made to evaluate the elastic wave-based methods for more complex conditions and more realistic scenarios, for example, the evaluation of concrete's properties at early stages ([PERSON], et al., 2020) [8], examination of concrete compressive strength ([PERSON], 2018) [9], and characterisation of defects such as sub-surface cracks ([PERSON], et al., 2018) [10] and honeycomb ([PERSON] et al., 2016) [11]. Defect location, size, orientation and other characteristics can be determined from the information carried by the signal received. During the early stages of development, wave propagation problems were studied either analytically or experimentally. The experimental approach is time-consuming and labour-intensive, which only allows limited cases to be studied. This is unfavourable due to the rapid increase in demand for the development of NDT methods. With the increase in computational ability and commercial software availability, numerical simulations with experimental model validation have become a popular combination. For example, in the evaluation of near-surface discontinuities, experiments monitor wave propagation on the surface, while numerical simulations provide details of vibration at any point within the body ([PERSON], et al., 2003) [12]. Understanding how a wave interacts with the defects is enhanced by the unparalleled insight provided by experiments and numerical simulations. Such understanding can later be utilised in the development of instrumentation design, experimental methodologies, and signal analysis schemes. Finite element modelling has been utilised to study various wave propagation problems in different materials. However, there is a limited number of papers addressing the heterogeneity inside concrete structures.