Analysis of the wave propagation paths in numerical reinforced concrete models

Abstract

The paper aims to study the characteristics of the wave propagation paths in reinforced concrete and to improve the existing velocity models. Therefore, coefficients of reflection and transmission with regard to energy were analyzed for each component of the reinforced concrete (cement matrix, aggregate grains, air voids and reinforcement bars) in case of a free- and joint-material boundary, respectively. The findings were employed to investigate the wave propagation paths in cracked concrete and reinforced concrete. Three-dimensional numerical models to approximate the heterogeneous concrete (numerical concrete model, NCM) and reinforced concrete (numerical reinforced concrete model, NRCM) were implemented in a rotated staggered-grid finite-differences scheme. Numerical simulations of the elastic wave propagation were performed to illustrate the interaction of waves with boundaries. Both velocity models, NCM and NRCM, were applied to localize acoustic emissions (AE). An established source localization estimation method (FastWay) served as a tool to validate the heterogeneous velocity models. FastWay was applied to a synthetic cracked reinforced concrete beam to localize six randomly located AE sources. The influence of non-straight wave propagation paths on the performance of the localization method was discussed.

Introduction

Acoustic emissions (AE) are caused by a sudden internal release of strained energy, for example due to material fracture [1], [2]. The released energy manifests in elastic waves radiating away from the source [3]. Sensors (primarily piezoelectric transducers) record the wave motion on the surface caused by these elastic waves. The recorded signals can be used subsequently as input for various analyses (e.g., source localization; see [4], [5], [6], [7], [8], [9], [10], [11], [12], [13]). The wave propagation path is of particular interest for a majority of the AE analysis application possibilities. Methods relying on the traditional Geiger algorithm [4], [8] assume a straight wave propagation path and a constant (homogeneous) velocity model. Such methods can also be combined with a heterogeneous velocity model to achieve better localization performance in heterogeneous materials [5], [14]. However, the assumed straight wave propagation path can differ from the actual fastest wave propagation path. Therefore, wave propagation in general and estimating the fastest wave propagation path in particular is an integral component of recent studies published in [15], [16]. Since computer capacity and processor speed rapidly increase, the physical relation between AE and elastic wave propagation can be treated numerically. For example, solutions of elastodynamic equations can be calculated immensely faster and be visualized almost plastically [17]. Parallel processing and high-speed computer cluster enable the simulation of complex elastic wave propagation in different geometries and with variable material models. In concrete modeling, some promising simplifications have been made that allow taking into account heterogeneous material properties. Sophisticated non-commercial tools for the numerical simulation of elastic wave propagation arose such as the elastodynamic finite-integration technique (EFIT) [18]. The equations of motion were discretized on a numerical time domain scheme to model elastic wave propagation in isotropic, anisotropic, homogeneous and heterogeneous media, which is based on a velocity-stress formulation on a staggered-grid. The EFIT scheme was validated for isotropic, homogeneous and unbounded media by discussing dispersion relation and convergence criteria. Schubert [19], [20] reconsidered the EFIT scheme and developed a randomly distributed concrete model that is employed in a modified version in recent scientific works to be shown later. Saenger et al. [21] presented a modified version of the classic velocity-stress formulation, discretized on a staggered-grid with finite differences (FD) method [22], [23]. Kocur et al. [24] applied the rotated staggered-grid FD method to simulate elastic wave propagation in numerical models obtained from X-ray computed tomography (CT) of real uncracked and cracked concrete cuboids [25]. Synergies were illustrated between numerical simulations in X-ray CT data for a concrete specimen and a self-developed purely numerical concrete model. The influence of concrete constituents such as aggregate grains and air voids on the wave propagation behavior was studied.