Estimating corrosion levels along confined steel bars in concrete using surface crack measurements and mesoscale simulations guided by model predictive control

Abstract

In corroded reinforced concrete (RC) structures, there is a need to understand the degree of internal corrosion of the reinforcing bars in order to evaluate residual performance and ensure a rational maintenance regime. The authors have developed a computational approach for estimating the distribution of corrosion along the length of a reinforcing bar from the observed surface crack widths. The approach is based on mesoscale simulations of reinforced concrete, using rigid-body-spring models (RBSM), guided by Model Predictive Control (MPC). The current study extends that research to account for differing (smaller) crack openings, multiple instances of localized corrosion, and added confinement due to the presence of stirrups. Accuracy of the proposed approach is demonstrated through comparisons with laboratory tests of steel corrosion within concrete. The crack distribution observed on the concrete surface is automatically reproduced by optimized application of internal expansion within the mesoscale model, from which the corrosion distribution is estimated. The estimated corrosion distribution is accurate when compared to the measured corrosion of bars removed from the test specimens. In the case of specimens with stirrups, crack distributions and openings are accurately simulated by the MPC-RBSM system. Estimated corrosion levels are close to the measured values with some variations. The main reasons for these variations are the greater crack widths and higher corrosion levels in the stirrup-confined specimens. The simulated crack patterns are similar to those observed on the experimental specimens, indicating that specimen damage is simulated well. The internal stress and cracking distributions simulated by this method of meso-scale discrete analysis provides useful information for evaluating damage level that cannot be observed at the surface.

Introduction

For many reinforced concrete (RC) structures, maintenance is a necessary task. During the serviceable life, periodic monitoring of deterioration is essential for residual performance estimation [[1], [2], [3]]. Among the various potential forms of deterioration, chloride-induced corrosion of the reinforcement is dominant [[4], [5], [6]]. Corrosion produces stresses that may result in cracking of the concrete. Initial surface cracks have been observed at low corrosion levels of micrometer loss of bar radius [7]. If cracking propagates until the cover concrete delaminates, spalling may occur [8]. Penetration of chloride ions to the bar surface depassivates the protective oxide layer on the bar and thus enables corrosion. The corrosion products are more voluminous than the original steel, causing radial stresses in the surrounding concrete [7,8].

Corrosion and related forms of damage are internal phenomena that alter the internal stress flow, possibly changing the overall behavior such as the failure mode [9,10], seismic performance [11] and flexural and shear capacity [12]. Hence, reduction in bar cross-section area and changes in bond performance are important parameters within quantitative analyses that support maintenance decisions. Previous attempts to estimate the influences of corrosion include probability based approaches such as the time-dependent reliability method for risk-cost optimization [13], using the concept of imprecise reliability for safety assessment [14] and durability monitoring [15]. The accuracy of these approaches is limited, and a more direct method is required. Non-destructive techniques to estimate corrosion include the half-cell potential method [16,17], the polarization resistance method [18] and thermography [19]. Others include the measurement of electrochemical potential [20], the Wenner four-electrode set up [21], direct wave radar [22], Fiber Bragg Grating [23], and infrared imaging [24]. In these techniques, degree of deterioration is calculated by a probabilistic approach or using instruments to measure corrosion. Mathematical approaches are approximate, while the use of heavy instruments may be impractical and difficult in the case of large infrastructure [25].

Numerical modeling is another useful tool for understanding concrete behavior and has been used to understand the effect of corrosion in concrete. Many studies have used the finite element method (FEM) to model non-uniform corrosion and study its effects on, for example, bond strength reduction, cover cracking and stress redistribution [[26], [27], [28], [29], [30]]. Other studies have used discrete analysis to accurately model crack propagation and damage in concrete [31,32]. Discrete analysis by the rigid-body-spring model (RBSM) has proven effective in simulating local cracking behavior [33,34], mesoscale behavior and fracturing [35,36] and corrosion [37,38] in reinforced concrete structures. The RBSM proposed by Kawai et al. [39] is one such discrete analysis technique, in which the simulation system developed by Nagai et al. [40,41] is used as a basis of a study to simulate the failure of concrete. The RBSM model can effectively simulate localized cracking in concrete [33,34,36,42]. The discretization of concrete into rigid bodies allows for realistic, discrete-like representation of local crack formation and propagation. Potential bias in cracking direction is reduced by generating random particle geometries. The applicability of RBSM to corrosion has been studied, leading to success in analyzing bond degradation [34,37,38,[43], [44], [45]]. Rebar shape can be accurately modeled in RBSM to account for the interlocking effect of a deformed bar. Therefore, it can be concluded that the damage and reduction in performance could be estimated if non-uniform corrosion data is available.

In practice, however, the corrosion of a rebar is nonuniform and occurs inside concrete, so it cannot be directly measured without removing the cover concrete. The only visible information is surface cracking and any effluence of corrosion products from such cracking. To avoid extensive cover removal, the internal non-uniform corrosion distribution therefore needs to be estimated from the observable surface crack distribution. The model predictive control-rigid body spring model (MPC-RBSM) [46] uses this surface information, which can be readily collected from a corroded structure, to estimate internal corrosion. Model predictive control (MPC) is a process control technique in which inputs are optimized to generate controlled outputs from the model. MPC has been adopted in various fields to produce target outputs [[47], [48], [49], [50], [51]]. In this study, MPC is used to control internal expansion within the RBSM representation of the reinforced concrete so as to produce cracking that is similar to that experimentally observed. The resultant expansion can then be used to estimate degree of corrosion using a linear relationship. For small crack openings and corrosion levels this linear relationship appears to be valid [[52], [53], [54]]. For larger crack openings or higher levels of corrosion, however, the relationship may exhibit nonlinearity due to significant leakage of corrosion products through the crack network, which can lead to discrepancies in the estimation results. In a previous study, the developed MPC-RBSM system successfully simulated the crack widths and damage patterns observed during laboratory testing of steel bar corrosion within concrete. However, due to the large crack width of 1.4 mm, and the presumed associated effect of corrosion product leakage, the estimated corrosion distribution exhibited differences with the experimental results [46]. Furthermore, that earlier study was limited to one specimen type, a single instance of localized corrosion along the bar length, and no lateral confinement (due to, for example, the presence of stirrups).

Since most RC structures contain multidirectional reinforcement, the practical application of MPC-RBSM technique demands the simulation of specimens with transverse confining reinforcement. In the earlier study, only longitudinal reinforcement was considered. Stirrup confinement significantly affects corrosion cracking behavior [55]. Tensile strain resulting from corrosion is borne by the stirrups and delays the propagation of corrosion cracks [56]. However, the threshold degree of corrosion required to initiate corrosion cracking is not affected by the presence of lateral confinement [54]. This delay may result in underestimation of corrosion during visual inspections and hence result in overestimates of residual performance. Mesoscale discrete analysis can directly accommodate these interactions and therefore, in this study, specimens with stirrup confinement are tested.

The research presented herein extends the previous study in several significant ways. Various specimen types are considered, providing a more comprehensive assessment of the MPC-RBSM capabilities for estimating corrosion degrees. In particular, some of the specimens contain multiple instances of localized corrosion, as would occur in practice. Some specimens include stirrup reinforcement to evaluate influences of the additional confinement on the corrosion distribution and its estimation. The specimen designs led to smaller crack openings, which largely avoids the uncertainties regarding the leakage of corrosion products through the crack networks. All simulation results are validated through comparisons with corresponding laboratory tests based on an accelerated corrosion setup. Crack widths for these specimens are recorded and used as targets for the MPC-RBSM system to estimate the distribution of corrosion along the bar lengths. Comparisons between the physically measured and estimated corrosion levels, and damage patterns, reveal that the MPC-RBSM system is accurate for the cases considered. With additional modifications, the MPC-RBSM system is a potentially viable means for the nondestructive evaluation of corrosion levels in structural concrete.