Identification Tools For Smeared Damage With Application To Reinforced Concrete Structural Elements

Abstract

Countries world-over have thousands of critical structures and bridges which have been built decades back when strength-based designs were the order of the day. Over the years, magnitude and frequency of loadings on these have increased. Also, these structures have been exposed to environmental degradation during their service life. Hence, structural health monitoring (SHM) has attracted the attention of researchers, world over. Structural health monitoring is recommended both for vulnerable old bridges and structures as well as for new important structures. Structural health monitoring as a principle is derived from condition monitoring of machinery, where the day-to-day recordings of sound and vibration from machinery is compared and sudden changes in their features is reported for inspection and trouble-shooting. With the availability of funds for repair and retrofitting being limited, it has become imperative to rank buildings and bridges that require rehabilitation for prioritization. Visual inspection and expert judgment continues to rule the roost. Non-destructive testing techniques though have come of age and are providing excellent inputs for judgment cannot be carried out indiscriminately. They are best suited for evaluating local damage when restricted areas are investigated in detail. A few modern bridges, particularly long-span bridges have been provided with sophisticated instrumentation for health monitoring. It is necessary to identify local damages existing in normal bridges. The methodology adopted for such identification should be simple, both in terms of investigations involved and the instrumentation. Researchers have proposed various methodologies including damage identification from mode shapes, wavelet-based formulations and optimization-based damage identification and instrumentation schemes and so on. These are technically involved but may be difficult to be applied for all critical bridges, where the sheer volume of number of bridges to be investigated is enormous. Ideally, structural health monitoring has to be carried out in two stages: (a) Stage-1: Remote monitoring of global damage indicators and inference of the health of the structure. Instrumentation for this stage should be less, simple, but at critical locations to capture the global damage in a reasonable sense. (b) Stage -2: If global indicators show deviation beyond a specified threshold, then a detailed and localized instrumentation and monitoring, with controlled application of static and dynamic loads is to be carried out to infer the health of the structure and take a decision on the repair and retrofit strategies. The thesis proposes the first stage structural health monitoring methodology using natural frequencies and static deflections as damage indicators. The idea is that the stage-1 monitoring has to be done for a large number of bridges and vulnerable structures in a remote and wire-less way and a centralized control and processing unit should be able to number-crunch the in-coming data automatically and the features extracted from the data should help in determining whether any particular bridge warrants second stage detailed investigation. Hence, simple and robust strategies are required for estimating the health of the structure using some of the globally available response data. Identification methodology developed in this thesis is applicable to distributed smeared damage, which is typical of reinforced concrete structures. Simplified expressions and methodologies are proposed in the thesis and numerically and experimentally validated towards damage estimation of typical structures and elements from measured natural frequencies and static deflections. The first-order perturbation equation for a dynamical system is used to derive the relevant expressions for damage identification. The sensitivity of Eigen-value-cumvector pair to damage, modeled as reduction in flexural rigidity (EI for beams, AE for axial rods and Et 12(1 2 )3− μ for plates) is derived. The forward equation relating the changes in EI to changes in frequencies is derived for typical structural elements like simply-supported beams, plates and axial rods (along with position and extent of damage as the other controlling parameters). A distributed damage is uniquely defined with its position, extent and magnitude of EI reduction. A methodology is proposed for the inverse problem, making use of the linear relationship between the reductions in EI (in a smeared sense) to Eigen-values, such that multiple damages could be estimated using changes in natural frequencies. The methodology is applied to beams, plates and axial rods. The performance of this inverse methodology under influence of measurement errors is investigated for typical error profiles. For a discrete three dimensional structure, computationally derived sensitivity matrix is used to solve the damages in each floor levels, simulating the post-earthquake damage scenario. An artificial neural network (ANN) based Radial basis function network (RBFN) is also used to solve the multivariate interpolation problem, with appropriate training sets involving a number of pairs of damage and Eigen-value-change vectors. The acclaimed Cawley-Adams criteria (1979) states that, “the ratio of changes in natural frequencies between two modes is independent of the damage magnitude” and is governed only by the position (or location) and extent of damage. This criterion is applied to a multiple damage problem and contours with equal frequency change ratios, termed as Iso_Eigen_value_change contours are developed. Intersection of these contours for different pairs of frequencies shows the position and extent of damage. Experimental and analytical verification of damage identification methodology using Cawley-Adams criteria is successfully demonstrated. Sensitivity expressions relating the damages to changes in static deflections are derived and numerically and experimentally proved. It is seen that this process of damage identification from static deflections is prone to more errors if not cautiously exercised. Engineering and physics based intuition is adopted in setting the guidelines for efficient damage detection using static deflections. In lines of Cawley-Adams criteria for frequencies, an invariant factor based on static deflections measured at pairs of symmetrical points on a simply supported beam is developed and established. The power of the factor is such that it is governed only by the position of damage and invariant with reference to extent and magnitude of damage. Such a revelation is one step ahead of Caddemi and Morassi’s (2007) recent paper, dealing with static deflection based damage identification for concentrated damage. The invariant factor makes it an ideal candidate for base-line-free measurement, if the quality and resolution of instrumentation is good. A moving damage problem is innovatively introduced in the experiment. An attempt is made to examine wave-propagation techniques for damage identification and a guideline for modeling wave propagation as a transient dynamic problem is done. The reflected-wave response velocity (peak particle velocity) as a ratio of incident wave response is proposed as a damage indicator for an axial rod (representing an end-supported pile foundation). Suitable modifications are incorporated in the classical expressions to correct for damping and partial-enveloping of advancing wave in the damage zone. The experimental results on axial dynamic response of free-free beams suggest that vibration frequency based damage identification is a viable complementary tool to wave propagation. Wavelet-multi-resolution analysis as a feature extraction tool for damage identification is also investigated and structural slope (rotation) and curvatures are found to be the better indicators of damage coupled with wavelet analysis. An adaptive excitation scheme for maximizing the curvature at any arbitrary point of interest is also proposed. However more work is to be done to establish the efficiency of wavelets on experimentally derived parameters, where large noise-ingression may affect the analysis. The application of time-period based damage identification methodology for post-seismic damage estimation is investigated. Seismic damage is postulated by an index based on its plastic displacement excursion and the cumulative energy dissipated. Damage index is a convenient tool for decision making on immediate-occupancy, life-safety after repair and demolition of the structure. Damage sensitive soft storey structure and a weak story structure are used in the non-linear dynamic analysis and the DiPasquale-Cakmak (1987) damage index is calibrated with Park-Ang (1985) damage index. The exponent of the time-period ratio of DiPasquale-Cakmak model is modified to have consistency of damage index with Park-Ang (1985) model.