Abstract

     Determining the relationship between the cause of damage and the subsequent structural behavior of infrastructure systems requires an accurate characterization of the propagation of cracks, which represents the evolution of the damage state. When no information about the cause of damage is available, kinematic approaches can be used to describe the motion of crack contours. Current image-based approaches to derive crack kinematics use digital image correlation (DIC) on a set of sequential images as the crack propagates. However, DIC is invasive in that the structure surfaces must be painted with random speckle patterns, limiting its use primarily to controlled experiments. In this paper, we propose a novel image-based methodology for computing crack opening in Mode I or Mode II. As an input, this method takes a binary image from a semantic segmentation of an image of a crack pattern. This binary image is used to detect the opposite edges along the crack, which are then registered using an optimization algorithm based on the Euclidean transformation model and non-linear least squares. As a final output, this method produces displacement maps in the tangential and normal directions to the crack skeleton. To demonstrate its performance, we validate our methodology first with synthetic crack patterns and then with real crack patterns. Because this methodology for determining crack openings requires only simple data (just a binary crack pattern image), it is straightforward, robust, and adaptable, thus contributing to the development of structural image-based damage assessments. The computational codes and datasets are available to the public for future research and benchmarking on https://github.com/eesd-epfl/crack_kinematics and https://doi.org/10.5281/zenodo.6632071.

Introduction

     Structural inspections of existing buildings and infrastructure comprise localizing and classifying damage features in the structure. These engineering inspections are conducted on a regular basis, as is common for infrastructure, as well as after extraordinary events, such as earthquakes. Among the various manifestations of damage that engineers evaluate, cracks are the most common feature in quasi-brittle structures, such as concrete and masonry [1].

     The likely causes of damage and the mechanical properties of the damaged structural element (e.g., stiffness, strength) can be estimated from the crack pattern and kinematics of a crack. Crack kinematics describes how two crack surfaces move in relation to each other, and provide important information about the stress state that caused the damage. A Mode I crack opens normal to the crack surface and is typically associated with normal stresses. A Mode II crack opens parallel to the crack surface and is associated with shear stresses in the plane of the element [2]. Shear stresses acting in the crack plane cause Mode III deformation as well, but in this case the deformation is out-of-plane [2]. Concrete and masonry elements that fail in shear (Mode II) have a lower deformation capacity than elements that fail in flexure (Mode I). Therefore, identifying cracks in structures and classifying their opening mode is important for preventing potential failures through timely interventions designed to minimize economic losses, future deterioration, and even loss of human life [3].

Conclusions

     In this paper, we proposed a novel methodology for determining the propagation of cracks in structural elements caused by unknown forces (crack kinematics). This procedure takes as inputs binary images obtained by semantically segmenting a crack from an image of a crack pattern. To the best of our knowledge, this is the first method to solve the crack kinematics determination problem based on single images, significantly advancing the state-of-the-art in the field.

     The first step of our developed technique consists of detecting the contours of a crack pattern as a 2D set of points that are divided into opposite edges along the crack length. Next, the edges are registered using Euclidean transformations encoding both normal and tangential displacements, which are used to determine whether the cracks propagated in Mode I or Mode II. Additional normal features are included in our loss function to improve the results of the registration problem. We validated our method with synthetic data based on lines and real crack contours, where pre-defined rotation and translation were used to generate crack patterns, obtaining an absolute error of less than a pixel. Monte Carlo simulations were used to demonstrate the stability of our method as well as to guide the selection of hyper-parameters. Then, we put our methodology to the test with challenging crack patterns that contained multiple cracks and branches, including two real structural applications (damaged wall during laboratory testing, damaged beam and damaged building due to an earthquake event). Extra validation of the performance, accuracy and robustness of our methodology is made comparing results with a DIC-based method and manual measurements with metric gauge. The results of both validation and test experiments showed that the developed approach has the potential to deduce the crack kinematics simply from spatial features (2D edges coordinates) extracted from a binary input image.