# Detection of Cracks in Arch Dams Using Monitoring Data and Numerical Models
## 2 Methods
### Numerical Approach  
The core work of this study consisted of a campaign of numerical simulations based on the finite element method (FEM) to measure displacements in a real dam when subjected to a crack of variable length and depth. Once the displacements are calculated, the records that would be obtained by monitoring devices at different points of the dam are determined to analyze whether they can detect the size of the cracks. To perform all the numerical simulations of the dam foundation system contemplated in this work, the Ansys Mechanical Finite Element Analysis Software for Structural Engineering 2022 [14] was employed, along with 3D models. In the calculations involving friction surfaces, the iterative Preconditioned Conjugate Gradient solver was used with a tolerance value of \(10^{-8}\), a maximum number of substeps equal to 4, and a maximum number of iterations equal to the number of nodes times the degrees of freedom of each node. The numerical model adopted presented the following features: (a) linear materials (stress-strain curve); (b) static models; (c) no separation between the dam and the ground; (d) nonlinear contacts (cracks). The self-weight of the dam, the thermal stress, and the hydrostatic pressure of the reservoir in the upstream part of the dam and the internal sides of the crack were the only active forces. The nonlinearity of the materials has not been considered since it makes no direct impact on the deformations of the dam after cracking, which is the purpose of this work. Instrumentation devices were used to capture the movement in a small range of years, for which concrete properties are considered constant. Since the main objective of this work was to analyze cases of dangerous cracking, it was necessary to consider cracks that open up enough to significantly affect the behavioral response of the dam. Therefore, it was of interest to study situations where dam conditions favor the opening of significant cracks; however, dams are specifically engineered to avoid crack opening under the usual loads they would normally bear. In addition to hydrostatic pressure and temperature variations, other causes can favor or reduce the opening of cracks in the dam: heterogeneity of concrete properties, concrete aging, expansive chemical reactions, shrinkage, alkali-aggregate reactions, microseismicity, foundation deformation, seepage, inadequate design or execution of construction and maintenance, freeze-thaw effects, or hydration heat during concrete curing. Simulating all these conditions in a general approach with the purpose of finding the most unfavorable cases for the creation of cracks would require an unaffordable amount of calculation time. For a specific dam, some of these conditions may need to be simulated. A previous analysis of the dam (history, behavior, etc.) will lead to the conclusion of which aspects to be considered in the analysis. As this study is interested in the cases that can favor the opening of cracks in the dam, the uncertainty in the results caused by not considering the rest of the forces is assumed to be smaller than the effect of including a large thermal effect. It is important to clarify that the objective of this work was not to achieve an extremely realistic stress distribution but rather to analyze the capacity of a monitoring device to identify a crack in the dam. For the analysis of the cracking effect, the presence of a significant crack in the dam was assumed; therefore, the mesh was designed to align the faces of the elements with the sides of the crack. These cracks were considered fully formed, so the development process was not considered. Cases in which two relevant cracks open simultaneously or in which cracking develops at the same time as one of the transverse joints opens are very rare, so these cases were not included in the study.