Embankment dams, like most other civil infrastructure systems, are exposed to harsh and largely unpredictable environments. However, unlike bridges, buildings and other structures, their design specifications and as-is properties are not generally known in the same level of detail due to, among other things, their age and the difficulties associated with assessing their internal structure. Hence, making sense of measurements collected from instruments used to monitor their behavior requires sound engineering judgment and analysis, as well as robust statistical analysis techniques to prevent misinterpretation. In the United States (US), the current practice of analyzing the structural integrity of embankment dams relies primarily on manual a posteriori analysis of instrument data by engineers, leaving much room for improvement through the application of automated data analysis techniques. In our previous work, we presented the effectiveness of applying statistical anomaly detection techniques such as Principal Component Analysis and Robust Regression Analysis when analyzing piezometer data collected from embankment dams. In this paper, we present how we could improve our work by testing with simulated anomalies that are indicative of internal erosion problems. In order to closely replicate more realistic anomalous scenarios, a physics-based model of an embankment dam was developed. By varying a hydraulic conductivity of a soil material in the model, corresponding detection accuracies and sensitivities of the statistical anomaly detection algorithm were evaluated. When we applied our proposed anomaly detection on more realistically simulated anomalous data using the numerical model, the detection accuracy came out to be 98.5%.