Recently, metamorphic testing (MT) has been used to augment test datasets by inclusion of new (follow-up) test cases transformed from existing (source) test cases using metamorphic relations (MRs). It has been reported that the augmented test dataset usually has higher fault detection capabilities. Intuitively, a question arises: why the metamorphic relations can improve the fault detection effectiveness of the augmented test dataset? To investigate this issue, we conducted an empirical study on three DNN models by feeding 70000 handwritten digits images, in which six sets of MRs were designed. Furthermore, the impacts of follow-up test cases percentages and test suite sizes on the fault detection capabilities were investigated.