Reply to the discussion on “The modified Vlasov model on a nonhomogeneous and nonlinear soil layer”

Abstract

The discussion suggests that the paper has left out four references (Haldar and Basu, 2013; Haldar and Basu, 2016; Elhuni and Basu, 2019; Elhuni and Basu, 2021), and the research work in the paper is not new. The authors would like to state that the literature review in the paper was kept as vast as and to stay as close as possible to the model given in the paper, which is a gross model. The study aimed to offer a method using a previously developed formulation for accounting for soil nonlinearity (Vallabhan and Das, 1988,1991a,1991b). The primary concentration in the literature was given to the most relevant works on the modified Vlasov model that employs the same concept for the solution method and algorithm, which lays the foundation of the paper (Vallabhan and Das 1988,1991a,1991b; Asik, 1999; Asik and Vallabhan,2001). On the other hand, as clearly indicated in the study, the literature in the field is extensive, including the works suggested by the discussion. Despite the author’s efforts, it was not possible to review or/ and mention all the works previously conducted to solve the problem with different approaches. In this respect, the previous studies by Haldar and Basu (2013) and Elhuni and Basu (2019) mentioned in the discussion are not directly related to the problem considered in the paper. Haldar and Basu (2016) proposed a framework incorporating the finite difference and the finite element methods.