A numerical approach and parametric study for the calculation of the s
oil and pile interaction under lateral loading are presented. The meth
od uses variational calculus to obtain the governing differential equa
tions of the soil and pile system. A principal parameter (gamma) is us
ed in this model to present the elastic foundation. The properties and
the significance of the primary model parameters, such as gamma, Pois
son's ratio upsilon, slenderness ratio PSI, and flexibility factor K(r
), are carefully investigated in order to have a better understanding
of the relationships between those parameters. A number of important f
eatures, including linear relationships between the coefficients and s
imple analytical equations, are presented here. On the basis of the ne
w aspect and related mathematical expressions, an improved predictive
capability is obtained. This general analytical perspective allows the
further improvement and simplification of the proposed model and sugg
ests a way to predict the response of laterally loaded piles for engin
eering design. The practical application guide has been produced. Some
graphics and examples illustrated in this paper can be used by a desi
gn engineer for engineering design.