By adopting the advantages of previous theories of laterally loaded pile

in this paper

the authors brought up a 3-parameter theory and deduced its theoretical common solution.At the same time

the theoretical range of n

a very important parameter

was given

too.In comparison with previous theories

the 3-parameter theory's basic differential equation is more common

and its deduction is stricter

and the convergence of its common solution is better.In addition

because for the 3-qarameter theory the idea that every parameter is variable has been adopted

it is able to break through the theoretical restriction of its linear-elastic basic equation.So the 3-parameter theory is essentially different from previous theories and its calculation result is better.