  Based on the mathematical-physical model of pavement mechanics, a multilayer
elastic system with interlayer friction conditions is constructed. Given the
complex boundary conditions, the corresponding variational inequalities of the
partial differential equations are derived, so that the problem can be analyzed
under the variational framework. First, the existence and uniqueness of the
solution of the variational inequality is proved; then the approximation error
of the numerical solution based on the finite element method is analyzed, and
when the finite element space satisfies certain approximation conditions, the
convergence of the numerical solution is proved; finally, in the trivial finite
element space, the convergence order of the numerical solution is derived. The
above conclusions provide basic theoretical support for solving the
displacement-strain problem of multilayer elastic systems under the framework
of variational inequalities.
