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.

翻译：基于路面力学的数学物理模型，构建了具有层间摩擦条件的多层弹性系统。针对复杂的边界条件，推导了相应偏微分方程的变分不等式，使得该问题可在变分框架下进行分析。首先证明了变分不等式解的存在唯一性；随后分析了基于有限元法的数值解逼近误差，并证明当有限元空间满足特定逼近条件时数值解具有收敛性；最后在分片有限元空间中推导了数值解的收敛阶。上述结论为在变分不等式框架下求解多层弹性系统的位移-应变问题提供了基础理论支撑。