Starting from the calculation model of the two-dimensional soil-cantilever rigid wall under horizontal simple harmonic resonance action

and based on the theory of wave mechanics

the dynamic response characteristics of two-dimensional soil-cantilever rigid wall were studied considering the vertical stress and vertical displacement of soil layer. Firstly

the vibration equation of the soil layer was transformed to obtain the equation of the volumetric strain ?

which was solved by the method of separation of variables. Then

the inhomogeneous equation of the displacement motion equation was obtained by substituting the solution back to the vibration equation. The definite solution of the vibration equation was obtained by combining the interaction conditions between the wall and the soil layer as well as the far-field boundary conditions. Then more strict analytical solutions of the earth pressure on the wall

the shear force at the bottom of the wall and the bending moment of the rigid underground wall were obtained. Compared with the vertical stress-neglected solution and the vertical displacement-neglected solution

it is shown that the obtained solution can reflect one more resonance frequency

and when the Poisson’s ratio of soil is greater than 0.45

the vertical displacement-neglected solution is meaningless. Through parameter analysis

it is shown that the excitation frequency and soil damping factor have great influence on the dynamic response of the wall

whereas the vibration mode order considered has less impact.