Abstract: Soil movement laws induced by shallow tunnel excavation had been covered by many researchers, but the research on the horizontal displacement induced by tunnel excavation is insufficient. Based on the summary and comparison of three formulas of soil layer’s settlement, a formula for calculating the horizontal displacements in the soil above the tunnel is derived by combining one of the soil settlement theories and the assumption that soil is incompressibility. Results of the formula are compared with the published data in relevant papers and verified by the finite-element simulation results. It is shown that the derived formula is capable enough for forecasting and describing the horizontal displacements of the soil induced by shallow tunnel. In addition, the vector angle’s formula of soil’s displacement is obtained based on the formulas of soil settlement and horizontal displacement; and it’s also compared with O’Reilly and New’s method. The comparison shows the agreement with some researchers’ published relevant conclusions, which verifies the applicability of this formula for soil displacement. The research results will provide theoretical references for calculating and controlling the horizontal displacements of soil in relevant practical projects.

Key words: shallow tunnel, horizontal displacement, displacement model, soil settlement theory, displacement vector