For the case of narrow excavations such as subway stations and underground pipe

the width of the soil mass in passive zone is limited

so it’s unsuitable to use the classical Coulomb or Rankine earth pressure theory to calculate the passive earth pressure. A finite element numerical model for retaining wall in narrow excavations is presented. The slip surfaces in the soils at passive limiting state with different widths of soils when the walls translating are investigated. Based on the concept of Coulomb sliding soil wedge

a new theoretical model for determining passive earth pressures against translating rigid retaining walls in narrow excavations is proposed. The formulae of the inclination angles of slip surfaces and coefficients of the resultant passive pressures are obtained. Then the horizontal differential element method is introduced and the unit passive pressures and the points of application of the resultant earth pressures are proposed. The factors that influence the inclination angle of slip surface under this circumstance are studied in detail. The comparisons between theoretical and numerical values show that the proposed equations satisfactorily predict the earth pressure on the wall. It is also shown that if the width of soil mass in passive zone is less than a critical value and the wall friction can not be negligible

the inclination angles of slip surface and the passive earth pressures are larger; while the heights of points of application of pressures are less than Coulomb’s solution. The narrower the pit or the rougher the wall-soil interaction is

the more significant the differences are.