Method for calculating seismic active earth pressures on cantilever retaining walls

In order to determine the seismic active earth pressures on the stem of a cantilever wall, the resultant of the earth pressures on the assumed plane wall back is firstly derived using the upper-bound limit analysis and the pseudo-static method for five types of potential failure modes based on the log-spiral slip surface. The oblique and horizontal slice methods are secondly adopted respectively for the slide wedge mass and the local soils between the stem and the plane wall back to determine the earth pressure distribution on the stem, in which the earth pressure on the plane wall back are calibrated by the upper bound solution for the resultant of earth pressures. Some examples show that the proposed distribution of the earth pressures on the stem with depth takes on a parabolic profile with the peak point on the lower segment of the stem under the static condition, whereas it presents a nonlinear decreasing mode fairly identical with the test results under the seismic condition. The application point of the resultant is located on the lower and upper segments of the stem under the static and seismic conditions, respectively. The parameter study shows that the increase of horizontal seismic coefficient, heel plate width and stem back inclination induces a significant increase of the seismic active earth pressures on the middle and upper segments of the stem. Under the seismic condition, broadening the width of heel plate can cause the increase of the stresses on the stem. In particular, the proposed earth pressures on the stem are 9%~14% higher than those by China's code for design of retaining structures of railway earth works under strong earthquakes, and the proposed bending moments at the stem bottom are noticeably greater than those by the above code, which naturally means the Norm is not safely suitable for the aseismic design under strong earthquakes.