ABSTRACT

Winkler modeling is usually used to calculate retaining wall deformation in Japan. Winkler model uses an elastic beam to express a retaining wall and assumes external pressure acting at the ground side and lateral ground reaction on the excavation side. Lateral ground reaction on the excavation side is calculated by use of soil springs at different depths. The method of setting soil springs is important in this case. A commonly used soil spring setting method is to assume that ground consists of elastic and plastic regions (bilinear model) and soil springs in the elastic region are constant (Architectural Institute of Japan, 2002). This method, however, ignores the nonlinearity of soil and in many cases unable to simulate retaining wall behaviors. As a result of various studies on soil spring setting based on observed retaining wall displacements, therefore, other methods have been reported. They include the method of reducing soil springs by use of vertical effective stress at each stage of excavation (Motoi, 2009) and the method of reducing soil springs on the basis of the G/G0 – γ relationship (Terada, 2005). A problem of the method by Motoi (2009) is that soil springs are calculated by use of post-excavation vertical effective stress, and changes in strain are ignored. A problem of the method Terada (2005) is that although changes in effective stress and strain are taken into consideration, the G/G0 – γ relationship under effective stress is used regardless of the

soil spring evaluation method for the calculation of the lateral ground reaction on the excavation side. Figure 2 shows the relationship between retaining wall displacement and the lateral pressure on the excavation side. This study does not take into account the decrease in the lateral pressure behind the retaining wall (Katsura, 1996). Changes in the lateral pressure on the excavation side due to excavation during the process from the beginning of excavation until after the first excavation (path a→c) can be expressed as

0 +− ∫∫ (2)

where pp,1 is the lateral pressure on the excavation side the end of the first excavation (kN/m2), peq,0 is lateral pressure on the excavation side at the start of excavation (kN/m2), peq,1 is equilibrium lateral pressure after the first excavation (kN/m2), y1 is retaining wall displacement at the end of the first excavation (m) and kht(y) is tangential soil spring at any depth on the excavation side (kN/m2/m). Path a→c consists of path a→b and path b→c. The second term of the right-hand side of Eq. (2) corresponds to the changes in the lateral pressure on the excavation side on path a→b, and the third term corresponds to changes in the lateral pressure on the excavation side on path b→c. If kht(y) is assumed to be constant, then the results will be identical to the results obtained by the conventional method (Architectural Institute of Japan, 2002) shown with the gray lines in Fig. 1. It is thought likely, however, that as in the case of decreases in soil stiffness in the vertical direction due to excavation and structural construction (Tamaoki et al., 1993), soil stiffness in the lateral direction also decreases because of decreases in overburden pressure and increases in soil strain. This indicates that a function capable of expressing nonlinearity should be used for the tangential soil spring on the excavation side, kht(y). In this study, it is assumed

that the tangential soil spring on the excavation side, kht(y), in the displacement-lateral pressure relationship can be expressed by a hyperbola, and the tangential soil spring on the excavation side, kht(y), on path b→c is expressed as

k y k p pht

{ (k y )}a , , =

where kh0 is the initial soil spring at any depth (kN/m2/m), and pmax,1 is the extreme lateral pressure on the excavation side (kN/m2) during the first excavation. To obtain the hyperbola, the initial soil spring kh0 is determined according to soil survey results, and the extreme lateral pressure is calculated from the Rankine-Resal formula. The brace preload path is assumed to be path c→d on the assumption that the post-excavation secant soil spring is maintained. To determine the soil spring during the second excavation, it is assumed that the initial soil spring at the start of excavation is the same as the secant soil spring after the first excavation, and Eq. (3) is applied by defining the point (e) at which the second excavation is started as the origin. By doing this, the soil spring that takes into consideration the changes in ground stress and strain at each stage of excavation can be evaluated easily.