The experiments were conducted under limited stress conditions, namely qh=60kPa, p'=100kPa in the shear history process (Toyota et al., 2001). Therefore, the uniqueness of the proposed elastic boundary was investigated by changing the stress level. qh=140kPa, p'=200kPa conditions were chosen as a new stress level. Not only the effective mean stress p', but also the stress ratio qh/p', was changed from 6 to 7 under these conditions.

Figure 5(a) shows the stress-strain relationships during the drained shear process where αs = 45o, qh=140kPa, p'=200kPa and αh has different values. The b values during the shear history and during the shear process are both equal to 0.5 in these tests. Where αh is coincident with αs, the linear section before yielding is maintained up to the largest deviator stress q. When the difference between αh and αs becomes larger, the deviator stress q, which can maintain elasticity, decreases during the drained shear process. Figure 5(b) shows the volumetric strain-shear strain relationships in the same case shown in Fig. 5(a). Where the difference between αh and αs becomes larger, a more contractive response is observed.

Figure 6(a) shows the stress-strain relationships of bs=0 where αhs=45o, qh=140kPa, p'=200kPa and different values of bh has different values. The yield points differ slightly in various values of bh, and where bh is coincident with bs, the initial linear section before yielding is maintained up to the largest deviator stress q. When the difference between bh and bs becomes larger, the deviator stress q, which maintains elasticity, is smaller. The εv - εs relationships for the same case given in Fig. 6(a) are shown in Fig. 6(b). These relationships have a similar tendency to the stress-strain relationships. That is, when the difference of b between the shear history and the shear process becomes larger, more contractive volumetric strain occurs. A similar tendency in the effects of αh has been indicated in Toyota et al. (2001).

It is described in Toyota et al. (2001) how the non-coaxiality between stress and strain is generated by the difference in the direction between the shear history and the shear. The relationships between αε and εs taking account of the effect of αh are shown in Fig. 7. The experiments were carried out under αs=45o, bh=bs=0.5 and qh=140kPa conditions. The gaps between αs and αε hardly exist in the cases of the virgin shear, αh=45o conditions and αs=-45o conditions. However, the direction of shear strain tends to converge on the direction of shear stress with the increase of shear strain. It is seen from Fig. 7 that non-coaxiality becomes almost extinct at 5% shear strain.

Figure 8 shows the relationships between ry, α' and b' in three dimensional space. The proposed elastic boundary between ry, α' and b' is indicated as follows (Toyota et al., 2001):

The yield points are determined by the same method as Toyota et al. (2001). The linear part of the stress-strain curve is moved in parallel with an offset of εs0.04% as the qemax of the tests which are subjected to qh=140kPa becomes approximately 140kPa by this method.

The contour lines of ry on the α' - b' plane are shown in Fig. 9. The contour lines were calculated in equation 1. In this figure, black points show experimental conditions and the values in brackets indicate the results of ry. Although it is a limited experimental case, it is clear from Figs. 8 and 9 that the results from this study correlate well with the results from Toyota et al. (2001). This means that the proposed elastic boundary is unique in spite of the stress level. Therefore, the universality of the elastic boundary concerning stress level is deduced.