DiscussionsThis study makes an atte

DiscussionsThis study makes an attempt to investigate the twin-tunnelling-induced ground stiffness change by extending the work of Divall et al. (2017). In order to realize the framework, several assumptions and simplifications are made. In addition, there are some important issues of this study that need to be discussed as:1. Based upon Eq. (4), the magnitude of G is also governed by the value of Su. As discussed previously, the undrained shear strength Su of surrounding soil is to a certain extent altered by tunnelling construction. However, in the framework of critical state soil mechanics (Schofield and Worth, 1968) and Mair and Taylor (1993), the change of Su is negligible in the elastic zone where is mainly investigated in this study. As depicted in Fig. 10(a), G2/G1 for radial distance of about 5r are 3.9 for ° and 0.23 for °, respectively. In comparison, thechange ratio of Su must be much slighter than G2/G1 as this area is far away fromthe tunnel, validated by Lin and Penumadu (2005). This phenomenon can verify that the assumption for determining G is reasonable.2. As shown in Fig. 8, the tested points for ° and ° are well fitted by linear functions, but °, 45° and 60° with relatively low linearity resulting from the factors like nonuniformity of soil because of sampling and measurement error. In real projects, the factors may include deposition effects and nonuniformdisturbance caused by nearby construction. Hence, the framework of this study can be used to evaluate the uniformity of the ground condition around a single tunnel by subsurface ground settlement.3. It is well recognized that the shear modulus of soils generally reduces with increasing levels of shear stress and shear strain (Atkinson and Sallfors, 1991). The straight line of graph of r1/r plotted against r/dr around T1 (Fig. 8) indicates thatthe shear modulus G remains constant in radial direction for a certain . Hence, thestraight line demonstrates that the linear elastic- perfectly plastic soil model used in the framework is reasonable. In addition, since shear modulus used herein is within linear elastic range (Mair and Taylor, 1993), the change of shear stiffness found in this study is reasonably believed to be attributed to the rotation of principal stress axes, but magnitudes of shear stress and shear strain.4. The green field stress state of soils around T2 is initially altered due to T1 construction. The stress state after T1 construction completed will be altered again due to T2 construction. After twin-tunnelling completed, magnitude and direction of shear stress and shear strain vary significantly with relative locations. In addition, during twin-tunnelling, the rotation of principal stress axes occurs. It is acknowledged that all these factors are unrealistic to be exactly determined. This study, hence, makes an attempt to determine and explain the shear stiffness changedue to twin-tunnelling. The tendency of shear stiffness change around T2 can explain the phenomenon of ground settlement above closely spaced twin tunnels in soft ground.