Shield tunnelling through densely populated urban areas inevitably disturbs the surrounding soil, potentially posing significant safety risks to nearby buildings and structures. The constitutive models currently employed in numerical simulations for tunnel engineering are predominantly confined to the assumptions of isotropy and coaxiality, making it challenging to adequately capture the complexity of the mechanical response of the soil surrounding the tunnel. Based on the proposed non-coaxial and anisotropic elastoplastic Mohr-Coulomb yield criterion, this study carries out numerical simulation analyses of soil disturbance induced by urban shield tunnelling. Herein, the anisotropic parameters n and /1 jointly determine the shape of the anisotropic yield surface. The results demonstrate that rotation of the principal stress axes is observed in most areas of the soil surrounding the tunnel face, with the phenomenon being particularly pronounced at the crown and the invert of the tunnel. As the anisotropic parameter n decreases, the maximum surface settlement above the tunnel axis increases. The influence of anisotropy on higher-stress unloading coefficients is significant, resulting in the development of a wider plastic zone around the tunnel. As the coefficient of lateral earth pressure at rest K0 increases, the maximum surface settlement gradually reduces. Under the influence of anisotropic parameter /1 or non-coaxial parameter k, the maximum surface settlement exhibits an approximately linear relationship with K0. However, the anisotropic parameter n has a significant influence on the trend of the maximum surface settlement with respect to K0, which leads to a non-linear relationship. Neglecting the effects of soil anisotropy, noncoaxiality, and the coefficient of lateral earth pressure at rest may lead to design schemes that are potentially unsafe. The results of this research can provide engineers with design bases for construction parameters and soil disturbance control while shield tunnelling in sandy pebble soil.

In this paper, the thermodynamics of granular material is developed to get constitutive relations for unified modelling of undrained viscoplastic flow behavior with complex combined effects of state, rate, time, and path. The proposed formulations of energy storages and dissipations lead to the state-dependent hyperelasticity with an elastic instable region and the viscoplasticity with considerations of the granular kinetic flow. Subjected to strict thermodynamic restraints, a generalized law of viscoplastic shear flow is proposed for granular material as the combination of state-based and rate-based viscoplastic flows, which predictively captures the diversity of undrained granular flow pattern with elastic-plastic coupled non-coaxialities among stresses, (total/ viscoplastic/elastic) strains, and their increments. The viscoplastic flow is also linked with the granular temperature that accounts for the granular kinetic fluctuation varying from dilative dense flow to large unlimited flow under shear-induced static liquefaction. This enables predictions of the creep and the stress relaxation as well as the over- and -under shooting of stress under stepwise changes in strain rate. The model is well validated by predicting the flow potential, phase transformation, critical state, and rate/time effects under undrained conventional triaxial shearing and simple shearing for Toyoura sand, which are strongly related to the void ratio, the confining pressure, the shear stress, and the shear mode.

Previous experimental tests on clays have confirmed the non-coincidence of principal strain increments with principal stress axes even though the stress rate is colinear with the current stress. To simulate the non-coaxial behavior of saturated clay subjected to monotonic proportional or non-proportional loading with constant principal stress rate directions, an anisotropic hypoplastic model is presented in this paper. The model is proposed by incorporating an improved anisotropic asymptotic state boundary surface (ASBS) and a non-coaxial asymptotic strain rate direction into the original explicit-ASBS hypoplastic model. The non-coaxial flow results from a non-coaxial stress rate defined by a Gram-Schmidt orthogonalization process based on a reference stress tensor. The capability of the proposed model is demonstrated by simulating the test data performed in hollow cylindrical apparatus (HCA) on Wenzhou clay and Shanghai clay with different drainage conditions and initial consolidation states. In addition, a series of numerical stress probing tests have been conducted to gain further insights into the properties of the proposed model.

Non-coaxiality refers to the non-coincidence of the principal stress direction and the principal plastic strain rate. In order to quantitatively investigate the non-coaxial behaviour of clay under cyclic loading, undrained cyclic simple shear tests are conducted on the red clay collected in Heilongtan. The Multi-directional Dynamic Cyclic Simple Shear (MDDCSS) was used to implement this experiment. Both monotonic and cyclic simple shearing are applied to the sample and the corresponding soil behaviours are analysed. Parametric analysis in terms of different moisture content and initial stresses are systematically performed. Conclusions can be drawn that the principal stress direction is advantageous to the principal plastic strain increment direction at the initial stage of shearing, and gradually coincide with the shear progression. In addition, the degree of non-coaxiality gradually reduces with an increase in the stress ratio. These results can provide an experimental basis for constitutive modelling under the principal stress rotation.