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.

Understanding the response of sand to complex loading conditions is vital for practical geotechnical engineering. Circular rotational shear is a special stress path where the magnitudes of three principal stresses vary following a circular stress trajectory in the it-plane with their directions fixed. Although experimental studies under such stress paths are limited, the discrete element method appears to be an appealing approach to examine the response of granular materials to varying complex loading paths in numerical virtual tests. This study presents comprehensive numerical simulations of granular samples subjected to a circular stress path under varying conditions, including samples prepared with different bedding-plane angles and densities and subjected to different stress ratios. Both macroscopic and microscopic behaviors are presented and interpreted. A contactnormal-based fabric tensor is adopted in a detailed analysis to measure the internal structure of the granular assembly. The fabric, strain, and strain increment tensors are decomposed with respect to the stress tensor, and the evolutions of these components are presented along with the key influential factors. The results obtained in this study provide useful physical insight for the development of constitutive models for granular soils under general loading conditions.

The constant volume behavior of sands is substantially influenced by the initial stress anisotropy. This research aims to investigate the stress anisotropy effect by conducting a series of bidirectional direct simple shear tests that can apply initial shear stress on a sample in different directions during the consolidation stage. The experimental program provides insights into the impacts of the initial shear stress and the subsequent principal stress rotation (PSR) on some critical aspects of soil behavior, including the onset of instability, brittleness index, phase transformation, and the critical state line. The findings show that the onset of instability and the brittleness indices are significantly dependent on the initial stress anisotropy. In contrast, the critical state and phase transformation lines are not influenced by the initial anisotropy of the stress state, even in the presence of PSR. Furthermore, the study gives particular attention to the non-coaxiality between the major principal stress and strain rates to illustrate how the non-coaxiality decreases with increasing shear strain. The research also explores the non-coaxiality between the resultant shear stress and shear strain rate and suggests a predictive flow rule accordingly. The results reveal that a substantial level of non-coaxiality may exist between the resultant shear stress and the shear strain rate.

This study investigated the impact of major principal stress direction angle (alpha) and intermediate principal stress coefficient (b) on the stress-strain behavior of silt sand soil through directional shear tests under isotropically consolidated drained conditions. Analyzing octahedral stress-strain relationships, shear stress-strain behaviors, radial and circumferential strains, shear stress ratios, and non-coaxial characteristics, findings show that both b and alpha significantly influence strain components with radial strain remaining stable and circumferential strain being dependent on both factors. Anisotropy in circumferential strain is notably affected by alpha and b, while radial strain transitions from tensile to compressive states by increasing b values. Initial loading stages exhibit similar characteristics, but it increased anisotropic with shear stress particularly at b = 0.5 and b = 1. Shear strength is notably influenced by b and alpha, with peak shear stress exhibiting direct proportionality to alpha angles between 0 and 45 degrees, and an inverted relationship beyond 45 degrees. Material strength is significantly impacted by stress orientation with pronounced non-coaxial behavior observed at angles other than 0 degrees, 45 degrees, and 90 degrees. These findings emphasize the intricate relationship between stress coefficients and material behavior providing significant insights into silt sand soil responses under varying stress conditions.

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.

The shape of the failure locus of a material is significant for its strength predictions. Even when constitutive models include the same critical stress surface, different critical stress ratios can be predicted for an identical applied isochoric strain path. In this article, we investigate critical stress predictions of different constitutive models, which include the surface according to Matsuoka-Nakai (MN). We perform analytical investigations, true triaxial test simulations with hypoplasticity and barodesy, and discrete element modelling (DEM) simulations to investigate the friction dependency of the stress Lode angle. Our results demonstrate that in hypoplasticity, the direction of the deviatoric stress state at critical state depends solely on the direction of the applied deviatoric strain path. In contrast, in barodesy, the predictions are also dependent on the friction angle of the material. In addition, we compare these results with those obtained with a standard elastoplastic MN model. To validate this friction dependency on the stress Lode angle, we conduct DEM simulations. The DEM results qualitatively support the predictions of barodesy and suggest that a higher friction results in a higher Lode angle at critical stress state.

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.