Huaning Wang

Analytical Solutions for the Construction of Deeply Buried Circular Tunnels with Two Liners in Rheological Rock

The construction of underground tunnels is a time-dependent process. The states of stress and strain in the ground vary with time due to the construction process. Stress and strain variations are heavily dependent on the rheological behavior of the hosting rock mass. In this paper, analytical closed-form solutions are developed for the excavation of a circular tunnel supported by the construction of two elastic liners in a viscoelastic surrounding rock under a hydrostatic stress field. In the solutions, the stiffness and installation times of the liners are accounted for. To simulate realistically the process of tunnel excavation, a time-dependent excavation process is considered in the development of the solutions, assuming that the radius of the tunnel grows from zero until its final value according to a time-dependent function to be specified by the designers. The integral equations for the supporting pressures between rock and first liner are derived according to the boundary conditions for linear viscoelastic rocks (unified model). Then, explicit analytical expressions are obtained by considering either the Maxwell or the Boltzmann viscoelastic model for the rheology of the rock mass. Applications of the obtained solutions are illustrated using two examples, where the response in terms of displacements and stresses caused by various combinations of excavation rate, first and second liner installation times, and the rheological properties of the rock is illustrated.

Analytical Solutions for Tunnels of Elliptical Cross-Section in Rheological Rock Accounting for Sequential Excavation

Time dependency in tunnel excavation is mainly due to the rheological properties of rock and sequential excavation. In this paper, analytical solutions for deeply buried tunnels with elliptical cross-section excavated in linear viscoelastic media are derived accounting for the process of sequential excavation. For this purpose, an extension of the principle of correspondence to solid media with time varying boundaries is formulated for the first time. An initial anisotropic stress field is assumed. To simulate realistically the process of tunnel excavation, solutions are developed for a time-dependent excavation process with the major and minor axes of the elliptical tunnel changing from zero until a final value according to time-dependent functions specified by the designers. In the paper, analytical expressions in integral form are obtained assuming the incompressible generalized Kelvin viscoelastic model for the rheology of the rock mass, with Maxwell and Kelvin models solved as particular cases. An extensive parametric analysis is then performed to investigate the effects of various excavation methods and excavation rates. Also the distribution of displacements and stresses in space at different times is illustrated. Several dimensionless charts for ease of use of practitioners are provided.

Investigation of the effect of different gravity conditions on penetration mechanisms by the Distinct Element Method

Purpose – The purpose of this paper is to present an investigation of the effect of different gravity conditions on the penetration mechanism using the two-dimensional Distinct Element Method (DEM), which ranges from high gravity used in centrifuge model tests to low gravity incurred by serial parabolic flight, with the aim of efficiently analyzing cone penetration tests on the lunar surface. Design/methodology/approach – Seven penetration tests were numerically simulated on loose granular ground under different gravity conditions, i.e. one-sixth, one-half, one, five, ten, 15 and 20 terrestrial gravities. The effect of gravity on the mechanisms is examined with aspect to the tip resistance, deformation pattern, displacement paths, stress fields, stress paths, strain and rotation paths, and velocity fields during the penetration process. Findings – First, under both low and high gravities, the penetration leads to high gradients of the value and direction of stresses in addition to high gradients in the ve...

Analytical Data Based Time-Dependent Mechanical Responses of an Intergranular Bond Considering Various Bond Sizes

Geo-materials usually exhibit time-dependent mechanical behavior sand deform gradually with time even under an applied constant strain. In this study, the time-dependent stiffness and strength of an intergranular bond in discrete element method (DEM) are proposed based on the modified Dvorkin’s analytical solutions. The proposed stiffness can provide an alternative approach to determine the reasonable micro parameters in DEM according to actual bond size and bond materials. Meanwhile, through introducing the long-term strength of materials into the unified strength theory, the time-dependent bond strength can be formulated by fitting the analytical data. It is believed that our achievements can give valuable reference to the determination of bond stiffness and bond strength at different time points for various bond sizes in DEM.

Exploring Grading-Dependency of Deformation Modulus of Loose Aggregates of Spherical Particles Using DEM

Aggregates of coarse grains are commonly used in earthworks. Their deformation parameters are usually extrapolated from experimental data obtained from finer materials with scaled grading. To ultimately achieve a rational and robust extrapolation law, this study employs the distinct element method to investigate the grading effect on the deformation modulus of coarse aggregates. Triaxial compression tests are simulated on a set of specimens with different grain size distribution (GSD). The relations are examined between the deformation modulus and the shape coefficients of GSD curve, coordination number, and volume weighted coordination number. The results show that the mechanical coordination number is insufficient to determine the deformation modulus under a wide range of GSD. Instead, regardless of variation in GSD, a unique correlation is found between the deformation modulus and the volume weighted coordination number, which can be estimated from the effective void ratio.

Effect of Inter-particle Rolling Resistance on Passive Earth Pressure against a Translating Rigid Retaining Wall

The presence of the inter-particle rolling resistance of soil grains results in higher bulk shear strength in the soil, which relates to the earth pressure calculation based on the classic theory. This paper focuses on the effect of the inter-particle rolling resistance on the earth pressure against a rigid retaining wall. A particle contact model considering the inter-particle rolling resistance was implemented into the distinct element code PFC2D, which was then used to simulate a rigid wall retaining a sandy backfill. The passive earth pressure against the wall subjected to a translational displacement was analyzed and compared with results without considering the inter-particle rolling resistance. The influence of the inter-particle rolling resistance was examined from the microscopic scale (e.g., averaged micro-pure rotation-rate) as well as the macroscopic scale (e.g., the magnitude and action point of resultant earth pressures). The results show that the inter-particle rolling resistance of the backfill strongly affects the value of passive thrust behind the wall, but it has no significant effect on the action position of the thrust. The distribution of micro-pure rotation-rate (APR) in the backfill provides an insight into the connection between inter-particle rolling resistance to the energy dissipation in the shear zone behind the wall.

DEM simulation of footpads quasi-statically penetrating into granular ground

The bearing capacity of a footpad used in a typical lunar detector is investigated using distinct element method (DEM) with a focus on the effect due to the wing plate of the footpad. In DEM simulation, a series of footpads with varying curvatures of wing plates were configured to penetrate quasi-statically into a granular ground. The ultimate capacity of the footpad is obtained from the relationship between the penetration resistance and the penetration displacement. The results indicate that the ultimate bearing capacity of the footpad is largely affected by the curvature radius of the wing plate. A smaller radius, i.e., smooth transition between the base and wing plates, is beneficial for a larger bearing capacity due to increasing contribution of the wing plate. The failure wedge of soils underneath the footpad is also affected by the wing plate. The wedge becomes shorter due to the presence of the wing plate.