Journal of Engineering Mechanics

The stability and deformation of shallow tunnel faces are hard to predict, and the associated failure mechanisms are also indistinct to date. In this work, we incorporate the softening function and strain-dependent dilation model into a smoothed particle hydrodynamics (SPH) framework to simulate the collapse behaviors of shallow tunnel faces in cohesive–frictional soils under the open-face excavation condition. To this end, the stratum is modeled as a cohesive–frictional soil described by the elastoplastic constitutive model in combination with the Drucker–Prager yield criterion. Softening and strain-dependent dilation behaviors of soils are described by the softening function and the dilation model, which are incorporated into the constitutive model in the framework of the SPH method. For the deformation analysis, the effects of the cover depth variation on face extrusion and ground surface subsidence are investigated. For the face stability analysis, the impacts of the cohesion and the internal friction angle of surrounding soils on the safety factor of shallow tunnel faces are highlighted. Then, comparison is made between the results obtained from the present SPH method and those given by the finite-element method (FEM) and existing centrifuge model tests to verify the proposed SPH procedure. Ultimately, the main outcomes of the current work, including deformation features and safety factors of shallow tunnel faces, are presented.

Simulation of fluctuating wind speed field is of paramount significance in the design of large flexible structures. To circumvent the difficulty due to the decomposition of cross power spectral density (PSD) matrix and the interpolation between discretized spatial points, a wavenumber–frequency joint spectrum-based spectral representation method (SRM) has been developed recently. To further improve the efficiency and accuracy, the stochastic harmonic function (SHF) representation is extended in the present paper for the simulation of stationary and nonstationary fluctuating wind fields in two spatial dimensions. In contrast to the SRM, in addition to the phase angles, the frequencies and wavenumbers are also random variables over partitioned wavenumber–frequency subdomains. Furthermore, a strategy of dependent random frequencies and wavenumbers based on the SHF is proposed so that the number of random variables can be considerably reduced by 3/7. A new acceptance–rejection criterion, which avoids the artificial intervene, is suggested based on the $p$-power joint spectrum, and the subdomains are correspondingly determined by the Voronoi cell partitioning. For illustrative purposes, two numerical examples for the simulation of stationary and nonstationary fluctuating wind speed fields in two spatial dimensions are addressed, demonstrating the effectiveness of the proposed method in considerably reducing the random variables as well as the computational efforts.

Shear banding is often regarded as a discontinuity problem that occurs in a sample of materials with finite dimension. The shear band thickness is studied in the context of classical continuum mechanics with apparently no intrinsic length scale to relate local and global behavior of the sample. The method of decomposed deformation field has been presented to simulate the behavior of a sample of finite dimension with a localized deformation. The procedure has been explained for a simple problem of biaxial loading, and a procedure to estimate the shear band thickness based on experimental observations is presented.

This paper presents an interface-capturing method for two-phase flows with large-amplitude free-surface motion. The method is developed by embedding the level-set equation in the momentum balance equations via dependency of the material properties on the signed distance field. Subsequent derivation of the fine-scale variational equation that is facilitated by the Variational Multiscale (VMS) framework leads to interfacial terms that stabilize the moving interface. These interfacial terms are operational across the zero contour of the signed distance field that implicitly represents the air–water interface. For plunging free-surface motions, the method is augmented with a reinitialization process that is based on a stabilized form of the Eikonal equation and reconstructs the signed distance field. Conservation of mass in extreme free-surface motions is maintained via a mass-conservation term that is based on the notion of minimizing the error in the computed signed distance field. Benchmark test cases of two-dimensional (2D) and three-dimensional (3D) dam-break problems are presented to validate the method and show its range of applicability.

The accurate computation of stress intensity factors (SIFs) of face-loaded cracks is of significant importance for engineering practices. Based on the analytical stress field of a central crack in an infinite plane subjected to a pair of crack-face concentrated forces, a simple stress substitution approach that replaces the unknown actual stress field by that of the Williams’ solution for traction-free cracks is proposed and used in conjunction with the subregion generalized variational principle and quadrature element method (QEM) for computation of the SIF. This approach is validated by a series of representative problems, including different crack configurations and loading conditions. The comparisons between the analytical or approximate solutions and the numerical results suggest that the approach produces reasonably accurate SIFs when the size of the complementary energy subregion is confined to be 0.2–0.3 times the (half) crack length, even with the coarsest mesh. The accuracy can be further improved by smaller subregion size and smaller elemental maximum aspect ratio.

To understand the sediment-transport process in an open-channel turbulent flow, the time-averaged profiles of streamwise fluid velocity and volumetric particle concentration in suspension must be given simultaneous treatment because they are closely interrelated through particle–turbulence interaction. Presence of sediment particles increases the density of a fluid-sediment mixture, which makes the flow stratified and obstructs the settling of sediment particles. The greater the amount of sediment particles in fluid, the stronger the effects of stratification and hindered settling. Therefore, generalizing existing works, this study attempts to model the velocity and concentration simultaneously, incorporating the aforementioned effects. The coupled system of odes arising from the derivation is strongly nonlinear in nature, and the analytical solution needs a special mathematical tool. To that end, a novel analytical method called the homotopy analysis method (HAM) is employed to obtain the explicit series solution to the system. The methodology is a nonperturbation approach, and the convergence can be tackled easily through some convergence control parameters. The solutions obtained are found to be stable and are validated with numerical solution as well as with relevant experimental data available in the literature. Further, the models have been physically interpreted through the effects of the turbulent factors incorporated.