Strength Model of Backfill-Rock Irregular Interface Based on Fractal Theory

In the two-step open stope subsequent filling mining method, the determination of the strength model for the backfill-rock interface is of great engineering significance to study the stress distribution and stability of the backfill in the stope. Considering the deformation mechanism of the interface and the interaction of the asperities, a strength model for backfill-rock with irregular interface has been proposed based on fractal theory, which can effectively describe the shear mechanical behavior of interfaces with random roughness. The model has been compared with the two-body mechanistic model and good agreements have been achieved. The results show that the shear strength of the interface changes non-linearly with increasing fractal dimension D, when the fractal dimension D is in the range of 1∼1.12. The complete relationship between the interface shear strength and the fractal dimension is given, as the fractal dimension increases from 1 to 2 based on the presented model. At the same time, the quantitative relationship between the interface and backfill friction angles during direct shear testing is analyzed.

An improved LTI algorithm for multiphase raytracing in undulating surface model

Based on the linear traveltime interpolation (LTI) algorithm, we propose an improved LTI (referred as ILTI) algorithm for multiphase seismic ray tracing, which uses a velocity node in model parameterization and introduces secondary nodes between adjacent velocity nodes. To better fit the undulating surface model, an irregular velocity node is used in near the irregular interface, and regular velocity nodes are still used in the region far away from the irregular interface. We derive an iterative fixed-point formula for calculating traveltime. By combining multistage computational technology and wavefront narrowband expansion technology, the proposed ILTI algorithm can efficiently trace the multiphase seismic raypath and compute the corresponding traveltime field. Through comparison and analysis with the traditional LTI algorithm, its computational accuracy can be highlighted by at least one order of magnitude. Compared with the popular fast marching method (FMM) and irregular shortest-path (ISPM) algorithms, it also has the advantages in terms of computational accuracy and efficiency. Numerical simulations in the Marmousi model show that the algorithm is also suitable for tracking multiphase seismic rays in the complex velocity model.

Fluid-solid coupled full-waveform inversion in the curvilinear coordinates for ocean-bottom cable data

Marine seismic exploration with ocean-bottom cable technology is able to record P- and S-wave information simultaneously. Elastic full-waveform inversion (EFWI) uses P- and S-waves to invert multiple parameters with adequate amplitude information and complete illumination of the subsurface. To calculate the wavefield within EFWI, we use different formats of wave equations in fluid and solid mediums and an appropriate boundary condition to convert waves on the interface. This partitioned simulation scheme is more stable and efficient than the traditional integrated simulation scheme. However, if the fluid-solid coupled medium has an extremely irregular interface, the conventional finite-difference method with rectangular grids cannot obtain accurate source and receiver wavefields. We use the curvilinear coordinates to overcome this limitation. In the curvilinear coordinates, the irregular interface can be transformed into a horizontal interface. To reduce the crosstalk of inverted P- ([Formula: see text]) and S-velocities ([Formula: see text]), we derive the gradient formulas of [Formula: see text] and [Formula: see text] based on P- and S-wave mode separation in the curvilinear coordinates, and, finally, we develop a 2D curvilinear-grid-based fluid-solid separated-wavefield EFWI (CFS-SEFWI) method. Numerical examples that include an anomaly model and a modified Marmousi II model demonstrate that CFS-SEFWI overcomes the influence of the irregular fluid-solid interface and efficiently reduces crosstalk effects between [Formula: see text] and [Formula: see text]. Our results also demonstrate that this method is less sensitive to noise compared to the conventional CFS FWI method without separating wave modes.

Anti-Plane Shear Wave in Microstructural Media

The present chapter encapsulates the characteristic behavior of anti-plane shear wave propagation in a micropolar layer/semi-infinite structural media. Two types of interfacial complexity have been considered at the common interface which give rise to two distinct mathematical models: (1) Model I: Anti-plane shear wave in a micropolar layer/semi-infinite structure with rectangular irregular interface and (2) Model II: Anti-plane shear wave in a micropolar layer/semi-infinite structure with non-perfect interface. For both models, dispersion equations have been deduced in algebraic-form and in particular, the dispersion equation of new type of surface wave resulted due to micropolarity has been obtained. The deduced results have been validated with classical cases analytically. The effects of micropolarity, irregularity, and non-perfect interface on anti-plane shear wave have been demonstrated through numerical study in the present chapter.

ON THE PROBLEM OF STRAIN LOCALIZATION AND FRACTURE SITE PREDICTION IN MATERIALS WITH IRREGULAR GEOMETRY OF INTERFACES

The interfacial mechanisms of the stress-strain localization in non-homogeneous media are investigated, using a steel substrate - iron boride coating composition subjected to tension as an example. A dynamic boundary-value problem in a plane-strain formulation is solved numerically by the finite-difference method. The curvilinear substrate-coating interface geometry is assigned explicitly in calculations and is in agreement with experiment. Constitutive relations accounting for an elastic-plastic response of the isotropically-hardened substrate and for a brittle fracture of the coating are employed. Three stages of the plastic strain localization in the steel substrate are found to occur due to the irregular interface geometry. Distributions of the stress concentration regions in the coating are shown to be different at different stages. The stress concentration in the coating is demonstrated to increase nonlinearly during the third stage. The location of fracture is found to depend on the strength of the coating.

On Solving the Poisson Equation with Discontinuities on Irregular Interfaces: GFM and VIM

We analyze the accuracy of two numerical methods for the variable coefficient Poisson equation with discontinuities at an irregular interface. Solving the Poisson equation with discontinuities at an irregular interface is an essential part of solving many physical phenomena such as multiphase flows with and without phase change, in heat transfer, in electrokinetics, and in the modeling of biomolecules’ electrostatics. The first method, considered for the problem, is the widely known Ghost-Fluid Method (GFM) and the second method is the recently introduced Voronoi Interface Method (VIM). The VIM method uses Voronoi partitions near the interface to construct local configurations that enable the use of the Ghost-Fluid philosophy in one dimension. Both methods lead to symmetric positive definite linear systems. The Ghost-Fluid Method is generally first-order accurate, except in the case of both a constant discontinuity in the solution and a constant diffusion coefficient, while the Voronoi Interface Method is second-order accurate in the L∞-norm. Therefore, the Voronoi Interface Method generally outweighs the Ghost-Fluid Method except in special case of both a constant discontinuity in the solution and a constant diffusion coefficient, where the Ghost-Fluid Method performs better than the Voronoi Interface Method. The paper includes numerical examples displaying this fact clearly and its findings can be used to determine which approach to choose based on the properties of the real life problem in hand.

Propagation of Love-Type Wave in Porous Medium over an Orthotropic Semi-Infinite Medium with Rectangular Irregularity

Propagation of Love-type wave in an initially stressed porous medium over a semi-infinite orthotropic medium with the irregular interface has been studied. The method of separation of variables has been adopted to get the dispersion relation of Love-type wave. The irregularity is assumed to be rectangular at the interface of the layer and half-space. Finally, the dispersion relation of Love wave has been obtained in classical form. The presence of porosity, irregularity, and initial stress in the dispersion equation approves the significant effect of these parameters in the propagation of Love-type waves in porous medium bounded below by an orthotropic half-space. The scientific effect of porosity, irregularity, and initial stress in the phase velocity of the Love-type wave propagation has been studied and shown graphically.