Analytical exploration of γ-function explicit method for pseudodynamic testing of nonlinear systems

It has been well studied that the γ-function explicit method can be effective in providing favorable numerical dissipation for linear elastic systems. However, its performance for nonlinear systems is unclear due to a lack of analytical evaluation techniques. Thus, a novel technique is proposed herein to evaluate its efficiency for application to nonlinear systems by introducing two parameters to describe the stiffness change. As a result, the numerical properties and error propagation characteristics of the γ-function explicit method for the pseudodynamic testing of a nonlinear system are analytically assessed. It is found that the upper stability limit decreases as the step degree of nonlinearity increases; and it increases as the current degree of nonlinearity increases. It is also shown that this integration method provides favorable numerical dissipation not only for linear elastic systems but also for nonlinear systems. Furthermore, error propagation analysis reveals that the numerical dissipation can effectively suppress the severe error propagation of high frequency modes while the low frequency responses are almost unaffected for both linear elastic and nonlinear systems.     

Numerical simulation for 1975 Haicheng and 1999 Xiuyan earthquake processes by DDA+FEM

Introduction The Xiuyan earthquake(MS=5.4)on Nov.29,1999,occurred between Hushan town and Pi-anling town at the southeast end of the aftershocks of Haicheng earthquake(MS=7.3).These two earthquakes′sequences are highly similar in the way that the foreshocks are very frequent,focal mechanisms of the main shocks are about the same and fault strikes are approximately in the same direction.It is important to study these earthquakes for further research on seismogenesis to fore-cast earthquake…     

Creation of the Cocos and Nazca plates by fission of the Farallon plate

Throughout the Early Tertiary the area of the Farallon oceanic plate was episodically diminished by detachment of large and small northern regions, which became independently moving plates and microplates. The nature and history of Farallon plate fragmentation has been inferred mainly from structural patterns on the western, Pacific-plate flank of the East Pacific Rise, because the fragmented eastern flank has been subducted. The final episode of plate fragmentation occurred at the beginning of the Miocene, when the Cocos plate was split off, leaving the much reduced Farallon plate to be renamed the Nazca plate, and initiating Cocos–Nazca spreading. Some Oligocene Farallon plate with rifted margins that are a direct record of this plate-splitting event has survived in the eastern tropical Pacific, most extensively off northern Peru and Ecuador. Small remnants of the conjugate northern rifted margin are exposed off Costa Rica, and perhaps south of Panama. Marine geophysical profiles (bathymetric, magnetic and seismic reflection) and multibeam sonar swaths across these rifted oceanic margins, combined with surveys of 30–20 Ma crust on the western rise-flank, indicate that (i) Localized lithospheric rupture to create a new plate boundary was preceded by plate stretching and fracturing in a belt several hundred km wide. Fissural volcanism along some of these fractures built volcanic ridges (e.g., Alvarado and Sarmiento Ridges) that are 1–2 km high and parallel to “absolute” Farallon plate motion; they closely resemble fissural ridges described from the young western flank of the present Pacific–Nazca rise. (ii) For 1–2 m.y. prior to final rupture of the Farallon plate, perhaps coinciding with the period of lithospheric stretching, the entire plate changed direction to a more easterly (“Nazca-like”) course; after the split the northern (Cocos) part reverted to a northeasterly absolute motion. (iii) The plate-splitting fracture that became the site of initial Cocos–Nazca spreading was a linear feature that, at least through the 680 km of ruptured Oligocene lithosphere known to have avoided subduction, did not follow any pre-existing feature on the Farallon plate, e.g., a “fracture zone” trail of a transform fault. (iv) The margins of surviving parts of the plate-splitting fracture have narrow shoulders raised by uplift of unloaded footwalls, and partially buried by fissural volcanism. (v) Cocos–Nazca spreading began at 23 Ma; reports of older Cocos–Nazca crust in the eastern Panama Basin were based on misidentified magnetic anomalies.There is increased evidence that the driving force for the 23 Ma fission of the Farallon plate was the divergence of slab-pull stresses at the Middle America and South America subduction zones. The timing and location of the split may have been influenced by (i) the increasingly divergent northeast slab pull at the Middle America subduction zone, which lengthened and reoriented because of motion between the North America and Caribbean plates; (ii) the slightly earlier detachment of a northern part of the plate that had been entering the California subduction zone, contributing a less divergent plate-driving stress; and (iii) weakening of older parts of the plate by the Galapagos hotspot, which had come to underlie the equatorial region, midway between the risecrest and the two subduction zones, by the Late Oligocene.     

On size and boundary effects in scaled model blasts spatial problems

This paper addresses size and boundary effects on wave propagation, fracture pattern development and fragmentation in small scale laboratory-size specimens for model blasting. Small block type specimens are centre-line loaded by linear explosive charges and supersonically detonated. Using elastic wave propagation theory and fracture mechanics it is shown that the type of boundary conditions which prevail at the outer boundary of the cylinder control the extension of bore-hole cracking and fragmentation within the body of the cylinder. In the case of a composite block where a cylindrical core of different material is embedded, the level of fracturing and fragmentation is controlled by the separation of the interface which in turn depends on the relative dimensions of the core and the block. The most important parameter is the ratio between the length of the pulse (space-wise or time-wise) and the characteristic dimensions of the models, i.e. in this case the dimensions of the core and the mantel. Stress wave superposition effects occur in the corner sections of the mantel. Theoretical results are in good agreement with recent experimental findings.     

Validating the ability of the discontinuous deformation analysis method to model normal P‐wave propagation across rock fractures

The effects of fractures on wave propagation problems are increasingly abstracting the attention of scholars and engineers in rock engineering field. This study aims to fully validate the ability of discontinuous deformation analysis (DDA) to model normal P‐wave propagation across rock fractures. The effects of a single fracture and multiple parallel fractures are all tested. The results indicate that DDA can accurately reflect the fracture effects, including the fractures stiffness, the fracture spacing and the fracture number, and the effects of incident wave frequency on one‐dimensional P‐wave propagation problems. Thus, DDA is able to deal well with normal incident P‐wave propagation problems. Copyright © 2017 John Wiley & Sons, Ltd.     

Discrete element model for crack propagation in brittle materials

We propose a discrete element model for brittle rupture. The material consists of a bidimensional set of closed‐packed particles in contact. We explore the isotropic elastic behavior of this regular structure to derive a rupture criterion compatible to continuum mechanics. We introduce a classical criterion of mixed mode crack propagation based on the value of the stress intensity factors, obtained by the analysis of two adjacent contacts near a crack tip. Hence, the toughness becomes a direct parameter of the model, without any calibration procedure. We verify the consistency of the formulation as well as its convergence by comparison with theoretical solutions of tensile cracks, a pre‐cracked beam, and an inclined crack under biaxial stress. Copyright © 2015 John Wiley & Sons, Ltd.     

Application of the numerical manifold method for stress wave propagation across rock masses

In this paper, the numerical manifold method (NMM) is extended to study wave propagation across rock masses. First, improvements to the system equations, contact treatment, and boundary conditions of the NMM are performed, where new system equations are derived based on the Newmark assumption of the space–time relationship, the edge‐to‐edge contact treatment is further developed for the NMM to handle stress wave propagation across discontinuities, and the viscous non‐reflection boundary condition is derived based on the energy minimisation principle. After the modification, numerical comparisons between the original and improved NMM are presented. The results show that the original system equations result in artificial numerical damping, which can be overcome by the Newmark system equations. Meanwhile, the original contact scheme suffers some calculation problems when modelling stress wave propagation across a discontinuity, which can be solved by the proposed edge‐to‐edge contact scheme. Subsequently, the influence of the mesh size and time step on the improved NMM for stress wave propagation is studied. Finally, 2D wave propagation is modelled, and the model's results are in good agreement with the analytical solution. Copyright © 2013 John Wiley & Sons, Ltd.     

Cracking risk of partially saturated porous media—Part I: Microporoelasticity model

Drying of deformable porous media results in their shrinkage, and it may cause cracking provided that shrinkage deformations are hindered by kinematic constraints. This is the motivation to develop a thermodynamics‐based microporoelasticity model for the assessment of cracking risk in partially saturated porous geomaterials. The study refers to 3D representative volume elements of porous media, including a two‐scale double‐porosity material with a pore network comprising (at the mesoscale) 3D mesocracks in the form of oblate spheroids, and (at the microscale) spherical micropores of different sizes. Surface tensions prevailing in all interfaces between solid, liquid, and gaseous matters are taken into account. To establish a thermodynamics‐based crack propagation criterion for a two‐scale double‐porosity material, the potential energy of the solid is derived, accounting—in particular—for mesocrack geometry changes (main original contribution) and for effective micropore pressures, which depend (due to surface tensions) on the pore radius. Differentiating the potential energy with respect to crack density parameter yields the thermodynamical driving force for crack propagation, which is shown to be governed by an effective macrostrain. It is found that drying‐related stresses in partially saturated mesocracks reduce the cracking risk. The drying‐related effective underpressures in spherical micropores, in turn, result in a tensile eigenstress of the matrix in which the mesocracks are embedded. This way, micropores increase the mesocracking risk. Model application to the assessment of cracking risk during drying of argillite is the topic of the companion paper (Part II). Copyright © 2009 John Wiley & Sons, Ltd.     

Extended finite element framework for fault rupture dynamics including bulk plasticity

We present an explicit extended finite element framework for fault rupture dynamics accommodating bulk plasticity near the fault. The technique is more robust than the standard split‐node method because it can accommodate a fault propagating freely through the interior of finite elements. To fully exploit the explicit algorithmic framework, we perform mass lumping on the enriched finite elements that preserve the kinetic energy of the rigid body and enrichment modes. We show that with this technique, the extended FE solution reproduces the standard split‐node solution, but with the added advantage that it can also accommodate randomly propagating faults. We use different elastoplastic constitutive models appropriate for geomaterials, including the Mohr–Coulomb, Drucker–Prager, modified Cam‐Clay, and a conical plasticity model with a compression cap, to capture off‐fault bulk plasticity. More specifically, the cap model adds robustness to the framework because it can accommodate various modes of deformation, including compaction, dilatation, and shearing. Copyright © 2013 John Wiley & Sons, Ltd.