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.     

Computational model coupling mode II discrete fracture propagation with continuum damage zone evolution

We propose a numerical method that couples a cohesive zone model (CZM) and a finite element‐based continuum damage mechanics (CDM) model. The CZM represents a mode II macro‐fracture, and CDM finite elements (FE) represent the damage zone of the CZM. The coupled CZM/CDM model can capture the flow of energy that takes place between the bulk material that forms the matrix and the macroscopic fracture surfaces. The CDM model, which does not account for micro‐crack interaction, is calibrated against triaxial compression tests performed on Bakken shale, so as to reproduce the stress/strain curve before the failure peak. Based on a comparison with Kachanov's micro‐mechanical model, we confirm that the critical micro‐crack density value equal to 0.3 reflects the point at which crack interaction cannot be neglected. The CZM is assigned a pure mode II cohesive law that accounts for the dependence of the shear strength and energy release rate on confining pressure. The cohesive shear strength of the CZM is calibrated by calculating the shear stress necessary to reach a CDM damage of 0.3 during a direct shear test. We find that the shear cohesive strength of the CZM depends linearly on the confining pressure. Triaxial compression tests are simulated, in which the shale sample is modeled as an FE CDM continuum that contains a predefined thin cohesive zone representing the idealized shear fracture plane. The shear energy release rate of the CZM is fitted in order to match to the post‐peak stress/strain curves obtained during experimental tests performed on Bakken shale. We find that the energy release rate depends linearly on the shear cohesive strength. We then use the calibrated shale rheology to simulate the propagation of a meter‐scale mode II fracture. Under low confining pressure, the macroscopic crack (CZM) and its damaged zone (CDM) propagate simultaneously (i.e., during the same loading increments). Under high confining pressure, the fracture propagates in slip‐friction, that is, the debonding of the cohesive zone alternates with the propagation of continuum damage. The computational method is applicable to a range of geological injection problems including hydraulic fracturing and fluid storage and should be further enhanced by the addition of mode I and mixed mode (I+II+III) propagation. Copyright © 2016 John Wiley & Sons, Ltd.     

A cavity expansion–based solution for interpretation of CPTu data in soils under partially drained conditions

A cavity expansion–based solution is proposed in this paper for the interpretation of CPTu data under a partially drained condition. Variations of the normalized cone tip resistance, cone factor, and undrained-drained resistance ratio are examined with different initial specific volume and overconsolidation ratio, based on the exact solutions of both undrained and drained cavity expansion in CASM, which is a unified state parameter model for clay and sand. A drainage index is proposed to represent the partially drained condition, and the critical state after expansion and stress paths of cavity expansion are therefore predicted by estimating a virtual plastic region and assuming a drainage-index–based mapping technique. The stress paths and distributions of stresses and specific volume are investigated for different values of drainage index, which are also related to the penetration velocity with comparisons of experimental data and numerical results. The subsequent consolidation after penetration is thus predicted with the assumption of constant deviatoric stress during dissipation of the excess pore pressure. Both spherical and cylindrical consolidations are compared for dissipation around the cone tip and the probe shaft, respectively. The effects of overconsolidation ratio on the stress paths and the distributions of excess pore pressure and specific volume are then thoroughly investigated. The proposed solution and the findings would contribute to the interpretation of CPTu tests under a random drained condition, as well as the analysis of pile installation and the subsequent consolidation.     

Material selection for the gas containment system of a compressed natural gas carrier fleet

In this work, the possible exploitation of fiber-reinforced composites in the context of maritime transportation of compressed natural gas (CNG) is investigated. In addition to a more conventional steel configuration, two different fiber materials, carbon and glass, are considered as construction materials for pressure vessels (PVs) to be stored on board ships, with thickness optimized by FEM analysis.The considered scenario is represented by the transportation of CNG from an offshore well to a terminal on shore. Fleets of ships carrying CNG in pressure vessels manufactured with the investigated materials are generated by means of a ship synthesis model (SSM) software and compared on the basis of technical and economical indicators.The choice of the construction material influences considerably the weight of the PVs, which represent a major item of total ship weight and reflects directly on the general transport performances in terms of resistance, seakeeping and reliability in the service. On the other hand, capital as well as operating expenditures are considerably affected by the choice. When exploring the design space, the ship synthesis model is able, at a preliminary stage of the design, to account for the various technical and economical aspects, their implications and relationships. Results are presented of computations carried out in a specific case, identified by the annual gas production and other characteristics of the well terminal and a cruising route for the ships. The comparison is carried out on the basis of the cost per transported unit of gas and of the percentage of success in the transportation process. The computations show that the choice of the PV material has a key influence on the results in terms of optimal number, dimensions and speed of the ships.     

Diagnosing snow accumulation errors in a rain‐snow transitional environment with snow board observations

Diagnosing the source of errors in snow models requires intensive observations, a flexible model framework to test competing hypotheses, and a methodology to systematically test the dominant snow processes. We present a novel process‐based approach to diagnose model errors through an example that focuses on snow accumulation processes (precipitation partitioning, new snow density, and snow compaction). Twelve years of meteorological and snow board measurements were used to identify the main source of model error on each snow accumulation day. Results show that modeled values of new snow density were outside observational uncertainties in 52% of days available for evaluation, while precipitation partitioning and compaction were in error 45% and 16% of the time, respectively. Precipitation partitioning errors mattered more for total winter accumulation during the anomalously warm winter of 2014–2015, when a higher fraction of precipitation fell within the temperature range where partition methods had the largest error. These results demonstrate how isolating individual model processes can identify the primary source(s) of model error, which helps prioritize future research.     

Modeling the 2D behavior of dry‐stone retaining walls by a fully discrete element method

The dry‐stone retaining walls (DSRW) have been tipped as a promising solution for sustainable development. However, before recently, their behavior is relatively obscure. In this study, discrete element method (DEM) approach was applied to simulate the plane strain failure of these walls. A commercial DEM package (PFC2D™) was used throughout this study. The authors used a fully discrete approach; thus, both the wall and the backfill were modeled as discrete elements. The methodology for obtaining the micromechanical parameters was discussed in detail; this includes the three mechanical sub‐systems of DSRWs: wall, backfill and interface. The models were loaded progressively until failure, and then the results were compared with the full‐scale experimental results where the walls were loaded, respectively, with hydrostatic load and backfill. Despite its complexity and its intensive calculation time, DEM model can then be used to validate a more simplified approach. Copyright © 2015 John Wiley & Sons, Ltd.     

Tensionless–frictionless interaction of flexible annular foundation with a transversely isotropic multi‐layered half‐space

A transversely isotropic multi‐layered half‐space, with axis of material symmetry perpendicular to the free surface, supports a flexible either annular or solid circle foundation. The contact area of the foundation and the half‐space is considered to be both frictionless and tensionless. The foundation is assumed to be affected by a vertical static axisymmetric load. Detailed analysis of the interaction of these two systems with different thickness of layers is the target of this paper. With the use of ring load Green's functions for both the foundation and the continuum half‐space, an integral equation accompanied with some inequalities is introduced to model the complex BVP. With the incorporation of ring‐shape FEM, we are capable of capturing both regular and singular solution smoothly. The validity of the combination of the analytical and numerical method is proved with comparing the results of this paper with a number of benchmark cases of both linear and nonlinear interaction of circular and annular foundation with half‐space. Some new illustrations are presented to portray the aspect of the anisotropy and layering of the half‐space. Copyright © 2014 John Wiley & Sons, Ltd.     

Dynamic response of a pile considering the interaction of pile variable cross section with the surrounding layered soil

Assuming that the pile variable cross section interacts with the surrounding soil in the same way as the pile toe does with the bearing stratus, the interaction of pile variable cross section with the surrounding soil is represented by a Voigt model, which consists of a spring and a damper connected in parallel, and the spring constant and damper coefficient are derived. Thus, a more rigid pile–soil interaction model is proposed. The surrounding soil layers are modeled as axisymmetric continuum in which its vertical displacements are taken into account and the pile is assumed to be a Rayleigh–Love rod with material damping. Allowing for soil properties and pile defects, the pile–soil system is divided into several layers. By means of Laplace transform, the governing equations of soil layers are solved in frequency domain, and a new relationship linking the impedance functions at the variable‐section interface between the adjacent pile segments is derived using a Heaviside step function, which is called amended impedance function transfer method. On this basis, the impedance function at pile top is derived by amended impedance function transfer method proposed in this paper. Then, the velocity response at pile top can be obtained by means of inverse Fourier transform and convolution theorem. The effects of pile–soil system parameters are studied, and some conclusions are proposed. Then, an engineering example is given to confirm the rationality of the solution proposed in this paper. Copyright © 2017 John Wiley & Sons, Ltd.     

Modeling deepwater seabed steady-state thermal fields around buried pipeline including trenching and backfill effects

Deepwater pipelines are designed to transport mixtures of oil and gas, and their associated impurities at wellhead temperatures that can be in excess of 149 °C (∼300 °F or 422 K) while the external temperature maybe in the range of 5 °C (∼41 °F or 278 K). Depending on the circumstances these pipelines may be buried for physical protection or for additional thermal insulation using robotic trenching equipment. This results in a complex cut and backfill geometry in the seafloor in addition to altering the thermal properties of the backfill. A two-dimensional boundary element model was developed specifically to address to investigate the local steady-state thermal field in the near field of the pipeline. The model allows one to account for the complex geometries in the near field associated with this burial technique, site-specific multi-layered soil conditions and the seawater adjacent to the seafloor. A parametric study was preformed to evaluate effects of the thermal power loss, burial depth, pipe diameter and soil thermal conductivity on the thermal field in the near field of a buried pipeline. The numerical examples illustrate the influence of the backfill thermal property on the temperature at the pipe wall, that the pipe diameter controls the required output thermal power needed to maintain the desired pipe wall temperature, and the importance of pipeline burial depth on seabed temperature distribution above the pipeline.     

Critical Top Tension for Static Equilibrium Configuration of A Steel Catenary Riser

This paper aims to present the critical top tension for static equilibrium configurations of a steel catenary riser（SCR） by using the finite element method. The critical top tension is the minimum top tension that can maintain the equilibrium of the SCR. If the top tension is smaller than the critical value, the equilibrium of the SCR does not exist. If the top tension is larger than the critical value, there are two possible equilibrium configurations. These two configurations exhibit the nonlinear large displacement. The configuration with the smaller displacement is stable, while the one with larger displacement is unstable. The numerical results show that the increases in the riser＇s vertical distances, horizontal offsets, riser＇s weights, internal flow velocities, and current velocities increase the critical top tensions of the SCR. In addition, the parametric studies are also performed in order to investigate the limit states for the analysis and design of the SCR.