Direct assessment of structural resistance against pressurized fracture

SUMMARYThis paper describes a fixed grid algorithm to simulate the propagation of shallow hydraulic fractures, under plane strain or axisymmetric conditions. Because of the low stress environment that exists near a free surface, these fractures are generally characterized by a fluid front that lags behind the fracture edge. The simulation of shallow hydraulic fractures requires therefore the tracking of two distinct fronts. The proposed algorithm, which traces its roots to the one described by Zhang et al. (Int. J. Numer. Anal. Methods Geomech. 2005; 29:1317-1340), advances the fracture by a constant step and computes the corresponding time required to reach this new fracture configuration as well as the matching location of the fluid front within the fixed grid. For any trial value of the time and of the front position, a non-linear system of algebraic equations is solved using either Newton's method or a fixed point iteration scheme, with preconditioning. The non-linear system is formulated by combining an implicit finite volume method for solving the lubrication equation and the displacement discontinuity method for solving the elasticity equation. The critical difference with the algorithm of Zhang et al. lays in the approach chosen to update the fluid front position. Rather than using a filling fraction method, the new algorithm adopts a velocity treatment of the fluid-front location that is akin to a one-dimensional implementation of a level set algorithm for front tracking. This conversion from a fluid volume to a fluid velocity-based approach to update the front position increases the degree of implicitness of the algorithm, which is responsible for a significant reduction of the CPU time by about two orders of magnitude.

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“…The condition w = 0 at the tip is evidently implied by the asymptote (10). The net pressure in the lag zone is set to…”

Section: Boundary Conditionsmentioning

confidence: 99%

A fixed grid algorithm for simulating the propagation of a shallow hydraulic fracture with a fluid lag

Gordeliy¹,

Detournay²

2011

Num Anal Meth Geomechanics

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“…However, the parameter identification methods considered in what follows with reference to opening mode crack alone are quite general. In particular, if the complementarity construct is preserved in passing from mode I to mixed mode (e.g., by piece-wise linearisation, see Figures 1a and 1b), then only changes in the number of variables and in the computational effort intervene, not in conceptual and mathematical terms; similar unified framework is provided by piecewise linear material models also to direct elasto-plastic analyses in rates, in finite steps and under the assumption of holonomic path-independent behaviour; see: Maier and Comi (2000); Tin-Loi and Xia (2001b); Cocchetti et al (2002); Bolzon and Cocchetti (2003).…”

Section: Piecewise-linear Cohesive Crack Modelsmentioning

confidence: 97%

Inverse Analyses in Fracture Mechanics

et al. 2006

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The present purpose is a survey of some engineering-oriented research results which may be representative of the main issues in the title subject. Some recent or current developments are pointed out in the growing area of fracture mechanics centered on the calibration of cohesive fracture models for quasi-brittle materials, by approaches which combine experimentation, experiment simulation and minimisation of the discrepancy between measured and computed quantities. Specifically, reference is made herein to the following topics in calibration of fracture constitutive models: (a) deterministic characterisation of concrete-like materials by traditional three-point-bending tests (TPBTs), supplemented by optical measurements; (b) wedge-splitting tests (WST) and extended Kalman filter (EKF) for the stochastic estimation of fracture parameters; (c) in situ parameter identification for the local diagnosis of possibly deteriorated concrete dams on the basis of flat-jack tests; (d) fracture properties of ceramic materials and coating-substrate interfaces identified through indentation tests, imprint mapping and inverse analysis in micro-technologies.

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“…The fluid flow along a propagating crack surface satisfies some natural flow law. Some hypotheses [9][10][11][12], such as linear distribution of the water pressure along crack case, full reservoir pressure case, for evaluating water pressure along a propagating crack cannot reflect accurately the variation of the water pressure along new developing cracks in structures.…”

Section: Introductionmentioning

confidence: 99%

Coupled Finite Volume Methods and Extended Finite Element Methods for the Dynamic Crack Propagation Modelling with the Pressurized Crack Surfaces

Jiang

2017

Shock and Vibration

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We model the fluid flow within the crack as one-dimensional flow and assume that the flow is laminar; the fluid is incompressible and accounts for the time-dependent rate of crack opening. Here, we discretise the flow equation by finite volume methods. The extended finite element methods are used for solving solid medium with crack under dynamic loads. Having constructed the approximation of dynamic extended finite element methods, the derivation of governing equation for dynamic extended finite element methods is presented. The implicit time algorithm is elaborated for the time descritisation of dominant equation. In addition, the interaction integral method is given for evaluating stress intensity factors. Then, the coupling model for modelling hydraulic fracture can be established by the extended finite element methods and the finite volume methods. We compare our present numerical results with our experimental results for verifying the proposed model. Finally, we investigate the water pressure distribution along crack surface and the effect of water pressure distribution on the fracture property.

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Direct assessment of structural resistance against pressurized fracture

Cited by 34 publications

References 33 publications

A fixed grid algorithm for simulating the propagation of a shallow hydraulic fracture with a fluid lag

A fixed grid algorithm for simulating the propagation of a shallow hydraulic fracture with a fluid lag

Inverse Analyses in Fracture Mechanics

Coupled Finite Volume Methods and Extended Finite Element Methods for the Dynamic Crack Propagation Modelling with the Pressurized Crack Surfaces

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