A novel strain-based finite element family for mesh-independent analysis of the tensile failure of reinforced concrete bars

The paper presents a novel family of strain-based beam finite elements (FE) for analysis of tensile failure of a reinforced concrete bar (RC bar), with results of the analysis being independent of the applied FE mesh. The composite bar consists of a continuous longitudinal ductile reinforcing bar(s) surrounded by brittle concrete cover, which are considered separately in the model. Longitudinal slip at the contact between the concrete cover and reinforcing bars is allowed, while their relative displacements perpendicular to the axis of the RC bar are prevented. Cracks in concrete cover occur when tensile stress in concrete exceeds its tensile strength. Propagation of partially connected crack, that is, softening of the material at the crack, is described through constitutive law in form of nonlinear relationship between stresses in concrete at the crack and the width of the crack. Each separate crack is considered discretely as a discontinuity in geometry of the element. In the analysis of cracking of concrete, it is commonly assumed that the discrete crack can occur at the nodes of FE only. However, this assumption leads to dependence of the analysis results on the employed FE mesh. The presented family of FE enables occurrence of the crack anywhere along the FE. In order to achieve this, the discrete crack is excluded from equations of FE and additional boundary conditions are introduced at the discontinuity. This approach ensures that the location of the cracks, their number and their propagation are independent of the applied FE mesh. Advantages of the novel family of FE are thoroughly presented in a parametric study which investigates influence of number of FE as well as influence of degrees of interpolation and integration on the cracking of RC bar under tensile loading. Experimental results of tensile tests on the analysed bar are available in literature. It can be concluded that the results obtained with the minimal possible number of novel FE and sufficiently high degree of numerical integration scheme, applied for solving integrals in equations of FE, are considerably more accurate than the results of previous analyses with model of discrete crack at the nodes of FE only.

Understanding Cohesive Law Parameters in Ductile Fracture Initiation and Propagation

Continuum Damage Mechanics is successfully employed to describe the behaviour of metallic materials up to the onset of fracture. Nevertheless, on its own, it is not able to accurately trace discrete crack paths. In this contribution, Continuous Damage Mechanics is combined with the XFEM and a Cohesive Law to allow the full simulation of a ductile fracture process. In particular, the Cohesive Law assures an energetically consistent transition from damage to crack for critical damage values lower than one. Moreover, a novel interpretation is given to the parameters of the cohesive law. A fitting method derived directly from the damage model is proposed for these parameters, avoiding additional experimental characterization.

Lateral Spreading and Stability of Embankments Supported on Fractured Unreinforced High-Modulus Columns

Construction of column-supported embankments (CSEs) with unreinforced high-modulus elements is now common practice to accelerate fill placement. These brittle columns are susceptible to column fracturing and CSE designs often limit the degree of lateral spreading such that tensile rupture will not occur, which stems from salient concerns that fracturing may trigger uncontrolled lateral spreading and/or the cessation of intended vertical load transfer. However, tensile rupture is unlikely to coincide with full mobilization of available passive resistance at the toe. Thus, it is disputed in industry whether some degree of column fracturing is tolerable. The objective of this study is to elucidate the influence of column fracturing on lateral spreading and stability of CSEs. A collective examination of available performance data is accompanied by a parametric 3D finite element study of hypothetical embankments, which considers the cessation of column bending resistance due to tensile rupture at discrete crack locations. A factor of safety, which reflects development of a passive failure wedge at the embankment toe, is used as a proxy for lateral stability. Factors of safety are linked to the magnitude of lateral spreading to address whether adequate confinement can be provided by foundation soils when fracturing occurs in unreinforced high-modulus columns that support embankments.

Modelling Rock Fracture Induced By Hydraulic Pulses

Soft cyclic hydraulic fracturing has become an effective technology used in subsurface energy extraction which utilises cyclic hydraulic flow pressure to fracture rock. This new technique induces fatigue of rock to reduce the breakdown pressure and potentially the associated risk of seismicity. To control the fracturing process and achieve desirable fracture networks for enhanced permeability, the rock response under cyclic hydraulic stimulation needs to be understood. However, the mechanism for cyclic stimulation-induced fatigue of rock is rather unclear and to date there is no implementation of fatigue degradation in modelling the rock response under hydraulic cyclic loading. This makes accurate prediction of rock fracture under cyclic hydraulic pressure impossible. This paper develops a numerical method to model rock fracture induced by hydraulic pulses with consideration of rock fatigue. The fatigue degradation is based on S–N curves (S for cyclic stress and N for cycles to failure) and implemented into the constitutive relationship for fracture of rock using in-house FORTRAN scripts and ABAQUS solver. The cohesive crack model is used to simulate discrete crack propagation in the rock which is coupled with hydraulic flow and pore pressure capability. The developed numerical model is validated via experimental results of pulsating hydraulic fracturing of the rock. The effects of flow rate and frequency of cyclic injection on borehole pressure development are investigated. A new loading strategy for pulsating hydraulic fracturing is proposed. It has been found that hydraulic pulses can reduce the breakdown pressure of rock by 10–18% upon 10–4000 cycles. Using the new loading strategy, a slow and steady rock fracture process is obtained while the failure pressure is reduced.

Viscoelastic phase-field fracture using the framework of representative crack elements

The promising phase-field method has been intensively studied for crack approximation in brittle materials. The realistic representation of material degradation at a fully evolved crack is still one of the main challenges. Several energy split formulations have been postulated to describe the crack evolution physically. A recent approach based on the concept of representative crack elements (RCE) in Storm et al. (The concept of representative crack elements (RCE) for phase-field fracture: anisotropic elasticity and thermo-elasticity. Int J Numer Methods Eng 121:779–805, 2020) introduces a variational framework to derive the kinematically consistent material degradation. The realistic material degradation is further tested using the self-consistency condition, which is particularly compared to a discrete crack model. This work extends the brittle RCE phase-field modeling towards rate-dependent fracture evolution in a viscoelastic continuum. The novelty of this paper is taking internal variables due to viscoelasticity into account to determine the crack deformation state. Meanwhile, a transient extension from Storm et al. (The concept of representative crack elements (RCE) for phase-field fracture: anisotropic elasticity and thermo-elasticity. Int J Numer Methods Eng 121:779–805, 2020) is also considered. The model is derived thermodynamic-consistently and implemented into the FE framework. Several representative numerical examples are investigated, and consequently, the according findings and potential perspectives are discussed to close this paper.