Stefano Secchi

A method for 3-D hydraulic fracturing simulation

We present a method for the simulation of 3-D hydraulic fracturing in fully saturated porous media. The discrete fracture(s) is driven by the fluid pressure. A cohesive fracture model is adopted where the fracture follows the face of the elements around the fracture tip which is closest to the normal direction of the maximum principal stress at the fracture tip. No predetermined fracture path is needed. This requires continuous updating of the mesh around the crack tip to take into account the evolving geometry. The updating of the mesh is obtained by means of an efficient mesh generator based on Delaunay tessellation. The governing equations are written in the framework of porous media mechanics theory and are solved numerically in a fully coupled manner. An examples dealing with a concrete dam is shown.

Cohesive fracture mechanics for a multi‐phase porous medium

This paper presents a mathematical model for the analysis of cohesive fracture propagation through a non‐homogeneous porous medium. Governing equations are stated within the frame of Biots theory, accounting for the flow through the solid skeleton, along the fracture and across its sides toward the surrounding medium. The numerical solution is obtained in a 2D context, exploiting the capabilities of an efficient mesh generator, and requires continuous updating of the domain as the fractures enucleate and propagate. It results that fracture paths and their velocity of propagation, usually assumed as known, are supplied directly by the model without introducing any simplifying assumption.

A Multi-Phase Media Formulation for Biomechanical Analysis of Periodontal Ligament*

A numerical analysis of the biomechanical response of the periodontal ligament is presented. A multi-phase media formulation is developed for representing soft tissue constitutive models, and implemented in a specific finite element code. It is possible to simulate the presence of liquid phase permeating the extra-cellular material and to interpret the consequent time-dependent behaviour due to the fluid flux through periodontal ligament. The analysis of the mobility of human upper incisor, under the application of short time transversal forces, is reported. The numerical results are compared with in vivo experimental data. The agreement of different approaches confirms the effectiveness of the proposed model for investigation of the biomechanical behaviour of periodontal ligament under application of low magnitude forces, and represents the basis for the definition of a general multi-phase constitutive model.

Hydraulic fracturing and its peculiarities

BackgroundSimulation of pressure-induced fracture in two-dimensional (2D) and three-dimensional (3D) fully saturated porous media is presented together with some peculiar features.MethodsA cohesive fracture model is adopted together with a discrete crack and without predetermined fracture path. The fracture is filled with interface elements which in the 2D case are quadrangular and triangular elements and in the 3D case are either tetrahedral or wedge elements. The Rankine criterion is used for fracture nucleation and advancement. In a 2D setting the fracture follows directly the direction normal to the maximum principal stress while in the 3D case the fracture follows the face of the element around the fracture tip closest to the normal direction of the maximum principal stress at the tip. The procedure requires continuous updating of the mesh around the crack tip to take into account the evolving geometry. The updated mesh is obtained by means of an efficient mesh generator based on Delaunay tessellation. The governing equations are written in the framework of porous media mechanics and are solved numerically in a fully coupled manner.ResultsNumerical examples dealing with well injection (constant inflow) in a geological setting and hydraulic fracture in 2D and 3D concrete dams (increasing pressure) conclude the paper. A counter-example involving thermomecanically driven fracture, also a coupled problem, is included as well.ConclusionsThe examples highlight some peculiar features of hydraulic fracture propagation. In particular the adopted method is able to capture the hints of Self-Organized Criticality featured by hydraulic fracturing.

Hydraulic fracturing in multiphase geomaterials

ABSTRACT This paper presents a mathematical model for the analysis of hydraulic cohesive fracture propagation through a non-homogeneous porous medium. Governing equations are stated within the frame of Biots theory, accounting for the flow through the solid skeleton, along the fracture and across its sides toward the surrounding medium. The numerical solution is obtained in a 2-D context, exploiting the capabilities of an efficient mesh generator, and requires continuous updating of the domain as the fractures enucleate and propagate. It results that fracture paths and their velocity of propagation, usually assumed as known, are supplied directly by the model without introducing any simplifying assumption.

2D and 3D numerical analysis of fluid pressure induced fracture

Simulation of 2D and 3D hydraulic fracturing in fully saturated porous media is presented. The discrete fracture/s is/are driven by the fluid pressure. A cohesive fracture model is adopted where in the 3D case the fracture follows the face of the element around the fracture tip which is closest to the normal direction of the maximum principal stress at the tip while in the 2D setting the fracture follows directly the direction normal to the maximum principal stress. No predetermined fracture path is needed. This requires continuous updating of the mesh around the crack tip to take into account the evolving geometry. The updating of the mesh is obtained by means of an efficient mesh generator based on Delaunay tessellation. The governing equations are written in the framework of porous media mechanics and are solved numerically in a fully coupled manner. Numerical examples dealing with well injection in a geological setting and hydraulic fracture in a concrete dam conclude the paper.