A case study of hydraulic fracturing using finite element methods

1999 ◽  
Vol 36 (5) ◽  
pp. 861-875 ◽  
Author(s):  
Axel KL Ng ◽  
John C Small
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Hydraulic Fracturing ◽  
Hydraulic Fracture ◽  
Water Pressure ◽  
Numerical Procedure ◽  
Tensile Fracture ◽  
Rock Fill ◽  
The Core ◽  
Element Method

Hydraulic fracturing can occur in the clay core of an earth and rock-fill dam if the vertical effective stress in the core is reduced to levels that are small enough to allow a tensile fracture to occur. This situation may arise if the total stress in the core is reduced by the "arching effect" where the core settles relative to the rock-fill shoulders of the dam. Water pressure increases in the core which occur on first impounding of water will reduce effective stresses further, and if they reach low enough values, a fracture will occur. The design of earth dams to resist hydraulic fracture is therefore of great importance (especially those dams with thin vertical or near-vertical central cores), as there have been several dam failures in the past that have been attributed to hydraulic fracture. This paper presents a method of predicting hydraulic fracture in the core of earth and rock-fill dams by using a numerical procedure based on the finite element method. The finite element procedure makes use of special joint elements that allow fluid flow and fracture to be modeled and is an advance over previous methods in that it allows the complete history of pore-pressure development in the core of a dam to be simulated. A study of the behaviour of the Hyttejuvet Dam, which was thought to have failed due to hydraulic fracturing, is also carried out, and the results of the analysis suggest that the failure of the dam was probably due to hydraulic fracturing that occurred during first filling of the reservoir. The fractures predicted occur at about the location that the actual fracture was thought to have been located. Key words: hydraulic fracture, earth and rock-fill dams, finite element method.

scholarly journals Numerical Modelling of Interaction between Hydraulic Fractures and Natural Fractures by Using the Extended Finite Element Method

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Peilun Li ◽  
Yan Dong ◽  
Sheng Wang ◽  
Peichao Li
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Hydraulic Fracturing ◽  
Hydraulic Fracture ◽  
Extended Finite Element Method ◽  
Natural Fracture ◽  
Hydraulic Fractures ◽  
Natural Fractures ◽  
Extended Finite Element ◽  
Element Method

Natural fractures usually develop in shale reservoirs. Thereby, in the process of hydraulic fracturing, it is inevitable that hydraulic fractures will intersect with natural fractures. In order to reveal the interaction mechanism between hydraulic-induced fractures and natural fractures, a two-dimensional fracture intersection model based on the extended finite element method (XFEM) is proposed, and the different types of intersecting criteria reported in the literature are compared. Then, the effects of natural fracture azimuth, fluid pressure in hydraulic fracture, and in situ principal stress difference on hydraulic fracturing are studied in detail. The results show that the fracture morphology is different under different criteria and working conditions. And the stress concentration phenomenon mainly concentrates on the tip in the obtuse angle side of natural fracture. Meanwhile, different fluid pressures in hydraulic fracture can also induce different intersection patterns. The obtained results in this work are of great benefit to understand the intersection mechanism between hydraulic fractures and natural fractures.

scholarly journals Influence of Retardation Time on Viscoelastic Behavior of Plane Beams Modeled by the Nonlinear Positional Formulation of the Finite Element Method

2021 ◽  
Vol 2021 ◽  
pp. 1-22
Author(s):  
Juliano dos Santos Becho ◽  
Marcelo Greco
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Rheological Model ◽  
Iterative Process ◽  
Numerical Procedure ◽  
Viscoelastic Behavior ◽  
Retardation Time ◽  
The Finite Element Method ◽  
Divergence Problem ◽  
Element Method

A numerical procedure is presented to avoid the divergence problem during the iterative process in viscoelastic analyses. This problem is observed when the positional formulation of the finite element method is adopted in association with the finite difference method. To do this, the nonlinear positional formulation is presented considering plane frame elements with Bernoulli–Euler kinematics and viscoelastic behavior. The considered geometrical nonlinearity refers to the structural equilibrium analysis in the deformed position using the Newton–Raphson iterative method. However, the considered physical nonlinearity refers to the description of the viscoelastic behavior through the adoption of the stress-strain relation based on the Kelvin–Voigt rheological model. After the presentation of the formulation, a detailed analysis of the divergence problem in the iterative process is performed. Then, an original numerical procedure is presented to avoid the divergence problem based on the retardation time of the adopted rheological model and the penalization of the nodal position correction vector. Based on the developments and the obtained results, it is possible to conclude that the presented formulation is consistent and that the proposed procedure allows for obtaining the equilibrium positions for any time step value adopted without presenting divergence problems during the iterative process and without changing the analysis of the final results.

On XFEM Applications to Crack Surface under External Force

2012 ◽  
Vol 152-154 ◽  
pp. 210-215
Author(s):  
Tian Tang Yu ◽  
Lu Yang Shi
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Stress Intensity ◽  
Extended Finite Element Method ◽  
Crack Surface ◽  
Water Pressure ◽  
Intensity Factors ◽  
Extended Finite Element ◽  
Modeling Growth ◽  
Element Method

The extended finite element method is applied to modeling growth of arbitrary crack with crack surface tractions. Firstly, the extended finite element method is investigated for the stress intensity factor solution of surface traction problems. Secondly, for different water pressure acting on the crack surfaces and different crack length, the variation of the stress intensity factors is investigated. Finally, the process of hydraulic fracturing is simulated with the method. Numerical simulations illustrate that the method can effectively model the fracture problems with surface tractions.

scholarly journals NURSE-2 DoF Device for Arm Motion Guidance: Kinematic, Dynamic, and FEM Analysis

2020 ◽  
Vol 10 (6) ◽  
pp. 2139
Author(s):  
Betsy D. M. Chaparro-Rico ◽  
Daniele Cafolla ◽  
Marco Ceccarelli ◽  
Eduardo Castillo-Castaneda
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Upper Limb ◽  
Numerical Procedure ◽  
Fem Analysis ◽  
Arm Movement ◽  
Assistive Device ◽  
Arm Motion ◽  
Element Method

Patients with neurological or orthopedic lesions require assistance during therapies with repetitive movements. NURSE (cassiNo-qUeretaro uppeR-limb aSsistive dEvice) is an arm movement aid device for both right- and left-upper limb. The device has a big workspace to conduct physical therapy or training on individuals including kids and elderly individuals, of any age and size. This paper describes the mechanism design of NURSE and presents a numerical procedure for testing the mechanism feasibility that includes a kinematic, dynamic, and FEM (Finite Element Method) analysis. The kinematic demonstrated that a big workspace is available in the device to reproduce therapeutic movements. The dynamic analysis shows that commercial motors for low power consumption can achieve the needed displacement, acceleration, speed, and torque. Finite Element Method showed that the mechanism can afford the upper limb weight with light-bars for a tiny design. This work has led to the construction of a NURSE prototype with a light structure of 2.6 kg fitting into a box of 35 × 45 × 30 cm. The latter facilitates portability as well as rehabilitation at home with a proper follow-up. The prototype presented a repeatability of ±1.3 cm that has been considered satisfactory for a device having components manufactured with 3D rapid prototyping technology.

Dynamic tensile process of blended fabric using finite element method

2020 ◽  
Vol 32 (5) ◽  
pp. 707-724
Author(s):  
Xuzhong Su ◽  
Xinjin Liu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Experimental Testing ◽  
Woven Fabrics ◽  
Weft Yarn ◽  
Tensile Fracture ◽  
Content Type ◽  
Tensile Process ◽  
Simulation Results ◽  
Element Method

PurposeTensile property is one basic mechanics performance of the fabric. In general, not only the tensile values of the fabric are needed, but also the dynamic changing process under the tension is also needed. However, the dynamic tensile process cannot be included in the common testing methods by using the instruments after fabric weaving.Design/methodology/approachBy choosing the weft yarn and warp yarn in the fabric as the minimum modeling unit, 1:1 finite element model of the whole woven fabrics was built by using AutoCAD software according to the measured geometric parameters of the fabrics and mechanical parameters of yarns. Then, the fabric dynamic tensile process was simulated by using the ANSYS software. The stress–strain curve along the warp direction and shrinkage rate curve along the weft direction of the fabrics were simulated. Meanwhile, simulation results were verified by comparing to the testing results.FindingsIt is shown that there are four stages during the fabric tensile fracture process along the warp direction under the tension. The first stage is fabric elastic deformation. The second stage is fabric yield deformation, and the change rate of stress begins to slow down. The third stage is fiber breaking, and the change of stress fluctuates since the breaking time of the fibers is different. The fourth stage is fabric breaking.Originality/valueIn this paper, the dynamic tensile process of blended woven fabrics was studied by using finite element method. Although there are differences between the simulation results and experimental testing results, the overall tendency of simulation results is the same as the experimental testing results.

A Maxwell's Second Equation Approach to the Finite Element Method Applied to Magnetic Field Determination

1987 ◽  
Vol 24 (3) ◽  
pp. 259-272 ◽  
Author(s):  
José Roberto Cardoso
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Undergraduate Students ◽  
Engineering Students ◽  
Numerical Procedure ◽  
The Finite Element Method ◽  
Cad Cam ◽  
New Formulation ◽  
The Galerkin Method ◽  
Element Method

The burst of modern computing systems like CAD/CAM has given rise to the use of the finite element method (FEM), which is, at present, the most used numerical procedure in the determination of fields in continuous media. Undergraduate students find difficulty in understanding the usual way of demonstrating FEM by variational analysis or the Galerkin method. This paper introduces a new formulation of FEM, based on a direct application of Maxwell's second equation, which can be easily understood by undergraduate engineering students.

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