Analysis of tunnels in shaly rock considering three-dimensional stress effects on swelling

2005 ◽  
Vol 42 (1) ◽  
pp. 1-12 ◽  
Author(s):  
B C Hawlader ◽  
K Y Lo ◽  
I D Moore
Keyword(s):  
Finite Element ◽  
Closed Form ◽  
Cold Water ◽  
Principal Direction ◽  
Three Dimensional ◽  
Closed Form Solution ◽  
Time Dependent ◽  
Stress Effect ◽  
Stress Effects ◽  
Laboratory Test Results

Underground structures in shales or shaly rocks endure time-dependent swelling effects. Laboratory test results show that the swelling of these shales is dependent on three-dimensional stresses; an external stress on a specimen in one principal direction reduces the swelling not only in that direction but also perpendicularly. The effectiveness of a time-dependent swelling model that considers the three-dimensional stress effect is presented in this paper. A finite element algorithm incorporating the new constitutive model is used for a numerical analysis. The finite element program is used to analyze two tunnels in southern Ontario: the Heart Lake storm sewer tunnel, and the Darlington cold-water intake tunnel. The predicted results agree well with the records of field performance of these tunnels. The comparison between present analyses and the existing closed-form solution shows that the existing solution overestimates the time-dependent swelling effects. The three-dimensional stress effects on swelling are not considered in the closed-form solutions and are the cause of this discrepancy. The pseudo-Poisson's effect is a key parameter for modelling the observed time-dependent swelling. The use of these solutions in design is discussed.Key words: time-dependent swelling, shale, modelling, three-dimensional stress effect, finite element method, tunnel.

Three-dimensional stress effects on time-dependent swelling behaviour of shaly rocks

2003 ◽  
Vol 40 (3) ◽  
pp. 501-511 ◽  
Author(s):  
B C Hawlader ◽  
Y N Lee ◽  
K Y Lo
Keyword(s):  
Applied Stress ◽  
Axial Stress ◽  
Three Dimensional ◽  
Biaxial Stress ◽  
Time Dependent ◽  
Stress Effect ◽  
Stress Effects ◽  
Proposed Model ◽  
Laboratory Test Results ◽  
Swelling Strain

This paper presents a time-dependent constitutive model that has been developed for the swelling of shaly rocks. Laboratory test results on many shales, including Queenston shale, show that the swelling of these rocks depends on the applied stresses. The applied stress in one principal stress direction reduces swelling strain not only in that direction but also in the perpendicular directions. It was found that swelling strain reductions are nonlinearly dependent on applied stress. The reduction in lateral swelling caused as a result of axial stress is modeled using the "pseudo-Poisson's effect". The proposed model is used to simulate the development of swelling strain with time under uniaxial and biaxial stress conditions. Comparison between the computed and experimental results shows that the pseudo-Poisson's effect is a key parameter for simulating the observed time-dependent swelling.Key words: swelling, Queenston shale, modeling, three-dimensional stress effect, nonlinearity.

The closed-form solution of vector finite element integral equations for three dimensional electromagnetic analysis

2011 ◽  
Vol 28 (4-6) ◽  
pp. 602-608
Author(s):  
Jin Tian ◽  
Li Gong ◽  
Xiaowei Shi ◽  
Zhiqing Lv ◽  
Xing Liu
Keyword(s):  
Finite Element ◽  
Closed Form ◽  
Integral Equations ◽  
Three Dimensional ◽  
Closed Form Solution ◽  
Form Solution ◽  
Electromagnetic Analysis ◽  
Vector Finite Element

Three-Dimensional Computations of Transport and Growth for Crystal Growth Systems

2000 ◽  
Author(s):  
Jeffrey J. Derby ◽  
Andrew Yeckel
Keyword(s):  
Finite Element ◽  
Crystal Growth ◽  
Finite Element Methods ◽  
Three Dimensional ◽  
Bulk Crystal ◽  
Time Dependent ◽  
Engineering Systems ◽  
Bulk Crystal Growth ◽  
Strongly Nonlinear ◽  
Parallel Supercomputers

Abstract Modern finite element methods implemented on parallel supercomputers promise to allow the study of three-dimensional, time-dependent continuum phenomena in many engineering systems. This paper shows several examples of the fruitful application of these approaches to bulk crystal growth systems, where strongly nonlinear coupled phenomena are important.

Analytical and Numerical Studies of a Thick Anisotropic Multilayered Fiber-Reinforced Composite Pressure Vessel

2018 ◽  
Vol 141 (1) ◽  
Author(s):  
Isaiah Ramos ◽  
Young Ho Park ◽  
Jordan Ulibarri-Sanchez
Keyword(s):  
Finite Element ◽  
Pressure Vessel ◽  
Structural Damage ◽  
Three Dimensional ◽  
Closed Form Solution ◽  
Form Solution ◽  
Fiber Reinforced ◽  
Element Analysis ◽  
Analytical Results ◽  
Composite Pressure Vessel

In this paper, we developed an exact analytical 3D elasticity solution to investigate mechanical behavior of a thick multilayered anisotropic fiber-reinforced pressure vessel subjected to multiple mechanical loadings. This closed-form solution was implemented in a computer program, and analytical results were compared to finite element analysis (FEA) calculations. In order to predict through-thickness stresses accurately, three-dimensional finite element meshes were used in the FEA since shell meshes can only be used to predict in-plane strength. Three-dimensional FEA results are in excellent agreement with the analytical results. Finally, using the proposed analytical approach, we evaluated structural damage and failure conditions of the composite pressure vessel using the Tsai–Wu failure criteria and predicted a maximum burst pressure.

Validation of Nitinol SMA Characteristics Using Finite Element Analysis and Closed Form Solutions

2013 ◽  
Vol 856 ◽  
pp. 147-152
Author(s):  
S.H. Adarsh ◽  
U.S. Mallikarjun
Keyword(s):  
Experimental Data ◽  
Finite Element Analysis ◽  
Finite Element ◽  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
Fe Analysis ◽  
Element Analysis ◽  
Complex Behaviour ◽  
Closed Form Solutions

Shape Memory Alloys (SMA) are promising materials for actuation in space applications, because of the relatively large deformations and forces that they offer. However, their complex behaviour and interaction of several physical domains (electrical, thermal and mechanical), the study of SMA behaviour is a challenging field. Present work aims at correlating the Finite Element (FE) analysis of SMA with closed form solutions and experimental data. Though sufficient literature is available on closed form solution of SMA, not much detail is available on the Finite element Analysis. In the present work an attempt is made for characterization of SMA through solving the governing equations by established closed form solution, and finally correlating FE results with these data. Extensive experiments were conducted on 0.3mm diameter NiTinol SMA wire at various temperatures and stress conditions and these results were compared with FE analysis conducted using MSC.Marc. A comparison of results from finite element analysis with the experimental data exhibits fairly good agreement.

Induction Proof for a General Exponential Integral Formula

1995 ◽  
Vol 80 (2) ◽  
pp. 424-426
Author(s):  
Frank O'Brien ◽  
Sherry E. Hammel ◽  
Chung T. Nguyen
Keyword(s):  
Closed Form ◽  
Integral Formula ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Closed Form Solution ◽  
Form Solution ◽  
Probability Method ◽  
Exponential Integral ◽  
Need To Evaluate ◽  
Three Dimensional Space

The authors' Poisson probability method for detecting stochastic randomness in three-dimensional space involved the need to evaluate an integral for which no appropriate closed-form solution could be located in standard handbooks. This resulted in a formula specifically calculated to solve this integral in closed form. In this paper the calculation is verified by the method of mathematical induction.

scholarly journals Three-dimensional Time-dependent Analysis of Rock by Finite Element Method.

1998 ◽  
Vol 114 (2) ◽  
pp. 79-85 ◽  
Author(s):  
Seisuke OKUBO ◽  
Katsunori FUKUI ◽  
Jiandong ZHANG
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Three Dimensional ◽  
Time Dependent ◽  
Time Dependent Analysis ◽  
Element Method

scholarly journals Reconstruction of three-dimensional maps based on closed-form solutions of the variational problem of multisensor data registration

2019 ◽  
Vol 484 (6) ◽  
pp. 672-677
Author(s):  
A. V. Vokhmintcev ◽  
A. V. Melnikov ◽  
K. V. Mironov ◽  
V. V. Burlutskiy
Keyword(s):  
Closed Form ◽  
Large Scale ◽  
Three Dimensional ◽  
Dynamic Environment ◽  
Closed Form Solution ◽  
Point Clouds ◽  
Accurate Method ◽  
Form Solution ◽  
Closed Form Solutions ◽  
Reconstruction Methods

A closed-form solution is proposed for the problem of minimizing a functional consisting of two terms measuring mean-square distances for visually associated characteristic points on an image and meansquare distances for point clouds in terms of a point-to-plane metric. An accurate method for reconstructing three-dimensional dynamic environment is presented, and the properties of closed-form solutions are described. The proposed approach improves the accuracy and convergence of reconstruction methods for complex and large-scale scenes.

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