A finite element solution of non-linear creep problems in rocks

doi:10.1016/0148-9062(81)90264-3

International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts

Volume 18, Issue 1, February 1981, Pages 35-46

International Journa...

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Abstract

A numerical procedure is presented, belonging to the class of ‘evolutive’ approaches, for the finite element solution of stress analysis problems involving non-linear creep of rocks. The approach proposed allows both for non-linear reversible behaviour (non-linear viscoelasticity) and for non-linear non-reversible behaviour (viscoplasticity); either associated or non-associated flow rules can be considered. Primary, secondary and tertiary creep can be accounted for by supplying suitable laws governing the variation of material parameters (such as viscosity) with stresses and strains. The numerical procedure is based on Newmark's time integration scheme; along each loading/ time step quadratic variation of the stress and strain fields and linear variation of the material parameters are assumed. As an example, a hollow cylinder test on a rock sample behaving according to a simple non-linear viscoplastic rheological model is simulated numerically.

References (22)

D.W. Hobbs
Stress-strain-time behaviour of a number of coal measure rocks
Int. J. Rock Mech. Min. Sci.
(1970)
K.H. Höfer et al.
Investigations into the mechanism of creep deformation in carnallite, and practical applications
Int. J. Rock Mech. Min. Sci.
(1971)
J. Cogan
Triaxial creep tests of Opohonga limestone and Ophir shale
Int. J. Rock Mech. Min. Sci. & Geomech. Abstr.
(1976)
A. Dragon et al.
A model for plastic creep of rock-like materials accounting for the kinetics of fracture
Int. J. Rock Mech. Min. Sci. & Geomech. Abstr.
(1979)
D.M. Cruden
The form of the creep law for rock under uniaxial compression
Int. J. Rock Mech. Min. Sci.
(1971)
R.M. Semple et al.
The effect of time-dependent properties of altered rock on tunnel support requirements
R.S. Sandhu
Finite element analysis of consolidation and creep
K. Runesson et al.
Computer implementation of non linear finite element analysis applied to some geotechnical problems
R.A. Feijóo et al.
Algunos principios y metodos variacionales en elasto-plasticidad, creep y su formulacion unificada a traves de la elasto-plasticidad
A. Singh et al.
General stress-strain-time function for Soil
J. Soil Mech. Fdn. Div. Am. Soc. civ. Engrs
(1968)

K.H. Gerstle et al.

Analysis of time-dependent deformations of openings in salt media

Int. J. Rock Mech. Min. Sci.

(1972)

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Excavation of long, deep, buried tunnels under high stress and soft rock conditions is highly challenging because the surrounding rock may undergo severe time-dependent squeeze deformation or may even collapse during construction, which poses a significant threat to the stability of tunnels. The creep constitutive model can be used to predict time-dependent extrusion deformation; however, the conventional creep model has limitations in estimating delayed squeezing deformation and does not describe time-dependent deformation in the accelerated creep stage. For this reason, the FCVISC-NP creep constitutive model is proposed, which can more accurately describe the nonlinear gradual characteristics of delayed squeezing deformation and can also estimate the accelerated creep characteristics of squeezing deformation. The constitutive equations of the FCVISC-NP model in the three-dimensional stress state are derived based on Perzyna overstress theory with the viscoplastic flow law. The customization of the FCVISC-NP model in FLAC3D is implemented by using object-oriented C++. The research results can be used to make reliable predictions of the surrounding rock deformation for similar deeply buried soft rock and can provide an important reference for the design, the construction, and the long-term safety assessment of tunnels.
Statistical study of squeezing for soft rocks based on factor and regression analyses of effective parameters
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The time-dependent deformation of rocks due to stress released by excavation is referred to as squeezing. Accurate evaluation of the squeezing at the design stage can dramatically reduce technical problems and the financial costs of underground structures. Although various methods are presented to predict tunnel squeezing at the preliminary stage, being site-specific and incorporating incomplete databases are deficiencies of the available procedures. In this study, based on a comprehensive literature review, we prepared a database of tunnel squeezing for soft rocks, including possible effective parameters. Statistical processing methods such as univariate, reduction, and cleaning were employed to improve the statistical quality of the database. The statistically-processed datasets were also validated based on various scales such as accuracy, convergence, and usefulness. Significant predictors of squeezing are recognized as the ratio of strength to stress and the rock mass classification system. New squeezing criteria were developed using binary and multi-class regression methods to predict the squeezing occurrence and intensity of soft rocks. The results are confirmed by a Multilayer Perceptron Feed-Forward Neural Network and are compared to well-known empirical equations. The developed equations are more accurate comparing the empirical equations used to predict the squeezing of soft rocks. This methodology can be utilized at the design stage for another database to predict squeezing rocks for topographic-stress and tectonic-stress-based cases.
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That is, common rock classification models calculate “instantaneous” stresses and strains but can not account for time-dependent weakening/strengthening nor time-dependent strains. Time-dependent models can be categorized into three categories: (a) empirical functions,29,51 (b) rheological models52–54 and models built upon them.55 Other researchers56 have grouped creep models into phenomenological models, statistical models, and micromechanical models.
The long-term strength and time-to-failure of brittle rocks has become increasingly important with the increased interest in the storage of used nuclear fuel in deep geological repositories. This paper critically reviews and analyzes the currently available time-to-failure data for various brittle rock types. The current best approach on estimating time-to-failure of rock samples at the lab scale under a constant stress is using semi-log data based on the driving stress ratio and the logarithm of time. In most studies, the applied driving stress ratio is calculated based on the average strength of the rock, however, sample strength can vary up to 15%. Therefore, it is proposed that the crack-initiation stress threshold for each sample be used to calculate sample specific ultimate strengths based on relationships determined in literature. It is proposed that if a sample fails during a long-term strength test within the first 1–10 s, the applied stress for that test can be assumed equivalent to the ultimate strength. Additionally, a modified exponential function with a horizontal asymptote at the crack-initiation threshold is explored as an alternative to the typical log-linear approach. The exponential approach is non-linear in semi-log space and does not require an arbitrary cut-off for time-to-failure at the static fatigue limit of the rock as is the case of the semi-log approach. Ultimately, it is shown that although the exponential function does usually provide a better overall fit to data at relatively short times (<1,000,000 s), there is little evidence to justify the asymptotic behaviour in the longer term. Common practice has been to present the driving stress ratio as a function of time-to-failure, however, in theory these axes should be reversed as the variable of interest to the reader is the time-to-failure based on in-situ stresses. The consequence of plot orientation and subsequent error calculation are explored. The goal of this paper is to provide users and researchers with a reliable methodology to predict time-to-failure of brittle rocks both at the lab and excavation scale as well as a basis for incorporating explicit time-to-failure calculations into a continuum numerical model.
Viscous-elastic-plastic response of tunnels in squeezing ground conditions: Analytical modeling and experimental validation
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The conventional elasto-plastic solutions for tunnels fail to reproduce the deformation response during tunnel excavation in squeezing ground. Researchers have proposed many methodologies to study tunnels in squeezing ground, such as experimental17–20; analytical21–29; computational,30,31,33,34 and empirical.13,35–44 The most used approaches for the tunnels in squeezing ground are empirical and computational methods.
Tunnels constructed in soft rock and high field stress show significant gradual convergence with even after the excavation. This paper proposes a new visco-elastic-plastic solution for deep circular tunnel under squeezing conditions. The model is composed of Mohr-Coulomb plasticity and Burger's model for visco-elastic material. The state of the stress around the tunnel boundary and the tunnel wall displacement due to elasto-plastic behavior is determined using a conventional closed-from solution. Additionally, Kelvin type Burger's creep material model is used to determine the viscous behavior of tunnel wall convergence with time. Burger's model and Mohr-Coulomb's parameters are determined from unconfined compressive strength tests, triaxial tests, and creep tests on the cylindrical specimen of the host rock. The results of the proposed solution are compared with tunnel convergence data from laboratory-scale model test. The comparison show that the proposed solution reflects the tunnel's time-dependent behavior and adequately predicts the tunnel wall displacement compared to the experimental data.
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Citation Excerpt :
These authors also found that the physical properties of different rocks also have an effect on SCG (Nara et al., 2010). Because creep experiments take a lot of time, numerical simulations, which can give good approximate results in a relatively short time (Gioda, 1981), are of great interest. Indeed, many researchers have used numerical simulations to study rock creep and SCG.
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It is critical to accurately predict the mechanical behaviour of nearby geomaterial during twin tunnel excavation, which is generally studied using the numerical and analytical methods. Numerical methods exhibit good visibilities and are widely used to simulate tunnel problems in the last century [5–8]. With the evolution of the computational performance of computers, the numerical methods are becoming mainstream.
Analytic solutions on twin tunnelling at great depth in viscoelastic geomaterial considering three-dimensional effects of tunnel faces are presented using the complex variable methods. According to the time interval between twin tunnel faces, the proposed solutions can be divided into two cases: A) newly constructing twin tunnels; and B) newly constructing single tunnel influencing an existing one. The analytic solutions can also consider sequential excavations and the mutual influence between twin tunnels. The three-dimensional effects of twin tunnel faces are transformed into equivalent plane-strain problems by introducing dimensionless coefficients. By means of a presented general case, the analytic solutions are verified via comparisons of both stresses and displacements with the numerical solution, in which a good agreement between these two solutions is observed. Subsequently, a parametric investigation is performed to study the influence of several parameters concerning twin tunnel geometry and excavation on stresses and displacements, together with the difference between Cases A and B. On the basis of the results, the analytic solutions provide quantitative insights into the essence of the three-dimensional effects of twin tunnel faces and would have certain values on the preliminary design stage of twin tunnels.

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A finite element solution of non-linear creep problems in rocks

Abstract

Int. J. Rock Mech. Min. Sci.

Int. J. Rock Mech. Min. Sci.

Int. J. Rock Mech. Min. Sci. & Geomech. Abstr.

Int. J. Rock Mech. Min. Sci. & Geomech. Abstr.

Int. J. Rock Mech. Min. Sci.

The effect of time-dependent properties of altered rock on tunnel support requirements

Finite element analysis of consolidation and creep

Computer implementation of non linear finite element analysis applied to some geotechnical problems

Algunos principios y metodos variacionales en elasto-plasticidad, creep y su formulacion unificada a traves de la elasto-plasticidad

General stress-strain-time function for Soil

J. Soil Mech. Fdn. Div. Am. Soc. civ. Engrs

Analysis of time-dependent deformations of openings in salt media

Int. J. Rock Mech. Min. Sci.