Numerical stability in quasi‐static elasto/visco‐plasticity

Cormeau, I.

doi:10.1002/nme.1620090110

Cited by 264 publications

(71 citation statements)

References 5 publications

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“…A critical time step, ∆t c , that cannot be exceeded by the computational time step ∆t, must be defined. Cormeau (1975) and Billaux and Cundall (1993) state that the evaluation of the critical time step can be done with the constraint that the velocity of the solution wave must be always greater than the velocity of the physical wave during a computational cycle, as discussed later. The solution is highly unstable during the first computational steps because of the magnitude of the unbalanced forces.…”

Section: Introduction Of Flac Algorithmmentioning

confidence: 99%

Seismic Earth Pressures on Retaining Structures and Basement Walls in Cohesionless Soils

Mikola

Candia

Sitar

2016

J. Geotech. Geoenviron. Eng.

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Observations of the performance of basement walls and retaining structures in recent earthquakes show that failures of basement or deep excavation walls in earthquakes are rare even if the structures were not designed for the actual intensity of the earthquake loading. Failures of retaining structures are most commonly confined to waterfront structures retaining saturated backfill with liquefaction being the critical factor in the failures. Failures of other types of retaining structures are relatively rare and usually involve a more complex set of conditions, such as sloping ground either above or below the retaining structure, or both. While some failures have been observed, there is no evidence of a systemic problem with traditional static retaining wall design even under quite severe loading conditions. No significant damage or failures of retaining structures occurred in the recent earthquakes such as Wenchuan earthquake in China (2008) and, or the large subduction zone earthquakes in Chile (2010) and Japan (2011). Therefore, this experimental and analytical study was undertaken to develop a better understanding of the distribution and magnitude of seismic earth pressures on cantilever retaining structures.The experimental component of the study consists of two sets of dynamic centrifuge model experiments. In the first experiment two model structures representing basement type setting were used, while in the second test a U-shaped channel with cantilever sides and a simple cantilever wall were studied. All of these structures were chosen to be representative of typical designs. Dry medium-dense sand with relative density on the order of from 75% to 80% was used as backfill. Results obtained from the centrifuge experiments were subsequently used to develop and calibrate a two-dimensional, nonlinear, finite difference model built on the FLAC platform.The centrifuge data consistently shows that for the height of structures considered herein, i.e. in the range of 20-30 ft, the maximum dynamic earth pressure increases with depth and can be reasonably approximated by a triangular distribution This suggests that the point of application of the resultant force of the dynamic earth pressure increment is approximately 1/3H 2 above the base of the wall as opposed to 0.5-0.6 H recommended by most current design procedures. In general, the magnitude of the observed seismic earth pressures depends on the magnitude and intensity of shaking, the density of the backfill soil, and the type of the retaining structures. The computed values of seismic earth pressure coefficient ( K ae ) back calculated from the centrifuge data at the time of maximum dynamic wall moment suggest that for free standing cantilever retaining structures seismic earth pressures can be neglected at accelerations below 0.4 g. While similar conclusions and recommendations were made by , their approach assumed that a wall designed to a reasonable static factor of safety should be able to resist seismic loads up 0.3 g. In the present study, experimental da...

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Section: Introduction Of Flac Algorithmmentioning

confidence: 99%

Seismic Earth Pressures on Retaining Structures and Basement Walls in Cohesionless Soils

Mikola

Candia

Sitar

2016

J. Geotech. Geoenviron. Eng.

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“…It is possible to calculate an estimate of the critical time step for stability of the forward EuKer operator based on the form of the flow potential and the elastic constants (Cormeau, 1975). Following procedures outlined in Cormeau (1973, the critical time step for stability is calculated to be 4( 1 + u)…”

Section: Power Law Creep Materials Modelmentioning

confidence: 99%

“…The key to the scheme is the accurate determination of the stable time step which is accomplished using the work of Cormeau (1975) who developed a method for analytically determining the stable time step for a particular constitutive model. To determine the analytical expression for the stable tiime step size, we introduce the following linearized differential equation where y is a column vector containing the stress components and A is a square matrix defined by A stability analysis of the forward Euler integrator shows that the time interval is stable if At < -where is the largest eigenvalue of the square matrix A.…”

Section: The Backward Euler Integrator Has the Following Formmentioning

confidence: 99%

“…An additional feature of this approach, which is unique to indirect solution schemes, is that each element bloclc may have its own unique number of subincrements. Thus, the amount of computation is minimal for elements in regions where the stress is small and the computational effort is concentrated where the stress is largest.The key to the scheme is the accurate determination of the stable time step which is accomplished using the work of Cormeau (1975) who developed a method for analytically determining the stable time step for a particular constitutive model. To determine the analytical expression for the stable tiime step size, we introduce the following linearized differential equation we can write an efficient, vectorized material model subroutine for implementation into SANTOS.…”

mentioning

confidence: 99%

“…The key to the scheme is the accurate determination of the stable time step which is accomplished using the work of Cormeau (1975) who developed a method for analytically determining the stable time step for a particular constitutive model. To determine the analytical expression for the stable tiime step size, we introduce the following linearized differential equation we can write an efficient, vectorized material model subroutine for implementation into SANTOS.…”

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confidence: 99%

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SANTOS - a two-dimensional finite element program for the quasistatic, large deformation, inelastic response of solids

Stone¹

1997

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SANTOS is a finite element program designed to compute the quasistatic, large deformation, inelastic response of two-dimensional planar or axisymmetric solids. The code is derived tiom the transient dynamic code PRONTO 2D.The solution strategy used to compute the equilibrium states is based on a self-adaptive dynamic relaxation solution scheme, which is based on explicit central difference pseudo-time integration and artificial mass proportional damping. The element used in SANTOS is a uniform strain 4-node quadrilateral element with an hourglass control scheme to control the spurious deformation modes. Finite strain constitutive models for many common engineering materials are included. A robust master-slave contact algorithm for modeling sliding contact is implemented. An interface for coupling to an external code is also provided. ACKNOWLEDGMENTSThe author acknowledges the technical contributions of L.M. Taylor and D.P. Flanagan, who developed the PRONTO architecture and provided the framework from which S A N T O S is derived. Much of this manual is derived from their original PRONTO manual. S i e c a n t contributions to the development of SANTOS were made by several of the early users. J.G. Argiiello and G.W. Wellman ran the various versions of the code and provided constructive feedback about its performance and capabilities. Greg Sjaardema produced the early scripts and system procedures that provided the users with an easy way to run the code. Martin Heinstein took a new look at the contact surface problem and significantly improved both the location and application phases of the contact d a c e algorithm. H.S. Morgan's early work in integration of unified-creep-plasticity models provided the basis for integrating the time-dependent constitutive models. The efforts of the many other individuals who ran early versions of the code and provided helpful comments are gratefully acknowledged. .O INTRODUCTIONSANTOS is a finite element program developed for quasistatic, large deformation, inelastic analysis of twodimensional solids. It is a powerful analysis tool that allows the user to address the solution of complex problems that include both material and geometric nonlinearities. The wide variety of constitutive models in the code allows SANTOS to be used for a wide class of problems from geomechanics to metal forming.In 1986, Taylor and Flanagan at Sandia National LaboratoriedNew Mexico developed a new transient dynamics finite element code, which they named PRONTO (Taylor and Flanagan, 1987), that replaced the widely used HONDO 11 (Key et al., 1978) code. PRONTO employed the same explicit central difference time integration operator as HONDO 11 in addition to some new state-of-the-art fahues such as a uniform strain quadrilateral element with single point integration, improved critical time step estimates, and more robust contact surfms. The code was written in a modular fashion with an easy-to-use interface for adding new constitutive models. The code architecture and storag...

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A numerical procedure for the analysis of the hydromechanical coupling in fractured rock masses

Azevedo

Vaz

Vargas

1998

Int. J. Numer. Anal. Meth. Geomech.

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SUMMARYThis work presents a finite element implementation to treat the Hydromechanical Coupling (HM) in fractured rock masses under the framework of the so-called 'equivalent continuum' approach. The multilaminar concept, introduced by Zienkiewicz and Pande, is used to simulate the mechanical behaviour of both the intact rock and the families of fractures. In that concept, the non-linearities in the constitutive relations are dealt by means of fictitious viscoplasticity. In the present implementation, the mechanical behaviour of the fractures is modelled by means of Barton-Bandis model. The shear stress/shear displacement/dilatancy relationship is modelled as viscoplastic and the normal stress/normal displacement as non-linear viscoelastic. Flow along fractures is considered to occur as a sequence of permanent states. The permeability tensor of the equivalent continuum is determined from the hydraulic apertures, in accordance of Barton et al. From the numerical point of view, the basic aim of the work is the implementation of an efficient scheme to solve the above described problem. This is done by designing a self-adaptive time step control, transparent to the user, which determines the highest possible time step while assuming the conditions of precision, stability and convergence. The paper presents the numerical details of such scheme together with validation/comparative examples and the results obtained on the analysis of the fractured rock foundation of a hypothetical dam. 1998 John Wiley & Sons, Ltd.

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Numerical stability in quasi‐static elasto/visco‐plasticity

Cited by 264 publications

References 5 publications

Seismic Earth Pressures on Retaining Structures and Basement Walls in Cohesionless Soils

Seismic Earth Pressures on Retaining Structures and Basement Walls in Cohesionless Soils

SANTOS - a two-dimensional finite element program for the quasistatic, large deformation, inelastic response of solids

A numerical procedure for the analysis of the hydromechanical coupling in fractured rock masses

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