共查询到20条相似文献，搜索用时 15 毫秒
1.
G. Y. Sheu 《Geotechnical and Geological Engineering》2009,27(6):729-740
This study presents the recognition of an elastic–plastic constitutive law by a multiobjective evolutionary algorithm (MOEA).
This idea is illustrated by the identification of ellipse aspect ratio and plastic modulus of a reported bounding surface
model. Based on the multi-goals of well predicting all available drained or undrained stress–strain behaviors simultaneously,
the compromising solutions of these two parameters are found by a strength Pareto evolutionary algorithm 2 (SPEA2). Their
fittest values are then determined by additionally introducing the Akaike information criterion. Experimental data for the
Ottawa sand are used to test such processes. The results show that an MOEA is an efficient and automatic tool to identify
the fittest form of an elastic–plastic constitutive law from a large amount of experimental data. However, sufficient data
are required to determine the correct searching range of parameters to be identified. 相似文献
2.
A second-order exact expression for the evolution of probability density function of stress is derived for general, one-dimensional
(1-D) elastic–plastic constitutive rate equations with uncertain material parameters. The Eulerian–Lagrangian (EL) form of
Fokker–Planck–Kolmogorov (FPK) equation is used for this purpose. It is also shown that by using EL form of FPK, the so called
“closure problem” associated with regular perturbation methods used so far, is resolved too. The use of EL form of FPK also
replaces repetitive and computationally expensive deterministic elastic–plastic computations associated with Monte Carlo technique.
The derived general expressions are specialized to the particular cases of point location scale linear elastic and elastic–plastic
constitutive equations, related to associated Drucker–Prager with linear hardening. In a companion paper, the solution of
FPK equations for 1D is presented, discussed and illustrated through a number of examples. 相似文献
3.
A large strain analysis of undrained expansion of a spherical/cylindrical cavity in a soil modelled as non‐linear elastic modified Cam clay material is presented. The stress–strain response of the soil is assumed to obey non‐linear elasticity until yielding. A power‐law characteristic or a hyperbolic stress–strain curve is used to describe the gradual reduction of soil stiffness with shear strain. It is assumed that, after yielding, the elasto‐plastic behaviour of the soil can be described by the modified Cam clay model. Based on a closed‐form stress–strain response in undrained condition, a numerical solution is obtained with the aid of simple numerical integration technique. The results show that the stresses and the pore pressure in the soil around an expanded cavity are significantly affected by the non‐linear elasticity, especially if the soil is overconsolidated. The difference between large strain and small strain solutions in the elastic zone is not significant. The stresses and the pore pressure at the cavity wall can be expressed as an approximate closed‐form solution. Copyright © 2001 John Wiley & Sons, Ltd. 相似文献
4.
In this article we present closed‐form solutions for the undrained variations in stress, pore pressure, deformation and displacement inside hollow cylinders and hollow spheres subjected to uniform mechanical pressure instantaneously applied to their external and internal boundary surfaces. The material is assumed to be a saturated porous medium obeying a Mohr–Coulomb model failure criterion, exhibiting dilatant plastic deformation according to a non‐associated flow rule which accounts for isotropically strain hardening or softening. The instantaneous response of a porous medium submitted to an instantaneous loading is undrained, i.e. without any fluid mass exchange. The short‐term equilibrium problem to be solved is now formally identical to a problem of elastoplasticity where the constitutive equations involve the undrained elastic moduli and particular equivalent plastic parameters. The response of the model is presented (i) for extension and compression undrained triaxial tests, and (ii) for unloading problems of hollow cylinders and spheres through the use of appropriately developed closed‐form solutions. Numerical results are presented for a plastic clay stone with strain hardening and an argilite with strain softening. The effects of plastic dilation, of the strain softening law and also of geometry of the cavity on the behaviour of the porous medium have been underlined. Analytical solutions provide valuable benchmarks enabling various numerical methods in undrained conditions with a finite boundary to be verified. Copyright © 2002 John Wiley & Sons, Ltd. 相似文献
5.
Summary A micromechanics-based model, able to quantify the effect of various parameters on the complete stress–strain relationship,
is described. The closed-form explicit expression for the complete stress–strain relationship of a rock material containing
an echelon cracks arrangement subjected to compressive loading is obtained. The complete stress–strain relationship including
the stages of linear elasticity, non-linear hardening and strain softening is established. The results show that the complete
stress–strain relationship and the strength of rock with echelon cracks depend on the crack interface friction coefficient,
the sliding crack spacing, the perpendicular distance between the two adjacent rows, the fracture toughness of rock material
and orientation of the cracks. The present model is used to evaluate the complete stress–strain relationship and strength
for crack-weakened rock at the underground cavern complex of the Ertan Hydroelectric Project. The predicted strength is in
agreement with that obtained by the Hoek–Brown criterion. The numerical results obtained with the complete stress–strain relationship
seem to be in good agreement with the measured values.
Author’s address: Xiao-Ping Zhou, School of Civil Engineering, Chongqing University, 443002 Chongqing, P.R. China 相似文献
6.
V. Palchik 《Rock Mechanics and Rock Engineering》2006,39(3):215-232
Summary. This paper presents a model created by the author to predict stress–strain relationships for weak to strong carbonate rocks
(σc < 100 MPa) exhibiting axial strains up to 1%. The stress–strain model based on Haldane’s distribution function (Haldane,
1919) relates the axial stress (or normalized axial stress) to the square of an exponential function where the exponent is
axial strain. To obtain accurate stress–strain relationship over the whole pre-failure strain with the proposed stress–strain
model, it is necessary to have only one datum point (peak axial stress and maximum axial strain at this peak stress). It is
shown that the stress–strain relationships observed in laboratory compression tests on samples collected from six carbonate
rock formations (chalk, dolomites and limestones) from different parts of Israel, agree well with the stress–strain prediction
model proposed by the author. 相似文献
7.
The paper presents a simple constitutive model for the behavior of sands during monotonic simple shear loading. The model
is developed specifically to account for the effects of principal stress rotation on the simple shear response of sands. The
main feature of the model is the incorporation of two important effects of principal stress on stress–strain response: anisotropy
and non-coaxiality. In particular, an anisotropic failure criterion, cross-anisotropic elasticity, and a plastic flow rule
and a stress–dilatancy relationship that incorporate the effects of non-coaxiality are adopted in the model. Simulations of
published experimental results from direct simple shear and hollow cylindrical torsional simple shear tests on sands show
the satisfactory performance of the model. It is envisioned that the model can be valuable in modeling in situ simple shear
response of sands and in interpreting simple shear test results. 相似文献
8.
This paper studies the excavation of a spherical cavity subjected to hydrostatic initial stresses in the infinite homogeneous and isotropic rock mass with strain‐softening Mohr–Coulomb (M‐C) and Hoek–Brown (H‐B) behaviors. Numerical solutions of the spherical cavity are obtained and the application to determining stress–strain curve of strain‐softening M‐C and H‐B rock mass is studied. A closed‐form solution for the elastic–brittle–plastic medium is introduced first, and then a numerical procedure that simplifies the strain‐softening process into a series of brittle–plastic ones is presented. The approach is validated against the facts that the strain‐softening process evolves into a brittle–plastic one when the softening slope is very steep, whereas it evolves into an elasto‐plastic one when the softening slope approaches zero. Numerical solutions for the prediction of displacements and stresses around the spherical cavity in the strain‐softening M‐C and H‐B rock mass are presented. On the basis of the analysis of the spherical cavity in strain‐softening rock mass, the stress–strain relationship at an infinitesimal cube around the cavity is obtained and discussed with different evolution laws for the strength parameters considered. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
9.
The paper presents a closed-form solution for the convergence curve of a circular tunnel in an elasto-brittle-plastic rock
mass with both the Hoek–Brown and generalized Hoek–Brown failure criteria, and a linear flow rule, i.e., the ratio between
the minor and major plastic strain increments is constant. The improvement over the original solution of Brown et al. (J Geotech
Eng ASCE 109(1):15–39, 1983) consists of taking into account the elastic strain variation in the plastic annulus, which was assumed to be fixed in the
original solution by Brown et al. The improvement over Carranza-Torres’ solution (Int J Rock Mech Min Sci 41(Suppl 1):629–639,
2004) consists of providing a closed-form solution, rather than resorting to numerical integration of an ordinary differential
equation. The presented solution, by rigorously following the theory of plasticity, takes into account that the elastic strain
components change with radial and circumferential stress changes within the plastic annulus. For the original Hoek–Brown failure
criterion, disregarding the elastic strain change leads to underestimate the convergence by up to 55%. For a rock mass failing
according to the generalized Hoek–Brown failure criterion, using the original failure criterion leads to a high probability
(97%) of underestimating the convergence by up to 100%. As a consequence, the onset or degree of squeezing may be underestimated,
and the loading on the support/reinforcement calculated with the convergence/confinement method may be largely underestimated. 相似文献
10.
Kasper D. Fischer 《International Journal of Earth Sciences》2006,95(2):239-249
The Aegean–Anatolian region is characterised by an inhomogeneous deformation pattern with high strain rates and a high seismicity both at the boundaries and in the plate interior. This pattern is controlled by the geometry and rheology of the structural units involved and their tectonic setting. A numerical analysis with a finite-element model of the region is used to quantify the influence of different rheological parameters. Viscoelastic material behaviour is implemented for the mantle lithosphere, whereas the crust is modelled with an elastic–plastic rheology. The variation of the inelastic material properties (viscosity and plastic strength) quantifies the influence of these material parameters on the deformation, stress, and strain patterns. Comparison of the modelled results with geodetic and geophysical observations reveals that the viscosity of the mantle lithosphere is the key to explaining the inhomogeneous deformation pattern. The best-fit model yields a viscosity of 1020 Pa s beneath Anatolia, whereas adjacent regions have viscosities between 1021 and 1023 Pa s. The model also explains the intra-plate seismicity and the stress field as well as its partitioning into regions with strike-slip and normal faulting. The final model is in good agreement with seismological, geodetic, and geological observations. Local deviations can be tracked down to small-scale structures, which are not included in the model. 相似文献
11.
12.
Geotechnical and Geological Engineering - The present work aims to understand the stress–strain response of an igneous rock, metadolerite, typically found in dyke form, under high loading... 相似文献
13.
Summary This paper is intended to describe the SHELVIP (Stress Hardening ELastic VIscous Plastic) model, a new viscoplastic constitutive
law which has been developed to incorporate the most important features of behaviour observed in tunnels excavated in severe
to very severe squeezing conditions. This model couples the elastoplastic and time-dependent behaviour by using a plastic
yield surface, as frequently adopted in tunnel design analysis, and the definition of a state of overstress referred to a
viscoplastic yield surface. The model is formulated in all its detailed aspects. The related analytical closed-form solution
for representing triaxial creep deformations is developed. Also developed is an incremental numerical solution for describing
the triaxial stress–strain behaviour under constant strain rate conditions. The model is shown to fit very satisfactorily
the results of creep tests on clay shales and relaxation tests on coal specimens, as recently performed for design analysis
of tunnels in squeezing conditions.
Correspondence: D. Debernardi, Department of Structural and Geotechnical Engineering, Politecnico di Torino, Torino, Italy 相似文献
14.
Improved Longitudinal Displacement Profiles for Convergence Confinement Analysis of Deep Tunnels 总被引：6，自引：1，他引：5
Summary Convergence-confinement analysis for tunneling is a standard approach for preliminary analysis of anticipated wall deformation
and support design in squeezing ground. Whether this analysis is performed using analytical (closed form) solutions or with
plane strain numerical models, a longitudinal displacement profile (LDP) is required to relate tunnel wall deformations at
successive stages in the analysis to the actual physical location along the tunnel axis. This paper presents a new and robust
formulation for the LDP calculation that takes into account the significant influence of ultimate (maximum) plastic radius.
Even after all parameters are appropriately normalized, the LDP function varies with the size of the ultimate plastic zone.
Larger yield zones take a relatively longer normalized distance to develop, requiring an appropriately calculated LDP. Failure
to use the appropriate LDP can result in significant errors in the specification of appropriate installation distance (from
the face) for tunnel support systems. Such errors are likely to result in failure of the temporary support. The equations
presented here are readily incorporated into analytical solutions and a graphical template is provided for use with numerical
modeling.
Correspondence: M. S. Diederichs, Associate Professor, Queen’s University, Ontario, Canada 相似文献
15.
A numerical technique is suggested that allows a prediction of the behaviour of a single phase, strain softening material during the expansion of a long cylindrical cavity. The method provides the entire pressure-expansion relationship, including the identification of the limit pressure at large deformations.The numerical solutions, obtained using the finite element technique and allowing for finite deformations, show very good agreement with closed form answers that are available for a restricted class of material models. Results are also presented for the more general, dilatant (or collapsing), strain softening materials for which closed form solutions do not exist. The importance of the rate of dilation and rate of softening in determining the behaviour during cavity expansion is illustrated. 相似文献
16.
In this paper, an experimental investigation of cement treated sand is performed under triaxial tests in order to quantify
the effects of cementation on the stress–strain behavior, stiffness and shear strength. Samples were cured up to 180 days.
The results show that the stress–strain behavior of cemented sands is nonlinear with contractive–dilative stages. The stress–strain
response is strongly influenced by effective confining pressure and cement content. Stiffness and strength are greatly improved
by an increase in binder content. An increase of the angle of shearing resistance and cohesion intercept with increasing cement
content is observed consistently. Brittle behavior is observed at low confining pressure and high cement content. After yielding,
the increase in the dilatancy accelerates. Two competing related processes determine the peak strength: Bond breakages cause
a strength reduction but the associated dilatancy leads to a strength increase. This finding and the experimental observation
that the dilatancy at the peak state increases with increasing cement content explain why the measured peak-state strength
parameters, c′ and φp′, are relevant to the binder content. 相似文献
17.
The paper presents the experimental investigation and analysis of the non-linear elasto-plastic stress–strain behaviour of
normally consolidated lacustrine clay. Drained triaxial stress path tests were performed on natural block samples of Swiss
lacustrine clay. Data were analysed using plasticity theory and the shape and extent of kinematic yield and bounding surfaces
were determined and found to be elliptical but not congruent. Cross-anisotropic elasticity was used to quantify elastic strains
to permit plastic strain increment vectors and hence a plastic potential surface to be defined. 相似文献
18.
A numerical algorithm for simulation of 2-D (axis-symmetric) wave propagation using a multidomain approach is proposed. The method uses a cylindrical coordinate system, Chebyshev and
Fourier differential operators to calculate the spatial derivatives along the radial and vertical direction, respectively,
and a Runge–Kutta time-integration scheme. The numerical technique is based on the solution of the equations of momentum conservation
combined with the stress–strain relations of the fluid (drilling mud) and isotropic elastic media (drill string and formation).
Wave modes and radiated waves are simulated in the borehole-formation system. The algorithm satisfies the reciprocity condition
and the results agree with an analytical solution and low-frequency simulation of wave-propagation modes reported in the literature.
Examples illustrating the propagation of waves are presented for hard and soft formations. Moreover, the presence of casing,
cement, and formation heterogeneity have been considered. Since the algorithm is based on a direct (grid) method, the geometry
and the properties defining the media at each grid point, can be general, i.e., there are no limitations such as planar interfaces
or uniform (homogeneous) properties for each medium.
相似文献
19.
E. Alonso L. R. Alejano F. Varas G. Fdez‐Manin C. Carranza‐Torres 《国际地质力学数值与分析法杂志》2003,27(13):1153-1185
A literature review has shown that there exist adequate techniques to obtain ground reaction curves for tunnels excavated in elastic‐brittle and perfectly plastic materials. However, for strain‐softening materials it seems that the problem has not been sufficiently analysed. In this paper, a one‐dimensional numerical solution to obtain the ground reaction curve (GRC) for circular tunnels excavated in strain‐softening materials is presented. The problem is formulated in a very general form and leads to a system of ordinary differential equations. By adequately defining a fictitious ‘time’ variable and re‐scaling some variables the problem is converted into an initial value one, which can be solved numerically by a Runge–Kutta–Fehlberg method, which is implemented in MATLAB environment. The method has been developed for various common particular behaviour models including Tresca, Mohr–Coulomb and Hoek–Brown failure criteria, in all cases with non‐associative flow rules and two‐segment piecewise linear functions related to a principal strain‐dependent plastic parameter to model the transition between peak and residual failure criteria. Some particular examples for the different failure criteria have been run, which agree well with closed‐form solutions—if existing—or with FDM‐based code results. Parametric studies and specific charts are created to highlight the influence of different parameters. The proposed methodology intends to be a wider and general numerical basis where standard and newly featured behaviour modes focusing on obtaining GRC for tunnels excavated in strain‐softening materials can be implemented. This way of solving such problems has proved to be more efficient and less time consuming than using FEM‐ or FDM‐based numerical 2D codes. Copyright © 2003 John Wiley & Sons, Ltd. 相似文献
20.
An analytical solution is presented for the stress and strain fields in a Mohr–Coulomb material in plane strain around a circular hole when it is compressed by an axisymmetric far-field pressure. It is shown that several solutions arise involving one to three plastic zones depending on the values of Poisson's ratio and the friction angle. The solution chosen for presentation was obtained and used to validate the functioning of the Mohr–Coulomb yield condition that was added to the NONSAP finite element code. Stress and strain field comparisons are made. 相似文献