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1.
Finite element discretization of Biot's consolidation equations can produce a symmetric indefinite system (commonly used in geomechanics) or a non‐symmetric system. While this difference appears to be minor, however, it will require the selection of entirely different Krylov subspace solvers with potentially significant impact on solution efficiency. The former is solved using the symmetric quasi‐minimal residual whereas the latter is solved using the popular bi‐conjugate gradient stabilized. This paper presents an extensive comparison of the symmetric and non‐symmetric forms by varying the time step, size of the spatial domain, choice of physical units, and left versus left–right preconditioning. The generalized Jacobi (GJ) preconditioner is able to handle the non‐symmetric version of Biot's finite element method equation, although there are no practical incentives to do so. The convergence behaviour of GJ‐preconditioned systems and its relation to the spectral condition number or the complete spectrum are studied to clarify the concept of ill‐conditioning within the context of iteration solvers. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
2.
The finite element (FE) simulation of large‐scale soil–structure interaction problems (e.g. piled‐raft, tunnelling, and excavation) typically involves structural and geomaterials with significant differences in stiffness and permeability. The symmetric quasi‐minimal residual solver coupled with recently developed generalized Jacobi, modified symmetric successive over‐relaxation (MSSOR), or standard incomplete LU factorization (ILU) preconditioners can be ineffective for this class of problems. Inexact block diagonal preconditioners that are inexpensive approximations of the theoretical form are systematically evaluated for mitigating the coupled adverse effects because of such heterogeneous material properties (stiffness and permeability) and because of the percentage of the structural component in the system in piled‐raft foundations. Such mitigation led the proposed preconditioners to offer a significant saving in runtime (up to more than 10 times faster) in comparison with generalized Jacobi, modified symmetric successive over‐relaxation, and ILU preconditioners in simulating piled‐raft foundations. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
3.
A challenging computational problem arises when a discrete structure (e.g. foundation) interacts with an unbounded medium (e.g. deep soil deposit), particularly if general loading conditions and non‐linear material behaviour is assumed. In this paper, a novel method for dealing with such a problem is formulated by combining conventional three‐dimensional finite‐elements with the recently developed scaled boundary finite‐element method. The scaled boundary finite‐element method is a semi‐analytical technique based on finite‐elements that obtains a symmetric stiffness matrix with respect to degrees of freedom on a discretized boundary. The method is particularly well suited to modelling unbounded domains as analytical solutions are found in a radial co‐ordinate direction, but, unlike the boundary‐element method, no complex fundamental solution is required. A technique for coupling the stiffness matrix of bounded three‐dimensional finite‐element domain with the stiffness matrix of the unbounded scaled boundary finite‐element domain, which uses a Fourier series to model the variation of displacement in the circumferential direction of the cylindrical co‐ordinate system, is described. The accuracy and computational efficiency of the new formulation is demonstrated through the linear elastic analysis of rigid circular and square footings. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
4.
M. Baumann R. Astudillo Y. Qiu E. Y. M. Ang M. B. van Gijzen R.-É. Plessix 《Computational Geosciences》2018,22(1):43-61
In this work, we present a new numerical framework for the efficient solution of the time-harmonic elastic wave equation at multiple frequencies. We show that multiple frequencies (and multiple right-hand sides) can be incorporated when the discretized problem is written as a matrix equation. This matrix equation can be solved efficiently using the preconditioned IDR(s) method. We present an efficient and robust way to apply a single preconditioner using MSSS matrix computations. For 3D problems, we present a memory-efficient implementation that exploits the solution of a sequence of 2D problems. Realistic examples in two and three spatial dimensions demonstrate the performance of the new algorithm. 相似文献
5.
Projection, or conjugate gradient like, methods are becoming increasingly popular for the efficient solution of large sparse sets of unsymmetric indefinite equations arising from the numerical integration of (initial) boundary value problems. One such problem is soil consolidation coupling a flow and a structural model, typically solved by finite elements (FE) in space and a marching scheme in time (e.g. the Crank–Nicolson scheme). The attraction of a projection method stems from a number of factors, including the ease of implementation, the requirement of limited core memory and the low computational cost if a cheap and effective matrix preconditioner is available. In the present paper, biconjugate gradient stabilized (Bi‐ CGSTAB) is used to solve FE consolidation equations in 2‐D and 3‐D settings with variable time integration steps. Three different nodal orderings are selected along with the preconditioner ILUT based on incomplete triangular factorization and variable fill‐in. The overall cost of the solver is made up of the preconditioning cost plus the cost to converge which is in turn related to the number of iterations and the elementary operations required by each iteration. The results show that nodal ordering affects the perfor mance of Bi‐CGSTAB. For normally conditioned consolidation problems Bi‐CGSTAB with the best ILUT preconditioner may converge in a number of iterations up to two order of magnitude smaller than the size of the FE model and proves an accurate, cost‐effective and robust alternative to direct methods. Copyright © 2001 John Wiley & Sons, Ltd. 相似文献
6.
In this article we present a series of tests to study how well suited the TPFA coefficient matrix is as a preconditioner for the MPFA discrete system of equations in an iterative solver, using a flux splitting method. These tests have been conducted for single-phase flow for a wide range of anisotropy, heterogeneity, and grid skewness (mainly parallelogram grids). We use the K-orthogonal part of the MPFA transmissibilities for a parallelogram grid to govern the TPFA transmissibilities. The convergence of the flux splitting method is for each test case measured by the spectral radius of the iteration matrix. 相似文献
7.
Investigation of influence of particle characteristics on the non‐coaxiality of anisotropic granular materials using DEM 
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下载免费PDF全文 As a result of deposition process and particle characteristics, granular materials can be inherently anisotropic. Many researchers have strongly suggested that the inherent anisotropy is the main reason for the deformation non‐coaxiality of granular materials. However, their relationships are not unanimous because of the limited understanding of the non‐coaxial micro‐mechanism. In this study, we investigated the influence of inherent anisotropy on the non‐coaxial angle using the discrete element method. Firstly, we developed a new discrete element method approach using rough elliptic particles and proposed a novel method to produce anisotropic specimens. Secondly, the effects of initial specimen density and particle characteristics, such as particle aspect ratio A m, rolling resistance coefficient β , and bedding plane orientation δ , were examined by a series of biaxial tests and rotational principal axes tests. Findings from the numerical simulations are summarized as follows: (1) the peak internal friction angle ? p and the non‐coaxial angle i both increase with the initial density, A m and β , and they both increase initially and then decrease with δ in the range of 0–90°; (2) among the particle characteristics, the influence of A m is the most significant; and (3) for anisotropic specimens, the non‐coaxial angle can be calculated using the double slip and rotation rate model. Then, an empirical formula was proposed based on the simulation results to depict the relationship between the non‐coaxial angle and the particle characteristics. Finally, the particle‐scale mechanism of non‐coaxiality for granular materials was discussed from the perspective of energy dissipation. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
8.
A numerically efficient and stable method is developed to analyze Biot's consolidation of multilayered soils subjected to non‐axisymmetric loading in arbitrary depth. By the application of a Laplace–Hankel transform and a Fourier expansion, the governing equations are solved analytically. Then, the analytical layer‐element (i.e. a symmetric stiffness matrix) describing the relationship between generalized displacements and stresses of a layer is exactly derived in the transformed domain. Considering the continuity conditions between adjacent layers, the global stiffness matrix of multilayered soils is obtained by assembling the inter‐related layer‐elements. Once the solution in the Laplace–Hankel transformed domain that satisfies the boundary conditions has been obtained, the actual solution can be derived by the inversion of the Laplace–Hankel transform. Finally, numerical examples are presented to verify the theory and to study the influence of the layered soil properties and time history on the consolidation behavior. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
9.
F. Tonon 《国际地质力学数值与分析法杂志》2007,31(14):1567-1608
After describing the kinematics of a generic rigid block subjected to large rotations and displacements, the Udwadia's General Principle of Mechanics is applied to the dynamics of a rigid block with frictional constraints to show that the reaction forces and moments are indeterminate. Thus, the paper presents an incremental‐iterative algorithm for analysing general failure modes of rock blocks subject to generic forces, including non‐conservative forces such as water forces. Consistent stiffness matrices have been developed that fully exploit the quadratic convergence of the adopted Newton–Raphson iterative scheme. The algorithm takes into account large block displacements and rotations, which together with non‐conservative forces make the stiffness matrix non‐symmetric. Also included in the algorithm are in situ stress and fracture dilatancy, which introduces non‐symmetric rank‐one modifications to the stiffness matrix. Progressive failure is captured by the algorithm, which has proven capable of detecting numerically challenging failure modes, such as rotations about only one point. Failure modes may originate from a limit point or from dynamic instability (divergence or flutter); equilibrium paths emanating from bifurcation points are followed by the algorithm. The algorithm identifies both static and dynamic failure modes. The calculation of the factor of safety comes with no overhead. Examples show the equilibrium path of a rock block that undergoes slumping failure must first pass through a bifurcation point, unless the block is laterally constrained. Rock blocks subjected to water forces (or other non‐conservative forces) may undergo flutter failure before reaching a limit point. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
10.
Studying the effect of non‐spherical micro‐particles on Hoek–Brown strength parameter mi using numerical true triaxial compressive tests 下载免费PDF全文
下载免费PDF全文 The strength parameter mi in the Hoek–Brown strength criterion is empirical and was developed by trial and error. To better understand the fundamental relationship between mi and the physical characteristics of intact rock, this paper presents a systematic study of mi by representing intact rock as a densely packed cemented particle material and simulating its mechanical behavior using particle flow modeling. Specifically, the three‐dimensional particle flow code (PFC3D) was used to conduct numerical true triaxial compression tests on intact rock and to investigate the effect of non‐spherical micro‐particle parameters on mi. To generate numerical intact rock specimens containing non‐spherical micro‐particles, a new genesis process was proposed, and a specific loop algorithm was used based on the efficiency of the process and the acceptability of generated specimens. Four main parameters—number, aspect ratio, size, and shape—of non‐spherical micro‐particles were studied, and the results indicated that they all have great effect on mi. The strength parameter mi increases when the number, aspect ratio, or size is larger or the shape becomes more irregular, mainly as a result of the higher level of interlocking between particles. This confirms the observations from engineering experience and laboratory experiments. To simulate the right strength parameter mi, it is important to use appropriate non‐spherical micro‐particles by controlling these four parameters. This is further demonstrated by the simulation of two widely studied rocks, Lac du Bonnet granite and Carrara marble. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
11.
The adiabatic elastic stiffness constants of synthetic single-crystal MnO were measured in this study using pulse superposition interferometry. Data were obtained up to 1.0 GPa in pressure and over the temperature range 273 to 473 K. As a result, we were able to determine the complete set of second-order stiffness moduli (C
ij
s
) and their pressure and temperature derivatives, as well as higher-order properties for selected modes. Relevant results for the adiabatic bulk modulus are: K
s=155.1±0.8 GPa; (Ks/P)T=4.70±0.13; and, (K
s/T)P= -0.0203±0.0009 GPa/K. Our results for the second-order moduli are generally consistent with the data from previous studies. However, relative to the estimated uncertainties, small and systematic discrepancies appear to characterize the data set. The available evidence indicates that the differences result from microstructural variations (in particular, microcracks and Mn3O4 inclusions) between the synthetic MnO specimens used in different investigations. The pure shear mode C
44 exhibits anomalous soft-mode behavior with both temperature (the ambient derivative is positive) and pressure (the ambient derivative is negative). In both cases the C
44 data trends appear to primarily reflect the influence of Mn-Mn magnetoelastic interactions associated with the onset of a paramagnetic-antiferromagnetic (PM AFM) phase transition. 相似文献
12.
This paper identifies imbalanced columns (or rows) as a significant source of ill‐conditioning in the preconditioned coefficient matrix using the standard Jacobi preconditioner, for finite element solution of Biot's consolidation equations. A simple and heuristic preconditioner is proposed to reduce this source of ill‐conditioning. The proposed preconditioner modifies the standard Jacobi preconditioner by scaling the excess pore pressure degree‐of‐freedoms in the standard Jacobi preconditioner with appropriate factors. The performance of such preconditioner is examined using the symmetric quasi‐minimal residual method. To alleviate storage requirements, element‐by‐element iterative strategies are implemented. Numerical experiment results show that the proposed preconditioner reduces both the number of iteration and CPU execution time significantly as compared with the standard Jacobi preconditioner. Copyright © 2001 John Wiley & Sons, Ltd. 相似文献
13.
In this paper, a simple semi‐analytical method has been developed to solve the one‐dimensional non‐linear consolidation problems by considering the changes of compressibility and permeability of the soil layer, subjected to complicated time‐dependent cyclic loadings at the ground surface. The solution presented here takes into account e ～ lg kv and e ～ lg σ′ linear responses. With ck the slope of the e ～ lg kv line and cc as the slope of the e ～ lg σ′ line, the identified parameter cc/ck is found to control the rate of consolidation. Using the solutions obtained, some diagrams are prepared and the relevant behaviours of one‐dimensional non‐linear consolidation of saturated soft soil under cyclic loadings are discussed. The method in this paper does not require any special data; conventional oedometer data can be used. Therefore, the method is particularly efficient and convenient for engineering practice. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
14.
Wei Dong Guo 《国际地质力学数值与分析法杂志》2016,40(14):1936-1967
This paper develops a three‐layer model and elastic solutions to capture nonlinear response of rigid, passive piles in sliding soil. Elastic solutions are obtained for an equivalent force per unit length ps of the soil movement. They are repeated for a series of linearly increasing ps (with depth) to yield the nonlinear response. The parameters underpinning the model are determined against pertinent numerical solutions and model tests on passive free‐head and capped piles. The solutions are presented in non‐dimensional charts and elaborated through three examples. The study reveals the following:
- On‐pile pressure in rotationally restrained, sliding layer reduces by a factor α, which resembles the p‐multiplier for a laterally loaded, capped pile, but for its increase with vertical loading (embankment surcharge), and stiffness of underlying stiff layer: α = 0.25 and 0.6 for a shallow, translating and rotating piles, respectively; α = 0.33–0.5 and 0.8–1.3 for a slide overlying a stiff layer concerning a uniform and a linearly increasing pressure, respectively; and α = 0.5–0.72 for moving clay under embankment loading.
- Ultimate state is well defined using the ratio of passive earth pressure coefficient over that of active earth pressure. The subgrade modulus for a large soil movement may be scaled from model tests.
- The normalised rotational stiffness is equal to 0.1–0.15 for the capped piles, which increases the pile displacement with depth.
15.
Corinne Dorais Antonio Simonetti Loretta Corcoran Tyler L. Spano Peter C. Burns 《Geostandards and Geoanalytical Research》2020,44(1):125-132
There is currently a lack of well‐characterised matrix‐matched reference materials (RMs) for forensic analysis of U‐rich materials at high spatial resolution. This study reports a detailed characterisation of uraninite (nominally UO2+x) from the Happy Jack Mine (UT, USA). The Happy Jack uraninite can be used as a RM for the determination of rare earth element (REE) mass fractions in nuclear materials, which provide critical information for source attribution purposes. This investigation includes powder X‐ray diffraction (pXRD) data, as well as major, minor and trace element abundances determined using a variety of micro‐analytical techniques. The chemical signature of the uraninite was investigated at the macro (cm)‐scale with micro‐X‐ray fluorescence (µXRF) mapping and at high spatial resolution (tens of micrometre scale) using electron probe microanalysis (EPMA) and laser ablation‐inductively coupled plasma‐mass spectrometry (LA‐ICP‐MS) analyses. Based on EPMA results, the uraninite is characterised by homogeneous UO2 and CaO contents of 91.57 ± 1.49% m/m (2s uncertainty) and 2.70 ± 0.38% m/m (2s), respectively. Therefore, CaO abundances were used as the internal standard when conducting LA‐ICP‐MS analyses. Overall, the major element and REE compositions are homogeneous at both the centimetre and micrometre scales, allowing this material to be used as a RM for high spatial resolution analysis of U‐rich samples. 相似文献
16.
Preconditioned projection (or conjugate gradient like) methods are increasingly used for the accurate and efficient solution to finite element (FE) coupled consolidation equations. Theory indicates that preliminary row/column scaling does not affect the eigenspectrum of the iteration matrix controlling convergence as long as the preconditioner relies on the incomplete factorization of the FE coefficient matrix. However, computational experience with mid‐large size problems shows that the above inexpensive operation can significantly accelerate the solver convergence, and to a minor extent also improve the final accuracy, as a result of a better solver stability to the accumulation and propagation of floating point round‐off errors. This is demonstrated with the aid of the least square logarithm (LSL) scaling algorithm on FE consolidation problems of increasing size up to more than 100 000. It is shown that a major source of numerical instability rests with the sub‐matrix which couples the structural to the fluid part of the underlying mathematical model. It is concluded that for mid‐large size, possibly difficult, FE consolidation problems left/right LSL scaling is to be always recommended when the incomplete factorization is used as a preconditioning technique. Copyright © 2003 John Wiley & Sons, Ltd. 相似文献
17.
Gu Xiaoqiang Li Youhong Hu Jing Shi Zhenhao Liang Fayun Huang Maosong 《Acta Geotechnica》2022,17(8):3229-3243
Natural clays usually show anisotropic stiffness due to their deposition process and anisotropic in situ stress state. The stiffness anisotropy depends on both of the stress anisotropy and fabric anisotropy, while the latter can be quantified by the stiffness anisotropy at isotropic stress states. This paper measures the K0 value (i.e., stress anisotropy) and elastic shear stiffness anisotropy of natural Shanghai clay in a triaxial apparatus with horizontal and vertical bender elements. The results show that the K0 value of Shanghai clay lies in the range of 0.40–0.66, and an empirical equation is proposed to estimate the K0 value based on the plasticity index and initial void ratio. The fabric anisotropy of natural Shanghai clay lies in the range of 1.2–1.4 with a stronger fabric in the horizontal plane. Moreover, the experimental data of the stiffness anisotropy and fabric anisotropy of different clays in the literature are reviewed and analyzed. It reveals that the stiffness anisotropy generally increases, while the fabric anisotropy remains nearly the same during K0 consolidation. For normally consolidated clay, the fabric anisotropy generally lies in the range of 1.1–1.7. For overconsolidated clays, the fabric anisotropy generally increases as the overconsolidation ratio increases. Empirical equations are proposed to approximately estimate the fabric anisotropy of clays based on its stress normalized elastic shear stiffness.
相似文献18.
Wei Dong Guo 《国际地质力学数值与分析法杂志》2000,24(2):135-163
Viscoelastic or creep behaviour can have a significant influence on the load transfer (t–z) response at the pile–soil interface, and thus on the pile load settlement relationship. Many experimental and theoretical models for pile load transfer behaviour have been presented. However, none of these has led to a closed‐form expression which captures both non‐linearity and viscoelastic behaviour of the soil. In this paper, non‐linear viscoelastic shaft and base load transfer (t–z) models are presented, based on integration of a generalized viscoelastic stress–strain model for the soil. The resulting shaft model is verified through published field and laboratory test data. With these models, the previous closed‐form solutions evolved for a pile in a non‐homogeneous media have been readily extended to account for visco‐elastic response. For 1‐step loading case, the closed‐form predictions have been verified extensively with previous more rigorous numerical analysis, and with the new GASPILE program analysis. Parametric studies on two kinds of commonly encountered loading: step loading, ramp (linear increase followed by sustained) loading have been performed. Two examples of the prediction of the effects of creep on the load settlement relationship by the solutions and the program GASPILE, have been presented. Copyright © 2000 John Wiley & Sons, Ltd. 相似文献
19.
Preconditioners in computational geomechanics: A survey 总被引：1，自引：0，他引：1
The finite element (FE) solution of geomechanical problems in realistic settings raises a few numerical issues depending on the actual process addressed by the analysis. There are two basic problems where the linear solver efficiency may play a crucial role: 1. fully coupled consolidation and 2. faulted uncoupled consolidation. A class of general solvers becoming increasingly popular relies on the Krylov subspace (or Conjugate Gradient‐like) methods, provided that an efficient preconditioner is available. For both problems mentioned above, the possible preconditioners include the diagonal scaling (DS), the Incomplete LU decomposition (ILU), the mixed constraint preconditioning (MCP) and the multilevel incomplete factorization (MIF). The development and the performance of these algorithms have been the topic of several recent works. The present paper aims at providing a survey of the preconditioners available to date in computational geomechanics. In particular, a review and a critical discussion of DS, ILU, MCP and MIF are given along with some comparative numerical results. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
20.
DONG Jin GAO Rui WANG Yong ZHANG Shihong YAO Peiyi CHI Zhenqing ZHAO Zhili 《《地质学报》英文版》2013,87(1):186-196
The detailed magnetic susceptibility anisotropy study on the sediments of two sections, which are located in the lake-center and the lakeshore of the Huangqihai Lake,Inner Mongolia, revealed their hydrodynamics and sedimentary environment changes in the recent 2000 years.The results show that the sediments of two sections both display normal depositional magnetic fabrics,of which the minimum susceptibility axes（K3） are oriented perpendicular to the bedding plane and the maximum magnetic susceptibility axes（K1） lie parallel with the bedding plane.In addition,the lakeshore presents higher magnetic anisotropy degree（P）,magnetic foliation（F） and current factor （Fs） than the lake-center,showing that the lakeshore has higher flow velocity.For the west Huangqihai Lake（HQW） section in the lake-center,the magnetic matrix grain degree（Q） and the inclination of the minimum susceptibility axes sharply increased and decreased,respectively,at a depth of about 10 cm,24 cm,45 cm and 74 cm,which indicate abnormal depositional events with strong kinetic energy.Through comparative analysis,the HQW section can be divided into three stages from top to bottom.The upper stage was a stable depositional environment with strong hydrodynamic energy and low water level,which shows relatively higher Fs value and the Q value varies similarly with P and F.The middle stage was a stable depositional environment with high water level and low hydrodynamic energy,intermitted with high-energy abnormal events,which shows relatively lower Fs and the Q value was negatively correlated with P and F.The lower stage was an unstable depositional environment with low hydrodynamic energy and high water level,which shows relatively lower P,F,and Fs value. 相似文献