The structure of non-hierarchical triple system stability regions

A detailed study of the two-dimensional initial conditions region section in the planar three-body problem is performed. The initial conditions for the three well-known stable periodic orbits (the Schubart’s orbit, the Broucke’s orbit and the eight-like orbit) belong to this section. Continuous stability regions (for the fixed integration interval) generated by these periodic orbits are found. Zones of the quick stability violation are outlined. The analysis of some concrete trajectories coming from various stability regions is performed. In particular, trajectories possessing varying number of “eights” formed by moving triple system components are discovered. Orbits with librations are also found. The new periodic orbit originated from the zone siding with the Schubart’s orbit region is discovered. This orbit has reversibility points (each of the outer bodies possess a reversibility point) and two points of close double approach of the central body to each of the outer bodies. The influence of the numerical integration accuracy on the results is studied. The stability regions structure is preserved during calculations with different values of the precision parameter, numerical integration methods and regularization algorithms of the equations of motion.     

Finite volume coupling strategies for the solution of a Biot consolidation model

In this paper a finite volume (FV) numerical method is implemented to solve a Biot consolidation model with discontinuous coefficients. Our studies show that the FV scheme leads to a locally mass conservative approach which removes pressure oscillations especially along the interface between materials with different properties and yields higher accuracy for the flow and mechanics parameters. Then this numerical discretization is utilized to investigate different sequential strategies with various degrees of coupling including: iteratively, explicitly and loosely coupled methods. A comprehensive study is performed on the stability, accuracy and rate of convergence of all of these sequential methods. In the iterative and explicit solutions four splits of drained, undrained, fixed-stress and fixed-strain are studied. In loosely coupled methods three techniques of the local error method, the pore pressure method, and constant step size are considered and results are compared with other types of coupling methods. It is shown that the fixed-stress method is the best operator split in comparison with other sequential methods because of its unconditional stability, accuracy and the rate of convergence. Among loosely coupled schemes, the pore pressure and local error methods which are, respectively, based on variation of pressure and displacement, show consistency with the physics of the problem. In these methods with low number of total mechanical iterations, errors within acceptance range can be achieved. As in the pore pressure method mechanics time step increases more uniformly, this method would be less costly in comparison with the local error method. These results are likely to be useful in decision making regarding choice of solution schemes. Moreover, the stability of the FV method in multilayered media is verified using a numerical example.     

Adaptive integration of constitutive rate equations

In finite element calculations the constitutive model plays a key role. The evaluation of the stress response of the constitutive relation for a given strain increment, which is a time integration in the case of models of the rate type, is a typical sub task in such calculations. Adaptive behaviour of the time integration is essential to assure numerical stability and to control the accuracy of the solution. An adaptive second order semi-implicit method is developed in this paper. Its numerical behaviour is compared with an adaptive second order explicit scheme. The two proposed methods control the local error and guarantee numerical stability of the time integration. We include several numerical geotechnical element tests using hypoplasticity with intergranular strain. The element tests simulate the behaviour of a finite element method based on the displacement formulation.     

Taking into account general boundary conditions in upscaling absolute permeability

Upscaling methods that need to solve local problems subject to boundary conditions are addressed in this article. We define a new upscaling method based on optimization problems, which can take into account general boundary conditions applied to local problems. The determination of upscaled permeability leads to minimizing the difference of dissipated energies (or averaged velocity) at fine and large scale. Using optimal control techniques, we obtain an effective computing algorithm that allows us to recover, with classical boundary conditions, the well-known results. The uniqueness issue is tackled for the optimization problems introduced in our approach. We show that the method is stable with respect to G-convergence, a property that establishes a link with homogenization theory, and finally, 2D numerical experiments are presented.     

Stability of a numerical scheme for methane transport in hydrate zone under equilibrium and non-equilibrium conditions

In this paper we carry out numerical analysis for a family of simplified gas transport models with hydrate formation and dissociation in subsurface, in equilibrium and non-equilibrium conditions. These models are adequate for simulation of hydrate phase change at basin and at shorter time scales, but the analysis does not account directly for the related effects of evolving hydraulic properties. To our knowledge this is the first analysis of such a model. It is carried out for the transport steps while keeping the pressure solution fixed. We frame the transport model as conservation law with a non-smooth space-dependent flux function; the kinetic model approximates this equilibrium. We prove weak stability of the upwind scheme applied to the regularized conservation law. We illustrate the model, confirm convergence with numerical simulations, and illustrate its use for some relevant equilibrium and non-equilibrium scenarios.

     

Evaluation of Nørsett methods for integrating differential equations in time

Some recently developed implicit time discretizations are discussed whose main application is to solving ordinary differential equations arising from finite element approximations to partial differential equations. Their theoretical properties, computer implementation and numerical behaviour, as observed in tests on simple examples, are compared with well-known discretizations such as the Crank-Nicholson method.     

Ranking the rock slope instability potential using the Interaction Matrix (IM) technique; a case study in Iran

All the conventional techniques for the analysis of slope stability ranging from simple kinematic analysis using stereonets, to the various widely used limit equilibrium methods, to sophisticated numerical methods belong to a category that are generally known as the analytic approaches and thus are only able to consider a limited number of affecting factors and then solve the problem in details. In contrast, the systems approaches not only can examine the problem in its totality with a complete list of the components, but also can take the interactions between the factors into account. This paper presents a complete application of a well-known systems technique named the Interaction Matrix (IM) in ranking the instability potential of rock slopes of the Khosh-Yeylagh Main Road, Iran as the case study of the research. For this purpose, 15 stations have been selected and a relatively comprehensive database containing the fieldwork information has been constructed. Following the IM technique, the most important factors relating to the general environment and to the rock mass characteristics have been considered. Their reciprocal causes and effects have been analyzed in order to weight each parameter according to its degree of interactivity in the system. Then, the slope instability index has been calculated which refers to the inherent potential instability of each slope of the examined region. The final instability ranking has been presented for the investigated slopes in Khosh-Yeylagh Main Road based on a simple classification. The main aim of the study is to extend the use of systems approach and specifically the IM technique in slope stability analysis. Also, this research shows the importance of consideration of an approximately complete set of key parameters affecting the stability of rock slopes.     

Seismic behavior of slopes by lower bound dynamic shakedown theory

Lower bound dynamic shakedown theory is a limit state method. It is employed herein to investigate the safety, which is associated with permanent displacement, of slopes under repeated dynamic loads, mainly earthquakes. An efficient numerical method, previously applied to the static shakedown of pavements, is extended to the dynamic shakedown of slopes in this study. It is shown that dynamic shakedown, unlike other limit state methods, is able to consider the dynamic properties of both the load and subsoil. The effect of the soil strength parameters and dynamic features of the soil and loads are examined thoroughly and some illustrative examples are employed. The short-term and long-term behavior of slopes under seismic loads are studied as well, comparing results of the present study with the well-known displacement method of Newmark.     

Probabilistic stability analyses of slopes using the ANN-based response surface

Slope stability analysis is a geotechnical engineering problem characterized by many sources of uncertainty. Some of these sources are connected to the uncertainties of soil properties involved in the analysis. In this paper, a numerical procedure for integrating a commercial finite difference method into a probabilistic analysis of slope stability is presented. Given that the limit state function cannot be expressed in an explicit form, an artificial neural network (ANN)-based response surface is adopted to approximate the limit state function, thereby reducing the number of stability analysis calculations. A trained ANN model is used to calculate the probability of failure through the first- and second-order reliability methods and a Monte Carlo simulation technique. Probabilistic stability assessments for a hypothetical two-layer slope as well as for the Cannon Dam in Missouri, USA are performed to verify the application potential of the proposed method.     

再论岩土工程有限元方法的应用问题

岩土工程数值分析方法对于研究复杂的岩土介质与多变的施工措施是一种得力的方法,比传统的解析方法、室内试验方法、模拟试验方法、现场试验方法等具有无可替代的优越性。按岩土工程数值方法的历史发展、作用及发展方向,将其分为4个层次：作为一种高级计算器,直接为某个具体岩土工程的设计服务,对该岩土工程在各种极端设计工况下进行安全性、稳定性的计算分析;作为一种强大的、无与伦比的模拟分析器,对复杂工况条件下复杂岩土工程的各种不利因素的相互作用、相互影响、耦合效应等进行模拟分析;作为一种无成本、可重复的多功能试验机,探索具体岩土工程的稳定机制或某工程措施的加固机制;作为岩土工程数值方法的终极目标,对数值分析方法进行二次开发——研发智能化、快速化、简便化的新型数值分析工具。对这4个层次进行了讨论,并对每个层次进行举例说明。     

Prediction of slope stability using multiple linear regression (MLR) and artificial neural network (ANN)

The stability problem of natural slopes, filled slopes, and cut slopes are commonly encountered in Civil Engineering Projects. Predicting the slope stability is an everyday task for geotechnical engineers. In this paper, a study has been done to predict the factor of safety (FOS) of the slopes using multiple linear regression (MLR) and artificial neural network (ANN). A total of 200 cases with different geometric and shear strength parameters were analyzed by using the well-known slope stability methods like Fellenius method, Bishop’s method, Janbu method, and Morgenstern and Price method. The FOS values obtained by these slope stability methods were used to develop the prediction models using MLR and ANN. Further, a few case studies have been done along the Jorabat-Shillong Expressway (NH-40) in India, using the finite element method (FEM). The output values of FEM were compared with the developed prediction models to find the best prediction model and the results were discussed.     

坐标投影作图法的计算机化及其在块体几何分析中的应用

块体塌落或滑动是岩石工程的重要破坏形式之一。为了解决此问题,需要对块体进行几何条件分析和稳定性分析。对此除采用传统的方法赤平极射投影图解法和三维数值法的方法等方法外,还可以采用坐标投影作图法。本文主要阐述坐标投影作图法在块体几何条件中的应用以及对它的计算机化。坐标投影法是一种以正投影为基础、借鉴赤平极射投影的方法而形成的以分析岩石工程中块体的几何条件和稳定性为目的的一种图解方法。该作图法的提出,为岩石工程块体稳定性研究提供了一个新的方法。为进一步提高坐标投影作图法的应用效率,作者提出了适用于现场的坐标投影作图法的计算机化问题。考虑到块体的几何条件是块体稳定分析的基础,本文主要针对块体几何条件的确定方法及其计算机化问题开展研究,并利用V isual C++将其编成CPH-Ⅰ软件。为了考核该软件,作者还以某一地下工程为实例,将该软件的计算结果和按坐标投影作图法图解法得出的结果进行了比较。对比结果表明该软件可用。     

一维畦灌施肥地表水流与溶质运移耦合模型——Ⅱ.模型验证

基于典型畦灌施肥试验观测结果及其模拟结果,对比分析利用混合数值解法和Roe有限体积法分别求解一维畦灌施肥地表水流与溶质运移过程控制方程在数值稳定性与收敛性、计算精度与效率上的差异,验证混合数值解法的计算性能与模拟效果.结果表明,混合数值解法比Roe有限体积法表现出更佳的数值稳定性和收敛性,产生的水平衡误差和平均相对误差...     

Rheological analysis of tunnel excavations by means of coupled finite element (FEM)–boundary element (BEM) analysis

To facilitate the practical numerical analysis of tunnel structures by means of the finite element method in the case of viscoplastic properties of the rock mass and viscoelastic properties of the shotcrete, this method is coupled to boundary elements. In this way, the unchanged properties of the boundary element region provide enormous savings in computing time. In order to improve the numerical stability of such calculations, a variable time-step analysis was employed for each time step with an iterative correction method. Characteristic values are obtained from measured values by back-analysis.     

Numerical solution for consolidation and desiccation of soft soils

The consolidation and desiccation behaviour of soft soils can be described by two time‐dependent non‐linear partial differential equations using the finite strain theory. Analytical solutions do not exist for these governing equations. In this paper, we develop efficient numerical methods and software for finding the numerical solutions. We introduce a semi‐implicit time integration scheme, and show numerically that our method converges. In addition, the numerical solution matches well with the experimental result. A boundary refinement method is also developed to improve the convergence and stability for the case of Neumann type boundary conditions. Interface governing equations are derived to maintain the continuity of consolidation and desiccation processes. This is useful because the soil column can undergo desiccation on top and consolidation on the bottom simultaneously. The numerical algorithms has been implemented into a computer program and the results have been verified with centrifuge test results conducted in our laboratory. Copyright © 2001 John Wiley & Sons, Ltd.     

海岸岩土工程的物理与数值模拟方法

采用物理模型试验来再现实际现象,验证数值模拟方法的有效性;同时采用数值模拟来弥补离心模型试验的缺陷,揭示模型试验规律,评价实际海岸岩土-结构系统在不同工况下的变形与强度稳定性及其变化.并简要地介绍了针对防波堤土工织物加筋垫层作用机理研究、黄骅港外航道防沙堤工程安全性评价、上海洋山港浅置式大圆筒结构试验段工程安全性评价三个具体项目进行评价的成果,初步展现了物理模型试验与数值模拟方法在海岸岩土工程的机理研究、方案论证、结构与施工优化、结构安全性评价等方面所能发挥的重要作用和广阔的应用前景.     

Using a shifted Grünwald-Letnikov scheme for the Caputo derivative to study anomalous solute transport in porous medium

We propose an extension of the shifted Grünwald-Letnikov method to solve fractional partial differential equations in the Caputo sense with arbitrary fractional order derivative α and with an advective term. The method uses the relation between Caputo and Riemann-Liouville definitions, the shifted Grünwald-Letnikov, and the traditional backward and forward finite difference method. The stability of the method is investigated for the implicit and explicit scheme with homogeneous boundary conditions, and a stability criterion is found for the advective-dispersive equation. An application of the method is used to solve contaminant diffusion and advective-dispersive problems. The numerical solution for the fractional diffusion and fractional advection-dispersion is compared with their respective analytical solutions for different time and space grid refinements. The diffusion simulation exhibited a good fit between the analytical and numerical solutions, with the explicit scheme going from stable to unstable as the time and space refinement changes. The fractional advection-dispersion application produced small deviations from the analytical solution. These deviations, however, are analogous to the numerical dispersions encountered in conventional finite difference solutions of the advection-dispersion equation. The new method is also compared with the traditional L2 method. Notably, an example that involves asymmetrical fractional conditions, a fractional diffusivity that depends on time, and a source term show how the methods compare. Overall, this study assesses the quality and easiness of use of the numerical method.     

The role of uncertainty in bedrock depth and hydraulic properties on the stability of a variably-saturated slope

We investigate the uncertainty in bedrock depth and soil hydraulic parameters on the stability of a variably-saturated slope in Rio de Janeiro, Brazil. We couple Monte Carlo simulation of a three-dimensional flow model with numerical limit analysis to calculate confidence intervals of the safety factor using a 22-day rainfall record. We evaluate the marginal and joint impact of bedrock depth and soil hydraulic uncertainty. The mean safety factor and its 95% confidence interval evolve rapidly in response to the storm events. Explicit recognition of uncertainty in the hydraulic properties and depth to bedrock increases significantly the probability of failure.     

A comparison of multiscale methods for elliptic problems in porous media flow

We review and perform comparison studies for three recent multiscale methods for solving elliptic problems in porous media flow; the multiscale mixed finite-element method, the numerical subgrid upscaling method, and the multiscale finite-volume method. These methods are based on a hierarchical strategy, where the global flow equations are solved on a coarsened mesh only. However, for each method, the discrete formulation of the partial differential equations on the coarse mesh is designed in a particular fashion to account for the impact of heterogeneous subgrid structures of the porous medium. The three multiscale methods produce solutions that are mass conservative on the underlying fine mesh. The methods may therefore be viewed as efficient, approximate fine-scale solvers, i.e., as an inexpensive alternative to solving the elliptic problem on the fine mesh. In addition, the methods may be utilized as an alternative to upscaling, as they generate mass-conservative solutions on the coarse mesh. We therefore choose to also compare the multiscale methods with a state-of-the-art upscaling method – the adaptive local–global upscaling method, which may be viewed as a multiscale method when coupled with a mass-conservative downscaling procedure. We investigate the properties of all four methods through a series of numerical experiments designed to reveal differences with regard to accuracy and robustness. The numerical experiments reveal particular problems with some of the methods, and these will be discussed in detail along with possible solutions. Next, we comment on implementational aspects and perform a simple analysis and comparison of the computational costs associated with each of the methods. Finally, we apply the three multiscale methods to a dynamic two-phase flow case and demonstrate that high efficiency and accurate results can be obtained when the subgrid computations are made part of a preprocessing step and not updated, or updated infrequently, throughout the simulation. The research is funded by the Research Council of Norway under grant nos. 152732 and 158908.     

A comparative study on linear and nonlinear site response analysis

Site response analysis is usually the first step of any seismic soil-structure study. Geotechnical earthquake engineers and engineering geologist have been trying to find both practical and most appropriate solution techniques for ground response analysis under earthquake loadings. The paper attempts to give a critical overview of the field of site response analysis. In this paper, the influences of nonlinearity on the site response analysis summarized and were evaluated with a numerical example. Site response of a two layered soil deposit with the assumption of linear and rigid base bedrock (or viscoelastic half-space) was analyzed by using linear and nonlinear approaches. The amplification spectrum of the soil column is computed between the top and the bottom of this soil deposit. Nonlinear analysis was compared with the linear method of analysis. Steps involved in ground response analyses to develop site-specific response spectra at a soil site are briefly summarized. Some of the well-known site response analysis methods are summarized and similarities and differences between linear and nonlinear methods are compared by a numerical example.