Two-level stabilized finite element method for Stokes eigenvalue problem

A two-level stabilized finite element method for the Stokes eigenvalue problem based on the local Gauss integration is considered. This method involves solving a Stokes eigenvalue problem on a coarse mesh with mesh size H and a Stokes problem on a fine mesh with mesh size h -- O（H2）, which can still maintain the asymptotically optimal accuracy. It provides an approximate solution with the convergence rate of the same order as the usual stabilized finite element solution, which involves solving a Stokes eigenvalue problem on a fine mesh with mesh size h. Hence, the two-level stabilized finite element method can save a large amount of computational time. Moreover, numerical tests confirm the theoretical results of the present method.

A new stabilized method for quasi-Newtonian flows

For a generalized quasi-Newtonian flow, a new stabilized method focused on the low-order velocity-pressure pairs, （bi）linear/（bi）linear and （bi）linear/constant element, is presented. The pressure projection stabilized method is extended from Stokes problems to quasi-Newtonian flow problems. The theoretical framework developed here yields an estimate bound, which measures error in the approximate velocity in the W 1,r（Ω） norm and that of the pressure in the L r＇ （Ω） （1/r ＋ 1/r＇ = 1）. The power law model and the Carreau model are special ones of the quasi-Newtonian flow problem discussed in this paper. Moreover, a residual-based posterior bound is given. Numerical experiments are presented to confirm the theoretical results.

Reinforcement strength reduction in FEM for mechanically stabilized earth structures

The factor of safety of mechanically stabilized earth(MSE) structures can be analyzed either using limit equilibrium method(LEM) or strength reduction method(SRM) in finite element/difference method. In LEM, the strengths of the reinforcement members and soils are reduced with the same factor. While using the SRM, only soil strength is reduced during the calculation of the factor of safety. This causes inconsistence in calculating the factor of safety of the MSE structures. To overcome this, an iteration method is proposed to consider the strength reduction of the reinforcements in SRM. The method is demonstrated by using PLAXIS, a finite element software. The results show that the factor of safety converges after a few iterations. The reduction of strength has different effects on the factor of safety depending on the properties of the reinforcements and the soil, and failure modes.

耦合拉格朗日-欧拉方法及其在海洋工程中的应用

Combining the strengths of Lagrangian and Eulerian descriptions,the coupled Lagrangian–Eulerian methods play an increasingly important role in various subjects.This work reviews their development and application in ocean engineering.Initially,we briefly outline the advantages and disadvantages of the Lagrangian and Eulerian descriptions and the main characteristics of the coupled Lagrangian–Eulerian approach.Then,following the developmental trajectory of these methods,the fundamental formulations and the frameworks of various approaches,including the arbitrary Lagrangian–Eulerian finite element method,the particle-in-cell method,the material point method,and the recently developed Lagrangian–Eulerian stabilized collocation method,are detailedly reviewed.In addition,the article reviews the research progress of these methods with applications in ocean hydrodynamics,focusing on free surface flows,numerical wave generation,wave overturning and breaking,interactions between waves and coastal structures,fluid–rigid body interactions,fluid–elastic body interactions,multiphase flow problems and visualization of ocean flows,etc.Furthermore,the latest research advancements in the numerical stability,accuracy,efficiency,and consistency of the coupled Lagrangian–Eulerian particle methods are reviewed;these advancements enable efficient and highly accurate simulation of complicated multiphysics problems in ocean and coastal engineering.By building on these works,the current challenges and future directions of the hybrid Lagrangian–Eulerian particle methods are summarized.

Three-dimensional stability of landslides based on local safety factor

Unlike the limit equilibrium method(LEM), with which only the global safety factor of the landslide can be calculated, a local safety factor(LSF) method is proposed to evaluate the stability of different sections of a landslide in this paper. Based on three-dimensional(3D) numerical simulation results, the local safety factor is defined as the ratio of the shear strength of the soil at an element on the slip zone to the shear stress parallel to the sliding direction at that element. The global safety factor of the landslide is defined as the weighted average of all local safety factors based on the area of the slip surface. Some example analyses show that the results computed by the LSF method agree well with those calculated by the General Limit Equilibrium(GLE) method in two-dimensional(2D) models and the distribution of the LSF in the 3D slip zone is consistent with that indicated by the observed deformation pattern of an actual landslide in China.

Direct discontinuous Galerkin method for the generalized Burgers-Fisher equation

In this study, we use the direct discontinuous Galerkin method to solve the generalized Burgers-Fisher equation. The method is based on the direct weak formulation of the Burgers-Fisher equation. The two adjacent cells are jointed by a numerical flux that includes the convection numerical flux and the diffusion numerical flux. We solve the ordinary differential equations arising in the direct Galerkin method by using the strong stability preserving Runge^Kutta method. Numerical results are compared with the exact solution and the other results to show the accuracy and reliability of the method.

Sensitivity analysis of influencing parameters in cavern stability

In order to analyze the stability of the underground rock structures,knowing the sensitivity of geomechanical parameters is important.To investigate the priority of these geomechanical properties in the stability of cavern,a sensitivity analysis has been performed on a single cavern in various rock mass qualities according to RMR using Phase 2.The stability of cavern has been studied by investigating the side wall deformation.Results showed that most sensitive properties are coefficient of lateral stress and modulus of deformation.Also parameters of Hoek-Brown criterion and r c have no sensitivity when cavern is in a perfect elastic state.But in an elasto-plastic state,parameters of Hoek-Brown criterion and r c affect the deformability;such effect becomes more remarkable with increasing plastic area.Other parameters have different sensitivities concerning rock mass quality(RMR).Results have been used to propose the best set of parameters for study on prediction of sidewall displacement.

Slope stability analysis of Southern slope of Chengmenshan copper mine,China

The engineering geology and hydrogeology in the southern slope of Chengmenshan copper mine are very complicated,because there is a soft-weak layer between two kinds of sandstones.Field investigations demonstrate that some instability problems might occur in the slope.In this research,the southern slope,which is divided into six sections(I-0,I-1,I-2,II-0,II-1 and II-2),is selected for slope stability analysis using limit equilibrium and numerical method.Stability results show that the values of factor of safety(FOS) of sections I-0,I-1 and I-2 are very low and slope failure is likely to happen.Therefore reinforcement subjected to seismic,water and weak layer according to sections were carried out to increase the factor of safety of the three sections,two methods were used;grouting with hydration of cement and water to increase the cohesion(c) and pre-stressed anchor.Results of reinforcement showed that factor of safety increased more than 1.15.

Intra-layer synchronization in duplex networks

This paper explores the intra-layer synchronization in duplex networks with different topologies within layers and different inner coupling patterns between, within, and across layers. Based on the Lyapunov stability method, we prove theoretically that the duplex network can achieve intra-layer synchronization under some appropriate conditions, and give the thresholds of coupling strength within layers for different types of inner coupling matrices across layers. Interestingly,for a certain class of coupling matrices across layers, it needs larger coupling strength within layers to ensure the intra-layer synchronization when the coupling strength across layers become larger, intuitively opposing the fact that the intra-layer synchronization is seemly independent of the coupling strength across layers. Finally, numerical simulations further verify the theoretical results.

Seismic stability evaluation of embankment slope based on catastrophe theory

An evaluation method for the seismic stability of embankment slope was presented based on catastrophe theory. Seven control factors, including internal frictional angle, cohesion force, slope height, slope angle, surface gradients, peak acceleration, and distance to fault were selected for analysis of multi-level objective decomposition. According to the normalization formula and the fuzzy subject function produced by combination of catastrophe theory and fuzzy math, a recursive calculation was carried out to obtain a catastrophic affiliated functional value, which can be used to evaluate the seismic stability of embankment slope. Fifteen samples were used to verify the effectiveness of this method. The results show that compared with the traditional quantitative method, the catastrophe progression owns higher accuracy and good application potential in predicting the seismic stability of embankment slope.

3D stability analysis method of concave slope based on the Bishop method

In order to study the stability control mechanism of a concave slope with circular landslide, and remove the influence of differences in shape on slope stability, the limit analysis method of a simplified Bishop method was employed. The sliding body was divided into strips in a three-dimensional model, and the lateral earth pressure was put into mechanical analysis and the three-dimensional stability analysis methods applicable for circular sliding in concave slope were deduced. Based on geometric structure and the geological parameters of a concave slope, the influence rule of curvature radius and the top and bottom arch height on the concave slope stability were analyzed. The results show that the stability coefficient decreases after growth, first in the transition stage of slope shape from flat to concave, and it has been confirmed that there is a best size to make the slope stability factor reach a maximum. By contrast with average slope, the stability of a concave slope features a smaller range of ascension with slope height increase, which indicates that the enhancing effect of a concave slope is apparent only with lower slope heights.

Design and operation problems related to water curtain system forunderground water-sealed oil storage caverns

The underground water-sealed storage technique is critically important and generally accepted for the national energy strategy in China. Although several small underground water-sealed oil storage caverns have been built in China since the 1970s, there is still a lack of experience for large-volume underground storage in complicated geological conditions. The current design concept of water curtain system and the technical instruction for system operation have limitations in maintaining the stability of surrounding rock mass during the construction of the main storage caverns, as well as the long-term stability. Although several large-scale underground oil storage projects are under construction at present in China, the design concepts and construction methods, especially for the water curtain system, are mainly based on the ideal porosity medium flow theory and the experiences gained from the similar projects overseas. The storage projects currently constructed in China have the specific features such as huge scale, large depth, multiple-level arrangement, high seepage pressure, complicated geological conditions, and high in situ stresses, which are the challenging issues for the stability of the storage caverns. Based on years’ experiences obtained from the first large-scale （millions of cubic meters） underground water-sealed oil storage project in China, some design and operation problems related to water curtain system during project construction are discussed. The drawbacks and merits of the water curtain system are also presented. As an example, the conventional concept of “filling joints with water” is widely used in many cases, as a basic concept for the design of the water curtain system, but it is immature. In this paper, the advantages and disadvantages of the conventional concept are pointed out, with respect to the long-term stability as well as the safety of construction of storage caverns. Finally, new concepts and principles for design and construction of the underground water-sealed oil storage caverns are proposed.

Characteristics of in situ stress field at Qingshui coal mine

In this study, the characteristics of geological structure at Qingshui coal mine were analyzed. And the hollow inclusion strain cell overcoring method was used to obtain the in situ stress. The effect of in situ stress on the stability of soft rock roadway was analyzed. The results show that the maximum principal stress is in the horizontal direction with a northeast orientation and has a value of about 1.2–1.9 times larger than gravity; the right side of roadway roof and floor is easily subject to serious deformation and failure, and the in situ stress is found to be a major factor. This paper presents important information for developing countermeasures against the large deformation of the soft rock roadway at Qingshui coal mine.

Safety assessment of waste rock dump built on existing tailings ponds

The construction of waste rock dumps on existing tailing ponds has been put into practice in China to save precious land resources. This work focuses on the safety assessment of the Daheishan molybdenum mine waste rock dump under construction on two adjoining tailings ponds. The consolidation of the tailings foundation and the filling quality of the waste rock are investigated by the transient electromagnetic method through detecting water-rich areas and loose packing areas, from which, the depth of phreatic line is also estimated. With such information and the material parameters, the numerical method based on shear strength reduction is applied to analyzing the overall stability of the waste rock dump and the tailings ponds over a number of typical cross sections under both current and designed conditions, where the complex geological profiles exposed by site investigation are considered. Through numerical experiments, the influence of soft lenses in the tailings and possible loose packing areas in the waste rock is examined. Although large displacements may develop due to the soft tailings foundation, the results show that the waste rock dump satisfies the safety requirements under both present and designed conditions.

Geotechnical investigations and remediation design for failure of tunnel portal section： a case study in northern Turkey

Mass movements are very common problems in the eastern Black Sea region of Turkey due to its climate conditions, geological, and geomorphological characteristics. High slope angle, weathering, dense rainfalls, and anthropogenic impacts are generally reported as the most important triggering factors in the region. Following the portal slope excavations in the entrance section of Cankurtaran tunnel, located in the region, where the highly weathered andesitic tuff crops out, a circular toe failure occurred. The main target of the present study is to investigate the causes and occurrence mechanism of this failure and to determine the feasible remedial measures against it using finite element method(FEM) in four stages. These stages are slope stability analyses for pre-and postexcavation cases, and remediation design assessments for slope and tunnel. The results of the FEM-SSR analyses indicated that the insufficient initial support design and weathering of the andesitic tuffs are the main factors that caused the portal failure. After installing a rock retaining wall with jet grout columns and reinforced slope benching applications, the factor of safety increased from 0.83 to 2.80. In addition toslope stability evaluation, the Rock Mass Rating(RMR), Rock Mass Quality(Q) and New Austrian Tunneling Method(NATM) systems were also utilized as empirical methods to characterize the tunnel ground and to determine the tunnel support design. The performance of the suggested empirical support design, induced stress distributions and deformations were analyzed by means of numerical modelling. Finally, it was concluded that the recommended stabilization technique was essential for the dynamic long-term stability and prevents the effects of failure. Additionally, the FEM method gives useful and reasonably reliable results in evaluating the stability of cut slopes and tunnels excavated both in continuous and discontinuous rock masses.

GPU-based discrete element simulation on flow stability of flat-bottomed hopper

In this study, the flow stability of the flat-bottomed hopper was investigated via GPU-based discrete element method(DEM) simulation. With the material height inside the hopper reducing, the fluctuation of the flow rate indicates an unstable discharge. The flow regions of the unstable discharge were compared with that of the stable discharge, a key transformation zone, where the voidage showed the largest difference between unstable and stable discharge, was revealed. To identify the relevance of the key transformation zone and the hopper flow stability, the voidage variation of the key transformation zone with material height reducing was studied.A sharp increase in the voidage in the key transformation zone was considered to be the standard for judging the unstable hopper flow, and the ‘Top–Bottom effect' of the hopper was defined, which indicated the hopper flow was unstable when the hopper only had the top area and the bottom area, because the voidage of particles in the top area and the bottom area were both variables.

Velocity plus displacement equivalent force control for real-time substructure testing

This paper employs a velocity plus displacement（V＋D）-based equivalent force control（EFC） method to solve the velocity/displacement difference equation in a real-time substructure test. This method uses type 2 feedback control loops to replace mathematical iteration to solve the nonlinear dynamic equation. A spectral radius analysis of the amplification matrix shows that the type 2 EFC-explicit, Newmark-β method has beneficial numerical characteristics for this method. Its stability limit of Ω = 2 remains unchanged regardless of the system damping because the velocity is achieved with very high accuracy during simulation. In contrast, the stability limits of the central difference method using direct velocity prediction and the EFC-average acceleration method with linear interpolation are shown to decrease with an increase in system damping. In fact, the EFC-average acceleration method is shown to change from unconditionally stable to conditionally stable. We also show that if an over-damped system with a damping ratio of 1.05 is considered, the stability limit is reduced to Ω =1.45. Finally, the results from an experiment with a single-degree-of-freedom structure installed with a magneto-rheological（MR） damper are presented. The results demonstrate that the proposed method is able to follow both displacement and velocity commands with moderate accuracy, resulting in improved test performance and accuracy for structures that are sensitive to both velocity and displacement inputs. Although the findings of the study are promising, additional test data and several further improvements will be required to draw general conclusions.

Limit analysis method for active earth pressure on laggings between stabilizing piles

Stabilizing pile is a kind of earth shoring structure frequently used in slope engineering. When the piles have cantilever segments above the ground,laggings are usually installed to avoid collapse of soil between piles. Evaluating the earth pressure acting on laggings is of great importance in design process.Since laggings are usually less stiff than piles,the lateral pressure on lagging is much closer to active earth pressure. In order to estimate the lateral earth pressure on lagging more accurately,first,a model test of cantilever stabilizing pile and lagging systems was carried out. Then,basing the experimental results a three-dimensional sliding wedge model was established. Last,the calculation process of the total active force on lagging is presented based on the kinematic approach of limit analysis. A comparison is made between the total active force on lagging calculated by the formula presented in this study and the force on a same-size rigid retaining wall obtained from Rankine's theory. It is found that the proposed method fits well with the experimental results.Parametric studies show that the total active force on lagging increases with the growth of the lagging height and the lagging clear span; while decreases asthe soil internal friction angle and soil cohesion increase.

Neutrality Criteria for Stability Analysis of Dynamical Systems through Lorentz and Rossler Model Problems

Two methods of stability analysis of systems described by dynamical equations are being considered. They are based on an analysis of eigenvalues spectrum for the evolutionary matrix or the spectral equation and they allow determining the conditions of stability and instability, as well as the possibility of chaotic behavior of systems in case of a stability loss. The methods are illustrated for nonlinear Lorenz and Rossler model problems.

Evaluation of embankment foundation creep in conditions of deep bedding of roof in permafrost soils

Railroad operating experience in permafrost conditions has shown that deformations of embankments on thawing foun- dations last for a long time. After an initial period of heat settlement due to permafrost degradation, the determining factor is the plastic flow of seasonal thawed soils of the foundation upper layer under the embankment. This paper provides a method to evaluate these deformations, and calculation examples using data from line sections of the Chum-Labytnangi Railway in northwestern Russia. It also discusses several methods of embankment stabilization, including the use of ver- tical thermosiphons.