Comparison of dynamic stiffnesses of rigid square and rectangular foundations by DBEM and IBEM

In this work, the Direct and Indirect Boundary Element Methods as applied to dynamic soil structure interaction problems, are compared. Both the methods are used to find the dynamic stiffnesses of rigid surface and embedded foundations. For surface foundations, the results obtained by the two methods were very close for the frequency range considered, but for embedded foundations at higher frequencies, the Indirect Boundary Element Method produced erroneous values for the real part of vertical compliance. The possible reasons for this discrepancy are also studied in this paper.     

Three-dimensional analysis of tunnels using infinite boundary elements

Methods of efficiently analyzing the three-dimensional state of stress and displacement in a rock or soil mass due to tunnelling is presented. The Boundary Element Method (B.E.M.) and the coupled BEM-Finite Element Method is used. Special infinite Boundary Elements are used to model the portion of the tunnel which is very long and can be assumed to extend to infinity. The methods are particularly efficient and accurate for determining the state of stress at the tunnel face and near tunnel intersections. A test example and a practical application in tunnelling is shown.     

Boundary element analysis methods for ground stress field of rock masses

Basing on the principle of the Boundary Element Method, the authors of this paper present two computational methods for the analysis of ground stress field of rock masses, namely, the Boundary Element Regression Method and the Boundary Direct Integral Method. If the stress values of certain points in the rock masses have been known, we can find the solution of the entire ground stress field using either of these two methods. In this paper, these two methods have been used in conducting practical engineering computations. A critical comparison is made of the results obtained using these two methods with those of Finite Element Regression Method and Photoelastic Model Experiment, and the results are all in agreement. This shows that the above two methods are both feasible for implementation and easy for operation.     

Simulation of sequential excavation with the Boundary Element Method

The paper deals with the application of the Boundary Element Method (BEM) to problems where the boundary geometry and conditions change with time. An example of this is the simulation of sequential excavation in underground construction. A novel approach is presented that is more efficient than the currently used methods. The method involves only one region, where the boundary conditions and the geometry are changed as time progresses. Test examples are presented and results are compared with the ones obtained from other methods. The examples show that the new method is more efficient than currently used methods.     

Influence functions for stress and displacement discontinuity elements in an anisotropic medium

Influence functions, that permit us to determine stresses and displacements at an arbitrary point in an infinite, homogeneous, linear elastic, anisotropic medium due to different three-dimensional (3-D) stress or displacement discontinuities distributed on infinite, flat, band-type elements, are presented. Any straight-line segment on the band, which is perpendicular to its infinite side, has the same distribution of the discontinuities. Along with the functions, their Taylor series approximations are also provided. The last can be useful to analyse stresses and displacements at points distant from the elements. The functions allow us to avoid procedures of numerical integration in the Indirect Boundary Element Method and/or the Displacement Discontinuity Method computer codes that are able to solve complete plane-strain problems with 3-D boundary conditions for an elastic, anisotropic medium. © 1997 by John Wiley & Sons, Ltd.     

Some applications of the boundary element method in geomechanics

This paper presents the complete formulation for the application of the Boundary Element Method to solve non-tension material problems. The formulation is based on including an extra term due to an initial stress field into the boundary integral statement. This is then used to iterate the solution until a state of non-tension is achieved. The resulting iteration process is very simple to apply and basically consists only of a single matrix–vector product. The applications show that accurate resultscan be obtained for boundary discretizations involving a small number of unknowns. Whenever possible, results are compared with analytical solutions or finite elements.     

分析煤层开采地表移动的一种新型边界元方法

煤系地层为成层分布的沉积岩,煤层的开采会引起地表大规模的沉陷,发展适应此类介质的分析方法一直是本领域的研究热点。本文发展了一种新型的边界元方法来分析煤层开采引起的地表移动。该边界元方法基于层状材料基本解,采用4～8变结点单元离散边界,并采用有效的数值方法计算各类奇异积分。然后,用有解析解的算例验证建议数值方法。最后,采用新型边界元方法分析煤层开采引起的地表移动。本文所建议的方法在分析煤层开采引起的地表沉陷时具有较高的计算精度和效率。     

Elastoplastic deformation around underground openings under biaxial initial stress field

Estimation of elastoplastic deformation around an underground opening induced by the excavation of it, especially displacement and strain field in plastic region, is presented in this paper, as well as the formulation for calculating the displacement and strain in the plastic region around the underground opening by the coupled Boundary Element Method - Characteristics Method (BEM-CM). In this method, the non-associated flow rule is adopted to calculate the displacement and strain field in the plastic region, which is determined by the integration of the displacement along characteristics lines under the boundary condition of the elastic displacement on an elastoplastic interface analysed. It is shown that this method is one of the accurate and effective methods for estimating not only the shape and extent of the plastic region but also the state of the displacement and strain in the plastic region around the underground opening, comparing the theoretical solution with numerical results by this method for a circular opening under hydrostatic initial stress condition. Furthermore, this method is applied to rectangular and horse-shoe shaped openings and the characteristics of the strain field in the plastic region are discussed. © 1997 by John Wiley & Sons, Ltd.     

On the use of infinite elements in the analysis of two-dimensional layered elastic systems via discretized integral equations

A boundary integral equation approach is presented for the two-dimensional plane strain analysis of horizontally layered elastic systems resting on a rough and rigid base. The validity of Somigliana identity for unbounded layers is discussed and an Infinite Boundary Element is proposed in order to take into account the lateral unboundedness of the physical problem in the discretized equations. This element is implemented in a computer code based on a successive stiffness solution procedure. A series of numerical tests concerning single- and multi-layered problems is illustrated, and the performance of the proposed solution method is compared with that of more traditional boundary element and finite element techniques.     

Particle finite element analysis of large deformation and granular flow problems

A version of the Particle Finite Element Method applicable to geomechanics applications is presented. A simple rigid-plastic material model is adopted and the governing equations are cast in terms of a variational principle which facilitates a straightforward solution via mathematical programming techniques. In addition, frictional contact between rigid and deformable solids is accounted for using an approach previously developed for discrete element simulations. The capabilities of the scheme is demonstrated on a range of quasi-static and dynamic problems involving very large deformations.     

Determination of Fracture Toughness of Anisotropic Rocks by Boundary Element Method

Summary  This paper presents a systematic procedure for determining fracture toughness of an anisotropic marble using the diametral compression test (Brazilian test) with a central crack on the discs. Additionally, a novel formulation to increase the accuracy in Stress Intensity Factor (SIF) calculations using Boundary Element Method (BEM) is applied to determine the stress intensity factors and the fracture toughness of anisotropic rocks under mixed-mode loading. The numerical results show that the SIFs for both isotropic and anisotropic problems are in good agreement with those reported by previous authors. The marble with clear white-black foliation from Hualien (in eastern Taiwan), was selected for the Brazilian tests. Diametral loading was conducted on the Cracked Straight Through Brazilian Disc (CSTBD) specimens to evaluate their fracture toughness. In addition, a new fracture criterion was developed to predict pure mode I, pure mode II or mixed mode (I–II) fracture toughness of the anisotropic marble. The new fracture criterion is based on the examination of mode I, mode II and mixed mode (I–II) fracture toughness for different crack angles and anisotropic orientation. Authors’ address: Associate Professor Chao-Shi Chen, Department of Resources Engineering, National Cheng Kung University, No. 1 Dasyue Rd., East District, Tainan 701, Taiwan     

Nonlinear analysis of NATM tunnel construction with the boundary element method

This paper presents a novel approach to the simulation of NATM tunnel construction using the Boundary Element Method (BEM) as principal numerical method. This new approach has the advantage that only the excavation surface, the possible plastic zones and the tunnel lining have to be discretised. The whole rock mass is represented by the BEM whereas the Finite Element Method (FEM) is used to represent the tunnel lining only. Thus, a general coupling strategy for coupling three-dimensional boundary elements with shell finite elements (shotcrete) and beam finite elements (steel arches) is presented. To achieve realistic results the effect of hydration of the shotcrete and yielding of the steel arches is considered in the excavation process. Furthermore, the nonlinear rock behaviour is modelled more realistically by using a powerful hierarchical constitutive model which considers a large range of rock materials. The combination of these ideas results in higher user-friendliness and efficiency. Some verification tests and practical applications in tunnelling are presented.     

Boundary integral analysis of transient thermoelasticity

A simple and efficient method for the solution of uncoupled transient thermoelastic problems using boundary integral techniques is presented. The method employs a Laplace transformation to remove temporarily the time dependence of the governing equations. Numerical analysis is then carried out in the transform space, and results in the time-position space are found by numerical inversion of the Laplace transform. The method has the advantage that it avoids time-stepping and the costly evaluation of domain integrals. Boundary element and analytic solutions are compared, and the effect of cooling on the stresses around a deep underground opening is examined.     

Two-dimensional numerical approach for the vibration isolation analysis of thin walled wave barriers in poroelastic soils

This paper is concerned with the vibration isolation efficiency analysis of total or partially buried thin walled wave barriers in poroelastic soils. A two-dimensional time harmonic model that treats soils and structures in a direct way by combining appropriately the conventional Boundary Element Method (BEM), the Dual BEM (DBEM) and the Finite Element Method (FEM) is developed to this aim. The wave barriers are impinged by Rayleigh waves obtained from Biot’s poroelasticity equations assuming a permeable free-surface. The suitability of the proposed model is justified by comparison with available previous results. The vibration isolation efficiency of three kinds of wave barriers (open trench, simple wall, open trench-wall) in poroelastic soils is studied by varying their geometry, the soil properties and the frequency. It is found that the efficiency of these wave barriers behaves similarly to these in elastic soils, except for high porosities and small dissipation coefficients. The efficiency of open trench-wall barriers can be evaluated neglecting their walls if they are typical sheet piles. This does not happen with walls of bigger cross-sections, leading in general to efficiency losses. Likewise, increasing the burial depth to trench depth ratio has a negative impact on the efficiency.     

Three-dimensional stress analysis: A formulation for mining problems

Mathematical and computational aspects of a three-dimensional boundary element formulation designed specifically for application to mining rock mechanics problems are described. Stress analysis of mining geometries differs in many respects from equivalent analyses of civil or mechanical engineering. These differences are highlighted and the manner in which these differences are accomodated by the formulation is described. The formulation has been implemented into a program BEAP (Boundary Element Analysis Package). A test problem is presented and compared with other formulations.Design goals for the program include the following: ease of use, ability to run on personal computers, use of an iterative equation solver to reduce total CPU for large problems, use of single precision to store matrix coefficients thereby reducing disk storage requirements, limited application to multi-subregion problems and easy inter-facing to third party software for pre- and post-processing.Finally, a practical mining example is presented. It is concluded that the formulation is very well suited to analysis of mining rock mechanics problems, providing a sound basis for future developments in this field.     

Simplified vibratory characterization of alluvial basins

For the analysis of seismic wave amplification, modal methods are interesting tools to study the modal properties of geological structures. Modal approaches mainly lead to information on such parameters as fundamental frequencies and eigenmodes of alluvial basins. For a specific alluvial deposit in Nice (France), a simplified modal approach involving the Rayleigh method is considered. This approach assumes a set of admissible shape functions for the eigenmodes and allows a fast estimation of the fundamental frequency of the basin. The agreement with other numerical results (Boundary Element Method) and experimental ones is fully satisfactory. The simplified modal method then appears as an efficient mean for the global vibratory characterization of geological structures towards resonance. To cite this article: J.-F. Semblat et al., C. R. Geoscience 335 (2003).     

Numerical modelling of seismic slope failure using MPM

The Finite Element Method (FEM) is widely used in the simulation of geotechnical applications. Owing to the limitations of FEM to model problems involving large deformations, many efforts have been made to develop methods free of mesh entanglement. One of these methods is the Material Point Method (MPM) which models the material as Lagrangian particles capable of moving through a background computational mesh in Eulerian manner. Although MPM represents the continuum by material points, solution is performed on the computational mesh. Thus, imposing boundary conditions is not aligned with the material representation. In this paper, a non-zero kinematic condition is introduced where an additional set of particles is incorporated to track the moving boundary. This approach is then applied to simulate the seismic motion resulting in failure of slopes. To validate this simulation procedure, two geotechnical applications are modelled using MPM. The first is to reproduce a shaking table experiment where the results of another numerical method are available. After validating the present numerical scheme for relatively large deformation problem, it is applied to simulate progression of a large-scale landslide during the Chi-Chi earthquake of Taiwan in which excessive material deformation and transportation is taking place.     

A complete formulation of an indirect boundary element method for poroelastic rocks

Rocks are naturally filled with cracks and pores that are saturated with one or more fluid phases. Many problems in rock mechanics, petroleum engineering, geophysics, etc. deal with cracks and discontinuities in rock formations. These problems should consider effects of a porous medium. Displacement discontinuity method (DDM) as an indirect boundary element method is particularly ideal for problems involving fractures and discontinuities. However, the DDM in its original form is limited to elastic problems. The paper uses a fundamental solution of a point displacement discontinuity in poroelastic medium to obtain the solution for a poroelastic DDM. Then it introduces a numerical formulation and implementation for the poroelastic DDM in a code named CEP-DDM (Constant Element Poroelastic DDM). The accuracy and validity of the proposed solution and the newly developed code are verified by two analytical solutions, another numerical solution, and some field measurements. These results showed good agreement between CEP-DDM and other methods’ results. The verifications prove the accuracy and applicability of the proposed numerical model in a wide range of real-world problems.     

局域地应力场获取的插值平衡方法

针对由整体地应场插值计算局域地应力场的问题计算量大、受地质结构的影响大、不过分追求高精度等特点,改进了反距离加权插值法,考虑了单元体积的影响,提高了该方法在此问题中的适用性。基于此,提出了平面问题、三维地面和地下工程局域地应力场的求取策略,建议了边界全平动约束和法向约束两种边界条件,并验证了其合理性和适用场合。最后,在大型水电工程深切河谷坝肩边坡分析中进行了应用分析。结果表明：该插值方法简单实用,能够满足工程分析的精度要求;局域地应力场的求取策略计算效率高,计算精度能够满足工程分析的要求。     

The engineering-physical basis of temperature regime regulation of ground massifs in northern construction

Artificial ground freezing at low temperatures provides a solution to such complicated problems as strengthening foundations, improvement of their reliability and the provision of the watertightness of the ground.

Ground cooling and freezing directly changes the stress—deformation state of foundations and underground constructions.

Basic diagrams on ways and means of forming low temperature frozen zones of a definite shape in the ground are given in the paper. Peculiarities of the work of the seasonally functioning heat-exchange devices and systems are discussed.

The development and refinements of methods of calculation and long-term forecast of temperature fields in artificially cooled ground massifs is of great importance.

Experimental data on migration phenomena in freezing soils and the methods of the numerical modeling of cooled massifs are discussed.

The paper is illustrated by diagrams, test results and calculation data.