Analysis of Three-dimensional Crack Propagation by Using Displacement Discontinuity Method

A technique for modelling of three-dimensional(3D)quasi-statically propagating cracks in elastic bodies by the displacement discontinuity method(DDM)was described.When the crack is closed,the Mohr-coulomb rule on the two contacted surfaces of the crack must be satisfied.A simple iterative method was adopted in order to consider three different states of cracks.Under the assumption that the advance of the point on the crack front would occur only in the normal plane which is through this edge point,the maximum energy release rate criterion is modified to be used as the criterion for the crack growth.With discretization,the process of crack propagation can be seen as the advance of the vertices of the crack front.The program MCP3D was developed based on these theories to simulate the 3D quasi-static crack propagation.A numerical example of a penny-shaped crack subject to tension and compression in an infinite elastic media was analyzed with MCP3D,and the results in comparison with others' show that the present method for 3D crack propagation is effective.

Two kinds of contact problems in three-dimensional icosahedral quasicrystals

Two kinds of contact problems, i.e., the frictional contact problem and the adhesive contact problem, in three-dimensional （3D） icosahedral quasicrystals are dis- cussed by a complex variable function method. For the frictional contact problem, the contact stress exhibits power singularities at the edge of the contact zone. For the adhe- sive contact problem, the contact stress exhibits oscillatory singularities at the edge of the contact zone. The numerical examples show that for the two kinds of contact problems, the contact stress exhibits singularities, and reaches the maximum value at the edge of the contact zone. The phonon-phason coupling constant has a significant effect on the contact stress intensity, while has little impact on the contact stress distribution regu- lation. The results are consistent with those of the classical elastic materials when the phonon-phason coupling constant is 0. For the adhesive contact problem, the indentation force has positive correlation with the contact displacement, but the phonon-phason cou- pling constant impact is barely perceptible. The validity of the conclusions is verified.

Numerical simulation of standing wave with 3D predictor-corrector finite difference method for potential flow equations

A three-dimensional （3D） predictor-corrector finite difference method for standing wave is developed. It is applied to solve the 3D nonlinear potential flow equa- tions with a free surface. The 3D irregular tank is mapped onto a fixed cubic tank through the proper coordinate transform schemes. The cubic tank is distributed by the staggered meshgrid, and the staggered meshgrid is used to denote the variables of the flow field. The predictor-corrector finite difference method is given to develop the difference equa- tions of the dynamic boundary equation and kinematic boundary equation. Experimental results show that, using the finite difference method of the predictor-corrector scheme, the numerical solutions agree well with the published results. The wave profiles of the standing wave with different amplitudes and wave lengths are studied. The numerical solutions are also analyzed and presented graphically.

Inner damage identification and residual strength assessment of a 3D printed tunnel with marble-like cementitious materials using piezoelectric transducers

Quantitative damage identification of surrounding rock is important to assess the current condition and residual strength of underground tunnels.In this work,an underground tunnel model with marble-like cementitious materials was first fabricated using the three-dimensional(3D)printing technique and then loaded to simulate its failure mode in the laboratory.Lead zirconate titanate piezoelectric(PZT)transducers were embedded in the surrounding rock around the tunnel in the process of 3D printing.A 3D monitoring network was formed to locate damage areas and evaluate damage extent during loading.Results show that as the load increased,main cracks firstly appeared above the tunnel roof and below the floor,and then they coalesced into the tunnel boundary.Finally,the tunnel model was broken into several parts.The resonant frequency and the peak of the conductance signature firstly shifted rightwards with loading due to the sealing of microcracks,and then shifted backwards after new cracks appeared.An overall increase in the root-mean-square deviation(RMSD)calculated from conductance signatures of all the PZT transducers was observed as the load(damage)increased.Damage-dependent equivalent stiffness parameters(ESPs)were calculated from the real and imaginary signatures of each PZT at different damage states.Satisfactory agreement between equivalent and experimental ESP values was achieved.Also,the relationship between the change of the ESP and the residual strength was obtained.The method paves the way for damage identification and residual strength estimation of other 3D printed structures in civil engineering.

Three-dimensional FDEM numerical simulation of failure processes observed in Opalinus Clay laboratory samples

This study presents the first step of a research project that aims at using a three-dimensional （3D） hybridfinite-discrete element method （FDEM） to investigate the development of an excavation damaged zone（EDZ） around tunnels in a clay shale formation known as Opalinus Clay. The 3D FDEM was first calibratedagainst standard laboratory experiments, including Brazilian disc test and uniaxial compression test. Theeffect of increasing confining pressure on the mechanical response and fracture propagation of the rockwas quantified under triaxial compression tests. Polyaxial （or true triaxial） simulations highlighted theeffect of the intermediate principal stress （s2） on fracture directions in the model： as the intermediateprincipal stress increased, fractures tended to align in the direction parallel to the plane defined by themajor and intermediate principal stresses. The peak strength was also shown to vary with changing s2. 2014 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences. Production and hosting byElsevier B.V. All rights reserved.

A modified maximum tangential tensile stress criterion for three-dimensional crack propagation

The three-dimensional （3D） crack propagation is a hot issue in rock mechanics. To properly simulate 3D crack propagation, a modified maximum tangential tensile stress criterion is proposed. In this modified criterion, it is supposed that cracks propagate only at crack front in the principal normal plane. The tangential tensile stress at crack front in the principal normal plane in local coordinates is employed to determine crack propagation, which is calculated through coordinate transformation from global to local coordinates. New cracks will propagate when the maximum tangential tensile stress at crack front in the principal normal plane reaches the tensile strength of rock-like materials. Compared with the previous crack propagation criteria, the modified crack propagation criterion is helpful in calculating 3D crack stress intensity factor, and can overcome the limitations of propagation step determined by individual experiences in previous studies. Finally, the 3D crack propagation process is traced by element-free Galerkin method. The numerical results agree well with the experimental ones for a frozen resin sample with prefabricated 3D cracks.

Quantitative determination of PFC3D microscopic parameters

It is important to calibrate micro-parameters for applying partied flow code(PFC)to study mechanical characteristics and failure mechanism of rock materials.Uniform design method is firstly adopted to determine the microscopic parameters of parallel-bonded particle model for three-dimensional discrete element particle flow code(PFC3D).Variation ranges of microscopic of the microscopic parameters are created by analyzing the effects of microscopic parameters on macroscopic parameters(elastic modulus E,Poisson ratio v,uniaxial compressive strengthσc,and ratio of crack initial stress to uniaxial compressive strengthσci/σc)in order to obtain the actual uniform design talbe.The calculation equations of the microscopic and macroscopic parameters of rock materials can be established by the actual uniform design table and the regression analysis and thus the PFC3D microscopic parameters can be quantitatively determined.The PFC3D simulated results of the intact and pre-cracked rock specimens under uniaxial and triaxial compressions(including the macroscopic mechanical parameters,stress−strain curves and failure process)are in good agreement with experimental results,which can prove the validity of the calculation equations of microscopic and macroscopic parameters.

三维Otsu阈值分割方法的递推算法

一维和二维Otsu法是常用的阈值分割方法,二维Otsu法对含噪图像的分割效果要优于一维Otsu法,但它存在的问题是"对象区域和背景区域上的概率和近似为1"的假设的普适性不够,鉴于此景晓军等人提出了三维Otsu法及其递归算法,使得对低对比度、低信噪比的图像有较好的分割效果.本文指出了景晓军等人给出的递推公式的错误,并进行了修正.鉴于他们给出的递推公式并不是真正意义的递推公式,本文给出了新的递推公式.实验结果表明,本文提出的递推公式进一步减少了运算时间.另外,本文还指出三维Otsu法对于叠加了混合噪声的图像有较好的分割效果.

改进的三维Otsu阈值分割法及其快速实现

常用的三维直方图一般由灰度级-平均灰度级-中值灰度级构成,其区域划分方式存在明显的不足。对此,本文提出了一种改进的三维Otsu法。该方法基于灰度级-平均梯度-中值梯度建立三维直方图,采用新的区域划分方式提高划分精度;为提高算法效率,推导了该方法的快速迭代公式。测试实验表明:与传统三维Otsu法相比,该方法的计算效率高,分割精度好、抗噪性强,表现出较好的应用价值。

Recursive super-convergence computation for multi-dimensional problems via one-dimensional element energy pro jection technique

This paper presents a strategy for computation of super-convergent solutions of multi-dimensional problems in the finite element method （FEM） by recursive application of the one-dimensional （1D） element energy projection （EEP） technique. The main idea is to conceptually treat multi-dimensional problems as generalized 1D problems, based on which the concepts of generalized 1D FEM and its consequent EEP formulae have been developed in a unified manner. Equipped with these concepts, multi-dimensional problems can be recursively discretized in one dimension at each step, until a fully discretized standard finite element （FE） model is reached. This conceptual dimension-by- dimension （D-by-D） discretization procedure is entirely equivalent to a full FE discretization. As a reverse D-by-D recovery procedure, by using the unified EEP formulae together with proper extraction of the generalized nodal solutions, super-convergent displacements and first derivatives for two-dimensional （2D） and three-dimensional （3D） problems can be obtained over the domain. Numerical examples of 3D Poisson＇s equation and elasticity problem are given to verify the feasibility and effectiveness of the proposed strategy.

Underground space planning in Helsinki

This paper gives insight into the use of underground space in Helsinki,Finland.The city has an underground master plan(UMP) for its whole municipal area,not only for certain parts of the city.Further,the decision-making history of the UMP is described step-by-step.Some examples of underground space use in other cities are also given.The focus of this paper is on the sustainability issues related to urban underground space use,including its contribution to an environmentally sustainable and aesthetically acceptable landscape,anticipated structural longevity and maintaining the opportunity for urban development by future generations.Underground planning enhances overall safety and economy efficiency.The need for underground space use in city areas has grown rapidly since the 21 st century;at the same time,the necessity to control construction work has also increased.The UMP of Helsinki reserves designated space for public and private utilities in various underground areas of bedrock over the long term.The plan also provides the framework for managing and controlling the city’s underground construction work and allows suitable locations to be allocated for underground facilities.Tampere,the third most populated city in Finland and the biggest inland city in the Nordic countries,is also a good example of a city that is taking steps to utilise underground resources.Oulu,the capital city of northern Finland,has also started to ‘go underground’.An example of the possibility to combine two cities by an 80-km subsea tunnel is also discussed.A new fixed link would generate huge potential for the capital areas of Finland and Estonia to become a real Helsinki-Tallinn twin city.

三维Otsu阈值分割方法的快速实现

针对图像分割中三维Otsu阈值法存在的计算复杂度高的问题，笔者提出了一种三维Otsu阈值分割方法的快速实现算法，该算法通过用递推的方法得到查找表，从而消除三维Otsu阈值法中的冗余计算，能够很好地提高三维Otsu阈值法的计算速度．实验结果表明，该算法不仅计算时间远远小于原始三维Otsu算法，并且求得的阀值跟原始的算法一样．

A practical parallel preprocessing strategy for 3D numerical manifold method

Over the past three decades,the numerical manifold method(NMM)has attracted many researchers from geotechnical community because it unifies the solutions of continuous and discontinuous problems in the same framework.However,due to the lack of ready-made preprocessing tools,the development of three dimensional NMM(3DNMM)is still limited.A practical strategy to generate the discretized models for a 3DNMM analysis is proposed.In the proposed strategy,regular hexahedral meshes are uniformly deployed to construct the mathematical cover system.The physical meshes including the joints,material interfaces,and problem domain boundaries are adopted to cut the mathematical cover system into physical cover system and manifold elements(MEs).To improve the efficiency of the proposed strategy,the Intel threading building blocks(TBB)parallel library for CPU paralleling is adopted.Several typical examples are adopted to validate the proposed strategy.The results show that the proposed strategy can effectively generate the discretized 3D models of some geotechnical problems for 3DNMM calculations.The proposed strategy deserves a further investigation.

Design of unidirectional emission silicon/llI-V laser for on-chip interconnects

We propose a unidirectional emission silicon/ III-V laser, which comprises an III-V quantum wells microdisk connected to an output waveguide and a siliconon-insulator （SOI） waveguide. Characteristics of the III-V microdisk with an output waveguide and mode coupling between the III-V output waveguide and the SO1 waveguide are investigated by three-dimensional （3D） finite-difference time-domain （FDTD） method. Simulation results show that the Q factor of a coupled mode for a 7.5 μm diameter microdisk connected to a 0.5 μm wide output waveguide is about 8.5×10^4. And the coupling efficiency between the III-V output waveguide and the SO1 waveguide is over 96% when the III-V waveguide width is 0.5 μm, the SO1 waveguide width is 0.565 μm and the vertical gap between those two waveguides is 0.1μm. The proposed hybrid laser would be of valuable applications for on-chip interconnects.