Design of the yielding support used highly deformable elements for a tunnel excavated in squeezing rock

Yielding support is often used in the squeezing tunnel to prevent damage to the lining induced by large deformation of the surrounding rock.Highly Deformable Elements(HDE)which is often installed along the circumferential direction of the shotcrete lining is a common type of yielding support.To determine the yield parameters of HDE,the support characteristic of the lining using HDE and the ground pressure considering strain-softening of soft rock were analyzed by an analytical method.The analytical solution showed that when considering the strain-softening of squeezing ground,the ground pressure has a non-zero minimum value.The minimum value of ground stress can be used to determine the constant yield stress of the HDE,and the corresponding deformation of the minimum ground pressure can be used to determine the deformation capacity of the HDE.Based on the variation in the design constant yield stress and yield displacement of HDE with the in-situ stress and the mechanical parameters of the soft rock,equations were proposed for determining of the yield parameters of the HDE.

DEFORMATION ANALYSIS OF SHEET METAL SINGLE-POINT INCREMENTAL FORMING BY FINITE ELEMENT METHOD SIMULATION

Single-point incremental forming （SPIF） is an innovational sheet metal forming method without dedicated dies, which belongs to rapid prototyping technology. In generalizing the SPIF of sheet metal, the deformation analysis on forming process becomes an important and useful method for the planning of shell products, the choice of material, the design of the forming process and the planning of the forming tool. Using solid brick elements, the finite element method（FEM） model of truncated pyramid was established. Based on the theory of anisotropy and assumed strain formulation, the SPIF processes with different parameters were simulated. The resulted comparison between the simulations and the experiments shows that the FEM model is feasible and effective. Then, according to the simulated forming process, the deformation pattern of SPIF can be summarized as the combination of plane-stretching deformation and bending deformation. And the study about the process parameters＇ impact on deformation shows that the process parameter of interlayer spacing is a dominant factor on the deformation. Decreasing interlayer spacing, the strain of one step decreases and the formability of blank will be improved. With bigger interlayer spacing, the plastic deformation zone increases and the forming force will be bigger.

CALCULATION OF MILL RIGIDITY BY THREE DIMENSION CONTACT BOUNDARY ELEMENT METHOD

Vertical rigidity of the space self adaptive 530 high rigidity mill is calculated by applying the boundary element method (BEM) of three dimension elastic contact problem,which can update the existed deforming separation calculating theory and corresponding methods of material mechanics,elastic mechanics and finite element method.The method has less hypotheses and stronger synthesis in contact type calculating model.The advantages of the method are high calculating rate,high calculating accuracy,etc..

Dynamic mechanism for horizontal deformation in part of North China area——Three-dimensional finite-element calculation and analysis of results from GPS remeasurement

A deformation monitoring network that covers part of North China area and takes the Beijing region as the center was measured for two times with high precision GPS in 1995 and 1996 respectively. The results from remeasurement indicate that present horizontal movement in the monitored area is characterized by relative motion among several main tectonic blocks. Considering the spatial distribution features obtained from geological survey and results on seismic wave and activity in the area, and stratified features of crustal medium in depth, a three dimensional finite element medium model is designed. And under the conditions of taking and not taking the action manner of the background stress field in the studied area into account, the relative motion between tectonic blocks is calculated and modeled. Based on the results from the analysis and calculations the dynamic mechanism for the present horizontal deformation in the area is discussed.

Thermo-hydro-mechanical-air coupling finite element method and its application to multi-phase problems

In this paper, a finite element method （FEM）-based multi-phase problem based on a newly proposed thermal elastoplastic constitutive model for saturated/unsaturated geomaterial is discussed. A program of FEM named as SOFT, adopting unified field equations for thermo-hydro-mechanical-air （THMA） behavior of geomaterial and using finite element-finite difference （FE-FD） scheme for so/l-water-air three-phase coupling problem, is used in the numerical simulation. As an application of the newly proposed numerical method, two engineering problems, one for slope failure in unsaturated model ground and another for in situ heating test related to deep geological repository of high-level radioactive waste （HLRW）, are simulated. The model tests on slope failure in unsaturated Shirasu ground, carried out by Kitamura et al. （2007）, is simulated in the framework of soil-water-air three-phase coupling under the condition of constant temperature. While the in situ heating test reported by Munoz （2006） is simulated in the same framework under the conditions of variable temperature hut constant air pressure.

DEFORMATION RIGIDITY OF ASSUMED STRESS MODES IN HYBRID ELEMENTS

The new methods to determine the zero-energy deformation modes in the hybrid elements and the zero-energy stress modes in their assumed stress fields are presented by the natural deformation modes of the elements. And the formula of the additional element deformation rigidity due to additional mode into the assumed stress field is derived. Based on, it is concluded in theory that the zero-energy stress mode cannot suppress the zero-energy deformation modes but increase the extra rigidity to the nonzero-energy deformation modes of the element instead. So they should not be employed to assume the stress field. In addition, the parasitic stress modes will produce the spurious parasitic energy and result the element behaving over rigidity. Thus, they should not be used into the assumed stress field even though they can suppress the zero-energy deformation modes of the element. The numerical examples show the performance of the elements including the zero-energy stress modes or the parasitic stress modes.

Hybrid natural element method for large deformation elastoplasticity problems

We present the hybrid natural element method（HNEM） for two-dimensional elastoplastic large deformation problems. Sibson interpolation is adopted to construct the shape functions of nodal incremental displacements and incremental stresses. The incremental form of Hellinger–Reissner variational principle for elastoplastic large deformation problems is deduced to obtain the equation system. The total Lagrangian formulation is used to describe the discrete equation system.Compared with the natural element method（NEM）, the HNEM has higher computational precision and efficiency in solving elastoplastic large deformation problems. Some numerical examples are selected to demonstrate the advantage of the HNEM for large deformation elastoplasticity problems.

ANALYSIS OF ROLLING BY ELASTO-PLASTIC FINITE DEFORMATION CONTACT BOUNDARY ELEMENT METHOD

A multinonlinear boundary element method is established dealing with elasto plastic finite deformation contact problem, and it is employed to analysis rolling process. With rollers as elastic bodies, workpieces as elastio plastic bodies, rolling problem can be viewed as a frictional elasto plastic contact problem. With fewer assumptions in the simulation of the rolling process, a novel and accurate method is proposed for analysis of rolling problems.

Analytical computation of support characteristic curve for circumferential yielding lining in tunnel design

Circumferential yielding lining is able to tolerate controlled displacements without failure,which has been proven to be an effective solution to large deformation problem in squeezing tunnels.However,up to now,there has not been a well-established design method for it.This paper aims to present a detailed analytical computation of support characteristic curve(SCC)for circumferential yielding lining,which is a significant aspect of the implementation of convergence-confinement method(CCM)in tunnel support design.Circumferential yielding lining consists of segmental shotcrete linings and highly deformable elements,and its superior performance mainly depends on the mechanical characteristic of highly deformable element.The deformation behavior of highly deformable element is firstly investigated.Its whole deforming process can be divided into three stages including elastic,yielding and compaction stages.Especially in the compaction stage of highly deformable element,a nonlinear stress-strain relationship can be observed.For mathematical convenience,the stress-strain curve in this period is processed as several linear sub-curves.Then,the reasons for closure of circumferential yielding lining in different stages are explained,and the corresponding accurate equations required for constructing the SCC are provided.Furthermore,this paper carries out two case studies illustrating the application of all equations needed to construct the SCC for circumferential yielding lining,where the reliability and feasibility of theoretical derivation are also well verified.Finally,this paper discusses the sensitivity of sub-division in element compaction stage and the influence of element length on SCC.The outcome of this paper could be used in the design of proper circumferential yielding lining.

Numerical evaluation of strength and deformability of fractured rocks

Knowledge of the strength and deformability of fractured rocks is important for design, construction and stability evaluation of slopes, foundations and underground excavations in civil and mining engineering. However, laboratory tests of intact rock samples cannot provide information about the strength and deformation behaviors of fractured rock masses that include many fractures of varying sizes, orientations and locations. On the other hand, large-scale in situ tests of fractured rock masses are economically costly and often not practical in reality at present. Therefore, numerical modeling becomes necessary. Numerical predicting using discrete element methods(DEM) is a suitable approach for such modeling because of their advantages of explicit representations of both fractures system geometry and their constitutive behaviors of fractures, besides that of intact rock matrix. In this study, to generically determine the compressive strength of fractured rock masses, a series of numerical experiments were performed on two-dimensional discrete fracture network models based on the realistic geometrical and mechanical data of fracture systems from feld mapping. We used the UDEC code and a numerical servo-controlled program for controlling the progressive compressive loading process to avoid sudden violent failure of the models. The two loading conditions applied are similar to the standard laboratory testing for intact rock samples in order to check possible differences caused by such loading conditions. Numerical results show that the strength of fractured rocks increases with the increasing confning pressure, and that deformation behavior of fractured rocks follows elasto-plastic model with a trend of strain hardening. The stresses and strains obtained from these numerical experiments were used to ft the well-known Mohr-Coulomb(MC) and Hoek-Brown(H-B) failure criteria, represented by equivalent material properties defning these two criteria. The results show that both criteria can provide fair estimates of the compressive strengths for all tested numerical models. Parameters of the elastic deformability of fractured models during elastic deformation stages were also evaluated, and represented as equivalent Young’s modulus and Poisson’s ratio as functions of lateral confning pressure. It is the frst time that such systematic numerical predicting for strength of fractured rocks was performed considering different loading conditions, with important fndings for different behaviors of fractured rock masses, compared with testing intact rock samples under similar loading conditions.

Theoretical Research and Experimental Validation of Elastic Dynamic Load Spectra on Bogie Frame of High-speed Train

When a train runs at high speeds, the external exciting frequencies approach the natural frequencies of bogie critical components, thereby inducing strong elastic vibrations. The present international reliability test evaluation standard and design criteria of bogie frames are all based on the quasi-static deformation hypothesis. Structural fatigue damage generated by structural elastic vibrations has not yet been included. In this paper, theoretical research and experimental validation are done on elastic dynamic load spectra on bogie frame of high-speed train. The construction of the load series that correspond to elastic dynamic deformation modes is studied. The simplified form of the load series is obtained. A theory of simplified dynamic load–time histories is then deduced. Measured data from the Beijing–Shanghai Dedicated Passenger Line are introduced to derive the simplified dynamic load–time histories. The simplified dynamic discrete load spectra of bogie frame are established. Based on the damage consistency criterion and a genetic algorithm, damage consistency calibration of the simplified dynamic load spectra is finally performed. The computed result proves that the simplified load series is reasonable. The calibrated damage that corresponds to the elastic dynamic discrete load spectra can cover the actual damage at the operating conditions. The calibrated damage satisfies the safety requirement of damage consistency criterion for bogie frame. This research is helpful for investigating the standardized load spectra of bogie frame of high-speed train.

Anisotropy of strength and deformability of fractured rocks

Anisotropy of the strength and deformation behaviors of fractured rock masses is a crucial issue for design and stability assessments of rock engineering structures, due mainly to the non-uniform and non- regular geometries of the fracture systems. However, no adequate efforts have been made to study this issue due to the current practical impossibility of laboratory tests with samples of large volumes con- taining many fractures, and the difficulty for controlling reliable initial and boundary conditions for large-scale in situ tests. Therefore, a reliable numerical predicting approach for evaluating anisotropy of fractured rock masses is needed. The objective of this study is to systematically investigate anisotropy of strength and deformability of fractured rocks, which has not been conducted in the past, using a nu- merical modeling method. A series of realistic two-dimensional （2D） discrete fracture network （DFN） models were established based on site investigation data, which were then loaded in different directions, using the code UDEC of discrete element method （DEM）, with changing confining pressures. Numerical results show that strength envelopes and elastic deformability parameters of tested numerical models are significantly anisotropic, and vary with changing axial loading and confining pressures. The results indicate that for design and safety assessments of rock engineering projects, the directional variations of strength and deformability of the fractured rock mass concerned must be treated properly with respect to the directions of in situ stresses. Traditional practice for simply positioning axial orientation of tunnels in association with principal stress directions only may not be adequate for safety requirements. Outstanding issues of the present study and su^zestions for future study are also oresented.

Extrusion deformation process of ground surface during the Lushan earthquake in China

Based on finite element method, the extrusion deformation process of ground surface during the Lushan earthquake （April 20, 2013） is investigated in this work. In order to construct the finite element model of Lushan earthquake structure, the geophysical layer model of Lushan area, the frictional characteristic of slip-weaken along the fault surface, and the Coulomb failure criterion are considered. Through the computation and the comparison with achievement on the Lushan focal dynamics, our researches indicate that： （1） The most extrusion deformation of ground surface occurred in the initial phase of earthquake procession, i.e., between the fourth and sixth seconds after the earthquake occurred. （2） Between the first and sixth seconds after the earthquake, the extrusion deformation concentrates on the surface projection of earthquake fault. （3） Between the first and third seconds after the earthquake, the extrusion deformation of ground surface is very tiny. Meanwhile, the extrusion deformation reaches maximum at the sixth second after earthquake. （4） After 6 s of Lushan earthquake, the extrusion deformation spread out of earthquake structure projection. （5） During the earthquake, the maximum of extrusion deformation on ground surface is larger than the final deformation of the post-earthquake, in other words, the ground extrusion deformation will lastly reach a relatively small value after the Lushan earthquake occurred.

Diatom-inspired Plastic Deformation Elements for Energy Absorption in Automobiles

We report on a biomimetic approach for the construction of a deformation element in vehicles which absorbs energy in the case of lateral collisions. We aim at simultaneously maximising the energy absorption capacity of the component and mini- mising its weight. The examined deformation element, a crash-pad is inspired by the structure of a diatom which is known for its structural stability. As the natural counterpart, our crash pad is characterized by an undulated shape. The three undulations of the crash pad are of different height and provide for a sequential absorption of the impact energy. Compression tests were performed on the prototypes of the crash pad that were produced from different materials, namely a conventional talc reinforced poly- propylene and a natural fibre reinforced plastic. Compression tests revealed that the bioinspired crash pads performed better or equal than their technical counterpart. As required, the bioinspired components deformed continuously with the increase in deformation force. Since the differences in the properties of the used materials were small, the increased energy absorption properties were predominantly due to the structure of the biomimetic deformation element.

Analysis on Shear Deformation for High Manganese Austenite Steel during Hot Asymmetrical Rolling Process Using Finite Element Method

Based on the rigid-plastic finite element method（FEM）, the shear stress field of deformation region for high manganese austenite steel during hot asymmetrical rolling process was analyzed. The influences of rolling parameters, such as the velocity ratio of upper to lower rolls, the initial temperature of workpiece and the reduction rate, on the shear deformation of three nodes in the upper, center and lower layers were discussed. As the rolling parameters change, distinct shear deformation appears in the upper and lower layers, but the shear deformation in the center layer appears only when the velocity ratio is more than 1.00, and the absolute value of the shear stress in this layer is changed with rolling parameters. A mathematical model which reflected the change of the maximal absolute shear stress for the center layer was established, by which the maximal absolute shear stress for the center layer can be easily calculated and the appropriate rolling technology can be designed.

Symmetric and Asymmetric Rolling Pure Copper Foil: Crystal Plasticity Finite Element Simulation and Experiments

A systematic study has been conducted aiming to attain an insight into the influence of coefficient of roll speed asymmetry, crystal orientation and structure on the deformation behavior, and crystallographic orientation development during foil rolling. Simulations were successfully carried out by using crystal plasticity finite element method（CPFEM）,and a novel computational framework is presented for the representation of virtual polycrystalline grain structures. It has been found that asymmetric rolling（ASR） is more efficient in producing plastic deformation since it develops additional shear strain and activity of slip system compared with symmetric rolling（SR）. For ASR, increase in the length of the shear zone, and decrease in the amount of the pressure and roll force would lead to further reduction. The shear strain path in SR and ASR is strictly influenced by the misorientation of neighbor grains, and corresponding {1 1 1} pole figures offer direct evidence of the spread of crystallographic orientation around the normal direction. The activity of slip systems was examined in detail and found that the predicted results are consistent with the surface layer model. The accuracy of the developed CPFEM model is verified by the fact that the simulated results of roll force coincide well with the experimental results.