Validation and application of three-dimensional discontinuous deformation analysis with tetrahedron finite element meshed block

In the last decade, three dimensional discontin- uous deformation analyses （3D DDA） has attracted more and more attention of researchers and geotechnical engineers worldwide. The original DDA formulation utilizes a linear displacement function to describe the block movement and deformation, which would cause block expansion under rigid body rotation and thus limit its capability to model block de- formation. In this paper, 3D DDA is coupled with tetrahe- dron finite elements to tackle these two problems. Tetrahe- dron is the simplest in the 3D domain and makes it easy to implement automatic discretization, even for complex topol- ogy shape. Furthermore, element faces will remain planar and element edges will remain straight after deformation for tetrahedron finite elements and polyhedral contact detection schemes can be used directly. The matrices of equilibrium equations for this coupled method are given in detail and an effective contact searching algorithm is suggested. Valida- tion is conducted by comparing the results of the proposed coupled method with that of physical model tests using one of the most common failure modes, i.e., wedge failure. Most of the failure modes predicted by the coupled method agree with the physical model results except for 4 cases out of the total 65 cases. Finally, a complex rockslide example demon- strates the robustness and versatility of the coupled method.

Experimental and measured research on three-dimensional deformation law of gas drainage borehole in coal seam

Using self-researched gas drainage borehole stability dynamic monitoring device, three-dimensional deformation characteristics of borehole under steady vertical load were researched experimentally and systematically. This research indicated that under the action of steady loading, the mechanical deformation path of the simulated gas drainage borehole is gradually complicated, and the decay of the borehole circumferential strain is an important characterization of the prediction and early warning of borehole instability and collapse. The horizontal position of borehole occurs compressive strain, and the vertical of which occurs tensile strain under the action of vertical stress. At the initial stage of loading, the vertical strain is more sensitive than that in the horizontal direction. After a certain period of time, the horizontal strain is gradually higher than the vertical one, and the intersection of the borehole horizontal diameter and the hole wall is the stress concentration point. With the increase of the depth of hole, the strain shows a gradual decay trend as a whole, and the vertical strain decays more observably, but there is no absolute position correlation between the amount of strain decay and the increase in borehole depth,and the area within 1.5 times the orifice size is the borehole stress concentration zone.

Stream Surface Strip Element Method and Simulation of Three-Dimensional Deformation of Continuous Hot Rolled Strip

A new method,the stream surface strip element method,for simulating the three-dimensional deformation of plate and strip rolling process was proposed.The rolling deformation zone was divided into a number of stream surface(curved surface)strip elements along metal flow traces,and the stream surface strip elements were mapped into the corresponding plane strip elements for analysis and computation.The longitudinal distributions of the lateral displacement and the altitudinal displacement of metal were respectively constructed to be a quartic curve and a quadratic curve,of which the lateral distributions were expressed as the third-power spline function,and the altitudinal distributions were fitted in the quadratic curve.From the flow theory of plastic mechanics,the mathematical models of the three-dimensional deformations and stresses of the deformation zone were constructed.Compared with the streamline strip element method proposed by the first author of this paper,the stream surface strip element method takes into account the uneven distributions of stresses and deformations along altitudinal direction,and realizes the precise three-dimensional analysis and computation.The simulation example of continuous hot rolled strip indicates that the method and the model accord with facts and provide a new reliable engineering-computation method for the three-dimensional mechanics simulation of plate and strip rolling process.

FORMULATIONS OF THE THREE-DIMENSIONAL DISCONTINUOUS DEFORMATION ANALYSIS METHOD

This paper extends the original 2D discontinuous deformation analysis(DDA)method proposed by Shi to 3D cases,and presents the formulations of the 3D DDA.The formulations maintain the characteristics of the original 2D DDA approach.Contacts between the blocks are detected by using Common-Plane (C-P) approach and the non-smooth contact,such as of vertex-to-vertex,vertex- to-edge and edge-to-edge types,can be handled easily based on the C-P method.The matrices of equilibrium equations have been given in detail for programming purposes.The C program codes for the 3D DDA are developed.The ability and accuracy of the formulations and the program are verified by the analytical solutions of several dynamic examples.The robustness and versatility of the algorithms presented in this paper are demonstrated with the aid of an example of scattering of densely packed cubes.Finally,implications and future extensions are discussed.

Geodetic constraints on contemporary three-dimensional crustal deformation in the Laji Shan—Jishi Shan tectonic belt

The Laji Shan—Jishi Shan tectonic belt(LJTB),located in the southern part of the northeastern Tibetan Plateau(NETP),is a tectonic window to reveal regional tectonic deformation in the NETP.However,its kinematics in the Holocene remains controversial.We obtain the latest and dense horizontal velocity field based on data collected from our newly constructed and existing GNSS stations.Combined with fault kinematics from geologic observations,we analyze the crustal deformation characteristics along the LJTB.The results show that:(1)The Laji Shan fault(LJF)is inactive,and the northwest-oriented Jishi Shan fault(JSF)exhibits a significant dextral and thrust slip.(2)The transpression along the arc-shaped LJTB accommodates deformation transformation between the dextral Riyue Shan fault and the sinistral west Qinling fault.(3)With the continuous pushing of the Indian plate,internal strains in the Tibetan Plateau are continuously transferred in the northeast via the LJTB as they are gradually dissipated near the LJTB and translated into significant crustal uplift in these regions.

Three-dimensional consolidation deformation analysis of porous layered soft soils considering asymmetric effects

Long-term settlements for underground structures, such as tunnels and pipelines, are generally observed after the completion of construction in soft clay. The soil consolidation characteristic has great influences on the long-term deformation for underground structures. A three-dimensional consolidation analysis method under the asymmetric loads is developed for porous layered soil based on Biot's classical theory. Time-displacement effects can be fully considered in this work and the analytical solutions are obtained by the state space approach in the Cartesian coordinate. The Laplace and double Fourier integral transform are applied to the state variables in order to reduce the partial differential equations into algebraic differential equations and easily obtain the state space solution. Starting from the governing equations of saturated porous soil, the basic relationship of state space variables is established between the ground surface and the arbitrary depth in the integral transform domain. Based on the continuity conditions and boundary conditions of the multi-layered pore soil model, the multi-layered pore half-space solutions are obtained by means of the transfer matrix method and the inverse integral transforms. The accuracy of proposed method is demonstrated with existing classical solutions. The results indicate that the porous homogenous soils as well as the porous non-homogenous layered soils can be considered in this proposed method. When the consolidation time factor is 0.01, the value of immediate consolidation settlement coefficient calculated by the weighted homogenous solution is 27.4% bigger than the one calculated by the non-homogeneity solution. When the consolidation time factor is 0.05, the value of excess pore water pressure for the weighted homogenous solution is 27.2% bigger than the one for the non-homogeneity solution. It is shown that the material non-homogeneity has a great influence on the long-term settlements and the dissipation process of excess pore water pressure.

Three-Dimensional Simulation of Plasma Deformation During Contact Opening in a Circuit Breaker,Including the Analysis of Kink Instability and Sausage Instability

A three-dimensional （3-D） transient model has been developed to investigate plasma deformation driven by a magnetic field and its influence on arc stability in a circuit breaker. The 3-D distribution of electric current density is obtained from a current continuity equation along with the generalized Ohm＇s law; while the magnetic field induced by the current flowing through the arc column is calculated by the magnetic vector potential equation. When gas interacts with an arc column, fundamental factors, such as Ampere＇s law, Ohm＇s law, the turbulence model, transport equations of mass, momentum and energy of plasma flow, have to be coupled for aria- lyzing the phenomenon. The coupled interactions between arc and plasma flow are described in the fl＇amework of time-dependent magnetohydrodynamic （MHD） equations in conjunction with a K-~ turbulence model. Simulations have been focused on sausage and kink instabilities in plasma （these phenomena are related tO pinch effects and electromagnetic fields）. The 3-D sjm- ulation reveals the relation between plasma deformation and instability phenomena, which affect arc stability during circuit breaker operation. Plasma deformation is the consequence of coupled interactions between the electromagnetic force and plasma flow described in simulations.

Three-dimensional numerical simulation on the coseismic deformation of the 2008 M_S8.0 Wenchuan earthquake in China

Based on the finite element numerical algorithm, the coseismic displacements of the Wenchuan Ms8.0 earthquake are calculated with the rupture slip vectors derived by Ji and Hayes as well as Nishimura and Yaji. Except in a narrow strip around the rupture zone, the coseismic displacements are consistent with those from GPS observation and InSAR interpretation. Numerical results show that rupture slip vectors and elastic properties have profound influences on the surface coseismic deformation, Results from models with different elastic parameters indicate that： （1） in homogeneous elastic medium, the surface displacements are weakly dependent on Poisson＇s ratio and independent of the elastic modulus; （2） in horizontally homogeneous medium with a weak zone at its middle, the thickness of the weak zone plays a significant role on calculating the surface displacements; （3） in horizontally and vertically heterogeneous medium, the surface displacements depend on both Poisson＇s ratio and elastic modulus. Calculations of eoseismic deformation should take account of the spatial variation of the elastic properties. The misfit of the numerical results with that from the GPS observations in the narrow strip around the rupture zone suggests that a much more complicated rupture model of the Wenchuan earthquake needs to be established in future study.

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.

Three-dimensional constitutive model for magneto-mechanical deformation of NiMnGa ferromagnetic shape memory alloy single crystals

Existing experimental results have shown that four types of physical mechanisms, namely, martensite transformation, martensite reorientation, magnetic domain wall motion and magnetization vector rotation, can be activated during the magneto-mechanical deformation of NiMnGa ferromagnetic shape memory alloy (FSMA) single crystals. In this work, based on irreversible thermodynamics, a three-dimensional (3D) single crystal constitutive model is constructed by considering the aforementioned four mechanisms simultaneously. Three types of internal variables, i.e., the volume fraction of each martensite variant, the volume fraction of magnetic domain in each variant and the deviation angle between the magnetization vector, and easy axis are introduced to characterize the magneto-mechanical state of the single crystals. The thermodynamic driving force of each mechanism and the thermodynamic constraints on the constitutive model are obtained from Clausius's dissipative inequality and constructed Gibbs free energy. Then, thermodynamically consistent kinetic equations for the four mechanisms are proposed, respectively. Finally, the ability of the proposed model to describe the magneto-mechanical deformation of NiMnGa FSMA single crystals is verified by comparing the predictions with corresponding experimental results. It is shown that the proposed model can quantitatively capture the main experimental phenomena. Further, the proposed model is used to predict the deformations of the single crystals under the non-proportional mechanical loading conditions.

Precise Three-Dimensional Deformation Retrieval in Large and Complex Deformation Areas via Integration of Offset-Based Unwrapping and Improved Multiple-Aperture SAR Interferometry:Application to the 2016 Kumamoto Earthquake

Conventional synthetic aperture radar(SAR)interferometry(InSAR)has been successfully used to precisely measure surface deformation in the line-of-sight(LOS)direction,while multiple-aperture SAR interferometry(MAI)has provided precise surface deformation in the along-track(AT)direction.Integration of the InSAR and MAI methods enables precise measurement of the two-dimensional(2D)deformation from an interferometric pair;recently,the integration of ascending and descending pairs has allowed the observation of precise three-dimensional(3D)deformation.Precise 3D deformation measurement has been applied to better understand geological events such as earthquakes and volcanic eruptions.The surface deformation related to the 2016 Kumamoto earthquake was large and complex near the fault line;hence,precise 3D deformation retrieval had not yet been attempted.The objectives of this study were to①perform a feasibility test of precise 3D deformation retrieval in large and complex deformation areas through the integration of offset-based unwrapped and improved multiple-aperture SAR interferograms and②observe the 3D deformation field related to the 2016 Kumamoto earthquake,even near the fault lines.Two ascending pairs and one descending the Advanced Land Observing Satellite-2(ALOS-2)Phased Array-type L-band Synthetic Aperture Radar-2(PALSAR-2)pair were used for the 3D deformation retrieval.Eleven in situ Global Positioning System(GPS)measurements were used to validate the 3D deformation measurement accuracy.The achieved accuracy was approximately 2.96,3.75,and 2.86 cm in the east,north,and up directions,respectively.The results show the feasibility of precise 3D deformation measured through the integration of the improved methods,even in a case of large and complex deformation.

Three-dimensional geodetic deformation surveying for Naner area in Daqing oilfield

Geodetic deformation severely affects the development of the oilfield and probably causes casing damage or abandonment of injection wells and producers. Therefore, it is meaningful to survey and study three-dimensional geodetic deformation in the process of the oilfield development. In order to study this issue, 11-year long term surveying of three-dimensional geodetic deformation has been carried out while developing Naner area in Daqing oilfield. Basic rules of 3-D geodetic deformation have been obtained through surveying. Results show that production and injection under high pressure may cause the changes of surface elevation, and geodetic deformation correlates with simultaneous formation pressure. Precautions and relative technological measurements have been put forward in the waterflood development in Naner region and provide theoretical guidelines for the production and casing preservation of the oilfield. Finally, surveying results are interpreted by porous elastic theory. Mathematical model to calculate 3-D geodetic deformation is put forward in the course of the oilfield development.

THREE-DIMENSIONAL DEFORMATION ALONG THE ALTYN TAGH FAULT ZONE AND UPLIFT OF THE ALTYN MOUNTAIN, NORTHERN TIBET

he convergence between India and Eurasia is partly accommodated by motion of a few large blocks along strike\|slip faults. About 1800km long Altyn Tagh fault strikes in N60～80°E and allows the northeastward displacement of the Tibet plateau relative to the Tarim. The Altyn Tagh fault zone is a typical transpressional fault zone, characterized by blocks rotation and crustal shortening and vertical extrusion of blocks within the Altyn Tagh strike\|slip system. Differences of three\|dimensional deformation and configuration of the active structures are recognized at different segment of the Altyn Tagh fault zone.1\ Structural configuration of the Altyn Tagh fault zone\;In the Altyn Tagh strike\|slip fault zone, the assemblage pattern of the (active) faults is in the form of parallel plumes, especially in the eastern and the western segments of the Altyn Tagh fault zone. These plumes structures in the eastern segment are assembled by string\|like left lateral strike\|slip fault and broom\|like thrusting faults, and in the western segment by arc\|like left lateral strike\|slip faults along with thrusting faults and normal faults. In the middle segment of the Altyn Tagh fault zone, the structures are characterized by the string\|like left lateral strike\|slip faults in the center and reverse thrusting faults on the two sides.

Three-dimensional coseismic deformation of the 2016 MW7.8 Kaikuora,New Zealand earthquake obtained by InSAR and offset measurements

The 2016 MW7.8 Kaikoura earthquake struck the northern part of south Island,New Zealand,within the active and complex Australia-Pacific plate boundary system.Firstly,we used the InSAR method to obtain coseismic LOS deformation fields based on SAR images and applied offset tracking methods to obtain offset measurements based on optical satellite images.The maximum displacement of about 6 m is detected in the direction away from the satellite on the south-west side and also towards the satellite on the north-east side.The 3D deformation field is then resolved by the combination of these measurements with a least-square solve method,and comparisons with 3 components of GPS stations show good consistency.Despite complex features demonstrated in the 3D deformation field,there are still clear spatial correlations between surface deformation and faults distribution.It reveals that more than ten faults were ruptured during the earthquake,including some faults were previously understudies for their tectonic activities.The maximum horizontal deformation of about 10 m occurs along the Kekerengu fault with the vertical deformation up to 2 m.The 3D deformation shows that the mainshock is a multisegments faulting with a rupture process of strike-slip,compression,transpressional rupture and strike-slip in space along the NE direction.

In-situ three-dimensional visualization of dynamic tension deformation in ferrite stainless steels

An improved three-dimensional （3-D） experimental visualization methodology is presented tor evaluating the fracture mechanisms of ferritic stainless steels by in-situ tensile testing with an environmental scanning electron microscope （ESEM）. The samples were machined with a radial notched shape and a sloped surface. Both planar surface deformation and sloping surface deformation-induced microvoids were observed during dynamic tension experiments, where a greater amount of information could be obtained from the sloping surface. The results showed that microvoids formed at the grain boundaries of highly elongated large grains. The microvoids nucleated in the severely deformed regions grew nearly parallel to the tensile axis, predominantly along the grain boundaries. The microvoids nucleated at the interface of particles and the matrix did not propagate due to the high plasticity of the matrix. The large microvoids propagated and showed a zigzag shape along the grain boundaries,seemingly a consequence of the fracture of the slip bands caused by dislocation pile-ups. The final failure took place due to the reduction of the load-beating area.

Deformation monitoring of long-span railway bridges based on SBAS-InSAR technology

The deformation monitoring of long-span railway bridges is significant to ensure the safety of human life and property.The interferometric synthetic aperture radar(In SAR)technology has the advantage of high accuracy in bridge deformation monitoring.This study monitored the deformation of the Ganjiang Super Bridge based on the small baseline subsets(SBAS)In SAR technology and Sentinel-1A data.We analyzed the deformation results combined with bridge structure,temperature,and riverbed sediment scouring.The results are as follows:(1)The Ganjiang Super Bridge area is stable overall,with deformation rates ranging from-15.6 mm/yr to 10.7 mm/yr(2)The settlement of the Ganjiang Super Bridge deck gradually increases from the bridge tower toward the main span,which conforms to the typical deformation pattern of a cable-stayed bridge.(3)The sediment scouring from the riverbed cause the serious settlement on the bridge’s east side compared with that on the west side.(4)The bridge deformation negatively correlates with temperature,with a faster settlement at a higher temperature and a slow rebound trend at a lower temperature.The study findings can provide scientific data support for the health monitoring of long-span railway bridges.

A theory for three-dimensional response of micropolar plates

Through combined applications of the transfer-matrix method and asymptotic expansion technique,we formulate a theory to predict the three-dimensional response of micropolar plates.No ad hoc assumptions regarding through-thickness assumptions of the field variables are made,and the governing equations are two-dimensional,with the displacements and microrotations of the mid-plane as the unknowns.Once the deformation of the mid-plane is solved,a three-dimensional micropolar elastic field within the plate is generated,which is exact up to the second order except in the boundary region close to the plate edge.As an illustrative example,the bending of a clamped infinitely long plate caused by a uniformly distributed transverse force is analyzed and discussed in detail.

Violent collisions can reveal hexadecapole deformation of nuclei

A new observable in heavy ion collision experiments was identified to be sensitive to the hexadecapole deformation of the colliding nuclei.Such deformation is difficult to measure in traditional nuclear electric transition measurements,as it is often overwhelmed by the nuclear quadrupole deformation.This opens the door to gain new insight into nuclear structure with experiments that were designed to study hot and dense nuclear matter.

Oxygen tension modulates cell function in an in vitro three-dimensional glioblastoma tumor model

Hypoxia is a typical feature of the tumor microenvironment,one of the most critical factors affecting cell behavior and tumor progression.However,the lack of tumor models able to precisely emulate natural brain tumor tissue has impeded the study of the effects of hypoxia on the progression and growth of tumor cells.This study reports a three-dimensional(3D)brain tumor model obtained by encapsulating U87MG(U87)cells in a hydrogel containing type I collagen.It also documents the effect of various oxygen concentrations(1%,7%,and 21%)in the culture environment on U87 cell morphology,proliferation,viability,cell cycle,apoptosis rate,and migration.Finally,it compares two-dimensional(2D)and 3D cultures.For comparison purposes,cells cultured in flat culture dishes were used as the control(2D model).Cells cultured in the 3D model proliferated more slowly but had a higher apoptosis rate and proportion of cells in the resting phase(G0 phase)/gap I phase(G1 phase)than those cultured in the 2D model.Besides,the two models yielded significantly different cell morphologies.Finally,hypoxia(e.g.,1%O2)affected cell morphology,slowed cell growth,reduced cell viability,and increased the apoptosis rate in the 3D model.These results indicate that the constructed 3D model is effective for investigating the effects of biological and chemical factors on cell morphology and function,and can be more representative of the tumor microenvironment than 2D culture systems.The developed 3D glioblastoma tumor model is equally applicable to other studies in pharmacology and pathology.

Three-dimensional cell-based strategies for liver regeneration

Liver regeneration and the development of effective therapies for liver failure remain formidable challenges in modern medicine.In recent years,the utilization of 3D cell-based strategies has emerged as a promising approach for addressing these urgent clinical requirements.This review provides a thorough analysis of the application of 3D cell-based approaches to liver regeneration and their potential impact on patients with end-stage liver failure.Here,we discuss various 3D culture models that incorporate hepatocytes and stem cells to restore liver function and ameliorate the consequences of liver failure.Furthermore,we explored the challenges in transitioning these innovative strategies from preclinical studies to clinical applications.The collective insights presented herein highlight the significance of 3D cell-based strategies as a transformative paradigm for liver regeneration and improved patient care.