3D DEM simulation of hard rock fracture in deep tunnel excavation induced by changes in principal stress magnitude and orientation

To achieve the loading of the stress path of hard rock,the spherical discrete element model(DEM)and the new flexible membrane technology were utilized to realize the transient loading of three principal stresses with arbitrary magnitudes and orientations.Furthermore,based on the deep tunnel of China Jinping Underground Laboratory II(CJPL-II),the deformation and fracture evolution characteristics of deep hard rock induced by excavation stress path were analyzed,and the mechanisms of transient loading-unloading and stress rotation-induced fractures were revealed from a mesoscopic perspective.The results indicated that the stressestrain curve exhibits different trends and degrees of sudden changes when subjected to transient changes in principal stress,accompanied by sudden changes in strain rate.Stress rotation induces spatially directional deformation,resulting in fractures of different degrees and orientations,and increasing the degree of deformation anisotropy.The correlation between the degree of induced fracture and the unloading magnitude of minimum principal stress,as well as its initial level is significant and positive.The process of mechanical response during transient unloading exhibits clear nonlinearity and directivity.After transient unloading,both the minimum principal stress and minimum principal strain rate decrease sharply and then tend to stabilize.This occurs from the edge to the interior and from the direction of the minimum principal stress to the direction of the maximum principal stress on theε1-ε3 plane.Transient unloading will induce a tensile stress wave.The ability to induce fractures due to changes in principal stress magnitude,orientation and rotation paths gradually increases.The analysis indicates a positive correlation between the abrupt change amplitude of strain rate and the maximum unloading magnitude,which is determined by the magnitude and rotation of principal stress.A high tensile strain rate is more likely to induce fractures under low minimum principal stress.

Modeling time-dependent mechanical behavior of hard rock considering excavation-induced damage and complex 3D stress states

To investigate the long-term stability of deep rocks,a three-dimensional(3D)time-dependent model that accounts for excavation-induced damage and complex stress state is developed.This model comprises three main components:a 3D viscoplastic isotropic constitutive relation that considers excavation damage and complex stress state,a quantitative relationship between critical irreversible deformation and complex stress state,and evolution characteristics of strength parameters.The proposed model is implemented in a self-developed numerical code,i.e.CASRock.The reliability of the model is validated through experiments.It is indicated that the time-dependent fracturing potential index(xTFPI)at a given time during the attenuation creep stage shows a negative correlation with the extent of excavationinduced damage.The time-dependent fracturing process of rock demonstrates a distinct interval effect of the intermediate principal stress,thereby highlighting the 3D stress-dependent characteristic of the model.Finally,the influence of excavation-induced damage and intermediate principal stress on the time-dependent fracturing characteristics of the surrounding rocks around the tunnel is discussed.

Mathematical Modelling and 3D FEM Analysis of the Influence of Initial Stresses on the ERR in a Band Crack’s Front in the Rectangular Orthotropic Thick Plate

This paper deals with the mathematical modelling and 3D FEM study of the energy release rate(ERR)in the band crack’s front contained in the orthotropic thick rectangular plate which is stretched or compressed initially before the loading of the crack's edge planes.The initial stretching or compressing of the plate causes uniformly distributed normal stress to appear acting in the direction which is parallel to the plane on which the band crack is located.After the appearance of the initial stress in the plate it is assumed that the crack's edge planes are loaded with additional uniformly distributed normal forces and the ERR caused with this additional loading is studied.The corresponding boundary value problem is formulated within the scope of the so-called 3D linearized theory of elasticity which allows the initial stress on the values of the ERR to be taken into consideration.Numerical results on the influence of the initial stress,anisotropy properties of the plate material,the crack’s length and its distance from the face planes of the plate on the values of the ERR,are presented and discussed.In particular,it is established that for the relatively greater length of the crack’s band,the initial stretching of the plate causes a decrease,but the initial compression causes an increase in the values of the ERR.

Modeling and simulation of 3D thermal stresses of large-sized castings in solidification processes

When heavy machines and large scaled receiver system of communication equipment are manufactured, it always needs to produce large-sized steel castings, aluminum castings and etc. Some defects of hot cracking by thermal stress often appear during solidification process as these castings are produced, which results in failure of castings. Therefore predicting the effects of technological parameters for production of castings on the thermal stress during solidification process becomes an important means. In this paper, the mathematical models have been established and numerical calculation of temperature fields by using finite difference method (FDM) and then thermal stress fields by using finite element method (FEM) during solidification process of castings have been carried out. The technological parameters of production have been optimized by the results of calculation and the defects of hot cracking have been eliminated. Modeling and simulation of 3D thermal stress during solidification processes of large-sized castings provided a scientific basis, which promoted further development of advanced manufacturing technique.

A new design of 3D-printed orthopedic bone plates with auxeticstructures to mitigate stress shielding and improve intra-operative bending

Orthopedic bone plates are most commonly used for bone fracture fixation for more than 100 years.The bone plate design had evolved over time overcoming many challenges such as insufficient strength and excessive plate–bone contact affecting the blood circulation.However,it is only made of two materials,either stainless steel(AISI 316L)or titanium(Ti–6Al–4V).There are two main limitations of metallic bone implants,namely stress shielding and the problem of malocclusion caused by the displacement of the fracture site during healing.To overcome the two problems,a new bone plate design with the incorporation of auxetic structures is proposed in this work.This study aims to use auxetic structure section in the bone plate that would decrease the stiffness of the region,thereby mitigating the stress-shielding effect and at the same time act as a deformable section to enable intra-operative bending for effective alignment while having enough bending strength and stiffness.Two different auxetic structures namely re-entrant honeycomb and missing rib structures were considered.The auxetic structure incorporated bone plates were designed,finite element analysis was done,fabricated using direct metal laser sintering technique,and tested.The results indicate that the re-entrant honeycomb structure incorporated bone plates serve as an effective bone design compared to the conventional bone plate design,in terms of stress shielding and intra-operative bending while offering similar mechanical and bending strength.

Elastoplastic 3D Deformation and Stress Analysis of Strip Rolling

An elastoplastic method for analyzing the 3D deformation, stress and transverse distribution of tension stress during cold strip rolling is developed. The analysis is based on the elastoplastic variational principle in which a kinematically admissible velocity field is constructed with the lateral flow function as an unknown function. The stress distribution and volume strain distribution are obtained by solving the simultaneous equations formed by the longitudinal differential equation of equilibrium and constitutive equations. The lateral flow function is determined by minimizing the total energy dissipation rate. Experimental investigation was carried out on a reversible cold mill. The front tension stress distributions in cold rolled strips were measured by a multi roll segmented tension sensing shapemeter. The calculated results are in good agreement with the measured ones.

3D morphology and formation mechanism of fractures developed by true triaxial stress

As main part of underground rock mass,the three-dimensional(3D)morphology of natural fractures plays an important role in rock mass stability.Based on previous studies on 3D morphology,this study probes into the law and mechanism regarding the influence of the confining pressure constraints on 3D morphological features of natural fractures.First,fracture surfaces were obtained by true triaxial compression test and 3D laser scanning.Then 3D morphological parameters of fractures were calculated by using Grasselli’s model.The results show that the failure mode of granites developed by true triaxial stress can be categorized into tension failure and shear failure.Based on the spatial position of fractures,they can be divided into tension fracture surface,S-1 shear fracture surface,and S-2 shear fracture surface.Micro-failure of the tension fracture surface is dominated by mainly intergranular fracture;the maximum height of asperities on the fracture surface and the 3D roughness of fracture surfaces are influenced by σ_(3) only and they are greater than those of shear fracture surfaces,a lower overall uniformity than tension fracture surface.S-1 shear fracture surface and S-2 shear fracture surface are dominated by intragranular and intergranular coupling fracture.The maximum height of asperities on the fracture surface and 3D roughness of fracture surface are affected by σ_(1),σ_(2),and σ_(3).With the increase of σ_(2) or σ_(3),the cutting off of asperities on the fracture surface becomes more common,the maximum height of asperities and 3D roughness of fracture surface further decrease,and the overall uniformity gets further improved.The experimental results are favorable for selecting technical parameters of enhanced geothermal development and the safety of underground mine engineering.

3D numerical simulation of heterogeneous in situ stress field in low-permeability reservoirs

Analysis of the in situ stress orientation and magnitude in the No.4 Structure of Nanpu Sag was performed on the basis of data obtained from borehole breakout and acoustic emission measurements.On the basis of mechanical experiments,logging interpretation,and seismic data,a 3 D geological model and heterogeneous rock mechanics field of the reservoir were constructed.Finite element simulation techniques were then used for the detailed prediction of the 3 D stress field.The results indicated that the maximum horizontal stress orientation in the study area was generally NEE-SWW trending,with significant changes in the in situ stress orientation within and between fault blocks.Along surfaces and profiles,stress magnitudes were discrete and the in situ stress belonged to theⅠa-type.Observed inter-strata differences were characterized as five different types of in situ stress profile.Faults were the most important factor causing large distributional differences in the stress field of reservoirs within the complex fault blocks.The next important influence on the stress field was the reservoir’s rock mechanics parameters,which impacted on the magnitudes of in situ stress magnitudes.This technique provided a theoretical basis for more efficient exploration and development of low-permeability reservoirs within complex fault blocks.

Effective grouting area of jointed slope and stress deformation responses by numerical analysis with FLAC^(3D)

To study the grouting reinforcement mechanism in jointed rock slope, first, the theoretical deduction was done to calculate the critical length of slipping if the slope angle is larger than that of joint inclination; Second, the numerical calculation model was founded by FLAG^3D, so as to find the stress and deformation responses of rock mass in the state before and after grouting, the analysis results show that the range between the boundary of critical slipping block and the joint plane that passes the slope toe is the effective grouting area （EGA）. After excavation, large deformation occurs along the joint plane. After grouting, the displacements of rock particles become uniform and continuous, and large deformations along the joint plane are controlled; the dynamic displacement can re- flect the deformation response of slope during excavation in the state before and after grouting, as well as the shear location of potential slip plane. After grouting, the dynamic displacement of each monitoring point reaches the peak value with very few time steps, which indicate that the parameters of the joint plane, such as strength and stiffness, are improved; the stress field becomes uniform. Tensile area reduces gradually; whole stability of the slope and its ability to resist tensile and shear stress are improved greatly.

Characterization of 3D pore nanostructure and stress-dependent permeability of organic-rich shales in northern Guizhou Depression,China

The three-dimensional(3D)pore structures and permeability of shale are critical for forecasting gas production capacity and guiding pressure differential control in practical reservoir extraction.However,few investigations have analyzed the effects of microscopic organic matter(OM)morphology and 3D pore nanostructures on the stress sensitivity,which are precisely the most unique and controlling factors of reservoir quality in shales.In this study,ultra-high nanoscale-resolution imaging experiments,i.e.focused ion beam-scanning electron microscopy(FIB-SEMs),were conducted on two organic-rich shale samples from Longmaxi and Wufeng Formations in northern Guizhou Depression,China.Pore morphology,porosity of 3D pore nanostructures,pore size distribution,and connectivity of the six selected regions of interest(including clump-shaped OMs,interstitial OMs,framboidal pyrite,and microfractures)were qualitatively and quantitatively characterized.Pulse decay permeability(PDP)measurement was used to investigate the variation patterns of stress-dependent permeability and stress sensitivity of shales under different confining pressures and pore pressures,and the results were then used to calculate the Biot coefficients for the two shale formations.The results showed that the samples have high OM porosity and 85%of the OM pores have the radius of less than 40 nm.The OM morphology and pore structure characteristics of the Longmaxi and Wufeng Formations were distinctly different.In particular,the OM in the Wufeng Formation samples developed some OM pores with radius larger than500 nm,which significantly improved the connectivity.The macroscopic permeability strongly depends on the permeability of OM pores.The stress sensitivity of permeability of Wufeng Formation was significantly lower than that of Longmaxi Formation,due to the differences in OM morphology and pore structures.The Biot coefficients of 0.729 and 0.697 were obtained for the Longmaxi and Wufeng Formations,respectively.

Tunable three-dimensional nonreciprocal transmission in a layered nonlinear elastic wave metamaterial by initial stresses

In this work,the three-dimensional(3 D)propagation behaviors in the nonlinear phononic crystal and elastic wave metamaterial with initial stresses are investigated.The analytical solutions of the fundamental wave and second harmonic with the quasilongitudinal(qP)and quasi-shear(qS_(1) and qS_(2))modes are derived.Based on the transfer and stiffness matrices,band gaps with initial stresses are obtained by the Bloch theorem.The transmission coefficients are calculated to support the band gap property,and the tunability of the nonreciprocal transmission by the initial stress is discussed.This work is expected to provide a way to tune the nonreciprocal transmission with vector characteristics.

AHermitian C^(2) Differential Reproducing Kernel Interpolation Meshless Method for the 3D Microstructure-Dependent Static Flexural Analysis of Simply Supported and Functionally Graded Microplates

This work develops a Hermitian C^(2) differential reproducing kernel interpolation meshless(DRKIM)method within the consistent couple stress theory(CCST)framework to study the three-dimensional(3D)microstructuredependent static flexural behavior of a functionally graded(FG)microplate subjected to mechanical loads and placed under full simple supports.In the formulation,we select the transverse stress and displacement components and their first-and second-order derivatives as primary variables.Then,we set up the differential reproducing conditions(DRCs)to obtain the shape functions of the Hermitian C^(2) differential reproducing kernel(DRK)interpolant’s derivatives without using direct differentiation.The interpolant’s shape function is combined with a primitive function that possesses Kronecker delta properties and an enrichment function that constituents DRCs.As a result,the primary variables and their first-and second-order derivatives satisfy the nodal interpolation properties.Subsequently,incorporating ourHermitianC^(2)DRKinterpolant intothe strong formof the3DCCST,we develop a DRKIM method to analyze the FG microplate’s 3D microstructure-dependent static flexural behavior.The Hermitian C^(2) DRKIM method is confirmed to be accurate and fast in its convergence rate by comparing the solutions it produces with the relevant 3D solutions available in the literature.Finally,the impact of essential factors on the transverse stresses,in-plane stresses,displacements,and couple stresses that are induced in the loaded microplate is examined.These factors include the length-to-thickness ratio,the material length-scale parameter,and the inhomogeneity index,which appear to be significant.

Extended Kantorovich method for local stresses in composite laminates upon polynomial stress functions

The extended Kantorovich method is employed to study the local stress concentrations at the vicinity of free edges in symmetrically layered composite laminates subjected to uniaxial tensile load upon polynomial stress functions. The stress fields are initially assumed by means of the Lekhnitskii stress functions under the plane strain state. Applying the principle of complementary virtual work,the coupled ordinary differential equations are obtained in which the solutions can be obtained by solving a generalized eigenvalue problem. Then an iterative procedure is established to achieve convergent stress distributions. It should be noted that the stress function based extended Kantorovich method can satisfy both the traction-free and free edge stress boundary conditions during the iterative processes. The stress components near the free edges and in the interior regions are calculated and compared with those obtained results by finite element method（FEM）. The convergent stresses have good agreements with those results obtained by three dimensional（3D） FEM. For generality, various layup configurations are considered for the numerical analysis. The results show that the proposed polynomial stress function based extended Kantorovich method is accurate and efficient in predicting the local stresses in composite laminates and computationally much more efficient than the 3D FEM.

Stress Analysis on Single-Crystal Diamonds by Raman Spectroscopy 3D Mapping

Results on stress analysis for single-crystal diamonds are presented. Isolated crystals were studied by Raman mapping and depth profiling techniques, using confocal microscopy. Diamonds were deposited on molybdenum and tantalum by hot filament and microwave CVD methods at growth rates between 10 and 30 μm·h-1. Crystals from 10 to 40 μm size were examined. Local stress was evaluated by analyzing the position, broadening and splitting of the 1332 cm-1 Raman peak in a 3D mapping. For the (001) orientation, the most stressed zone was found at the center of the crystal base, close to the interface with the substrate: a Raman peak around 1340 cm-1 was measured, corresponding to a pressure c.a. 3 GPa, according to our dynamical calculations. This peak disappears few microns out of the center, suggesting that this highly concentrated stress sector was the nucleation zone of the crystal. A shifting and slight broadening of the 1332 cm-1 band was observed in the rest of the crystal. The causes of these effects are discussed: they proved not to be due to anisotropic stress but to refractive effects. Same results were found for different crystal sizes and growth rates.

Anti-post-traumatic stress disorder effect of dopamine D3 receptor antagonist

OBJECTIVE To explore the antipost-traumatic-stress-disorder(PTSD) effects and its probable mechanism of YQA14,a dopamine D3 receptor antagonist.METHODS Two PTSD animal models,the rat single prolonged stress(SPS) model and the mouse pre-shock model,were used in this experiment.In the SPS model,adult male Sprague-Dawley(SD) rats were randomly divided into control group,model group,positive group and YQA14 groups with different dosages.In the mouse pre-chock model,dopamine D3 receptor knockout(KO) and wild type(WT) mice were randomly divided into control group,model group,positive group and YQA14 group.After the establishment of animal models,the saline,sertraline(ig) and YQA14(ip)were administered to the animals in the control,model,positive control and test groups respectively.The open field test(OFT) was used to evaluate the locomotor activity while the contextual freezing(CF) measurement and elevated plus maze(EPM) test were used to evaluate the PTSD-like behaviors.RESULTS In the rat SPS model,neither SPS nor drug treatment affected the locomotor activity in rats.However,SPS rats showed significant PTSD-like behaviors with enhanced freezing time in CF(P<0.01) and decreased percentage of entries into open arms and time spent in open arms in EPM(P<0.05,P<0.01).Moreover,compared with the model group,the repeated administration of YQA14(3.125,6.25 and 12.5 mg·kg-1)significantly reduced the freezing time(P<0.01)and increased the percentages of entries into open arms and time spent in open arms(P<0.05).In the mouse pre-shock model,when both model groups showed significant higher freezing time compared with the respective control groups(P<0.05,P<0.01),YQA14 selectively alleviated the freezing time on WT mice(P<0.05) while had no effect on KO mice.In the EPM tests,the WT mice model group showed a significant reduction in the percentage of entries into open arms and time spent in open arms(P<0.05) while D3 R KO mice model group didn′ t show any reduction,compared with respective control groups.Furthermore,daily administration of YQA14 at 12.5 mg·kg-1 both significantly reduced the percentages of entries into and time spent in open arms(P<0.05) but not D3 R KO mice.None of the locomotor activity were significantly affected.CONCLUSION YQA14 could significantly alleviate the PTSD-like behaviors in rodents and the effects were mediated by the blockade of brain D3 receptors.

In-situ 3D contour measurement for laser powder bed fusion based on phase guidance

In-situ layerwise imaging measurement of laser powder bed fusion(LPBF)provides a wealth of forming and defect data which enables monitoring of components quality and powder bed homogeneity.Using high-resolution camera layerwise imaging and image processing algorithms to monitor fusion area and powder bed geometric defects has been studied by many researchers,which successfully monitored the contours of components and evaluated their accuracy.However,research for the methods of in-situ 3D contour measurement or component edge warping identification is rare.In this study,a 3D contour mea-surement method combining gray intensity and phase difference is proposed,and its accuracy is verified by designed experiments.The results show that the high-precision of the 3D contours can be achieved by the constructed energy minimization function.This method can detect the deviations of common ge-ometric features as well as warpage at LPBF component edges,and provides fundamental data for in-situ quality monitoring tools.

Vitamin D_(3) attenuates anxiety-like behavior in long-term ovariectomized rats with unpredictable mild stress

The impact of various vitamin D3(VD3)doses(1.0,2.5,or 5 mg/kg,s.c.)in mitigating the negative consequences of chronic unpredictable mild stress(CUMS)was investigated.Adult female rats with long-term estrogen deficiency were assessed using the sucrose preference test(SPT),the elevated plus-maze(EPM),the light/dark test(LDT),and the open-field test(OFT)to measure anhedonia-like and anxiety-like behavior.The corticosterone(CS)and adrenocorticotrophic hormone(ACTH)concentrations in blood serum and the brain-derived neurotrophic factor(BDNF)expression in the hippocampus of long-term ovariectomized(OVX)rats were measured by ELISA kits and/or western blotting.Treatment with VD3(5.0 mg/kg),similarly to fluoxetine(10.0 mg/kg),significantly reduced the anhedonia profile in the SPT and anxiety-like behavior in the EPM and LDT,and CS and ACTH levels in blood serum.It also elevated BDNF levels in the hippocampus of long-term OVX/CUMS compared to OVX/CUMS/solvent rats.Thus,these findings suggest that VD3(5.0 mg/kg)administration might attenuate the anxiety-like profile in long-term OVX adult rats subjected to the CUMS.This might occur via activation of the BDNF signaling pathway in the hippocampus and via restoration of CS and ACTH levels in blood serum.

Evolution of 3D tectonic stress field and fault movement in North China

Based on data of fault movement surveying, we simulate the evolution process of three dimensional stress field in North China by three dimensional finite element method. Evolutional patterns in one-year time scale from 1986 to 1997 have been illustrated and the evolution characteristics of stress field have been analyzed. In comparison with the seismic activity among that time interval in North China, we have primarily discussed the relationship between the evolution of stress field and seismic activity.

Determination of the full-field stress and displacement using photoelasticity and sampling moirémethod in a 3D-printed model

The quantitative characterization of the full-field stress and displacement is significant for analyzing the failure and instability of engineering materials.Various optical measurement techniques such as photoelasticity,moiréand digital image correlation methods have been developed to achieve this goal.However,these methods are difficult to incorporate to determine the stress and displacement fields simultaneously because the tested models must contain particles and grating for displacement measurement;however,these elements will disturb the light passing through the tested models using photoelasticity.In this study,by combining photoelasticity and the sampling moirémethod,we developed a method to determine the stress and displacement fields simultaneously in a three-dimensional(3D)-printed photoelastic model with orthogonal grating.Then,the full-field stress was determined by analyzing 10 photoelastic patterns,and the displacement fields were calculated using the sampling moirémethod.The results indicate that the developed method can simultaneously determine the stress and displacement fields.

Study on the trauma and stress level of the pelvic fracture treated by 3D printing combined with lateral rectus abdominis approach surgery

Objective: To study the trauma and stress level of the pelvic fracture treated by 3D printing combined with lateral rectus abdominis approach surgery. Methods: A total of 50 patients with pelvic fractures who were treated in the hospital between July 2015 and Jun 2017 were collected anddivided into control group (n=25) and observation group (n=25) by random number table method. Control group underwent lateral rectus abdominis approach surgery, and the observation group received 3D printingcombined with lateral rectus abdominis approach surgery. The differences in perioperative inflammatory response, coagulation function and stress degree were compared between the two groups. Results: 24 h before surgery, the differences in inflammatory response, coagulation function and stress degree were not statistically significant between the two groups. 24 h after surgery, serum IL-1, TNF-α, CRP, FIB, D-D, Cor, AngⅡ and NE levels of both groups of patients were higher than those 24h before surgery, and serum IL-1, TNF-α, CRP, FIB, D-D, Cor, AngⅡ and NE levels of observation group were lower than those of control group. Conclusion: 3D printing combined with lateral rectus abdominis approach surgery can effectively reduce the degree of surgical trauma and reduce the systemic stress response in patients with pelvic fracture.