Support design method for deep soft-rock tunnels in non-hydrostatic high in-situ stress field

Due to the long-term plate tectonic movements in southwestern China,the in-situ stress field in deep formations is complex.When passing through deep soft-rock mass under non-hydrostatic high in-situ stress field,tunnels will suffer serious asymmetric deformation.There is no available support design method for tunnels under such a situation in existing studies to clarify the support time and support stiffness.This study first analyzed the mechanical behavior of tunnels in non-hydrostatic in-situ stress field and derived the theoretical equations of the ground squeezing curve(GSC)and ground loosening curve(GLC).Then,based on the convergence confinement theory,the support design method of deep soft-rock tunnels under non-hydrostatic high in-situ stress field was established considering both squeezing and loosening pressures.In addition,this method can provide the clear support time and support stiffness of the second layer of initial support.The proposed design method was applied to the Wanhe tunnel of the China-Laos railway in China.Monitoring data indicated that the optimal support scheme had a good effect on controlling the tunnel deformation in non-hydrostatic high in-situ stress field.Field applications showed that the secondary lining could be constructed properly.

Effect of Modulus Heterogeneity on the Equilibrium Shape and Stress Field ofαPrecipitate in Ti-6Al-4V

For media with inclusions(e.g.,precipitates,voids,reinforcements,and others),the difference in lattice parameter and the elastic modulus between the matrix and inclusions cause stress concentration at the interfaces.These stress fields depend on the inclusions’size,shape,and distribution and will respond instantly to the evolving microstructure.This study develops a phase-field model concerningmodulus heterogeneity.The effect of modulus heterogeneity on the growth process and equilibrium state of theαplate in Ti-6Al-4V during precipitation is evaluated.Theαprecipitate exhibits strong anisotropy in shape upon cooling due to the interplay of the elastic strain and interfacial energy.The calculated orientation of the habit plane using the homogeneous modulus ofαphase shows the smallest deviation fromthat of the habit plane observed in the experiment,compared to the case where the homogeneous modulus ofβphase is adopted.In addition,the equilibrium volume ofαphase within the systemusing homogeneousβmodulus exhibits the largest dependency on the applied stresses.The stress fields across theα/βinterface are further calculated under the assumption of modulus heterogeneity and compared to those using homogeneous modulus of eitherαorβphase.This study provides an essential theoretical basis for developing mechanics models concerning systems with heterogeneous structures.

The 2023 Turkey earthquake doublet: Earthquake relocation, seismic tomography, and stress field inversion

On February 6,2023,two earthquakes with magnitudes of M_(W) 7.8 and M_(W) 7.5 struck southeastern Turkey,causing significant casualties and economic losses.These seismic events occurred along the East Anatolian Fault Zone,a convergent boundary between the Arabian Plate and the Anatolian Subplate.In this study,we analyze the M_(W) 7.8 and M_(W) 7.5 earthquakes by comparing their aftershock relocations,tomographic images,and stress field inversions.The earthquakes were localized in the upper crust and exhibited steep dip angles.Furthermore,the aftershocks occurred either close to the boundaries of low and high P-wave velocity anomaly zones or within the low P-wave velocity anomaly zones.The East Anatolia Fault,associated with the M_(W) 7.8 earthquake,and the SürgüFault,related to the M_(W) 7.5 earthquake,predominantly experienced shear stress.However,their western sections experienced a combination of strike-slip and tensile stresses in addition to shear stress.The ruptures of the M_(W) 7.8 and M_(W) 7.5 earthquakes appear to have bridged a seismic gap that had seen sparse seismicity over the past 200 years prior to the 2023 Turkey earthquake sequence.

Stress corrosion cracking behavior of buried oil and gas pipeline steel under the coexistence of magnetic field and sulfate-reducing bacteria

Magnetic field and microorganisms are important factors influencing the stress corrosion cracking(SCC)of buried oil and gas pipelines. Once SCC occurs in buried pipelines, it will cause serious hazards to the soil environment. The SCC behavior of X80 pipeline steel under the magnetic field and sulfate-reducing bacteria(SRB) environment was investigated by immersion tests, electrochemical tests, and slow strain rate tensile(SSRT) tests. The results showed that the corrosion and SCC sensitivity of X80 steel decreased with increasing the magnetic field strength in the sterile environment. The SCC sensitivity was higher in the biotic environment inoculated with SRB, but it also decreased with increasing magnetic field strength, which was due to the magnetic field reduces microbial activity and promotes the formation of dense film layer. This work provided theoretical guidance on the prevention of SCC in pipeline steel under magnetic field and SRB coexistence.

A novel indirect optical method for rock stress measurement using microdeformation field analysis

Stress measurement plays a crucial role in geomechanics and rock engineering,especially for the design and construction of large-scale rock projects.This paper presents a novel method,based on the traditional stress relief approach,for indirectly measuring rock stress using optical techniques.The proposed method allows for the acquisition of full-field strain evolution on the borehole’s inner wall before and after disturbance,facilitating the determination of three-dimensional(3D)stress information at multiple points within a single borehole.The study focuses on presenting the method’s theoretical framework,laboratory validation results,and equipment design conception.The theoretical framework comprises three key components:the optical imaging method of the borehole wall,the digital image correlation(DIC)method,and the stress calculation procedure.Laboratory validation tests investigate strain field distribution on the borehole wall under varying stress conditions,with stress results derived from DIC strain data.Remarkably,the optical method demonstrates better measurement accuracy during the unloading stage compared to conventional strain gauge methods.At relatively high stress levels,the optical method demonstrates a relative error of less than 7%and an absolute error within 0.5 MPa.Furthermore,a comparative analysis between the optical method and the conventional contact resistance strain gauge method highlights the optical method’s enhanced accuracy and stability,particularly during the unloading stage.The proposed optical stress measurement device represents a pioneering effort in the application of DIC technology to rock engineering,highlighting its potential to advance stress measurement techniques in the field.

Impact of well placement and flow rate on production efficiency and stress field in the fractured geothermal reservoirs

Geothermal energy has gained wide attention as a renewable alternative for mitigating greenhouse gas emissions.The advancements in enhanced geothermal system technology have enabled the exploitation of previously inaccessible geothermal resources.However,the extraction of geothermal energy from deep reservoirs poses many challenges due to high‐temperature and high‐geostress conditions.These factors can significantly impact the surrounding rock and its fracture formation.A comprehensive understanding of the thermal–hydraulic–mechanical(THM)coupling effect is crucial to the safe and efficient exploitation of geothermal resources.This study presented a THM coupling numerical model for the geothermal reservoir of the Yangbajing geothermal system.This proposed model investigated the geothermal exploitation performance and the stress distribution within the reservoir under various combinations of geothermal wells and mass flow rates.The geothermal system performance was evaluated by the criteria of outlet temperature and geothermal productivity.The results indicate that the longer distance between wells can increase the outlet temperature of production wells and improve extraction efficiency in the short term.In contrast,the shorter distance between wells can reduce the heat exchange area and thus mitigate the impact on the reservoir stress.A larger mass flow rate is conducive to the production capacity enhancement of the geothermal system and,in turn causes a wider range of stress disturbance.These findings provide valuable insights into the optimization of geothermal energy extraction while considering reservoir safety and long‐term sustainability.This study deepens the understanding of the THM coupling effects in geothermal systems and provides an efficient and environmentally friendly strategy for a geothermal energy system.

SUPPLEMENTARY STUDY ON ANISOTROPIC PLASTIC STRESS FIELDS AT A STATIONARY PLANE-STRESS CRACK-TIP

Under the hypothesis that all the perfectly plastic stress components at a orach tip are the functions of θ only, making use of yield conditions and equilibrium equations. we derive the generally analytical expressions of the perfectly plastic stress field at a crack tip. Applying these generally analytical expressions to the concrete cracks, the analytical expressions of perfectly plastic stress fields at the tips of Mode Ⅰ Mode Ⅱ, Mode Ⅲ and Mixed Mode Ⅰ-Ⅱ cracks are obtained.

HYDROSTATIC STRESS-DEPENDENT PERFECTLY-PLASTIC STRESS FIELDS AT A STATIONARY PLANE-STRESS CRACK-TIP

Under the condition that all the stress components at a crack-tip are the functions ofθonly,making use of equilibrium equations and hydrostatic stress-dependent yield condition,in this paper,we derive the generally analytical expressions of the hydrostatic stress-dependent perfectly-plastic stress fields at a stationary plane-stress crack-tip.Applying these generally analytical expressions to the concrete cracks,the analytical expressions of hydrostatic stress-dependent perfectly-plastic stress fields at the tips of mode I and mode II cracks are obtained.

ANISOTROPIC PLASTIC FIELDS AT A RAPIDLY PROPAGATING PLANE-STRESS CRACK-TIP

Under the condition that all the stress components at a crack-tip are the functions of 0 only, making use of the equations of steady-state motion. Hill anisotropic yield condition and stress-strain relations, we obtain the general solution of anisotropic plastic field at a rapidly propagating plane-stress crack-tip. Applying this general solution to four particular cases of anisotropy, the general solutions of these four particular cases are derived. Finally, we give the anisotropic plastic field at the rapidly propagating plane-stress mode I crack-tip in the case of X=Y=Z

Temperature and stress fields in electron beam welded Ti-15-3 alloy to 304 stainless steel joint with copper interlayer sheet

Electron beam welding of Ti-15-3 alloy to 304 stainless steel （STS） using a copper filler metal was carried out. The temperature fields and stress distributions in the Ti/Fe and Ti/Cu/Fe joint during the welding process were numerically simulated and experimentally measured. The results show that the rotated parabola body heat source is fit for the simulation of the electron beam welding. The temperature distribution is asymmetric along the weld center and the temperature in the titanium alloy plate is higher than that in the 304 STS plate. The thermal stress also appears to be in asymmetric distribution. The residual tensile stress mainly exists in the weld at the 304 STS side. The copper filler metal decreases the peak temperature and temperature grade in the joint as well as the residual stress. The longitudinal and lateral residual tensile strengths reduce by 66 MPa and 31 MPa, respectively. From the temperature and residual stress, it is concluded that copper is a good filler metal candidate for the electron beam welding of Ti-15-3 titanium alloy to 304 stainless steel.

Simulation Analysis of Stress Field of Walnut Shell Composite Powder in Laser Additive Manufacturing Forming

A calculation model of stress field in laser additive manufacturing of walnut shell composite powder(walnut shell/Co-PES powder)was established.The DFLUX subroutine was used to implement the moveable application of a double ellipsoid heat source by considering the mechanical properties varying with temperature.The stress field was simulated by the sequential coupling method,and the experimental results were in good accordance with the simulation results.In addition,the distribution and variation of stress and strain field were obtained in the process of laser additive manufacturing of walnut shell composite powder.The displacement of laser additive manufacturing walnut shell composite parts gradually decreased with increasing preheating temperature,decreasing laser power and increasing scanning speed.During the cooling process,the displacement of laser additive manufacturing of walnut shell composite parts gradually increased with the increasing preheating temperature,decreasing scanning speed and increasing laser power.

The Structure of Ore-controlling Strain and Stress Fields in the Shangzhuang Gold Deposit in Shandong Province,China

The Shangzhuang altered-rock type gold ore deposit is located in the middle segment of and controlled by the Wang＇ershan fault zone in the northwestern part of the Jiaodong gold province, China. The deformation evolution, the structure of strain and stress fields and its ore-controlling effect in the Shangzhuang deposit are discussed in this paper. It is revealed that the deformation evolution has mainly undergone four phases： the early ductile deformation, the second NE-striking horizontal simple shear, the third NE-striking compression-shear and the final NW-striking compression. The mineralization happened during the third stage in which the maximum principal stress gradually transited from NE to NW. The 3-D numerical simulations of the stress field show that, on the condition that the maximum principal stress is NE-striking, the fracture development in the fault zone is favored, while when the maximum principal stress is NW-striking, the fault zone is relatively extensional and it is suitable for the influx and emplacement of ore-forming fluids. The compression-shear strain field during the mineralization is characterized by the λ-type structure, the positive flower structure, etc. Orebodies are mostly equidistantly located in the dilatational spaces, which are distributed in the integral compressional circumstances. And the dilatational spaces are developed where the fault attitude changes or shear joint systems develop. In the overall compression-shear stress field, the strain field bears self-similarity at multiple scales, including the orebody, ore deposit and orefield. The selfsimilarity of the structure comprises the subequidistant distribution of fractures at the same scale and the similar shape of the fractures at various scales. Yet, due to the special geological structure, the orebodies are mostly located in the hanging wall in the Shangzhuang deposit, which is different from most deposits in the Jiaodong gold province. Analyses of the ore-controlling stress and strain fields in the deposit provide an important basis for deposit seeking.

Simulation of Paleotectonic Stress Fields and Distribution Prediction of Tectonic Fractures at the Hudi Coal Mine, Qinshui Basin

Study on tectonic fractures based on the inversion of tectonic stress fields is an effective method. In this study, a geological model was set up based on geological data from the Hudi Coal Mine, Qinshui Basin, a mechanical model was established under the condition of rock mechanics and geostress, and the finite element method was used to simulate the paleotectonic stress field. Based on the Griffith and Mohr-Coulomb criterion, the distribution of tectonic fractures in the Shanxi Formation during the Indosinian, Yanshanian, and Himalayan period can be predicted with the index of comprehensive rupture rate. The results show that the acting force of the Pacific Plate and the India Plate to the North China Plate formed the direction of principal stress is N-S, NW - SE, and NE - SW, respectively, in different periods in the study area. Changes in the direction and strength of the acting force led to the regional gradients of tectonic stress magnitude, which resulted in an asymmetrical distribution state of the stress conditions in different periods. It is suggested that the low-stress areas are mainly located in the fault zones and extend along the direction of the fault zones. Furthermore, the high-stress areas are located in the junction of fold belts and the binding site of multiple folds. The development of tectonic fractures was affected by the distribution of stress intensity and the tectonic position of folds and faults, which resulted in some developed areas with level I and II. There are obvious differences in the development of tectonic fractures in the fold and fault zones and the anticline and syncline structure at the same fold zones. The tectonic fractures of the Shanxi Formation during the Himalayan period are more developed than those during the Indosinian and Yanshanian period due to the superposition of the late tectonic movement to the early tectonic movement and the differences in the magnitude and direction of stress intensity.

Numerical simulation of spatial distributions of mining-induced stress and fracture fields for three coal mining layouts

In this study, the spatial distributions of stress and fracture fields for three typical underground coal mining layouts, Le, non-pillar mining （NM）, top-coal caving mining （TCM） and protective coal-seam mining （PCM）, are modeled using discrete element software UDEC, The numerical results show that different mining layouts can lead to different mining-induced stress fields, resulting in diverse fracture fields, For the PCM, the mining influenced area in front of the mining faces is the largest, and the stress concentration factor in front of the mining faces is the lowest, The spatial shapes of the mining-induced fracture fields under NM, TCM and PCM differ, and they are characterized by trapezoidal, triangular and tower shapes, respectively, The fractal dimensions of mining-induced fractures of the three mining layouts decrease in the order of PCM, TCM and NM, It is also shown that the PCM can result in a better gas control effect in coal mines with high outburst potential, The numerical results are expected to provide a basis for understanding of mining-induced gas seepage fields and provide a reference for high- efficiency coal mining,

Temperature and stress fields of multi-track laser cladding

Based on genetic algorithm and neural network algorithm,the finite element analyses on the temperature fields and stress fields of multi-track laser cladding were carried out by using the ANSYS software.The results show that,in the multi-track cladding process,the temperature field ellipse leans to the cladding formed,and the front cladding has preheating function on the following cladding.During cladding,the longitudinal stress is the largest,the lateral stress is the second,and the thickness direction stress is the smallest.The center of the cladding is in the tensile stress condition.The longitudinal tensile stress is higher than the lateral or thickness direction stress by several times,and the tensile stress achieves the maximum at the area of joint between the cladding and substrate.Therefore,it is inferred that transversal crack is the most main crack form in multi-track laser cladding.Moreover,the joint between cladding and substrate is the crack sensitive area,and this is consistent with the actual experiments.

Three dimensional K-Tz stress fields around the embedded center elliptical crack front in elastic plates

Through detailed three-dimensional （3D） finite element （FE） calculations, the out-of-plane constraints Tz along embedded center-elliptical cracks in mode I elastic plates are studied. The distributions of Tz are obtained near the crack front with aspect ratios （a/c） of 0.2, 0.4, 0.5, 0.6, 0.8 and 1.0. Tz decreases from an approximate value of Poisson ratio v at the crack tip to zero with increasing normalized radial distances （r/a） in the normal plane of the crack front line, and increases gradually when the elliptical parameter angle φ changes from 0° to 90°at the same r/a. With a/c rising to 1.0, Tz is getting nearly independent of φ and is only related to r/a. Based on the present FE calculations for Tz, empirical formulas for Tz are obtained to describe the 3D distribution of Tz for embedded center-elliptical cracks using the least squares method in the range of 0.2 ≤ a/c ≤ 1.0. These Tz results together with the corresponding stress intensity factor K are well suitable for the analysis of the 3D embedded centerelliptical crack from field, and a two-parameter K-Tz principle is proposed.

Petrel2ANSYS: Accessible software for simulation of crustal stress fields using constraints provided by multiple 3D models employing different types of grids

Crustal stresses play an important role in both exploration and development in the oil and gas industry.However,it is difficult to simulate crustal stress distributions accurately,because of the incompatibilities that exist among different software.Here,a series of algorithms is developed and integrated in the Petrel2ANSYS to carry out two-way conversions between the 3D attribute models that employ corner-point grids used in Petrel and the 3D finite-element grids used in ANSYS.Furthermore,a modified method of simulating stress characteristics and analyzing stress fields using the finite-element method and multiple finely resolved 3D models is proposed.Compared to the traditional finite-element simulation-based approach,which involves describing the heterogeneous within a rock body or sedimentary facies in detail and simulating the stress distribution,the single grid cell-based approach focuses on a greater degree on combining the rock mechanics described by 3D corner-point grid models with the finely resolved material characteristics of 3D finite-element models.Different models that use structured and unstructured grids are verified in Petrel2ANSYS to assess the feasibility.In addition,with minor modifications,platforms based on the present algorithms can be extended to other models to convert corner-point grids to the finite-element grids constructed by other software.

ANTIPLANE SHEAR FIELDS NEAR A CRACK-TIP IN A BRITTLE DAMAGED MATERIAL

In this paper,a simplified brittle damage model is proposed according to the Mazars-Lemaitre damage model for concrete.A closed-form solution for a mode Ⅲ crack is obtained based on the simplified model under small scale damage conditions,which allows for discontinuities of displacement-gradient and tangential stress on the damage boundary.It is pointed out that the discontinuities of field variables near the tip region exist for the brittle damaged material induced by the softening effect of the material.

Finite element analysis of temperature and stress fields during selective laser melting process of Al−Mg−Sc−Zr alloy

A 3D finite element model was established to investigate the temperature and stress fields during the selective laser melting process of Al−Mg−Sc−Zr alloy.By considering the powder−solid transformation,temperaturedependent thermal properties,latent heat of phase transformations and molten pool convection,the effects of laser power,point distance and hatch spacing on the temperature distribution,molten pool dimensions and residual stress distribution were investigated.Then,the effects of laser power,point distance and hatch spacing on the microstructure,density and hardness of the alloy were studied by the experimental method.The results show that the molten pool size gradually increases as the laser power increases and the point distance and hatch spacing decrease.The residual stress mainly concentrates in the middle of the first scanning track and the beginning and end of each scanning track.Experimental results demonstrate the accuracy of the model.The density of the samples tends to increase and then decrease with increasing laser power and decreasing point distance and hatch spacing.The optimum process parameters are laser power of 325−375 W,point distance of 80−100μm and hatch spacing of 80μm.

Effect of hydraulic fracturing induced stress field on weak surface activation during unconventional reservoir development

Unconventional reservoirs usually contain many weak surfaces such as faults,laminae and natural fractures,and effective activation and utilization of these weak surfaces in reservoirs can significantly improve the extraction effect.In hydraulic fracturing,when the artificial fracture approaches the natural fracture,the natural fracture would be influenced by both the original in-situ stress field and the hydraulic fracturing-induced stress field.In this paper,the hydraulic fracturing-induced stress field is calculated based on the relative position of hydraulic fracture and natural fracture,the original in-situ stress,the net pressure inside the hydraulic fracture and the pore pressure of the formation.Furthermore,the stability model of the natural fracture is established by combining the Mohr-Coulomb rupture criterion,and extensive parametric studies are conducted to explore the impact of each parameter on the stability of the natural fracture.The validity of the proposed model is verified by comparing with the reservoir characteristics and fracturing process of the X-well 150e155 formation in the Songliao Basin.It is found that the stress field induced by the hydraulic fracture inhibits the activation of the natural fracture after the artificial fracture crossed the natural fracture.Therefore,for similar reservoirs as X-well 150e155,it is suggested to connect natural fractures with hydraulic fractures first and then activate natural fractures which can effectively utilize the natural fractures and form a complex fracture network.