Thermal expansivity of geikielite and ilmenite utilizing in-situ synchrotron X-ray diffraction at high temperature

The unit-cell parameters and volumes of geikielite(MgTiO_(3))and ilmenite(FeTiO_(3))were investigated at high temperatures up to 700 K and ambient pressure,using in-situ angle-dispersive synchrotron X-ray diffraction.No phase transition was detected over the experimental temperature range.Using(Berman in J Petrol29:445-522,1988.10.1093/petrology/29.2.445)equations to fit the temperature-volume data,the volumetric thermal expansion coefficients at ambient conditions(α_(V0))of MgTiO_(3) and FeTiO_(3) were obtained as follows:2.55(6)×10^(-5)K^(-1)and 2.82(10)×10^(-5)K^(-1),respectively.We infer that the larger effective ionic radius of Fe^(2+)(Ⅵ)(0.78 A)than that of Mg^(2+)(Ⅵ)(0.72?)renders FeTiO_(3)has a larger volumetric thermal expansivity than MgTiO_(3).Simultaneously,the refined axial thermal expansion coefficients under ambient conditions areα_(a0)=0.74(3)×10^(-5)K^(-1)andα_(c0)=1.08(5)×10^(-5)K^(-1)for the aaxis and c-axis of MgTiO_(3),respectively,andα_(a0)=0.95(5)×10^(-5)K^(-1)andα_(c0)=0.92(12)×10^(-5)K^(-1)for the aaxis and c-axis of FeTiO_(3),respectively.The axial thermal expansivity of MgTiO_(3) is anisotropic,but that of FeTiO_(3) is nearly isotropic.We infer that the main reason for the different axial thermal expansivity between MgTiO_(3) and FeTiO_(3) is that the thermal expansion mode of the Mg-O bond in MgTiO_(3) is different from that of the Fe-O bonds in FeTiO_(3).

Molar volume, thermal expansivity and isothermal compressibility of trans-decahydronaphthalene up to 200MPa and 446K

The molar volume isotherms of trans-decahydronaphthalene （C10H18） between 293 and 446 K and at pressures from 10 to 200 MPa have been determined. A modified Tait equation of state is used to fit each experimental molar volume isotherm with a maximum average deviation of 0.029%. The thermal expansivity （cubic expansion coefficient） α and isothermal compressibility κ were determined by fitting the slopes of the isobaric curves and isotherms, respectively. The coefficients in the equation Vm=C1＋C2T＋C3T^2-C4p-C5pT have been fitted with an average deviation of 1.03%.

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.

Semi-analytical solution for drained expansion analysis of a hollow cylinder of critical state soils

The expansion of a thick-walled hollow cylinder in soil is of non-self-similar nature that the stress/deformation paths are not the same for different soil material points.As a result,this problem cannot be solved by the common self-similar-based similarity techniques.This paper proposes a novel,exact solution for rigorous drained expansion analysis of a hollow cylinder of critical state soils.Considering stress-dependent elastic moduli of soils,new analytical stress and displacement solutions for the nonself-similar problem are developed taking the small strain assumption in the elastic zone.In the plastic zone,the cavity expansion response is formulated into a set of first-order partial differential equations(PDEs)with the combination use of Eulerian and Lagrangian descriptions,and a novel solution algorithm is developed to efficiently solve this complex boundary value problem.The solution is presented in a general form and thus can be useful for a wide range of soils.With the new solution,the non-self-similar nature induced by the finite outer boundary is clearly demonstrated and highlighted,which is found to be greatly different to the behaviour of cavity expansion in infinite soil mass.The present solution may serve as a benchmark for verifying the performance of advanced numerical techniques with critical state soil models and be used to capture the finite boundary effect for pressuremeter tests in small-sized calibration chambers.

Linear Stability Analysis on the Influences of the Spatial Variations in Thermal Conductivity and Expansivity on the Flow Patterns of Thermal Convection with Strongly Temperature-Dependent Viscosity

A series of linear stability analysis is carried out on the onset of thermal convection in the presence of spatial variations of viscosity, thermal conductivity and expansivity. We consider the temporal evolution of an infinitesimal perturbation superimposed to a static （motionless） and con- ductive state in a basally-heated planar layer. From the changes in flow patterns with increasing the amplitudes of temperature dependence of viscosity, we identified the transition into the ＂stagnant-lid＂ （ST） regime, where the convection occurs only beneath a thick and stagnant-lid of cold fluid at the top surface. Detailed analysis showed a significant increase of the aspect ratio of convection cells in ST regime induced by the spatial variations in thermal conductivity and/or expansivity： the horizon- tal length scale of ST convection can be enlarged by up to 50% with 10 times increase of thermal conductivity with depth. We further developed an analytical model of ST convection which success- fully reproduced the mechanism of increasing horizontal length scale of ST regime convection cells for given spatial variations in physical properties. Our findings may highlight the essential roles of the spatial variation of thermal conductivity on the convection patterns in the mantle.

Swelling pressure evolution characterization of strong expansive soil considering the influence of reserved expansion deformation

Numerous engineering cases have demonstrated that the expansive soil channel slope remains susceptible to damage with the implementation of a rigid or closed protective structure. It is common for the protective structure to experience bulging failure due to excessive swelling pressure. To investigate the swelling pressure properties of expansive soil, the constant volume test was employed to study the influence of water content and reserved expansion deformation on the characteristics of swelling pressure in strong expansive soils, and also to explore the evolution mechanism of the swelling pressure. The findings demonstrate that the swelling pressure-time curve can be classified into swelling pressure-time softening and swelling pressure-time stability type. The swelling pressuretime curve of the specimen with low water content is the swelling pressure-time softening type, and the softening level will be weakened with increasing reserved expansion deformation. Besides, the maximum swelling pressure Psmax decreases with increasing water content and reserved expansion deformation, especially for expansion ratio η from 24% to 37%. The reserved deformation has little effect on reducing Psmax when it is beyond 7% of the expansion rate. The specimen with low water content has a more homogeneous structure due to the significant expansion-filling effect, and the fracture and reorganization of the aggregates in the specimens with low water content cause the swelling pressure-time softening behavior. In addition, the proposed swelling pressure-time curve prediction model has a good prediction on the test results. If necessary, a deformation space of about 7% expansion rate is recommended to be reserved in the engineering to reduce the swelling pressure except for keeping a stable water content.

Significant lake expansion has accelerated permafrost degradation on the Qinghai-Tibet Plateau

In recent years, lakes on the Qinghai-Tibet Plateau have become more responsive to climate change. In September 2011, Zonag Lake in Hoh Xil experienced sudden drainage, the water eventually flowed into Yanhu Lake, which caused Yanhu Lake to continue to expand. The potential collapse of Yanhu Lake could directly threaten the operational safety of the adjacent Qinghai-Tibet Highway, Qinghai-Tibet Railway. To explore the implications of expanding lakes on the surrounding permafrost, we selected Hoh Xil Yanhu Lake on the Qinghai-Tibet Plateau to study the effect of lake expansion on permafrost degradation. The permafrost degradation in the Yanhu Lake basin from October 2017 to December 2022 was inverted using Sentinel-1 satellite image data and small baseline subset interferometry synthetic aperture radar(SBAS-In SAR) technology. Additionally, permafrost degradation from February 2007 and February 2010 was analyzed using advanced land observing satellite phased array-type L-band synthetic aperture radar(ALOS PALSAR) satellite images and differential interferometric synthetic aperture radar(D-In SAR) technique. The results showed that the permafrost around Yanhu Lake experienced accelerated degradation. Prior to the expansion of Yanhu Lake, the average annual deformation rate along the line of sight(LOS) direction was 6.7 mm/yr. After the expansion, the rate increased to 20.9 mm/yr. The integration of spatial-temporal distribution maps of surface subsidence, Wudaoliang borehole geothermal data, meteorological data, Yanhu Lake surface area changes, and water level changes supports the assertion that the intensified permafrost degradation could be attributed to lake expansion rather than the rising air temperature. Furthermore, permafrost degradation around Yanhu Lake could impact vital infrastructure such as the adjacent Qinghai-Tibet Highway and Qinghai-Tibet Railway.

An agent-based model of agricultural land expansion in the mountain forest of Timor Island,Indonesia

The Mutis-Timau Forest Complex,located on Timor Island,Indonesia,is a mountainous tropical forest area that gradually decreases due to deforestation and forest degradation.Previous modelling studies based on patterns indicate that deforestation primarily occurs at lower elevations and near the boundaries of forests and settlements,often associated with shifting cultivation by local farmers.This study adopts a process-based modelling approach,specifically the agent-based model,to simulate land changes,particularly farmers'expansion of agricultural land around the Mutis mountain forest.The underlying concept of this agent-based approach is the interaction between the human and environmental systems.Farmers,representing the human system,interact with the land,which represents the environmental system,through land use decision-making mechanisms.The research was conducted in the Community Forest of the Timor Tengah Utara District,one of the sites within the Mutis-Timau Forest Complex with the highest deforestation rate.Land use change simulations were performed using agent-based modelling from 1999 to 2030,considering the socio-economic conditions of farmers,spatial preferences,land use decisions,and natural transitions.The results revealed that the agricultural area increased by 14%under the Business as Usual scenario and 5%under the Reducing Emission from Deforestation and Forest Degradation scenario,compared to the initial agricultural area of 245 hectares.The probability of farmers deciding to extend agricultural activities was positively associated with the number of livestock maintained by farmers and the size of the village area.Conversely,the likelihood of farmers opting for agricultural extensification decreased with an increase in the area of private land and the farmer's age.These findings are crucial for the managers of the Mutis-Timau Forest Complex and other relevant stakeholders,as they aid in arranging actions to combat deforestation,designing proper forest-related policies,and providing support for initiatives such as reducing emissions from deforestation and forest degradation programs or further incentive schemes.

Linear magnetoresistance and structural distortion in layered SrCu_(4-x)P_(2) single crystals

We report a systematic study on layered metal SrCu_(4-x)P_(2) single crystals via transport, magnetization, thermodynamic measurements and structural characterization. We find that the crystals show large linear magnetoresistance without any sign of saturation with a magnetic field up to 30T. We also observe a phase transition with significant anomalies in resistivity and heat capacity at T_(p)~140 K. Thermal expansion measurement reveals a subtle lattice parameter variation near Tp, i.e.,?L_(c)/L_(c)~0.062%. The structural characterization confines that there is no structure transition below and above T_(p). All these results suggest that the nonmagnetic transition of SrCu_(4-x)P_(2) could be associated with structural distortion.

Expansion of human umbilical cord derived mesenchymal stem cells in regenerative medicine

BACKGROUND Stem cells are undifferentiated cells that possess the potential for self-renewal with the capacity to differentiate into multiple lineages.In humans,their limited numbers pose a challenge in fulfilling the necessary demands for the regeneration and repair of damaged tissues or organs.Studies suggested that mesenchymal stem cells(MSCs),necessary for repair and regeneration via transplantation,require doses ranging from 10 to 400 million cells.Furthermore,the limited expansion of MSCs restricts their therapeutic application.AIM To optimize a novel protocol to achieve qualitative and quantitative expansion of MSCs to reach the targeted number of cells for cellular transplantation and minimize the limitations in stem cell therapy protocols.METHODS Human umbilical cord(hUC)tissue derived MSCs were obtained and re-cultured.These cultured cells were subjected to the following evaluation pro-cedures:Immunophenotyping,immunocytochemical staining,trilineage differentiation,population doubling time and number,gene expression markers for proliferation,cell cycle progression,senescence-associatedβ-galactosidase assay,human telomerase reverse transcriptase(hTERT)expression,mycoplasma,cytomegalovirus and endotoxin detection.RESULTS Analysis of pluripotent gene markers Oct4,Sox2,and Nanog in recultured hUC-MSC revealed no significant differences.The immunophenotypic markers CD90,CD73,CD105,CD44,vimentin,CD29,Stro-1,and Lin28 were positively expressed by these recultured expanded MSCs,and were found negative for CD34,CD11b,CD19,CD45,and HLA-DR.The recultured hUC-MSC population continued to expand through passage 15.Proliferative gene expression of Pax6,BMP2,and TGFb1 showed no significant variation between recultured hUC-MSC groups.Nevertheless,a significant increase(P<0.001)in the mitotic phase of the cell cycle was observed in recultured hUC-MSCs.Cellular senescence markers(hTERT expression andβ-galactosidase activity)did not show any negative effect on recultured hUC-MSCs.Additionally,quality control assessments consistently confirmed the absence of mycoplasma,cytomegalovirus,and endotoxin contamination.CONCLUSION This study proposes the development of a novel protocol for efficiently expanding stem cell population.This would address the growing demand for larger stem cell doses needed for cellular transplantation and will significantly improve the feasibility of stem cell based therapies.

Deformation mechanisms and microstructural characteristics of AZ61 magnesium alloys processed by a continuous expansion extrusion approach

The unique continuous extrusion-based severe plastic deformation approaches were proposed recently to process high-performance magnesium(Mg)alloys,while the in-depth deformation mechanisms under such complicated thermomechanical conditions were not well understood.In the present work,the fundamental deformation behaviors of AZ61 Mg alloy from 25 to 400°C were firstly examined under uniaxial compression deformation.Then the deformation mechanisms and microstructural characteristics of AZ61 Mg alloy during continuous expansion extrusion forming(CEEF)were systematically investigated by microstructural observations,finite element and cellular automata simulations.The results showed that the continuous evolutions of temperature,larger strain level and complex stress state with strain rate range of 0∼5.98 s−1 during CEEF brought the distinctive dynamic recrystallization behaviors and texture development in AZ61 Mg alloy,which were different to that of uniaxial compression deformation.In details,a remarkable grain refinement was achieved via CEEF processing due to the simultaneous actions of continuous dynamic recrystallization(CDRX)and discontinuous dynamic recrystallization(DDRX).Gradually enhanced CDRX were observed from center to edge region,which had significant effects on the texture distribution and texture strength.The c-axis of most grains rotated under distinctive shear strain following parabolic metal flow,resulting in stable fiber texture.In addition,the evolution of the internal texture of the alloy led to an obvious increase in the Schmid factor for the activation of basalc+aslip system.©2022 Chongqing University.Publishing services provided by Elsevier B.V.on behalf of KeAi Communications Co.Ltd.

At-rest lateral earth pressure of compacted expansive soils:Experimental investigations and prediction approach

This paper presents experimental studies on a compacted expansive soil,from Nanyang,China for investigating the at-rest lateral earth pressureσL of expansive soils.The key studies include(i)relationships between theσL and the vertical stressσV during soaking and consolidation,(ii)the influences of initial dry densityρd0 and moisture content w 0 on the vertical and lateral swelling pressures at no swelling strain(i.e.σV0 andσL0),and(iii)evolution of theσL during five long-term wetting-drying cycles.Experimental results demonstrated that the post-soakingσL-σV relationships are piecewise linear and their slopes in the passive state(σL>σV)and active state(σL<σV)are similar to that of the consolidationσL-σV relationships in the normal-and over-consolidated states,respectively.The soakingσL-σV relationships converge to the consolidationσL-σV relationships at a thresholdσV where the interparticle swelling is restrained.TheσL0 andσV0 increase monotonically withρd0;however,they show increasing-then-decreasing trends with the w 0.The extent of compaction-induced swelling anisotropy,which is evaluated byσL0/σV0,reduces with an increase in the compaction energy and molding water content.TheσL reduces over moisture cycles and the stress relaxation in theσL during soaking is observed.An approach was developed to predict the at-rest soakingσL-σV relationships,which requires conventional consolidation and shear strength properties and one measurement of theσL-σV relationships during soaking.The proposed approach was validated using the results of three different expansive soils available in the literature.

Research on the Generation Mechanism and Suppression Method of Aerodynamic Noise in Expansion Cavity Based on Hybrid Method

The expansion chamber serves as the primary silencing structure within the exhaust pipeline.However,it can also act as a sound-emitting structure when subjected to airflow.This article presents a hybrid method for numerically simulating and analyzing the unsteady flow and aerodynamic noise in an expansion chamber under the influence of airflow.A fluid simulation model is established,utilizing the Large Eddy Simulation(LES)method to calculate the unsteady flow within the expansion chamber.The simulation results effectively capture the development and changes of the unsteady flow and vorticity inside the cavity,exhibiting a high level of consistency with experimental observations.To calculate the aerodynamic noise sources within the cavity,the flow field results are integrated using the method of integral interpolation and inserted into the acoustic grid.The acoustic analogy method is then employed to determine the aerodynamic noise sources.An acoustic simulation model is established,and the flow noise source is imported into the sound field grid to calculate the sound pressure at the far-field response point.The calculated sound pressure levels and resonance frequencies show good agreement with the experimental results.To address the issue of airflow regeneration noise within the cavity,perforated tubes are selected as a means of noise suppression.An experimental platformfor airflow regeneration noise is constructed,and experimental samples are processed to analyze and verify the noise suppression effect of perforated tube expansion cavities under different airflow velocities.The research findings indicate that the perforated tube expansion cavity can effectively suppress low-frequency aerodynamic noise within the cavity by impeding the formation of strong shear layers.Moreover,the semi-perforated tube expansion cavity demonstrates the most effective suppression of aerodynamic noise.

An Interpolation Method for Karhunen-Loève Expansion of Random Field Discretization

In the context of global mean square error concerning the number of random variables in the representation,the Karhunen–Loève(KL)expansion is the optimal series expansion method for random field discretization.The computational efficiency and accuracy of the KL expansion are contingent upon the accurate resolution of the Fredholm integral eigenvalue problem(IEVP).The paper proposes an interpolation method based on different interpolation basis functions such as moving least squares(MLS),least squares(LS),and finite element method(FEM)to solve the IEVP.Compared with the Galerkin method based on finite element or Legendre polynomials,the main advantage of the interpolation method is that,in the calculation of eigenvalues and eigenfunctions in one-dimensional random fields,the integral matrix containing covariance function only requires a single integral,which is less than a two-folded integral by the Galerkin method.The effectiveness and computational efficiency of the proposed interpolation method are verified through various one-dimensional examples.Furthermore,based on theKL expansion and polynomial chaos expansion,the stochastic analysis of two-dimensional regular and irregular domains is conducted,and the basis function of the extended finite element method(XFEM)is introduced as the interpolation basis function in two-dimensional irregular domains to solve the IEVP.

Stochastic programming based coordinated expansion planning of generation,transmission,demand side resources,and energy storage considering the DC transmission system

With the increasing penetration of wind and solar energies,the accompanying uncertainty that propagates in the system places higher requirements on the expansion planning of power systems.A source-grid-load-storage coordinated expansion planning model based on stochastic programming was proposed to suppress the impact of wind and solar energy fluctuations.Multiple types of system components,including demand response service entities,converter stations,DC transmission systems,cascade hydropower stations,and other traditional components,have been extensively modeled.Moreover,energy storage systems are considered to improve the accommodation level of renewable energy and alleviate the influence of intermittence.Demand-response service entities from the load side are used to reduce and move the demand during peak load periods.The uncertainties in wind,solar energy,and loads were simulated using stochastic programming.Finally,the effectiveness of the proposed model is verified through numerical simulations.

A study of the soil water potential threshold values to trigger irrigation of ‘Shimizu Hakuto’ peach at pivotal fruit developmental stages

Water management is an important practice that affects fruit size and quality.Effective implementation of irrigation scheduling requires knowledge of the appropriate indicators and thresholds,which are established manly based on the effects of water deficits on final fruit quality.Few studies have focused on the real-time effects of water status on fruit and shoot growth.To establish soil water potential (ψ_(soil)) thresholds to trigger irrigation of peach at pivotal fruit developmental stages,photogrammetry,^(13)C labelling,and other techniques were used in this study to investigate real-time changes in stem diameter,fruit projected area,net leaf photosynthetic rate (P_(n)),and allocation of photoassimilates to fruit under soil water potential conditions ranging from saturation to stress in 6-year-old Shimizu hakuto’peach.Stem growth,fruit growth,and P_n exhibited gradually decreasing sensitivity to water deficits during fruit developmental stages I,II,and III.Stem diameter growth was significantly inhibited whenψ_(soil)dropped to-8.5,-7.6,and-5.4 k Pa,respectively.Fruit growth rate was low,reaching zero when theψ_(soil)was-9.0 to-23.1,-14.9 to-21.4,and-16.5 to-23.3 k Pa,respectively,and P_ndecreased significantly when theψ_(soil)reached-24.2,-22.7,and-20.4 kPa,respectively.In addition,more photoassimilates were allocated to fruit under moderateψ_(soil)conditions (-10.1 to-17.0 k Pa) than under otherψ_(soil)values.Our results revealed threeψ_(soil)thresholds,-10.0,-15.0,and-15.0 kPa,suitable for triggering irrigation during stages I,II,and III,respectively.These thresholds can be helpful for controlling excessive tree vigor,maintaining rapid fruit growth and leaf photosynthesis,and promoting the allocation of more photoassimilates to fruit.

Seismic stability of expansive soil slopes reinforced by anchor cables using a modified horizontal slice method

Earthquake-induced slope failures are common occurrences in engineering practice and pre-stressed anchor cables are an effective technique in maintaining slope stability,especially in areas that are prone to earthquakes.Furthermore,the soil at typical engineering sites also exhibit unsaturated features.Explicit considerations of these factors in slope stability estimations are crucial in producing accurate results.In this study,the seismic responses of expansive soil slopes stabilized by anchor cables is studied in the realm of kinematic limit analysis.A modified horizontal slice method is proposed to semi-analytically formulate the energy balance equation.An illustrative slope is studied to demonstrate the influences of suction,seismic excitations and anchor cables on the slope stability.The results indicate that the stabilizing effect of soil suction relates strongly to the seismic excitation and presents a sine shape as the seismic wave propagates.In higher and steeper slopes,the stabilizing effect of suction is more evident.The critical slip surface tends to be much more shallow as the seismic wave approaches the peak and vice versa.

The Negative Thermal Expansion Property of NdMnO_(3) Based on Pores Effect and Phase Transition

A novel negative thermal expansion(NTE) material NdMnO_(3) was synthesized by solid-state method at 1 523 K. The crystal structure, phase transition, pores effect and negative expansion properties of NdMnO_(3) were investigated by variable temperature X-ray diffraction(XRD), scanning electron microscope(SEM) and variable temperature Raman spectra. The compound exhibits NTE properties in the orderly O' phase crystal structure. When the temperature is from 293 to 759 K, the ceramic NdMnO_(3) shows negative thermal expansion of-4.7×10^(-6)/K. As temperature increases, the ceramic NdMnO_(3) presents NTE property range from 759 to 1 007 K. The average linear expansion coefficient is-18.88×10^(-6)/K. The physical mechanism of NTE is discussed and clarified through experiments.

Can Industrial Structure Upgrading Restrain Industrial Land Expansion?Evidence from China

China has made great achievements in industrial development and is transforming into a powerful manufacturing country.Meanwhile,the industrial land scale is also expanding.However,whether industrial structure upgrading achieves the purpose of restraining industrial land expansion remains unanswered.By calculating the industrial land structure index(ILSI)and industrial land expansion scale(ILES),this study analyzed their temporal and spatial distribution characteristics at both regional and city levels from 2007to 2020 in China.Results show that industrial land expansion presents a different trend in the four regions,the ILES in the eastern region is the largest,and the speed of industrial land expansion has declined since 2013,but it has gradually increased since 2016.The ILSI of the eastern and central regions is higher than that of the western and northeastern regions.Furthermore,a spatial Durbin model(SDM)has been established to estimate the spatial effect of industrial structure upgrading on industrial land expansion from 2007 to2020.Notably,industrial structure upgrading has not slowed industrial land expansion.The eastern and western regions require a greater amount of industrial land while upgrading the industrial structure.The improvement of the infrastructure level and international trade level has promoted industrial land expansion.

Frost heaving and crack initiation characteristics of tunnel rock mass in cold regions under low-temperature degradation

Water freezing in rock fractures causes volumetric expansion and fracture development through frost heaving.This study introduces a novel analytical model to investigate how uneven freezing force and surrounding rock pressure influence fracture initiation,based on mass conservation,elasticity,and water-ice phase transition principles.A model for rock fracture initiation considering freezing temperature,uneven freezing expansion,in-situ stress,and lateral pressure was proposed based on fracture mechanics.Equations for stress intensity factors were developed and validated using the phase field method.The effects of rock elastic modulus anisotropy and critical fracture energy density on fracture initiation were also discussed.The results show that the values of KI and KII exhibit an upward trend as the freezing temperature,uneven expansion,in-situ stress,and lateral pressure increase.The uneven freezing expansion has the most significant influence on KI and KII values among these parameters.As the uneven freezing expansion coefficient increases to 0.5,the fracture initiation mode shifts from tensile fracture to shear fracture.As the lateral pressure coefficient increases to 1,the fracture initiation mode shifts from tensile fracture to shear fracture.Rock elastic modulus anisotropy causes fractures to propagate in a clockwise direction,forming a'butterfly'pattern.Critical fracture energy density an isotropy causes counterclockwise deviation in propagation direction,resulting in branching paths and an'H'-shaped pattern.