Anisotropy Of Tensile Strength Research Articles

Fracture-initiation pressure analysis of horizontal well in anisotropic formations

Lost circulation is a classic wellbore instability problem encountered during drilling. To minimise or avoid lost circulation, preventing the initiation of fracture is the best measure. However, because rocks are naturally anisotropic, the classic fracture pressure model is not applicable for anisotropic formations. Some researchers therefore investigated the influence of transverse isotropic material parameters, but they ignored the influence of anisotropic tensile strength. The present work proposes a novel fracture-initiation pressure model of a horizontal well to investigate the influence of anisotropy on fracture-initiation pressure. Laboratory hydraulic fracturing testing verified the present method. The results indicated that anisotropic modulus and tensile strength have distinct influences on fracture-initiation pressure. Fracture-initiation pressure declines obviously under the influence of anisotropic modulus and anisotropic tensile strength, thus, the anisotropy of modulus and tensile strength cannot be ignored. The present model provides more accurate predictions of fracture-initiation pressure for horizontal wells in anisotropic formations. [Received: July 26, 2017; Accepted: December 19, 2017]

Fracture-initiation pressure analysis of horizontal well in anisotropic formations

Lost circulation is a classic wellbore instability problem encountered during drilling. To minimise or avoid lost circulation, preventing the initiation of fracture is the best measure. However, because rocks are naturally anisotropic, the classic fracture pressure model is not applicable for anisotropic formations. Some researchers therefore investigated the influence of transverse isotropic material parameters, but they ignored the influence of anisotropic tensile strength. The present work proposes a novel fracture-initiation pressure model of a horizontal well to investigate the influence of anisotropy on fracture-initiation pressure. Laboratory hydraulic fracturing testing verified the present method. The results indicated that anisotropic modulus and tensile strength have distinct influences on fracture-initiation pressure. Fracture-initiation pressure declines obviously under the influence of anisotropic modulus and anisotropic tensile strength, thus, the anisotropy of modulus and tensile strength cannot be ignored. The present model provides more accurate predictions of fracture-initiation pressure for horizontal wells in anisotropic formations. [Received: July 26, 2017; Accepted: December 19, 2017]

Effect of α texture on the tensile deformation behavior of Ti–6Al–4V alloy produced via electron beam rapid manufacturing

In the present work, the characteristics of α texture transformed from the strong <100>β fiber texture and their effect on the tensile deformation behavior of Ti–6Al–4V alloy fabricated using electron beam rapid manufacturing (EBRM) have been investigated. The results show a concentrated distribution of transformed α texture along the transverse direction (TD) while a relatively random distribution along the longitudinal direction (LD). This different orientation distribution of α phase leads to anisotropy in tensile strength. Moreover, inhomogeneous deformation is found in the longitudinal sample, which is not observed in the transverse sample. This can also be attributed to the relatively discrete α orientation distribution in the LD. The relationship between the deformation ability of each columnar prior β grain and its corresponding crystallographic orientation was investigated. Both the calculated and experimental results indicate that a relatively low deformation resistance is found when the angle of the [001]β direction of a columnar grain to the LD is relatively small and a higher deformation resistance is found when the angle is about 45°. During the loading process in the LD, deformation may concentrate in some “weak” columnar grains with relatively low deformation resistance, resulting in decreased integral ductility compared to the transverse sample.

Engineering Anisotropic Muscle Tissue using Acoustic Cell Patterning.

Tissue engineering has offered unique opportunities for disease modeling and regenerative medicine; however, the success of these strategies is dependent on faithful reproduction of native cellular organization. Here, it is reported that ultrasound standing waves can be used to organize myoblast populations in material systems for the engineering of aligned muscle tissue constructs. Patterned muscle engineered using type I collagen hydrogels exhibits significant anisotropy in tensile strength, and under mechanical constraint, produced microscale alignment on a cell and fiber level. Moreover, acoustic patterning of myoblasts in gelatin methacryloyl hydrogels significantly enhances myofibrillogenesis and promotes the formation of muscle fibers containing aligned bundles of myotubes, with a width of 120–150 µm and a spacing of 180–220 µm. The ability to remotely pattern fibers of aligned myotubes without any material cues or complex fabrication procedures represents a significant advance in the field of muscle tissue engineering. In general, these results are the first instance of engineered cell fibers formed from the differentiation of acoustically patterned cells. It is anticipated that this versatile methodology can be applied to many complex tissue morphologies, with broader relevance for spatially organized cell cultures, organoid development, and bioelectronics.

Additive Manufactured A357.0 Samples Using the Laser Powder Bed Fusion Technique: Shear and Tensile Performance

New aluminium alloys, with lower silicon content than in the first-developed formulations, have recently been introduced in the field of Additive Manufacturing and are dedicated to automotive applications. As they are relatively new, mechanical characterization under standard protocols of the automotive field are of utmost scientific as well as industrial relevance. The paper addresses the mechanical properties and microstructure of A357.0. Static tensile and shear tests of samples built by Laser Powder Bed Fusion, with different orientations in the machine work volume, have been performed. The aim was to identify possible anisotropy in the tensile and shear behaviour of this innovative alloy. Particularly for shear, the effect of adhesion between the layers onto shear strength was studied. Results analysis, by means of statistical tools, allows for the affirmation that no tensile modulus or yield strength anisotropy is observed. Instead, a small (yet statistically significant) increase in both shear- and tensile strength and a decrease in ductility are obtained as the direction of the specimens approaches the growth direction. Scanning Electron Microscope (SEM) observation of the failure mechanisms assisted in the interpretation of the results, by relating different failure modes to the relative orientation of loads versus the directions of inherent anisotropy in Laser Powder Bed Fusion processes.

Three-dimensional bonded-particle discrete element modeling of mechanical behavior of transversely isotropic rock

This paper presents the three-dimensional bonded-particle discrete element modeling of mechanical behavior of transversely isotropic rock as an extension to the previous work conducted in two dimensions (Park B, Min K-B. Bonded-particle discrete element modeling of mechanical behavior of transversely isotropic rock. Int J Rock Mech Min Sci 2015a;76:243–55). Systematic verifications of the elastic and strength anisotropy were performed by comparing the numerical results with the analytical solutions, which indicated that there was good agreement with appropriate consideration of overlapping ratio of smooth-joint contacts. Two validation cases are presented in this study. First, the three-dimensional bonded-particle DEM model successfully captured the monotonic and concave variations of elastic and strength anisotropy and Brazilian tensile strength anisotropy observed in the laboratory tests of Asan gneiss, Boryeong shale, and Yeoncheon schist. Improved match in Brazilian tensile strength was attributed to higher average coordination number in three-dimensional numerical model than that in two-dimensional model whereby leading to higher interlocking. The second validation case was conducted against CIU (isotropically consolidated undrained triaxial) and Brazilian tensile strength tests of a Tertiary shale from the Norwegian Continental Shelf (NCS). The three-dimensional bonded-particle DEM modeling of the triaxial tests with different initial effective confining pressures showed that the peak strength at failure provided by the numerical model reasonably simulated the strength variation as well as the various elastic moduli with respect to the inclination angles. Brazilian tensile strength of the numerical model was in range of the laboratory data. Furthermore, the numerical model produced similar post failure patterns as exhibited on the disk-shaped NCS shale, e.g., axial splitting and crushing failure. The results demonstrated that the three-dimensional bonded-particle DEM model with embedded smooth-joint contacts is a viable model for emulating the mechanical behavior of transversely isotropic rock with the potential of enhanced predictive capability of anisotropic numerical model.

Effect of heat treatment on the inherent anisotropy of cold sprayed copper deposits

In the present investigation, the effect of post-spray heat treatment (PSHT) on the microstructural and mechanical anisotropies of cold spray (CS) Cu deposits was investigated. The electron back-scattered diffraction and nanoindentation techniques were employed to characterize the microstructure and micromechanical properties in the cross-sectional (v-face) and parallel direction (p-face) to the surface following PSHT. Tensile tests were performed at various loading angles to identify the effect of PSHT on the in-plane tensile anisotropic behavior. It is revealed that microstructural anisotropy exists in both the as-sprayed and annealed CS deposits. And PSHT can effectively reduce the micromechanical anisotropy between the v-face and p-face. Tensile results show that the strong anisotropy of in-plane tensile strength can be moderated with PSHT. However, its effect on elongation anisotropy is quite limited, and the anisotropy is greatly increased at 700 °C. The existence of parallel multiple passes during CS remains the main factor hampering the further modification of the inherent in-plane tensile anisotropy especially elongation anisotropy.

Fracture Initiation Model of Shale Fracturing Based on Effective Stress Theory of Porous Media

Unconventional oil and gas are important resources of future energy supply, and shale gas is the focus of the development of unconventional resources. Shale is a special kind rock of porous medium, and an orderly structure of beddings aligned in the horizontal direction where causing the strong elastic anisotropy of shale is easy. A new model has been established to calculate the fracture initiation pressure with the consideration of mechanical characteristics of shale and the anisotropic tensile strength when judging rock failure. The fracture initiation model established in this paper accurately reflects the stress anisotropy and matches well with the actual situation in porous media. Through the sensitivity analysis, the results show that σv/σH, Ev/EH, υv/υH, m/s, and A/B have a certain impact on the tangential stress when the circumferential angle changes, and there is a positive relationship between the initiation pressure and the above sensitive factors except for A/B. The results can provide a valuable and effective guidance for the prediction of fracture initiation pressure and fracture propagation mechanism under special stratum conditions of shale.

OBTAINING AND PHYSICO-CHEMICAL PROPERTIES OF MATERIALS BASED ON EXPANDED VERMICULITES OF VARIOUS COMPOSITIONS

Optimal conditions for chemical and thermal treatments of natural vermiculites from various deposits were determined. The aim of obtaining expanded vermiculites with a minimum bulk density was pursued. Optimum temperature for producing thermal expanded vermiculites was 700 °C. According to scanning electron microscopy chemical expanded vermiculite has more developed surface in comparison with thermal expanded vermiculite. Chemical composition of natural vermiculites of various deposits and expanded vermiculites based on them was defined by X-ray fluorescence. It was shown that the vermiculite of the Tatar deposit contains a large amount of iron distributed over the surface. As a result, the vermiculite from Tatarstan can not be modified by hydrogen peroxide because of the active decomposition reaction of hydrogen peroxide on the surface of vermiculite. It was established that the chemical compositions of natural vermiculites as well as expanded vermiculites based on them do not differ. According to Mössbauer spectroscopy the ratio Fe(II)/Fe(III) in natural vermiculate was 1:4 and in thermal expanded vermiculite was 1:8. It should be noted that chemical expanded vermiculate contains only Fe(III). According to X-ray phase analysis the phase composition of natural vermiculite changes at 350 °C. It was defined that natural vermiculite and thermal expanded vermiculite after adsorption of moisture from the air have the same position of the X-ray maximum. When natural vermiculite was heated two areas of water loss were observed by the thermogravimetric analysis. The anisotropy of tensile strength for samples of the same density taken along and across the rolling axis of vermiculite foil obtained by pressing expanded vermiculite without a binder was described. The thermal conductivity coefficient of vermiculite foil was determined. This makes it possible to use the material as heat shield and fire protector.Forcitation:Kalashnik A.V., Ionov S.G. Obtaining and physico-chemical properties of materials based on expanded vermiculites of various compositions. Izv. Vyssh. Uchebn. Zaved. Khim. Khim. Tekhnol. 2018. V. 61. N 6. P. 76-82

Characterization of wire arc additive manufacturing 2Cr13 part: Process stability, microstructural evolution, and tensile properties

Wire arc additive manufacturing (WAAM) technology was adopted to deposite 2Cr13 thin-wall part using robotic cold metal transfer (CMT) equipment; the process stability, phase identification, microstructural evolution, and tensile properties in different layers were investigated. The results showed that a smooth surface was obtained for each layer due to the stable droplet transfer process, which ensured a stable deposition process. Positions in different layers had no significant influence on the structural aspects of the as-fabricated part according to XRD results. Elongated ferrite grains and fine-grained acicular martensite within the matrix in the top layer were recrystallized, instead of a spatial periodicity of martensite laths within equiaxed ferrite grains in the inner layers. Martensite content was increased gradually away from the base metal in the 05–25 th layers except nearly 100% martensite in the first layer. Long axis of martensite laths was randomly distributed in the X-Y plane in the both top and middle regions, while an epitaxial growth parallel to the building direction was found in the X-Z and Y-Z planes. Higher homogeneous ultimate tensile strength (UTS) and strong anisotropy in poorer ductility were obtained for the AM part when compared with the as-solutioned counterpart. Fracture behavior was transformed from ductile to mixed-mode, and finally to brittle from the 01 st layer to the 25 th layer.

Brazilian Tensile Strength of Anisotropic Rocks: Review and New Insights

Strength anisotropy is one of the most distinct features of anisotropic rocks, and it also normally reveals strong anisotropy in Brazilian test Strength (“BtS”). Theoretical research on the “BtS” of anisotropic rocks is seldom performed, and in particular some significant factors, such as the anisotropic tensile strength of anisotropic rocks, the initial Brazilian disc fracture points, and the stress distribution on the Brazilian disc, are often ignored. The aim of the present paper is to review the state of the art in the experimental studies on the “BtS” of anisotropic rocks since the pioneering work was introduced in 1964, and to propose a novel theoretical method to underpin the failure mechanisms and predict the “BtS” of anisotropic rocks under Brazilian test conditions. The experimental data of Longmaxi Shale-I and Jixi Coal were utilized to verify the proposed method. The results show the predicted “BtS” results show strong agreement with experimental data, the maximum error is only ~6.55% for Longmaxi Shale-I and ~7.50% for Jixi Coal, and the simulated failure patterns of the Longmaxi Shale-I are also consistent with the test results. For the Longmaxi Shale-I, the Brazilian disc experiences tensile failure of the intact rock when 0° ≤ βw ≤ 24°, shear failure along the weakness planes when 24° ≤ βw ≤ 76°, and tensile failure along the weakness planes when 76° ≤ βw ≤ 90°. For the Jixi Coal, the Brazilian disc experiences tensile failure when 0° ≤ βw ≤ 23° or 76° ≤ βw ≤ 90°, shear failure along the butt cleats when 23° ≤ βw ≤ 32°, and shear failure along the face cleats when 32° ≤ βw ≤ 76°. The proposed method can not only be used to predict the “BtS” and underpin the failure mechanisms of anisotropic rocks containing a single group of weakness planes, but can also be generalized for fractured rocks containing multi-groups of weakness planes.

Investigation of the anisotropy of black shale in dynamic tensile strength

Shale usually exhibits strong anisotropy due to depositional environment and pre-existed microcracks caused by geological loading for a long time. Characterizing mechanical anisotropy properties of shale, especially the tensile strength anisotropy, plays an important role in the successful exploitation of shale gas. In this work, static and dynamic tests with semi-circular bending (SCB) specimen are conducted using hydraulic servo-control machine and modified split Hopkinson pressure bar (SHPB) system, respectively. To survey the tensile strength anisotropy of shale induced by stratification, samples are cored and cut into half by diametrical cutting along different angles relative to the stratification (0°, 30°, 45°, 60°, 90°, C0°). For dynamic tests, the utilization of pulse shaping technique ensures that the samples obtain dynamic equilibrium. The tensile strength values exhibit clear anisotropy under both static and dynamic loading conditions and show typical loading rate dependence at a given angle. An anisotropic index named αk is defined to describe the tensile strength anisotropy at a certain loading rate. The outcomes illustrate that the anisotropic index decreases as the loading rate increases. In addition, failure pattern owns different characteristic under different loading angles with respect to the stratification. These phenomena may be explained by the pre-existing microcracks, and cracks interaction during dynamic loading conditions.

Anisotropy and directionality of tensile behaviours of a jointed rock mass subjected to numerical Brazilian tests

Strong anisotropy of tensile behaviros and spatial anisotropic deformation have been found in transversely isotropic rock discs. There is seldom attention paid for the insightful analysis of anisotropy and spatial variability of tensile behaviours for jointed rock masses. In the paper, an index termed as the “directionality” was proposed to quantitatively assess both the directionality and spatial variability of tensile strength of jointed rock masses. Experimental Brazilian tensile tests were carried out on stratified biotite granulite rocks. Corresponding to the configurations of laboratory tests, numerical simulations of rock specimens with different joint distributions and discrete fractures network (DFN) models were then performed using PFC2D code. The results indicated that the stratified rock discs displayed distinct anisotropy and directionality in tensile strength, manifested by the decreasing strength with inclination angle. The maximum directionality of the stratified rocks measured in laboratory was 2.40/0°, which was perpendicular to the layered discontinuities, while the tensile strength determined by DFN models showed a lower anisotropy and directionality (1.38/30°). Obvious anisotropic characteristics were observed in the fracture patterns of failure in DFN models. This paper implies the necessity of consideirng the anisotropy and directionality for the study of failure mechanisms of surrounding rocks in underground tunnels.

Anisotropic response of cold sprayed copper deposits

Cold spray (CS) is characterized as a solid-state process of high deposition efficiency for metallic coatings as well as additive manufacturing of metals. However, due to high velocity impact and extensive deformation of particles during CS, the as-received coatings or deposits may present anisotropic characteristics which could influence the performance of deposits. Hence this study aims to investigate the anisotropic behaviors of CSed copper deposits in a systematic way. The microstructure and micromechanical properties of the deposits both in the cross-section (v-face) and in the parallel plane to the surface (p-face) were characterized. Tensile tests were performed at various loading angles with respect to the nozzle moving direction in the p-face. It is revealed that there exist strong microstructural and mechanical anisotropies in CSed deposits. Different interparticle interaction results in more severe particle impact deformation in v-face than p-face, with larger elastic modulus and microhardness values. The tensile tests show an unexpected anisotropy in both ultimate tensile strength and elongation, with the highest performance occurring at the angle of 20°. The in-plane tensile anisotropy could be attributed to the parallel multiple passes. Therefore, a novel weave-spraying method was proposed, which can greatly reduce the tensile anisotropy of CSed deposits.

Assessment of the influence of hydraulic and mechanical anisotropy on the fracture initiation pressure in permeable rocks using a complex potential approach

This work aims at studying the fracture initiation pressure of a horizontal wellbore drilled in an anisotropic poroelastic medium based on an analytical model. Using the complex potential approach, the closed-form solution of stresses in the surrounding formation is deduced as a function of the orientation in respect with stratification and the pressure inside wellbore. The analytical solution is developed for the steady state flow in a permeable formation due to the difference between pressures applied at well wall and the pore pressure at the far-field. Once the stress distribution on the borehole wall is obtained, it is possible, by using a known anisotropic tensile strength criterion for the rock, to infer the explicit expression of the fracture initiation pressure as a function of different parameters, such as the anisotropic poroelastic properties, the anisotropic initial stresses, the bedding dip angle and the anisotropic tensile strength of the formation. The validation of the analytical is conducted by comparing it with the numerical results using the finite element method. Finally, through the parametric study, we highlight the influence of different factors on the fracture initiation pressure.

Microstructure and mechanical properties of selective laser melted Ti6Al4V alloy

The present work was focused on the properties of porous Ti6Al4V specimens processed by selective laser melting (SLM) and tested in tension and compression before and after heat treatment. The SLM samples were annealed at 955 °C, water quenched and aged at 600 °C with following air cooling. The values of the mechanical tests showed that the samples exhibited high mechanical properties. The anisotropy of tensile and compressive strength was observed, which was related to the occurrence of voids. The plastic properties of specimens were improved by means of the heat treatment that led to the transformation of martensitic to lamellar structure composed of α + β phases. The microstructure of SLM samples were evaluated before and after the heat treatment. The brittle nature of failures of non-heat treated samples can be explained by synergy of martensite presence, microcracks and residual stresses produced by SLM.

Brazilian Test for Tensile Failure of Anisotropic Shale under Different Strain Rates at Quasi-static Loading

Shale formations show obvious anisotropic characteristics in their mechanical properties due to pronounced bedding planes and natural fractures. This anisotropic behavior generally creates complex fracturing networks and is crucial to gas shale stimulation. Although much research has been done to study the anisotropic compression behaviors of shale with static and quasi-static strain rates, there are limited investigations addressing the anisotropic tensile behaviors of shale at quasi-static strain rate. In this work, the anisotropic tensile behaviors of Longmaxi shales were studied systematically at different strain rates from 10−5 to 10−2 s−1 by performing Brazilian splitting tests. Testing results reveal the tensile strength anisotropy, rate dependency, and the stimulated fracture pattern morphology. The results show that the orientation between the applied force and bedding direction has an obvious effect on the tensile strength and fracture pattern. The rate dependency of shale under different loading rates is different for shale samples with various orientations. It was suggested that a complex tensile fracture pattern can be easily formed when using a high loading rate. The result sheds light on how to stimulate a complex fracturing network during field hydraulic fracturing treatment.

Plastic anisotropy and deformation behavior of extruded Mg-Y sheets at elevated temperatures

The plastic anisotropy in terms of tensile mechanical property, Lankford coefficient (r), and microstructure evolution of as-extruded Mg-1Y (wt%) and Mg-5Y (wt%) sheets along the extrusion direction (ED), transverse direction (TD), and diagonal direction (DD) were investigated in detail at temperatures between 25℃ (RT) and 300℃. The sheets exhibited anisotropic deformation behavior at lower temperatures, and nearly isotropic for Mg-5Y at 300℃ in these three directions. For both sheets, the ultimate tensile strength anisotropy (UA) and elongation anisotropy (EA) was not sensitive to the temperature, while the yield strength anisotropy (YA) decreased significantly from 49.1% (Mg-1Y) and 40.2% (Mg-5Y) at RT to 7.2% and 2.7% at 300℃, respectively. The r values of Mg-1Y in all directions first increased from 0.66-1.4 (RT) to 0.81–1.98 (200℃) then decreased to 0.67–1.56 (300℃), while those of Mg-5Y decreased from 1.04-2.05 (RT) to 1.18–1.35 (300℃) with increasing temperature. Few twins were observed in Mg-5Y after tension at RT while large amounts of twins occurred in Mg-1Y. The huge reduction of twins and the weakened basal texture are believed to increase the r value from 0.66 (Mg-1Y) to 1.04 (Mg-5Y) at RT. At 300℃, dynamic recrystallized (DRX) grains appeared in Mg-1Y while only a few DRX grains showed up in the vicinity of grain boundaries in Mg-5Y, which may be closely related to grain boundary segregation of the yttrium atoms.

Fracture pressure prediction for layered formations with anisotropic rock strengths

Strength anisotropy is one of the most distinct features of layered formations, but anisotropic tensile strength has received scarce attention in the prediction of fracture pressure. Therefore, the characteristics of anisotropic tensile strength of layered rocks were investigated, main anisotropic tensile failure criteria were reviewed and compared, and the fracture pressure models were deduced for three different anisotropic failure criteria. The results demonstrate that the tensile strength of layered rocks is strongly anisotropic. The Nova–Zaninetti criterion is recommended for the characterization of the anisotropic tensile strength. The variation of the fracture pressure caused by anisotropic tensile strength is close to 10% (it even exceeds 10%), and the anisotropy has a greater influence on the fracture pressure with increasing anisotropic degree. The higher the degree of anisotropy is, the lower the fracture pressure is; the higher the horizontal stress ratio and pore pressure are, the higher the impact of anisotropy on the fracture pressure is. A low dip angle of the bedding plane is beneficial for the fracture of the vertical wellbore, and it is the worst when the minimum horizontal stress is perpendicular to the bedding planes.

Fracture pressure model for inclined wells in layered formations with anisotropic rock strengths

Fracture pressure is one of the most important foundations of drilling engineering, and the anisotropy of tensile strength is also a distinct feature of layered formations, but the anisotropy of tensile strength has seldom received attention in the analysis of fracture pressure. In the present paper, a novel fracture pressure model was proposed for inclined wells in layered formations with anisotropic rock strengths. Firstly, the characteristics of anisotropic tensile strength were investigated. Secondly, four typical anisotropic tensile criteria were collected and assessed using the maximum absolute relative error (MARE), the average absolute relative error (AARE), and the standard error (SE). Thirdly, the fracture pressure model was proposed based on the stress distribution model and anisotropic tensile criterion. Finally, the influences of anisotropy ratio, bedding planes' occurrence, well path, in-situ stress and pore pressure on fracture pressure were investigated. The results indicated that the layered rocks display the distinct anisotropy in tensile strength, and the strength increases with the loading angle. The MARE, AARE and SE of the Nova-Zaninetti criterion is the lowest for all six kinds of typical layered rocks, followed by the Lee-Pietruszczak, Hobbs-Barron, and Single Plane of Weakness criteria, and therefore the Nova-Zaninetti criterion is recommended. The higher the anisotropy ratio in tensile strength, the higher the influence on fracture pressure involved. The influence of bedding planes’ occurrence mainly depends on the initiation position of the fractures, the influence increases with increasing the horizontal stress ratio and pore pressure. Thus, the influence of anisotropy cannot be ignored in the prediction of fracture pressure.