Maximum Principle Stress Research Articles

Geological conditions of coalbed methane accumulation in the Hancheng area, southeastern Ordos Basin, China: Implications for coalbed methane high-yield potential

The Hancheng area is a hot spot for coalbed methane exploration and exploitation in China. Structure is a key factor affecting coalbed methane accumulation and production in the Hancheng area. For a better understanding of the coalbed methane accumulation conditions and high-yield potential, this study investigates the structural patterns and evolution, the hydrogeological conditions, and the geothermal field in the coal-bearing strata in the Hancheng area. Then, the spatial distribution of the coalbed methane content and the tectonic deformation of the coal seam are evaluated. Finally, the critical depth for coalbed methane enrichment and a high-yield potential are revealed, and the favorable areas for coalbed methane development are predicted. The following conclusions are obtained: (1) Under the Yanshanian SE–NW trending maximum principle stress, the Hancheng overturned anticline was formed and subsequently subjected to uplift and erosion along its axis, which led to the NW limb of the anticline forming the current uniclinal structure of the Hancheng area; (2) Four degrees of tectonic deformation in the coal seam are identified based on structural curvature analysis. The moderately deformed area shallower than 800 m would benefit coalbed methane production with higher permeability. Most of the locations of coal and gas outburst events that occur during coal mining were distributed along the highly and very highly deformed areas; (3) The gas content gradually increases along the NW-trending inclination of the coal seam. 400 m and 800 m are discriminated as the critical depth levels for controlling coalbed methane accumulation and a high yield. Secondary biogenic methane was generated in the shallow formations; and (4) The Hancheng area is divided into four ranks for determining coalbed methane development potential. From high to low, they are ranked A, B-1, B-2, and C. Most of the high-yield wells are located in the areas ranked A and B-1.

Improved stress concentration factors for circular shafts for uniaxial and combined loading

Abstract Stress concentration factors (SCF) related to specific geometries, loadings and stress quantities can be calculated efficiently using approximate equations. Those relations are typically based on metamodeling via the results of linear elastic analyses. Existing equations for the, technically speaking, very important circular shafts with shoulder fillets or U-shaped notches under bending, torsion or tension/compression can be appropriated, for example, from the DIN 743-2 : 2012-12. Using these relations requires compliance with underlying constraints and assumptions. For example, equations from that code do not provide SCFs larger than 6 and refer only to the maximum principle stress. Furthermore, DIN 743-2 : 2012-12 does not provide SCFs for combined loading, i. e. simultaneous bending, torsion and tensile/compressive loading. This paper presents new and improved equations based on sampling computational finite element simulations and subsequent regression analyses. Multiple improvements could be achieved: The six equations for circular shafts with shoulder fillets or U-shaped grooves derived from DIN 743-2 : 2012-12 were simplified down to two equations. Despite this simplification, the new equations have been generalized for combined loading and include SCFs larger than 6 as well. Choosing between various equations for each type of loading is no longer necessary. Only one equation for each of the two basic geometries is needed. Moreover, two further equations which refer to von Mises equivalent stress have been added. Although the new equations are easier to handle and allow for an estimation of stress concentration factors larger than 6, the accuracy of the new equations is higher than the accuracy of DIN 743-2 : 2012–12 when compared to SCFs derived from finite element simulation as reference values.

Effects of mechanical vibration on miniscrew implants and bone: Fem analysis

The aim of this FEM study was to assess the effect of mechanical vibration force on miniscrews and stress distribution in cortical and trabecular bone around miniscrews. A 3D model was created using a CBCT image of a patient. Three different analyses were performed on a single model. Material properties, boundary conditions and the quality of applied forces (direction and magnitude) were defined. 150gf, 150gf and 30Hz (0.2N), 150gf and 111Hz (0.06N) were applied to miniscrew from distal to mesial and from sulcus to alveolar crest direction like a power arm application. The first moment effect of force and vibration were evaluated by using Algor Fempro FEM analysis program. Von Mises and principal stress distribution on miniscrews and bone layers were evaluated by different force and vibration applications. It was seen that Von Mises stress distribution on miniscrew was located on the neck region and the highest stress levels were observed in the 1st analysis (27,0159N (mm2)), which was only force application. The loading of the cortical bone in the proximity of the miniscrew was clearly greater with only force application rather than force and vibration application together. Maximum and minimum principle stress values gradually decreased while vibration value increased. It was concluded that mechanical vibration force might reduce the peri-implant loading of the bone and stress levels on the miniscrews.

Interaction between two neighboring tunnel using PFC2D

In this paper, the interaction between two neighboring tunnel has been investigated using PFC2D. For this purpose, firstly calibration of PFC was performed using Brazilian experimental test. Secondly, various configuration of two neighboring tunnel was prepared and tested by biaxial test. The maximum and minimum principle stresses were 0.2 and 30 MPa respectively. The modeling results show that in most cases, the tensile cracks are dominant mode of cracks that occurred in the model. With increasing the diameter of internal circle, number of cracks decreases in rock pillar also number of total cracks decreases in the model. The rock pillar was heavily broken when its width was too small. In fixed quarter size of tunnel, the crack initiation stress decreases with increasing the central tunnel diameter. In fixed central tunnel size, the crack initiation stress decreases with increasing the quarter size of tunnel.

Finite Element Modeling of Shrink-Fit Design for Improvement of Die-Service Life in Hot Forging Process of a Bevel Gear

In a hot forging process, die-service life is one of the most important factors affecting the production cost. This paper illustrates about a shrink-fit design used to improve the die-service life in the hot forging process of a bevel gear. In this process, there are two-operation steps of forming, preform and finishing steps. The major problem was that the forging die in finishing step prematurely fractured at small fillet radius due to mechanical fatigue. In order to eliminate the problem, the forging die was redesigned to shrink fit into the optimum shrink ring. Furthermore, Finite Element Modeling (FEM), which was set up and verified by the existing process, was used as a tool to study the effect of a shrink-fit ratio and diameter of a shrink ring on the die stress. The FEM results showed that both parameters influent on the die stress directly and the maximum principle stress of the new design at the fracture area significantly reduces because of pre-compression stress from the shrink ring. Finally, the FEM result was proved by experiment in the actual process and then it was found that the die-service life is improved approximately 17 times when comparing to the initial design.

Patient-Specific Static Structural Analysis of Femur Bone of different lengths

Background:The femur bone is an essential part of human activity, providing stability and support in carrying out our day to day activities. The inter-human anatomical variation and load bearing ability of humans of different heights will provide the necessary understanding of their functional ability.Objective:In this study, femur bone of two humans of different lengths (tall femur and short femur) were subjected to static structural loading conditions to evaluate their load-bearing abilities using Finite Element Analysis.Methods:The 3D models of femur bones were developed using MIMICS from the CT scans which were then subjected to static structural analysis by varying the load from 1000N to 8000N. The von Mises stress and deformation were captured to compare the performance of each of the femur bones.Results:The tall femur resulted in reduced Von-Mises stress and total deformation when compared to the short femur. However, the maximum principle stresses showed an increase with an increase in the bone length. In both the femurs, the maximum stresses were observed in the medullary region.Conclusion:When the applied load exceeds 10 times the body weight of the person, the tall femur model exceeded 134 MPa stress value. The short femur model failed at 9 times the body weight, indicating that the tall femur had higher load-bearing abilities.

A novel fixture for mixed mode I/II/III fracture testing of brittle materials

AbstractA novel test‐loading device was suggested in order to study the fracture behavior of brittle materials under mixed mode I/II/III loading conditions. A version of the compact tension shear specimen was used as the test configuration. Using a three‐dimensional finite element analysis, the influence of mode mixity on the stress intensity factors, the T‐stress, and 3‐D plastic zone around the crack tip was investigated. In addition, an experimental study was performed on an epoxy polymer using the proposed setup. Finally, the fracture toughness of pure epoxy was measured under several loading conditions. The numerical and experimental results manifested that the proposed setup is able to determine a full range of mixed mode I/II/III fracture properties. At the end, the fracture envelope obtained using the practical study was compared with various three‐dimensional fracture criteria. A negligible discrepancy was concluded between the practical data and the theoretical data estimated by the maximum mean principle stress criterion.

Optimised Analysis, Design, and Fabrication of Trans-Tibial Prosthetic Sockets

In this study, two laminated composite materials were used to manufacture residual-limb prosthetic sockets using the vacuum moulding method. Acrylic was used as a matrix material and reinforced with two types of fibres, perlon and carbon. The mechanical properties were calculated using tensile and bending tests, and socket failure characteristics at room temperature were determined by using a fatigue test. F-socket apparatus was used to measure the interface pressure between the residual limb and socket in two subjects with unilateral trans-tibial amputations using patellar tendon bearing prosthetics (PTB). The ANSYS program was used to calculate the deformation, maximum principle stress, and safety factors. The results showed that laminations laid-up from eight layers of perlon plus four layers of carbon gave optimum mechanical properties. Comparing this lamination with other laminations of six layers of perlon plus two layers of carbon, in spite the minimal increase in perlon and carbon layers (from eight layers to twelve layers), the ultimate stress increased by 12.46%. The Young’s modulus of a lamination with six layers of perlon and four layers of carbon was 3.66 GPa, higher than other laminations investigated. A high Young’s Modulus will result in a total contact socket that produces the best comfort level for patients. The maximum principle stress and total deformation increased with an increase in the length of stump: The maximum principle stress of a long socket increased by 0.3% of medium stress, while the total deformation of the medium socket was lower than that of the long socket.

Experimental and numerical study on rockburst triggered by tangential weak cyclic dynamic disturbance under true triaxial conditions

The excavation and/or dynamic disturbance induced critically stressed (stress close to the strength of the rocks) rocks near the excavation boundary of deep openings are highly unstable, and they may fail violently in the form of rockburst triggered by weak dynamic disturbance in the maximum principle stress direction (tangential). In this paper, true triaxial coupled static and dynamic loading tests and a 3D discrete element method (DEM) simulation were carried out to investigate the characteristics and the mechanisms of rockburst triggered by tangential weak dynamic disturbance. Test results indicate that, compared to self-initiated rockburst under corresponding test conditions, the weak dynamically-triggered rockburst has much longer development duration, much lower kinetic energy, and the failure of the specimen is dominated by tensile splitting. The DEM simulation results show that, the occurrence of tensile cracks generally precedes that of shear cracks, and shear cracks are mainly result from the slipping displacement dipping in the free face direction after the tensile cracks accumulated to a certain extent. The tangential weak dynamic disturbance significantly increases the cracking and damage degree, and the dissipated energy of the rocks. The released kinetic energy accounts for a very small proportion (0.27%) of the dissipated energy due to the dynamic disturbance. In conclusion, the mechanism of rockburst triggered by tangential weak dynamic disturbance can be summarized as the “activation” (activating cracks), “magnification” (driving dynamic propagation of cracks), and the “inducing energy release” (inducing release of the stored strain energy of the rocks) effects of the weak dynamic disturbance.

Numerical Investigation to Influence of Perforation Angle on Hydraulic Fracturing Process

Considering the heterogeneous characteristics of rock in a meso-scale, a flow–stress–damage coupling model was created based on the finite element method firstly. Then the hydraulic fracturing process of the heterogeneity rockmass under different perforation angles were investigated by the RFPA2D-flow software. The numerical simulation results show that the maximum principle stress controls the fracture propagation direction no matter how perforation angle changes. With the increase of the perforation angle, a turning fracture becomes more obvious and the turning distance bigger. The best perforation angle area is from 0° to 30°. Above results are of some significance to hydraulic fracturing tests and engineering practice.

Fracture Interaction during Temporarily Plugging Staged Fracturing

Temporarily plugging staged fracturing technique has been successfully applied in unconventional reservoirs.Using XFEM-based CZM (cohesive zone model based on the extended finite element method), a 2D capturing stress interference and coupling fluid –solid model was established to investigate the process of the technique. The key points are as follows: (1) The diameter of the whole model was 1000m. The enriched zone is a square with the length of 200 m. The whole model has 162299 nodes and 161901 elements. The quality of meshes meets the requirement of XFEM convergence. (2) plugging efficiency of diverting agents is simulated by changing injection rate. (3) the boundary condition of propped fractures is maintained by surface pressure, change of which simulates filtrate loss rate; (4) heterogeneity along horizontal well is simulated by setting various properties surrounding the subsequent fractures. The simulation results reveal that: (1) in-situ stress contrast affects the extent of the stress alteration zone, while in-situ stress magnitude impacts fracture length and width; (2) proper plugging efficiency will help to achieve even treated effect along the horizontal well; (3) with the augment of formation permeability, the extents of stress reversal and reorientation become small, thus subsequent fractures tend to propagate along the direction of maximum principle stress. (4) Young modulus and tensile strength have a great influence on propagation path, propagation rates, fracture length and width.

Bond behaviour of CFRP/steel strap joints exposed to overloading fatigue and wetting/drying cycles

Carbon fibre reinforced polymer (CFRP) has been widely used in strengthening of deficient steel structures in subtropical regions following their application in concrete structure rehabilitation. However, after the strengthening, both hygrothermal conditions and overloading fatigue can further promote the mechanical degradation of the strengthened structures, and the tendency remains unclear. Therefore, to predict the service life of steel structures after CFRP strengthening, the bond behaviour of CFRP-strengthened steel plates that are affected by overloading fatigue damage and/or wetting/drying cycles (WDCs) with 3.5 wt% NaCl solution was investigated in this study. In total, 12 CFRP/steel strap joints were tested in six cases, where six specimens experienced overloading damage by axial fatigue tensile loading. Then, both specimens with and without predamage were exposed to WDCs (0, 90 and 180). After WDC exposure, the tensile tests were conducted. The load-strain curves, tensile-bearing capacities, failure modes and interfacial stress distributions were obtained. As observed, with increasing WDCs, the strength of the overloading fatigue-damaged specimens continuously decreased. However, the strength of the specimens without overloading damage decreased during the first 90 WDCs and then slightly increased during the next 90 WDCs. In addition, a simple expression of the maximum interfacial principle stress at the gap location of the CFRP/steel strap joints was developed. A model based on the maximum stress was proposed to evaluate the long-term bond strength degradation of CFRP-strengthened steel structures under overloading fatigue and/or WDC conditions, and good consistency was reached with the test results.

Effects of the Notch Angle, Notch Length and Injection Rate on Hydraulic Fracturing under True Triaxial Stress: An Experimental Study

This study focused on the effects of the notch angle, notch length, and injection rate on hydraulic fracturing. True triaxial hydraulic fracturing experiments were conducted with 300 × 300 × 300 mm cement mortar blocks. The test results showed that the fracture initiation pressure decreased as the notch length and injection rate increased, whereas, the fracture initiation pressure decreased as the notch angle decreased. Furthermore, the direction of the hydraulic fracture was always along the direction of the maximum principle stress.

Fracture mechanism due to blast-imposed loading under high static stress conditions

Using a dynamic-static experimental loading device and a digital laser dynamic caustic system, the effect rules for blasting induced main cracks responding to an initial static stress field are studied. The propagation rules of a 45° oblique crack subjected to different initial static stress fields and of cracks with different angles and initial static stress fields are also studied. The experiment results show that: (1) Under an initial static stress load, different stress concentrations are generated around boreholes, and the maximum tensile stresses are generated in the direction of the maximum principle stress of the borehole. The combined action of the initial static stress field and dynamic blasting stress field causes the longest crack to propagate in the direction of initial static stress preferentially. The initial static stress field changes the distribution characteristics of the blasting-induced cracks. (2) The level of the stress concentration increases, the propagation direction of the main crack is deflected along the direction of the principle stress, the propagation time of the main crack becomes shorter, the mode II fractures of specimens are more severe, and the maximum deflection angle of the main crack increases as initial static stress load increases. (3) As the angle between crack and initial static stress load direction increases, the propagation times of the main cracks decrease, and the occurrence of an obvious shear fracture occurs in the main crack more quickly. Also, with the increased angle between crack and initial static stress load direction, the peak values of the reflecting angles gradually increase, and the displacement along the pre-existing crack direction decreases showing the crack path becomes more flexural.

Numerical simulation on near-wellbore temporary plugging and diverting during refracturing using XFEM-Based CZM

Refracturing can effectively enhance hydrocarbon production from hydraulically fractured wells. Using self-degradable diverting agents, people can temporarily plug previously generated fractures, and generate a new pair of fractures perpendicular to the direction of the original maximum principle stress (i.e., near-wellbore temporary plugging and diverting technique). To simulate the plugging and diverting process, a numerical model is established using the cohesive zone model (CZM) based on the extended finite element method (XFEM). After this model is verified by the published laboratory testing results, it is applied to understand the influences of stress contrast, formation permeability, rock tensile strength, Young's modulus and injection rate, so as to improve the applicability of temporary plugging and diverting technique under various reservoir conditions. Furthermore, “deflection angle” is proposed to quantitatively analyze the simulation results. This new concept enables the comparison among various cases without the restrictions of fracture length and simulation time. Simulation results indicate that: (1) with increases of stress contrast, rock permeability and Young's modulus, the diverting fractures reorient to the direction of the preferred fracture plane (PFP) more rapidly, which reduces the effectiveness of this technique; (2) propping previously-formed fractures can create higher defection angles of the diverting fractures, which enhances the effectiveness of this technique; (3) enhancing the injection rate can also enhance the effectiveness of this technique, yet there is one optimal injection rate for a given reservoirs. This study provides a systematic guideline for optimizing the temporary plugging and diverting technique under different reservoir conditions.

Permeability Anisotropy of Columnar Jointed Rock Masses

This paper investigated the anisotropic permeability of columnar jointed rock masses at Baihetan hydropower station in Southwest China. Discrete element analysis is conducted to evaluate the hydraulic Representative Elemental Volume (REV) size of jointed rock masses. It is found to be 5m×5m and it is seven times of the column length. Research shows that permeability tensor of the jointed rocks exists. The maximum principle permeability is 3.47 × 10−14 m2 and the minimum principle permeability is 1.39 × 10−14 m2. The direction of maximum principle permeability is 72 degrees anticlockwise from the positive x-axis direction, which is along the same direction of the column length. A continuum hydro-mechanical coupling analysis is carried out on water infill of a tailrace tunnel in columnar basalt. An equivalent anisotropic mechanical model is applied in the numerical simulation. Anisotropic deformation and anisotropic permeability characteristics are investigated under the condition that the angle between maximum principle stress axis and maximum principle permeability axis is 72 degrees. Results show that anisotropic seepage field has an effort on anisotropic deformation field.

Coupling stress caused by thermal and slicing force in KDP crystal slicing with fixed abrasive wire saw

KDP (KH2PO4) crystal is an important functional crystalline material that can be used in the area of laser frequency conversion. As the first process of machining, the slicing process of the KDP crystal is of vital importance to the yield rate of wafers. While the KDP crystal often cracks in the slicing process by the traditional method of band saw because of its properties of high brittleness, low strength, and high thermal sensitivity, the cracks may lead to waste of the whole KDP crystal and should be avoided. Fixed abrasive wire saw slicing is considered a preferred method for KDP crystal slicing due to its advantage of low sling stress. In this paper, a finite element model in fixed abrasive wire saw slicing of the KDP crystal is established with respect to distributed slicing force and thermal stress. Distribution of slicing force and heat around the kerf area is deduced and applied to the finite element model. Based on the model, temperature field and stress field of the KDP crystal in the slicing process is obtained. The maximum principle stress caused by slicing force, thermal stress, and coupling of the slicing force and thermal stress is obtained. The maximum principle stress of different slicing parameters is analyzed; function equation between the maximum principle stress and slicing parameter is obtained by the least squares method. The critical slicing parameter at which cracks would not occur in the slicing is obtained. The simulation results in this paper are useful to avoid cracking in KDP crystal slicing with fixed abrasive wire saw.

Experimental study on crack propagation control and mechanism analysis of directional hydraulic fracturing

Hydraulic fracturing is mainly used for increasing large-scale coal seam permeability in coal mines to exploit coalbed methane and prevent coal and gas outbursts. However, conventional hydraulic fracturing cracks tend to propagate along the direction of maximum principal stress, which is inconsistent with reinforcement direction engineering and/or project area needs and makes identification of the orientation or specified location of increased coal seam permeability difficult. To address these problems, we have conducted physical similarity simulation experiments and numerical analysis of directional hydraulic fracturing (DHF) and obtained the crack propagation law of DHF technology. By analyzing the variation law of the maximum principal stress inside the rock mass, the crack propagation control mechanism of DHF technique is revealed. The influence of horizontal stress difference coefficients and angles between the hydraulic slotting direction and maximum principal stress direction (i.e., the hydraulic slotting deviation angle) on the crack propagation deflection is investigated. The results show that the DHF technique can achieve crack-oriented propagation along the desired direction. The maximum principal stress range in the rock mass is redistributed after slotting. A directional fracturing induction region is formed between the slots. In addition, DHF hydraulic pressure curves show a secondary fracturing stage when cracks connect the hydraulic fracturing and hydraulic slotting boreholes. Initiation pressures and values of maximum principle stress in the directional fracturing zone increase with increasing horizontal stress difference coefficients and slotting deviation angles. However, increasing the horizontal stress difference coefficient does not significantly influence the directional fracturing zone range. The results provide a reliable basis for subsequent theoretical research and engineering applications.

Cretaceous stress field evolution and origin of the Jiaolai Basin, Eastern North China

The Jiaolai Basin, to the east of the Tan-Lu Fault Zone (TLFZ), is a Cretaceous NE-trending basin in eastern North China and has a multi-episodic evolution. Different from other contemporary NW-trending en-echelon graben systems west to the TLFZ, the origin of the Jiaolai Basin (three episodes: K1l, 135–120 Ma; K2q, 120–105 Ma; K2w, 88–65 Ma) cannot be simply explained by the sinistral displacement of the TLFZ at the beginning of the Early Cretaceous (around ca. 135 Ma). The purpose of this paper is to investigate the critical factors (e.g., bounding faults, tectonic setting, stress field) driving the development of the Jiaolai Basin and constraint its evolution. Three episodes of two-dimensional finite element models were generated in order to determine the roles of the boundary conditions and to reveal the tectonic development of the basin. When compared to the calculated maximum horizontal compressive stress (σHmax) trajectories and the observed data, along with a comparison between the Von Mises Stress (uVon) and the depocenters of the basin, the calculated results can be well proved by the geological evidence both in stress field evolution and in the basin patterns. Our analysis show that the three episodes of the maximum principle stress trajectories changed from NE-SW (earlier Early Cretaceous, K1l) NNE-SSW (later Early Cretaceous, K1q) then E-W (Late Cretaceous, K2w). Moreover, the results show a good consistency between the uVonand the depocenters in the basin through geological cross-sections. Via models we suggest that the origin and evolution of the Jiaolai Basin were controlled by three episodes of tectonic events, (i) the reactivated bounding faults and the post-orogenic extension of the Sulu Orogen during the earlier Early Cretaceous, (ii) the lithospheric delamination of the thickened lithosphere during the later Early Cretaceous, and (iii) the likely far-field effects produced by the collision between the Kohistan-Drags arc complex and Asia during the Late Cretaceous. The Jiaolai Basin evolved from extension to pull-apart experiencing volcanic activity during the three episodes of the Cretaceous.

Research of Rock Burst Risk Induced by Mining and Field Case in Anticlinal Control Area

Stress concentration caused by tectonic stress and mining disturbance in coal mines induces a unique type of rock burst. No. 3201 working face controlled by an anticline structure in the Shandong mining area is used as the research background. The formation mechanism for anticlines is analyzed. Theoretical research shows that the bigger the tectonic couple is, the smaller the foundation stiffness, and the greater the bending degree and elastic strain energy of the coal will be. The distribution characteristics of abutment pressure and maximum principle stress in anticlinal control areas are analyzed using UDEC numerical software. The results show that rock bursts result from interactions between abutment pressure and residual tectonic stress. The “connection‐overlay‐separation” phenomenon of abutment pressure presents with working face advancement. Furthermore, the energy criterion for rock burst initiation is established based on the energy principle. Residual energy “E0 − EC” and rock burst danger characteristics during mining are discussed. Based on the simulation results, microseismic monitoring data for No. 3201 working face are analyzed, and the law of microseismic energy is consistent with the variation law for the residual energy “E0 − EC” at the peak of the simulated abutment pressure. The microseismic energy and frequency are higher during mining, increasing the risk of rock burst events. It can provide scientific basis for prevention and control of rock burst.