Increase Of Intermediate Principal Stress Research Articles

Strength characteristics and energy evolution of cement stone under true-triaxial loading conditions

Oil well cement is a commonly used cementing material in oil and gas extraction engineering. Due to the change of stress conditions, it is prone to microcracks or micro annular gaps, leading safety concerns. To study the strength characteristics and energy evolution of oil well cement stone under three-dimensional stress states, a series of true-triaxial compression tests were carried out. Based on the experimental results, the mechanical properties and energy evolution mechanisms during the true-triaxial compression process of cement stone under different stress states were explored. The research results indicate that there is an intermediate principal stress effect on the true-triaxial compressive strength of cement stone specimens. When the minimum principal stress remains constant, the strength of cement stone first increases and then decreases with the increase of intermediate principal stress. When the minimum principal stress is 5 MPa, the specimen exhibits brittle failure, with ε1 at peak stress approximately 0.015. As the minimum principal stress increases to 20 MPa, the specimen gradually transits to plastic failure, with ε1 at failure exceeding 0.04. The type of failure is determined by the energy ratio at the time of failure; when there is more elastic energy, it results in brittle failure, otherwise it leads to ductile failure. Due to the high porosity of cement stone samples, most of the input energy is converted into dissipated energy. At minimum principal stresses of 5 MPa, 10 MPa and 20 MPa, the ratio of peak dissipated energy to total input energy fluctuates around 0.55, 0.73 and 0.85, respectively. There is a strong linear relationship between the peak elastic energy, peak dissipated energy, and total input energy, with fitting correlation coefficients of 0.847 and 0.996, indicating that the cement stone sample also follows the linear energy storage law. A strength criterion for cement stone was established based on the modified Lade criterion, which is more suitable for describing the strength of high porosity materials compared to traditional strength criteria. Finally, based on the interaction mechanism between energy accumulation and energy dissipation, a nonlinear model of energy evolution in cement stone was established. The results of the theoretical model are in good agreement with the experimental data.

A constitutive model for caprock siltstone subject to three-dimensional compression with emphasis on plastic potential and hardening law

Investigation of the strength, deformation and constitutive model of rocks under true three-dimensional stress is of much significance to scientifically and accurately predict the integrity of underground gas storage caprock. In general the intermediate principal stress and the minimum principal stress to which the caprock is subjected are not equal, and there is uncertainty in the in-situ stress test. In this study, the siltstone is taken from the caprock of the Hutubi gas storage in Xinjiang, with a buried depth of 3600 m. A series of true triaxial compression tests on siltstones were carried out using a true triaxial testing system for rocks, and the strength and deformation characteristics of siltstones under different intermediate principal stress conditions were studied. The elastoplastic constitutive model of rocks has been established: in the plastic part, the Mogi-Coulomb yield criterion has been modified so as to obtain the triple-mean-normal-stress yield function and triple-mean-normal-stress potential function suitable for rocks under the true three-dimensional stress state. The hardening law has been determined by fitting the relationship between the plastic deviatoric shear strain and the deviatoric stress in the true triaxial compression test. The constitutive model and the test data of siltstones have been verified by fitting. Finally, the influence of true triaxial stress on the permeability and breakthrough pressure of caprock siltstones has been discussed. The result indicates that with the increase of intermediate principal stress within a certain range, the peak strength of siltstones will also increase, and deformation in the direction of the intermediate principal stress will be restrained. Compared with the potential functions in other constitutive models, the triple-mean-normal-stress potential function proposed in this paper can accurately describe the plastic flow direction of siltstones under the true three-dimensional stress state. And the hardening law truly reflects the plastic deformation of siltstone specimens under different stress states during the loading process. The calculation result of the constitutive model is in good agreement with the test result. Under the true three-dimensional stress, the permeability of siltstones shows anisotropy. With the increase of the intermediate principal stress, the minimum value of siltstone permeability decreased by 8%, and the maximum value of breakthrough pressure increased by 4.3%.

Dynamic strength and failure modes of sandstone under biaxial compression

Geomaterials are increasingly being subjected to the quasi-static confinements and dynamic loadings, and thus it is critical to characterise dynamic behaviour under the coupled static-dynamic loading conditions. In this study, a series of dynamic biaxial compression tests was performed on cubic specimens of sandstone by using a triaxial Hopkinson bar system, high-speed three-dimensional digital image correlation (3D-DIC) and synchrotron-based micro-computed-tomography (μCT). This testing apparatus allows for determining dynamic stress-strain behaviour of the specimen under biaxial static pre-stress (σ1, σ2) conditions and different impact velocities (i.e. 15, 20 and 26 m/s), corresponding to average axial strain rates of 80, 200 and 250 s−1. Both σ1 and σ2 applied in the tests varied from 0 to 40 MPa with an interval of 10 MPa. Dynamic strength and fracture behaviours of biaxially confined rocks were systematically characterised from macroscopic to microscopic, surface to interior and 2D to 3D by using the 3D-DIC and synchrotron-based μCT techniques. Experimental results show that, under the same biaxial pre-stresses, dynamic biaxial compressive strength of sandstone increases with strain rate, i.e. rate dependence. At a given impact velocity, dynamic biaxial compressive strength decreases with increasing pre-stress values (σ1) along the impact direction, while it enhances with the increase of intermediate principal stress (σ2) in the lateral direction, which is so-called confinement dependence. Besides, two types of dynamic stress-strain curves of rocks are observed under biaxial compression, which is associated with post-peak fracturing characteristics. High-speed 3D-DIC shows that rock fragments are ejected out of the free surface (σ3 = 0) with certain velocities including the translation and rotation, which resembles the rock ejection observed during drilling and blasting and even strong rockbursts. μCT reveals that the double “V” shapes of shear fractured zones are symmetrically generated under biaxial compression. The crack surface area, volume and dynamic fracture energy are also estimated under different confinements to characterise the damage of impacted rock.

Effect of the intermediate principal stress on hydraulic fracturing in granite: an experimental study

The fracturing behavior of hard rock under fluid pressure is affected by maximum, minimum, and intermediate principal stress. To investigate the effect of the intermediate principal stress on the hydraulic fracturing behavior, including the fracturing pressure, fracture pattern, fluid pressure evolution, etc., a series hydraulic fracturing experiments of granite under true triaxial compression conditions was conducted. Constant minor and major principal stresses (10 and 30 MPa, respectively) and variational intermediate principal stresses (10, 15, 20, and 25 MPa) were considered. Acoustic emission was used to monitor the hydraulic fracturing process. The effect of different intermediate principal stresses, i.e., various horizontal principal stresses, on the fluid fracturing pressure and failure pattern was studied. With higher intermediate principal stress, the hydraulic pressure fluctuates in the hydraulic fracturing process, whereas at lower intermediate principal stress, the pressure fluctuation phase becomes shorter. The higher intermediate principal stress makes the fracture plane simpler, straighter, and more planar. When the intermediate principal stress equals to the minimum principal stress, the fracture plane tends to be non-planar. In this case, the hydraulic fracture is mainly influenced by heterogeneity of the rocks. With the increase of intermediate principal stress, the formation breakdown pressure of granite decreases, which is different from the effect of minor principal stress. A modified criterion is proposed to reflect the influence of intermediate principal stress on the formation breakdown pressure.

Case Study of Modified H–B Strength Criterion in Discrimination of Surrounding Rock Loose Circle

Intermediate principal stress is a significant factor when calculate to determine the surrounding rock loose circles. Based on it, this paper is trying to modify the Hoek–Brown strength criterion, and put forwards a theoretical formula of the loose circle radius. The theoretical formula is applied to Shimen Tunnel, and a comparative analysis between theoretical calculations and field test results is conducted. Here are the results as follows: 1) With an increase of intermediate principal stress, the strength of the rock mass increases and the surrounding rock becomes more difficult to break. Consequently, loose circle thickness is gradually reduced and forms a significant negative linear relationship with the Lode parameter. 2) The results indicate that with a decrease of surrounding rock level in a three-lane hard rock tunnel, the radius of the loose circle increases continuously. 3) The results of the field acoustic wave test show that the theoretical calculation values are consistent with the field measurement results. According to above analysis, the deduced formula is feasible.

Experimental study on propagation behavior of three-dimensional cracks influenced by intermediate principal stress

Many laboratory experiments on crack propagation under uniaxial loading and biaxial loading have been conducted in the past using transparent materials such as resin, polymethyl methacrylate (PMMA), etc. However, propagation behaviors of three-dimensional (3D) cracks in rock or rock-like materials under tri-axial loading are often considerably different. In this study, a series of true tri-axial loading tests on the rock-like material with two semi-ellipse pre-existing cracks were performed in laboratory to investigate the acoustic emission (AE) characteristics and propagation characteristics of 3D crack groups influenced by intermediate principal stress. Compared with previous experiments under uniaxial loading and biaxial loading, the tests under true tri-axial loading showed that shear cracks, anti-wing cracks and secondary cracks were the main failure mechanisms, and the initiation and propagation of tensile cracks were limited. Shear cracks propagated in the direction parallel to pre-existing crack plane. With the increase of intermediate principal stress, the critical stress of crack initiation increased gradually, and secondary shear cracks may no longer coalesce in the rock bridge. Crack aperture decreased with the increase of intermediate principal stress, and the failure is dominated by shear fracturing. There are two stages of fracture development: stable propagation stage and unstable failure stage. The AE events occurred in a zone parallel to pre-existing crack plane, and the AE zone increased gradually with the increase of intermediate principal stress, eventually forming obvious shear rupture planes. This shows that shear cracks initiated and propagated in the pre-existing crack direction, forming a shear rupture plane inside the specimens. The paths of fracturing inside the specimens were observed using the Computerized Tomography (CT) scanning and reconstruction.

A Mogi-Type True Triaxial Testing Apparatus for Rocks With Two Moveable Frames in Horizontal Layout for Providing Orthogonal Loads

The Mogi-type true triaxial apparatus (TTA) for rocks provides numerous advantages in terms of complexity, loading capacity, permeability measurement, and cost. However, the spring support design limits the improvements to the loading capacity and stiffness of the vertical frame, which are essential in acquiring the complete stress-strain behavior of relatively large specimens. In this paper, a new TTA achieved by modifying the original Mogi-type design with two moveable frames in a horizontal layout is developed. In addition to the design of stiffer frames with low moving resistance, such a modification provides convenience for experimental operation. Moreover, a positioning device built in the triaxial vessel enables the accurate placing of the specimen. Technical details, including off-center loading, end friction effect, and strain measurement are carefully examined. Calibration and repeatability tests show that the apparatus is stable and reliable. The apparatus is used to conduct tests to examine the influence of intermediate principal stress on the mechanical behaviors of marble. The results demonstrate that, in addition to strength, some other characteristics, including brittleness, fracture angle, volumetric modulus, and stress at the onset of dilatancy of marble also increase initially, but subsequently decrease with an increase of intermediate principal stress. The measurement of the permeability of mudstone during compression reveals that the increase in permeability is closely related to the dilatancy of the mudstone.

Strength model and mesoscopic mechanism of intermediate principal stress effect on rock strength

Intermediate principal stress effect on rock strength, strain, energy dissipation and micro crack distribution are studied by using particle discrete element numerical simulation software PFC3D. Numerical simulation reproduces the typical phenomenon that rock strength has an initial increase and a subsequent decrease with the increase of intermediate principal stress. On micro level, the increase of intermediate principal stress makes the micro cracks distribution in horizontal plane from symmetrical to asymmetrical. When intermediate principal stress ratio b is large than 0.5, micro cracks have a substantial increase at yield stage and energy dissipated by frictional sliding also has a substantial increase. Intermediate principal stress restrains the expansion of micro cracks normal to intermediate principal stress direction (or with component in this direction), which makes rock strength increases. On the other side, intermediate principal stress promotes the expansion of micro cracks normal to minimum principal stress direction (or with component in this direction), which makes rock strength decreases. The restraint and promotion of micro cracks in different directions lead to the intermediate principal stress effect. Based on Weibull theory, a failure probability model is developed to describe the effect of the intermediate principal stress on rock strength. Using shear stress to express the computed strength of each micro-unit, a strength criterion is proposed to quantitatively reflect the intermediate principal stress effect on rock strength. New criterion can be regarded as a modified Mohr-Coulomb criterion with a uniformity coefficient and it becomes Mohr-Coulomb criterion when materials are absolutely homogeneous. New criterion matches previously published experimental results and numerical simulation results better than common strength criterion.

The influence of the intermediate principal stress on rock failure behaviour: A numerical study

The influence of the intermediate principal stress on rock strength has been studied comprehensively by previous researchers. However, the reason why rock strength firstly increases and subsequently decreases with the increase of intermediate principal stress is still unclear. In this paper, the mechanism of the intermediate principal stress effect on rock failure behaviour is revealed through a numerical method using the EPCA3D system (Elasto-Plastic Cellular Automaton). In this study, both homogeneous and heterogeneous rocks are considered. The heterogeneity of a rock specimen is modelled by introducing Weibull's statistical distribution. Two criteria, i.e. the Drucker–Prager and Mohr–Coulomb models, are used to determine whether a meso-scopic element in the rock specimen is in a failure state or not during the polyaxial stress loading process. The EPCA3D simulation reproduces the typical phenomenon of the intermediate principal stress effect that occurs in some rock experiments. By studying the EPCA3D simulated acoustic emission and complete stress–strain curves illustrating failure initiation, propagation and coalescence in the failure process of rocks, the essence of the intermediate principal stress effect is tracked. It is concluded that the heterogeneous stress distribution induced by the natural heterogeneity of rocks and the effect of the loading platen are two of the reasons producing the intermediate stress effect. Studies indicate that a moderate intermediate principal stress delays the onset of local failure, which in turn leads to an increase in the rock strength. However, once the intermediate principal stress reaches a certain value, local failure will be formed through the application of the intermediate principal stress. It is the number of failed elements in the pre-peak region that determines whether the rock strength decreases or not. The extent of rock strength reduction when the intermediate principal stress reaches a certain value is lessened with the increase in the minimum principal stress.