Dynamic modeling of bedding-plane slip during hydraulic fracturing

Geophysics ◽  
2019 ◽  
Vol 84 (3) ◽  
pp. KS95-KS104 ◽  
Author(s):  
Zhenhua He ◽  
Benchun Duan

Whether the tip stresses around a dynamically propagating hydraulic fracture (HF) could activate a bedding plane (BP) or not is an important question for HF propagation and microseismicity generation. BP slip has been proposed to be one main source of microseismicity during HF treatments in unconventional reservoirs. However, a BP perpendicular to a principal stress direction is unlikely to be activated in a simple geomechanical model. We have applied a dynamic finite-element geomechanics method to examine the induced dynamic shear stress and the activation of BPs that are perpendicular to the HF based on the Cotton-Valley tight-sand reservoir properties. We work in a 2D vertical-plane framework. The induced dynamic stresses around a HF tip could be significant. We explore three different scenarios for the BP activation. In the first scenario, an HF is dynamically propagating toward two symmetric BPs, but has not touched them yet. We find that only low-strength BPs can be activated in this scenario. In the second scenario, an HF dynamically propagates toward two symmetric BPs and then it crosses them by a short distance. The BPs could be more easily activated in this scenario compared with the first scenario. The slip length and maximum slip decrease with cohesion, critical slip distance, or maximum principal stress. In the third scenario, an HF dynamically propagates toward two symmetric BPs, and then fluid invasion into the BPs occurs after the HF touches them. Large shear slippage and slip length happen in this scenario because fluid invasion weakens the BPs. In all of the scenarios, different senses of shear could occur along the BPs and a rupture typically propagates bilaterally from the initiation point on the BPs.

2013 ◽  
Vol 709 ◽  
pp. 936-941
Author(s):  
Xing Hua Xiang ◽  
Zhi Yuan Li ◽  
Xiao Ting Zhang

Rainfall infiltration can induce landslides and influence engineering treatment effects. With a landslide uncounted in expressway construction in Shanxi province as an example, the bad effect of water was analyzed. Based on changes in soil strength caused by rainfall infiltration and shear experiments of undisturbed and water-saturated sliding zone soil under several conditions, the calculation parameters of soil were determined. Distribution of the maximum principal stress and shear stress inside the supported landslide before and after the rain was calculated through FEM numerical simulation and then deformation and failure mechanism of landslide was analyzed; the results reveal that for the supported landslide, the principal stress is mainly caused by gravity before and after the rain, meanwhile infiltration can induce increase in instantaneous strain and dramatic change in maximum shearing stress which is focused on the sliding surface adjacent to the bedding plane. As mentioned above, the drainage of surface water and groundwater in landslide treatment can delay landslide deformation effectively.


2016 ◽  
Vol 138 (6) ◽  
Author(s):  
M. Serrani ◽  
J. Brubert ◽  
J. Stasiak ◽  
F. De Gaetano ◽  
A. Zaffora ◽  
...  

Styrene-based block copolymers are promising materials for the development of a polymeric heart valve prosthesis (PHV), and the mechanical properties of these polymers can be tuned via the manufacturing process, orienting the cylindrical domains to achieve material anisotropy. The aim of this work is the development of a computational tool for the optimization of the material microstructure in a new PHV intended for aortic valve replacement to enhance the mechanical performance of the device. An iterative procedure was implemented to orient the cylinders along the maximum principal stress direction of the leaflet. A numerical model of the leaflet was developed, and the polymer mechanical behavior was described by a hyperelastic anisotropic constitutive law. A custom routine was implemented to align the cylinders with the maximum principal stress direction in the leaflet for each iteration. The study was focused on valve closure, since during this phase the fibrous structure of the leaflets must bear the greatest load. The optimal microstructure obtained by our procedure is characterized by mainly circumferential orientation of the cylinders within the valve leaflet. An increase in the radial strain and a decrease in the circumferential strain due to the microstructure optimization were observed. Also, a decrease in the maximum value of the strain energy density was found in the case of optimized orientation; since the strain energy density is a widely used criterion to predict elastomer's lifetime, this result suggests a possible increase of the device durability if the polymer microstructure is optimized. The present method represents a valuable tool for the design of a new anisotropic PHV, allowing the investigation of different designs, materials, and loading conditions.


1966 ◽  
Vol 3 (5) ◽  
pp. 579-596 ◽  
Author(s):  
G. K. Muecke ◽  
H. A. K. Charlesworth

Five thousand joints were examined in gently folded sandstones of the Cretaceous Cardium formation along the Bow River in the Rocky Mountain foothills of central Alberta. Twenty domains, based on homogeneity of bedding and joint orientation, were established. Joint sets from all domains fall into four classes, J1–4, all normal to bedding. J1 parallels the structural trend of the foothills, and occurs in all domains. J3 and J4 form conjugate pairs whose acute bisectrices are approximately normal to J1, and occur in western domains; the dihedral angle between conjugate pairs tends to decrease eastward. J2 is approximately normal to J1; poles to J2 sets have elongate maxima, and the sets replace conjugate J3−J4 sets in eastern domains. No joints are displaced by bedding-plane slip.J1 and J2 sets are interpreted as extension sets, and J3 and J4 sets as conjugate shear sets. Each J2 set represents conjugate shear sets with a dihedral angle too small to allow their separation. J2, J3, and J4 sets are older than J1 sets. By analogy with experimentally produced internal fractures, the easterly decrease in dihedral angle associated with the older sets resulted from an easterly decrease in the magnitude of the causative stress system, the effective minimum principal stress of which was tensile and approximately parallel to fold axes. This stress system was a residual of the orogenic system modified by postorogenic horizontal extension related to uplift. After the older joints had formed, further uplift led to the maximum principal stress becoming normal to bedding and to the development of J1 joints.


2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Guanfeng Chang ◽  
Xinzhu Hua ◽  
Jie Zhang ◽  
Peng Li

Rock excavation has experienced complex stress paths. The development of the original crack under the path of principal stress magnitude and principal stress direction is a key scientific problem that needs to be solved in rock underground engineering. The principal stress magnitude dominates the initiation and propagation of the crack and increases rock damage under the action of principal stress rotation. In this study, the theoretical calculation and numerical analysis method have been combined with the crack propagation conditions to study the stress-driven mechanism of brittle rock crack propagation under principal stress rotation. The results show that the “relative initial angle” of crack angle is being updated in time during the principal stress rotation process; once the stress is rotated, it will become the next initial crack angle; the crack propagation direction is deviated under the applied shear load, and it is always in the direction of minimum shear load, leading to a certain degree of inhibition of crack propagation depth in the initial direction. According to the results of numerical simulation, the effect of principal stress rotation caused by mining excavation is obvious and has a certain range of influence depth, the stress of surrounding rock of roadway is the highest within the depth range of 1∼2 m, and the maximum principal stress is as high as 26.89 MPa. The rotation of principal stress direction on the roadway surrounding rock surface is the strongest, which makes the surrounding rock more fragmented, and the middle principal stress and the maximum principal stress rotate about 90° counterclockwise along the Ox axis. Studying the action mechanism of principal stress rotation on fractured rock masses can provide scientific basis for geotechnical engineering design and rock mass surrounding support.


2021 ◽  
Author(s):  
Haimeng Shen ◽  
Xiaying Li ◽  
Qi Li

<p>Velocity anisotropy is particularly important in field applications of seismic monitoring or exploration [1]. We investigate the stress-dependent P-wave velocity anisotropy of sandstones with triaxial experiments and PFC based numerical simulation [2-3]. The sandstone sample was taken from the lower Shaximiao formation, Sichuan Basin, China [4]. The evolution of anisotropy is discussed with the ellipse least-squares fitting method. The results show that the P-wave velocity is affected by both the bedding plane and loading conditions. As confining pressure increases, the anisotropy magnitude decreases for each sample. The direction of anisotropy is along with the direction of the bedding plane. Under deviator loading, the anisotropy is strengthened for the sample with bedding parallel to the maximum principal stress. The direction of anisotropy reversal occurs in the sample with bedding normal to the maximum principal stress. And the anisotropy magnitude of that sample is reduced firstly and then improved. The P-wave velocity anisotropy is originated from preferred mineral orientation and aligned cracks in these samples. The stress has little effect on the mineral orientation. The evolution of P-wave velocity anisotropy is related to closing and reopening of microcracks.</p><p> </p><p>Keywords: Velocity anisotropy; Anisotropy reversal; Triaxial experiment; PFC2D; Sandstone</p><p> </p><p>[1] Li, X., Lei, X. & Li, Q. 2018. Response of Velocity Anisotropy of Shale Under Isotropic and Anisotropic Stress Fields. Rock Mechanics and Rock Engineering, 51, 695-711, http://doi.org/10.1007/s00603-017-1356-2</p><p>[2] Li, X., Lei, X. & Li, Q. 2016. Injection-induced fracturing process in a tight sandstone under different saturation conditions. Environmental Earth Sciences, 75, 1466, http://doi.org/10.1007/s12665-016-6265-2</p><p>[3] Shen, H., Li, X., Li, Q. & Wang, H. 2020. A method to model the effect of pre-existing cracks on P-wave velocity in rocks. Journal of Rock Mechanics and Geotechnical Engineering, 12, 493-506, http://doi.org/10.1016/j.jrmge.2019.10.001</p><p>[4] Li, X., Lei, X., Li, Q. & Chen, D. 2021. Influence of bedding structure on stress-induced elastic wave anisotropy in tight sandstones. Journal of Rock Mechanics and Geotechnical Engineering, -, http://doi.org/10.1016/j.jrmge.2020.06.003</p>


2013 ◽  
Vol 184 (4-5) ◽  
pp. 485-500 ◽  
Author(s):  
Hao-Tsu Chu ◽  
Jian-Cheng Lee ◽  
Françoise Bergerat ◽  
Jyr-Ching Hu ◽  
Shen-Hsiung Liang ◽  
...  

Abstract The main purpose of this study is to analyse striated micro-faults and other types of fractures (including tensile and shear joints, and veins), in order to elucidate their relationships with regional folds and thrusts and regional tectonic stress. We take the fold-thrust belt (i.e., the foothills and the Hsuehshan range) in NW Taiwan as a case study, which is a product of the Plio-Pleistocene arc-continent collision. A total of about 760 and 1700 faults and other fractures, respectively, were collected at 41 sites in the field. We have identified four sets of bed-perpendicular joints in the study area. The observation of joints and bedding at each site indicates that most of the penetrative joint sets developed in the earlier tectonic stage of the pre-folding/pre-tilting event, illustrating the fact that the intersection of joint sets lies along the line perpendicular to the bedding plane. We thus interpret these sets as tectonic fractures under deep-seated tectonic stress. We used the regional fold axes as reference to define the four fracture sets. However, we found that complexity in the study area makes this rather tentative. Principal stress axes σ1, σ2, σ3, were calculated by means of inversion of fault slip data at each site. The ratio Φ that defines the shape of stress ellipsoid is generally small, indicating that the value of the maximum principal stress axe σ1 is much larger compared to that of σ2 and σ3, which are approximately equal. The paleostress regime was characterized by a combination of thrust and strike-slip tectonic regimes. Based on their geometric relationships with tilted bedding, we found most of striated micro-faults were strongly related to the regional folding and can be categorized as early-, during, and late-folding stages. We characterized two major directions for the compressive event, oriented N110–120°E and N150–160°E respectively, which provide additional evidence to delineate the debates about paleostress changes in the Taiwan mountain building process.


2021 ◽  
Vol 11 (15) ◽  
pp. 6900
Author(s):  
Su-Kyung Sung ◽  
Sang-Won Han ◽  
Byeong-Seok Shin

Skinning, which is used in skeletal simulations to express the human body, has been weighted between bones to enable muscle-like motions. Weighting is not a form of calculating the pressure and density of muscle fibers in the human body. Therefore, it is not possible to express physical changes when external forces are applied. To express a similar behavior, an animator arbitrarily customizes the weight values. In this study, we apply the kernel and pressure-dependent density variations used in particle-based fluid simulations to skinning simulations. As a result, surface tension and elasticity between particles are applied to muscles, indicating realistic human motion. We also propose a tension yield condition that reflects Tresca’s yield condition, which can be easily approximated using the difference between the maximum and minimum values of the principal stress to simulate the tension limit of the muscle fiber. The density received by particles in the kernel is assumed to be the principal stress. The difference is calculated by approximating the moment of greatest force to the maximum principal stress and the moment of least force to the minimum principal stress. When the density of a particle increases beyond the yield condition, the object is no longer subjected to force. As a result, one can express realistic muscles.


Author(s):  
Toshiyuki Sawa ◽  
Yuya Hirayama ◽  
He Dan

The stress wave propagation and stress distribution in scarf adhesive joints have been analyzed using three-dimensional finite element method (FEM). The FEM code employed was LS-DYNA. An impact tensile loading was applied to the joint by dropping a weight. The effect of the scarf angle, Young’s modulus of the adhesive and adhesive thickness on the stress wave propagations and stress distributions at the interfaces have been examined. As the results, it was found that the point where the maximum principal stress becomes maximum changes between 52 degree and 60 degree under impact tensile loadings. The maximum value of the maximum principal stress increases as scarf angle decreases, Young’s modulus of the adhesive increases and adhesive thickness increases. In addition, Experiments to measure the strains and joint strengths were compared with the calculated results. The calculated results were in fairly good agreements with the experimental results.


2013 ◽  
Vol 404 ◽  
pp. 365-370 ◽  
Author(s):  
Qi Tao Pei ◽  
Hai Bo Li ◽  
Ya Qun Liu ◽  
Jun Gang Jiang

During the construction of hydropower station, the change of slope gradient in river valleys often takes place. In order to study influence of slope gradient change on distribution rule of geostress field, the three dimensional unloading models under different slope gradients were established by finite difference software (FLAC3D). After numerical simulation, the results were as follows: (1) The phenomenon of stress concentration at the bottom of river valleys was obvious, which appeared the typical stress fold. Both the depth of stress concentration zone and the principal stress values significantly increased with the increment of slope gradient. (2) Maximum principal stress values increased less in shallow part of upper bank slope (low stress zone) but increased more in the nearby slope foot with the increment of slope gradient, causing great difference in geostress field of bank slope. (3) There was some difference in released energy of bank slope due to slope gradient change in river valleys. In order to distinguish the difference, stress relief zone was further divided into stress stably released zone and stress instability released zone. Finally, take Ada dam area of the western route project of South-to-North Water Transfer as an example, the results by numerical simulation were reliable through comparing the distribution rule of geostress field for the dam, which could provide important reference for stability of the design and construction of steep and narrow river valleys.


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