Maximum Principal Compressive Stress Research Articles

Obstructed swelling and fracture of hydrogels.

Obstructions influence the growth and expansion of bodies in a wide range of settings-but isolating and understanding their impact can be difficult in complex environments. Here, we study obstructed growth/expansion in a model system accessible to experiments, simulations, and theory: hydrogels swelling around fixed cylindrical obstacles with varying geometries. When the obstacles are large and widely-spaced, hydrogels swell around them and remain intact. In contrast, our experiments reveal that when the obstacles are narrow and closely-spaced, hydrogels fracture as they swell. We use finite element simulations to map the magnitude and spatial distribution of stresses that build up during swelling at equilibrium in a 2D model, providing a route toward predicting when this phenomenon of self-fracturing is likely to arise. Applying lessons from indentation theory, poroelasticity, and nonlinear continuum mechanics, we also develop a theoretical framework for understanding how the maximum principal tensile and compressive stresses that develop during swelling are controlled by obstacle geometry and material parameters. These results thus help to shed light on the mechanical principles underlying growth/expansion in environments with obstructions.

Evolution of tensile fractures in feldspar porphyroclast and its implication in paleostress estimation

Fractures are ubiquitous brittle features of the upper crust. Syntectonic granites are often replete with fractures of various attitudes, cross-cutting each other, which develop under the prevalent states of stress. In this article, we study the origin and mechanism of formation of tensile fractures restricted within rectangular alkali feldspar porphyroclasts found in Closepet granite (Dharwar Craton, India), and venture on the possibility of using them as potential paleostress marker. The study is conducted using finite-element-method (FEM) to assess the distribution of induced stresses within the porphyroclasts considering the geometry and varying mechanical properties of the porphyroclast and the embedding matrix. We infer that fractures in the porphyroclast develop due to amplification and concentration of far-field stresses within it. The direction of maximum principal compressive stress as indicated by the fractured porphyroclasts lies in close proximity to the paleostress direction derived from fault-slip analysis of adjacent bodies such as Chitradurga Schist Belt and Koppal syenite (Dharwar craton). Therefore, we advocate that fractured feldspar porphyroclasts are a reliable indicator of paleostress orientations.

The effect of temperature on the mechanical behavior of Berea sandstone under confining pressure: experiments

For the first time, axial and circumferential (diametral) strains are measured directly on Berea sandstone cylindrical samples at different high temperatures as a function of confining pressure. The maximum compressive principal stress was in the direction perpendicular to the bedding plane. Tri-axial compression tests have been conducted under confining pressures ranging from atmospheric pressure to 12,000 psi “82.73 MPa” (gage), and the temperature was varied from room temperature (RT) to 250°F (121.11 °C). In all the experiments, specimens are dry, and no pore pressure is applied. Uniaxial axial force (100 lbs/min or 444.82 N/min) and strains in the three directions (varepsilon1, varepsilon2, varepsilon3) is directly measured from the strain gages mounted on the specimen; hence the study reflects the behavior of the Berea sandstone up to the initiation of the failure only. The experimental observations involving yield, failure, transition from brittle to ductile behavior, and their dependence on temperature and confining pressure are presented. Parameters like ductility and dilatancy (reflecting volumetric behavior before failure) and their variation with temperature and confining pressure are given. The initial yield and failure of Berea sandstone are presented in terms of the generalized von-Mises criteria, i.e., variation of octahedral shear stress () with the mean stress. The loads at yield and failure are found to decrease with increasing temperature and augment with increasing confining pressure. The ductility and dilatancy reduction are computed using measured strains with increasing temperature. With an increase in temperature, the volume decreases first, partly due to the initial closure of micro cracks and voids, then increases due to generation of additional microcracks and voids (damage). There is less volume decrease in the uniaxial test response at higher temperature as compared to the corresponding ambient temperature response. A monotonic increase in the octahedral shear stress at yield and failure is observed with increasing confining pressure.

Research on Mechanical Characteristics and Load-bearing Behavior of Nodes of Steel Fiber Concrete Arch Bridges

Steel fiber reinforced concrete (SFRC) is a new type of composite material formed by dispersing discontinuous short steel fibers in a uniform and random direction throughout the concrete, which has excellent properties of tensile, shear and high toughness, can effectively improve the load-bearing capacity of arch bridges. In this paper, the mechanics of SFRP in the nodal structure of an arch bridge is initially explored by means of indoor model tests and numerical simulation studies. The results show that the maximum principal tensile stress occurs at the intersection of arch rib, arch foot and tie beam, and the maximum principal compressive stress occurs at the connection between arch rib and arch seat, which should be considered in the design. In this paper, we hope to understand the characteristics of the force and bearing capacity of this type of structure to provide a reference for similar projects.

Numerical simulation study on the spontaneous rupture process and its influencing factors of the 2001 MS 8.1 Kunlun earthquake in China

On November 14, 2001, the MS 8.1 Kunlun earthquake occurred in the west of Kunlun Mountain pass in the East Kunlun fault zone of the Qinghai-Tibet Plateau, China. The field investigation and the results of kinematic inversion indicate that it is a strike-slip earthquake with a complex rupture process. The study of the spontaneous rupture process of this earthquake and its influencing factors is of great significance for understanding the occurrence mechanism of continental large earthquakes. First, based on the results of geological survey and kinematic inversion, a three-dimensional non-planar fault model is established. Then, using the curved-grid finite difference method (CG-FDM), the dynamic rupture process of the 2001 MS 8.1 Kunlun earthquake is numerically reproduced by adjusting the parameters for numerical simulation experiments. On this basis, the influence of background stress field, fault geometry and friction coefficient on the surface slip distribution, seismic moment rate function and rupture velocity are discussed respectively. The results show that the important reasons for the super-long rupture scale and super-shear rupture velocity of this earthquake may be the clockwise rotation of the maximum horizontal principal compressive stress along the NNE ∼ NE direction and the low friction coefficient distribution on the whole fault surface. The difference between the dynamic and static friction coefficients along the fault strike may be non-uniform, and it may be larger on the main fault than that on the secondary fault. This will result in a higher level of stress drop on the main fault, leading to the occurrence of super-shear rupture and the slip distribution with the Kusai Lake as the macroseismic epicenter. The large local geometric variation along the strike of the main fault may also have some influence on the distribution of co-seismic slip and the location of the super-shear rupture. In addition, the numerical simulation results in this paper confirm the conclusion that the East Kunlun fault zone has low friction coefficient.

Seismic anisotropy in the upper crust around the north segment of Xiaojiang faults in the SE margin of Tibetan Plateau

The Xiaojiang faults located in the SE margin of the Tibetan Plateau is a fault system of left-lateral strike-slip, striking NS, between the 2nd-order Sichuan-Yunnan block and the 1st-order South China block. The Xiaojiang faults and the surrounding areas are characterized by strong tectonic movements and intense seismic activities. Using seismic data from January 2013 to November 2020 recorded at the stations of the temporary QiaoJia seismic Array (QJ Array), deployed by the Institute of Geophysics, China Earthquake Administration, this study investigates the upper crustal anisotropy by the shear-wave splitting analysis on small local earthquakes, discusses the deformation patterns in the upper crust in the north segment of the Xiaojiang faults, evaluates the stress distribution in the study area, and analyzes its relationship with the regional tectonic structure. Adopting the data processing technique of shear-wave splitting, a total of 875 effective records were obtained at 50 stations. The mean direction of polarizations of fast shear-wave (PFS) is 162° ± 44° in the study areaand the mean normalized time-delay is 4.96 ± 2.38 ms/km. Based on the spatial distribution of the PFS and the regional geologic structure, the study area is divided into two zones: the zone N and the zone S. The PFS in the zone N is scattered, but the dominant PFS direction is in NNW, which is consistent with the direction of the regional maximum principal compressive stress. In the zone N, there are a few smaller local areas (i.e., subzones A, B, C, and D) in which the orientations of the PFS are quite different from the surrounding area. In the zone S, the dominant directions at most stations are in nearly NS, consistent with the strike of the Xiaojiang fault. It reveals the detailed spatial distribution of seismic anisotropy in the upper crust, as well as in situ principal compressive stress, indicating the influence of the regional stress, the complex tectonic environment, and maybe also the impact of the South China block. It also reveals that there also might be an upper-crust scale of tectonic line at near 26°20′N under Xiaojiang faults, which coincides with the north-south tectonic boundary in the lithospheric anisotropy.

Effect of tension and compression on dynamic alveolar histomorphometry

Here, we tested the hypothesis that tensile and compressive stresses generated in the alveolar bone proper regulate site-specific cellular and functional changes in osteoclasts and osteoblasts. Thirty-two 13-week-old male mice were randomly divided into four groups: two experimental groups with vertical loading obliquely from the palatal side to the buccal side of the maxillary molar (0.9 N) 30 min per day for 8 or 15 days and unloaded controls (n = 8). Calcein and alizarin were administered 8 and 2 days before euthanization, respectively, to detect the time of bone formation. Undecalcified sections parallel to the occlusal plane were prepared on the palatal root and the surrounding alveolar bone in the middle of the root length. The alveolar perimeter was divided into 12 equal regions for site analysis, and the bone histomorphometric parameters were obtained for each region. Data from in vivo microfocus computed tomography were used to construct animal-specific finite element models. 2D stress distribution images were overlain on histology images obtained from the same location. Significant differences in the total perimeter between groups and between loading and unloading in each region were statistically analyzed (α = 0.05). Osteoclast counts and the alizarin label ratio were significantly higher in the loaded group than in the unloaded group in regions where the maximum von Mises and principal tensile stresses were the highest along the perimeter. The label ratio of calcein was significantly lower in the 8-day loaded group than in the unloaded group, indicating that the calcein-labeled surface was resorbed by osteoclasts that appeared during the loading period. The effect of loading was mitigated by an increase in the maximum principal compressive stress. We conclude that bone resorption and bone formation are functions of site-specific tension and compression in the alveolar bone proper, confirming our hypothesis. This finding is critical for the advancement of diagnosis and treatment planning in clinical dentistry.

A control method for hydraulic fracturing of the hard roof with long and short boreholes

During the mining of the working face, the hard roof can lead to a series of problems, such as air leakage in goafs, gas emission and concentration, casualties, and damages to buildings and ecological environment. The treatment of the hard roof has always been a difficult problem in major coal-producing countries. Although many scholars have conducted some theoretical research and field practice in this field in recent years, the aforementioned safety problems still occur frequently. In order to understand the mechanism of crack propagation caused by hydraulic fracturing of the roof, based on the theoretical analysis of linear elastic fracture mechanics and coal rock mechanics, the shear fracture criterion was determined for the formation of horizontal fractures in the natural cracks. The anisotropy of the crack tip, the adhesion forces in the coal and rock fracture surface and the conditions for hydraulic-induced crack propagation were also considered. The formation of cracks involves a vertical main crack and multiple extended-airfoil branch cracks which interconnect transversely and longitudinally. Under the effect of hydrodynamic water wetting and hydraulic fracturing, the stress of coal and mass changed. Meanwhile, the mechanical parameeters, such as compression, tensile strength and elasticity modulus and etc., were weakened, thus achieving the goal of structural transformation and slight weakening of coal and rock mass. According to the bidirectional stress of coal and rock mass, the maximum principal compressive stress of crack opening was calculated, and the propagation mechanism of hydraulic fracturing cracks in the hard roof was obtained. The hydraulic fracturing technology for controlling the hard roof was illustrated and has been applied in No. 2 Well of Sihe Coal Mine for many years. The research results could provide reference for the control of the hard roof in other similar mines.

Modeling Sequences of Earthquakes and Aseismic Slip (SEAS) in Elasto‐Plastic Fault Zones With a Hybrid Finite Element Spectral Boundary Integral Scheme

AbstractWe present a coupled finite element spectral boundary integral framework for modeling sequences of earthquakes and aseismic slip on a 2‐D planar rate‐and‐state fault with off‐fault visco‐plastic response in the plane strain approximation. The model resolves both slow aseismic deformation and inertia effects during rapid slip. As an application, we perform two sets of simulations with different choices of cohesion to explore the co‐evolution of fault slip, bulk plasticity and local stress fields. The first set implements a relatively large value of the cohesion parameter, which results in limiting inelastic strain accumulation to dynamic rupture phases. The second set implements a smaller cohesion, allowing for plastic strain to accumulate in both seismic and aseismic phases. For the first model, our results indicate that the extent and distribution of plastic strain depend on the angle of maximum compressive principal stress. At larger angles, inelastic strain accumulates on the extensional side of a dynamically propagating rupture. At smaller angles, the extent of plasticity is limited to the compressional side of the domain. At smaller cohesion values, off‐fault plasticity may occur during aseismic slip, which alters the nucleation characteristics and earthquake sequence pattern. Furthermore, our results at lower cohesion values indicate that plastic strain accumulation may occur in both the extensional and compressional sides of the off‐fault bulk even at higher angles of maximum compression. This produces damage patterns that deviate from the traditional off‐fault fan‐like distribution observed in dynamic rupture simulations and emphasizes the significance of long‐term deformation in interpreting observations.

Fragility Curves for Historical Structures with Degradation Factors Obtained from 3D Photogrammetry

The influence of the effects of the degradation of materials on the seismic fragility of Cultural Heritage buildings in Granada (Spain) is investigated. The degradation of the material, which mainly happens at the lower levels of the façades, is obtained by using 3D photogrammetry data. Fragility curves for three cultural heritage constructions in Granada are calculated by using FE nonlinear dynamic analyses for both non-deteriorated and deteriorated geometries. The Finite Elements (FE) models, based on the macro-modelling technique, are subjected to ground motions for the city of Granada, which were selected by considering Probabilistic Seismic Hazard Analysis (PSHA) methodology with their probability of occurrence. The response of each model is analyzed for different seismic Intensity Measure (IM) levels, which, in this study, correspond to average pseudo-acceleration. The procedure is applied to three monuments in Granada that were built with two different constructions materials: calcarenite and rammed earth. The damage mechanisms considered are roof displacement or maximum compressive principal stress, depending on each case. The results show that the restoration works that have been carried out has prevented structural failures in the rammed earth construction studied, and that, during future seismic events, special attention must be paid to the level of compressive strengh reached in the Santa Pudia calcarenite used at the San Jerónimo monastery.

The propagation paths of fluid-driven fractures in layered and faulted rocks

AbstractFractures that form when fluid pressure ruptures the rock are referred to as fluid-driven fractures or hydrofractures. These include most dykes, inclined sheets and sills, but also many mineral veins and joints, as well as human-made hydraulic fractures. While considerable field and theoretical work has focused on the geometry and arrest of hydrofractures, how they select their propagation paths, particularly in layered and faulted rocks, has received less attention. Here I propose that of all the possible paths that a given hydrofracture may follow, it selects the path of least (minimum) action as determined by Hamilton’s principle. This means that the selected path is that along which the energy transformed (released) multiplied by the time taken for the propagation is a minimum. Hydrofractures advance their tips/fronts in steps, with a time lag between the fracture front and the fluid front. In the present framework, each step is then controlled by Hamilton’s principle. The results suggest that when the hosting rock body is regarded as homogeneous, isotropic and non-fractured, hydrofracture paths are everywhere perpendicular to the trajectories of the minimum compressive (maximum tensile) principal stress σ3 and follow the trajectories of the maximum principal compressive stress σ1. When applied to layered and faulted rock body, the results indicate that hydrofracture paths may follow existing faults for a while, depending primarily on (1) the dip of the fault (steep faults are the most likely to be used by vertically propagating hydrofractures), and (2) the tensile strength across the fault compared with the tensile strength of the host rock along a path following the direction of σ1. The results suggest that hydrofractures may use faults as parts of their paths primarily if the fault is steeply dipping and with close to zero tensile strength.

Damage of reservoir rock induced by CO2 injection

The study of reservoir rock damage induced by gas injection is of great significance to the design of reservoir stimulation and the improvement of oil and gas recovery. Based on an example horizontal well in the Hudson Oilfield of the Tarim Basin and considering the multi-physics coupling effects among high-pressure fluid, rock deformation, and damage propagation during CO 2 injection, a three-dimensional finite element model for CO 2 injection in deep reservoir considering seepage-stress-damage coupling was developed. The evolution of reservoir rock damage under different CO 2 injection conditions was systematically investigated. The results show that tensile damage and shear damage are concentrated in the vertical direction and the horizontal maximum compressive principal stress direction, respectively, and the tensile damage is the main damage mode. At higher CO 2 injection rate and pressure, the damaged areas near the wellbore are mainly distributed in the direction of the maximum compressive principal stress, and the development of the damaged area near the wellbore will be inhibited by the formation and evolution of far-field damage. CO 2 injection aggravates the extension of tensile damage, but inhibits the initiation of shear damage, and eventually leads to the gradual transition from shear damage to tensile damage. Under the same injection conditions, CO 2 injection has superior performance in creating rock damage compared with the injection of nitrogen and water. The results in this study provide guidance for enhanced oil recovery in deep oil and gas reservoirs with CO 2 injection.

Anisotropic change in apparent resistivity before earthquakes of M S ⩾ 7.0 in China mainland

Since 1967 when DC apparent resistivity observation was carried out in China, there have been 16 times or groups of earthquake of M S ≥ 7.0 occurred within about 400 km from the monitoring stations. The apparent resistivity showed medium-short term continuous changes before 13 times or groups of these earthquakes. The medium-term changes usually lasted for several months to about two years. Apparent resistivity of monitoring arrays placed in different directions at the same station showed anisotropic change related to the maximum principal compressive stress orientation (i.e. P axis). The larger the angle between a monitoring array and the P axis is, the greater the magnitude of change in apparent resistivity is. According to the results from rock physics experiments, resistivity model of cracked rock-soil medium, and fault virtual dislocation model, the changes in apparent resistivity before earthquakes may be related to the seismogenic process through a way of resistivity change caused by medium deformation.

Characteristics of Local Geomagnetic Field Variations and the Tectonic Stress Field Adjacent to the 21 May 2021, Ms 6.4 Yangbi Earthquake, Yunnan, China

The tectonic processes leading up to an earthquake and the occurrence of the earthquake itself will cause local changes in the geophysical field (geomagnetic field, stress field, etc.). In this paper, the variation characteristics of the tectonic stress field (TSF) and local geomagnetic field (LGF) before and after the Yangbi Ms 6.4 earthquake are studied. The regional stress tensor damping inversion method was used to invert the TSF using focal mechanism solutions (FMSs). The change characteristics of the TSF before and after the earthquake were analyzed. An annual variation model of the LGF was constructed, and the variation of the horizontal vector was analyzed. The azimuth and plunge of the maximum principal compressive stress axis of the TSF in the epicentral region before and after the earthquake were −4.4° and 2.7°, 172.7° and 6.6°, respectively. The variations in the declination, inclination and total intensity of the epicenter one year before and one month after the earthquake were −0.20′ (0.07′), 0.29′ (−0.12′), and −1.7 nT (−1.9 nT), respectively. The epicenter is located at the boundary of the “weak variation region” of the horizontal vector. This research is of great significance concerning the TSF background and incubation mechanism of earthquakes.

Fault Geometry and Mechanism of the Mw 5.7 Nakchu Earthquake in Tibet Inferred from InSAR Observations and Stress Measurements

Different types of focal mechanism solutions for the 19 March 2021 Mw 5.7 Nakchu earthquake, Tibet, limit our understanding of this earthquake’s seismogenic mechanism and geodynamic process. In this study, the coseismic deformation field was determined and the geometric parameters of the seismogenic fault were inverted via Interferometric Synthetic Aperture Radar (InSAR) processing of Sentinel-1 data. The inversion results show that the focal mechanism solutions of the Nakchu earthquake are 237°/69°/−70° (strike/dip/rake), indicating that the seismogenic fault is a NEE-trending, NW-dipping fault dominated by the normal faulting with minor sinistral strike-slip components. The regional tectonic stress field derived from the in-situ stress measurements shows that the orientation of maximum principal compressive stress around the epicenter of the Nakchu earthquake is NNE, subparallel to the fault strike, which controlled the dominant normal faulting. The occurrence of seven M ≥ 7.0 historical earthquakes since the M 7.0 Shenza earthquake in 1934 caused a stress increase of 1.16 × 105 Pa at the hypocenter, which significantly advanced the occurrence of the Nakchu earthquake. Based on a comprehensive analysis of stress fields and focal mechanisms of the Nakchu earthquake, we propose that the dominated normal faulting occurs to accommodate the NE-trending compression of the Indian Plate to the Eurasian Plate and the strong historical earthquakes hastened the process. These results provide a theoretical basis for understanding the geometry and mechanics of the seismogenic fault that produced the Nakchu earthquake.

Characteristics of crustal stress field in Tienshan area

Based on 1143 focal mechanisms in Tienshan area from 1900 to 2019, according to the world stress map classification criterion, the main types of focal dislocations are thrust and strike slip; The results of parameter statistics show that the nodal plane of focal mechanism solution is basically consistent with the main tectonic strike in Tienshan area, and the orientation of P axis is perpendicular to the main tectonic strike in Tienshan area, which shows the horizontal nearly NS thrust. The direction of the maximum principal compressive stress is 175.1°, the minimum principal stress direction is 67.8°, the plunge angle of the maximum principal compressive stress axis is 4.3°, the plunge angle of the minimum principal compressive stress axis is 75.8°, the relative stress ratio R is 0.80, and the stress state is compressional, which indicates that the area is in the background of compressional orogeny.

Analysis of Ground Settlement Caused by Double-line TBM Tunnelling Under Existing Building

TBM tunnelling is less used in the subway construction in prosperous city due to the limitation of the engineering geological conditions. The studies on the influence of the TBM construction on the existing buildings are also limited. Therefore, based on the engineering case of tunnel crossing existing building in the section of Haiboqiao ~ Xiaocunzhuang station of Qingdao Metro Line 1, the numerical model that simulates the construction process of TBM tunnelling in slightly weathered granite layer is established by three-dimensional finite difference software FLAC3D to analyze the influence of TBM tunnelling. The comparisons between ground deformations obtained by FLAC3D and field monitoring data in different construction stages of double-line tunnel have been made firstly to validate the numerical model. Then the ground settlement characteristics, differential settlement and the stress distribution of the existing building and the stress of segment structure have been analyzed. During TBM tunnelling under existing building, the settlement of the building as a whole tends to increase, with the maximum measured settlement of 5.45 mm and the maximum differential settlement of 1.58 mm, which meets the control standard of relevant codes. Ground settlement groove along the transverse and vertical sections occurs near the building and tunnels, and the settlement becomes smaller with the farther the distance from the building and tunnels. The settlement curve on the cross section changes dynamically and is approximately V-shaped, and its width is about 5 ~ 6 times diameter of the tunnel. For the same cross section, the range of the settlement groove after tunnelling right line increases obviously compared with that after tunnelling left line (first construction), the settlement values also increase, and the symmetrical axis of the settlement curve is shifted to the right. For the segment structure, the maximum principal tensile stress occurs inside the arch bottom of the tunnel, while the maximum principal compressive stress occurs near the arch top and arch waist, with obvious stress concentration. For the existing building, the maximum principle tensile stress occurs at the door opening of the wall on the first floor and the maximum principal compressive stress is at the corner of wall. They are less than the tensile strength and compressive strength of the segment structure and building respectively, and have enough safety margins. This paper can provide important practical reference for the deformation control and protection design of surrounding buildings for relative construction.

Stress changes associated with the significant first subevent of the 2008 Wenchuan earthquake and implications for the rupture behavior transition

The rupture process of the Wenchuan earthquake demonstrated a transition from thrust-dominated slip to northeastward strike-slip motion along the Longmen Shan Fault Zone. The initial stress has been reported as playing a critical role in this process; however, the stress changes, especially those caused by the significant first subevent of the Wenchuan earthquake are not well understood. Here, we employ a three-dimensional finite element model of the Sichuan-Yunnan region to analyze the stress change caused by the significant first subevent and explore the possible influence on the following ruptures. The results indicate that the auxiliary maximum principal compressive stress (SH) associated with the significant first subevent was horizontal and that the auxiliary stress regime was SH>Sh>Sv, supporting the ongoing regional thrust motion near the southwestern segment of the rupture plane. However, in the northeastern segment, the auxiliary stress regime transitioned to SH>Sv>Sh, demonstrating that the stress changes promoted the transition of the rupture behavior from predominantly thrust motion in the southwest to right-lateral strike-slip motion in the northeastern segment, which was also supported by the dominant shear stress change and the subtle normal stress change along the fault plane in the northeastern segment. In addition, our modeled results also indicate that the orientation of the maximum principal compressive stress changed from SEE to northeastward NEE along the strike of Longmen Shan Fault Zone. This anticlockwise rotation hastened the rupture behavior transition, suggesting that both the initial stress and the stress changes associated with the first subevent jointly controlled the following northeastward rupture of the Mw7.9 Wenchuan earthquake.

Numerical study on strength and failure characteristics of rock samples with different hole defects

In a rock mass, holes of various sizes and geometries naturally occur, which in turn can affect the mechanical properties of the rock mass. These defects often cause engineering problems in subsurface construction. In this study, PFC2D was used to perform uniaxial compression tests on a rock mass containing ten different types of hole defects to analyze their failure behavior and mechanical properties. Four failure modes were determined, and crack propagation and stress field evolution were studied. The results show that the hole defect reduces the uniaxial compressive strength, peak strain, and elastic modulus of a rock mass. Also, these defects accelerate the generation of cracks and promote the destruction of the rock. The failure modes can be classified as Y-type, inverted Y-type, upper left to lower right type, and upper right to lower left type. Before cracks are generated, the compressive stress concentration area is located on the left and right sides of the hole and distributed as a butterfly shape, and the tensile stress concentration area is located in the upper and lower parts of the hole. A zone where stress is decreasing is located near the tip of the tensile stress triangular area. The magnitude and concentration area of compressive and tensile stresses are greatly affected by various hole geometries. Finally, the maximum principal compressive stress decreases instantly after a crack coalesces. Overall, the hole shape has a noticeable influence on the stress distribution surrounding the hole, and a hole defect reduces the degree of failure of a rock mass.

Relocation, Focal Mechanisms and Stress Field Characteristics of Earthquake Swarms in the Songyuan Area of Jilin Province, China

Two earthquake swarms, the Qianguo swarm and Ningjiang swarm, have been observed since 2013 in the Songyuan area, Jilin Province, China. Using the seismic data of broadband permanent and temporal stations that recorded a larger number of earthquakes in the two swarms, we analyze the distribution of aftershocks and the focal mechanisms of these earthquakes and investigate the stress field and faulting properties of the Songyuan area. The relocated hypocenters of the Qianguo earthquakes are distributed along a NNW direction at focal depths of 4–13 km, while the dominant distribution of relocated Ningjiang earthquakes is along a NE direction at depths of 8–16 km. The focal mechanism solutions of 36 earthquakes with ML ≥ 3.6 demonstrate a combined strike-slip and thrust faulting mechanism with centroid depth concentrated at 3–7 km for the Qianguo swarm and a strike-slip mechanism with centroid depth at 5–7 km for the Ningjiang swarm. The full moment tensors of seven moderate–strong earthquakes show that these earthquakes contain a high percentage of non-double-couple components. The regional stress field is inverted using the focal mechanism parameters of the 36 earthquakes. In the Qianguo area, the horizontal maximum principal compressive stress ( $$\sigma_{1}$$ ) is in the E–W direction with a dip angle of 14.1°. In the Ningjiang area, the $$\sigma_{1}$$ is in the ENE–WSW direction with a dip angle of 9.2°. The $$\sigma_{1}$$ directions of the two areas are slightly different, but both approximately along an E–W direction. The comprehensive results of this study show that the Qianguo swarm is likely caused by the movement of a buried fault in the NNW direction oblique to the Changling–Dashanzi fault, whereas the Fuyu–Zhaodong fault in the NE direction is responsible for the Ningjiang swarm. Both the Qianguo and Ningjiang swarms are probably closely related to the thrusting effect of the subduction of the Pacific Plate into the Northeast Asian continental margin and the complex geological conditions in the Songyuan area.