Local Stress Changes Research Articles

Using U–Pb carbonate dating to constrain the timing of extension and fault reactivation within the Bristol Channel Basin, SW England

The Bristol Channel Basin is a Mesozoic continental rift basin. The basin is an important analogue for offshore reservoirs. Relative cross-cutting relationships and correlation with adjacent sedimentary basins have previously been used to constrain the timing of basin development. In situ U–Pb carbonate geochronology has been used to date calcite slickenfibre development in the cores of normal, thrust and strike-slip faults in the East Quantoxhead and Kilve region of Somerset for the first time. Protracted north–south extension from c. 150 to 120 Ma formed normal faults. Subsequent north–south shortening from c. 50 to 20 Ma was accommodated by (1) mutually cross-cutting strike-slip faults, (2) minor east–west-striking thrust faults and (3) the reactivation of pre-existing normal faults. Throughout Cenozoic contraction, σ 2 and σ 3 remained similar in magnitude and periodically flipped to become vertical; this was probably controlled by local stress permutations and changes in fluid pressure. The timing of inversion is contemporaneous with dominant Pyrenean and later Alpine orogenic events, as well as the opening of the Mid-Atlantic Rift. Early inversion of the Bristol Channel Basin was probably driven by far-field Pyrenean deformation, with later contraction caused by Alpine forces. Ridge push from the Mid-Atlantic Rift exacerbated the reactivation of the basin.

In-situ thermal Raman mapping and stress analysis of CNT/CF/epoxy interfaces

A study of the interfacial behavior and internal thermal stress distribution in fiber-reinforced composites is essential to assess their performance and reliability. CNT/carbon fiber (CF) hybrid fibers were constructed using electrophoretic deposition. The interfacial properties of CF/epoxy and CNT/CF/epoxy composites were statistically investigated and compared using in-situ thermal Raman mapping by dispersing CNTs as a Raman sensing medium (CNTR) in a resin. The associated local thermal stress changes can be simulated by capturing the G‘ band position distribution of CNTR in the epoxy at different temperatures. It was found that the G‘ band shifted to lower positions with increasing temperature, reaching a maximum difference of 2.43 cm−1 at 100 °C. The interfacial bonding between CNT/CF and the matrix and the stress distribution and changes during heat treatment (20–100 °C) were investigated in detail. This work is important for studying thermal stress in fiber-reinforced composites by in-situ thermal Raman mapping technology.

Near-infrared spectroscopy to quantify overall thermal process intensity during high-moisture extrusion of soy protein concentrate

High-moisture extrusion (HME) is widely used to produce meat analogues. During HME the plant-based materials experience thermal and mechanical stresses. It is complicated to separate their effects on the final products because these effects are interrelated. In this study we hypothesize that the intensity of the thermal treatment can explain a large part of the physicochemical changes that occur during extrusion. For this reason, near–infrared (NIR) spectroscopy was used as a novel method to quantify the thermal process intensity during HME. High–temperature shear cell (HTSC) processing was used to create a partial least squares (PLS) regression curve for processing temperature under controlled processing conditions (root mean standard error of cross-validation (RMSECV) = 4.00 °C, coefficient of determination of cross-validation (R2CV) = 0.97). This PLS regression model was then applied to HME extrudates produced at different screw speeds (200–1200 rpm) and barrel temperatures (100–160 °C) with two different screw profiles to calculate the equivalent shear cell temperature as a measure for thermal process intensity. This equivalent shear cell temperature reflects the effects of changes in local temperature conditions, residence time and thermal stresses. Furthermore, it can be related to the degree of texturization of the extrudates. This information can be used to gain new insights into the effect of various process parameters during HME on the thermal process intensity and extrudate quality.

Precursory Signals to Injection Induced Fault Reactivation in the Laboratory Using Active Ultrasonic Monitoring Methods

AbstractInduced earthquakes are still highly unpredictable, and often caused by variations in pore fluid pressure. Monitoring and understanding the mechanisms of fluid‐induced fault slip is essential for seismic risk mitigation and seismicity forecasting. Fluid‐induced slip experiments were performed on critically stressed faulted sandstone samples, and the evolution of the actively sent ultrasonic waves throughout the experiment was measured. Two different fault types were used: smooth saw‐cut fault samples at a 35° angle, and a rough fault created by in situ faulting of the samples. Variations in the seismic slip velocity and friction along the fault plane were identified by the coda of the ultrasonic waves. Additionally, ultrasonic amplitudes show precursory signals to laboratory fault reactivation. Our results show that small and local variations in stress before fault failure can be inferred using coda wave interferometry for time‐lapse monitoring, as coda waves are more sensitive to small perturbations in a medium than direct waves. Hence, these signals can be used as precursors to laboratory fault slip and to give insight into reactivation mechanisms. Our results show that time‐lapse monitoring of coda waves can be used to monitor local stress changes associated with fault reactivation in this laboratory setting of fluid‐induced fault reactivation. This is a critical first step toward a method for continuous monitoring of natural fault zones, contributing to seismic risk mitigation of induced and natural earthquakes.

Establishment and experimental verification of a three-dimensional finite element model for residual stress in surface processing of Inconel 718 alloy by laser cladding

The local load and residual stress changes of conventional forged Inconel 718 alloy can be simulated in a two-dimensional (2D) cutting simulation model, but the type and distribution of global residual stress field of the alloy cannot be predicted during laser cladding layer cutting. To address the shortcomings of conventional 2D cutting simulation models for forging Inconel 718 alloy, this paper proposed a 3D closed-loop finite element model, and taking the dry-side milling process of Inconel 718 alloy laser cladding layer as an example, the generation mechanism and distribution of residual stress are predicted during the machining process. Further testing of surface, near-surface, and subsurface residual stresses was conducted to analyze the specific distribution of residual stresses in the workpiece. The results indicated that the uneven distribution of cutting stress and temperature on the workpiece had a significant non-stationary thermal-mechanical effect on the surface of the machined workpiece; the distribution of surface residual stress was uneven, with the significant tensile residual stress at the workpiece boundary. As the depth increases, the influence of mechanical effects dominated, and the compressive residual stress was generated on the subsurface of the workpiece. Residual stress testing was conducted on the surface/near-surface, and the experimental results were consistent with the simulation results of the closed-loop simulation model. In the subsurface, residual stress showed a similar trend of change. This study compensated for the shortcomings of conventional finite element simulation and provided the reference value for the application of three-dimensional finite element simulation in laser cladding materials.

Effect of Thermal Growth Oxide Composition and Morphology on Local Stresses in Thermal Barrier Coatings

The failure of thermal barrier coatings (TBCs) during operation depends mainly on the thermal mismatch between the ceramic top coat (TC) and the metal bond coat (BC). The thermal mismatch at the interface is influenced by the dynamic changes in the composition and morphology of the thermally grown oxide (TGO) between TC and BC during thermal cycling. This work focuses on the establishment of a TGO dynamic growth model, which considers the changes in TGO composition and morphology for investigating the effect of dynamic growth of TGO on local mismatch stresses during thermal cycling. The results show that the sharp locations at the TGO/BC interface are more prone to high tensile stresses during thermal cycling due to the uneven growth behavior of TGO, leading to crack initiation. The valley region of the interface is in a state of compressive stress σxx during the early stages of thermal exposure. The peak region preferentially forms a concentration of tensile stress σyy. Once large-scale "layer" (Ni, Co)Al2O4-based spinel-like mixed oxides(MO) growth occurs in TGO, the stress σxx changes from compressive stress to tensile stress in the valley region, eventually forming high tensile stress (Max: +158 MPa). The maximum tensile stress σyy in the peak region is increased to 256 MPa, which is more than two times larger than the early period of thermal exposure. As a result, the dramatic changes in local stresses seriously affect the time and location of microcracks.

On the Origin of Seismic Anisotropy in the Shallow Crust of the Northern Volcanic Zone, Iceland

AbstractThe Icelandic crust is a product of its unique tectonic setting, where the interaction of an ascending mantle plume and the Mid‐Atlantic Ridge has caused elevated mantle melting, with the melt accreted and cooled in the crust to form an oceanic plateau. We investigate the strength and orientation of seismic anisotropy in the upper crust of the Northern Volcanic Zone using local earthquake shear‐wave splitting, with a view to understanding how the contemporary stress field may influence sub‐wavelength structure and processes. This is achieved using a data set comprising 50,000 earthquakes located in the top 10 km of the crust, recorded by up to 70 stations over a 9 year period. We find that anisotropy is largely confined to the top 3–4 km of the crust, with an average delay time of 0.10 ± 0.05 s, and an average orientation of the fast axis of anisotropy of N014°E ± 27°, which is perpendicular to the spreading direction of the Eurasian and North American plates (N106°E). These results are consistent with the presence of rift‐parallel cracks that gradually close with depth, the preferential opening of which is controlled by the regional stress field. Lateral variations in the strength of shear wave anisotropy (SWA) reveal that regions with the highest concentrations of earthquakes have the highest SWA values (∼10%), which reflects the presence of significant brittle deformation. Disruption of the orientation of the fast axis of anisotropy around Askja volcano can be related to local stress changes caused by underlying magmatic processes.

Measurement of Elastic Stresses and Dissipated Energies at Cracks Is the Lock-In-Evaluation an Appropriate Tool?

Lock-In-Thermography is a common technique for determining local stresses in cyclic-loaded components. This so-called Thermographic Stress Analysis (TSA) uses the cyclic change of the temperature, which results from the elastic stress by the thermoelastic effect. To reduce the noise in the measured temperature signal, the evaluation is performed using a Discrete Fourier Transformation. Brémond [1] and Sakagami [2] have shown that in case of plastic deformation a second mode, coupled with the double loading frequency appears in the DFT-evaluation. This part is known as the so-called D-Mode and is assigned to dissipative energies. Investigations of Bär et al. [3] have shown that there are discrepancies in the elastic and dissipative temperature changes between the Lock-In evaluation and an analytical evaluation, showing that the Lock-In evaluation is just qualitatively but not quantitatively correct. In this study a detailed study of the temperature changes in the vicinity of a crack in AISI 316L was undertaken. A determination of temperature-force hysteresis was carried out on a precracked specimen. The comparison of temperature-force hysteresis based on a frequency synthesis of the different modes of the Lock-In evaluation with an analytical evaluation showed only an approximate match. The compensation of the thermoelastic effect with force proportional local stress changes uncovers the dissipative temperature behavior at the crack. A simple isolation of the stress change or rather the dissipative temperature changes out of the E Mode and D-Mode is not generally possible. Crack opening and compressive loads cause thermoelastic temperature changes, which affect the E-Mode as well as the D-Mode and higher harmonic Dk-Modes.

Applied Research of Deep-hole Presplitting Blasting Technology in Coal

Deep-hole presplitting blasting is a method to solve the problems of gas outburst and low recovery rate in thick and hard coal seam. After explosion, the coal seam permeability is higher than before, and the mass of coal-dropping is increased in result of the local stress change caused by loose blasting. Blasting parameters and cracking zone is calculated based on the theory of explosion. The application indicated that the gas content of the coal seam decreased and the recovery rate increased. The experiment result is in concordance with the result of calculation by theory .

Wastewater Disposal Has Not Significantly Altered the Regional Stress State in Southern Kansas

Abstract Wastewater disposal is primarily responsible for the increased seismicity rate since ∼2013 in southern Kansas. Previous work that used shear-wave splitting (SWS) in southern Kansas interpreted an ∼90° temporal rotation in the fast polarization direction and attributed it to increased pore pressures resulting from fluid injection. However, this interpreted rotation coincided with a change in the stations used to make the SWS measurements. We investigate the temporal variability of fast azimuths in southern Kansas by making SWS measurements on earthquake families with similar source–receiver paths recorded on a stable local seismic network. We select high-quality SWS measurements by investigating the stability of results across 65 different frequency bands between 0.5 and 15 Hz. We find that the fast polarization direction in southern Kansas is relatively constant with an average east-northeast (∼N79°E) orientation between 2014 and 2017. Our fast polarization measurements are primarily a reflection of the maximum principal horizontal stress direction (SHmax). We observe a slight spatial change in SHmax to the northeast (∼N55°E) near the Nemaha ridge in Oklahoma. However, we do not observe any significant temporal rotation of SHmax or variation in delay time (i.e., crack density) in southern Kansas, contrary to the earlier study. The previously interpreted ∼90° rotation may either be a reflection of a very local stress change or a misinterpretation of SWS results potentially due to the use of inconsistent source–receiver paths. Our SWS measurements cover the period of peak wastewater disposal and seismicity rates and suggest an absence of significant temporal rotations in the local anisotropy and stress orientations associated with wastewater disposal.

Spatial and temporal heterogeneity of Kohlrausch–Williams–Watts stress relaxations in metallic glasses

We perform a molecular dynamics (MD) stress relaxation simulation for Zr50Cu40Al10 metallic glass to confirm that the time dependency of stress relaxation conforms with the Kohlrausch–Williams–Watts (KWW) equation, and to derive the temperature dependency of the Kohlrausch exponent βKWW. We also calculate local plastic deformation based on atomic strain, then discuss the morphology of relaxation and calculate the probability density of stress relaxation with respect to the characteristic time of relaxation from the number of deformed atoms. Afterward, we derive the time dependency of stress relaxation as a mode-averaged decay function, which expresses spatial and temporal heterogeneity. Both the results of simulation and calculation reproduce the KWW relaxation form and are in good agreement, confirming the spatially and temporally heterogeneous nature of KWW relaxation. The heterogeneity of the stress relaxation of metallic glass is determined by local stress changes caused by microscopic local plastic deformation.

Sustained Decadal Warming Phase in the Southwestern Indian Ocean since the Mid-1990s

Regardless of the slowdown in global warming during the hiatus period, sea surface temperatures (SSTs) in the southwestern Indian Ocean (SWIO) have experienced sustained decadal warming for more than two decades since the mid-1990s. The SWIO SSTs warmed steadily during 1996–2016, causing a warming hot spot of 0.4 K decade−1 in a large region east of Madagascar. An upper-layer heat budget analysis indicated that heat advection by ocean currents was the greatest contributor to the warming of the SWIO SSTs. The existence of an anticyclonic geostrophic current along the western boundary of the SWIO tended to maintain such warming by transporting warmer water from the west into the SWIO region. In addition, net positive heat transport by ocean currents also occurred at the southern boundary of the SWIO as the climatological northward transport of cold water from the Southern Ocean weakened. This reduction in northward ocean currents at the surface was caused by local wind stress changes, leading to a southward Ekman current. Below the surface, an anticyclonic geostrophic current pattern existed around the warming center near the southeastern SWIO, which reduced the transport of cold waters from the Southern Ocean and warmed the SWIO. These processes near the two boundaries formed a self-sustaining positive feedback mechanism and favored the maintenance of sustained warming in the SWIO. More attention is needed to analyze the sustained long-lasting warming in the SWIO, as it is a unique phenomenon occurring under the background of the ongoing global warming.

The Late Quaternary dip–slip characteristics of the left-lateral strike-slip Yuanmou fault, the southwestern margin of the north–south seismic belt of China

The North–South Seismic Belt distributed along the eastern margin of the Tibetan Plateau is a regional-scale seismically active zone. The Yuanmou Fault, located at the junction of the North–South Seismic Belt and the Central Yunnan Sub-Block, is an important boundary of earthquakes distribution and topography. Therefore, the studying of the Late Quaternary activity of the Yuanmou Fault is of great significance to understand the regional geodynamic mechanism and its efforts on the regional tectonic activities, seismic distribution and future risk. Based on field observations and analysis of earthquake geology and tectonic geomorphology and the dating results of Quaternary chronology, together with the previous studies, revealed that: (1) the fluvial terrace T1 was cut by the Yuanmou fault on the northern section of Jiangbian, and the most recent earthquake event happened about 7 ka B.P. age on the Jiangbian–Luochuan segment. (2) Based on the offset measurement and dating results of deformed terraces, the horizontal and vertical average slip rate of the Yuanmou fault were determined to be ~ 1.0 mm/year and ~ 0.1 mm/year, respectively. (3) Moreover, the latest activity time of the southern segment of the Yuanmou Fault is late Pleistocene, indicating the segmentation between the northern and southern segments of the Yuanmou Fault. (4) The differential activity intensity and activity ways of the Yuanmou Fault on different segments is probably associated with the change of local stress. Therefore, these findings concerning with seismic activities and activity segmentation of the Yuanmou Fault reveal the complexity of the regional dynamic mechanisms and provide a new insight for exploring regional differences in the tectonic deformation mechanisms of the southeastern margin of the Tibetan Plateau during the Late Cenozoic.

Hydro-mechanical modeling of the first and second hydraulic stimulations in a fractured geothermal reservoir in Pohang, South Korea

This study presents comprehensive coupled hydro-mechanical numerical modeling of the first and second hydraulic stimulations at the Pohang enhanced geothermal system (EGS) site in order to improve the understanding on the key stimulation mechanisms in the fractured reservoir. Two models for PX-2 and PX-1 wells were developed including fracture zones of different orientations and permeability. Shear dilation and frictional plastic strain-softening were implemented in a non-linear stress dependent fracture model. A history matching of the wellhead pressure curves was carried out in the early days of each stimulation. The PX-2 model with a fracture jacking mechanism achieved the reproduction of highly reversible non-linear aperture changes observed in situ. The PX-1 model successfully simulated a wellhead pressure peak and drop associated with shear slip and dilation by applying frictional plastic strain softening. Simulated critical wellhead pressure for shear slip near the PX-1 well was greater than the prediction by a simple slip potential analysis due to local stress changes by the poroelastic effect. The numerical modeling confirmed that the combination of shear dilation and jacking was adequate to capture the pressure evolution during the increasing step-rate test at PX-1. Besides, spatio-temporal changes in pressure, total stress, and permeability evaluated in the fracture zones greatly enhanced the understanding on the coupled behavior caused by the hydraulic stimulations. The possibility of zones with lower permeability away from the PX-1 well was suggested by an alternative model. The current numerical study demonstrates that the key hydro-mechanical processes of shear slip and dilation and hydraulic jacking observed in the fractured reservoir can be successfully reproduced.

Size-frequency distribution of coral assemblages in insular shallow reefs of the Mexican Caribbean using underwater photogrammetry.

The characterisation of changes in coral communities depends heavily on systematic monitoring programs and the collection of necessary metrics to assess reef health. Coral cover is the most used metric to determine reef health. The current organizational shift in coral requires the evaluation of complementary metrics, such as colony size and frequency distributions, which help to infer the responses of the coral populations to local stress or larger scale environmental changes. In this study, underwater digital photogrammetry techniques were used to assess the live cover of all coral colonies ≥3 cm2 and determine the size-frequency distribution of the dominant species in the shallow reefs of the Cozumel Reefs National Park (CRNP). In addition, the minimum sampling area (m2) needed to obtain a representative sample of the local species pool was estimated. Areas between 550 and 825 m2 per reef were photographed to generate high-resolution digital ortho-mosaics. The live area of the colonies was digitised to generate community matrices of species and abundance. EstimateS software was used to generate accumulation curves and diversity (Shannon H′) at increasing area intervals. Chi-Square tests (χ2, p = 0.05) were used to compare the observed vs estimated species richness. Spearman’s coefficients (rs), were calculated to correlate the increase in sampling area (m2) vs H′, and the Clench’s function was used to validate the observed richness (R2 = 1 and R > 90%). SIMPER analysis was performed to identify dominant species. Comparisons in terms of abundance, coral cover and size-frequencies were performed with Kruskal-Wallis (H test, p = 0.05), and paired Mann-Whitney (U test, p = 0.05). In order to obtain 90% of the species richness, a minimum sampling area of 374 m2is needed. This sampling area could be used in shallow Caribbean reefs with similar characteristics. Twelve (mainly non-massive) species: Agaricia agaricites, A humilis, A. tenuifolia, Eusmilia fastigiata, Meandrina meandrites, Montastrea cavernosa, Orbicella annularis, Porites astreoides, P. porites, Pseudodiploria strigosa, Siderastrea radians andS. siderea, were dominant in terms of abundance and coral cover. A significant increase (p < 0.05) in the number of colonies and live coral (m2) was observed from north to south of the study area. Furthermore, a wide intraspecific variation of size-frequency, even between adjacent reefs, was also observed. The size-frequency distributions presented positive skewness and negative kurtosis, which are related to stable populations, with a greater number of young colonies and a constant input of recruits. Considering the increase in disturbances in the Caribbean and the appearance of a new coral disease, digital photogrammetry techniques allow coral community characteristics to be assessed at high spatial resolutions and over large scales, which would be complementary to conventional monitoring programs.

Cracking behavior and local stress characteristics around the opening surrounded by two intermittent joints: experiment and numerical simulation

In this research, the Strength and deformation behaviors, cracking process, and local stress evolution of sandstone specimens containing a circular opening and two joints (called H-J sandstone specimens in this study) were researched by experiment and numerical simulation (two-dimension particle flow code). The effect of different joint positions around the opening has been specifically studied by changing the ligament angle (β). The test results show that peak strength and peak strain firstly decrease then increase with the increasing β, while the peak strain presents an overall upward trend. Three types of coalescence failure patterns between the opening and joints formed, and the corresponding cracking process and acoustic emission (AE) characteristics are highly related to the ligament angle. Based on the micro-parameters calibration, a good agreement was achieved between experimental and numerical simulation. The numerical results show that the local stress evolution around the opening is highly corresponding to the cracking process. The microcracks initiation and propagation cause obvious stress fluctuations, drops or increasements of minimum principal stress, while the cracks coalescence results in obvious reduction of maximum principal stress and drops of stress-strain curve. It also be found that the stress distribution and magnitude around the opening tend to be closely related to both coalescence failure and strength characteristics of H-J specimens. Finally, the cracking mechanism between the opening and joints was revealed based on particle displacement fields. The results show that different cracking mechanism may cause different local stress changes, which finally determines the overall mechanical behavior of specimens.

Induced seismicity in geologic carbon storage

Abstract. Geologic carbon storage, as well as other geo-energy applications, such as geothermal energy, seasonal natural gas storage and subsurface energy storage imply fluid injection and/or extraction that causes changes in rock stress field and may induce (micro)seismicity. If felt, seismicity has a negative effect on public perception and may jeopardize wellbore stability and damage infrastructure. Thus, induced earthquakes should be minimized to successfully deploy geo-energies. However, numerous processes may trigger induced seismicity, which contribute to making it complex and translates into a limited forecast ability of current predictive models. We review the triggering mechanisms of induced seismicity. Specifically, we analyze (1) the impact of pore pressure evolution and the effect that properties of the injected fluid have on fracture and/or fault stability; (2) non-isothermal effects caused by the fact that the injected fluid usually reaches the injection formation at a lower temperature than that of the rock, inducing rock contraction, thermal stress reduction and stress redistribution around the cooled region; (3) local stress changes induced when low-permeability faults cross the injection formation, which may reduce their stability and eventually cause fault reactivation; (4) stress transfer caused by seismic or aseismic slip; and (5) geochemical effects, which may be especially relevant in carbonate-containing formations. We also review characterization techniques developed by the authors to reduce the uncertainty in rock properties and subsurface heterogeneity both for the screening of injection sites and for the operation of projects. Based on the review, we propose a methodology based on proper site characterization, monitoring and pressure management to minimize induced seismicity.

Stiffness based technique to probe cyclic damage accumulation in micro-structurally graded bond coats via micro-beam bending tests

ABSTRACTThis paper highlights a novel technique to delineate the fatigue response of different regions within thin microstructurally graded platinum nickel aluminide bond coats. Notched clamped beam structures fabricated from distinct microstructural zones of these coatings are subjected to programmed cyclic bending using the nano-indentation system. A methodical approach is established herein to quantify the cyclic damage preceding crack pop-in by using the cyclic stiffness of the beam as an indicator to mark failure. Preliminary results from these tests show that there is a characteristic change in the stiffness of the beam before a crack pop-in event occurs and different regions within the coating show different stiffening characteristics. Factors affecting the measured stiffness such as offsets in the loading position and blunting of the notch tip have been estimated using the finite element method. A graded flow stress model has been proposed and implemented in FEM to quantify the local flow stress changes accompanying the measured rise in stiffness. Electron transparent foils lifted off from the notched region of the beam post-testing suggests that the cyclic stiffening of the beams occurs due to dislocation hardening in the plastically deformed region close to the notch tip. Toughening mechanisms active in the crack wake have thus been investigated and correlated to the measured cyclic stiffness.

Curvature-driven spatial patterns in growing 3D domains: A mechanochemical model for phyllotaxis.

Here we discuss the formation of phyllotactic patterns in the shoot apical meristem (SAM) of plants, where the spatial distribution of the phytohormone auxin determines phyllotaxis in a domain that is growing and changing in time. We assume that the concentration of auxin modifies the mechanical properties of the domain and that the mechanical stress field in the SAM orients the flux of auxin. To study this problem we propose a mechanism for pattern formation in growing domains with variable curvature. The dynamics of chemicals is modeled by a reaction-diffusion system that produces a three dimensional pattern of chemical concentrations that changes the stress field in the domain while growing. The growth process is modeled by a phase-field order parameter which determines the location of the boundaries of the domain. This field is coupled to the chemical concentration through a curvature term that affects the local mechanical stress in the domain. The local stress changes in turn modify the chemical patterns. Our model constitutes a useful and novel approach in theoretical biology, as many developmental processes in organisms seem to be affected by the changes of curvature, size, mechanical stress and other physical aspects. Several patterns seen in many plants are reproduced under certain conditions by our model.

Application of Dimensional Analysis to Project Laboratory Scale Numerical Modelling Prescribed Hydraulic Fracturing Results to Field Scales

Hydraulic fracturing has been applied in the cave mining industry with the purpose of re-creating an orebody rock mass condition that is suitable for caving. Prescribed hydraulic fracturing was proposed in a previous study as a supplement to the conventional hydraulic fracturing strategy. In this paper; dimensional analysis is used to project laboratory scale numerical modelling results to field scales in order to study the applicability of creating prescribed hydraulic fractures (PHFs) under field conditions. The results indicate that field scale PHFs are feasible if the stress shadows of the pre-located fractures are properly utilized. Water can be used to create the pre-located fractures that induce the local stress change in a low differential stress state; and the use of more proppants and a shorter pre-located fracture spacing lead to PHFs propagating more quickly towards the pre-located fractures. For field condition having high differential stresses, more viscous fluid must be used to create the pre-located fractures in order to enhance the stress shadows. In this case, a shorter pre-located fracture spacing does not necessarily result in the re-orientation of PHFs towards the pre-located fractures and may even lead to unsatisfactory pre-conditioning. A sufficiently high pre-located fracture net pressure to the differential stress ratio (close to 0.5) is the prerequisite for creating PHFs.