Unpredictable change will sweep through America, while old problems, from war to inflation, are likely to afflict other countries The global economy is entering the new year with rising geopolitical tensions looming over its prospects, as the world’s leading central banks attempt to cut interest rates after the worst inflation shock in decades. Donald Trump’s second term in the White House is expected to dominate the economic agenda. Global trade tensions are on the horizon as the president-elect threatens to impose sweeping tariffs on US imports. Britain’s economy is faltering while inflationary pressures remain. The largest economies of the eurozone are engulfed in political turmoil. Beijing is battling to revive the Chinese economy, while countries in the global south are facing soaring debt interest payments. Here are the five key charts underpinning economic prospects for 2025. Trump’s unambiguous victory has raised the prospect of global battles on a much bigger scale than in his first term, when his clashes with China rippled through world trade. However, many economists are hopeful he will stop short of deploying the full arsenal of threats he made on the campaign trail, which included import tariffs of up to 60% on China and up to 20% on America’s enemies and allies alike. The president-elect’s pledges to cut business taxes and regulations have investors hoping for a surge in the American stock market, but there are fears his measures would open up a gaping hole in the US federal budget. Households being hit with higher taxes on imports could also stoke inflation. Elsewhere, tensions remain high with conflicts in Ukraine and the Middle East, while political uncertainty is mounting in the eurozone core, where the French and German governments are under strain. The world’s most powerful central banks began cutting interest rates in 2024 after inflation cooled more quickly than expected. The big focus for the year ahead will be on how much further borrowing costs will be reduced amid fears over lingering inflationary pressures and the outlook for economic growth. The Bank of England has signalled a gradual approach after forecasting inflation would remain above its 2% target until 2027. Headline inflation has fallen back from a peak of 11.1% in the second half of 2022, and briefly dipped below 2% in September 2024, but has risen back to 2.6%. Wage growth has remained stronger than anticipated, with potential to stoke inflation. The Bank is also monitoring the impact of Rachel Reeves’s autumn budget, after the chancellor announced a £25bn rise in employer national insurance contributions from April. Business leaders have warned this could hit jobs or be passed on to consumers through higher prices. City investors have reduced expectations for deep interest rate cuts in 2025. Financial markets predict two cuts from the current rate of 4.75% by the end of the year, far fewer than anticipated in the autumn when some analysts were forecasting a rate reduction to as low as 2.75%. Britain’s economy is on the brink of stagnation, raising the prospect of a period of “stagflation” – when growth is stalling but inflation is high. The UK grew at the fastest rate in the G7 in the first half of 2024, partly as it was bouncing back from a shallow recession in the second half of 2023. However, a sharp fall in consumer and business confidence has weighed on the economy, which some analysts have blamed on Labour’s gloomy rhetoric and tax-raising plans. In an early blow to Keir Starmer’s target to hit the fastest sustained growth in the G7 by the end of the parliament, the economy contracted by 0.1% in October, while the Bank forecasts zero growth over the final three months of 2024. Some experts are, however, more optimistic. Kallum Pickering, chief economist at the stockbroker Peel Hunt, said economic confidence should recover, as Britain’s political backdrop is far more stable than in recent years, and compared with other countries. Sign up to Observed Analysis and opinion on the week’s news and culture brought to you by the best Observer writers after newsletter promotion “Politics is kind of boring here. This will basically be the first normal year. The last time you could say that is probably 2015. I just think it’ll take another six months until people realise we’ve returned to normal. “The UK has had PTSD ever since the EU referendum, the pandemic, and the first war on European soil since the 1940s.” Britain is one of the few developed countries with a lower employment rate than before the Covid pandemic. More than 9 million people are “economically inactive” – neither working nor looking for a job. For almost 3 million, the main reason is long-term ill-health, which is near to its highest level on record. Getting more people back to work is seen by the government as one of the most powerful ways to reboot economic growth, and will be one of its top priorities in 2025. Part of this effort will be targeted at fixing battered public services, while there will be changes to jobcentres and employment support from the spring. Governments around the world are facing challenges from higher borrowing costs. Unlike the years of ultra-low interest rates after the 2008 financial crisis, when debt-fuelled public spending helped bolster fragile growth, the risk of stickier inflation and higher interest rates in 2025 will make this tougher. “In a new regime of higher real interest rates, expansionary fiscal policy in bad times is no longer a free lunch. It now requires proper fiscal consolidation in good times,” analysts at Bank of America wrote in a note to clients. Trump’s tax-cutting plans could widen the US fiscal deficit. Reeves will face a challenge in her 2025 spending review to meet her self-imposed fiscal rules without raising taxes or cutting spending. France is also battling to reduce its budget deficit amid political turmoil. Investors could demand higher returns if lending to governments with elevated deficits, in the return of “bond vigilantes” who might further drive up sovereign borrowing costs. Marc Seidner and Pramol Dhawan of the asset manager Pimco, the world’s largest bond investor, said: “At some point, if you borrow too much, lenders may question your ability to pay it all back. It doesn’t take a vigilante to point that out.”
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Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript. Advertisement Scientific Reportsvolume 14, Article number: 30971 (2024) Cite this article Metrics details In order to investigate the influence of shear on contact characteristics and fluid flow evolution of rough rock fractures, a series of shear-flow tests were carried out by numerical experiments. Firstly, a sandstone specimen with a rough fracture was made in the laboratory, and the numerical model of the fracture was reconstructed in FLAC3D software. Experiments were conducted to investigate the depth of penetration of the fracture under different normal stress (1, 3, and 5 MPa) and shear displacement (2, 4, 6, 8, and 10 mm). By establishing the relationship between the shear direction and the apparent inclination of the fracture asperity, the effects on the asperity contact characteristics and seepage properties are explored. The results of the study indicated that the larger the normal stress the larger the surface contact section and the smaller the aperture, showing the opposite trend with increasing shear displacement. Positive apparent inclination distribution can effectively predict the location of shear damage during the shear process. Negative apparent dip implies that those regions increase permeability after shear, and decrease with increasing crack opening. Fracture seepage shows obvious nonlinear characteristics, where the nonlinear coefficients are 5–6 orders of magnitude larger than the linear coefficients. The critical Reynolds number Rec is used to distinguish the linear and nonlinear categories of fluid flow, and the calculated results show that the range of Rec is between 0.0081 and 0.11.3, and the Rec increases with shear displacement and decreases with normal stress. There are a large number of fracture joints within the rock mass, and numerous engineering practices have demonstrated that the stability of projects is closely related to the slip failure of these discontinuous surfaces1,2,3,4,5. For instance, disturbances generated during underground mining activities and tunneling can activate faults, leading to failures that pose significant risks to mining spaces. Earthquakes and rockbursts, which result from mining-induced fault slips, are among the primary hazards impacting underground safety6,7. Consequently, an in-depth study of the shear properties of fractures holds great significance for guiding engineering practices in the prevention and control of engineering disasters. The distance between the upper and lower surfaces of a fracture, known as the aperture, serves as the primary channel for fluid flow. Numerous fissure joints are distributed throughout natural rock masses, and understanding fluid flow in a single fissure is fundamental to modeling seepage in complex fracture networks8. Typically, fracture flow can be described by the Navier-Stokes Equation9. However, due to the complexity of solving the NS equation, the inertia term is often neglected, leading to a simplified form10,11,12. The cubic law, which expresses the flow rate and permeability coefficient of a fissure as a linear relationship, is derived by assuming the upper and lower surfaces of the fracture act as parallel plates. Yet, in nature, joint surfaces are rough, and the complexity of surface morphology along with high water pressure can cause seepage to deviate from the linear cubic law. In such cases, the cubic law overestimates the transmissivity of the fracture13,14. Scholars often characterize this nonlinearity using the Forchheimer formula, which includes both primary and secondary flow forms and has been verified for its accuracy in describing nonlinear seepage15,16,17. Ronget et al. noted that this equation does not account for the effect of crack surface geometry on seepage, thus failing to explain the triggering mechanism of nonlinear seepage due to fracture surface contact and roughness18. Chen et al. indicated that the roughness, contact area, and tortuosity of the cracks generate inertial forces, leading to nonlinear seepage19. Similar conclusions were reached by Bursh and Thomson in their study, concluding that complex flow lines in a laminar state also result in inertia losses20. Gao et al. proposed a new theoretical model for predicting the nonlinear flow behavior in rough rock fractures under shear, effectively characterizing the nonlinearity of fluid flow by combining the Darcy-Weisbach equation with the Izbash equation21. Many factors affecting nonlinear flow in fractures, such as roughness, normal stress, and fracture aperture, were investigated in previous studies. These studies usually select a critical value to define whether the fluid is in a linear flow state or not, such as the critical flow rate, the critical hydraulic gradient, or the critical Reynolds number. Ranijth and Darlington studied the effect of normal pressure on seepage and found that Rec decreases with increasing normal stress22. Wang et al. noted that the JRC and Rec values of the fracture exhibit a negative exponential relationship23. Liu et al. found that an order of magnitude up in fracture aperture decreases the critical hydraulic gradient by a multiple of about 1,00024. The above studies mainly focused on conformable contact fractures. However, joint fractures are weak segments in the rock mass and are prone to shear failure along discontinuous surfaces. The evolution of contact relations and aperture distribution of fracture walls induced by shear displacement is the main factor affecting the fluid flow state in rough fractures25,26,27. Rong (2016) investigated the shear-fluid behavior of roughness cracks with different JRC and showed that the shear displacement increased from 0 to 10 mm, corresponding to critical Reynolds number values from 1.5 to 1324. Yin et al. indicated that critical hydraulic gradient is positively correlated with shear displacement and negatively correlated with normal stress27. Through the review of the above studies, most of the studies focused on the effect of JRC and positive stress on nonlinear seepage in shear. It has been pointed out that the contact area of the fracture is also an important factor affecting the phenomenon. However, laboratory tests or empirical equations are difficult to quantitatively describe the laws of fracture contact area and aperture evolution during shear, and numerical simulation provides an excellent alternative. Although previous studies have extensively investigated the fluid flow characteristics in rough fractures, there has been a lack of in-depth understanding and quantitative description of the dynamic evolution of fracture contact characteristics and aperture distribution during shear, as well as how these factors influence the nonlinear characteristics of fluid flow. Building on this foundation, we developed a numerical simulation framework for fluid flow in shear-induced rough fractures to delve into the evolution of fracture contact characteristics and aperture distribution. Using the INTERFACE module in FLAC3D, we conducted a detailed study of the dynamic contact behavior of fractures during shear, while the application of COMSOL software has enabled us to analyze the fluid flow characteristics of sheared fractures. In this study, we also considered the relationship between the shear direction and the micro-slope of the fracture, analyzing the significant role of the apparent dip angle in predicting the damage areas and flow line distribution in rough shear fractures. Furthermore, we systematically analyzed the sensitivity of key parameters such as fracture contact area, aperture frequency, nonlinear fluid flow parameters, normalized permeability, and critical Reynolds number under different normal stress and shear displacement conditions. Initially, a cubic sandstone specimen measuring 150 × 150 × 150 mm was prepared. An initial fracture was introduced through a split test conducted on the specimen. The direct shear test was then carried out using the RMT301 shear testing system, which is capable of withstanding a maximum horizontal load of 500 kN and a maximum vertical load of 1500 kN. The shear test was performed under a constant normal stress boundary condition. After the normal load was applied at a rate of 0.5 kN/s, reaching 3 MPa, the bottom shear box was loaded at 0.5 kN/s to provide the shear load. The loading was ceased once the shear displacement reached 10 mm. Experimental equipment and joint modeling. The three-dimensional scanning equipment used in this study is the JR-AF model 3D scanner provided by Beijing JiRuiXinTian Technology Co., Ltd., featuring non-contact grating photogrammetry scanning technology with high precision measurement capabilities, achieving a scanning accuracy of ± 0.015 mm, providing accurate 3D data for the experiment. The roughness of the fracture was quantified using the Joint Roughness Coefficient (JRC), which was calculated with reference to the established methods28: where Zi represents the crack opening, n is the number of data points, and (Delta x)is the spacing between data points. In our tests, n is 2061 and the spacing is 0.0028, and JRC is calculated as 5.75. The high-precision non-contact 3D laser scanner was employed to capture the fracture morphology data (see Fig. 1). Subsequently, the scanned data were imported into FLAC3D to construct the numerical fracture model. In this study, the INTERFACE module within FLAC3D was utilized to investigate the dynamic contact behavior of rock fracture surfaces under compressive shear. The developed model comprised 50,000 zone elements, 9,236 element nodes, 2,601 INTERFACE nodes, and 5,000 INTERFACE elements (Fig. 1). The shear properties of rock fractures are influenced by the shear direction, which is primarily manifested through the interaction between the inclination of micro-bumps and the direction of shear29. FLAC3D divides the INTERFACE elements into two triangular elements. The apparent inclination is defined as the angle between a line within a triangular element along the shear direction and its horizontal projection30. This apparent inclination can be determined using the coordinates of the INTERFACE nodes and the shear direction vector: The micro-slope angle of the asperities varies from 0° to 90° as the upper and lower surfaces interact. As they move in opposite directions, the magnitude of the asperity micro-slope angle ranges from 0° to -90°, at which point the fractures may open, creating highly permeable channels (as illustrated in Fig. 2). Characterization of fracture surface structure. The penetration depth of INTERFACE can indicate the contact state of the fracture. When the penetration depth is greater than zero, the element node penetrates the surface of the element and overlaps the element (see Fig. 3). It has been shown that these overlaps can be a reasonable representation of the contact area in a shear test31. Depth of penetration and contact relationships. For this numerical test, three sets of shear test programs were designed. The normal stresses are set to 1, 3, and 5 MPa. Applying load to the Matrix below the fracture at a rate of 1 × 10− 6 m/step. The constraints is described in Fig. 3. The penetration depth (delta n) and contact area of INTERFACE at shear displacements (Delta u)= 2, 4, 6, 8, and 10 mm, were recorded for each set of test. The fracture aperture in regions with penetration depths > 0 is zero, and in regions with penetration depths < 0 are their opposites (see Eq. 4). In this way, a three-dimensional aperture model is established. The seepage tests for different fracture patterns were carried out in COMSOL software. FLAC3D software provides the INTERFACE module to address issues of sliding or separation in geomechanics. The Coulomb sliding criterion is employed to describe the shear stresses during interface sliding. If the normal stress is tensile, the element cannot undergo shear stress. The FLAC3D program calculates the absolute penetration velocity and relative shear velocity for each time step, which are used to determine the normal and shear stresses. The intrinsic model of the fracture surface is defined by a linear Coulomb shear strength criterion. This criterion limits the tangential and normal forces at the interface nodes, the normal and shear stiffness, the shear bond and tensile strengths, and the shear dilation angle. The normal and shear forces that describe the elastic interface response are determined in real-time using the following relations: The Coulomb shear-strength criterion restricts the shear force by the relation: where c represents the cohesion along INTERFACE; (varphi) is the friction angle of the surface of the structural face. The INTERFACE element has two states, bonded and broken. Once the element yielded either by reaching shear strength (Eq. 7) or tensile strength, it no longer bears tensile stress. In this study, the dilation angle of the shear plane is assumed to be zero. This assumption is based on the premise that the normal lift due to shear slip is primarily dictated by the intrinsic morphology of the structural surface. Consequently, the dilation angle is set to zero to align with this premise. The specific physical parameters that underpin our model are presented in Table 1. In the context of fracture seepage processes, water is characterized as a viscous, incompressible fluid, and its behavior is commonly modeled using the Navier-Stokes (NS) Equations20,32,33. These equations encapsulate the dynamics of fluid flow by incorporating inertial forces, pressure gradients, viscous forces, and any external forces that may influence the fluid’s motion. where ρ is the density; P is the fluid pressure; f is the volumetric force acting on the fluid; T is the shear stress of the fluid; (nabla) is the Hamiltonian operator; u is the fluid flow rate. The expression of the continuity equation for an incompressible fluid is given by: Cube’s law is used to calculate the relationship between flow and pressure gradient for smooth parallel fractures, where the permeability of the fracture is controlled by the aperture of the fracture. where w is the fracture width; e is the fracture aperture; Q is the volume flow rate. When the water velocity exceeds a certain threshold, the flow rate and pressure gradient are not in a linear relationship34. The nonlinear seepage formula is expressed by a quadratic binomial equation, where the first term represents linear seepage and the second term represents nonlinear seepage. where (hat {a}= – mu /kA) is a linear coefficient; (hat {b}= – beta mu /{A^2}) is a nonlinear coefficient. Another expression of the Forchheimer formula can be obtained from the relationship between hydraulic gradient and pressure: where (J=frac{P}{{rho g}})is hydraulic gradient; (a=frac{{hat {a}}}{{rho g}}); (b=frac{{hat {b}}}{{rho g}}). These two coefficients are related to the aperture size and the morphology of the fracture surface. Zeng and Grigg proposed a characterization method to determine the fluid flow state inside the fracture based on a large number of experiments35. E is the scale factor which is a dimensionless number between 0 and 1. E = 0.1 indicates the critical point for linear and nonlinear seepage in the fractured rock mass. Reynolds number reflects the ratio relationship between the inertia force and the cohesion force of a fluid, and can be used to characterize the nonlinear characteristics of a fluid. where Re is the Reynolds number; µ is the fluid viscosity. Figure 4(a) illustrates the apparent inclination of the shear direction within the numerical model, where varying colors denote distinct angles of inclination. Figure 4(b) captures the characteristics of shear damage on the fracture’s rough surface as observed in the laboratory setting. In Fig. 4(b), the blue areas specifically highlight regions that have experienced shear damage. Conversely, in Fig. 4(a), regions depicted in hues closer to red signify a steeper apparent dip angle, suggesting that these areas are prone to exhibit relative extrusion of the fracture’s asperities during shear deformation. It is evident that there is a significant correlation between the regions of shear damage identified in Fig. 4(b) and those with a higher apparent dip angle in Fig. 4(a). Furthermore, areas with an apparent inclination angle below zero, indicating a reverse slope, result in a separation of the fracture’s upper and lower surfaces post-shear testing. In the case of the rough fracture under examination, the negative apparent dip angles, primarily located in the lower left quadrant of Fig. 4(a), are anticipated to correspond to zones of enhanced permeability following shear. This permeability will be further explored in the subsequent seepage test outcomes. Overall, the numerical simulation methodology outlined in this paper effectively replicates the contact characteristics throughout the shear process of the fracture. Distribution of (a) the angle of visual inclination, (b) shear damage in laboratory tests. Figure 5 illustrates the relationship between shear stress and displacement, including a comparison between experimental and simulation results. During the initial stage of shear displacement (0–7.5 mm), shear stress increases nonlinearly with the increase in displacement, indicating the mechanical behavior of the material as it transitions from elastic to plastic deformation. The peak shear stress is reached at approximately 7.5 mm of displacement, signifying the maximum shear strength of the material. The occurrence of peak stress suggests that the material experiences the most significant shear resistance at this displacement. Following the peak, the shear stress begins to decline, a trend that may be associated with the propagation of micro-cracks within the material or a reduction in frictional effects. As displacement continues to increase, the shear stress stabilizes after 10 mm, which could imply that the material has reached a new state of equilibrium or that damage has become stable. The simulation results correspond well with the experimental data across most of the range, particularly before the peak shear stress is attained. This validation confirms the effectiveness of the simulation method in predicting the shear behavior of the material. However, there is a noticeable discrepancy between the simulation and experimental results after the peak stress, which may be due to the simulation not fully capturing the complexity of the material’s behavior. Shear test displacement-stress curve. The aperture of a fracture is a pivotal factor influencing seepage flow, with this aperture being characterized by the penetration depth. As delineated in Sect. 2.1, fractures are categorized into regions of contact and non-contact based on specific criteria (Fig. 6(a)). In these regions, a negative penetration depth signifies the presence of a seepage channel, where the aperture’s magnitude is equivalent to the absolute value of the penetration depth, as depicted in Fig. 6(a). The green areas indicate zones of contact where the fracture aperture is effectively closed during the fluid flow experiments. Figure 6(b) presents the calculated distribution of penetration depths for the INTERFACE elements under a normal stress of 3 MPa and a shear displacement of 2 mm. The distribution aligns with a normal distribution pattern, with a maximum aperture of 0.719 mm. Concurrently, the laboratory-measured maximum normal displacement of 0.683 mm substantiates the accuracy of the numerical simulation. Distribution of (a) the angle of visual inclination, (b) shear damage in laboratory tests. Figure 7 illustrates the distribution of penetration depths for the INTERFACE elements throughout the shearing process. The colored regions denote areas of contact depth, while the white regions indicate areas of separation. It is evident that as the shear displacement increases, the contact area diminishes, and the penetration depth augments, a phenomenon attributable to stress concentration. To elucidate, consider the contact area’s evolution under a constant normal stress of 3 MPa. At shear displacements of 0, 2, 4, 6, 8, and 10 mm, the contact area’s proportion relative to the total interface area is 100%, 67.53%, 42.76%, 32.77%, 31.52%, and 24.45%, respectively. Correspondingly, the maximum contact depths recorded are 0, 0.58, 0.94, 1.19, 1.52, and 1.69 mm. Contour plot of penetration depth distribution on fracture surface under (a) 1 MPa, (b) 3 MPa, and (c) 5 MPa normal load. Figure 8 depicts the correlation between shear displacement and the proportion of contact area under varying normal stress conditions. As the normal stress increases, the rate of reduction in the contact area diminishes. This trend is attributed to the increased resistance to separation within the fracture under higher normal stress, which suppresses dilatancy. Consequently, the contact depth increases, and the aperture of the fracture decreases. Specifically, at normal stresses of 1, 3, and 5 MPa, the maximum contact depths recorded are 1.35 mm, 1.69 mm, and 1.94 mm, respectively. Contact area versus shear displacement under 1, 3, and 5 MPa normal loads. Figure 9 presents the frequency distribution characteristic curves of INTERFACE penetration depths at a constant normal stress of 3 MPa across various shear displacements. The curves exhibit several notable characteristics: The peak frequencies for different shear displacements are consistently located within the range of penetration depths, suggesting that the mean (µ) of the frequency distribution remains relatively stable. As the shear displacement increases, the peak value of the frequency curve diminishes, while the curve’s spread widens. This indicates an increase in the maximum aperture of the fracture. Throughout the testing, the area designated as the separation zone, where the penetration depth is negative, expands progressively with greater shear displacement. The contact area experiences a significant reduction when the shear displacement is below 4 mm, with minimal further change observed beyond 6 mm. Specifically, at shear displacements of 2, 4, 6, 8, and 10 mm, the mean penetration depths are 0.086 mm, -0.058 mm, -0.21 mm, -0.24 mm, and − 0.42 mm, respectively. Correspondingly, the standard deviations are 0.186 mm, 0.38 mm, 0.52 mm, 0.60 mm, and 0.73 mm. Penetration distributions of fractures under different shear displacement. Figure 10 illustrates the frequency distribution characteristic curve of INTERFACE penetration depths at a shear displacement of 6 mm. As the normal stress increases, there is a corresponding increase in both the contact area and the maximum penetration depth of the structural plane. While normal stress exerts minimal influence on the overall shape of the frequency curve, it does affect the curve’s position. Specifically, an increase in normal stress shifts the curve to the right, reducing the mean value of penetration depth, while the standard deviation remains relatively unaffected. The relationship between normal stress and contact depth is linear, a finding consistent with the research of Wang et al.36. This linearity is attributed to the geometry of the fracture surface and the direction of shear during the shearing process. The enhancement of normal stress leads to an increased penetration depth at the convexities of the fracture surface, thereby expanding the contact area. Penetration distributions of fractures under different normal load. Figure 11 presents the characteristic distribution of fluid streamlines within the fracture under varying conditions of normal stress and shear displacement at a constant hydraulic gradient (J = 1). The flow is oriented perpendicularly to the direction of shear, resulting in a pronounced grooving effect. This effect arises from the morphological alterations and the separation occurring at the fracture’s rough surfaces. As observed in Fig. 6, the white regions, indicative of separation areas, correspond to the primary distribution of streamlines. It is evident that an increase in normal stress leads to a reduction in the number of streamlines, with a concurrent increase in their density within the dominant flow channel. This suggests that higher normal stresses constrict fluid movement, localizing it within the primary channel. The compressive effect of elevated normal stress confines the fluid, thereby compacting the streamlines within this channel. Moreover, as shear displacement augments, there is an initial increase in the number of streamlines, with the distribution becoming relatively stable once the displacement surpasses 2 mm. Notably, the predominant region of negative apparent inclination angles aligns with the lower section of the flow outlet depicted in Fig. 10. Prior analyses have indicated that these regions with negative apparent inclination angles are associated with enhanced fracture permeability post-shearing. The streamlines in Fig. 11 exhibit a propensity to diverge downward from the intended hydraulic slope direction, which is horizontal to the right. This divergence demonstrates that the distribution of apparent inclination angles significantly influences the seepage behavior of the fracture following shear. The impact of these angles is contingent upon the normal stress and shear displacement conditions to which the fracture is subjected. In general, the influence of local variations in permeability, attributed to the stochastic distribution of fracture asperities, diminishes as the fracture aperture widens. This is because the larger aperture tends to average out the effects of localized asperity distribution on the overall flow pattern. Flow streamlines for different shear displacements under (a) 1 MPa; (b) 3 MPa; and (c) 5 MPa normal load. Figure 12 depicts the relationship between the hydraulic slope (J) and the volumetric flow rate (Q). This figure documents the behavior of fracture flow across a spectrum of normal stresses, with the hydraulic slope varying from 0.1 to 10. In accordance with Eq. 12, the curves plotting volumetric flow against hydraulic slope display distinct nonlinear traits. The collected monitoring data have been fitted using a quadratic model, yielding goodness-of-fit coefficients (R2) that exceed 0.99, indicating a high degree of model accuracy. At lower shear displacements, the curves exhibit steeper slopes, reflecting the subtle initial growth of cracks. Conversely, under conditions of elevated normal stress, a more substantial hydraulic gradient is necessary to achieve an equivalent flow rate. It is noteworthy that in the C5-2 test, the linear coefficients of the J-Q relationship significantly surpass those of the nonlinear terms. This suggests that, under these specific conditions, the flow of water through the fracture can be approximated as linear. This observation will be subjected to further scrutiny in subsequent analyses. Relationships between the hydraulic gradient and volumetric flow rate during the shear process. The Forchheimer equation is extensively utilized to characterize nonlinear seepage behavior. Utilizing Eq. 10, the linear coefficient a and the nonlinear coefficient b were determined. Both coefficients exhibit a decline as shear displacement increases, with a more pronounced rate of decrease observed in the range of 2 to 4 mm compared to 4 to 10 mm. The nonlinear coefficient b is significantly larger, being 5 to 6 orders of magnitude greater than the linear coefficient a, a trend also observed in reference8. It is established that a is inversely related to the permeability coefficient; hence, as normal stress increases, reducing fracture permeability, the positive correlation between a and normal stress is evident in the distinct curves of Fig. 13. The value of b is derived from the quadratic relationship with the cross-sectional area A of the flow. With increasing shear displacement, the contact area within the fracture diminishes, and the aperture expands. Consequently, the flow’s curvature reduces, leading to a decrease in b. Notably, the C5-2 dataset displays pronounced linear behavior, with a values substantially higher and b values considerably lower than those of other groups. This can be correlated with Fig. 7, which indicates a large fracture contact area and poor fracture connectivity, restricting fluid flow to a limited channel, as depicted in Fig. 11, thereby accentuating the linear flow characteristic. Relationships between the forchheimer coefficient and shear displacement. Based on Eq. (14), the relationship between shear displacement and critical flow is plotted (as shown in Fig. 14), and in general these two variables show a negative correlation law. In addition, the critical flow rate exhibits a negative correlation with normal stress, a phenomenon that can be ascribed to the influence of fracture aperture on the variation in nonlinear seepage. As demonstrated by Schrauf and Evans37, variations in flow velocity along the seepage path lead to a loss of fluid inertia, which is a primary cause of nonlinear seepage. The modification of crack openings within the seepage path induces adjustments in water velocity to adhere to the principle of mass conservation. The interplay of fluid acceleration and deceleration causes the relationship between the hydraulic gradient and the volumetric flow rate to diverge from linearity, as discussed in reference23. The nonlinearity of flow within fractures is intricately linked to the aperture field’s distribution. Given the rugged nature of fracture morphology, shear displacement prompts the rough surfaces to slide against each other, leading to an irregular pattern of grooves and protrusions. The flow path is governed by the fracture’s aperture, as illustrated in Fig. 9, where an increase in displacement corresponds to a greater standard deviation ((:sigma:)) of aperture sizes. This signifies a broader range of aperture distributions and a more intricate seepage network. The heterogeneous pore size distribution is conducive to the manifestation of nonlinear flow characteristics. Relationship between the critical volume flow and shear displacement. Transmissivity is a crucial parameter for evaluating the flow characteristics of fluids within fractures. Typically, the relationship between transmissivity and the Reynolds number (Re) is employed to delineate the linear and nonlinear flow regimes. The intrinsic permeability coefficient, denoted as T0, is a constant that is independent of the flow rate and reflects the inherent capacity of the fracture channel to transmit fluid. The apparent transmissivity, T, which is assessable through Eq. 11, is instrumental in evaluating nonlinear flow rates. where T is transmissivity. Figure 15 shows the relationships between transmissivity and Reynolds number. T exhibits a power function relationship with the Reynolds number. The transmissivity curve demonstrates a distinct bimodal behavior; for Re < 0.1, changes in Re have a negligible impact on T, whereas for Re > 0.1, T diminishes precipitously with increasing Re. Furthermore, T augments with increasing shear displacement (Δu), and the velocity of this increase is modulated by the normal stress. Higher normal stresses result in a reduced rate of change for T and a lower ultimate permeability coefficient. The relationship between T and Re was modeled using an exponential function, and the model’s accuracy was confirmed with a mean square deviation of R2 > 0.98, as depicted in Fig. 15. This fitting equation is valuable for ascertaining the intrinsic permeability of the fracture, T0. Relationships between transmissivity and Reynolds number. In Zimmerman’s study, the normalized transmissivity (T/T0) is correlated with both the Reynolds number (Re) and the Forchheimer coefficient (β)10. Figure 16 presents the normalized transmissivity (T/T0) versus Reynolds number (Re) curves for a variety of compressive stress conditions. The data depicted in this figure reveal that the permeability coefficient transitions from linear to nonlinear behavior as the Reynolds number increases. The curves are observed to ascend as the shear displacement grows, with the curve corresponding to Δu = 2 mm exhibiting a notably greater offset compared to those associated with other shear displacements. This observation is in accordance with the research conducted by Wang et al.36. Upon equivalent transformation, a normalized transmissivity of T/T0 = 0.9 is identified as having equivalent physical significance to an efficiency coefficient (E) of 0.1. The Reynolds number at this juncture is designated as the critical Reynolds number (Rec ). The values of Rec derived from this study range from 0.0081 to 0.113, which are consistent with the findings of Javadi et al.33, Rong et al.4, and Wang et al.31, whose calculations spanned a range of 0.001 to 48.73. It is important to note that, in contrast to the laboratory tests, this study’s simulation did not factor in the presence of crushed particles within the cracks, maintained a crack expansion angle of zero, and considered average crack widths that were narrower than those observed in laboratory settings. It is noteworthy that the curve’s position ascends with increasing tangential displacement when T/T0 < 0.9 under a normal stress of 5 MPa, excluding the case where Δu = 2. This positive correlation is observed for T/T0 < 0.6 under a normal stress of 3 MPa; however, no such correlation is evident at a normal stress of 1 MPa. A comparison between the relationships derived from experimental and numerical computational methods reveals that the Forchheimer equation introduces a degree of variability in predicting experimental outcomes within the transition zone from linear to nonlinear flow, approximately in the range 5 < Re < 2010. Although this study only examines a single case, the findings from Fig. 13 clearly indicate the presence of a discernible transition zone. The magnitude of this transition zone is contingent upon the normal stress applied to the fracture; higher normal stresses result in a more confined transition area. Relationships between normalized transmissivity and Reynolds number. In this study, a numerical model of the same scale was constructed using FLAC3D software, with a laboratory-created fracture serving as the template. The dynamic contact characteristics during the shear process were simulated using the INTERFACE module, while the nonlinear seepage characteristics of the open space generated by shear were modeled with COMSOL software. The findings indicate the following: As the shear displacement (Δu) increases, the contact area of the structural surface diminishes progressively, the contact depth intensifies, and the crack aperture widens. Conversely, an increase in normal stress leads to an expansion of the contact area and a reduction in the crack opening. The distribution map of apparent inclination, which is correlated with the shear direction and the micro-slope of the fracture asperities, provides an accurate prediction of the shear damage extent within the fracture. A negative apparent inclination effectively demarcates regions of heightened permeability post-shear, influencing the pattern of flow lines. However, this influence diminishes as the crack opening enlarges. The flow rate and the drop in hydraulic slope display a nonlinear relationship, with the Forchheimer equation adeptly characterizing the curve’s attributes. The linear coefficient and the nonlinear coefficient vary by five to six orders of magnitude. Both coefficients exhibit a negative correlation with shear displacement and a positive correlation with normal stress. The critical flow rate escalates with shear displacement and wanes with increasing normal stress. When the transmissivity surpasses the critical Reynolds number, it transitions from linear to nonlinear behavior. The critical transmissivity (Rec) ascends with greater shear displacement and descends with higher normal stress. Data will be made available on reasonable request to author Yu Zhao (zytyut1@126.com). Chen, L. L., Wang, Z. F. & Wang, Y. Q. Failure analysis and treatments of tunnel entrance collapse due to sustained rainfall: A case study. Water14, 2486. https://doi.org/10.3390/w14162486 (2022). ArticleCASMATH Google Scholar Ma, T., Wang, L., Suorineni, F. T. & Tang, C. Numerical analysis on failure modes and mechanisms of mine pillars under shear loading. Shock Vib.2016, 1–14. https://doi.org/10.1155/2016/6195482 (2016). ArticleMATH Google Scholar Yun, C. et al. Micro-cracking morphology and dynamic fracturing mechanism of natural brittle sandstone containing layer structure under compression. Constr. Build. Mater. (2024). Yun, C., Zhanping, S., Zhiwei, X., Tengtian, Y. & Xiaoxu, T. Failure mechanism and infrared radiation characteristic of hard siltstone induced by stratification effect. J. Mt. Sci. (2024). Zhao, Y. Study on damage-stress loss coupling model of rock and prestressed anchor cable in dry-wet environment. Int. J. Min. Sci. Technol. (2023). Ju, Y. et al. Quantification of continuous evolution of full-field stress associated with shear deformation of faults using three-dimensional printing and phase-shifting methods. Int. J. Rock Mech. Min. Sci.126, 104187. https://doi.org/10.1016/j.ijrmms.2019.104187 (2020). ArticleMATH Google Scholar Zhan-ping, S., Yun, C. & Ze-kun, Z. Y. Teng-tian, Tunnelling performance prediction of cantilever boring machine in sedimentary hard-rock tunnel using deep belief network. J. Mt. Sci. (2023). Rong, G., Yang, J., Cheng, L. & Zhou, C. Laboratory investigation of nonlinear flow characteristics in rough fractures during shear process. J. Hydrol.541, 1385–1394. https://doi.org/10.1016/j.jhydrol.2016.08.043 (2016). ArticleADSMATH Google Scholar Koyama, T., Neretnieks, I. & Jing, L. A numerical study on differences in using Navier–Stokes and Reynolds equations for modeling the fluid flow and particle transport in single rock fractures with shear. Int. J. Rock Mech. Min. Sci.45, 1082–1101. https://doi.org/10.1016/j.ijrmms.2007.11.006 (2008). ArticleMATH Google Scholar Zhang, Z. & Nemcik, J. Fluid flow regimes and nonlinear flow characteristics in deformable rock fractures. J. Hydrol.477, 139–151. https://doi.org/10.1016/j.jhydrol.2012.11.024 (2013). ArticleADSMATH Google Scholar Tzelepis, V., Moutsopoulos, K. N., Papaspyros, J. N. E. & Tsihrintzis, V. A. Experimental investigation of flow behavior in smooth and rough artificial fractures. J. Hydrol.521, 108–118. https://doi.org/10.1016/j.jhydrol.2014.11.054 (2015). ArticleADSMATH Google Scholar Li, B., Liu, R. & Jiang, Y. Influences of hydraulic gradient, surface roughness, intersecting angle, and scale effect on nonlinear flow behavior at single fracture intersections. J. Hydrol.538, 440–453. https://doi.org/10.1016/j.jhydrol.2016.04.053 (2016). ArticleADSMATH Google Scholar Oron, A. P. & Berkowitz, B. Flow in rock fractures: the local cubic law assumption reexamined. Water Resour. Res.34, 2811–2825. https://doi.org/10.1029/98WR02285 (1998). ArticleADSMATH Google Scholar Robert, W., Zimmerman, G. S. & Bodvarsson Hydraulic conductivity of rock fractures. Transp. Porous Med.23https://doi.org/10.1007/BF00145263 (1996). Moutsopoulos, K. N. Exact and approximate analytical solutions for unsteady fully developed turbulent flow in porous media and fractures for time dependent boundary conditions. J. Hydrol.369, 78–89. https://doi.org/10.1016/j.jhydrol.2009.02.025 (2009). ArticleADSMATH Google Scholar Qian, J., Zhan, H., Chen, Z. & Ye, H. Experimental study of solute transport under non-darcian flow in a single fracture. J. Hydrol.399, 246–254. https://doi.org/10.1016/j.jhydrol.2011.01.003 (2011). ArticleADSMATH Google Scholar Cherubini, C., Giasi, C. I. & Pastore, N. Bench scale laboratory tests to analyze non-linear flow in fractured media. Hydrol. Earth Syst. Sci.16, 2511–2522. https://doi.org/10.5194/hess-16-2511-2012 (2012). ArticleADSMATH Google Scholar Rong, G., Hou, D., Yang, J., Cheng, L. & Zhou, C. Experimental study of flow characteristics in non-mated rock fractures considering 3D definition of fracture surfaces. Eng. Geol.220, 152–163. https://doi.org/10.1016/j.enggeo.2017.02.005 (2017). Article Google Scholar Chen, Z., Narayan, S. P., Yang, Z. & Rahman, S. S. An experimental investigation of hydraulic behaviour of fractures and joints in granitic rock. Int. J. Rock Mech. Min. Sci.37, 1061–1071. https://doi.org/10.1016/S1365-1609(00)00039-3 (2000). ArticleMATH Google Scholar Brush, D. J. & Thomson, N. R. Fluid flow in synthetic rough-walled fractures: Navier-Stokes, Stokes, and local cubic law simulations. Water Resour. Res.39https://doi.org/10.1029/2002WR001346 (2003). Gao, M. A new theoretical model for the nonlinear flow in a rough rock fracture under shear. Computers and Geotechnics (2024). Ranjith, P. G. & Darlington, W. Nonlinear single-phase flow in real rock joints. Water Resour. Res.43https://doi.org/10.1029/2006WR005457 (2007). Wang, C. et al. Effects of gas diffusion from fractures to coal matrix on the evolution of coal strains: Experimental observations. Int. J. Coal Geol.162, 74–84. https://doi.org/10.1016/j.coal.2016.05.012 (2016). ArticleADSCASMATH Google Scholar Liu, R., Li, B., Jiang, Y. & Huang, N. Review: Mathematical expressions for estimating equivalent permeability of rock fracture networks. Hydrogeol. J.24, 1623–1649. https://doi.org/10.1007/s10040-016-1441-8 (2016). ArticleADSMATH Google Scholar Yeo, I. W., Freitas, M. H. D. & Zimmerman, R. W. Effect of shear displacement on the aperture and permeability of a rock fracture, (n.d.). Esaki, T., Du, S., Mitani, Y., Ikusada, K. & Jing, L. Development of a shear-¯ow test Apparatus and Determination of Coupled Properties for a Single rock Joint (International Journal of Rock Mechanics and Mining Sciences, 1999). Yin, Q. et al. Hydraulic properties of 3D rough-walled fractures during shearing: An experimental study. J. Hydrol.555, 169–184. https://doi.org/10.1016/j.jhydrol.2017.10.019 (2017). ArticleADSMATH Google Scholar Tse, R. & Cruden, D. M. Estimating joint roughness coefficients. Int. J. Rock. Mech. Min. Sci. Geomech. Abstracts. 16, 303–307. https://doi.org/10.1016/0148-9062(79)90241-9 (1979). Article Google Scholar Zhao, J. Joint surface matching and shear strength part B: JRC-JMC shear strength criterion. Int. J. Rock Mech. Min. Sci.34, 179–185. https://doi.org/10.1016/S0148-9062(96)00063-0 (1997). ArticleMATH Google Scholar Park, J. W. & Song, J. J. Numerical method for the determination of contact areas of a rock joint under normal and shear loads. Int. J. Rock Mech. Min. Sci.58, 8–22. https://doi.org/10.1016/j.ijrmms.2012.10.001 (2013). ArticleMATH Google Scholar Liu, X., Zhu, W., Yu, Q., Chen, S. & Guan, K. Estimating the joint roughness coefficient of rock joints from translational overlapping statistical parameters. Rock. Mech. Rock. Eng.52, 753–769. https://doi.org/10.1007/s00603-018-1643-6 (2019). ArticleADSMATH Google Scholar Xiong, X., Li, B., Jiang, Y., Koyama, T. & Zhang, C. Experimental and numerical study of the geometrical and hydraulic characteristics of a single rock fracture during shear. Int. J. Rock Mech. Min. Sci.48, 1292–1302. https://doi.org/10.1016/j.ijrmms.2011.09.009 (2011). ArticleMATH Google Scholar Xie, L. Z., Gao, C., Ren, L. & Li, C. B. Numerical investigation of geometrical and hydraulic properties in a single rock fracture during shear displacement with the Navier–Stokes equations. Environ. Earth Sci.73, 7061–7074. https://doi.org/10.1007/s12665-015-4256-3 (2015). ArticleADSMATH Google Scholar Bordier, C. & Zimmer, D. Drainage equations and non-darcian modelling in coarse porous media or geosynthetic materials. J. Hydrol.228, 174–187. https://doi.org/10.1016/S0022-1694(00)00151-7 (2000). ArticleADSMATH Google Scholar Zeng, Z. & Grigg, R. A criterion for non-darcy flow in porous media. Transp. Porous Med.63, 57–69. https://doi.org/10.1007/s11242-005-2720-3 (2006). ArticleCASMATH Google Scholar Wang, C. et al. Experimental study of the nonlinear flow characteristics of fluid in 3D rough-walled fractures during shear process. Rock. Mech. Rock. Eng.53, 2581–2604. https://doi.org/10.1007/s00603-020-02068-5 (2020). ArticleADSMATH Google Scholar Schrauf, T. W. & Evans, D. D. Laboratory studies of gas flow through a single natural fracture. Water Resour. Res.22, 1038–1050. https://doi.org/10.1029/WR022i007p01038 (1986). ArticleADSMATH Google Scholar Download references This research was supported by National Natural Science Foundation of China (No. 52264006, No. 52064006, and No. 52164001), the Guizhou Provincial Science and Technology Foundation (No. GCC[2022]005 − 1), Specialized Research Funds of Guizhou University (Grant No. 201903, No. 202011). College of Civil Engineering, Guizhou University, Huaxi District, Guiyang, 550025, Guizhou, China Tao Wei, Chaolin Wang, Yu Zhao, Mingxuan Shen & Zhongqian Chen You can also search for this author in PubMedGoogle Scholar You can also search for this author in PubMedGoogle Scholar You can also search for this author in PubMedGoogle Scholar You can also search for this author in PubMedGoogle Scholar You can also search for this author in PubMedGoogle Scholar “Tao Wei, Chaolin Wang, Yu Zhao, Mingxuan Shen, and Zhongqian Chen wrote the main manuscript text and Zhongqian Chen prepared Figs. 1-4. All authors reviewed the manuscript.” Correspondence to Yu Zhao. The authors declare no competing interests. Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. 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The special was filmed three days before Lively filed a lawsuit against Justin Baldoni, alleging he had sexually harassed her A new Netflix comedy roast special includes a joke that targets Blake Lively, filmed before the actress filed a lawsuit against her It Ends With Us co-star Justin Baldoni for an alleged smear campaign. Torching 2024: A Roast of the Year sees comedians reflect on the biggest pop culture stories of the year, and was released on the streaming platform yesterday (December 27). One joke made about Lively has garnered particular attention. Comedian Hannah Berner begins to tell the audience: “The word c*** was trending this year,” before adding: “I don’t think Blake Lively was that bad.” Netflix and Berner have since confirmed that the special was filmed on December 17, three days before Lively filed a sexual harassment and retaliation complaint against her former co-star and director on December 20. As reported by TMZ, the suit claimed that Baldoni exhibited behaviour that caused Lively “severe emotional distress”. Taking to her Instagram story today (December 28), Berner wrote: “My joke in the Netflix roast was filmed before news of the lawsuit. To be 100 percent clear, I support Blake xoxo” Blake Lively called c-word in horribly timed Netflix comedy special pic.twitter.com/6KSltOTpYO — Page Six (@PageSix) December 27, 2024
The suit claims Baldoni sexually harassed Lively on the set of the film. She states that a meeting was held between the two parties and their lawyers, as well as Lively’s husband Ryan Reynolds, to address the problems. It is said that the meeting included a number of demands made by Lively, including “no more showing nude videos or images of women to Blake, no more mention of Baldoni’s alleged previous ‘pornography addiction,’ no more discussions about sexual conquests in front of Blake and others, no further mentions of cast and crew’s genitalia, no more inquiries about Blake’s weight, and no further mention of Blake’s dead father.” It added that she demanded “no more adding of sex scenes, oral sex or on camera climaxing by BL outside the scope of the script BL approved when signing onto the project”, as reported by TMZ. Lively said in a statement to The New York Times, “I hope that my legal action helps pull back the curtain on these sinister retaliatory tactics to harm people who speak up about misconduct and helps protect others who may be targeted.” Baldoni’s lawyer Bryan Freeman told TMZ that he believed the suit had been filed to “fix” Lively’s “negative reputation”, describing her allegations as “false, outrageous and intentionally salacious with an intent to publicly hurt”. Freeman added that Lively “threatened to not [show] up to set, threatened to not promote the film, ultimately leading to its demise during release”.
Justin Baldoni and Blake Lively are seen on the set of ‘It Ends with Us’ on January 12, 2024 in Jersey City, New Jersey. (Photo by Jose Perez/Bauer-Griffin/GC Images)
Connecticut is one of 11 states including Louisiana, Mississippi and Wyoming, that share the badge of shame for allowing vehicle passengers to swig a beer. Making a beer run? If you’re not behind the wheel, there’s no law against cracking open that six-pack before you make it home. Connecticut is one of the few states where motor vehicle passengers can, if they so choose, drink alcohol. The lack of prohibition of open alcohol containers in motor vehicles has and continues to cost Connecticut millions of dollars in federal funds every year, and though there have been numerous attempts over the course of decades to change that, to date, all have failed. Advertisement Article continues below this ad Here’s everything to know about Connecticut’s open container laws: Yes. Connecticut is one of only 11 states that allow passengers in motor vehicles to drink alcohol from open containers. The law specifically allows one open container for each passenger, so long as the driver doesn’t drink. The other states with no prohibition against open alcohol containers in the passenger areas of the vehicle are Alaska, Arkansas, Delaware, Louisiana, Mississippi, Missouri, Tennessee, Virginia, West Virginia and Wyoming. Advertisement Article continues below this ad Connecticut does prohibit open alcohol containers in the driver’s seat. In fact, it is illegal to drink alcohol while operating a motor vehicle on a public highway, in a parking lot for 10 or more cars or on school property, according to the state Office of Legislative Research. If you are driving with no passengers, Connecticut law prohibits any open alcohol containers in the car, except if they are in a locked container. There has been decades of discussion in the state legislature on the topic, and the majority of arguments in favor of prohibiting passengers from drinking alcohol is the number of fatalities related to drunken driving. Advertisement Article continues below this ad Back in 1999, then-Groton state Rep. Lenny Winkler argued in the General Assembly in favor of an open container law. “I think it sets a bad precedent that we don't believe in drinking and driving yet it's perfectly alright for somebody to stop at a package store, pick up a six pack of beer, open the can of beer and drive down the street,” she said. “I think we should address that issue and I hope that next year we can come back and improve what's here.” That argument, or a version of it, has been made nearly every year since then and is often backed by the state Department of Transportation among other officials. One argument against open container laws is that they are often selectively enforced against working-class individuals and are used as an excuse for unnecessary traffic stops. Advertisement Article continues below this ad “It’s another racist law used almost universally against the poor, it’s usually an excuse for police to stop and investigate,” Niki Ganong, author of “The Field Guide To Drinking In America,” told Eater. Connecticut, like every state, gets millions in federal funding every year for highway maintenance. But federal law mandates that a portion of those highway maintenance funds may only be used for “alcohol-impaired driving countermeasures, enforcement of drunk driving laws, or the state's hazard elimination program,” if a state does not prohibit passengers from drinking alcohol. Advertisement Article continues below this ad That means that 2.5 percent of Connecticut’s federal highway repair dollars must be diverted away from highway repair. Connecticut’s penalty amounts to 2.5 percent of the $521 million in the two largest programs, including a block grant. As of 2023, $164 million in federal funds has been diverted since 2001, when the federal law was enacted. It’s unknown if the law will ever change, but it’s a relative certainty that there will be attempts to do so in upcoming legislative sessions. Advertisement Article continues below this ad The most recent such attempt was in the 2023 legislative session, when a provision to prohibit open alcohol containers was included in a larger bill. That provision was ultimately removed from the final version of the measure before it passed. Jordan Nathaniel Fenster is a reporter with CT Insider. He’s worked as a journalist covering politics, cannabis, public health, social justice and more for 25 years. Jordan’s work has appeared in The New York Times and USA Today in addition to multiple regional and local newspapers. He is an award-winning reporter, podcaster and children’s book author. He serves as senior enterprise reporter and lives in Stamford with his dog, cat and three daughters. He can be reached at jordan.fenster@hearstmediact.com. About Contact Services Account
Jupiter, Solana’s largest decentralized exchange (DEX) aggregator, has announced an exceptional token airdrop for January 2025. Dubbed “Jupuary,” this project will provide qualified participants 700 million JUP tokens—with an estimated worth of $590 million. BREAKING: Jupiter has released the JUPuary Airdrop Allocation Overview 700M $JUP will be airdropped next month ($590M+) pic.twitter.com/4GvUrPCznK — Cloudz (@FamousCloudzz) December 26, 2024
The airdrop seeks to honor active users and community volunteers while encouraging involvement inside the platform’s ecosystem. With over 2.3 million wallets expected to qualify according to their trading activity over the past year, this airdrop is poised to be among the biggest in Solana’s history, unlike preceding promotions. Along with members of Jupiter’s active community, lovingly referred to as “Carrots and Good Cats,” the Jupuary airdrop will center on two primary groups: active traders and stakers. This double strategy guarantees equitable distribution of benefits among platform users as well as those helping the community to develop. Emphasizing long-term activity, eligibility conditions inspire consistent interaction with Jupiter’s features, especially those related to trade and staking. Jupiter carried out a similarly massive January 2024 airdrop in the past, handing 1 billion JUP tokens to about a million wallets. That project confirmed Jupiter’s centrality in the Solana ecosystem and greatly enlarged its user base. Following this custom, the forthcoming Jupuary airdrop presents Jupiter as a leader in community-centric tokenomics. Furthermore, Jupiter’s constant attention on community involvement and creative reward systems highlights its will to propel long-term environmental development. Jupiter, meanwhile, has been aggressive in offering extra incentives to its patrons. For example, the site just started the Active Staking Rewards program, which distributes $60 million to honor Solana users that engage in staking events. This action complements Jupiter’s continuous attempts to improve its ecosystem and keep user loyalty. Furthermore, as we previously reported, last July’s addition of the SOL Index to the Jup Research Forum has given Solana investors an improved diversification tool, therefore confirming Jupiter’s importance in the blockchain space. Meanwhile, JUP is swapped hands at about $0.8068 at the time of writing, down 2.74% over the last 24 hours and by 12.98% over the last 7 days. Muhammad Syofri Ardiyanto is an active forex and crypto trader who has been diligently writing the latest news related to the digital asset sector for the past six years. He enjoys maintaining a balance between investing, playing music, and observing how the world evolves. Business Email: info@crypto-news-flash.com Phone: +49 160 92211628 About us Contact us Editorial Guidelines Terms of Use Legals Data protection policy Cookie Policy *= Affiliate-Link Type above and press Enter to search. Press Esc to cancel.
North Carolina football is appearing in its sixth consecutive bowl game on Saturday, the first time the Tar Heels have enjoyed such a streak since 1992-98. But the coach who led both of those bowl game streaks, Mack Brown, will not be leading his team at the Fenway Bowl against UConn on Saturday. Three days prior to the Tar Heels’ regular season finale against NC State, UNC announced it was parting ways with Brown and wouldn’t bring him back for the 2025 season. It was the closing chapter to Brown’s long history with the Tar Heels program, as the 73-year-old spent 16 years of his 35-year coaching career in Chapel Hill across two separate stints. The decision came after UNC dropped four consecutive games from Sept. 21 through Oct. 12, including one to James Madison. REQUIRED READING:‘It’s time to go’: Everything UNC football coach Mack Brown said after final game Run game coordinator and tight ends coach Freddie Kitchens will serve as UNC’s interim coach vs. UConn on Saturday. Here’s what you need to know on why Brown was fired at UNC, including a look at how the Tar Heels fared under him and more: After an underwhelming 6-6 regular season, UNC announced on Nov. 26 that it wasn’t bringing Brown back for the 2025 season — which came shortly after Brown had expressed interest in returning the following year. “Mack Brown has won more games than any football coach in UNC history, and we deeply appreciate all that he has done for Carolina football and our university,” UNC athletic director Bubba Cunningham in a statement. “Over the last six seasons — his second campaign in Chapel Hill — he has coached our team to six bowl berths, including an Orange Bowl, while mentoring 18 NFL draft picks. “Coach Brown has led the Carolina football program back into the national conversation as we improved the program’s facilities, significantly increased the size of the staff, invested in salaries and bolstered our nutrition and strength and conditioning programs. He also has been a dedicated fundraiser, strengthening the football endowment while also supporting our other sports programs. “We thank Coach Brown for his dedication to Carolina, and wish him, Sally and their family all the best.” While the Tar Heels had overall success in his six years of his second tenure in Chapel Hill — UNC finished with four winning seasons — the program came up short in the postseason under Brown. In the five bowl games appearances under Brown, UNC had only won one game: the 2019 Military Bowl. As previously reported by The Fayetteville Observer, Brown told reporters following the NC State loss that he had hoped to discuss his future at UNC with the Tar Heels administration — including Cunningham — after the game. “As far as the he said, she said … I don’t need any of that. There were three people that talked about this. It was me and John Preyer, who’s our chairman for the board of trustees, and athletics director (Bubba) Cunningham,” Brown said. “I never talked to the (UNC) chancellor, didn’t have one conversation with him. And all I wanted to do was wait until the end of the year. They wanted me to retire on Monday before the State game. … I didn’t want to break their hearts on Monday. I said, ‘No, I won’t do that.’ Then, they wanted me to do it on Friday. I sure wasn’t going to do it on Friday before the game.” Brown continued to speak openly following UNC’s 35-30 loss to in-state rival NC State on Nov. 30 about his future, even saying he agrees with the decision by the administration for a new change at top. “I agree with the administration that we need a change of leadership at the top. I just wanted it to happen after the season was over,” Brown said. “These poor kids have had so much turmoil in their lives. I think the administration’s into finding a football coach and I’m into saving lives.” He added: “I think it’s time to go. I always said for God to tell me when it’s time to go” Here’s a year-by-year breakdown of how the Tar Heels fared under Brown during his second tenure in Chapel Hill: Postseason result in parentheses * Note: Mack Brown led UNC to the Fenway Bowl but won’t coach in the game. Former New England Patriots head coach Bill Belichick was hired as Brown’s replacement at UNC on Dec. 11. The six-time Super Bowl winning coach is the oldest coach in college football at 72-years-old.
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