Power Law Relationship Research Articles

Measuring Precipitation via Microwave Bands with a High-Accuracy Setup

The urgent need for timely and accurate precipitation estimations in the face of ongoing climate change and the increasing frequency and/or intensity of extreme weather events underscores the necessity for innovative approaches. Recently, several studies have focused on estimating the precipitation rate through induced attenuation of radio frequency (RF) signals, which are abundant in modern communication systems. Most research has concentrated on frequencies exceeding 10 GHz, as attenuation at lower frequencies is minimal, posing measurement challenges. This study aims to confront this limitation by introducing a high-precision experimental setup capable of detecting this subtle attenuation at frequencies under 10 GHz. The setup includes a transmitter and receiver optimized for operation at 2.07, 4.63, and 6.22 GHz, where minimal worldwide research exists. A power resolution below 10−5 dB in preliminary measurements demonstrated its effectiveness in quantifying signal attenuation due to precipitation across the specified frequencies. Moreover, a strong power law relationship was observed between signal attenuation and precipitation rate for all three frequencies, while, as expected, the higher the frequency, the more pronounced the signal attenuation was.

Investigation of fracture performance of asphalt mixtures considering size effect law and equivalent crack propagation law

The integration of the Size Effect Law (SEL) and the equivalent Linear Elastic Fracture Mechanics (LEFM) in characterizing the fracture behavior of asphalt mixtures has received limited attention. This study presents a preliminary exploration into the application of equivalent LEFM on the fracture characteristics of two asphalt mixtures, AC10 and AC16, accounting for variations in specimen size. Semi-circular Bending (SCB) tests were conducted on specimens with four different diameters (D = 76 mm, 100 mm, 125 mm, and 150 mm) and three notch-to-radius ratios (α = 0.2, 0.4, and 0.6) at a temperature of −10 °C. The equivalent crack propagation (ECP) length, crack growth resistance, and the size of the Fracture Process Zone (FPZ) were determined and subjected to analysis. The findings revealed a size effect on the ECP length, crack growth resistance, and FPZ size, with an increase in specimen size leading to a corresponding increase in these parameters. Conversely, an increase in α resulted in a decrease in all three types of data. A power law relationship was established between the ECP length and crack growth resistance. It was observed that AC16 demonstrated superior fracture resistance compared to AC10, particularly in terms of crack growth resistance. The initial notch length, ECP length, and FPZ size were found to be of the same order of magnitude, suggesting that the equivalent LEFM can produce more accurate fracture results under low temperatures than the traditional LEFM.

Predictive control of pore architecture in ice-templated scaffolds via heat flux density modulation

Replicating the intricate architecture of native tissues remains a significant challenge in tissue engineering. Ice-templated biomimetic scaffolds possess controlled porosity that conveniently resembles the native parenchyma of many tissues. In this study, we investigate the relationship between the porous architecture of lyophilised collagen scaffolds and key processing parameters during production. We establish a predictive model that correlates specific lyophilisation conditions with the resulting pore sizes. Systematic variations in the freeze-drying conditions resulted in scaffolds with average pore sizes ranging from 46 μm to 251 μm, effectively matching the length scale of extracellular matrix features found in native tissues. We introduce the concept of heat flux density (HFD) at equilibrium as a metric for quantifying latent heat extraction efficiency during the freezing process. Our findings reveal a power law relationship between HFD at equilibrium and pore size, with an exponent of −0.44. This approach provides a non-destructive and non-intrusive method for precisely controlling pore architecture, advancing the potential for creating scaffolds that closely emulate the complex structures of native tissues.

Penetration of jet piles on submerged granular beds

The study examines the dynamics of jet pile penetration into submerged granular beds through laboratory experiments with the jet pile positioned atop the granular bed. It examines how varying water jet velocities affect penetration depth across different pile diameters and granular media sizes. Results show that high-velocity water jets locally fluidize particles around the pile, reducing inter-particle resistance within the bed, which, in turn, cannot support the self-weight of the pile, allowing smoother penetration. The onset of fluidization and pile penetration, marked by a critical jet velocity, increases with bed depth. Jet pile penetration is governed by a balance of forces: water jet force (FJet), pile self-weight (Fsw), buoyancy (FB), and resistance from the granular bed (FR). A power law relationship is proposed to predict penetration depth across different grain and pile sizes, providing a predictive model for jet pile penetration depth. This scaling law, validated with another experimental study, demonstrates consistent accuracy.

A Parameter Study of 1D Atmospheric Models of Pulsating AGB Stars

Using the atmospheric pulsation code written by George Bowen, we have performed a parameter study examining the effects of modifying various parameters of models of oxygen-rich AGB atmospheres pulsating in the fundamental and first-overtone modes. For each pulsation mode, we have examined the effects of adjusting the dust condensation temperature, dust condensation temperature range, pulsation amplitude, dust opacity, and metallicity. Our model grids are generated with the constraint that their luminosities are chosen to span the range of observed mass loss rates at a chosen mass. The dust condensation temperature, pulsation amplitude, and dust opacity have strong effects on the ultimate location and shape of the final model grids in the mass luminosity plane. The mass loss rate evolution of the fundamental and first-overtone mode models show a significant difference in behavior. While the fundamental mode models exhibit the typically assumed power–law relation with mass and luminosity, the first-overtone mode models show significant non-power law behavior at observed mass loss rates. Effectively, models in the first-overtone mode require somewhat higher luminosities to reach the same mass loss rates seen in fundamental mode models of the same mass, consistent with observed AGB stars.

Dynamic in-situ CT imaging to study meso-structure evolution and fracture mechanism of shale during thermal-mechanical coupling condition

Temperature has a significant impact on the occurrence characteristics and flow properties of oil and gas in shale reservoirs at in-situ conditions. Under thermal–mechanical coupling conditions, the macroscopic deformation instability characteristics and the evolution of the internal microstructure of shale are of great importance for the exploitation of shale oil and gas. However, most studies on the macroscopic and microscopic characteristics of shale only analyze the deformation and instability mechanisms of shale from observations of the post-failure microscopic structures. This paper employs a self-developed THM-CT coupling test system to study the macroscopic deformation characteristics of shale under triaxial compression at real-time temperatures, and simultaneously uses in-situ CT imaging technology to characterize the internal microstructure of shale under different stress levels. Real-time CT porosity obtained via in-situ CT imaging technology represents the mesoscopic structural parameters, together with macroscopic deformation characteristics, delineate the four stages of the entire deformation process in shale: initial compression, linear elastic deformation, yielding deformation, and post-failure. The deformation after peak-stress (σf) in shale is 1–3 times that before peak-stress (σf). The dissolution and softening of clay minerals within the internal micro-lamination of shale, along with the weakening of the internal structure, result in a decline in mechanical parameters such as stress strength (σf) and elastic modulus (E) with increasing temperature. The reconstruction of three-dimensional μCT digital volumes further reconstructs the internal fracture spatial structure under different stress levels during the deformation process, precisely characterizing the dynamic evolution of internal fracture nucleation, expansion, and coalescence during the whole test process. The failure characteristics of shales display notable heterogeneity and anisotropy. Internally, fractures experience a sequence of initiation, formation of vertical and oblique main fractures along the axial direction, and crossing connections between fractures. During test process, multiple occurrences of horizontal secondary micro-fractures extend along weakly cemented lamination, playing a connecting role between the main fractures. Importantly, a real-time quantitative relationship between the macroscopic and microscopic mechanics of rock has been established by linking the mesoscopic damage factor with the applied stress. It was found that the damage factor increases according to a power-law relationship with stress in the yield deformation phase. The variation in the mesoscopic damage factor serves as an intuitive index reflecting the systematic failure of rock, providing an early warning for the impending failure of shale.

A framework for generating rating curves in Mahanadi River using hydrodynamic model and radar altimetry data

ABSTRACT The limited availability of in-situ data has drawn attention towards using remote sensing techniques to monitor river flow. Radar altimetry data has been used to generate stage-discharge rating curves through power-law relations and empirical methods. However, evaluating hydrodynamic models for rating curve generation using multi-mission altimetry data in data-scarce regions is lacking. We used altimetry data (Jason 2, Jason 3, SARAL/AltiKa, Sentinel 3A, and Sentinel 3B) over the Mahanadi River to evaluate rating curves at virtual stations. The HEC-RAS hydrodynamic model was set up, identifying seven virtual stations along the Mahanadi River from Boudh to Mundali Barrage. Statistical evaluation of ‘water level’ (RMSE 0.27-0.88 m) and ‘discharge’ (KGE 0.52 to 0.88) components of the generated rating curves showed significant agreement with radar altimetry data. These rating curves at virtual stations offer a cost-effective tool for monitoring river flows at additional locations.

Revealing the synergistic contribution of PWV and CAPE to extreme precipitation throughout China

Precipitable water vapor (PWV) and convective available potential energy (CAPE) are two key variables affecting the formation and persistence of rainfall. Most previous studies only independently and qualitatively analyzed the long-term relationship between PWV/CAPE and extreme precipitation, but their synergistic contribution of PWV and CAPE to extreme precipitation (EP) was rarely investigated. Therefore, a novel model named PCEP (comprising PWV, CAPE, and EP), that integrates Global Navigation Satellite System (GNSS)-derived PWV and the fifth-generation ECMWF reanalysis (ERA5)-derived CAPE, is proposed in this study, where the joint contribution of PWV and CAPE on EP was investigated. Precipitation data is derived from the China Meteorological Administration (CMA). The daily PWV, CAPE and precipitation from 219 GNSS collocated meteorological stations in China from 2011 to 2018 were collected to perform the PCEP model. The tendency and periodic information of the three variables were revealed based on the multichannel singular spectral analysis and Lomb-scale methods. Moreover, the power-law relationships of PWV to loge(EP) varied with the seasons in China, while the linear relationships existed between loge(CAPE) and loge(EP). Finally, to solve the collinearity issue among PWV, CAPE and EP that occurred on the regional scale, the partial least square (PLS) method was first introduced to investigate their relationships on the seasonal scale. The PLS method found that PWV and CAPE also complement each other to EP on the seasonal scale, on the basis of regional complementarity. Additionally, the qualitative relationship between PWV, CAPE and the frequency of EP was elucidated. These results showed that the close relationships between high PWV and CAPE and the intensity and frequency of EP events on the annual and seasonal scales throughout China.

Three-dimensional clustering characteristics of large-Stokes-number dilute sprays interacting with turbulent swirling co-flows

Three-dimensional (3-D) clustering characteristics of large-Stokes-number sprays interacting with turbulent swirling co-flows are investigated experimentally. The astigmatic interferometric particle imaging (AIPI) technique is used for simultaneous measurement of the spray droplets position in 3-D space and their corresponding diameter. The Stokes number estimated based on the Kolmogorov time scale varies from 34 to 142. The results show that the degree of droplet clustering plateaus at about 0.4 and at large Stokes numbers. It is obtained that the mean length scale of the clusters normalized by the Kolmogorov length scale follows a power-law relation, and the mean void length scale normalized by the integral length scale plateaus at about 1.5 and at large Stokes numbers. It is shown that the ratio of the number density of the droplets residing within the clusters to the global number density increases with increasing Stokes number and is about 8 for the largest Stokes number examined in this study. The joint characteristics of cluster's normalized volume and the mean diameter of droplets residing within the clusters show that small-volume clusters accommodate droplets with a relatively broad range of diameters. However, large clusters carry droplets with the most probable diameter. The developed AIPI technique in the present study and the corresponding spray characteristics are of importance for engineering applications that aim to understand the 3-D clustering characteristics of large-Stokes-number droplets sprayed into turbulent swirling co-flows.

Nanoscale mapping of local intrinsic strain-induced anomalous bandgap variations in WSe2 using selective-wavelength scanning photoconductivity microscopy

Nanoscale defects can locally tailor the optoelectronic properties of two-dimensional materials such as bandgap. However, it is still challenging to directly map and analyze the defect-induced bandgap variations in a quantitative manner. Here, we report the nanoscale mapping of local intrinsic strain-induced anomalous bandgap variations in as-grown WSe2 by using a selective-wavelength scanning photoconductivity microscopy. In this method, a conducting nanoprobe is utilized to map the spatial distributions of strain, sheet-conductance, and charge trap density (Neff) of epitaxially-grown WSe2 on sapphire while illuminating monochromatic light of selective wavelengths. Under un-illuminated conditions, the maps showed WSe2 domain structures with boundaries having slightly lower sheet-conductance and higher Neff than those in domains, presumably due to low misorientation angles between adjacent epitaxially-grown domains. By measuring wavelength-dependent photoconductance maps and fitting each pixel value of the maps, we could successfully obtain the map of local bandgap. The map clearly showed bandgap variations inside domains as well as rather low bandgaps at boundaries. By comparing with local strain map, we found that tensile strain effectively reduced bandgap following two different power-law relationships. Such anomalous bandgap variations in WSe2 could be explained by strain-induced weakening of d-orbital couplings. Furthermore, in a monolayer-bilayer WSe2 interface, bilayer WSe2 exhibited lower bandgap than the underlying monolayer WSe2, while interfacial boundaries exhibited the strain-induced bandgap values in between those of monolayer and bilayer WSe2. Since our method allows us to directly map the intrinsic strain-induced bandgap variations with a nanoscale resolution down to tens-of-nm, it can be a powerful tool for basic research and practical applications of optoelectronic devices based on two-dimensional materials.

An Analytical Study of Tsunamis Generated by Submarine Landslides

In this work, the problem of tsunamis generated by underwater landslides is addressed. Two new solutions are derived in the framework of the linear shallow water equations and linear potential wave theory, respectively. Those solutions are analytical (1 + 1D) and another is semi-analytical (2 + 1D). The 1 + 1D model considers a solid body sliding over a sloping beach at a constant speed, and the 2 + 1D model considers a solid landslide that moves at a constant velocity on a flat bottom. The solution 1 + 1D is checked numerically using a different finite scheme. The 2 + 1D model examines the kinematic and geometric features of the landslide at a constant ocean depth and its influence on the generation of tsunamis. Landslide geometry significantly influences run-up height. Our results reveal a power law relationship between normalized run-up and landslide velocity within a realistic range and a negative power law for the landslide length–thickness. Additionally, a critical aspect ratio between the length and width of the sliding body is identified, which enhances the tsunamigenic process. Finally, the results show that the landslide shape does not have a decisive influence on the pattern of tsunami wave generation and propagation.

Characteristics and development of steepland gullies in the dry valleys of Southwest China.

In semi-arid and arid areas, gully erosion is one of the most destructive forms of erosion and causes serious land degradation and resource destruction. Steepland gullies are widely distributed in the dry valleys of southwest China, and their formation is one of the main causes of soil erosion and the destruction of sloping farmland in the region. Previous research on the development of steepland gullies is limited, and further study is needed. In this study, 11 steepland gullies at various stages of development located in Guobu Village, Xide County, Liangshan, Sichuan Province, were selected for investigation using a digital elevation model (DEM) derived from unmanned aerial vehicle data as the primary data source. These data had a spatial resolution of 0.1 m. Fundamental parameters such as the gully length, width, depth, area, and volume were extracted from the remote sensing data. Other characteristic parameters, including the coefficient of main and tributary gullies, vertical gradient, gully elongation, and gully openness, were also investigated. The results indicate a significant linear positive correlation between the gully's degree of openness and elongation as the gully's length, width, and depth increase. Furthermore, the vertical gradient and coefficient of main and tributary gullies exhibit power-law relationships with these gully dimensions. The development of steepland gullies was divided into infancy, youth, maturity, and old age based on the use of the gully length as an ergodic indicator in space-for-time substitution. The morphological characteristics of these different stages were quantitatively analyzed, and a proposed mechanism for how the evolution of the gullies proceeds was developed. An empirical model of volume-length erosion was established to investigate the development process of steepland gullies in the dry valleys. It has been observed that the development law of steepland gullies is essentially consistent with the very active stage of typical gully formation, suggesting that steepland gully may represent the initial stage of gully development. The results show that these steepland gullies have their origin in high-intensity rainfall events that are accompanied by the formation of steps and drop water. The effects of gravity erosion and hydraulic erosion then cause the gullies to expand rapidly, forming gullies with a large head and a small tail before they gradually stabilize. The results of this study will help with the understanding of the formation and evolution of steepland gullies and will be of practical significance for the prevention of gully erosion and the protection of sloping farmland in the dry valley region of southwest China.

Testing kinematic distances under a realistic Galactic potential. Investigating systematic errors in the kinematic distance method arising from a non-axisymmetric potential

Obtaining reliable distance estimates to gas clouds within the Milky Way is challenging in the absence of certain tracers. The kinematic distance approach has been used as an alternative, and it is derived from the assumption of circular trajectories around the Galactic centre. Consequently, significant errors are expected in regions where gas flow deviates from purely circular motions. We aim to quantify the systematic errors that arise from the kinematic distance method in the presence of a Galactic potential that is non-axisymmetric. We investigated how these errors differ in certain regions of the Galaxy and how they relate to the underlying dynamics. We performed 2D isothermal hydrodynamical simulation of the gas disk with the moving-mesh code Arepo adding the capability of using an external potential provided by the Agama library for galactic dynamics. We introduced a new analytic potential of the Milky Way, taking elements from existing models and adjusting parameters to match recent observational constraints. In line with results of previous studies, we report significant errors in the kinematic distance estimate for gas close to the Sun along sight lines towards the Galactic centre and anti-centre and associated with the Galactic bar. Kinematic distance errors are low within the spiral arms, as gas resides close to local potential minima and the resulting line-of-sight velocity is similar to what is expected for an axisymmetric potential. Interarm regions exhibit large deviations at any given Galactic radius, and this is caused by the gas being sped up or slowed down as it travels into or out of spiral arms. In addition, we identify ‘zones of avoidance’ in the $lv$-diagram, where the kinematic distance method is particularly unreliable and should only be used with caution and we find a power-law relation between the kinematic distance error and the deviation of the projected line-of-sight velocity from circular motion.

Modulation of Luttinger liquid behavior by multi-channel electron transport in aligned multi-walled carbon nanotube arrays

In the case of one-dimensional systems, Luttinger liquid states are typically anticipated, which have previously been identified primarily in nanoscopic devices fabricated from isolated bundles of single- or multi-walled carbon nanotubes. In this study, the electrical transport properties of aligned multi-walled carbon nanotube arrays were investigated. The resistance of both aligned arrays and those covered with metal Mo exhibits a strong dependence on temperature, demonstrating a power-law relationship of R∼T–α below 100 K. The Luttinger liquid behavior was modulated by tuning the electron-transport channels via alerting the number of walls that contribute to the conductance within the multi-walled carbon nanotubes. The exponent α, derived theoretically as a parameter that depends on the number of conducting channels, exhibits minimal variation across the arrays and declines rapidly with the tubular structure opening due to the solid-solid reaction between the magnetron-sputtered molybdenum and the carbon atoms.

Anomalous scaling of branching tidal networks in global coastal wetlands and mudflats

Branching networks are key elements in natural landscapes and have attracted sustained research interest across the geosciences and numerous intersecting fields. The prevailing consensus has long held that branching networks are optimized and exhibit fractal properties adhering to power-law scaling relationships. However, tidal networks in coastal wetlands and mudflats exhibit scaling properties that defy conventional power-law descriptions, presenting a longstanding enigma. Here we show that the observed atypical scaling represents a universal deviation from an ideal fractal branching network capable of fully occupying the available space. Using satellite imagery of tidal networks from diverse global locations, we identified an inherent “laziness” in this deviation—where the increased ease of channel formation paradoxically decreases the space-filling efficiency of the network. We developed a theoretical model that reproduces the ideal fractal branching network and the laziness phenomenon. The model suggests that branching networks can emerge under a localized competition principle without adhering to conventionally assumed optimization-driven processes. These results reveal the dual nature of branching networks, where “laziness” complements the well-known optimization process. This property provides more flexible strategies for controlling tidal network morphogenesis, with implications for coastal management, wetland restoration, and studies in fluvial and planetary systems.

A computer simulation study of a chiral active ring polymer.

We investigate a ring polymer under the influence of chiral active Brownian forces in two dimensions using coarse-grained computer simulations. We observe a non-monotonic behavior of the radius of gyration of an active Brownian ring as a function of active force. However, the shrinkage of the ring in the intermediate strength of active forces becomes more pronounced in the presence of chiral active forces, and the shrinkage is monotonic at a given activity level as a function of the angular frequency controlling the direction of the active force. The distribution of radius of gyration, inter-monomer distance, and radial distribution suggest that the monomers come close to each other, eventually leading to the shrinkage of the ring. Moreover, the bond-correlation suggests that the chirality introduces a local folding of the monomers. Furthermore, using the diameter correlation function, we show that the ring performs tank-treading motion with a frequency following power-law relation with active force with exponent 3/2. The mean squared displacement of the monomers further assists the tank-treading dynamics by exhibiting oscillatory behavior.

A Monte Carlo study on a 3-dimensional comb polymer translocation through a nanopore driven by an electric field

Abstract A lattice Monte Carlo simulation study of the translocation of comb polymers through a nanopore subjected to an electric field is presented. The translocation dynamics was extensively studied in terms of the applied electric field strength, the pore size, and the comb polymer topology. The variations of the most probable translocation time $\tau_p$ and the mean translocation time \mt\ as a function of the applied electric field strength show distinct features, the latter exhibiting a nonmonotonic dependence on the electric field. We were able to show the existence of a critical field strength $\delta \epsilon_c$ defined by the narrowest distribution of the translocation time, which is closely related to the size of the nanopore. In addition, we have found that the critical field strength also defines a transition point between two regimes of translocation: a smooth translocation for a field strength below $\delta \epsilon_c$ and a chaotic translocation for a field strength above $\delta \epsilon_c$. Moreover, for the smallest pore size ($r_p = 1$), monomers can only cross the nanopore in a single file, while for larger pores different modes of polymer translocation are identified. Finally, the dependence of the mean translocation time on the backbone length is governed by a power law relationship $\left < \tau \right > \sim {N_B}^{\alpha}$, where the scaling exponent $\alpha$ is found to be in the range of 1.3--1.7 for the set of side chain lengths and nanopore sizes investigated. As for the side chain length $N_S$, the mean translocation time is found to follow a linear dependence $\left < \tau \right > \sim {N_S}$.

Predicting straw drinking ability of liquid foods by pipe-flow rheometry

Designing the straw drinking experience is increasingly important in consumer-oriented liquid food innovation. The perceived ‘straw drinking ease’ of liquid foods could be assessed by sensory analysis. However, challenges arise in linking instrumental measurements to the subjective quantification of sensory attributes due to the complexity of perceptual behaviors in drinking. Here, we developed a pipe-flow rheometry approach to predict straw drinking ability with minimized reliance on panel tests. We measured the instantaneous flow of liquid samples within straws and compared their flow profiles based on different yielding behaviors. The dynamic flow processes were simplified into steady-state pipe flow, and perceived straw drinking ability was modeled as the shear viscosity of liquid foods at specific flow rates. A power-law relationship was found between viscosity at sample-specific shear rates and straw drinking ability, regardless of whether the liquid foods exhibit yield stress. This approach provides opportunities for directly addressing the straw drinking experience through simple laboratory measurements when developing texture modulation systems for liquid foods.

Fatigue Behavior of Polymer Nanocomposites under Low-Strain Cyclic Loading: Insights from Molecular Dynamics Simulation.

Understanding the structural evolution and bond-breaking behavior under cyclic loading is crucial for designing polymer nanocomposites (PNCs) with superior fatigue resistance. Coarse-grained models of PNCs filled with spherical carbon black nanoparticles (NPs) at varying filling fractions of φ were successfully constructed using molecular dynamics simulations. Structural and dynamic simulation results reveal that higher φ leads to increased aggregation of NPs and markedly restricts the relaxation behavior of the polymer matrix. Subsequently, fatigue testing of PNCs was conducted under low-strain cyclic tensile deformation, and the real-time bond-breaking behavior was tracked. The decay behavior of the bond number autocorrelation function was found to be accurately described by the KWW equation, enabling precise determination of the characteristic lifetime τf. With increasing φ, the dominant factor influencing bond-breaking behavior gradually shifts from the polymer network, including entanglements and cross-linking networks, to the filler network. This suggests the presence of a critical filling fraction φc where τf is maximized. For low-strain failure mechanisms, temperature field observations at varying cycles reveal that localized temperature rise emerges as the predominant factor. Furthermore, the mobility of both polymers and NPs increases with cycles. Specifically, the diffusion coefficient of polymer monomers shows a clear power-law relationship with the bond-breaking rate, characterized by . Finally, the stiffness of polymer chains significantly influences the fatigue behavior, evidenced by an initial increase followed by a decrease in the τf with increasing bending energy k. This behavior is attributed to the competitive relationship between high entanglement density at low k and enhanced preorientation at high k. In summary, this study provides a general paradigm for describing failure behavior under cyclic deformation and offers insights into fatigue mechanisms at the molecular level, thereby guiding the development of improved fatigue-resistant PNCs.

Induced polarization of clay-rich materials. 4. Water content and temperature effects in bentonites

Deep geological disposals (DGDs) are widely seen to be the best solution to contain high-level radioactive wastes safely. Compacted bentonite and bentonite-sand mixtures are considered the most appropriate buffers or sealing materials for access drifts, ramps, and shafts due to their favorable physicochemical and hydro-mechanical properties. Bentonite-sand mixtures are expected to swell and seal all voids when in contact with water, forming an impermeable barrier to radioactive elements. The parameters that will most affect the hydraulic performance of these seals are their water content, dry density, water salinity, and temperature. Monitoring and assessing these parameters are, therefore, crucial to confirm that the seals’ safety functions are fulfilled during the life of a DGD. Induced polarization (IP) is a nonintrusive geophysical method able to perform this task. However, the underlying physics of bentonite sand mixtures has not been checked. The complex conductivity spectra of 42 compacted bentonite-sand mixtures were measured in the frequency range of 1 Hz–45 kHz in order to develop workable relationships between in-phase and quadrature conductivities versus water content and saturation, pore water conductivity, bentonite-sand ratio (10% to 100%), temperature (10°C–60°C), and dry density (0.97 to 1.64 g cm−3). We observe that conductivity is mostly dominated by surface conductivity associated with the Stern layer (SL) coating the surface of smectite, the main component of bentonite. At a given salinity and temperature, the in-phase and quadrature conductivities obey the power law relationships with water content and saturation. The in-phase and quadrature conductivities depend on the temperature according to a classical linear relationship with the same temperature coefficient. An SL-based model is used to explain the dependence of the complex conductivity with water content, dry density, water salinity, and temperature. It could be used to interpret the IP field data to monitor the efficiency of the seal of DGD facilities.