Hydraulic Pressure Gradient Research Articles

Mechanically Controlled Landslide Deformation

AbstractMany landslide models assume a fully deformable body without any resistance against deformation. However, in reality, landslide bodies can display negligible to large deformation during motion. Examples for limited deformation include the prehistoric giant landslides of Flims and Köfels, or the Vajont landslide of 1963, where the structure of rock largely remained intact and the slides did not evolve into rock avalanches. Here, we propose a novel mechanical model for the controlled deformation of landslides. The model is based on the principle of material strength or resistance and includes a user‐specified function that reflects the mechanisms (internal friction, cohesion, viscosity, and yield strength) that act against the deformation induced by the free‐surface or the hydraulic pressure gradient of the landslide. This controls the landslide deformation and, in turn, also the motion and run‐out, and offers a unique possibility to describe the landslide motion ranging from a fully non‐deformable body sliding along the mountain slope to a completely fluidized motion without any resistance against the force associated with the free‐surface pressure gradient. The latter is the situation often considered for the motion of granular flows such as avalanches of snow or rock, or debris flows. The former can play a substantial role in the dynamics, however, has not yet been considered in mass flow simulations, severely limiting the applicability of those models. We demonstrate the performance of the new model and its applicability, also with the advanced open‐source computational mass flow simulation tool r.avaflow.

Extended landslide velocity and analytical drag

The landslide velocity plays a dominant role in estimating the impact force and devastated area. Here, based on Pudasaini and Krautblatter (Earth Surf Dyn 10:165–189, 2022. https://doi.org/10.5194/esurf-10-165-2022), I develop a novel extended landslide velocity model that includes the force induced by the hydraulic pressure gradient, which was neglected by all the existing analytical landslide velocity models. By a rigorous conversion between this force and inertia, which facilitates constructing exact analytical solutions for velocity, I develop two peer systems expecting to produce the same result. However, this contradicts with our conventional wisdom. This raises a legitimate question of whether we should develop some new balance equations such that these phenomena can be better explained naturally. I compare the two velocity models that neglect and include the force induced by the hydraulic pressure gradient. Analytical solutions produced by the two systems are fundamentally different. The new model is comprehensive, elegant, and yet an extraordinary development as it reveals serendipitous circumstance resulting in a pressure–inertia paradox. Surprisingly, the mass first moves upstream for quite a while; then, it winds back and continues accelerating down slope. The difference between the extended and simple solution is significant, and widens strongly as the force associated with the hydraulic pressure gradient increases, demonstrating the importance of this force in the landslide velocity. The viscous drag is an essential dissipative force mechanism and plays an important role in controlling the landslide dynamics. However, no explicit mechanical and analytical model exists to date for this. The careful sagacity of the graceful form of new velocity equation results in a plain, yet mechanically extensive, analytical model for viscous drag, the first of this kind. It contains several physical and geometrical parameters, and evolves dynamically as it varies inversely with the flow depth. A dimensionless drag number is constructed characterizing the drag dynamics. Importance of the drag model is explained. In contrast with the prevailing practices, I have proved that drags are essentially different for the expanding and contracting motions. This is an entirely novel revelation. Drag coefficients are close to the empirical or numerical values often used in practice. But, now, I offer an innovative, physically founded analytical model for the drag that can be instantly applied in mass flow simulations.

Study on the Influence of Machining Deviation of Vehicle Automatic Transmission Shifting Control Components on Calibration Parameters

An automatic transmission (AT) shift control model was completed by commercial code Simulation X based on AT shift control system mechanism. The AT shift process under condition of varied machining deviation was analysed by virtual calibration method based on this AT shift model. The results show that the machining deviation of AT shifting control component causes effect on the shift quality, especially affecting the shift impact during the shift process. The machining deviation is larger, accordingly the calibrated parameters such as the hydraulic pressure gradient and the control time increase. It is helpful to improve the shift quality to set the suitable calibration parameters of clutch shift according to different machining deviation.

Impacts of Water and Stress Transfers from Ground Surface on the Shallow Earthquake of 11 November 2019 at Le Teil (France)

The 4.9 Mw earthquake of 11 November 2019 at Le Teil (France) occurred at a very shallow depth (about 1 km), inducing the surface rupture of La Rouvière fault. The question was raised shortly after about the potential impact of a nearby surface quarry. Thanks to satellite differential interferometry, here, we revealed the existence of a secondary surface rupture of the quasi-parallel Bayne Rocherenard fault. A newly processed seismic cross-section allowed us to shape the three-dimensional geometry of the local three-fault system. Assuming that the earthquake was triggered by the impact of meteoric water recharge, our numerical simulations show that the hydraulic pressure gradient at depth was at a maximum during the period of 2010–2019, just before the seismic event. The estimated overpressure at the intersection of the two faults, which is the most probable place of the hypocenter, was close to 1 MPa. This hydraulic effect is about two and a half times larger than the cumulative effect of mechanical stress release due to the mass removal from the surface quarry over the two past centuries. This work suggests a rapid hydraulic triggering mechanism on a network of faults at a shallow depth after a heavy rainfall episode.

Linking fluid-axons interactions to the macroscopic fluid transport properties of the brain.

Many brain disorders, including Alzheimer's Disease and Parkinson's Disease, and drug delivery procedures are linked to fluid transport in the brain; yet, while neurons are extremely soft and can be easily deformed, how the microscale channel flow interacts with the neuronal structures (especially axons) deformation and how these interactions affect the macroscale tissue function and transport properties is poorly understood. Misrepresenting these relationships may lead to the erroneous prediction of e.g. disease spread, drug delivery, and nerve injury in the brain. However, understanding fluid-neuron interactions is an outstanding challenge because the behaviours of both phases are not only dynamic but also occur at an extremely small length scale (the width of the flow channel is ∼100nm), which cannot be captured by state-of-the-art experimental techniques. Here, by explicitly simulating the dynamics of the flow and axons at the microstructural level, we, for the first time, establish the link between micromechanical tissue response to the physical laws governing the macroscopic transport property of the brain white matter. We found that interactions between axons and the interstitial flow are very strong, thus playing an essential role in the brain fluid/mass transport. Furthermore, we proposed the first anisotropic pressure-dependent permeability tensor informed by microstructural dynamics for more accurate brain modelling at the macroscale, and analysed the effect of the variation of the microstructural parameters that influence such tensor. These findings will shed light on some unsolved issues linked to brain functions and medical treatments relying on intracerebral transport, and the mathematical model provides a framework to more realistically model the brain and design brain-tissue-like biomaterials. STATEMENT OF SIGNIFICANCE: This study reveals how neurons interact with the fluid flowing around them and how these microscale interactions affect macroscale transport behaviour of the brain tissue. The findings provide unprecedented insights into some unsolved issues linked to brain functions and medical treatments relying on intracerebral fluid transport. Furthermore, we, for the first time, established a microstructure-informed permeability tensor as a function of local hydraulic pressure and pressure gradient for the brain tissue, which inherently captures the dynamic transport property of the brain. This study is a cornerstone to advance the predicting accuracy of brain tissue transport property and neural tissue engineering.

Deviation from Darcy Law in Porous Media Due to Reverse Osmosis: Pore-Scale Approach

Shale and tight hydrocarbons are vital to global energy dynamics. The fluid flow in sub-micron pores of tight oil reservoirs varies from bulk fluid flow. The Darcy law is widely accepted to model creeping flow in petroleum reservoirs. However, traditional reservoir modeling approaches fail to account for the sub-micron mechanisms that govern fluid flow. The accuracy of tight oil reservoir simulators has been improved by incorporating the influence of sub-micron effects. However, there are still factors that affect sub-micron fluid mobility that need investigation. The influence of a chemical potential gradient on fluid flow in sub-micron pores was modeled by solving Darcy and the transport and diluted species equations. The findings indicate that when a chemical potential gradient acts in the opposite direction of a hydraulic pressure gradient (reverse osmosis), there exists a limiting pressure threshold below which a non-linear flow pattern deviating from the Darcy equation is observed. Furthermore, the simulation based on tight reservoir pore parameters shows that when the effect of a chemical potential gradient is added, the resultant flux is 8–49% less. Hence, including the effect of the chemical potential gradient will improve the accuracy of sub-micron pressure dynamics and flow velocity.

Kidney epithelial cells are active mechano-biological fluid pumps

The role of mechanical forces driving kidney epithelial fluid transport and morphogenesis in kidney diseases is unclear. Here, using a microfluidic platform to recapitulate fluid transport activity of kidney cells, we report that renal epithelial cells can actively generate hydraulic pressure gradients across the epithelium. The fluidic flux declines with increasing hydraulic pressure until a stall pressure, in a manner similar to mechanical fluid pumps. For normal human kidney cells, the fluidic flux is from apical to basal, and the pressure is higher on the basal side. For human Autosomal Dominant Polycystic Kidney Disease cells, the fluidic flux is reversed from basal to apical. Molecular and proteomic studies reveal that renal epithelial cells are sensitive to hydraulic pressure gradients, changing gene expression profiles and spatial arrangements of ion exchangers and the cytoskeleton in different pressure conditions. These results implicate mechanical force and hydraulic pressure as important variables during kidney function and morphological change, and provide insights into pathophysiological mechanisms underlying the development and transduction of hydraulic pressure gradients.

Salt and Water Transport in Reverse Osmosis Membranes: Beyond the Solution-Diffusion Model

Understanding the salt-water separation mechanisms of reverse osmosis (RO) membranes is critical for the further development and optimization of RO technology. The solution-diffusion (SD) model is widely used to describe water and salt transport in RO, but it does not describe the intricate transport mechanisms of water molecules and ions through the membrane. In this study, we develop an ion transport model for RO, referred to as the solution-friction model, by rigorously considering the mechanisms of partitioning and the interactions among water, salt ions, and the membrane. Ion transport through the membrane is described by the extended Nernst-Planck equation, with the consideration of frictions between the species (i.e., ion, water, and membrane matrix). Water flow through the membrane is governed by the hydraulic pressure gradient and the friction between the water and membrane matrix as well as the friction between water and ions. The model is validated using experimental measurements of salt rejection and permeate water flux in a lab-scale, cross-flow RO setup. We then investigate the effects of feed salt concentration and hydraulic pressure on salt permeability, demonstrating strong dependence of salt permeability on feed salt concentration and applied pressure, starkly disparate from the SD model. Lastly, we develop a framework to analyze the pressure drop distribution across the membrane, demonstrating that cross-membrane transport dominates the overall pressure drop in RO, in marked contrast to the SD model that assumes no pressure drop across the membrane.

Ferric hydroacid & diamine complex as draw solute for forward osmosis (FO) desalination processes

Forward osmosis (FO) is being one of the recent technologies widely studied for desalination. FO mainly uses osmotic pressure gradient unlike reverse osmosis (RO) that uses hydraulic pressure gradient. So increasing the osmotic pressure is highly influencing the water flux in FO systems. A new type of draw solute used for enhancing the FO process is mixed ligand PDA-Fe-CA complex (Ferric hydroacid & diamine). Mixed ligand PDA-Fe-CA complex is a complex from iron–citric complex (Fe-CA) functionalized by 1,2phenylenediamine ligand. The resulting complex suggested structure was investigated by FTIR, elemental analysis, and spectrophotometric analysis proving the successful coordination of 1,2phenylenediamine to Fe, besides the successful coordinating of citric acid to Fe. The molar ratio for this complex was found to be 1:1:2 of Fe: CA: PDA. The performance of the produced complex was investigated using commercial FO membranes in batch FO system. 40 g/L (0.06 M) of PDA-Fe-CA produces water flux of 21.5 LMH when tested with distilled water as feed solution, and water flux values of 18, 15.8, 14, and 12.3 L/m2hr were gained when saline water were used as feed solution with concentrations of 3,000, 7,000, and 12,000 mg/L respectively. And the water flux was 7.9 LMH when synthetic sea water (35,000 mg/L NaCl) was used as feed solution.

True driving force and characteristics of water transport in osmotic membranes

Diffusion cannot be a major water transport mechanism in osmotic membranes because of the lack of true water concentration gradient within the membrane. Due to the semipermeable property of osmotic membranes, water concentration in the membrane is virtually constant because of the absence of salts. The recently confirmed porous structure of the skin layer of osmotic membranes cannot support the basis to exclude bulk water flow in the membrane as assumed in the classic solution-diffusion model. Herein we demonstrate that the concentration difference of water at the membrane-solution interface manifests itself as a negative hydraulic pressure in the membrane. Hence, the only possible driving force for water movement in osmotic membranes is hydraulic pressure gradient. Osmotically driven membrane processes are characterized with negative pressure within the membrane below the water vapor pressure, inevitably leading to the formation of vapor or small bubbles within the membrane matrix. This phenomenon is expected to markedly reduce the effectiveness of osmotic pressure as a driving force for water transport. Delineation of the breakdown and possible restoration of water continuity under negative pressure is essential for proper understanding of the principles governing water transport in osmotic membranes.

Evolution and management of thick-hard roof using goaf-based multistage hydraulic fracturing technology—a case study in western Chinese coal field

The mining-induced breaking of thick-hard roof is characterized by the microseisms and energy release. To preliminary control rock burst caused by the breakage of the thick-hard roof in panel #42202 of Shengdong coal field, a goaf-based multistage hydraulic fracturing technology was developed, and corresponding mathematical model for hydraulic fracturing position determination and synergetic support system comprised of collapse filling, coal pillars, and load-bearing strata were established. The results show that a distressed zone with a height of 29 m along the drilling direction and a width of 230–300 m along the radial direction of the drilling hole was created. Compared with the effect of single-hole fracturing, the influence scope increased into 70 m for double-hole fracturing. The hydraulic pressure gradient drop of 12.8 MPa was observed, as the termination of hydraulic fracturing with an initiation hydraulic pressure of 33.1 MPa. Additionally, the mining weighting period interval, front abutment coefficient, peak pressure, and roadway surrounding rock stress were reduced by 20.0–69.7%, 5.8–7.9%, 13.4–18.6%, and 22.2–32.1%, respectively.

Performance of supercritical nitrogen in a double flow space well for uniform injection of unconventional reservoirs

ABSTRACT Nitrogen is widely used in the development of unconventional reservoirs. Due to relatively strong heterogeneity, a double flow space well (DFSW) has been proposed for nitrogen injection. In the DFSW, the flow behaviors of nitrogen in the inner flow space (IFS) and outer flow space (OFS) will influence each other. In this paper, a series works were done on modeling of the nitrogen flow in DFSW. Results show that: (a) when the length of microelement section is equal to 5 m, the heat conduction rates in both IFS and OFS increases with the DFSW depth. For IFS, it increases from 0 W/m to 29.5919 W/m, while for OFS, it increases from 0 W/m to 101.89 W/m. (b) when the mass flux increases from 0.9 kg/s to 2.9 kg/s, the hydraulic pressure gradient, and the Joule-Thompson effect alternately dominate. (c) As the DFSW depth increases from 0 m to 1500 m, the thermal conductivity rates in IFS and OFS are always positive.

Using Geomembrane Liners to Reduce Seepage through the Base of Tailings Ponds—A Review and a Framework for Design Guidelines

Geomembranes are used worldwide as basin liners in tailings ponds to decrease the permeability of the foundation and prevent further transportation of harmful contaminants and contaminated water. However, leakage into the environment and damage to the geomembrane have been reported. This paper reviews available literature and recommendations on geomembrane structures for use as a basal liner in tailings ponds, and presents a framework to achieve early involvement and an integrated approach to geomembrane structure design. Cohesive planning guidelines or legislative directions for such structures are currently lacking in many countries, which often means that the structure guidelines for groundwater protection or landfill are applied when designing tailings storage facilities (TSF). Basin structure is generally unique to each mine but, based on the literature, in the majority of cases the structure has a single-composite liner. The type of liner system used depends mainly on the material to be used on top of the structure, local hydraulic pressure gradient, and climate conditions. More practical information and scientific knowledge on the use of base liners in various cases are needed. A sustainable approach could be risk-based design, where the life cycle of the basin is taken into consideration. To this end, this paper proposes geomembrane-lined tailings pond to be assessed as a stakeholder. Emphasis on this, early enough, can ensure critical factors for tailings ponds to be considered from the outset in the design of mines and reduces the environmental footprint of the mining industry. More holistic project management and early involvement and integration are recommended to improve construction quality during the entire life cycle of the pond. In the long term, use of dry stacking or other alternative methods should be encouraged, despite the higher costs for operators.

Oedometric-like setup for the study of water transport in porous media by quasi-elastic neutron scattering.

In comparison to condensed matter, soft matter is subject to several interplaying effects (surface heterogeneities and swelling effect) that influence transport at the nanoscale. In consequence, transport in soft and compliant materials is coupled to adsorption and deformation phenomena. The permeance of the material, i.e., the response of the material to a pressure gradient, is dependent on the temperature, the chemical potential, and the external constraint. Therefore, the characterization of water dynamics in soft porous materials, which we address here, becomes much more complex. In this paper, the development of an original setup for scattering measurements of a radiation in the transmitted geometry in oedometric conditions is described. A specially designed cell enables a uniaxial compression of the investigated material, PIM-1 (Polymers of Intrinsic Microporosity), in the direction perpendicular to the applied hydraulic pressure gradient (up to 120 bars). High pressure boosting of the circulating water is performed with a commercially available high-pressure pump Karcher. This particular setup is adapted to the quasi-elastic neutron scattering technique, which enables us to probe diffusion and relaxation phenomena with characteristic times of 10-9 s-10-12 s. Moreover, it can easily be modified for other scattering techniques.

Simulation of groundwater contamination by leakage from waste-filled mine

Mining wastes are a great source of pollutants. Open-pit backfill materials can be found as waste rock and as tailings. The aim of the current study was the investigation of the contaminant transportation pathways by groundwater flow from these waste materials through heterogeneous porous media. Numerical Lattice Boltzmann Method (LBM) was used for examining the effects of different factors on pollutant transportation through groundwater beneath the waste materials. Grain size, vertical and horizontal fracturing, and hydraulic pressure gradient were factors considered here. The results showed that contaminant transportation by the groundwater flow from the waste materials through porous media depends on primary and secondary matrix porosity of the open-pit material, heterogeneity in permeability of aquifer rock, and hydraulic head of groundwater.

Lymphatic Vessels and Their Surroundings: How Local Physical Factors Affect Lymph Flow.

Simple SummaryLymphatic vessels are responsible for the drainage of liquids, solutes, and cells from interstitial spaces and serosal cavities. Their task is fundamental in order to avoid fluid accumulation leading to tissue swelling and edema. The lymphatic system does not possess a central pump, instead lymph is propelled against an overall hydraulic pressure gradient from interstitial spaces to central veins thanks to two pumping mechanisms, which rely on extrinsic forces or the intrinsic rhythmic contractility of lymphatic muscle cells embedded in vessel walls. This latter mechanism can very rapidly adapt to subtle changes in the microenvironment due to hydraulic pressure, lymph flow-induced wall shear stress, liquid osmolarity, and local tissue temperature. Thus, endothelial and lymphatic muscle cells possess mechanosensors that sense these stimuli and promote a change in contraction frequency and amplitude to modulate lymph flow accordingly. In this review, we will focus on the known physical parameters that can modulate lymph flow and on their putative cellular and molecular mechanisms of transduction.Lymphatic vessels drain and propel lymph by exploiting external forces that surrounding tissues exert upon vessel walls (extrinsic mechanism) and by using active, rhythmic contractions of lymphatic muscle cells embedded in the vessel wall of collecting lymphatics (intrinsic mechanism). The latter mechanism is the major source of the hydraulic pressure gradient where scant extrinsic forces are generated in the microenvironment surrounding lymphatic vessels. It is mainly involved in generating pressure gradients between the interstitial spaces and the vessel lumen and between adjacent lymphatic vessels segments. Intrinsic pumping can very rapidly adapt to ambient physical stimuli such as hydraulic pressure, lymph flow-derived shear stress, fluid osmolarity, and temperature. This adaptation induces a variable lymph flow, which can precisely follow the local tissue state in terms of fluid and solutes removal. Several cellular systems are known to be sensitive to osmolarity, temperature, stretch, and shear stress, and some of them have been found either in lymphatic endothelial cells or lymphatic muscle. In this review, we will focus on how known physical stimuli affect intrinsic contractility and thus lymph flow and describe the most likely cellular mechanisms that mediate this phenomenon.

Quantification of seasonal and diurnal dynamics of subglacial channels using seismic observations on an Alpine glacier

Abstract. Water flowing below glaciers exerts a major control on glacier basal sliding. However, our knowledge of the physics of subglacial hydrology and its link with sliding is limited because of lacking observations. Here we use a 2-year-long dataset made of on-ice-measured seismic and in situ-measured glacier basal sliding speed on Glacier d'Argentière (French Alps) to investigate the physics of subglacial channels and its potential link with glacier basal sliding. Using dedicated theory and concomitant measurements of water discharge, we quantify temporal changes in channels' hydraulic radius and hydraulic pressure gradient. At seasonal timescales we find that hydraulic radius and hydraulic pressure gradient respectively exhibit a 2- and 6-fold increase from spring to summer, followed by comparable decrease towards autumn. At low discharge during the early and late melt season channels respond to changes in discharge mainly through changes in hydraulic radius, a regime that is consistent with predictions of channels' behaviour at equilibrium. In contrast, at high discharge and high short-term water-supply variability (summertime), channels undergo strong changes in hydraulic pressure gradient, a behaviour that is consistent with channels behaving out of equilibrium. This out-of-equilibrium regime is further supported by observations at the diurnal scale, which prove that channels pressurize in the morning and depressurize in the afternoon. During summer we also observe high and sustained basal sliding speed, which supports that the widespread inefficient drainage system (cavities) is likely pressurized concomitantly with the channel system. We propose that pressurized channels help sustain high pressure in cavities (and therefore high glacier sliding speed) through an efficient hydraulic connection between the two systems. The present findings provide an essential basis for testing the physics represented in subglacial hydrology and glacier sliding models.

A mechanical model for phase separation in debris flow

Understanding the physics of phase separation between solid and fluid phases as a mixture mass moves down-slope is a long-standing challenge. Here, we propose an extension of a two phase mass flow model (“Pudasaini (2012), A general two-phase debris flow model, Journal of Geophysical Research, 117, F03010, doi:10.1029/2011JF002186”) by including a new mechanism, called separation-flux, that leads to strong phase separation in avalanche and debris flows while balancing the enhanced solid flux with the reduced fluid flux. The relative velocity between the phases is key in triggering the phase separation mechanism, which is induced by the effective forces that appear in the system. The novel separation-flux can be written as a product of the separation-rate, solid and fluid volume fractions, and the flow depth which amplify the separation-flux. Its magnitude is further controlled by the separation-rate-intensities which are functions of volume fractions and the density ratio. The separation-fluxes are multi-directional. One of the most important characteristics of the separation-flux is that phase separation ceases as soon as one of the components in the mixture vanishes. As the solid density approaches the fluid density, the phase separation intensity is reduced. Furthermore, as the drag increases, the phase separation decreases. The separation velocity emerges from the separation-flux as a function of the relative phase velocity, volume fraction of solid or fluid, and the respective separation-rate-intensity. The separation-rate takes into account different dominant physical and mechanical aspects of the mixture flow, such as the hydraulic pressure gradients, topography induced pressure gradients, the gradients of the volume fractions of solid and fluid phases, flow depths, grain size, densities, friction, viscosities, and buoyancy. The separation-flux mechanism is capable of describing the dynamically evolving phase separation and levee formation in a multi-phase, geometrically three-dimensional debris flow. These are often observed phenomena in natural debris flows and industrial processes that involve the transportation of particulate solid-fluid mixture material. Due to the inherent separation mechanism, as the mass moves down-slope, more and more solid particles are transported to the front and the sides, resulting in solid-rich and mechanically strong frontal surge head, and lateral levees followed by a weaker tail largely consisting of viscous fluid. The primary frontal solid-rich surge head followed by secondary fluid-rich surges is the consequence of phase separation. Such typical and dominant phase separation phenomena are revealed for two-phase debris flow simulations. Finally, changes in flow composition, that are explicitly considered by the new modelling approach, result in significant changes of impact pressure estimates. These are highly important in hazard assessment and mitigation planning and highlight the application potential of the new approach.

A general analytical model for superelevation in landslide

Superelevation is an often observed phenomenon in landslide and debris flow down a complex three-dimensional topography. The degree of superelevation is controlled by the geometry of the channel, the material involved and also the flow dynamics. Empirical methods are usually applied to estimate superelevation. However, those models are incomplete and lack important aspects of the channel geometry, material properties and flow dynamics, instigating serious errors in estimating flow velocities that could only be controlled empirically by introducing ad hoc correction factors. Here, we present new and complete analytical models for superelevation and superelevation velocities down a general topography providing a fully dynamical method. New models formally include essential forces that play an important role in the flow dynamics, namely gravitational forces, topographic- and hydraulic-pressure gradients and Coulomb friction. We discuss the importance of geometry in inducing superelevation and that one directional channel without twist cannot produce superelevation. With the new models we can, in principle, exactly obtain the flow velocities of deformable landslide, dynamic impact pressures and the explicit description of deposition. We have formally provided two alternative analytical representations for superelevation: geometrical and dynamical definitions of superelevation, which is a new concept. We proved that for superelevation to take place, the transversal velocity must have a gradient across the channel. We have analytically constructed a new non-dimensional superelevation number. Superelevation velocity appears to be a non-linear function of the superelevation number. We can now explicitly quantify the superelevation intensity in landslide motion. It has several implications. We proved that superelevation is higher for fluid-saturated debris flows than for dry granular flows. New superelevation models have been validated against a laboratory granular flow down a multi-dimensionally curved channel, and a natural debris flow event in Chamoson, Valais, Switzerland. Our theoretical superelevation velocities appear to be very close to the velocity measured in laboratory and in the field, which however, are largely overestimated by the empirical models. We further validated the model by constructing an exact analytical solution and by applying it to describe superelevation-induced propagation and deposition of the natural debris flow event. New simulations produced observed propagating fronts.

Transient Pulse Test for Non‐Darcy Flow Behaviors and Hydromechanical Coupling Effect of Fractured Limestone

In this paper, the transient pulse test is used to study the permeability and hydromechanical coupling effect of the fractured limestone. The permeability parameters (permeability, β factor of non‐Darcy flow, and acceleration coefficient) of non‐Darcy flow in fractured limestone are obtained by experimental data. The experimental results show that, in the process of transient seepage test of fractured Maokou limestone, the relationship between hydraulic pressure gradient and seepage velocity does not conform to Darcy’s law but meets Forchimer relationship. The relationship between hydraulic pressure difference and time can be fitted by quartic polynomial. The larger the confining pressure is, the more obvious the non‐Darcy seepage effect of fractured rock seepage is. The seepage of rock fracture under high confining pressure is a highly nonlinear time‐varying seepage. The permeability coefficient of rock decreases with the increase of volume stress. Under the action of low volume stress, the relationship between permeability coefficient and stress is more sensitive, while under the action of high volume stress, the relationship between permeability coefficient and volume stress is not significant. In the process of volume stress increasing, the β factor of non‐Darcy flow appears negative. Under the action of low volume stress, the acceleration coefficient and β factor of non‐Darcy flow increase, while under the action of high volume stress, the acceleration coefficient and β factor of non‐Darcy flow decrease.