We propose a theory for preventing instabilities in frictionally unstable systems such as earthquakes are. We exploit the dependence of friction on fluid pressure and use it as a backdoor for provoking controlled, slow-slip over a single mature seismic fault. We use the mathematical Theory of Control and notions from passivity in order to (a) stabilize and restricting chaos, (b) impose slow frictional dissipation and (c) tune the system toward desirable global asymptotic equilibria of lower energy. Our control approach is robust and does not require exact knowledge of the frictional behavior of the system and its fluid diffusion properties (e.g. permeability, viscosity, compressibility) or of other parameters related to complex physical processes that are hard to determine in practice. We expect our methodology to inspire earthquake mitigation strategies regarding anthropogenic and/or natural seismicity.

References

[1] Stefanou, I. (2019). Controlling Anthropogenic and Natural Seismicity: Insights From Active Stabilization of the Spring‐Slider Model. Journal of Geophysical Research: Solid Earth, 124(8), 8786–8802. https://doi.org/10.1029/2019JB017847
[2] Tzortzopoulos G., Braun P., Stefanou I. (2021), Absorbent Porous Paper Reveals How Earthquakes Could be Mitigated, Geophysical Research Letters 48. https://doi.org/10.1029/2020GL090792.
[3] Stefanou, I., Tzortzopoulos, G. (2022). Preventing instabilities and inducing controlled, slow-slip in frictionally unstable systems. Journal of Geophysical Research: Solid Earth. https://doi.org/10.1029/2021JB023410
[4] Gutiérrez-Oribio D., Tzortzopoulos G., Stefanou I., Plestan F. (2022). Earthquake Control: An Emerging Application for Robust Control. Theory and Experimental Tests. http://arxiv.org/abs/2203.00296
[5] Papachristos, E., Stefanou, I. (2022), Controlling earthquake-like instabilities using artificial intelligence. http://arxiv.org/abs/2104.13180.
[6] Gutiérrez-Oribio D., Stefanou I., Plestan F. (2022). Passivity-based Control of a Frictional Underactuated Mechanical System: Application to Earthquake Prevention. https://arxiv.org/abs/2207.0718

How to cite: Stefanou, I., Tzortzopoulos, G., and Gutierrez-Oribio, D.: Preventing earthquake instabilities and inducing controlled, slow-slip by active fluid pressure control in the vicinity of a single seismic fault, EGU General Assembly 2023, Vienna, Austria, 23–28 Apr 2023, EGU23-14939, https://doi.org/10.5194/egusphere-egu23-14939, 2023.

Rock mass has complex block-hierarchical structure involving various scale levels, which should be considered both in dynamic and static conditions. Because the interlayer has weak mechanical properties compared with rock blocks, the deformation of rock mass mainly concentrates at the interlayers both in dynamic and static conditions, which provides the possibility of translation and rotation for rock blocks. The basic carriers of pendulum-type wave in rock mass are geoblocks with translational and rotational degrees of freedom involving various hierarchical levels. The major part of the energy of a blast is spent to fragmentation of rocks and is transferred to rock blocks of the stressed geomedium in the form of kinetic energy (including translational kinetic energy and rotational kinetic energy). The in-situ experimental data has shown that the block-rock mass has significant angular deformation under dynamic impact, and the rotation of blocks can deeply affect the wave propagation and dynamic behavior of rock mass. Previous research on 1D dynamic model of block-rock mass cannot reflect the rotation effect of blocks, and the new 2D dynamic model should take into account the rotation of blocks and energy transfer. Consequently, aiming at the investigation of rotation of blocks, the 2D dynamic model of block-rock mass is established based on the accurate consideration of rotation effect. The research based on this model reveals the mechanism of the rotation of blocks, and determines the characteristics of energy transfer and the influence of the rotation of blocks on the inhomogeneous deformation of interlayers. Research shows that the rotation of blocks is not directly related to whether the structure of rock mass is symmetrical, or whether the interlayer is deformed or not, or the form of external loads, but is caused by the non-equilibrium shear between interfaces in the absence of the external torque. The rotation of blocks results in the inhomogeneous deformation of interlayers, and has a significant influence on the shear deformation of interlayers. At some local positions, in addition to the deformation of the interlayer caused by translation, the block-rock mass also produces additional tension and compression deformation caused by the rotation of blocks, which may lead to the phenomenon of rock crushing. This study theoretically solves the problems of wave propagation in block medium under arbitrary loads and torque, and is helpful for the research of seismic wave propagation in block medium with inhomogeneous complex structures.

How to cite: Jiang, K. and Qi, C.: Study on the rotation of blocks in two-dimensional block-rock mass, EGU General Assembly 2023, Vienna, Austria, 23–28 Apr 2023, EGU23-4271, https://doi.org/10.5194/egusphere-egu23-4271, 2023.

Underground chambers or tunnels often contain inclusions, the interface between the inclusion and the surrounding rock is not always perfect, which influences stress wave propagation. In this study, the spring model and Ricker wavelet were adopted to represent the imperfect interface and transient seismic wave. Based on the wave function expansion method and Fourier transform, an analytical formula for the dynamic stress concentration factor (DSCF) for an elliptical inclusion with imperfect interfaces in infinite space subjected to a plane SH-wave was determined. The theoretical solution was verified via numerical simulations using the LS-DYNA software, and the results were analyzed. The effects of the wave number (k), radial coordinate (ξ), stiffness parameter (β), and differences in material properties on the dynamic response were evaluated. The numerical results revealed that the maximum DSCF always occurred at both ends of the elliptical minor axis, and the transient DSCF was generally a factor of 2-3 greater than the steady-state DSCF. Changes in k and ξ led to variations in the DSCF value and spatial distribution, changes in β resulted only in variations in the DSCF value, and lower values of ω_p and β led to a greater DSCF under the same parameter conditions. In addition, the differences in material properties between the medium and inclusion significantly affected the variation characteristics of the DSCF with k and ξ.

How to cite: Ming, T., Hao, L., Rui, Z., and Gongliang, X.: Dynamic response of an elliptic cylinder inclusion with imperfect interfaces subjected to plane SH wave, EGU General Assembly 2023, Vienna, Austria, 23–28 Apr 2023, EGU23-7726, https://doi.org/10.5194/egusphere-egu23-7726, 2023.

The key to increasing shale gas production is to construct fracture networks in shale reservoir to provide channels for shale gas. Understanding the cracking characteristics of shale is necessary for oil and gas exploitation engineering. Given this, uniaxial compression tests were conducted on Longmaxi shale in China to study the mechanical properties and cracking behaviors affected by bedding layers and pre-existing slot. Sandstone specimens with different pre-existing slot angles were also tested as a comparison. A mechanical-optical-acoustical comprehensive data acquisition system consisting of a rigid hydraulic machine, high-speed industrial camera and acoustic emission acquisition instrument was established to monitor the cracking behaviors in real time. The results show that the cracking behaviors of shale specimens are quite different from sandstone specimens in the uniaxial compression tests. Crack initiation is predominantly controlled by the pre-existing slot and is also affected by bedding layers. Crack propagation is mainly controlled by bedding layers and stress field distribution. When the bedding layers are vertical, the cracks are most likely to propagate along the direction of the bedding and tensile cracks are observed. When the bedding is 30°, the shale specimens are most likely to be controlled by the bedding layers, resulting in shear slip failure along the bedding layers. The experimental results contribute to the understanding of cracking properties in layered anisotropic materials.

How to cite: Ban, Y., Duan, J., Xie, Q., Fu, X., and Sun, W.: Cracking properties of shale influenced by bedding layers and a pre-existing slot, EGU General Assembly 2023, Vienna, Austria, 23–28 Apr 2023, EGU23-6464, https://doi.org/10.5194/egusphere-egu23-6464, 2023.

After the impoundment of a high dam reservoir, the water pressure environment of the rock masses in dam base and reservoir bank changes, which may easily induce engineering problems such as bank slope instability and dam collapse. In order to investigate the differences and mechanisms of different constant water pressures on the rock mass of dam base, triaxial loading tests were conducted on sandstone with initial damage under different high constant porewater pressures, and the multidirectional fracture mechanism was analyzed by combining CT and electron scans. The test results show that:(1) Under the confining pressure of 80 MPa, the greater the pore water pressure, the more brittle the sandstone is, the lower the peak strength, the smaller the volume expansion stress, the pore water pressure increases from 10 MPa to 50 MPa, and the peak strength decreases by 33%.  (2) For different pore water pressure, there are significant differences in sandstone internal deterioration range and deterioration effect  as the fracture surfaces of sandstone specimens have various forms and directions. Due to CT scaning results, with the pore water pressure increases, the deterioration effect spreads from specimen middle to both ends. When the water pressure-confining pressure ratio is less than 25.0%, the deterioration of pore water pressure is mainly concentrated in the middle 1/3 of the specimen. When the water pressure-confining pressure ratio is bigger than 62.5%, the pore water pressure has obvious deterioration effect on the whole specimen. (3) Electron microscopy scanning reveals that with the increase of pore water pressure: the microgranular structure of sandstone changes from shear slip failure to shear fracture failure, and the microcrystalline structure of sandstone changes from cauliflower to rice granular. The macroscopic failure mode changes from plastic failure to brittle failure, and multidirectional fracture plane is formed, which is related to the migration of fine particles and the fracture of large particles in the meso-particle structure under pore water pressure. The formation of the multidirectional fracture plane is directly related to the shear strength of the microscopic crystal structure.

How to cite: Fu, X., Ban, Y., Xie, Q., and Sun, W.: Triaxial compression mechanical properties and multidirectional fracture mechanism of sandstone under different pore pressure, EGU General Assembly 2023, Vienna, Austria, 23–28 Apr 2023, EGU23-6852, https://doi.org/10.5194/egusphere-egu23-6852, 2023.

Over the past years in the development of oil and gas fields, there has been a trend towards an increase in the development of unconventional low-permeability reservoirs. In this regard, it is becoming increasingly important to study the problems associated with the use of hydraulic fracturing technology (HF) in rocks with a complex internal structure. To achieve the maximum oil and gas production rate and increase the drainage zone in the near-wellbore space, it is necessary to carry out hydraulic fracturing with the most extensive system of fractures.

In this work the authors investigate the propagation of a hydraulically driven fracture in a fully saturated, permeable, and porous medium at the pore scale. To achieve a goal, at the first stage, we set a system of determining ratios and a crack propagation criterion. At the next stage, a three-dimensional numerical poroelastic model of a rock sample is prepared based on a three-dimensional image of the pore space of rock samples. Then numerical poroelastic modeling of the processes of one- and two-phase filtration and rock destruction using the extended finite element method is performed. For a more accurate description of filtration processes, the authors have prepared a physico-mathematical model that takes into account the flow rate and leakage of fluid into the rock during fracture growth at the pore scale. The obtained numerical results are compared with the previously conducted results of laboratory studies.

As a result of the numerical simulation, the authors prepared a digital rock model (DRM) based on microCT data, performed numerical simulation of the filtration process in the DRM and numerical simulation of fracture propagation in a fully saturated, permeable, and porous medium at the pore scale. Then, the dependences of filtration, initiation and fracture propagation were investigated depending on various conditions of HF fluid injection.

How to cite: Taurenis, D. and Nachev, V.: Three-dimensional numerical simulation of multiphase filtration and fracture propagation at the pore scale, EGU General Assembly 2023, Vienna, Austria, 23–28 Apr 2023, EGU23-9483, https://doi.org/10.5194/egusphere-egu23-9483, 2023.

Wind fields are extremely variable in space and time over a wide range of scales. This extreme variability is transferred to the wind turbine torque and ultimately to wind energy production. The Universal Multifractal (UM) framework is a powerful tool that allows to characterise and simulate the extreme variability of geophysical fields across scales with the help of only three parameters (α, C1 and H) with physical interpretation; while the 4th, the power a of a conservative flux, is absorbed by the empirical estimation of the mean singularity over a non-conservative field.

The main challenge is to simulate over 2D space plus time vector fields which realistically reproduce observed spatial and temporal variability of wind fields. The outer scale of the simulated fields should basically correspond to the size of the wind turbine in space and ten minutes in time. To achieve that, we combine two broad classes of stochastic processes: stable Levy processes and Clifford algebra. We use as input characteristic parameters obtained from the multifractal analysis of the data collected by two high-resolution 3D anemometers with approx. 33 m vertical distance on a meteorological mast. The data is collected as part of the RW-Turb measurement campaign (https://hmco.enpc.fr/portfolio-archive/rw-turb/), supported by the French National Research Agency (ANR-19-CE05-0022). The expected behaviour of the simulated field is confirmed by multifractal analysis. 

In the second step, we investigate the effect of small-scale wind variability on the wind turbine torque computation by imputing the simulated vector fields to three modelling chains with increasing complexity. The first one only considers the temporal variability, averaging the wind field and considering it at hub height. The second one is based on the angular moment definition and allows us to consider both spatial and temporal variability by computing the torque at each blade point and integrating it along the radius for each time step. Finally, the third one uses the realistic software OpenFAST developed by the US National Renewable Energy Laboratory (NREL). To analyse and physically interpret wind variability's effect, we compared the torque obtained by the three modelling chains focused on the small scales. As we expected, we found pronounced differences on small scales with stronger fluctuations exhibited in the second modelling chain, followed by OpenFAST and the first one. 

How to cite: García Gago, Á., Gires, A., Veers, P., Tchiguirinskaia, I., and Schertzer, D.: Small Scales Space-Time Variability of Wind Fields: Simulations with Vector Fields and Transfer to Turbine Torque Computation, EGU General Assembly 2023, Vienna, Austria, 23–28 Apr 2023, EGU23-11767, https://doi.org/10.5194/egusphere-egu23-11767, 2023.

Rainfall fields exhibit extreme variability over wide range of space-time scales which make them complex to characterize, model and even measure. Furthermore, rainfall, as most geophysical fields, is strongly anisotropic. Fortunately, scaling anisotropy has been developed for a few decades to generalise scaling in an anisotropic framework, e.g., in the simplest case iso-surfaces become self-affines ellipsoids instead of self-similar spheres. This is particularly straightforward for continuous in scale cascades. For them, as well as for discrete in scale cascades, Universal Multifractals (UM) have been widely used to analyse and simulate such geophysical fields with the help of a very limited number of physically meaningful parameters. Recently blunt cascades have been introduced. They enable to remain in the simple framework of discrete cascades while partly overcoming their well known strong limitations such as non-stationnarity. It basically consists in geometrically interpolating over moving windows the multiplicative increments at each cascade steps.

Here we suggest to incorporate observed features in blunt 2D and 3D (space-time) blunt discrete cascade simulations. The data analysis corresponds to a 1D analysis along various directions ,considering each lof them as a different “sample” of the process. Analysing how the UM parameters change with the angle of the chosen direction enables to unveil underlying rainfall anisotropy features. Impacts, and notably potential biases, of these features on standard spatial analysis in 2D are also explored and discussed. For this purpose high resolution space-time rainfall data collected with help of a dual polarisation X-band radar operated by HM&Co-ENPC is used .

To simulate anisotropy features with the help of blunt extension of discrete UM cascades, we tentatively suggest to use moving window shaped as ellipses instead of squares. Tuning the eccentricity and orientation of the ellipses enables to introduce various levels of anisotropy within the simulated fields. First, multifractal expected behaviour is theoretically established and then it is numerically confirmed with the help of ensembles of stochastic simulations and the previously developed analysis approach.

Authors acknowledge the RW-Turb project (supported by the French National Research Agency - ANR-19-CE05-0022), for partial financial support.

How to cite: Gires, A., Tchiguirinskaia, I., and Schertzer, D.: Characterizing and simulating with blunt extension of discrete cascades rainfall anisotropy in a Universal Multifractals framework, EGU General Assembly 2023, Vienna, Austria, 23–28 Apr 2023, EGU23-9020, https://doi.org/10.5194/egusphere-egu23-9020, 2023.

Abstract

Several equations and their simplified versions already exist for estimating evapotranspiration. Still, the practical difficulty in using them is that they contain too many variables and empirical parameters including some non-atmospheric vegetation-based ones which may not be appropriate for all plant types. Therefore, a simple empirical equation is suggested here to approximately estimate evapotranspiration loss in a deterministic manner as a function of the green roof’s water content, ambient air temperature, wind speed, relative humidity, and total net radiation flux. For nonlinear processes such as evapotranspiration clearly, such deterministic estimates are not representative of the extreme values observed in evapotranspiration losses. Therefore, a universal multifractal-based simulation procedure is proposed here to improve such deterministic estimates, so that the simulated evapotranspiration loss has realistic intermittency and temporal scaling behaviour, while preserving its diurnal variability.

Keywords

Multifractals, Non-linear geophysical systems, Cascade dynamics, Scaling, Hydrology, Meteorology.

How to cite: Ramanathan S, A., Versini, P.-A., Schertzer, D., Tchiguirinskaia, I., Perrin, R., and Sindt, L.: Simulating Evapotranspiration in Green roofs using a Multifractal approach, EGU General Assembly 2023, Vienna, Austria, 23–28 Apr 2023, EGU23-7767, https://doi.org/10.5194/egusphere-egu23-7767, 2023.

Wind power production plays an important role in achieving UN’s (United nations) Sustainable development goal (SDG) 7 - affordable and clean energy for all; and in the increasing global transition towards renewable and carbon neutral energy, understanding the uncertainties associated with wind and turbulence is extremely important. Characterization of wind is not straightforward due to its intrinsic intermittency: activity of the field becomes increasingly concentrated at smaller and smaller supports as the scale decreases. When it comes to power production by wind turbines, another complexity arises from the influence of rainfall, which only a limited number of studies have addressed so far suggesting short term as well as long term effects. To understand this, the project RW-Turb (https://hmco.enpc.fr/portfolio-archive/rw-turb/; supported by the French National Research Agency, ANR-19-CE05-0022) employs multiple 3D sonic anemometers (manufactured by Thies), mini meteorological stations (manufactured by Thies), and disdrometers (Parsivel2, manufactured by OTT) on a meteorological mast in the wind farm of Pays d’Othe (110 km south-east of Paris, France; operated by Boralex). With this simultaneously measured data, it is possible to study wind power and associated atmospheric fields under various rain conditions.

Variations of wind velocity, power available at the wind farm, power produced by wind turbines and air density are examined here during rain and dry conditions using the framework of Universal Multifractals (UM). UM is a widely used, physically based, scale invariant framework for characterizing and simulating geophysical fields over wide range of scales which accounts for the intermittency in the field. While statistically analysing the power produced by turbine, rated power acts like an upper threshold resulting in biased estimators. This is identified and quantified here using the theoretical framework of UM along with the actual sampling resolution of instruments under study. Further, from event based analysis, differences in UM parameters were observed between rain and dry conditions for the fields illustrating the influence of rain. This is further explored using joint multifractal analysis and an increase in correlation exponent was observed between various fields with increase in rain rate.

How to cite: Jose, J., Gires, A., Schnorenberger, E., Tchiguirinskaia, I., and Schertzer, D.: Joint multifratcal analysis of available wind power and rain intensity from an operational wind farm, EGU General Assembly 2023, Vienna, Austria, 23–28 Apr 2023, EGU23-7495, https://doi.org/10.5194/egusphere-egu23-7495, 2023.