Displays

A short review on weakly nonlinear and weakly dispersive dynamics of soliton ensembles, the so-called soliton turbulence is given. Such processes take place in shallow water waves, internal waves in the atmosphere and the ocean, solid mechanics and astrophysical plasma; they are described by the integrable models of Korteweg – de Vries equation type (modified Korteweg – de Vries equation, Gardner equation). Here, soliton turbulence means an ensemble of solitons with random parameters. The property of solitons to interact elastically with each other gives rise to an obvious association with the gas of elastically colliding particles. Strictly speaking, soliton turbulence (soliton gas) is a deterministic dynamical system due to the integrability of equations describing the evolution of waves (solitons). However, due to the great complexity of its behavior (due to the large number of participating solitons and nonlinear nature of their interactions), the dynamics of the system can be considered random and, accordingly, may be investigated using methods typical for such problems. 

Firstly, pair soliton collisions have been analyzed as an elementary act of the soliton turbulence for further understanding of their impact on multi-soliton dynamics. Different types of solitons have been considered: “thick” or “top-table” solitons, algebraic solitons, solitons of different polarities. From the point of view of the turbulence theory, the interactions of waves (particles) should be described by the statistical moments of the wave field. These moments, with the exception of the first two, are not invariants of the equation and are not preserved within the time. It was shown that the interaction of solitons of the same polarity leads to a decrease in the third and fourth moments characterizing the skewness and kurtosis. However, the interaction of solitons of different polarity leads to an increase in these moments of the soliton field.

 Then, the study of collision patterns of breathers (localized oscillating packets) with each other and with solitons has been carried out. The determination of conditions leading to an extreme scenario, as well as statistical properties, probability and features of large wave manifestation has been provided. 

As a result of numerical modeling of the multi-soliton fields’ dynamics, the appearance of anomalously large waves in bipolar soliton fields has been demonstrated. Though most of the soliton collisions occur between the pairs of solitons, which may result in maximum two-fold wave amplification, multiple collisions also happen (they make about 10% of the total number of collisions).  The long-term simulation of the soliton gas dynamics has shown a significant decrease in skewness and significant increase in kurtosis, confirming the fact of abnormally large waves’ (so-called “freak/rogue waves”) occurrence.

The reported study was funded by RFBR according to the research projects 19-35-60022 and 18-02-00042.

How to cite: Didenkulova, E.: Soliton turbulence in weakly nonlinear and weakly dispersive media, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-4439, https://doi.org/10.5194/egusphere-egu2020-4439, 2020.

The method of numerical simulation based on the theory of an orthotropic elastic-plastic Cosserat continuum with a plasticity condition, that takes into account both the shear and rotational nature of irreversible deformation, is applied to the analysis of plastic deformation of structurally inhomogeneous materials. Within the assumption of a blocky structure of a material with elastic blocks interacting through compliant plastic interlayers, this condition limits the tangential components of the asymmetric stress tensor, which characterize shears, as well as the couple stresses, which limit values lead to an irreversible change in the curvature of deformed state of the continuum. The equations of translational and rotational motion together with the constitutive relations of the model are formulated as a variational inequality that correctly describes both the state of elastic-plastic deformation under active loading and the state of elastic unloading, [1]. For numerical implementation of mathematical model, the parallel computational algorithm and author’s software package for multiprocessor computer systems of the cluster architecture are used. With the help of the developed computational technology, [2], the problem of squeezing a rectangular block-type rock massif of a masonry by a rough non-deformable plate making a uniformly accelerated rotation is analysed. The influence of the yield strengths of compliant interlayers during shear and bending on the stress-strain state of the massif is investigated. The fields of displacements, stresses, couple stresses, angle of rotation, plastic energy dissipation of the structural elements are studied numerically. A detailed analysis of numerical solutions shows that the couple stresses and the associated curvatures have small effect on the final macroscale deformed state of the massif, which is characterized by the main quantities – displacements and corresponding stresses. The distribution of couple stresses takes a cellular structure, reflecting the heterogeneity of a material and the change in heterogeneity in the process of loading. Therefore, unlike conventional stresses, they should be associated with a mesoscale level of deformation of a structurally inhomogeneous material. Chaotic distribution of the energy of plastic dissipation due to a change in curvature in the entire volume of a medium confirms the hypothesis that the plasticization of a material at the meso-level is due to the rotational degrees of freedom of the particles.

This work was supported by the Russian Foundation for Basic Research, Government of Krasnoyarsk Territory, Krasnoyarsk Regional Fund of Science to the research project No. 18-41-242001.

References

1. Sadovskaya O., Sadovskii V. Mathematical Modeling in Mechanics of Granular Materials. Ser.: Advanced Structured Materials, vol. 21. Springer, Heidelberg – New York – Dordrecht – London, 2012. 390 p.
2. Sadovskii V.M., Sadovskaya O.V. Modeling of elastic waves in a blocky medium based on equations of the Cosserat continuum // Wave Motion. 2015. V. 52. P. 138–150.

How to cite: Sadovskii, V. and Sadovskaya, O.: Simulation of the dynamics of blocky media based on the Cosserat continuum theory using high-performance computations, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-2741, https://doi.org/10.5194/egusphere-egu2020-2741, 2020.

It is unavoidable that in rock engineering practices such as mining and tunnel constructions rocks are subjected to dynamic loading impacts including blasting, seismic loading, rock burst, and so on. The mechanical parameters for rock strength obtained via traditional static tests are not capable of characterizing the dynamic strength of rock mass. Therefore, the conventionally adopted tests cannot be further applied to guide the design of rock engineering subjected to dynamic loadings. Therefore the determination of the dynamic strength is essential for practical engineering. In this study, sandstone is chosen as the experimental sample for Split Hopkinson Pressure Bar (SHPB) numerical simulation by FLAC3D. The validation demonstrated that rocks are prone to fail under dynamic loading impacts. Extensive simulations are also carried out to investigate the development of rock dynamic strength and evolution process of energy accumulation and release in rock mass for samples of various sizes subjected to different levels of dynamic loading and axial loading. The simulation results may provide design guidance for the safety protection of rock engineering subjected to dynamic impacts.

How to cite: Zhang, W., Meng, F., and Wang, Q.: Study on dynamic strength of sandstone based on SHPB numerical experimentation, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-3229, https://doi.org/10.5194/egusphere-egu2020-3229, 2020.

Models that adequately describe the effect of crack-like defects on the elastic moduli of solids are one of the key "ingredients" needed to obtain diagnostic conclusions about the structural features of the material. The change in the velocities of longitudinal and shear elastic waves depending on the pressure is one of the most popular methods of measuring the connection of these moduli with the cracks present in the material. For commonly considered models with an isotropic crack orientation (which makes the medium on average isotropic), the measurement of these two velocities is sufficient to determine two independent moduli (for example, the shear and bulk moduli) through which other characteristics of interest can be expressed. In this case, the applied pressure, gradually closing the cracks, is a control parameter that regulates the concentration of cracks.

It is quite natural when constructing models to obtain expressions relating the elastic moduli with the crack concentration (the latter cannot be to directly monitored when the applied pressure is varied). In this regard, some additional considerations are used about the relationship of crack concentration to pressure, which allows one to relate the model expressions with the moduli measured during the pressure variation. Assuming some approximations relating the pressure and concentration with free fitting parameters in the model, it is possible to achieve the best agreement of model with the experimental dependences on pressure. This approach looks natural and is conventionally used, resulting in apparently satisfactory agreement between the model predictions and the measurement data.

Here we show that this apparent agreement is often achieved at the expense of strong violation of self-consistency between the input data fed into the model and the output of the model. This violation is far from obvious in conventional approaches based on the use of an auxiliary (and not directly measurable) relationship between concentration and pressure. To find out the fact of either violation or fulfillment of the condition of self-consistency, here we describe such a form of the model, in which its input parameters can be expressed in terms of experimentally measured values (in contrast to the crack concentration that cannot be monitored as a function of pressure). In the proposed description of the fractured material, the cracks are characterized by the shear- and normal compliances, the ratio of which is not a priori fixed and can be extracted from the experimental data.The proposed procedure of interpretation of experimental pressure dependences allows one to explicitly verify the model self-consistency and assess the elastic properties of real cracks that is many cases appear to be strongly different from the properties intrinsic to the standard penny-shape-crack model.

The reported study was supported by RFBR, project number 19-05-00536.

How to cite: Radostin, A. V. and Zaitsev, V. Yu.: Self-consistency between input and output data for models describing elastic properties of fractured media: does conventional models satisfy this criterion?, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-5882, https://doi.org/10.5194/egusphere-egu2020-5882, 2020.

Abstract: Uniaxial and biaxial tests are performed to investigate the evolution mechanism of crack propagation and coalescence through developing newly cement mortar materials with horizontal and inclined pre-existing flaws. Additionally, a new numerical method-CDEM (Continuous discrete element method) is employed to analyze the evolution laws of stress field of crack tips under hydraulic coupling. The results reveal that the maximum principal stress of the wing crack tip gradually decreases with increase of internal water pressure, and the initiation stress, initiation angle and peak strength show decreasing trend. The results of crack propagation and coalescence obtained by numerical simulation is consistent with laboratory results. With the water pressure increases, prior to the occurrence of wing cracks, the coplanar cracks firstly initiate around inclined flaws. Under the coupling action of uniaxial compression and internal water pressure, the lateral pressure would limit the initiation of the wing cracks, while the increasing water pressure weakens the inhibition of lateral pressure on wing cracks.

How to cite: Li, Y., Zhu, W., Wei, C., Cai, W., Wu, G., Wang, Z., and Kong, W.: Experimental and CDEM Analysis on Crack Propagation Mechanism of Rock-Like Material Containing Flaws Under Uniaxial and Biaxial Compression, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-12195, https://doi.org/10.5194/egusphere-egu2020-12195, 2020.

In this study, the data obtained during a series of laboratory experiments on hydraulic fracturing were analyzed. The main goal was to determine the time of the fracture closure, the pressure of the fracture closure, and the permeability of the sample, where the fracture was formed and propagated.

A special laboratory setup was used to conduct the experiments. The design of this setup allows to provide a three-axis load on the model sample, which makes the conditions of the laboratory experiment on hydraulic fracturing closer to the real conditions in the field. To produce the fracture, viscous fluid was injected under constant rate through the preliminary created cased borehole with perforations.

As results of the experiments, the curves of the fluid injection pressure variations with time were obtained. Their analysis was carried out using the G-function technique developed by Nordgren [1] and Nolte [2]. It is based on the plotting and analyzing of the behavior of the following dependencies: the injection pressure, first derivative of the pressure and the semi-logarithmic derivative of the pressure with respect to G-function. The curves processing allows to estimate the time of the fractures closure, with the help of which the fracture closure pressure was determined. The obtained pressure values were compared with the minimum stresses known from the experimental conditions.

Additionally, the permeability of the model reservoir sample was calculated using a technique developed by Horner [3] and improved by Nolte et al. [4]. The approach is based on an assumption that the fracture in the formation has been already closed, and a radial regime of fluid flow has been established. The obtained results were compared with the actual permeability, which was determined in the preliminary laboratory experiment.

Acknowledgements

The reported study was funded by RFBR, project number 20-35-80018, and state task 0146-2019-0007.

References

1. Nordgren, R. P. [1972] Propagation of a vertical Hydraulic Fracture. SPE 45^th Annual Fall Meeting, Houston, SPE-3009-PA.
2. Nolte, K. G. [1979] Determination of Fracture Parameters from Fracturing Pressure Decline. The 54^th Annual Fall Technical Conference and Exhibition of the Society of Petroleum Engineers of AIME, Las Vegas, SPE-8341-MS.
3. Horner, D. R. [1951] Pressure Build-Up in Wells. 3^rd World Petroleum Congress, Netherlands, WPC-4135.
4. Nolte, K. G., Maniere, J. L., Owens, K. A. [1997] After-Closure Analysis of Fracture Calibration Tests. SPE Annual Technical Conference and Exhibition, San Antonio, Texas, SPE-38676-MS.

How to cite: Novikova, H. and Trimonova, M.: Analysis of the laboratory hydraulic fracturing curves., EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-9960, https://doi.org/10.5194/egusphere-egu2020-9960, 2020.

Induced seismicity associated with fluid injection into the subsurface is an important issue worldwide. Sometimes the fluid injection into a fault leads to aseismic creep of the fault or to microseismic events, but other times it results in more significant seismicity. In our work, we analyze the influence of various parameters of the fault and the rock, as well as the geometry of the model on induced seismicity. A case of well injecting water near a single fault was considered. To describe the slip process, several versions of the rate-and-state friction law was used. It was analyzed, how the model parameters, such as the position of the well relative to the fault, the permeability of the rock, the frictional properties of the fault affect the fault displacements. The problem of the poroelastic effect influence on the fault motion was also considered. Conditions that are favorable for the occurrence of noticeable seismicity were obtained. Difference in the fault behavior with one-parameter and two-parameter rate-and-state friction law were also considered.

How to cite: Riga, V. and Turuntaev, S.: Analysis of seismicity caused by fluid injection, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-6008, https://doi.org/10.5194/egusphere-egu2020-6008, 2020.

We developed a computational technology for numerical modeling of wave fields generated by seismic sources in blocky-layered geological media, and applied it to the analysis of efficiency of the electromagnetic pulse source of new generation "Yenisei", created recently by international geotechnical company "Geotech Seismic Services". To describe wave processes, we worked out new mathematical models of the dynamics of elastic, viscoelastic and elastic-plastic media, of porous and granular materials taking into account the increase in stiffness of such materials as pores collapse, [1]. Algorithms of numerical implementation of governing equations were realized for the cluster-type supercomputers, based on the method of two-cyclic splitting with respect to spatial variables. The conducted computational experiments have demonstrated that the proposed technology allows reproducing the system of waves near the region of excitation of seismic oscillations in 3D setting with a high degree of details and accuracy, [2]. We analysed frequencies and amplitudes of waves generated in the near-surface soils, and showed that our computational results are in a good agreement with seismic parameters of a real electromagnetic pulse source. We studied seismic efficiency of the pulse source as the ratio of the energy passing through the reflecting surface in the depth of layered massif to the energy of pulse effect on the surface. Besides, the energy of surface waves, which is obviously useless for the excitation of reflected waves, was estimated. To compare the energy efficiency of pulse sources with seismic sources of periodic action (vibrators), the problem of cyclic loading through the platform was solved numerically by the same method and the same geometric scheme. The seismic efficiency of vibrator was calculated by the maximum value of the energy fluxes during large time interval. Judging by computations, the pulse seismic sources are not inferior to the sources of vibratory type by seismic efficiency in the range of low frequencies. However, it is necessary to take into account that they differ sharply by the level of expended energy, because the energy of a pulse source, needed for generation of incident wave of a given amplitude, is many times lower than the energy of a vibrator.

The reported study was supported by the Russian Foundation for Basic Research, Government of Krasnoyarsk Territory, Krasnoyarsk Regional Fund of Science to the research project No. 18-41-242001: "Analysis of wavy seismic fields generated by the electromagnetic pulse source "Yenisei" in heterogeneous soil massifs during geological exploration in the conditions of northern regions of Eastern Siberia".

References

1. Sadovskaya O., Sadovskii V. Mathematical Modeling in Mechanics of Granular Materials. Ser.: Advanced Structured Materials, vol. 21. Springer, Heidelberg – New York – Dordrecht – London, 2012. 390 p.
2. Sadovskii V.M., Sadovskaya O.V., Efimov E.A. Analysis of seismic waves exited in near-surface soils by means of the electromagnetic pulse source "Yenisei". Materials Physics and Mechanics. 2019. V. 42, No. 5. P. 544–557.

How to cite: Sadovskaya, O., Sadovskii, V., and Efimov, E.: Analysis of seismic efficiency of the electromagnetic pulse source "Yenisei", EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-2754, https://doi.org/10.5194/egusphere-egu2020-2754, 2020.

In the last few years, tight oil production has increased significantly. This is why the study of the filtration properties of low-permeable rocks (permeability near 1 mD) has acquired particular significance. Such rocks can be subject to considerable compaction during development, which manifests itself in the non-linear permeability loss in time at constant net confining stress. In the laboratory, the compaction (or creep) of porous rock samples under constant stress conditions was observed by many researchers for experiment durations ranging from several hours to several weeks. Conducting such lengthy flow experiments accompanies by a number of challenges. First of all, it is necessary to exclude factors not related to the deformation of the sample. In this study we analyzed possible causes of time trends observed under constant net confining stresses in long-term measurements of low-permeable sample permeabilities. Experimental study of flow in a limestone core sample was conducted. During the experiment with duration of 40 days, the fluid pumping was carried out in several stages with different constant values of the confining pressure and the pore pressure gradient. As a result, the permeability of the sample decreased by 10 times. It was shown that such significant decrease in the permeability in time can be caused by clogging of the sample pore space. The additional experiment with sequential pumping of single-phase gas and liquid through the sample showed that when pumping gas, the sample permeability remained almost constant most of the time. We propose that gas bubbles contained in the flow of liquid can act as a dispersed phase that clogs pores. The estimations show that even very low particle concentrations at large time periods lead to significant decrease in the permeability. The possibility of clogging of the core sample pore space must be considered when conducting the long-term experiments on study of the permeability by the steady-state method.

How to cite: Baryshnikov, N., Zenchenko, E., and Turuntaev, S.: Probable reasons of Rock Sample Apparent Permeability Loss over Time in Long-term Measurements , EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-3837, https://doi.org/10.5194/egusphere-egu2020-3837, 2020.

The review paper by Oleg Rudenko [1] suggests several examples of elastic systems with so-called modular nonlinearities. In this study we consider the modular Korteweg - de Vries (KdV) equation in the form u_t + 6 u u_x + u_{xxx} = 0. This equation is not integrable by means of the Inverse Scattering Transform in the general case, but sign-defined functions which never change the sign satisfy the integrable KdV equation, and hence possess an exact solution. Firstly, we consider the dispersionless limit of the modular KdV equation and analyze the evolution of a simple nonlinear wave (Riemann wave) and its Fourier transform including the asymptotics when the wave tends to break [2]. Then, we study the structure of travelling waves. If the waves propagate on a pedestal and do not cross the zero level u = 0, they coincide with the well-known travelling wave solutions of the classic KdV equation in the form of cnoidal and solitary waves. If the pedestal is zero, the structure of sign-varying travelling waves is expressed through Jacobi elliptic functions. The interaction of solitary waves of different polarities is studied numerically using an implicit pseudo-spectral method. The simulation has revealed the inelastic character of the collision; in the course of the interaction the solitons can alter their amplitudes (the small soliton decreases and the large one grows) and emit small-amplitude waves. The inelastic effects are most pronounced when the solitons’ amplitudes are close. When their amplitudes differ significantly, the maximum wave height which is attained during the absorb-emit interaction tends to the sum of the heights of the solitons with the polarity inherited from the large soliton, as predicted in the frameworks of different long-wave integrable models in [3, 4]. As a result of the collision the solitons may experience non-classic phase shifts as they both jump back.

[1] O.V. Rudenko. Physics – Uspekhi, Vol. 56(7), 683-690 (2013).

[2] E. Tobisch, and E. Pelinovsky. Appl. Math. Lett., Vol. 97, 1-5 (2019).

[3] A.V. Slunyaev, and E.N. Pelinovsky. Phys. Rev. Lett., Vol. 117, 214501 (2016).

[4] A. Slunyaev. Stud. Appl. Math., Vol. 142, 385-413 (2019).

How to cite: Pelinovsky, E., Kokorina, A., Slunyaev, A., and Tobisch, E.: Modular Korteweg - de Vries equation: Riemann, cnoidal and solitary waves, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-3993, https://doi.org/10.5194/egusphere-egu2020-3993, 2020.

Fragmented geomaterials are discontinuous solids assembled of blocks, which are not joined together by any binder. The integrity of these solids is provided by interlocking of the interfaces between the fragments and compression applied at the boundary of the assembly. The main distinctive feature of these solids is the ability of separate fragments to move and rotate independently within the geometric constraints imposed by the neighbouring elements. Under application of external loads the fragments partially lose contact – the blocks get detached in a part of their contact area – that reduces the stiffness of entire blocky structure. The compression applied at the boundaries of the structure restores these contacts and brings shifted blocks back to their place. At the same time, this external compression can cause instability of the assembly, in particular when applied over heavily detached interfaces. This instability mechanism is highly non-linear due to the rotation of the fragments that produce elbowing effect and increases the compression.       

In order to assess the stability of fragmented solids, we carried out a series of experiments on the fragmented beams assembled of prismatic blocks and topologically interlocked osteomorphic blocks. The beams were axially prestressed and loaded in the transverse direction.  We observed that the blocky beams can exhibit negative stiffness in the certain testing regimes.  The block rotations observed during bending decrease the bending stiffness of the beam through the partial detachments between the fragments, while increasing the axial force due to the elbowing effect, which allows the beam to sustain additional bending deformations without increase in the external loading. This apparent negative stiffness is controlled by the combination of the prestress levels and rigidity of the axial beam constraints. We also verified these results through finite element simulations and analytical modelling.

Acknowledgements: This research was supported by the ISRAEL SCIENCE FOUNDATION (grant No. 1345/19).

How to cite: Shufrin, I., Pasternak, E., and Dyskin, A.: Stability of fragmented and blocky solids, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-21399, https://doi.org/10.5194/egusphere-egu2020-21399, 2020.

In this study, surface contact involving sections with symmetric and asymmetric friction (different magnitudes of friction are encountered when moving in opposite direction) is considered. The asymmetric friction phenomenon considered here is created when blocks of anisotropic material with symmetric axis inclined to the contact area moves in a constraint environment. Bafekrpour et al. (2015) have shown this arrangement can create high levels of asymmetric friction by coupling shear and normal forces. We consider a spring- blocks model of the type proposed by Burridge and Knopoff (1967): multiple blocks – some blocks with asymmetric friction property and others with symmetric friction property – connected by springs. Each of these blocks are connected by a spring to a driving block. Two types motion for the driving block are considered: moving at constant velocity and constant velocity with an oscillation. Parametric analysis has been conducted to compare the difference in dynamics when comparing surface interaction involving only symmetric friction blocks to different combinations of asymmetric and symmetric friction blocks. We show that threshold for instability/motion can be controlled by the proportion of asymmetric friction section present in the system and the magnitude of friction involved in the asymmetric friction section. The characteristic of the system’s motion is also shown to be affected by the arrangement asymmetric and symmetric friction sections.

Bafekrpour, E., A.V. Dyskin, E. Pasternak, A. Molotnikov and Y. Estrin (2015), Internally architectured materials with directionally asymmetric friction. Scientific Reports, 5, Article 10732.

Burridge, R. and L. Knopoff, 1967. Model and theoretical seismicity. Bulletin of the Seismological Society of America, 57(3) 341-371.

How to cite: Wong, R. X.: Asymmetric friction effects in surface interaction, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-22426, https://doi.org/10.5194/egusphere-egu2020-22426, 2020.

Nowadays hydraulic fracturing is an essential part of the development of low-permeability oil and gas fields. Moreover, the well productivity dynamics is radically depends on the effectiveness of fracturing treatment. One of the main hydraulic fracturing design problem is create a long fracture without crack height growth into the intervals saturated with non-target fluid (e.g. water). The obtaining self-similar solution to this problem in the framework of the Pserudo3D [1-3] model is considered in the presented study.

The presented crack propagation analysis shows that in the case of constant bottom hole pressure the automodel solution of one variable could be derived. A study on the dependence of the solution on pressure, time, hydraulic fluid properties and leak off is also conducted.

REFERENCES
[1] J.I. Adachi, E. Detournay, and A. P. Peirce // Analysis of the classical pseudo-3D model for hydraulic fracture with equilibrium height growth across stress barriers. International Journal of Rock Mechanics and Mining Sciences. 2010. 47 (4): 625–639. 
[2] X. Weng, O. Kresse, C. Cohen, R. Wu, and H. Gu // Modeling of hydraulic-fracture-network propagation in a naturally fractured formation. SPE Production & Operations  2011. 26 (4): 368–380. doi:10.2118/140253-PA.
[3] G.V. Paderin // Proxy Pseudo3D model: the optimum of speed and accuracy in hydraulic fracturing simulation. IOP Conference Series: Earth and Environmental Science. 2018.

How to cite: Paderin, G.: Self-similar solution analysis of hydraulic fracture growth with bottom hole pressure restriction, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-22252, https://doi.org/10.5194/egusphere-egu2020-22252, 2020.

The detailed study of rock response to cyclic loading induced by natural phenomena, such as seismic and volcanic activities, and man-made explosions and excavation is necessary for failure prediction and hazard mitigation. The effect of the maximum stress level, loading amplitude, and frequency of stress cycles on the fatigue life and failure mechanisms of two microstructurally different rocks of granite/granodiorite and sandstone is investigated. Test data obtained from comprehensive experiments conducted on these rock types incorporated with the results of previous studies show that the fatigue life time of both rock types increases with a decrease in either maximum stress level or stress amplitude. Nevertheless, the fatigue strength threshold of hard rocks like granite is generally lower than that of soft rocks like sandstone. The study also shows that the low-frequency cyclic loading has more damaging effect on both rock types than the high frequency loading. This investigation demonstrates that the failure mechanism of rocks under cyclic loading is characterized by the development of more tensile microcracks compared to the monotonic loading and the opening and extension of the axial tensile microfractures are more evident at higher maximum stresses or loading amplitudes or at lower loading frequencies. The results presented in this study will contribute to a deeper understanding of the fatigue responses of sandstone and granite to seismic-generated loading–unloading processes under different conditions of stress cycles.

How to cite: Geranmayeh Vaneghi, R., V. Dyskin, A., Thoeni, K., Sharifzadeh, M., and Sarmadivaleh, M.: The effect of seismic-like induced cyclic loading on damage response of sandstone and granite, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-4046, https://doi.org/10.5194/egusphere-egu2020-4046, 2020.

Formation and growth of hydraulic fractures can be strongly affected by pre-existing fractures in the rock mass. Until now the main attention was directed towards the investigation of the interaction between the hydraulic fracture and the pre-existing fractures intersecting its path, as they could significantly hamper its formation and growth, alter the geometry and produce additional leak-off. Less attention was paid to the interaction of the hydraulic fracture with parallel and coplanar pre-existing fractures, yet their interaction and coalescence can lead to unwelcome increase in the hydraulic fracture dimensions, change the direction of growth and in some cases result in undesirable effects such as environmental damage.  

In order to investigate the hydraulic fracture interaction with parallel pre-existing fractures we conducted a series of tests on transparent rectangular samples with two artificial cracks. One of the crack was loaded with pressurised fluid. The types of interaction were classified and the conditions of fracture coalescence formulated. The results will contribute to the understanding of hydraulic fracture propagation in fractured rock masses and mitigating environmental damage.

Acknowledgements. Wang acknowledge support from the Natural Scinece Foundation of Jiangsu (BK20171130). The AVD and EP acknowledge support from the Australian Research Council through project DP190103260. AVD acknowledges the support from the School of Civil and Transportation, Faculty of Engineering, Beijing University of Civil Engineering and Architecture. Wang acknowledge support from the National Natural Science Fund (51409170,U1765204)

How to cite: Wang, H., Yu, S., Ren, X., Tang, L., Dyskin, A., and Pasternak, E.: Interaction of a hydraulic fracture with parallel pre-existing fractures, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-10275, https://doi.org/10.5194/egusphere-egu2020-10275, 2020.

Hydraulic fractures and the natural fractures in rock masses are closed by the in-situ compressive stress such that their opposite faces are in contact either with each other or with the proppant in hydraulic fractures or with gouge in the natural fractures. Subsequently, a pressure increase can produce negligible deformation in already closed fractures as compared to the deformation associated with the opening caused by sufficiently large tensile stress. This suggests a simple model of closed fracture as a bilinear spring with a certain stiffness in tension and a very high (potentially infinite) stiffness in compression. Therefore the oscillations of fractures can be reduced to the oscillations of a bilinear oscillator or impact oscillator [1] when the compressive stiffness considerably exceeds the tensile one. We use the simplest model of the impact oscillator with preload representing the action of the in-situ compressive stress. Based on this model, two sets of multiple resonances are identified and the reaction to impulsive load is determined. The harmonics of free oscillations are calculated. The knowledge of the first two harmonics is sufficient to recover the tensile stiffness and hence identify the geometric parameters of the fracture. The results of the research contribute to the development of the methods of fracture reconstruction and the hydraulic fracture monitoring.

1. Dyskin, A.V., E. Pasternak and E. Pelinovsky, 2012. Periodic motions and resonances of impact oscillators. Journal of Sound and Vibration 331(12) 2856-2873. ISBN/ISSN 0022-460X, 04/06/2012.

Acknowledgements. The authors acknowledge support from the Australian Research Council through project DP190103260. AVD acknowledges the support from the School of Civil and Transportation, Faculty of Engineering, Beijing University of Civil Engineering and Architecture.

How to cite: Pasternak, E. and Dyskin, A.: Hydraulic fracture oscillations in response to strong impulse, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-19507, https://doi.org/10.5194/egusphere-egu2020-19507, 2020.

Seismic events associated with pre-existing faults are traditionally assumed to be caused by rupture propagation, that is in-plane shear crack propagation. However what appears to be a shear crack is a sliding zone over a fault; it grows by overcoming friction (either in direct contact or in the gouge) rather than rock rupture. When modelling frictional sliding, two important factors need to be considered: (1) the elasticity of the surrounding rocks which causes self-oscillations resulting in the movement resembling stick-slip even in constant friction; (2) the rotation of real gouge particles which being non-spherical lead, in the presence of compression, to the effect of negative shear stiffness. The latter effectively works to transfer the elastic energy stored in the compressed rock into the energy of the sliding zone propagation.

This presentation introduces 1D models accounting for these factors. Both lead to the so-called telegraph equation which is a wave equation with a non-derivative term referring to the fact that the movement is considered against a stationary solid. The equation with respect to displacement corresponds to the case of apparent negative stiffness, while the equation with respect to the displacement rate corresponds to the pure frictional sliding. The rock elasticity leads to the sliding zone propagation speed equal to the p-wave velocity making the propagation speed intra-sonic [1]. The rate-dependent friction can slightly reduce the speed. It is interesting that the sliding zone propagation is related to p-wave rather than s- or Raylegh waves as one would anticipate. The results of this research contribute to the understanding of the mechanics of seismicity.

1. Karachevtseva, I, A.V. Dyskin and E. Pasternak, 2017. Generation and propagation of stick-slip waves over a fault with rate-independent friction. Nonlinear Processes in Geophysics (NPG), 24, 343-349.

Acknowledgements. AVD acknowledges the support from the School of Civil and Transportation, Faculty of Engineering, Beijing University of Civil Engineering and Architecture.

How to cite: Dyskin, A. and Pasternak, E.: Intra-sonic propagation of sliding zones in a fault, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-19431, https://doi.org/10.5194/egusphere-egu2020-19431, 2020.

An important mechanism of oscillation and wave propagation in fragmented and blocky geomaterials such as rock masses and the Earth’s crust is the movement and rotation of the fragments/blocks as rigid bodies with deformation mainly residing at the interfaces. There are cases when the gouge in the interfaces is very weak and soft such that the resistance to parting the fragments is provided by the ambient compression which prevents the fragments/blocks from parting but allows their mutual rotation.

In order to investigate this type of block movement we performed a series of vibration tests on blocky beams of different heights under horizontal vibrations of the base. The fragmented/blocky geomaterial was modelled using osteomorphic blocks. The osteomorphic blocks have a special shape that ensures topological interlocking. The assembly is an engineered material with internal architecture which captures the fragmented and blocky nature of geomaterials [1]. The observations using the DIC technique confirm that the blocks undergo relative rotational movement. The associated rotational waves travel within the assembly transferring the energy within the blocks. This is an extension of our previous analysis that established the formation of stationary points in fragmented bodies [2]. There is energy exchange between the assembly and the loading device. The energy calculations show that the energy fluctuates around a constant value. The spectrum of block oscillations exhibits the main peak corresponding to the driving frequency as well as secondary peaks that correspond to the multiples of the driving frequency. This is in line with our previous results on bilinear oscillators [3]. The results contribute to the understanding of wave propagation in blocky/fragmented rock mass and the Earth’s crust.

1. Pasternak, E., A.V. Dyskin and Y. Estrin, 2006. Deformations in transform faults with rotating crustal blocks. PAGEOPH, 163, 2011-2030.
2. Dyskin, A.V., E. Pasternak and I. Shufrin, 2014. Structure of resonances and formation of stationary points in symmetrical chains of bilinear oscillators. Journal of Sound and Vibration 333, 6590–6606.
3. Dyskin, A.V., E. Pasternak and E. Pelinovsky, 2012. Periodic motions and resonances of impact oscillators. Journal of Sound and Vibration 331(12) 2856-2873. ISBN/ISSN 0022-460X, 04/06/2012.

Acknowledgements. The authors acknowledge support from the Australian Research Council through project DP190103260. The authors acknowledge the UWA workshop in developing and manufacturing the experimental setup. In the experiments some setup fixtures previously developed by M. Khudyakov were used. AVD acknowledges the support from the School of Civil and Transportation, Faculty of Engineering, Beijing University of Civil Engineering and Architecture.

How to cite: He, J., Pasternak, E., Dyskin, A., and Shufrin, I.: Rotational waves in fragmented and blocky geomaterials, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-9064, https://doi.org/10.5194/egusphere-egu2020-9064, 2020.

Fracture growth produced by compressive stress is typically restricted to the sizes of the pre-existing defect seeding the fracture. However the biaxial compression acting near a free surface (e.g. a wall of an opening or at a large scale, the Earth’s surface) can change the fracture growth mechanism. Our experiments demonstrate that in the presence of the second, intermediate principal stress (the minor principal stress is nearly zero in the vicinity of free surface) leads to extensive fracture propagation. Furthermore, the interaction of the propagating fracture with the free surface makes the growth unstable (catastrophic). This produces a seismic event and can lead to such a dangerous and hazardous dynamic rock failure such as skin rockburst.

Our previous experiments on brittle transparent samples with an internal initial crack under biaxial compression showed that a small magnitude of the intermediate principal stress, around 5% of the major principal stress, is sufficient to ensure extensive fracture propagation [1- 3]. The catastrophic fracture propagation is then induced by the interaction between the fracture and the free surface as the presence of the free surface imposes additional tensile stresses on the growing fracture. The type of the associated seismic event is the Compensated Linear Vector Dipole (CLVD) source. We present a simple model that allows the determination of the conditions of unstable fracture propagation and the energy of the associated seismic event. The results of this research contribute to the understanding of the nature of seismic events and the mechanics of skin rockburst.

1. Wang, H., Dyskin, A.V. Pasternak, E Dight, P Sarmadivaleh, M. 2018. Effect of the intermediate principal stress on 3-D crack growth. Engineering Fracture Mechanics, 204, 404-420.
2. Wang, H., Dyskin, A.V. and Pasternak, E. (2019) Comparative analysis of mechanisms of 3-D brittle crack growth in compression, Engineering Fracture Mechanics220, 106656.
3. Wang, H., Dyskin, A. Pasternak, E., Dight, P. and Sarmadivaleh, M. (2019) Experimental and numerical study into 3D crack growth from a spherical pore in biaxial compression, Rock Mechanics and Rock Engineering, doi.org/10.1007/s00603-019-01899-1.

Acknowledgements. AVD and EP acknowledge support from the Australian Research Council through project DP190103260. The first author acknowledges financial support from the Australian Centre for Geomechanics. The authors are grateful to Mr. Frank EE How Tan for his assistance with specimen preparation. AVD acknowledges the support from the School of Civil and Transportation, Faculty of Engineering, Beijing University of Civil Engineering and Architecture.

How to cite: Wang, H., Dyskin, A., Pasternak, E., and Dight, P.: Seismic events associated with catastrophic fracture propagation in rock under compression, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-20936, https://doi.org/10.5194/egusphere-egu2020-20936, 2020.

The hydraulic fracturing (HF) is one of the most commonly used methods for improving oil recovery. Improvement of HF efficiency requires the generation of an extensive network of secondary (non-main) fractures in the reservoir rock. This work aims to study the fracture propagation at the microscale for determining the optimal stress-strain states sustaining the most extensive network of secondary fractures. The solution accounts for rock microstructure at various scales, elastic strength parameters and elastic-plastic type of rock behavior during fracture propagation. The object of investigation is Berezov formation that features low permeability (< 1 mD) and pore dimensions down to tens of nanometers. Microstructural characterization employed computed tomography (CT) before and after geomechanical tests, quantitative evaluation of minerals by scanning electron microscopy (QEMSCAN) and energy dispersive spectroscopy. Geomechanical characterization included multi-stage compressive strength tests, Brazilian tensile strength testing. Data processing included the segmentation of micro-CT data, the 2D-QEMSCAN to 3D- micro-CT registration. For the digital rock model, the preparation we built the mesh, then populated the model with mechanical properties, defined the contact behavior between mineral grains and set boundary conditions. Using an advanced commercial mechanical simulator, we modeled fracture propagation at the microscale, obtained the simulations of fracture initiation and propagation in a 3D-homogeneous porous matrix, 2D stress-strain state of the heterogeneous material with nine minerals and fracture evolution through intergranular contacts. We found the appearance of a plasticity region in the heterogeneous matrix associated with fracture propagation. The research results allow improving the efficiency of HF operations at unconventional reservoirs and increasing production from isolated pore systems by creating an extensive secondary-fracture network.

How to cite: Nachev, V., Kazak, A., and Turuntaev, S.: 3D Simulation of Fracture Propagation in Complex Reservoirs Rocks at Microscale, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-20594, https://doi.org/10.5194/egusphere-egu2020-20594, 2020.

Based on the large-arc assumption, an analytical model is established and solved by using the complex variable function method to illustrate the dynamic stress concentration around a shallow-buried cavity under transient loads. The jump points in the dynamic stress concentration factor (DSCF) curve that do not in line with the overall trend is filtered out to obtain more reasonable results. The convergence speed of the Graf addition formula is examined, as well as the effects of the incidence angle, frequency, and burial depth on the DSCF around the cavity. Examples show that a larger arc radius and a higher incident frequency correspond to slower convergence of the Graf addition formula. There are differences between the DSCF distributions of high-frequency incidents (such as blasting waves) and low-frequency incidents (such as seismic waves). There are three tensile-stress zones and three compressive-stress zones approximately equally spaced around the cavity in the low-frequency case, and there are two tensile-stress zones and two compressive-stress zones in the high-frequency case. Regarding the variation of the DSCFs with respect to the cavity depth, incidence angle and position of wave peak there are significant differences between the high- and low-frequency cases.

How to cite: Tao, M., Huang, L., Li, X., and Wang, S.: Dynamic Stress Concentration Around Shallow-Buried Circle Cavity Under Transient P Wave Loads in Different Conditions, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-13081, https://doi.org/10.5194/egusphere-egu2020-13081, 2020.

        In the present work, a foam rubber sheet installed between two transparent thick flat glasses was used as a physical model of a permeable oil reservoir. The elastic properties of foam rubber and its coefficient of friction on glass are supposed to be measured in separate experiments. In the center of the foam sheet there is a round hole, which is a model of the end face of the well in the oil reservoir. Before the experiment, cuts are made from the hole in opposite directions and to a certain length, simulating a previously closed crack. Using a vacuum pump it is possible to change the pressure of glasses per layer and thereby simulate the increase in "rock pressure" on a productive oil reservoir . A fluid is pumped through the hole in the end of the well. Under the action of fluid filtration, the surface of the walls along the cut of the foam layer are moved apart, forming a gap.The dependence of the pressure gradient on the length of the crack formed was obtained. The overall picture of the growth of hydraulic fracturing is recorded by camera. Continuous physical observations of the formation of a fracture in time allow subsequently predict the optimal fracture geometry.

The reported study was funded by RFBR, project number №. 20-35-80028 and state task 0146-2019-0007

How to cite: Tairova, A., Belyakov, G., Iudochkin, N., and Molokoedov, A.: Hydraulic fracture propagation in high porosity media, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-20233, https://doi.org/10.5194/egusphere-egu2020-20233, 2020.

The results of laboratory experiments will be considered, that are carried out in a laboratory setup that differs from the standard ones in the shape and size of the test samples. The setup consists from two disks and wide ring between them, which form a high-pressure chamber, and it is capable to produce true 3D stresses in the samples. Laboratory experiments are performed on saturated artificial porous samples created according to similarity criteria using gypsum with Portland cement added as a model material. The samples are created directly in the high-pressure chamber and have the forms of disks with diameters of 430 mm and heights of 70 mm. This sample is saturated with water gypsum solution and loaded with vertical and two horizontal stresses using special chambers. In the upper, lower and lateral parts of the installation there are pressure sensors, ultrasonic transducers and generators. The first fracture was created by viscous fluid (mineral oil) injection through a cased borehole preliminary created in the center of the sample. After the first fracturing, the principal maximal and minimal stress axis orientations were changed, and refracturing was carried out. We failed to create two fractures oriented along the borehole, but we succeeded in creation one fracture perpendicular to the borehole and the second fracture along the borehole. Comparison of the ultrasonic wave amplitude changes during the fracturing with the fracturing pressure variations allowed us to distinct the fracture propagation and the fracture fill-up by the fracturing fluid. It was also found that for an adequate calculation of the minimum compressive stresses from the characteristic parameters ​​of the pressure change in the well, it is necessary to take into account the plastic properties of the rock, the diffusion of the fluid pore pressure in the vicinity of the well and the hydraulic fracture, the lag of the filling of the fracture with the fluid.

How to cite: Turuntaev, S., Zenchenko, E., Zenchenko, P., Trimonova, M., and Baryshnikov, N.: Laboratory study of hydraulic refracturing possibility, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-7956, https://doi.org/10.5194/egusphere-egu2020-7956, 2020.