NP7.1 | Non-linear Waves and Fracturing
Poster session
Non-linear Waves and Fracturing
Convener: Arcady Dyskin | Co-conveners: Elena Pasternak, Sergey Turuntaev
Posters on site
| Attendance Mon, 15 Apr, 10:45–12:30 (CEST) | Display Mon, 15 Apr, 08:30–12:30
 
Hall X4
Posters virtual
| Attendance Mon, 15 Apr, 14:00–15:45 (CEST) | Display Mon, 15 Apr, 08:30–18:00
 
vHall X4
Mon, 10:45
Mon, 14:00
Waves in the Earth’s crust are often generated by fractures in the process of their sliding or propagation. Conversely, the waves can trigger fracture sliding or even propagation. The presence of multiple fractures makes geomaterials non-linear. Therefore, the analysis of wave propagation and interaction with pre-existing or emerging fractures is central to geophysics. Recently new observations and theoretical concepts were introduced that point out to the limitations of the traditional concept. These are:
• Multiscale nature of wave fields and fractures in geomaterials
• Rotational mechanisms of wave and fracture propagation
• Strong rock and rock mass non-linearity (such as bilinear stress-strain curve with high modulus in compression and low in tension) and its effect on wave propagation
• Apparent negative stiffness associated with either rotation of non-spherical constituents or fracture propagation and its effect on wave propagation
• Triggering effects and instability in geomaterials
• Active nature of geomaterials (e.g., seismic emission induced by stress and pressure wave propagation)
• Mechanics of granular material blowout by gas filtration
• Non-linear mechanics of hydraulic fracturing
• Synchronization in fracture processes including earthquakes and volcanic activity

Complex waves are now a key problem of the physical oceanography and atmosphere physics. They are called rogue or freak waves. It may be expected that similar waves are also present in non-linear solids (e.g., granular materials), which suggests the existence of new types of seismic waves.

It is anticipated that studying these and related phenomena can lead to breakthroughs in understanding of the stress transfer and multiscale failure processes in the Earth's crust, ocean and atmosphere and facilitate developing better prediction and monitoring methods.

The session is designed as a forum for discussing these and relevant topics.

Posters on site: Mon, 15 Apr, 10:45–12:30 | Hall X4

Display time: Mon, 15 Apr 08:30–Mon, 15 Apr 12:30
Chairperson: Panos Papanastasiou
X4.50
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EGU24-8165
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NP7.1
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ECS
Charalampos Konstantinou and Panos Papanastasiou

The fundamental processes of fluid flow and fracturing within porous media play a crucial role in various applications within the fields of energy geomechanics and groundwater hydrology. Design parameters include the composition and properties of the fluid, the hydraulic and mechanical properties of the porous media, and the injection methods. These parameters are selected based on the specific objectives of each application, such as inducing fractures or uniformly replacing pore fluids through infiltration, the depth of the operation, and whether the application is conducted in soil or rock.

Many of these operations take place in weakly-cemented and poorly-consolidated sands, which constitute the host rock for a significant portion of active aquifers and oil and gas reservoirs. These materials exhibit higher porosity and permeability compared to stronger rocks, resulting in a different response under fluid injection conditions. Fluid experiments are conducted on artificially cemented porous media to reveal the underlying mechanisms. The synthetic rock specimens used in the experiments are generated via microbially induced carbonate precipitation (MICP), a method that leads to the formation of calcium carbonate around silica particles. The resulting bio-treated specimens have prescribed properties (i.e., permeability, porosity, strength). The experimental behavior is then analyzed, encompassing factors such as infiltration/fracturing response regimes and fracturing patterns. Critical concepts from advanced geomechanics and groundwater hydrology are utilized to interpret the findings, including the brittleness index (BI), the cavity expansion theory, and the sand erosion problem.

How to cite: Konstantinou, C. and Papanastasiou, P.: Understanding the mechanisms of fluid flow and fracturing in poorly consolidated porous media, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-8165, https://doi.org/10.5194/egusphere-egu24-8165, 2024.

X4.51
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EGU24-18250
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NP7.1
Panos Papanastasiou, Charalampos Konstantinou, Daniel Garolera Garolera, and Ignacio Carol

Numerous applications in hydrogeology, geo-environmental and geo-energy engineering require the injection of a fluid into the formation. The interaction between the soil or rock matrix and the selected fluids is pivotal for each application, and relevant parameters in the design must be adjusted accordingly. Such designs must also prioritize safety, operational effectiveness, and the minimization of potential environmental impacts and infrastructure failure risks. Given that these weak materials have different hydraulic and mechanical properties compared to competent rocks, their infiltration and fracturing response remains largely unknown.

This study focuses on modelling the results of a series of experimental tests that were carried out on artificially cemented porous media which were generated via microbially induced carbonate precipitation (MICP), a process that results in the cementation of silica particles. The cores were subjected to an anisotropic triaxial stress state, and a prescribed fluid injection along a central small-diameter axial perforation. Depending on the flow rate, degree of cementation and stress intensity and anisotropy, the fluid caused radial fractures of various configurations in the samples.

The modelling has been undertaken with code DRAC, based on the FEM with multi-phase multi-physics features and zero-thickness interface elements (also known as cohesive elements). These elements are inserted in between standard continuum elements to represent the effect of existing or potential fractures, not only in the mechanical behavior but also flow or diffusion-wise. From the mechanical viewpoint, these elements are equipped with constitutive laws incorporating fracture mechanics principles including fracturing parameters Gf.

For the numerical simulation of the lab tests, the sample geometry includes the representation of individual grains generated randomly by Voronoi Tesselation, separated from each other by interface elements. The anisotropic confinement stresses are applied on the outer boundary while the injection is applied on a central circle (experimental perforation). The fracture parameters are adjusted to the cementation level, and the fluid flow along inter-grain interfaces follows the cubic law. The paper includes a sample of the results obtained, exhibiting realistic fracture values and fracture patterns as compared to experiments. The conclusion is that the approach used seems to be a valid approach to model the fracture of weakly consolidated sandstone samples subjected to fluid injection.

The developed micro-scale model can be used in applications where fluid flow in porous media serves as the underlying mechanism. Such applications include the generation of hydraulic barriers, fluid injection for groundwater contamination remediation, water decontamination, leaching-induced flow to groundwater, artificial ground freezing for groundwater containment, CO2 sequestration, managed aquifer recharge (MAR), and subsurface transportation of various fluids.

How to cite: Papanastasiou, P., Konstantinou, C., Garolera, D. G., and Carol, I.: Numerical Modeling of Fluid injection in unconsolidated formations using the FEM with zero-thickness interfaces at the micro-scale, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-18250, https://doi.org/10.5194/egusphere-egu24-18250, 2024.

X4.52
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EGU24-11981
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NP7.1
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ECS
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Abdallah Aoude, Ioannis Stefanou, Jean-François Semblat, and Vito Rubino

In this study, we present a new apparatus for creating earthquake-like instabilities in the laboratory and testing earthquake control theories (Stefanou, 2019a; Stefanou & Tzortzopoulos, 2022; Gutiérrez-Oribio et al., 2022). This experimental setup incorporates an analogue fault surrounded by an elastic medium. The frictional properties of the analogue fault are imposed by 3D printing. The elastic medium was chosen such as to have a very low Young's modulus and allow reasonable sampling rates for testing the earthquake control theories, while enabling the upscaling of the results based on appropriate scaling laws.

The apparatus allows the application of a slow, uniform deformation of the elastic medium through a system of pantographs installed at the lateral boundaries of the device. Then, when the critical state is reached, an earthquake-like instability occurs. The slip front and its propagation are measured using digital image correlation. Preliminary results show qualitative similarities with natural seismic slip, as expected.

The next step is to adjust the effective stress over the analogue fault to achieve a controlled slow slip rate of prescribed amplitude, according to our earthquake control theories and compare the results with those from existing, but simpler, experiments we have performed in the past (Gutiérrez-Oribio et al., 2023).

How to cite: Aoude, A., Stefanou, I., Semblat, J.-F., and Rubino, V.: Design of a new laboratory earthquake experiment, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-11981, https://doi.org/10.5194/egusphere-egu24-11981, 2024.

Posters virtual: Mon, 15 Apr, 14:00–15:45 | vHall X4

Display time: Mon, 15 Apr 08:30–Mon, 15 Apr 18:00
Chairpersons: Arcady Dyskin, Elena Pasternak, Sergey Turuntaev
vX4.7
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EGU24-1172
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NP7.1
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ECS
Hao Wang

Liquefaction is one of the main causes of pile foundation failure under earthquake loading. To solve this problem, seismic responses of pile foundation are typically analyzed by centrifugal shaking table test and numerical model. In this paper, a 3-D numerical model is established based on the open-source finite element platform (OpenSees). The PDMY02 multi-yield plastic model is adopted to simulate the dynamic behavior of saturated sand, with soil simulated by u-p fluid-solid coupling element and pile by beam-column elastic element respectively. Based on the data of centrifuge test of single pile, the validity of the numerical model is verified; and the influences of the upper structure mass, pile head fixation and ground inclination on the seismic response of single pile are analyzed. The results show that soil liquefaction can increase the lateral displacement and bending moment of single pile; the mass block at pile cap can magnify the pile inertial force and increase the pile-soil interaction, resulting in the augment of lateral displacement and bending moment; pile head fixation can effectively reduce lateral displacement, but intensify bending moment; sloping ground has a key influence on the pile dynamic response, and greater inclination leads to larger lateral displacement and bending moment of single pile.

How to cite: Wang, H.: Numerical simulation on pile-soil interaction under seismic loading in liquefiable ground, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-1172, https://doi.org/10.5194/egusphere-egu24-1172, 2024.

vX4.8
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EGU24-7154
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NP7.1
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ECS
Nhan Nguyen, Giang Nguyen, Ha Bui, and Terry Bennett

Permeability, a crucial factor in assessing porous reservoir rock quality, can be influenced by localised deformation such as fractures, shear bands, or compaction bands. Considering the arbitrary occurrence of these bands and the need to investigate the permeability difference between the overall specimen and within the localised zone, existing literature lacks a quantitative measure for such complexity. This study proposes a numerical concept that focuses on the permeability-stress connection across multiple levels from macroscopic to grain-scale bridging via the localised band, referred to as mesoscale. This framework integrates breakage mechanics into a dual-scale continuum model, tracking the permeability evolution of Bentheim sandstone under triaxial compression. The key feature lies in the link from stress to grain size distribution, due to breakage mechanics, that governs the constitutive responses, including macro, inside and outside of the localisation zone, produced from the dual-scale model following traction equilibrium condition. The successful outcome should capture the permeability inside the localisation band that is significantly lower compared to that of the outer bulk. The achievement provides insight into how important a correct mechanism of small details can influence the overall material behaviour while opening possible studies on many other material quantities while respecting the fundamental mechanics at multiple scales.

How to cite: Nguyen, N., Nguyen, G., Bui, H., and Bennett, T.: Permeability evolution of localised failure sandstone, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-7154, https://doi.org/10.5194/egusphere-egu24-7154, 2024.

vX4.9
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EGU24-4966
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NP7.1
Qiang Xie, Zhilin Cao, Weichen Sun, Zhanping Song, Xiang Fu, and Yuxin Ban

In this study, an ABAQUS-PFC3D coupling program framework based on the Computational Fluid Dynamics (CFD)-Discrete Element Method (DEM) coupled fluid-solid analysis method is constructed, which can be run in Windows computer system and Python language environment, and takes into account the high efficiency, simplicity, and computational stability of the bi-directional interaction of fluid-solid field information. The coupled program framework is validated using a classical particle-fluid coupling model case to assess its stability and accuracy. Further, the ABAQUS-PFC3D coupling program is used to study the evolution characteristics of internal erosion of gap-graded soil-rock mixtures of different fines contents (indoor test scale) and reproduce the whole process of water and mud-surge disaster in the Yonglian water-rich fault tunnel in Jiangxi, China, including the disaster-causing stages of palm collapse, accumulation of broken rock inside the tunnel, collapse within the fault, and surface collapse (engineering scale). The results show the stability of the coupling program framework, which improves a good reference for the popularization and application of the CFD-DEM fluid-solid coupling model.

How to cite: Xie, Q., Cao, Z., Sun, W., Song, Z., Fu, X., and Ban, Y.: Implementation and application of ABAQUS-PFC3D coupling program framework based on CFD-DEM fluid-solid coupling model: indoor test scale and engineering scale, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-4966, https://doi.org/10.5194/egusphere-egu24-4966, 2024.

vX4.10
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EGU24-3203
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NP7.1
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Sergey Turuntaev, Evgeny Zenchenko, Petr Zenchenko, Victor Nachev, and Tikhon Chumakov

Hydraulic fracturing remains the primary method of increasing hydrocarbon inflow to a borehole. Despite the many years of experience in using this method and the existence of various hydraulic fracturing simulators, companies often face problems during hydraulic fracturing, which are associated with insufficient elaboration of the physical models used in these simulators. There are a lot of theoretical and experimental studies of the occurrence and propagation of hydraulic fractures. All the models have their limitations, which can be evaluated by conducting experiments on natural or artificial rock samples. An essential aspect of hydraulic fracturing is accounting for the natural fractures of rocks. On the one hand, the natural fractures can increase the hydraulic fracturing efficiency. On the other hand, the interaction of hydraulic fractures with tectonic faults can lead to undesirable consequences in the form of induced earthquakes.

We present the results of laboratory experiments on the study of a hydraulic fracture interaction with a preliminary created fracture that simulates a natural fracture. In the experiments, under conditions of triaxial loading, the initiation and growth of a hydraulic fracture in a poroelastic material initially containing a fracture was investigated. A distinctive feature of the experiments is the ability to use an ultrasonic sounding to measure the fracture propagation and opening simultaneously with the fluid pore pressure measurements at the several points of the porous saturated sample. It allows to obtain the pressure distributions at various experiment stages and to establish a relation between the pore pressure distribution and the hydraulic fracture propagation and its interaction with pre-existing fracture. The possibilities of active ultrasonic monitoring have been expanded due to preliminary calibration experiments, which make it possible to measure the fracture opening value by attenuation of ultrasonic pulses. The profile of the existing fracture opening has been restored.The experiments show that the fracture propagation is influenced by the natural fracture. This is caused by the hydraulic fracturing fluid leaks into the natural fracture, so both hydraulic fracture and natural fracture compose united hydraulic system. The results obtained can be used to refine models of secondary fracture network formations during hydraulic fracturing in unconventional fractured reservoirs.

How to cite: Turuntaev, S., Zenchenko, E., Zenchenko, P., Nachev, V., and Chumakov, T.: Experimental laboratory study of hydraulic fracture interaction with pre-existing fault, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-3203, https://doi.org/10.5194/egusphere-egu24-3203, 2024.

vX4.11
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EGU24-6821
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NP7.1
Andrew Bunger, Arcady Dyskin, Elena Pasternak, Bunker Hill, Henry Lau, and Dane Kasperczyk

A field experiment in the Western Canadian Sedimentary Basin, Alberta, Canada entails creation of a horizontal subsurface lens (fluid-driven fracture) through fluid injection from a vertical well. The initial lens creation is followed by cycling of smaller injection and flowback stages. After completion of these smaller injection/flowback cycles, the lens is (presumably) expanded through a larger scale injection followed by another series of smaller injection/flowback cycles. Tiltmeter data indicates subhorizontal lens orientation and nearly circular shape. Combining the lens radius inferred from tiltmeter inversion with measurements of downhole pressure and downhole caliper width (opening) measurements indicate the compliance is far below the linear elastic fracture prediction based on assumption that the parting between the fracture surfaces is complete and no intact rock bridges constrain opening of the lens. Additionally, the compliance is shown to increase with increasing maximum width attained by the lens. This history-dependence suggests intact rock bridges are progressively broken as larger injected volumes are used to attain larger widths. In this view, as the bridges break, the lens compliance increases. By considering a model wherein bridges are accounted for by springs with a prescribed ultimate breaking length, the observed crack compliance and dependence of the compliance on the width history are matched. Hence, the detailed field data combined with a suitable bridge constriction model comprises compelling evidence for rock bridges constricting fluid-driven crack apertures at field scale.

 

Acknowledgements. AB, AD and EP acknowledge support from the Australian Research Council through project DP190103260.

How to cite: Bunger, A., Dyskin, A., Pasternak, E., Hill, B., Lau, H., and Kasperczyk, D.: Field Evidence for Rock Bridges Constricting the Opening of Fluid-Driven Cracks, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-6821, https://doi.org/10.5194/egusphere-egu24-6821, 2024.

vX4.12
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EGU24-15854
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NP7.1
Serge Shapiro, Arcady Dyskin, and Pasternak Pasternak

Fracture growth in rocks is not continuous; the fracture traces exhibit numerous interruptions
and overlapping. This is an indication of the presence of bridges distributed (in 3D) all over
the fracture. While the bridges themselves make little obstruction for the fluid flow in the
hydraulic fracture, they constrict the fracture opening and thus narrow the channel transmitting
the fracturing fluid. The effect of distributed bridges on the fracture opening can be modelled
by introducing a Winkler layer in the fracture with an effective stiffness combining the average
bridge stiffness and the number of bridges per unit area of the fracture.
When the fracturing fluid is injected and the leakoff is not negligible, the fracture size is
controlled by the fracturing fluid left in the fracture after leakoff rather than by the stress
concentration/singularity at the fracture contour. The flow of the fluid and filling of the fracture
depends upon the fracture geometry and is also controlled by the bridges. However, the bridges
weakly influence the time dependence of the fracture dimensions: the KGD and PKN fractures
grow proportionally to the square root of time: the effect is only in coefficients. Only in disc-
like cracks the constriction reduces the rate of crack growth and weakens the time dependence
of the fracture radius.
Acknowledgement. The authors acknowledge support from the Australian Research Council
through project DP190103260.

How to cite: Shapiro, S., Dyskin, A., and Pasternak, P.: Growth of hydraulic fractures with constricted opening and leakoff, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-15854, https://doi.org/10.5194/egusphere-egu24-15854, 2024.

vX4.13
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EGU24-12467
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NP7.1
Elena Pasternak and Arcady Dyskin

The sliding surfaces of faults and shear fractures in rocks are rarely smooth. They possess local undulations or asperities that act as distributed points of sliding disturbance. These asperities work as bridges connecting the opposite sliding surfaces and creating forces that non-linearly depend on deformation. These forces can even act in the direction of sliding. The mechanism of generating these forces is the local dilation caused by the fact that the sliding makes some asperities of one surface climb over the asperities of the opposite surface in the presence of the external compressive stress. Therefore, the dilation creates an effective friction angle which is the original (microscopic) friction angle controlling friction between the surfaces of the opposite asperities plus the inclination angle between the tangent line to the asperity surfaces at the point of contact and the direction of the movement. The inclination angle depends upon the position of the contact between the asperities making the effective friction angle non-linearly dependent upon the displacement. After passing the point of maximum dilation, the inclination angle becomes negative. Therefore, depending upon the surface friction angle, the effective friction angle can become negative. This creates the effect of local negative stiffness, where the energy is supplied by the convergence of the opposite faces of the fault/fracture (after the top of the contacting asperity is passed) in the presence of the external pressure.

 

The development of the zones of negative friction which are the zones of energy release can be accompanied by microseismisity (one zone - one signal) generated without involving local fracturing. Understanding this mechanism will contribute to refining of the existing monitoring methods of faults/fracture movement.

Acknowledgement. The authors acknowledge support from the Australian Research Council through project DP190103260.

How to cite: Pasternak, E. and Dyskin, A.: Asperities in sliding surfaces as frictional bridges. Negative friction, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-12467, https://doi.org/10.5194/egusphere-egu24-12467, 2024.

vX4.14
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EGU24-12306
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NP7.1
Arcady Dyskin and Elena Pasternak

The presence of multiple asperities in the contacting fault surfaces produces sliding resistance associated with the contact between asperities of the opposite sliding surfaces. The pairs of contacting asperities essentially work as frictional bridges: the fault sliding can only proceed when all bridges are broken, that is the corresponding pairs of asperities are either broken or their resistance is overcome by one asperity climbing over its counterpart. Furthermore, each step of sliding produces new pairs of contacting asperities forming new frictional bridges independent of the previous ones. The number of new bridges is usually high. We assume it to be proportional to the sliding velocity. The condition of producing a step of sliding is the failure of all the bridges resisting to the sliding in the area associated with the sliding step. Each bridge is characterised by a different strength (either the actual asperity strength or the force needed to make one asperity to climb over its counterpart). Given the large number of bridges involved in each step, this condition can be expressed in terms of the distribution of the maximum strengths. Using the theory of order statistics, we obtained a logarithmic dependence of the resulting friction coefficient upon the sliding velocity, which is observed in the experiments. Thus, our model suggests a new interpretation of the experimentally observed rate-dependent friction. The model parameters are associated with the parameters of bridge distribution, which are related to the morphology of the sliding surfaces.

Acknowledgement. The authors acknowledge support from the Australian Research Council through project DP190103260.

How to cite: Dyskin, A. and Pasternak, E.: Rate-dependent friction associated with frictional bridges, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-12306, https://doi.org/10.5194/egusphere-egu24-12306, 2024.

vX4.15
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EGU24-13562
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NP7.1
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ECS
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David Riley, Itai Einav, and Francois Guillard

Elastic wave speeds are crucial in geomechanics for measuring elastic stiffness. Traditionally, these speeds are calculated using an analytic formula based on a linearly elastic solid medium. However, empirical evidence suggests that stiffness is state-dependent, creating a mismatch between the theoretical assumptions and the observed stiffness constants. Recent advancements have addressed this gap by deriving wave speeds for hyperelastic (energy conserving) and hypoelastic (non-energy-conserving) constitutive models that are dependent on pressure and density. These new derivations align with conventional empirical findings for isotropic states. However, the hyperelastic model predicts variations in the ratio of longitudinal to transverse wave speeds, as observed in experiments and discrete element simulations. This prediction emerges from energy-conservation terms in the model, eliminating the need for fabric assumptions previously considered in research. Our study expands on this by exploring various density-dependent relationships and extending wave speed calculations to saturated granular media. This research enhances our understanding of granular media stiffness in dry and saturated scenarios, offering new insights for interpreting wave speed experiments.

How to cite: Riley, D., Einav, I., and Guillard, F.: Derivation of wave speed for dry and saturated nonlinearly elastic models, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-13562, https://doi.org/10.5194/egusphere-egu24-13562, 2024.

vX4.16
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EGU24-3271
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NP7.1
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ECS
Kuan Jiang and Cheng-zhi Qi

Rock masses consist of nesting rock blocks with various scales separated by weak structural layers, and their complex hierarchical structures play a significant role in dynamic deformation and stress wave propagation. Based on the Cosserat theory, a dynamic model of pendulum-type and rotational waves in blocks rock mass with complex hierarchical structures is established to determine the influence of hierarchical structures on dynamic deformation. Then, aiming to low-frequency and low-velocity characteristics of pendulum-type waves, dispersion equations of waves are determined and solved in different hierarchical structures based on the Bloch theorem, and furthermore, the dispersion relation and velocity characteristics of waves are investigated. Finally, mechanism of low-frequency characteristics of pendulum-type waves is revealed on the basis of solid energy band theory, and the possibility of pendulum-type and rotational waves inducing rock bursts is discussed based on the research results. It is indicated that ignoring higher-order hierarchical structures of rock masses may underestimate displacement and overall deformation of rock masses, resulting in unsafe numerical results. Under the action of long wave disturbance, for the first mode pendulum-type waves (the acoustic branches), the dispersion is not significant and propagation velocity decreases, and higher-order hierarchical structures inside rock masses hinder the wave propagation. However, the dispersion of other waves (the optical branches) is significant so that they hardly exist and propagate independently. The low-frequency pendulum-type waves are dominant, which have slower attenuation and longer propagation distance than the high-order mode waves and traditional P and S-waves.

How to cite: Jiang, K. and Qi, C.: Research on pendulum-type and rotational waves in 2D discrete blocky rock masses with complex hierarchical structures, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-3271, https://doi.org/10.5194/egusphere-egu24-3271, 2024.