Boris Tarasov

Physical Modelling of Stress-dependent Permeability in Fractured Rocks

This paper presents the results of laboratory experiments conducted to study the impact of stress on fracture deformation and permeability of fractured rocks. The physical models (laboratory specimens) consisted of steel cubes simulating a rock mass containing three sets of orthogonal fractures. The laboratory specimens were subjected to two or three cycles of hydrostatic loading/unloading followed by the measurement of displacement and permeability. The results show a considerable difference in both deformation and permeability trends between the first loading and the subsequent loading/unloading cycles. However, the micrographs of the contact surfaces taken before and after the tests show that the standard deviation of asperity heights of measured surfaces are affected very little by the loadings. This implies that both deformation and permeability are rather controlled by the highest surface asperities which cannot be picked up by the conventional roughness characterization technique. We found that the dependence of flow rate on mechanical aperture follows a power law with the exponent n smaller or larger than three depending upon the loading stage. Initially, when the maximum height of the asperities is high, the exponent is slightly smaller than 3. The first loading, however, flattens these asperities. After that, the third loading and unloading yielded the exponent of around 4. Due to the roughness of contact surfaces, the flow route is no longer straight but tortuous resulting in flow length increase.

On the Numerical Analysis of Fan-Shaped Waves

The fan-shaped mechanism of rotational motion transmission in a system of elastically bonded slabs on flat surface is studied. This mechanism governs the propagation of shear ruptures in super brittle rocks at stress conditions of seismogenic depths. The current paper analyzes a built laboratory physical model, which demonstrates the process of fan waves propagation. Equations of the dynamics of the fan-structure as a mechanical system with a finite number of degrees of freedom are obtained. Computational algorithm, taking into account contact interaction of slabs, is worked out. The computations, showing the incomplete disclosure of fans with different opening angles due to fast or slow change in the velocity of rotation of the first slab, are performed. Comparison of the results of computations of length and velocity of a fan by means of a discrete model with laboratory measurements and observations shows good correspondence between the results.

Mathematical Modeling of Fan-Structure Shear Ruptures Generated in Hard Rocks.

The main goal of this paper is to analyze the fan-mechanism of rotational motion transmission in a system of elastically bonded slabs on flat surface, simulating growth of shear ruptures in super brittle rocks. A physical model recently designed demonstrates that the fan-structure formation can be stable at the absence of distributed shear stress applied. The action of distributed shear stress causes the fan propagation as a wave representing the rupture head. The developed mathematical model of a fan-structure as a continuous system establishes the relation between the fan velocity and the fan length. It is shown that in the absence of friction the fan velocity may be arbitrary, but not greater than the limit velocity which is determined by the moment of inertia of slabs, the initial angle of their orientation and the elastic coefficient of bonds. In a system with friction the velocity of traveling fan is solely determined by the opening angle. The action of distributed shear stress leads to the instability start before the fan-structure completion. The fan length decreases with increasing velocity.

Shear Fractures of Extreme Dynamics

Natural and laboratory observations show that shear ruptures (faults) can propagate with extreme dynamics (up to intersonic rupture velocities) through intact materials and along pre-existing faults with frictional and coherent (bonded) interfaces. The rupture propagation is accompanied by significant fault strength weakening in the rupture head. Although essential for understanding earthquakes, rock mechanics, tribology and fractures, the question of what physical processes determine how that weakening occurs is still unresolved. The general approach today to explain the fault weakening is based upon the strong velocity-weakening friction law according to which the fault strength drops rapidly with slip velocity. Different mechanisms of strength weakening caused by slip velocity have been proposed including thermal effect, high-frequency compressional waves, expansion of pore fluid, macroscopic melting and gel formation. This paper proposes that shear ruptures of extreme dynamics propagating in intact materials and in pre-existing frictional and coherent interfaces are governed by the same recently identified mechanism which is associated with an intensive microcracking process in the rupture tip observed for all types of extreme ruptures. The microcracking process creates, in certain conditions, a special fan-like microstructure shear resistance of which is extremely low (up to an order of magnitude less than the frictional strength). The fan-structure representing the rupture head provides strong interface weakening and causes high slip and rupture velocities. In contrast with the velocity-weakening dependency, this mechanism provides the opposite weakening-velocity effect. The fan-mechanism differs remarkably from all reported earlier mechanisms, and it can provide such important features observed in extreme ruptures as: extreme slip and rupture velocities, high slip velocity without heating, off-fault tensile cracking, transition from crack-like to pulse-like rupture mode at variation in loading conditions, dramatic embrittlement of hard rocks at highly confined compression, abnormally low transient strength of hard rocks at high confining stresses, etc. All these questions are discussed in the paper.

Mathematical Model of Fan-Head Shear Rupture Mechanism

Today frictional shear resistance along pre-existing ruptures (faults) is considered as the lower limit on rock shear strength for confined conditions. The paper proposes a mathematical model of recently identified shear rupture mechanism which can provide propagation of faults through the highly confined intact rock mass at shear stress levels significantly less than frictional strength of pre-existing faults. The model demonstrates that due to the self-unbalancing structure of the rupture head, representing the core of this mechanism, the failure process caused by the mechanism is always spontaneous and violent. It allows a novel point of view for understanding the nature of spontaneous failure processes including earthquakes.

An approach to large-scale field stress determination

The construction of stable structures in rock masses requires knowledge of the in situ stresses at the scale of excavations. However, the measurements obtained by the conventional overcoring technique are related to a small scale (centimetres). To extrapolate them to the scales of interest to rock mechanics (from meters to kilometres) requires a large number of individual stress measurements, followed by statistical analysis to avoid a considerable scatter of the measured values. In this paper, a method is proposed based on (a) large-scale surface stress and modulus measurements using the cylindrical jack method complemented by a special measuring scheme and then (b) back analysis for a given excavation shape. The method allows the simultaneous reconstruction of the stress components at the scale of excavation. A numerical simulation for a cylindrical excavation in an isotropic rock mass demonstrates the high accuracy and robustness of the method. The presence of a fractured zone surrounding the excavation can hamper the stress reconstruction, hence special measures should be taken to conduct the measurements in competent rock.

Features of the Energy Balance and Fragmentation Mechanisms at Spontaneous Failure of Class I and Class II Rocks

Practically, all types of rockbursts are accompanied by release of seismic energy, rock bulking (due to fracturing and fragmentation), and ejection of fragmented rocks in the opening. Principles of the energy redistribution during rockbursts in some regards are comparable with principles taking place at spontaneous failure of rock specimens under compression in loading systems. In both cases, the total potential elastic energy accumulated in the failing material and in the loading system (or surrounding rock mass) is converted into such components of dynamic energy as rupture energy, seismic energy (or energy of oscillation of the loading system due to dynamic energy release), and kinetic energy of flying fragments of the failed material. It is known that spontaneous failure takes place at the post-peak failure stage and is determined by the ratio between stiffness of the loading system and stiffness (or brittleness) of the failing material. However, principles of the energy redistribution between different components of the energy balance are still unclear. The paper discusses results of laboratory experiments conducted on rock specimens of different brittleness (including Class I and Class II) that were loaded in testing machines of different loading stiffness. The most brittle of the tested specimens are represented by quartzite and glass, and the less brittle by salt. The loading stiffness of testing machines used in experiments was variable within three decimal orders of magnitude. The specific variations of the dynamic energy balance depending on rock brittleness and loading stiffness were established. The role of each portion of elastic energy stemming from the specimen and from the loading system in determining the dynamic energy balance and fragmentation mechanisms operating at spontaneous failure is analysed. The results obtained contribute to the understanding of dynamic processes taking place during rockbursts.

Fan-hinged shear as a unique mechanism of dynamic shear ruptures

Recently a new fan-hinged shear rupture mechanism has been identified as a unique mechanism of dynamic shear ruptures. In the fan-mechanism, the shear rupture propagation is driven by a fan-shaped rupture head consisting of an echelon of intercrack (domino-like) blocks formed due to the consecutive creation of small tensile cracks in the rupture tip. The fan-structure propagates through the intact material as a wave and has a number of extraordinary features, one of which is extremely low shear resistance of the rupture head (below the frictional strength). Here we present a mathematical model elucidating the principles of this new mechanism. The model will support comprehensive studies of unique features of the discovered phenomenon.