Rock Elastic Modulus Research Articles

Analytical analysis of pullout resistance of the hydraulic expansion rockbolts on a frictionally coupled model

This paper proposes an empirical formula to estimate the shear strength of hydraulic expansion rockbolts. The field experimental results were obtained from eleven pullout tests to evaluate the results computed by the proposed formula. It was found that shear resistance of hydraulic expansion rockbolts significantly depends on the uniaxial compressive strength and elastic modulus of rock, with high correlation coefficients of 0.7651 and 0.8587, respectively. The developed formula enables estimation of the maximum pullout load in an analytical process without pullout tests in the field. Conversely, due to the poor interlocking at the initial pullout load, the measured displacements were higher than the estimated ones. To reduce the interlocking effects between bolt and rock, we recommend preloading of 29.4 kN. Preload allows reducing the distance between the measured and estimated displacement and making two load-displacement curves practically identical with marginal differences of 1.1 to 1.5 mm at the maximum pullout load.

New Equations for Estimating Radial Loads on Deep Shaft Linings in Weak Rocks

Structural support in soft rock can be very difficult in deep mining. Shaft sinking is typically a critical phase of the project. An analytical method called the convergence-confinement method (CCM), often applied in tunnels, can be used to calculate both the radial displacements associated with the construction of the shafts and the equivalent loads that the planned shaft support must guarantee. Also, the CCM can be used to calculate the plastic zone. A relationship between the stress acting on a shaft lining and the most important parameters governing the behavior of the rock (cohesion, friction angle, and elastic modulus) and the geometric parameters of the shaft (depth, radius, and lining thickness) has been obtained. The Mohr-Coulomb model was used to represent shear failure in weak rocks, considering ductile behavior (ideal strength criterion). The equations found in this paper allow for the quick estimation of the stress acting on the lining extrados.

The assessment of correlation between rock drillability and mechanical properties in the laboratory and in the field under different pressure conditions

Drillability, used for evaluating penetration rate and in selecting suitable bit types, is greatly influenced by the mechanical properties of rock. To investigate the correlation between drillability and rock mechanical properties, compressive strength, elastic modulus and Poisson's ratio were measured separately under uniaxial, 30 MPa and 60 MPa confined pressure conditions. Drillability numbers were obtained using Rollow's microbit method. Regression analysis results demonstrated the correlation between drillability grade and rock mechanical properties. The correlation improved with increased confining pressure. Additionally, the best correlation was shown between drillability grade (DG) and compressive strength under varying confined pressure conditions, as opposed to the correlation between DG and the elastic modulus or DG and Poisson's ratio under uniaxial conditions. The calculation results of rock compressive strength and DG under varying confined pressure conditions illustrated that the rock effective porosity, wellbore fluid pressure and formation pore pressure played an important role in determining the confined pressure at bottom hole. This further affects DG and compressive strength distribution along the wellbore during field drilling process. These preliminary studies could contribute significantly to understanding the effect of rock mechanical properties on confining pressure and thus on safety and efficiency of drilling in the field.

Methods to Analyze Flexural Buckling of the Consequent Slabbed Rock Slope under Top Loading

The consequent slabbed rock slope is prone to flexural buckling failure under its self-weight and top loading. However, nearly none of the existing studies consider the effect of the top loading on the slope flexural critical buckling height (CBH). Therefore, on the basis of Euler’s Method and the flexural buckling failure mode of the consequent slabbed rock slope, the calculation method of the CBH of the vertical slabbed rock slope under the self-weight is firstly proposed, and then it is extended to that of the consequent slabbed rock slope. The effect of slope dip angle, friction angle, and cohesion between the neighboring rock slabs and rock elastic modulus on the slope CBH is discussed. Secondly, the calculation method of the CBH of the consequent slabbed rock slope under its self-weight and top loading is proposed according to the superposition principle. Finally, on the basis of the hypothesis that the rock mechanical behavior obeys the statistical damage model, the effect of the rock mechanical parametersnandε0on the slope CBH is studied. The results show that the rock strength has much effect on the slope CBH. If the rock is supposed to be a linear elastic body without failure in Euler’s Method, the result from it is the maximum of the slope CBH.

Micro–macro approach of salt viscous fatigue under cyclic loading

The objective of this work is to explain the origin of fatigue observed in salt rock subject to cyclic loading. We used a self-consistent homogenization scheme to upscale the viscoplastic and damage behavior of halite polycrystals from mono-crystal viscous glide and breakage mechanisms. We modeled mono-crystals as spherical inclusions embedded in an infinite homogeneous matrix, and we assumed purely elastic inclusion/matrix interactions. We introduced a failure criterion at the mono-crystal scale in order to predict grain breakage and the subsequent damage effects on salt rock elastic moduli. We wrote an algorithm that allows computing macroscopic and microscopic stresses and strains during creep and cyclic axial loading. Although some simplifying assumptions were made in our micro–macro approach, the model provided micro-mechanical interpretations to important aspects of salt rock viscoplastic and fatigue behavior, which had not been explained so far, such as strain hardening, creep recovery, as well as damage and accelerated creep due to grain breakage. Moreover, incremental viscoplastic strains decreased over the cycles, which is in agreement with the phenomenon of “shakedown” observed in elasto-plastic media. Salt rock can be viewed as a model material. More generally, this research is expected to bring new perspectives to study the microscopic origin of fatigue in viscous polycrystalline materials.

Stress state of rocks surrounding excavations under variable Young’s modulus

Deep-level mining needs extra data on physical behavior of rocks at great depths (under high stresses). Without such data, any computations for deep-level technologies based on analogy with shallowdepth technologies are non-diagnostic. Elastic moduli of rocks may depend on the accumulated plastic deformation and their reduction is considerable in the known tests of metals. It seems interesting to study the influence of this property of rocks on distribution of residual stresses and displacements. Elastic transformation of an excavation after drivage (relief of stresses) largely affects surrounding rock mass and results in origination of a transition layer around the excavation. A local drop of deformation energy takes place in the surrounding rocks, which reduces stress concentration. The problem is studied based on an analytical solution obtained for a deep round excavation subjected to constant value compressive stresses at infinity and a solution taking into account the Young modulus. The article offers an algorithm for geomechanical condition of rocks and determines ranges for stresses and displacements in the zone of influence of excavation. Examples of calculations are given, and the results are discussed.

Application of a modified method of ultrasonic measurements for determination of elastic moduli of rocks

The velocities of elastic waves with quasi-longitudinal and quasi-transverse polarizations in a spherical rock sample have been measured. The experimental values of velocities are used to calculate 21 elastic moduli of the sample. For comparison, the effective elastic properties of the sample are simulated based on the data on the crystallographic textures of rock-forming minerals obtained by neutron diffraction. It is shown that the largest discrepancy between the model predictions and experimental velocity values is observed for transversely polarized waves.

New approach for compaction prediction in oil reservoirs

As reservoir fluids are produced, pore pressure decreases and compacting rock loses capacity to support the overburden pressure, while the effective stress increases rapidly leading to pore collapse. Reservoir can elastically compact itself until pore pressure drops to the elastic limit, then initiates a plastic deformation known as mechanical compaction. Using numerical models is a good tool for compaction prediction; as they can predict reservoir behavior. This paper is purported by some models that allow providing for an approximate representation and prediction of the compaction magnitude at the wellbore developed in oil reservoirs during production (another model could be used to amplify the range until reservoir limits), integrating a uniaxial compaction mathematical model with pressure drawdown equation in formation face, and then a numerical model is built aimed reproducing the phenomenon and its changes over time. The mathematical model is built with the uniaxial compaction model and the drawdown pressure equation. The model is not complex but integrates the mean variables and rock properties involved in compaction phenomenon, like rock compressibility, elastic modulus, porosity, permeability and fluid pressure. This paper develops new numerical model based on the foundations of the Geertsma (1973) model, adding a step-by-step procedure to calculate the new rock properties over time, in order to have a more realistic compaction magnitude result.

Bulk rock elastic moduli at high pressures, derived from the mineral textures and from extrapolated laboratory data

The elastic anisotropy of bulk rock depends on the mineral textures, the crack fabric and external parameters like, e.g., confining pressure. The texture-related contribution to elastic anisotropy can be predicted from the mineral textures, the largely sample-dependent contribution of the other parameters must be determined experimentally. Laboratory measurements of the elastic wave velocities are mostly limited to pressures of the intermediate crust. We describe a method, how the elastic wave velocity trends and, by this means, the elastic constants can be extrapolated to the pressure conditions of the lower crust. The extrapolated elastic constants are compared to the texture-derived ones. Pronounced elastic anisotropy is evident for phyllosilicate minerals, hence, the approach is demonstrated for two phyllosilicate-rich gneisses with approximately identical volume fractions of the phyllosilicates but different texture types.

Analysis between Water Contain and Lithology

Water content has a great influence on the rock mechanics properties. Four kinds of rock samples have been tested in the MTS Electro hydraulic Tri-axial Servo Test System. The result shows that with the increase of water content, the rock uniaxial compressive strength and elastic modulus value are declining. We get the fitting equation between water content and rock mechanical properties with four kind of rocks, provide a new basis for slope stability analysis and landslide prevention and control measures.

A Fractal Model for the Stress-Dependent Permeability and Relative Permeability in Tight Sandstones

Stress-dependent permeability and relative permeability in porous media are important in petroleum-engineering fields. It has been shown that stress-dependent permeability and relative permeability play important roles in determination of flow characteristics for tight-sandstone porous media. In this work, novel predictive models for stress-dependent permeability and relative permeability in microporous media with lower permeability are developed on the basis of fractal theory. The predictions of irreducible water saturation, normalized porosity, normalized permeability, and the ratio Krw/Krg by the proposed model show a variation trend similar to that of the available experimental data. On the basis of the proposed normalized porosity and normalized permeability model, it is found that the normalized porosity and permeability decrease with effective stress, thus predicted results are in good agreement with former experiments. The proposed normalized porosity and normalized permeability are expressed as a function of the effective stress, rock elastic modulus, microstructural parameters, and initial irreducible water saturation. The theoretical study of relative permeability under stress demonstrates that wetting phase relative permeability is related to the effective stress, microstructural parameters, and initial irreducible water saturation.

The Applicability of Different Fluid Media to Measure Effective Stress Coefficient for Rock Permeability

Effective stress coefficient for permeability (ESCK) is the key parameter to evaluate the properties of reservoir stress sensitivity. So far, little studies have clarified which ESCK is correct for a certain reservoir while rock ESCK is measured differently by different fluid media. Thus, three different fluids were taken to measure a fine sandstone sample’s ESCK, respectively. As a result, the ESCK was measured to be the smallest by injecting nitrogen, the largest by injecting water, and between the two by brine. Besides, those microcharacteristics such as rock component, clay mineral content, and pore structure were further analyzed based on some microscopic experiments. Rock elastic modulus was reduced when water-sensitive clay minerals were encountered with aqua fluid media so as to enlarge the rock ESCK value. Moreover, some clay minerals reacting with water can spall and possibly block pore throats. Compared with water, brine can soften the water sensitivity; however, gas has no water sensitivity effects. Therefore, to choose which fluid medium to measure reservoir ESCK is mainly depending on its own exploitation conditions. For gas reservoirs using gas to measure ESCK is more reliable than water or brine, while using brine is more appropriate for oil reservoirs.

The Effect on the Stress Distribution of the Slope for Rock and Soil Characteristics

Failure of slope generally sites along the slope of the stress concentration, while there are too many factors affecting stress distribution of slope, including the geometry of the slope, the strength parameters, the boundary conditions and constraints, etc. In this paper, considering the edge affect the elastic modulus of rock and soil slope, Poisson's ratio, shear strength parameters and other characteristics factors, by using finite element modeling to analyze the distribution forms of stress of the different slope, every factors affecting on the stress distribution of the different slope can be obtained. Through in-depth analysis, getting some understanding of regularity, it can be used to guide the engineering practice and has some promotional value.

Effect of oil composition on fluid substitution in heavy oil reservoirs

ABSTRACTUnlike light oils, heavy oils do not have a well‐established scheme for modelling elastic moduli from dynamic reservoir properties. One of the main challenges in the fluid substitution of heavy oils is their viscoelastic nature, which is controlled by temperature, pressure, and fluid composition. Here, we develop a framework for fluid substitution modelling that is reliable yet practical for a wide range of cold and thermal recovery scenarios in producing heavy oils and that takes into account the reservoir fluid composition, grounded on the effective‐medium theories for estimating elastic moduli of an oil–rock system. We investigate the effect of fluid composition variations on oil–rock elastic moduli with temperature changes. The fluid compositional behaviour is determined by flash calculations. Elastic moduli are then determined using the double‐porosity coherent potential approximation method and the calculated viscosity based on the fluid composition. An increase in temperature imposes two opposing mechanisms on the viscosity behaviour of a heavy‐oil sample: gas liberation, which tends to increase the viscosity, and melting, which decreases the viscosity. We demonstrate that melting dominates gas liberation, and as a result, the viscosity and, consequently, the shear modulus of the heavy oils always decrease with increasing temperature. Furthermore, it turns out that one can disregard the effects of gas in the solution when modelling the elastic moduli of heavy oils. Here, we compare oil–rock elastic moduli when the rock is saturated with fluids that have different viscosity levels. The objective is to characterize a unique relation between the temperature, the frequency, and the elastic moduli of an oil–rock system. We have proposed an approach that takes advantage of this relation to find the temperature and, consequently, the viscosity in different regions of the reservoir.

Effect of rock strength on failure mode and mechanical behavior of composite samples

Many dynamic events in coal mine are caused by the instability of coal–rock body. In order to study the influence of rock strength on this type of instability, uniaxial compression experiments of rock–coal–rock composite samples with different rock strengths are carried out, and the effect and mechanism of rock strength on the mechanical behavior and fracture mode of the composite samples are analyzed. The results show that major failure modes of the composite samples are conjugate X-shaped shearing fracture and splitting fracture. The angle between the shear fracture surface and the end face increases with rock strength. The splitting fracture in the coal body expands to the rock when the rock strength is low. The strength properties of the composite samples mainly depend on the coal strength instead of the rock strength. With the rock strength increasing, the peak strain of the composite samples decrease, and the differences from the coal strain and strain rate to rock strain and strain rate become greater. These failure modes and characteristics of deformation are shown to be determined by the difference between the elastic modulus of rock and coal constituting the composite samples.

Analysis on Rock Properties Based on Exploration of Hole Wall's Stability

Hole wall's stability is a complex problem which exploration engineering has been working to solve. There are many reasons which may lead to hole wall's instability. Aiming at hole wall's stability in coal exploration, this paper takes shale as objects of study and uses the MPC method (for example: analyzing on rock's microstructure characteristics, physical and mechanical properties, and chemical characteristics) to make a thorough research on unstable coal shale formations in a work area in LuoPing district. The results show that the shale in the area has high content of the mixed-layer of illite and smectite, water intrusion dramatically decreases rock strength and elastic modulus and leads to poor mechanical properties. Considering the coupling effects of mechanical properties as well as the drilling fluid sealing characteristics of drilling fluid must be improved and its osmotic pressure should be reduced.

New insight into mechanisms of fracture network generation in shale gas reservoir

Abstract The generation mechanisms of complex fracture mesh and the mechanism of activating existing natural fractures during shale fracturing are studied based on rock fracture dynamics. It is found that steering conditions should be satisfied at both the left and right ends of a natural fracture to form an intensive fracture mesh after the induced hydraulic fracture reaches the natural fracture; there exists a minimum critical pump rate (critical pump rate) to form an intensive fracture mesh. The critical pump rate increases as the inclination of the natural fracture increases and reaches a maximum value (constant) when the inclination of the natural fracture is 90°. When the inclination of the natural fracture is less than 90°, the critical pump rate first decreases and then increases as the angle between horizontal wellbore and the natural fracture increases; the critical pump rate reaches a minimum value for the natural fractures perpendicular to the wellbore. The critical pump rate increases as natural the fracture length increases and the rock elastic modulus decreases. When hydraulic fractures reopen existing natural fractures, the release of the original shear stress in the fracture surface would lead to the fracture surface slippage, which would greatly enhance the flow conductivity of the natural fracture. Very small or very large inclination of natural fracture is not conducive to fracture activation, best activating result can be reached at 30–60° inclination. Rise in elastic modulus inhibits fracture surface slippage and Poisson's ratio has little effect on fracture surface slippage.

Novel approach for simulating the elastic properties of porous rocks including the critical porosity phenomena

We tested an approach for calculating the effective elastic properties of rocks taking into account their critical porosity (the percolation threshold). The concept of critical porosity considers that when the porosity of a rock exceeds the critical value, the shear modulus of the rock tends to zero, making it lose its rigidity and the rock falls apart. The classical homogenization schemes do not describe the mechanical properties of a rock near the critical porosity. The approach proposed here is based on the generalized differential effective medium (GDEM) method. We introduce a model of porous elastic media composed of an elastic solid host containing ellipsoidal inclusions of two types. Inclusions of the first type (phase 1) represent pores, and inclusions of the second type (phase 2) contain elastic solid material described by the same elastic properties as the host (phase 0). In this model, with an increase in porosity, the concentration of the host decreased, and it tended to zero near the critical porosity. The model was used for simulation of rock elastic moduli. We compared the modeling results for elastic moduli and acoustic velocities with the experimental data and empirical petrophysical equations. The comparison showed that the GDEM model describes the elastic properties behavior in a wide range of porosity up to the critical value.

An Anisotropic Geomechanical Model for Jointed Rock Masses at Taishan Nuclear Power Station, Southern China

Abstract:An anisotropic geomechanical model for jointed rock mass is presented. Simultaneously with deriving the orthotropic anisotropy elastic parameters along the positive axis, the equivalent compliance matrix for the deflection axis orthotropic anisotropy was derived through a three‐dimensional coordinate transformation. In addition, Singh's analysis of the stress concentration effects of intermittent joints was adopted, based on two groups of intermittent joints and a set of cross‐cutting joints in the jointed rock mass. The stress concentration effects caused by intermittent joints and the coupling effect of cross‐cutting joints along the deflection‐axis are also considered. The proposed anisotropic mechanics parameters method is applied to determine the deformation parameters of jointed granite at the Taishan Nuclear Power Station. Combined with the deterministic mechanical parameters of rock blocks and joints, the deformation parameters and their variability in jointed rock masses are estimated quantitatively. The computed results show that jointed granite at the Taishan Nuclear Power Station exhibits typical anisotropic mechanical characteristics; the elastic moduli in the two horizontal directions were similar, but the elastic modulus in the vertical direction was much greater. Jointed rock elastic moduli in the two horizontal and vertical directions were respectively about 24% and 37% of the core of rock, showing weakly orthotropic anisotropy; the ratio of elastic moduli in the vertical and horizontal directions was 1.53, clearly indicating the transversely isotropic rock mass mechanical characteristics. The method can be popularized to solve other rock mechanics problems in nuclear power engineering.

The Effects of Temperature and Pressure on the Porosity Evolution of Flechtinger Sandstone

A porosity change influences the transport properties and the elastic moduli of rock while circulating water in a geothermal reservoir. The static and dynamic elastic moduli can be derived from the slope of stress–strain curves and velocity measurements, respectively. Consequently, the acoustic velocities were measured while performing hydrostatic drained tests. The effect of temperature on static and dynamic elastic moduli and porosity variations of Flechtinger sandstone was investigated in a wide range of confining pressure from 2 to 55 MPa. The experiments were carried out in a conventional triaxial system whereas the pore pressure remained constant, confining pressure was cycled, and temperature was increased step wise (25, 60, 90, 120, and 140 °C). The porosity variation was calculated by employing two different theories: poroelasticity and crack closure. The porosity variation and crack porosity were determined by the first derivative of stress–strain curves and the integral of the second derivative of stress–strain curves, respectively. The crack porosity analysis confirms the creation of new cracks at high temperatures. The porosity variation was increasing with an increase in temperature at low effective pressures and was decreasing with a rise in temperature at high effective pressures. Both compressional and shear wave velocities were increasing with increasing pressure due to progressive crack closure. Furthermore, the thermomechanical behavior of Flechtinger sandstone was characterized by an inversion effect where the sign of the temperature derivative of the drained bulk modulus changes.