Anisotropic Rock Mass Strength

The strength of jointed rock mass is strongly controlled by the degree of interlock between its constituent rock blocks. The degree of interlock constrains the kinematic freedom of individual rock blocks to rotate and slide along the block forming joints. The HoekeBrown (HB) failure criterion and the geological strength index (GSI) were developed based on experiences from mine slopes and tunneling projects in moderately to poorly interlocked jointed rock masses. It has since then been demonstrated that the approach to estimate the HB strength parameters based on the GSI strength scaling equations (called the 'GSI strength equations') tends to underestimate the confined peak strength of highly interlocked jointed rock masses (i.e. GSI > 65), where the rock mass is often non-persistently jointed, and the intact rock blocks are strong and brittle. The estimation of the confined strength of such rock masses is relevant when designing mine pillars and abutments at great depths, where the confining pressure is high enough to prevent block rotation and free sliding on block boundaries. In this article, a grain-based distinct element modeling approach is used to simulate jointed rock masses of various degrees of interlock and to investigate the influences of block shape, joint persistence and joint surface condition on the confined peak strengths. The focus is on non-persistently jointed and blocky (persistently jointed) rock masses, consisting of hard and homogeneous rock blocks devoid of any strength degrading defects such as veins. The results from this investigation confirm that the GSI strength equations underestimate the confined strength of highly interlocked and non-persistently jointed rock masses. Moreover, the GSI strength equations are found to be valid to estimate the confined strength of persistently jointed rock masses with smooth and non-dilatant joint surfaces.

Production of hydrocarbon causes changes in pore pressure and effective stresses acting on the reservoir rocks. This will be followed by reservoir compaction, surface subsidence and may lead to fault reactivation, casing or wellbore failure and closure of micro-cracks. Nonetheless, acquiring a good understanding of rock strength, pore pressure and in-situ stress will be critical to successful horizontal drilling and hydraulic fracturing. Bakken Formation of Williston Basin, North Dakota, which is identified by three distinct members, is a huge unconventional, self-sourced, naturally-fractured reservoir. It is one of the least studied sedimentary rock units in the basin. The over pressured nature of this formation have made the study of its geomechanical properties even more important. Natural fractures are also considered as another major source of problems in this reservoir. To investigate these problems, Mechanical Earth Model (MEM), a numerical representation of the reservoir properties, was built. This enabled to predict the alterations and changes of the geomechanical properties in the reservoir. The results show that the lower and upper members are mechanically transverse isotropic whereas the middle member is isotropic. Besides, the numerical geomechanical modeling demonstrate that the elastic anisotropic characteristics of the upper and lower members will result in elastic failure of the region around the wellbore following a shear failure phase but the elastic isotropic middle member will mostly stay in the shear failure state.

The importance of the geomechanical modeling and wellbore instability analysis is increasing in the petroleum industry with recent growth of drilling plans in unconventional reservoirs. Recently, a large majority of field developments are occurring in shale oil and shale gas reservoirs as a novel source of energy. Many of these reservoirs are thin and highly layered, anisotropic and naturally fractured; these make their geomechanical modeling and wellbore instability analysis remarkably crucial; subsequently a good understanding of elastic properties of the formation such as Young's modulus, Poison's ratio and in-situ stresses are necessary for accurate results. Bakken Formation is one of the major unconventional plays in North America which is identified by three distinct members: layerd upper and lower shale and fractured middle dolomite. The thin beddings have made them extremely anisotropic, which originates from the platey shaped clay particles, high kerogen content plus the existence of natural fractures. This has made the wellbore instability analysis and modeling of this formation highly challenging. For this study elastic properties along with the petrophysical values are collected and reported from several numbers of cores along with the wireline log data. Then, these values are used as input parameters in poroelasticity equations to calculate the magnitude of the principal stresses for instability analysis especially in the inclined section of the well. Finite Difference 3D numerical modeling was conducted under Mohr-Columb failure criterion with anisotropic assumptions to evaluate the deformations around the wellbore for instable regions. In addition, the effects of different inclination angles of the wellbore versus depth were studied. Results indicated a strong of a relation between the magnitude of the wellbore deformations with the the drilling inclination angle from vertical to horizontal. Stress contours are plotted around the wellbore resulting in zones of higher stresses concenrteation and deformation. Different failure regions are developed as well.

This thesis describes an investigation of the possibilities to measure ground-mass and especially joint parameters (joint direction and joint density) for engineering purposes by means of seismic waves. Therefore a literature study and a field investigation in the United Kingdom were done. The results show that seismic wave behaviour in one ground-mass can vary widely as result of an anisotropic ground-mass, where the anisotropic character is caused by orientated discontinuities, e.g. jointing, and that fan-shooting can be a very useful method to determine these anisotropic groundmass parameters. In some cases it even is a necessary measuring method in order to determine the proper number of ground-mass layers.

The present work proposes an approach to adapt existing isotropic models to transversely isotropic materials. The main idea is to introduce equivalence relations between the real material and a fictitious isotropic one on which one can take all the advantages of the well-established isotropic theory. Two applications of this approach are presented here: a failure criterion and a damage model that takes into account the load-induced anisotropy. In both cases, theoretical predictions are in agreement with the experimental data. In the present paper, the developed approach is applied to sedimentary rock materials; nevertheless, it can be generalized to any material that exhibits transverse isotropy.

Stress distribution in anisotropic rock medium especially shales are very complex. This anisotropic behavior has a dramatic effect on wellbore stability during fracturing operation to extract oil. To overcome a high quality drilling in the medium, understanding of stress distribution and deformation regime is required. Different parameters of rock medium such as pore pressure, rock strength, and in-situ stresses make a crucial role in evaluating the wellbore stability. The Bakken Formation in Williston Basin, North Dakota, has different layers of shales with anisotropic geomechanical parameters such as Poisson's ratio, Young's modulus, shear modulus, and rock strengths based on the laboratory experiments. Although vertical drilling is the most frequent drilling method, it is not an efficient method for oil production; thus inclined wells are inevitable. In this study, mechanical performance of the inclined drilling method was investigated to fill the current lack of knowledge about its effect on wellbore stability in this anisotropic formation. The elastic anisotropic geomechanical model based on Mohr-Coulomb failure criteria was applied to analyze inclined wellbore stability in Bakken Formation shale layers using Finite Difference Method. To study the mechanical response of drilling in the anisotropic medium, stress distribution, deformation and plastic zones of the rock adjacent to the hole were examined. In addition, the effects of different inclination angles of the wellbore versus depth were studied. Results indicate a correlation between wellbore deformations as the drilling inclination angle changes from vertical to inclined orientation. Stress contours and maximum principle stress distribution indicate an extended zone of higher stresses around the symmetric line of wellbore.

This thesis describes an investigation of the possibilities to measure ground-mass and especially joint parameters (joint direction and joint density) for engineering purposes by means of seismic waves. Therefore a literature study and a field investigation in the United Kingdom were done. The results show that seismic wave behaviour in one ground-mass can vary widely as result of an anisotropic ground-mass, where the anisotropic character is caused by orientated discontinuities, e.g. jointing, and that fan-shooting can be a very useful method to determine these anisotropic groundmass parameters. In some cases it even is a necessary measuring method in order to determine the proper number of ground-mass layers.

There are numerous occurrences of soil–rock–water interaction in the natural geo-environment involving saturated clayey gouge consolidating amid permeating rock masses and draining laterally through a network of joints. In this paper, the concept of two-dimensional drainage for consolidation along the vertical direction for saturated clay has been applied to a layer of gouge amid rock joints. Solutions for pore water pressure distribution and average degree of consolidation have been computed. The orthogonal directions along which the drainage has been assumed for the derivation of these expressions are vertical direction (as in Terzaghi’s theory of one-dimensional consolidation) and lateral direction. Initially, such a case corresponds to a Dirichlet problem applied to a rectangular gouge lamina. The deformations appearing in the vertical direction are a result of the effects of drainage in the lateral and vertical directions together. An expression for the relationship of time fac...

This study combines novel and previously published data to create a new method of estimating anisotropic rock-mass strength in three dimensions that considers both the orientation and the non-persistence of multiple joint sets. Equations are developed to evaluate joint persistence as a function of joint set spacing-to-length ratio, strength reduction as a function of joint persistence, and strength reduction as a function of dip and dip direction difference between a joint set and the shear plane. Vector rotations are used to calculate the dip and dip direction difference between the orientations of joint sets and the assumed shear plane orientation, allowing anisotropic rock-mass shear strength to be estimated for any three-dimensional direction of shear. The result is reduced strength for shear in the directions parallel to jointing and increased strength for shear in directions non-parallel to jointing, with a continuous function of strength in between the two extremes. Input parameters for the system are rock discontinuity set statistics, intact rock strength, discontinuity strength, and RQD. A slope instability case history example is back analyzed using the strength estimation procedure. A calculation sheet that implements the methodology is presented and shared for digital download.