Wave velocity and stress/strain in rock brittle failure

This paper reports the relationship between wave velocity and stress/strain during rock brittle failure under compression. It is assumed that the rock is a strain-softening medium whose strength can be described by Weibull’s distribution. Based on renormalization group theory, it is found that the stress ratio λ _c (the ratio of the stress at the critical point to the peak stress) depends mainly on the homogeneity index or shape parameter m in the Weibull’s distribution for the rock. Measured stress–strain curves and corresponding wave velocity–strain curves in four case studies suggest that the changes caused by internal cracking are correlated to variations of rock wave velocity, and the stress at the critical point on the stress–strain curve is considered to correspond to the rapid decreasing point on the wave velocity–strain curve. For uniaxial compression, the critical stress ratio λ _c is derived to be about 75.4 %, which is very close to the measured value.     

Application of the strain energy to estimate the rock load in squeezing ground condition of Eamzade Hashem tunnel in Iran

Estimation of rock load is a very important issue because the selection of a support system is highly related to this parameter. Several methods are used to estimate this parameter such as experimental, empirical, and numerical methods. This study propose a new empirical method to estimate the rock load in squeezing ground condition using actual collapses data of Emamzade Hashem tunnel of Iran based on the ration of the post-failure residual strain energy to the pre-failure stored strain energy. Prediction of squeezing ground condition in this study is performed based on Jethwa, Singh, and Hoek criterions. Results show that some sections in shale and sandstone of the Shemshak formation are prone to squeezing. Finally, the relation between the rock load and the ratio of the post-failure residual strain energy to the pre-failure stored strain energy, Ψ, in squeezing ground condition is estimated. Based on the statistical analysis, the maximum correlation between both parameters is achieved when Alejano’s equations are used to estimate the drop modulus. As the rock mass behavior changes from elastic–plastic to elastic–brittle, the drop modulus changes from 0 to infinite. The reason is that by increasing the quality of rock mass and reducing the minimum principal stresses, the ratio of post-failure residual strain energy to pre-failure stored strain energy and rock load height (H _p) reduce. So, regression analysis is used to investigate the relation between the rock load height and the ratio of post-failure residual strain energy to pre-failure stored strain energy, and finally, a formulation is presented to determine rock load height based on power function.     

A quantitative study of deformation mechanisms and finite strain in quartzites

The Weverton quartzites in the Maryland Blue Ridge are deformed by one major period of greenschist-grade deformation. The components of finite strain due to different independent mechanisms have been measured for these rocks. The total strain is split up into two major components: $$\varepsilon ^t = \varepsilon ^p + \varepsilon ^d .$$ The finite natural strain caused by dislocation creep (? ^d ) is measured by a new technique using folded and stretched rutile needles which are good strain markers within the quartz crystals. Pressure solution strain (? ^p ) is measured from the ratio of the area of new crystals and fibers to the whole rock area in principal sections. Grain boundary sliding is a dependent process which accompanies both mechanisms. Pressure solution obeys a linear Newtonian flow law, \(\left| {\dot \gamma _0^p } \right| = A_p \left| {\tau _0 } \right|\) , while dislocation creep obeys a power law of the form \(\left| {\dot \gamma _0^d } \right| = A_d \left| {\tau _0 } \right|^n \) where \(\dot \gamma _0^p ,\dot \gamma _0^d \) are octahedral shear strain rates, τ₀ is the octahedral shear stress and A _p , A _p and n are constants. A direct correlation between finite strain measurements and the operating flow laws can be made. Application of these methods and principles to a few field examples indicates that the rocks obey a flow law partly governed by each mechanism. Any set of physical conditions defines a unique flow law and there is a transition in creep behavior from dominantly Newtonian to a power law with increasing strain rate.     

Estimation of viscosity contrast and finite strain from deformed elliptical inclusions

A method of strain analysis is described which takes into account a possible competence difference between the strain markers and the rest of the rock. Using data consisting of the sectional shapes and orientations of groups of inclusions from conglomerate-like rocks, limits are placed on the possible effective viscosity contrast between the inclusions and the rock as a whole as well as on the bulk finite strain suffered by the rock. These results are calculated using a computer program, based on the theory for the deformation of elliptical cylinders. The method can be considered an extension of the Rf/φ method, but provides more information and involves less restrictive assumptions.     

The effect of sample size on geological strain estimation from passively deformed clastic sedimentary rocks

The role of sample size in the estimation of geological strain, both finite strain (R_s) and that of the orientation of the finite strain ellipse (φ_s), is investigated for clastic sedimentary rocks. This study looks at four strain methods, the Robin method, the linearization method, the Mulchrone and Meere method and the mean radial length method that are initially tested using simulated strained data sets and subsequently by applying the methods to real data. It is found that the optimum strain analysis sample size for a clastic sedimentary rock is primarily dependant on the intensity of strain suffered by that rock because of the error behavior associated with R_s estimates. An iterative process is therefore recommended starting with a minimum sample size of 150, which can be maintained or reduced based on the initial R_s estimates.     

Geochronology of Archaean gneisses and tonalites from north of the Frederikshåbs isblink,S.W. Greenland

The main rock types in the area north of the Frederikshåbs isblink are streaky gneisses, massive tonalites and ‘supracrustals’. The gneisses are thought to be the parent rocks of the tonalite and can be seen to merge into tonalite across a narrow zone of nebulite. Rb-Sr whole rock points from samples of gneiss and tonalite fall on a common isochron with an age of 2662 ± 116 m.y. (2σ) and initial ratio of 0.7032 ± 0.0008 (2σ) (half-life of ⁸⁷Rb = 50 b.y.). The uncertainties in the isochron could mask small age and initial ratio differences between the gneiss and tonalite. However, our present interpretation is that the isochron reflects a homogenization of Sr isotopes within and between the two rock types. The presence of two out of four K-feldspar points on the whole rock isochron is interpreted as evidence that the K-feldspar became closed to Sr isotope migration at the same time as the whole rocks. Subsequent local isotopic disturbance has resulted in a minor loss of radiogenic strontium from two of the samples. The interpretation of the K-feldspar as a product of the epidoteamphibolite facies metamorphism allows the conclusion that the whole rock-K-feldspar isochron is recording a Sr isotopic homogenization during this event and is not related to the formation of the gneiss or the tonalite. Rb-Sr closure ages of ca. 2515 m.y. for muscovite and ca. 1950 m.y. for biotite could be recording separate isotopic disturbances or the cessation of strontium isotope migration as the minerals cooled through their characteristic blocking temperatures. Zircons from both the gneiss and the tonalite have igneous morphological features. Their U-Pb systems are complex, however, and suggest a multistage history of isotopic disturbance. Whereas the zircon U-Pb and whole rock Rb-Sr results suggest a maximum age of approximately 3000 m.y. for the parent rocks of the gneiss and tonalite they do not entirely exclude the possibility that the rocks represent older crust in which the isotopic systems have been almost completely reset ca. 2700 m.y. ago.     

Determination of finite strain in bedding surfaces using sedimentary structures and trace fossils: A comparison of techniques

Determination of the two-dimensional finite strain in turbidite bedding surfaces is important in both structural and sedimentological investigations of deformed sediments. The Meguma Group of Nova Scotia is one such sequence, in which the directional distribution of paleocurrent markers has been modified by strain. Previous strain determinations have used sand volcanoes as strain markers, which do not deform homogeneously with their matrix and, hence, may underestimate the true strain ratio. Intraclasts and concretions also suffer inhomogeneous deformation and are of limited use as strain markers. Hexagonal trace fossil networks can provide more reliable strain estimates but are rare. Widths of burrows exposed on bedding surfaces provide a new, straightforward means of measuring strain. Each burrow is represented by a pair of parallel lines. The separation of the lines is proportional to the burrow width, and their direction represents burrow orientation. The lines are tangential to the strain ellipse, which can be discerned despite initial scatter in burrow widths.     

Comparison of methods of algebraic strain estimation from Rf/ɸ data: A unified theory of 2D strain analysis

A unified development of the subject of the algebraic strain analysis methods using Rf/ɸ data is outlined, embodying the main features the theories of Shimamoto and Ikeda, Mulchrone et al. and Yamaji. It is shown that the theories yields an identical strain ellipse from the same data set. However, error estimation in that of Shimamoto and Ikeda is difficult owing to the distortion of its parameter space: Resolution of their method depends on the choice of a reference orientation in the plane where strain markers are observed. In this respect, the remaining two theories have advantages. The hyperbolic vector mean method was developed in the Minkowski 3-space, thereby linked seamlessly with the visualizing methods of Rf/ɸ data, optimal strain and its confidence region. In addition, the residuals of the optimal strain ellipse determined by this method have clear physical meanings concerning logarithmic strains needed to transform a unit circle to given ellipses.     

Novel C15 sesquiterpanes in Niger Delta oils: Structural identification and potential application as new markers of angiosperm input in light oils

Two new C₁₅ sesquiterpanes have been isolated from a Niger Delta oil. Based on nuclear magnetic resonance (NMR) data, their structures are similar to the ring D and E part of oleanane. The mass spectra show an m/z 193 base peak typical of rearranged drimanes. They have been found only in oleanane-containing oils with a Cretaceous or Tertiary source. Data are presented for 34 such oils from Angola, Canada, Greece, India, Indonesia, Iran, New Zealand, Nigeria, Thailand and Vietnam. The ratio between the new sesquiterpanes and rearranged drimanes roughly follows the oleanane index. They are absent from marine oils whose source rock age (Jurassic or older) predates the evolution and proliferation of angiosperms. They are probably formed via degradation of functionalized oleanoids or by cleavage of seco-oleananes. These sesquiterpanes may be useful as markers of angiosperm input in light oils (jet fuel, diesel or condensates) usually devoid of higher molecular weight markers for higher plant input.     

Methanol proplyds and a double protoplanetary system in the constellation Norma

We have carried out detailed studies of a star-forming region containing two maser sources in the constellation Norma. The sources display a complex spectral distribution of the maser lines and spatial distribution of the maser condensations. The maser condensations may have formed around objects that are hidden by dense molecular cocoons; the velocities of the maser features may represent Keplerian orbital motions. The cocoons, which radiate in thermal methanol and CS lines, correspond to the centers of mass in the maser sources + dense molecular core systems. The velocities of the CS lines or thermal methanol lines can be used to identify the locations of the centers of mass of these systems. If the maser radiation is generated in the atmospheres of protoplanets, the Norma radio source may correspond to two protoplanetary disks, each with a protostar and protoplanetary system. In this case, the masses of the protostars are approximately 13 M_⊙ and 38 M_⊙.     

Biological markers from Green River kerogen decomposition

Isoprenoid and other carbon skeletons that are formed in living organisms and preserved essentially intact in ancient sediments are often called biological markers. The purpose of this paper is to develop improved methods of using isoprenoid hydrocarbons to relate petroleum or shale oil to its source rock. It is demonstrated that most, but not all, of the isoprenoid hydrocarbon structures are chemically bonded in kerogen (or to minerals) in Green River oil shale. The rate constant for thermally producing isoprenoid, cyclic, and aromatic hydrocarbons is substantially greater than for the bulk of shale oil. This may be related to the substantial quantity of CO₂ which is evolved coincident with the isoprenoid hydrocarbons but prior to substantial oil evolution. Although formation of isoprenoid alkenes is enhanced by rapid heating and high pyrolysis temperatures, the ratio of isoprenoid alkenes plus alkanes to normal alkenes plus alkanes is independent of heating rate. High-temperature laboratory pyrolysis experiments can thus be used to predict the distribution of aliphatic hydrocarbons in low temperature processes such as in situ shale oil production and perhaps petroleum formation. Finally, we demonstrate that significant variation in biological marker ratios occurs as a function of stratigraphy in the Green River formation. This information, combined with methods for measuring process yield from oil composition, enables one to relate time-dependent processing conditions to the corresponding time-dependent oil yield in a vertical modified-in situ retort even if there is a substantial and previously undetermined delay in drainage of shale oil from the retort.     

A hybridized numerical and regression method for estimating the minimum rock pillar width of twin circular tunnels

Twin tunnels can be used for many applications. Interaction between two tunnels is an important problem in tunnel engineering that should be studied specially. Numerical investigations are well adapted to field data and numerical methods can be used in design of rock pillar of twin circular tunnels. So far, no relationship has been provided to estimate the minimum stable rock pillar width. In this paper, the interaction between twin circular tunnels has been studied using 2D finite element analysis. To do this, a great number of twin tunnels were modeled in Phase2 software with different conditions of rock mass (RMR value) and depth of tunnel. Models were analyzed and minimum stable rock pillar width was determined. This process was repeated for three different ratios of K (ratio of horizontal stress to vertical stress, 0.5, 1, and 1.5). Finally, according to the linear and nonlinear regression methods, the best merit function was fitted to result of numerical analysis. Then, new approximate formula was proposed to estimate the minimum rock pillar width according to RMR value and depth of twin circular tunnels with different K values. The formulae are very accurate (coefficient of correlation equals to minimum 0.96) that can be used for estimating the minimum rock pillar width of twin circular tunnels.     

Influence of rock property correlation on reliability analysis of rock slope stability: From property characterization to reliability analysis

Cohesion(c) and friction angle(φ) of rock are important parameters required for reliability analysis of rock slope stability. There is correlation between c and φ which affects results of reliability analysis of rock slope stability. However, the characterization of joint probability distribution of c and φ through which their correlation can be estimated requires a large amount of rock property data, which are often not available for most rock engineering projects. As a result, the correlation between c and φ is often ignored or simply assumed during reliability studies, which may lead to bias estimation of failure probability. In probabilistic rock slope stability analysis, the influence of ignoring or simply assuming the correlation of the rock strength parameters(i.e., c and φ) on the reliability of rock slopes has not been fully investigated. In this study, a Bayesian approach is developed to characterize the correlation between c and φ, and an expanded reliability-based design(RBD) approach is developed to assess the influence of correlation between c and φ on reliability of a rock slope. The Bayesian approach characterizes the sitespecific joint probability distribution of c and φ, and quantifies the correlation between c and φ using available limited data pairs of c and φ from a rock project. The expanded RBD approach uses the joint probability distribution of c and φ obtained through the Bayesian approach as inputs, to determine the reliability of a rock slope. The approach gives insight into the propagation of the correlation between c and φ through their joint probability into the reliability analysis, and their influence on the calculated reliability of the rock slope. The approaches may be applied in practice with little additional effort from a conventional analysis. The proposed approaches are illustrated using real c and φ data pairs obtained from laboratory tests of fractured rock at Forsmark, Sweden.     

Analytical methods for measuring the parameters of interstellar gas using methanol observations

The excitation of methanol in the absence of external radiation is analyzed, and LTE methods for probing interstellar gas considered. It is shown that rotation diagrams correctly estimate the gas kinetic temperature only if they are constructed using lines whose upper levels are located in the same K-ladders, such as the J₀?J_?1E lines at 157 GHz, the J₁?J₀E lines at 165 GHz, and the J₂?J₁E lines at 25 GHz. The gas density must be no less than 10⁷ cm^?3. Rotation diagrams constructed from lines with different K values for their upper levels (e.g., 2_K?1_K at 96 GHz, 3_K?2_K at 145 GHz, 5_K?4_K at 241 GHz) significantly underestimate the temperature, but enable estimation of the density. In addition, diagrams based on the 2_K?1_K lines can be used to estimate the methanol column density within a factor of about two to five. It is suggested that rotation diagrams should be used in the following manner. First, two rotation diagrams should be constructed, one from the lines at 96, 145, or 241 GHz, and another from the lines at 157, 165, or 25 GHz. The former diagram is used to estimate the gas density. If the density is about 10⁷ cm^?3 or higher, the latter diagram reproduces the temperature fairly well. If the density is around 10⁶ cm^?3, the temperature obtained from the latter diagram should be multiplied by a factor of 1.5–2. If the density is about 10⁵ cm^?3 or lower, then the latter diagram yields a temperature that is lower than the kinetic temperature by a factor of three or more, and should be used only as a lower limit for the kinetic temperature. The errors in the methanol column density determined from the integrated intensity of a single line can be more than an order of magnitude, even when the gas temperature is well known. However, if the J₀?(J ? 1)₀E lines, as well as the J₁?(J ? 1)₁A⁺ or A^? lines are used, the relative error in the column density is no more than a factor of a few.     

A lead isotope method for the accurate dating of disturbed geologic systems: numerical demonstrations, some applications and implications

Lead isotopes are compared in two equivalent diagrams. With a range in U/Pb, a closed system that evolved its radiogenic Pb in a single stage yields data that define a line of exactly the same age in the two presentations. This strict reproducibility (within ± a few 10⁶ yr, at most) is the crux of the concept of Pb-isotope synchronism. In contrast, an open system produces data that disperse variably in the two diagrams, yielding ages which are often different by ?10⁷ yr. However, because an age-calculation reconciles uncertainty in the age with the degree of dispersion in the data, a highly disturbed system yields false ages (from both diagrams), which nevertheless overlap within the calculated errors.This dichotomy (tightly reproduced linearity of a closed system vs. loosely correlated dispersion of an open one) is exploited in a new procedure, termed differential Pb correlation. This procedure allows filtering the data, so that an imperfect isochron may be improved or an invisible one may be identified within a dispersion field.Applying the synchronism method to the whole rock Pb isotopic data on the Amîtsoq gneisses results in their resolution into three synchronous lines, yielding the single-stage ages of 4.42, 3.74 and 3.45 Ga. In an attempt to reconcile this observation with geology, the mechanisms which may have produced these lines (multi-stage lineation) are explored. In addition, the possibility that the 4.42-Ga line is an actual isochron, and that vestiges of an ancient terrestrial crust of that age exist, are contemplated in some detail.The utility of the method is further demonstrated by application to meteorites as well as terrestrial rocks. Isochrons of crustal rocks intersect with each other as subgroups in multiple places (that is, at multiple Pb isotope values). This indicates the apparent existence of terrestrial reservoirs distinct in isotopic composition from each other. One of these reservoirs, characterized by a low (U/²⁰⁴Pb) = 4 may represent a depleted complement to the U-enriched source(s) of the ocean-island basalt (OIB). If so, then the so-called “Pb paradox” may no longer exist.     

Theoretical and natural strain patterns in ductile simple shear zones

A simple empirical model representing the variation of shear strain throughout a simple shear zone allows us to determine the evolution of finite strain as well as the progressive shape changes of passive markers. Theoretical strain patterns (intensity and orientation of finite strain trajectories, deformed shapes of initially planar, equidimensional and non-equidimensional passive markers) compare remarkably well with patterns observed in natural and experimental zones of ductile simple shear (intensity and orientation of schistosity, shape changes of markers, foliation developed by deformation of markers).The deformed shapes of initially equidimensional and non-equidimensional passive markers is controlled by a coefficient P, the product of

1. (1) the ratio between marker size and shear zone thickness

2. (2) the shear gradient across the zone.

For small values of P (approximately P < 2), the original markers change nearly into ellipses, while large values of P lead to “ retort” shaped markers.This theoretical study also allows us to predict, throughout a simple shear zone, various relationships between the principal finite strain trajectory, planar passive markers and foliations developed by deformation of initially equidimensional passive markers.     

Numerical Modeling of Pore Pressure Influence on Fracture Evolution in Brittle Heterogeneous Rocks

Rock is a heterogeneous geological material. When rock is subjected to internal hydraulic pressure and external mechanical loading, the fluid flow properties will be altered by closing, opening, or other interaction of pre-existing weaknesses or by induced new fractures. Meanwhile, the pore pressure can influence the fracture behavior on both a local and global scale. A finite element model that can consider the coupled effects of seepage, damage and stress field in heterogeneous rock is described. First, two series of numerical tests in relatively homogeneous and heterogeneous rocks were performed to investigate the influence of pore pressure magnitude and gradient on initiation and propagation of tensile fractures. Second, to examine the initiation of hydraulic fractures and their subsequent propagation, a series of numerical simulations of the behavior of two injection holes inside a saturated rock mass are carried out. The rock is subjected to different initial in situ stress ratios and to an internal injection (pore) pressure at the two injection holes. Numerically, simulated results indicate that tensile fracture is strongly influenced by both pore pressure magnitude and pore pressure gradient. In addition, the heterogeneity of rock, the initial in situ stress ratio (K), the distance between two injection holes, and the difference of the pore pressure in the two injection holes all play important roles in the initiation and propagation of hydraulic fractures. At relatively close spacing and when the two principal stresses are of similar magnitude, the proximity of adjacent injection holes can cause fracturing to occur in a direction perpendicular to the maximum principal stress.     

An examination of in situ rock stress estimation using the Kaiser effect

When rock cores are loaded in uniaxial compression, acoustic emission occurs when the stress reaches a level greater than that which the rock has previously experienced. This phenomenon, known as the Kaiser Effect, has been used as an indirect method of estimating the in situ stress field in rock masses. If the procedure is valid, then the Kaiser Effect method has the advantage that the stress field can be estimated through laboratory tests on rock cores, rather than the field drillhole methods of overcoring and hydraulic fracturing. However, the Kaiser Effect method is an enigma: on the one hand, there are good reasons why the method cannot be valid; on the other hand, there are reports in the literature of it being successfully applied. In this paper, we explore the variety of geological and mechanical factors involved and report on a case example for the Olkiluoto crystalline rock site in western Finland. We conclude that the Kaiser Effect method for stress measurement is only likely to be successful if it is supported by key geological and other stress measurement information and if certain procedures are followed as explained in the paper.     

Organic acids from source rock maturation: generation potentials,transport mechanisms and relevance for mineral diagenesis

Hydrous pyrolysis has been used to simulate maturation of source rocks with respect to the generation of organic acids and CO₂. The results from pyrolysis experiments on eight different source rocks at this laboratory are given and compared with published data. The investigation show levels of generation for acetic acid equivalent to 0.2–1.2% of the TOC of the source rock and total acids at a level of 1–2% of the TOC. The generated CO₂ is equivalent to 1–10% of the TOC. The relative amounts of CO₂ and organic acids and the maturity dependence of the yield are a function of the source rock type.The amounts of acids generated are sufficient to give significant concentrations in the fluid phases of the source rock and, after migration, in adjacent rocks. Reaction and equilibration with minerals will occur at the first contact, which in most cases will be in or close to the source rock. The organic acids may initially be dissolved in the oil phase, but their high aqueous solubilities will make them diffuse rapidly out of the oil phase and into the surrounding water phase as soon as the oil has migrated into porous carrier beds. The migration of the petroleum phase is driven by buoyancy and there is no equivalent drive for water flow from source rock to reservoir. If the distance between source and reservoir s large, the organic acids found in the reservoir formation waters must therefore have been transported in the oil phase or generated in situ from emplaced oil or disseminated kerogen. The high water solubility of the acids will, however, limit the distances they can be transported in the oil phase. In situ generation in the reservoir must therefore be seriously considered.