Lower bound limit analysis of unsupported vertical circular excavations in rocks using Hoek-Brown failure criterion

The stability of vertical unsupported circular excavations in rock media, obeying generalized Hoek-Brown yield criterion, has been investigated by using the lower bound finite elements limit analysis. An axisymmetric analysis, composed of a planar domain with a mesh of three-noded triangular elements, has been carried out. The optimization problem is dealt with by using the semidefinite programming technique avoiding the need of either smoothing the yield surface or making any assumption associated with the circumferential stress (σ_θ). A detailed parametric study has been executed, and the effects of different input material parameters, namely, geological strength index (GSI), yield parameter (m_i), and the disturbance factor (D) on the results have been studied. For different height to radius ratios of the excavation, the computed results are presented in the form of nondimensional stability numbers. Failure mechanisms have also been investigated for a few typical cases. The results from the analysis have been compared with that evaluated separately with the application of the software OptumG2.     

Interplay between stress permutations and overpressure to cause strike‐slip faulting during tectonic inversion

Field data from an orogenic foreland and an orogenic belt (the Mesozoic rocks of southern England and the Umbria‐Marche Apennines of Italy respectively) indicate the following. Firstly, stress evolution during the tectonic cycle, between maximum compressive stress (σ₁) being vertical during extension and least compressive stress (σ₃) being vertical during contraction, can involve phases when the intermediate compressive stress (σ₂) is vertical, promoting strike‐slip deformation. Secondly, variations in the relative magnitudes of the stress axes are caused by variations in overburden and tectonic forces. Thirdly, overpressure can develop because of compaction during burial, and, as overburden is reduced during uplift and erosion, the vertical stress (σ_V) reduces but fluid pressure (P_f) remains approximately constant. Brittle deformation, including transient strike‐slip faults, reverse‐reactivated normal faults and normal‐reactivated thrusts, is preferentially developed in overpressured areas because high P_f promotes faulting.     

The effects of intermediate principle stress on the mechanical behavior of transversely isotropic rocks: Insights from DEM simulations

The discrete element method (DEM) is used to study the response of anisotropic rocks under true triaxial testing. Numerical samples of seven different bedding orientations (β = 0^o, 15^o, 30^o, 45^o, 60^o, 75^o, and 90^o) are created. Six series of test simulations (σ₃ = 0, 10, 30, 50, 70, and 100 MPa) are conducted on each sample, with five different σ₂ values, varied from σ₃ to σ₁. The effects of anisotropy and intermediate stress on the peak strength, brittle-ductile transition, and degree of anisotropy are subsequently explained through underlying micromechanics. Results show a “fan-shaped” variation of the peak strength with σ₂, displaying an ascending-then-descending trend. An increasing brittleness with σ₂ is observed at lower confining pressures for all, but medium anisotropy angles. For higher confining pressures, increasing ductility with σ₂ is seen for every anisotropy angle. A U-shaped variation of peak strength with anisotropy angles is noted that flattens under high intermediate stress. Hence, for numerical models of Posidonia shale under normalized σ₂ higher than 0.76, the anisotropy effect is found to be negligible. Micromechanical analyses reveal that the stress asymmetry, suppression of weak plane action as well as the localization and coalescence of microcracks in the intact rock matrix, due to σ₂, are the contributors towards the obtained trends. Since existing failure criteria do not weigh in these features in geotechnical assessments, this paper helps future studies by providing a deeper understanding of these effects and a comprehensive data set for the analyses of anisotropic rocks under polyaxial stress conditions.     

Assessment of test data for selection of 3‐D failure criterion for sand

Data from three‐dimensional experiments performed on sand in true triaxial equipment have been reviewed to sort out apparent disarray resulting from their interpretation. This has been done based on analyses made possible by recent developments and understanding of factors influencing sand behaviour: occurrence of shear banding, boundary conditions and/or specimen slenderness ratio, cross‐anisotropy, and stability of experimental technique. These factors are reviewed and test data from the literature are evaluated. Experimental data are divided into three groups in which: (a) homogeneous behaviour controls the sand strength; (b) shear banding affects the shape of the three‐dimensional failure surface in the midrange of values of b=(σ₂?σ₃)/(σ₁?σ₃), and (c) the data has been misinterpreted. Appropriate interpretation of three‐dimensional strength data for sand exhibiting isotropic, homogeneous behaviour is represented by a smoothly rounded triangular failure surface expressible in terms of the first and third stress invariants. Shear banding effects will cause the failure surface to be ‘indented’ in the midrange of b‐values in all sectors of the octahedral plane. Effects of cross‐anisotropy will result in lower strengths in sector III than in sector I of the octahedral plane, and the failure surface will appear as rotated around the stress origin in principal stress space. Copyright © 2005 John Wiley & Sons, Ltd.     

A new method to calculate the equivalent Mohr–Coulomb friction angle for cohesive and frictional materials

In this note, a new method to calculate the equivalent Mohr–Coulomb friction angle ?′_mc for cohesive and frictional materials is presented. This method makes a transformation from the failure surface for cohesive materials to the failure surface for cohesionless materials and obtains ?′_mc as well as the principal stress ratio σ′₁/σ′₃ for cohesionless materials in the transformed space first, then obtains ?′_mc for cohesive materials by linking σ′₁/σ′₃ in the transformed space and in the original space. In the application example, an analytical solution of the invariant stress ratio L is derived from the failure function in the transformed space. The influence of the intermediate effective principal stress σ′₂ is also demonstrated using the already calculated ?′_mc. Copyright © 2010 John Wiley & Sons, Ltd.     

Installation effects of the post-grouted micropile in marine soft clay

The grouted steel pipe micropile is widely used as structural support and in situ improvement in China. This paper presents measurement of the radial soil stress and excess pore water pressure during the construction processes of the grouted steel pipe micropile (with an enlarged driving shoe) embedded in marine soft clay. Comparative analysis was conducted between the predictions by cavity expansion method (CEM) and maximum stress values in situ. The results show that the existence of the enlarged driving shoe has an effect on the stress change in the surrounding soils during penetration. The maximum radial total stress and excess pore water pressure generated during micropile penetration are approximately 4–6σ_v0′ and 1.5–2.5σ_v0′, respectively. The maximum radial total stress and excess pore water pressure, which appeared near the pile wall during the process of post-grouting, are approximately 5–7c_u and 4–6c_u, respectively. The predictions of CEM for pore water pressure during micropile penetration and post-grouting are in reasonable agreement with the field test data.

     

A Study on Crack Damage Stress Thresholds of Different Rock Types Based on Uniaxial Compression Tests

When rock samples are loaded until macroscopic fractures develop, the failure process can be divided into several stages based on axial and lateral strain responses or the acoustic emission sequence during uniaxial compression tests. Several stress thresholds may be identified: the crack closure stress σ _cc, crack initiation stress σ _ci, crack damage stress σ _cd, and uniaxial compressive strength σ _ucs; these may be used as a warning indicator for rock rupture. We investigated the crack damage stress σ _cd, its threshold, and a possible relationship between σ _cd and the uniaxial compressive strength. The σ _cd of different rock types were compiled from previous studies based on uniaxial compression tests. The results showed that the overall averages and standard deviations of σ _cd /σ _ucs for igneous, metamorphic, and sedimentary rocks were ~0.78 (±0.11), ~0.85 (±0.11), and ~0.73 (±0.18), respectively. There were no significant differences in σ _cd /σ _ucs between the different rock types, except that the sedimentary rock had a slightly larger standard deviation attributed to the variation of porosity in the samples, while the metamorphic rock had higher average σ _cd /σ _ucs resulting from the small statistical sample size. By excluding the higher-porosity (>10 %) rock samples, the averages and standard deviations of σ _cd /σ _ucs for igneous, metamorphic, and sedimentary rocks were ~0.78 (±0.09), ~0.85 (±0.09), and ~0.78 (±0.11), respectively. The results imply that the rock origin process (i.e., igneous, metamorphic, and sedimentary) has a minimal effect on σ _cd /σ _ucs. The ratio σ _cd/σ _ucs could be an essential intrinsic property for low-porosity rocks, which could be used in rock engineering for predicting the failure process.     

A synthesis: Late Cenozoic stress field distribution at northeastern corner of the Eastern Mediterranean,SE Turkey

Fault kinematic analysis and inversion of focal mechanisms of shallow earthquakes reveal significant evolution of the regional stress regime in the northeastern most corner of the Eastern Mediterranean region since the Mio-Pliocene to the present time. This study was carried out in the interaction area between the Arabian/African plates and the Anatolian block. The evolution of stress regimes consists of a change from older transpression to younger transtension. Both strike-slip stress regimes having a NNW- to northwest-trending σ_Hmax (σ₁) and ENE- to northeast-trending σ_Hmin (σ₃) axes induce a sinistral component of displacement on the major intra-continental Karatas–Osmaniye and Misis–Ceyhan faults elongated with the northeast-trending Misis Range between Adana and Osmaniye provinces (sub-area i) and by a NNE-trending plate boundary Amanos fault running along Amanos Range between Antakya and Kahramanmaras provinces (sub-area ii). The inversion results show that the transtensional stress regime is dominantly strike-slip to extension, with an ENE- to northeast-trending σ_Hmin (σ₃) axis for sub-areas (i) and (ii), respectively. The inversions of earthquake focal mechanisms indicate that the transtensional stress regime is still active in the whole study area since probably recent Quaternary time. To cite this article: S. Over et al., C. R. Geoscience 336 (2004).     

THE ‘NEW IMPLICIT METHOD’ FOR TUNNEL ANALYSIS

Tunnel excavation is a coupled three-dimensional problem dealing with two different structures: lining and rockmass. For a simple application it is useful to develop simplified methods by treating the problem as plane strain. If the problem of tunnel face advance presents an axisymmetric geometry, then we show that the major parameter governing the ground–interface–lining interaction is the convergence of the tunnel U₀ at the moment of the lining installation. The ‘New Implicit Method’ (NIM) presented in this paper makes use of principles similar to those of the ‘convergence–confinement’ method, but it provides a better appreciation of the coupled behaviour of rockmass and lining. For independent time constitutive laws (elasticity and plasticity), we point out that the convergence U₀ depends not only on the mechanical behaviour of the rockmass and on the distance from the tunnel face, as predicted by the ‘convergence–confinement’ method, but also on the stiffness of the lining previously set. We present the ‘NIM’ for elastic and perfect elastoplastic rockmasses without dilatancy for many criteria. The development of this new method is based on the results of tunnel calculations with an axisymmetric FEM numerical model that takes into account the three-dimensional aspect of the problem. Using this method is simple and its results agree well with the FEM numerical results. Its accuracy is highly satisfactory for a geotechnical study.     

Distribution rule of the in situ stress state and its influence on the permeability of a coal reservoir in the southern Qinshui Basin,China

The recent development of the coalbed methane (CBM) industry has a significant role in advancing hydraulic fracturing theory and technology. However, further development requires a better understanding of how fractures influence reservoir permeability. In situ stress data from 54 CBM wells in the southern Qinshui Basin, China, were obtained by the injection/falloff test method to analyse the effect of in situ stress on the permeability of the CBM reservoir. The types of in situ stress states were classified, and the coal reservoir permeability under different in situ stress states was analysed. The results indicate that the maximum horizontal principal stress (σ_H), minimum horizontal principal stress (σ_h) and vertical principal stress (σ_v) all have positive linear relationships with the coal seam burial depth. Three in situ stress states were observed from the shallow to deep regions of the CBM reservoir in the study area: σ_H?>?σ_h?>?σ_v, σ_H?>?σ_v?>?σ_h and σ_v?>?σ_H?>?σ_h, which account for 9, 76 and 15% of the test wells, respectively. Coal reservoir permeability decreases with increasing horizontal principal stress, whereas it first decreases with increasing σ_v, then increases and finally decreases. The variation in permeability with σ_v is due to the conversion of the in situ stress states. Coal reservoir permeability has obvious differences under different in situ stress states. The permeability is the largest when σ_v?>?σ_H?>?σ_h, followed by σ_H?>?σ_h?>?σ_v and smallest when σ_H?>?σ_v?>?σ_h. The permeability differences are caused by the fracture propagation shape of the rock strata under different in situ stress states.     

In situ stress field of eastern Australia

New in situ data based on hydraulic fracturing and overcoring have been compiled for eastern Australia, increasing from 23 to 110 the number of in situ stress analyses available for the area between and including the Bowen and Sydney Basins. The Bowen Basin displays a consistent north‐northeast maximum horizontal stress (σ_H) orientation over some 500 km. Stress orientations in the Sydney Basin are more variable than in the Bowen Basin, with areas of the Sydney Basin exhibiting north‐northeast, northeast, east‐west and bimodal σ_H orientations. Most new data indicate that the overburden stress (σ_V) is the minimum principal stress in both the Bowen and Sydney Basins. The Sydney Basin is relatively seismically active, whereas the Bowen Basin is relatively aseismic. Despite the fact that in situ stress measurements sample the stress field at shallower depth than the seismogenic zone, there is a correlation between the stress measurements and seismicity in the two areas. Mohr‐Coulomb analysis of the propensity for failure in the Sydney Basin suggests 41% of the new in situ stress data are indicative of failure, as opposed to 13% in the Bowen Basin. The multiple pre‐existing structural grains in the Sydney Basin further emphasise the difference between propensity for failure in the two areas. Previous modelling of intraplate stresses due to plate boundary forces has been less successful at predicting stress orientations in eastern than in western and central Australia. Nonetheless, stress orientation in the Bowen Basin is consistent with that predicted by modelling of stresses due to plate boundary forces. Variable stress orientations in the Sydney Basin suggest that more local sources of stress, such as those associated with the continental margin and with local structure, significantly influence stress orientation. The effect of local sources of stress may be relatively pronounced because stresses due to plate boundary forces result in low horizontal stress anisotropy in the Sydney Basin.     

Bearing capacity of foundations on rock mass using the method of characteristics

The method of stress characteristics has been used for computing the ultimate bearing capacity of strip and circular footings placed on rock mass. The modified Hoek‐and‐Brown failure criterion has been used. Both smooth and rough footing‐rock interfaces have been modeled. The bearing capacity has been expressed in terms of nondimensional factors N_σ0 and N_σ, corresponding to rock mass with (1) γ = 0 and (2) γ ≠ 0, respectively. The numerical results have been presented as a function of different input parameters needed to define the Hoek‐and‐Brown criterion. Slip line patterns and the pressure distribution along the footing base have also been examined. The results are found to compare generally well with the reported solutions.     

Shear strengths of sandstone fractures under true triaxial stresses

True triaxial shear tests have been performed to determine the peak shear strengths of tension-induced fractures in three Thai sandstones. A polyaxial load frame is used to apply mutually perpendicular lateral stresses (σ_p and σ_o) to the 76 × 76 × 126 mm rectangular block specimens. The normal to the fracture plane makes an angle of 59.1° with the axial (major principal) stress. Results indicate that the lateral stress that is parallel to the fracture plane (σ_p) can significantly reduce the peak shear strength of the fractures. Under the same normal stress (σ_n) the fractures under high σ_p dilate more than those under low σ_p. According to the Coulomb criterion, the friction angle decreases exponentially with increasing σ_p/σ_o ratio and the cohesion decreases with increasing σ_p. The lateral stress σ_p has insignificant effect on the basic friction angle of the smooth saw-cut surfaces. The fracture shear strengths under σ_p = 0 correlate well with those obtained from the direct shear tests. It is postulated that when the fractures are confined laterally by σ_p, their asperities are strained into the aperture, and are sheared off more easily compared to those under unconfined condition.     

Identification of non‐linear stress–strain–time relationship of soils using genetic algorithm

Recognition of non‐linear constitutive rock/soil model from experimental results is often multi‐modal in the large parameter space. A genetic evolution algorithm is thus proposed for its recognition, including that of structure of the model and coefficients in the model. The structure of the model can be firstly determined according to mechanical mechanism if the mechanism is clearly understood or searched by using evolutionary algorithm. The coefficients to be determined are then searched in global optional space. With the new evolutionary algorithm, the non‐linear stress–strain–time constitutive law to describe strain softening behaviours of diatomaceous soil under consolidated and undrained state was recognized by learning stress–strain–time behaviour of an intact sample under consolidated pressure of σ_c=0.1 MPa and strain velocity of_a=0.175%/min. This model gave reasonable prediction for diatomaceous soils under varying consolidated pressures (0.1–3.5 MPa) and strain velocities (0.0044–1.75%/min). It indicates that the methodology proposed in this paper is robust enough and strongly attractive for recognition of non‐linear constitutive model of soil and rock materials. Copyright © 2002 John Wiley & Sons, Ltd.     

State of stress in the northern Tabas block, east-central Iran, as inferred from focal mechanisms of the 1978 Tabas earthquake sequence

In this paper, the state of stress in the northern Tabas block in east-central Iran is analyzed based on the systematic inversion of aftershock focal mechanisms from the 1978.09.16 Tabas earthquake, to characterise the stress regime that controls most earthquakes in this area. Here, stress inversions of double-couple focal mechanisms of earthquakes recorded during the 30 days following the main shock have been carried out. The calculated average stress regime indicates dominant major 226° to 237° trending compression for the Tabas region. The dominating regime in east-central Iran is thrusting with a minimum stress axis, σ ₃, close to vertical. The reconstruction of the main seismotectonic stress in east-central Iran with a NE-SW compression is consistent with independent information of the active plate convergence related to Arabia-Eurasia convergence. Most earthquakes in the mentioned area occur near or around concealed Quaternary thrust faults with their activity being controlled by the NE-SW compression. Where ?, the ratio of principal stress differences, is 0.5, a small difference between σ ₂; σ ₃ and σ ₁ and small amounts of deviatoric stress is indicated. Therefore, for small deviatoric horizontal σ ₁ it is not possible to increase and reactivate small sections of basement thrust faults and create secondary basement aftershocks. Reconstructed stress regimes in this study for sedimentary cover (237) and basement (226) of Tabas are similar. Therefore, it seems that the basement and cover were coupled together, possibly along the 2–4 km of upper Precambrian low-grade metamorphic rocks. Then these segments of the fold-and-thrust belt were involved in similar seismic activity under a similar stress regime.     

Role of heterogeneities in jointing (fracturing) of geological media: Numerical analysis of fracture mechanisms

Fracture process is investigated using finite-difference simulations with a new constitutive model. It is shown that both geometry and fracture mechanism itself depend on the preexisting heterogeneities that are stress concentrators. In the brittle regime (low pressure, P), Mode-I fractures propagate normal to the least stress σ₃ from the imposed weak zones. At high P, shear deformation bands are formed oblique to σ₃. At intermediate values of P, the fracture process involves both shear banding and tensile cracking and results in the initiation and propagation of pure dilation bands. The propagating band tip undulates, reacting on the failure mechanism changes, but its global orientation is normal to σ₃. The σ₃-normal fractures are joints. There are thus two types of joints resulting from Mode-I cracking and dilation banding, respectively. The obtained numerical results are in good agreement with and explain the results from previous similar experimental study.     

Numerical modelling of the late stage of subduction zone transference after an accretion event

The resumption of subduction of an oceanic plate at a contact with a docked island (continental) margin is modelled numerically in 2D. The mechanical properties of the crustal and mantle rock masses are treated with visco‐plastic rheologies where the viscosities are described by a dynamic power law phenomenologically accounting for the transient texture evolution of the deforming rock masses. The study is limited to the extreme case of a fluid weakened lithosphere characterized by a uniform effective yield stress. At a constant push of 8 cm a^?1, the shear zones split the oceanic slab into blocks at the contact with the island. At a moderate yield stress (σ_Y < 80 MPa) and normal relaxation rate of viscosity, subduction resumes in less than ca 1 Ma. High σ_Y = 100 MPa leads to the island edge bending. A detached block of the island is subducted after the plunge of the oceanic plate reverses.     

Discrete element modeling of tool‐rock interaction II: rock indentation

The failure mechanisms induced by a wedge‐shaped tool indenting normally against a rock surface are investigated using the discrete element method (DEM). The main focus of this study is to explore the conditions controlling the transition from a ductile to a brittle mode of failure. The development of a damage zone and the initiation and propagation of a brittle fracture is well captured by the DEM simulations. The numerical results support the conjecture that initiation of brittle fractures is governed by a scaled flaw length Λ, a ratio between the flaw size λ and the characteristic length (where K_Ic is the toughness and σ_c the uniaxial compressive strength). The size of the damage zone agrees well with analytical predictions based on the cavity expansion model. The effects of a far‐field confining stress and the existence of a relief surface near the indenter are also examined.Copyright © 2012 John Wiley & Sons, Ltd.     

Conditions for veining and origin of mineralizing fluids in the Alpi Apuane (NW Tuscany,Italy): Evidence from structural and geochemical analyses on calcite veins hosted in Carrara marbles

This work deals with structural and geochemical (chemical and isotopic) analyses of calcite veins hosted in Carrara marbles in the Alpi Apuane, NW Tuscany, Italy. Geometric features and spatial distribution of veins provided estimations of stress ratio (Φ = (σ2 − σ3)/(σ1 − σ3)), driving stress ratio (R′ = (Pf − σ3)/(σ1 − σ3)) and fluid overpressure (Δs_i = Pf − σ3) at the time of vein formation. The obtained values of Φ = 32 and R′ = 0.43 reveal that fluid pressure was higher than the intermediate principal stress at the time of veins formation, whereas the estimated Δs_i ranging from 129 to 207 MPa indicates that veins formed under supra-hydrostatic to lithostatic pressure conditions. Carbon (δ¹³C_V-PDB = 1.81–2.10‰ for veins and 1.95–2.51‰ for host marbles), oxygen (δ¹⁸O_V-SMOW = 28.71–29.57‰ for veins and 28.90–29.36‰ for host marbles) and strontium (⁸⁷Sr/⁸⁶Sr = 0.707716–0.707985 for veins and 0.0707708–0.707900 for host marbles) isotope compositions in vein/host marble pairs were internally quite consistent. Combining our structural and geochemical data, a modeling approach was performed to investigate the compositional features and temperatures of calcite depositing fluids. The results of our studies give evidence that (1) pore-fluids in Carrara marble, consisting of metamorphic formation waters, were re-mobilized during veining event and migrated within the veins in closed system conditions, (2) veins formed after ductile folding phases and before high-angle brittle faulting events, at temperature and pressure around 250 °C and 210 MPa, and finally (3) about 12 g H₂O/m³ marble are calculated to have been available as vein parental fluid at the time of vein formation.     

Depth dependency of stress ratios during the sedimentation of NW Gyeongsang Basin (Cretaceous), southeast Korea: Estimate of stress parameters and timing of tectonic episodes

The natural stress state in the lithosphere consists of the vertical load and Poisson ratio, and then additional horizontal compression and extension (denoted by Δσ_H and Δσ_T, respectively) are assumed to be superimposed upon this gravitational stress field. The resulting stress state is composed of the maximum, medium and minimum stresses denoted by σ₁, σ₂, and σ₃, respectively. The stress ratio is given as Φ = (σ₂ − σ₃)/(σ₁ − σ₃). A linear relation is found between Φ or 1/Φ and the vertical load in wrench-faulting and extensional stress regimes, respectively. The slope and intercept of the linear relation result in the additional horizontal stresses and level of (average) paleo-surface, respectively. Stress ratio is also determinable by the stress tensor inversion of fault-slip data. The earliest tectonic event (T_1 Event) in the Cretaceous Gyeongsang Basin consists of coexisting E–W compression and N–S extensional faulting episodes. Plots of Φ or 1/Φ against the burial depth (or vertical load) display several linear trends: two clusters in extensional episodes, and two or three clusters in wrench-faulting episodes. Because Δσ_H is assumed to be null or negligible in the extensional regime, Δσ_T is determinable from the slopes of two linear clusters as being −2.5 to −4.0 MPa. In wrench-faulting episodes, the values of Δσ_H are given to be 61.6–101.4 MPa by applying determined additional horizontal extensions. Determined levels of average paleo-surfaces and those of syndepostional structures illustrate that more than five wrench-faulting or extensional episodes have occurred during the T_1 Event, whose active age, consequently, ranges from the Barremian to the Coniacian. This supports that the coexisting coaxial faulting episodes with the same extension may correspond to the alternation of wrench-faulting and extensional episodes.