Deformation of lower-mantle ferropericlase (Mg,Fe)O across the electronic spin transition

Recent high-pressure studies have shown that an electronic spin transition of iron in ferropericlase, an expected major phase of Earth’s lower mantle, results in changes in its properties, including density, incompressibility, radiative thermal conductivity, electrical conductivity, and sound velocities. To understand the rheology of ferropericlase across the spin transition, we have used in situ radial X-ray diffraction techniques to examine ferropericlase, (Mg_0.83,Fe_0.17)O, deformed non-hydrostatically in a diamond cell up to 81 GPa at room temperature. Compared with recent quasi-hydrostatic studies, the range of the spin transition is shifted by approximately 20 GPa as a result of the presence of large differential stress in the sample. We also observed a reduction in incompressibility and in the unit cell volume of 3% across the spin transition. Our radial X-ray diffraction results show that the {0 0 1} texture is the dominant lattice preferred orientation in ferropericlase across the spin transition and in the low-spin state. Viscoplastic self-consistent polycrystal plasticity simulations suggest that this preferred orientation pattern is produced by {1 1 0}<1–10> slip. Analyzing our radial X-ray diffraction patterns using lattice strain theory, we evaluated the lattice d-spacings of ferropericlase and Mo as a function of the ψ angle between the compression direction and the diffracting plane normal. These analyses give the ratio between the uniaxial stress component (t) and the shear modulus (G) under constant stress condition, which represents a proxy for the supported differential stress and elastic strength. This ratio in the mixed-spin and low-spin states is lower than what is expected from previous studies of high-spin ferropericlase, indicating that the spin transition results in a reduced differential stress and elastic strength along with the volume reduction. The influence of the spin transition on the differential stress and strength of ferropericlase is expected to be less dominant across the wide spin transition zone at high pressure–temperature conditions relevant to the lower mantle.     

Equation of state, elasticity, and shear strength of pyrite under high pressure

 Physical properties including the equation of state, elasticity, and shear strength of pyrite have been measured by a series of X-ray diffraction in diamond-anvil cells at pressures up to 50 GPa. A Birch–Murnaghan equation of state fit to the quasihydrostatic pressure–volume data obtained from laboratory X-ray source/film techniques yields a quasihydrostatic bulk modulus K _0T =133.5 (±5.2) GPa and bulk modulus first pressure derivative K ^′ _0T =5.73 (±0.58). The apparent equation of state is found to be strongly dependent on the stress conditions in the sample. The stress dependency of the high-pressure properties is examined with anisotropic elasticity theory from subsequent measurements of energy-dispersive radial diffraction experiments in the diamond-anvil cell. The calculated values of K _0T depend largely upon the angle ψ between the diffracting plane normal and the maximum stress axis. The uniaxial stress component in the sample, t=σ₃−σ₁, varies with pressure as t=−3.11+0.43P between 10 and 30 GPa. The pressure derivatives of the elastic moduli dC ₁₁/dP=5.76 (±0.15), dC ₁₂/dP=1.41 (±0.11) and dC ₄₄/dP=1.92 (±0.06) are obtained from the diffraction data assuming previously reported zero-pressure ultrasonic data (C ₁₁=382 GPa, C ₁₂=31 GPa, and C ₄₄=109 GPa). Received: 21 December 2000 / Accepted: 11 July 2001     

青藏高原东北缘水压致裂地应力测量

在青藏高原东北缘首次采用水压致裂法进行了地应力测量,结果显示：在测量深度域内,青藏高原东北缘三个主应力之间的关系表现为σＨｍａｘ〉σＨｍｉｎ〉σｖ,水平主应力占主导地位,现今地壳应力场的主压应力方向为ＮＥ－ＮＥＥ,测量结果与地质事实较吻合。     

Relation Between Normalized Axial Stress and Failure Strain in Heterogeneous Carbonate Rocks Exhibiting Large Axial Strains

A semi-analytical equation for the modeling of stress–strain relationship for heterogeneous carbonate rocks exhibiting large axial strains (ε_af > 1%) is formulated. The equation is derived by modifying the stress–strain model based on Haldane’s distribution proposed by Palchik (2006) for carbonate rocks exhibiting ε _af ≤ 1%. The developed exponential model is used to relate normalized axial stress (σ _a/σ _c) over the whole pre-failure strain range to current axial strain (ε _a) and failure strain (ε _af). For carbonate rocks exhibiting ε _af > 1%, the value of pre-calculated parameter δ involved in the stress–strain model is not constant, but dependent on the failure strain value (ε _af). The normalized stress–strain model can be used to calculate the failure strain in terms of uniaxial compressive strength and stress–strain measurement at one point only. The advantages of the failure strain model and ways of its use in engineering practice are discussed.     

A New Approach to the Modeling of the Pressure Dependency of the Strength of Rocks

Based on the hypothesis that shearing stresses and normal tensile stresses both play a decisive role in fracturing and brittle failure of rock material, a novel strength criterion was developed in one of the earlier works of the author. In the criterion, a certain parameter ν′ occurs which depends on the structure of the material. Originally, the parameter was treated as a constant, which resulted in a linear form of the strength function ^F σ ₁ = f(σ ₃), where σ ₃ = σ ₂. Although the linear strength criterion is sometimes found to be applicable to various particular rock materials, it is not, in general, of a universal character. Analysis of the triaxial test results for 75 different sandstones revealed that parameter ν′ usually increases in an exponential or linear manner as confining pressure increases, and only in isolated cases does it seem to be independent of the confining pressure. For these three types of function ν′ = f(p) appropriate strength criteria ^F σ ₁ = f(σ ₃) are given in the present paper. These criteria were used to fit all of the collected empirical data sets. In general, a very good fit to the data was obtained.     

Strength Anisotropy of Compacted Decomposed Granite Soils

In order to investigate the strength and deformation anisotropy of compacted decomposed granite soils, a series of drained triaxial compression tests was performed on unsaturated and saturated decomposed granite soils. The specimens were subjected to compression tests such that the angle δ of the direction of the major principal stress, σ ₁, during triaxial compression relative to the compaction plane (bedding plane) varies, with δ = 0°, 45° and 90°. Test results indicated that the compressive strain of the specimens subjected to isotropic consolidation was influenced strongly by the angle δ. In addition, the effect of the angle δ on the triaxial compressive strength and deformation was more evident in unsaturated specimens than in saturated specimens. Based on the test results, a procedure which can be used to estimate the shear strength of unsaturated soils taking into account various angles δ was proposed.     

Memory Effects in Rock Salt Under Triaxial Stress State and Their Use for Stress Measurement in a Rock Mass

Summary Regularities of memory effects in rock salt specimens under triaxial stress state were investigated. Each specimen was subjected to two loading cycles. The first cycle was axisymmetric triaxial compression (σ₁ >σ₂=σ₃). The second cycle was uniaxial compression in the direction of σ₁ of the first cycle. Distinct acoustic emission (AE) and deformation memory effects were observed in the second cycle at the stress value equal to a linear combination of the first cycle principal stresses given by σ₁− (k + 1) σ₃, where k is about 0.5–0.6 for rock salt. Anomalies in deformation curves were found to be more reliable than the AE methods in distinguishing memory symptoms. The necessary pre-requisite for memory formation in the first cycle was that σ₁ exceeded the elastic limit, corresponding to the given confining stress σ₃. Inflections in uniaxial stress versus axial strain and lateral strain curves, in the second cycle, were observed at equal stress values if in the first cycle σ₁ exceeded the elastic limit and memory-forming damage was induced. If there was no memory-forming damage, those inflections were seen at different stress values. This characteristic was used to distinguish between true memory effects and natural characteristic points in deformation curves derived from rock salt testing. A new memory symptom was established, namely a turn point in curve “uniaxial stress versus differential coefficient of lateral strains”. The results form a basis for application of the memory effects for stress measurement in rock salt masses.     

The Shear Behavior of Bedding Planes of Weakness Between Two Different Rock Types with High Strength Difference

In this article, the shear behavior of discontinuities caused by bedding planes of weakness between two different rock types with high strength difference is investigated. The effect of roughness and compressive strength of joint wall in such discontinuities are studied. The designed profiles consist of two regular and three irregular artificial joints molded by three types of plaster mortars with different uniaxial compressive strengths. Firstly, it is demonstrated that the shear behavior of discontinuities with different joint wall compressive strengths (JCS) is different from rock joints with identical wall compressive strengths by showing that Barton’s empirical criterion is not appropriate for the former discontinuities. After that, some correlation equations are proposed between the joint roughness coefficient (JRC) parameter and some surface statistical/fractal parameters, and the normal stress range of Barton’s strength criterion is also modified to be used for such discontinuities. Then, a new empirical criterion is proposed for these discontinuities in such a way that a rational function is used instead of JRC log₁₀(JCS/σ _n) as i ₀(σ _c/σ _n)^a/[b + (σ _c/σ _n) ^a ] by satisfying the peak dilation angle boundary conditions under zero and very high normal stress (physical infinite normal stress causing zero peak dilation angle). The proposed criterion has three surface parameters: i ₀, a, and b. The reason for separation of i ₀ from JRC is indicated and the method of its calculation is mentioned based on the literature. The two remaining coefficients (a and b) are discussed in detail and it is shown that a shows a power-law relationship with b, introducing the coefficient c through b = c ^a . Then, it is expressed that a is directly related to discontinuity surface topography. Finally, it is shown that the coefficient c has higher values in irregular profiles in comparison with regular profiles and is dominated by intensity of peak dilation angle reduction (majorly related to the surface irregularity and minorly related to roughness). The coefficient c is to be determined by performing regression analysis on experimental data.     

Constraining stress magnitudes using petroleum exploration data in the Cooper–Eromanga Basins, Australia

The magnitude of the in situ stresses in the Cooper–Eromanga Basins have been determined using an extensive petroleum exploration database from over 40 years of drilling. The magnitude of the vertical stress (S_v) was calculated based on density and velocity checkshot data in 24 wells. Upper and lower bound values of the vertical stress magnitude are approximated by S_v = (14.39 × Z)^1.12 and S_v = (11.67 × Z)^1.15 functions respectively (where Z is depth in km and S_v is in MPa). Leak-off test data from the two basins constrain the lower bound estimate for the minimum horizontal stress (S_hmin) magnitude to 15.5 MPa/km. Closure pressures from a large number of minifrac tests indicate considerable scatter in the minimum horizontal stress magnitude, with values approaching the magnitude of the vertical stress in some areas. The magnitude of the maximum horizontal stress (S_Hmax) was constrained by the frictional limits to stress beyond which faulting occurs and by the presence of drilling-induced tensile fractures in some wells. The maximum horizontal stress magnitude can only be loosely constrained regionally using frictional limits, due to the variability of both the minimum horizontal stress and vertical stress estimates. However, the maximum horizontal stress and thus the full stress tensor can be better constrained at individual well locations, as demonstrated in Bulyeroo-1 and Dullingari North-8, where the necessary data (i.e. image logs, minifrac tests and density logs) are available. The stress magnitudes determined indicate a predominantly strike-slip fault stress regime (S_Hmax > S_v > S_hmin) at a depth of between 1 and 3 km in the Cooper–Eromanga Basins. However, some areas of the basin are transitional between strike-slip and reverse fault stress regimes (S_Hmax > S_v ≈ S_hmin). Large differential stresses in the Cooper–Eromanga Basins indicate a high upper crustal strength for the region, consistent with other intraplate regions. We propose that the in situ stress field in the Cooper–Eromanga Basins is a direct result of the complex interaction of tectonic stresses from the convergent plate boundaries surrounding the Indo-Australian plate that are transmitted into the center of the plate through a high-strength upper crust.     

Bubble nucleation in rhyolite and dacite melts: temperature dependence of surface tension

Surface tension (σ) profoundly influences the ability of gas bubbles to nucleate in silicate melts. To determine how temperature impacts σ, experiments were carried out in which high-silica rhyolite melts with 5 wt% dissolved water were decompressed at temperatures that ranged from 775 to 1,085°C. Decompressions were also carried out using dacite melts with 4.3 wt% dissolved water at 1,150°C. Water bubbles nucleated in rhyolite only when decompressions exceeded 95 MPa at all temperatures. Bubbles nucleated in number densities that increased as decompression increased and at hotter temperatures at a given amount of decompression. After correcting decompression amounts for temperature differences, values for σ were estimated from nucleation rates and found to vary between 0.081 and 0.093 N m⁻¹. Surface tension decreases as temperature increases from 775 to 875°C, but then increases as temperature increases to 1,085°C. Those values overlap previous results, but only when melt viscosity is less than 10⁴ Pa s. For low-viscosity rhyolite, there is a strong correlation of σ with temperature, in which σ increases by 6.9 × 10⁻⁵ N m⁻¹ C⁻¹. That variation is robust for 5–9 wt% dissolved water, as long as melt viscosity is ≤10⁴ Pa s. More viscous rhyolite deviates from that correlation probably because nucleation is retarded in stiffer melts. Bubbles nucleated in dacite when decompressions exceeded 87 MPa, and occured in one or more events as decompression increased. Surface tension is estimated to be 0.083 (±0.001) N m⁻¹ and when adjusted for temperature agrees well with previous results for colder and wetter dacite melts. At a given water content, dacite melts have lower surface tensions than rhyolite melts, when corrected to a fixed temperature.     

Paleostress-tensor analysis of late deformation events in the Odenwald Crystalline Complex and comparison with other units of the Mid-German Crystalline Rise, Germany

Summary Geometric data of fault planes and fault plane lineations, together with the observed sense of shear on the slip planes, were used to calculate paleostress tensors and fields responsible for the post metamorphic peak D3 and D4 deformation events in the four Odenwald units sensu Krohe (1991). The paleostress fields were calculated using the method of Will and Powell (1991). As inferred from the paleostress analysis, the D3 strike-slip deformation west of the Otzberg fault zone was caused by a, ± N-S directed, compressional regional stress field, with shallowly plunging σ₁ axes and σ₃ directions that plunge at shallow to moderate angles to the E or W; the calculated mean orientations are: σ₁ 06 → 350, σ₂ 77 → 234 and σ₃ 12 → 085. The B?llsteiner Odenwald east of the Otzberg fault zone was not affected by this stress field. This implies that the Bergstr?sser and B?llsteiner Odenwald were spatially separated and formed independent crustal blocks during D3. The D4 faulting event is recognised in all areas investigated, even though most prominently in units III and IV, and juxtaposed the Bergstr?sser and B?llsteiner Odenwald. This faulting episode was caused by a paleostress field with a steeply westerly plunging σ₁ axis and a shallowly southsoutheasterly plunging σ₃ axis. The orientations of the principal stresses are: σ₁ 52 → 270, σ₂ 38 → 085 and σ₃ 06 → 174. With continued deformation from D3 to D4, there was a progressive change in the orientation of the stress field indicating a change from a N-S compressional to extensional stress field, accompanied by the progressive development of strike-slip faults and late normal faults. Paleostress field orientations in the Pfalz Forest, SW of the Odenwald, determined by Fl?ttmann and Oncken (1992) are very similar to those obtained for the Odenwald region and indicate a regionally consistent stress pattern in the southwestern part of the Mid-German Crystalline Rise (MGCR) during strike-slip and normal faulting deformations.

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Zusammenfassung Paleostress-Tensor Analyse sp?ter Deformationsereignisse im Odenwald-Kristallin und ein Vergleich mit anderen Einheiten der Mitteldeutschen Kristallinzone, Deutschland Für die vier Odenwald-Einheiten im Sinne von Krohe (1991) wurden Pal?ostressfelder für die Blattverschiebungs- und Abschiebungsereignisse D3 und D4 mit der Methode von Will und Powell (1991) berechnet. Die Analyse ergibt, da? das regionale Spannungsfeld, das westlich der Otzberg-Zone im Bergstr?sser Odenwald zum D3-Ereignis führte, ein ± N-S gerichtetes kompressives Stresssfeld war. Die σ₁-Achse f?llt flach nach N bzw. S ein, die σ₃-Achse mit kleinen bis moderaten Winkeln nach E bzw. W; die berechneten Orientierungen der Hauptspannungsrichtungen sind: σ₁ 08 → 350, σ₂ 77 → 234 and σ₃ 12 → 085. Der B?llsteiner Odenwald, ?stlich der Otzberg-Zone, wurde von diesem Spannungsfeld nicht erfa?t. Dies impliziert, da? Bergstr?sser und B?llsteiner Odenwald w?hrend des D3-Ereignisses voneinander getrennt waren und separate Krusteneinheiten darstellten. Auswirkungen der D4-Deformation k?nnen im gesamten Untersuchungsgebiet erkannt werden, am st?rksten jedoch in den Einheiten III und IV. Dieses Ereignis wurde von einem Pal?ostressfeld mit einer steil nach W einfallenden σ₁- und einer flach nach SSE einfallenden σ₃-Achse verursacht und führte zum Zusammenschlu? von Bergstr?sser und B?llsteiner Odenwald. Die berechneten Orientierungen der Hauptspannungsrichtungen sind: σ₁ 52 → 270, σ₂ 38 → 085 und σ₃ 06 → 174. Die Rotation der Hauptspannungsrichtungen war mit einer ?nderung von einem kompressionalen N-S gerichteten (D3) hin zu einem extensionalen (D4) Stressfeld verbunden. Die erzielten Ergebnisse sind sehr ?hnlich mit Resultaten, die Fl?ttmann und Oncken (1992) im Pf?lzer Wald ermittelten. Dies weist auf ein regional übereinstimmendes Spannungsfeld im SW-Teil der Mitteldeutschen Kristallinzone hin.

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Received July 8, 1999; revised version accepted March 28, 2000     

On the Ratios between Elastic Modulus and Uniaxial Compressive Strength of Heterogeneous Carbonate Rocks

The ratios M _R = E/σ _c for 11 heterogeneous carbonate (dolomites, limestones and chalks) rock formations collected from different regions of Israel were examined. Sixty-eight uniaxial compressive tests were conducted on weak-to-strong (5 MPa < σ _c < 100 MPa) and very strong (σ _c > 100 MPa) rock samples exhibiting wide ranges of elastic modulus (E = 6100–82300 MPa), uniaxial compressive strength (σ _c = 14–273.9 MPa), Poisson's ratio (ν = 0.13–0.49), and dry bulk density (ρ = 1.7–2.7 g/cm³). The observed range of M _R = 60.9–1011.4 and mean value of M _R = 380.5 are compared with the results obtained by Deere (Rock mechanics in engineering practice, Wiley, London, pp 1–20, 1968) for limestones and dolomites, and the statistical analysis of M _R distribution is performed. Mutual relations between E, σ _c, ρ, M _R for all studied rocks, and separately for concrete rock formations are revealed. Linear multiple correlations between E on the one hand and σ _c and ρ on the other for Nekorot and Bina limestone and Aminadav dolomite are obtained. It is established that the elastic modulus and M _R in very strong carbonate samples are more correlated with ρ−σ _c combination and ε _a max, respectively, than in weak to strong samples. The relation between M _R and maximum axial strain (ε _a max) for all studied rock samples (weak-to-strong and very strong) is discussed.     

Modelling the pore fluid diffusion process in aftershock initiation for 2004 Sumatra earthquake: implications for marine geohazard estimation in the Andaman region

The role of fluid injection on the occurrence and migration path for the aftershocks of 2004 Sumatra earthquake (Mw 9.3) and January 2005 Andaman earthquake swarm within the aftershock sequence is investigated here from the viewpoint of pore fluid diffusion process. The Sumatra earthquake created a regionally extensive crustal rupture plane exceeding 1,200 km length below the Andaman Sea. The r–t plots (Shapiro et al. 1997) are constructed for these aftershocks in order to examine the role of poroelastic effects as rupturing progressed with time. Their main results are as follows: the r–t plot corresponding to first 3 h of aftershock activity (when only 44 events of mb ≥ 4.5 originated) reveals that 95% of the data points occurred below the modelled parabola with relatively high D value of 20 m²/s, whereas a significantly low D value of 3.5 m²/s characterises the aftershock activity for the first 24 h (when 420 events of mb ≥ 4.0 occurred). Here, the Coulomb stress was transferred from the main shock with a rapid imposition of normal stress, thus inducing the pore-pressure change that started diminishing almost immediately by fluid diffusion, at a rate, defined by the diminishing D value. The modelling results for fault seismicity at far off distances from the main epicentre are interpreted here as potential indicators for large-scale sub-seabed rupturing—consequent to stress changes induced by bending of the Indian Ocean plate. Bathymetric slopes under the Andaman subduction zone are particularly amenable to sub-marine slides where crustal E–W hinge faults inferred seismically cut across the N–S trending regional thrust and strike-slip faults. Seabed rupturing appears to allow deep-slab hydration in these areas, producing pressure gradients along the normal faults. These features are important since they can herald marine geohazards in the Andaman region.     

Deformability characteristics of a rock mass under true-triaxial stress compression

In this paper an experimental study was planned on rock mass model with three joint sets under triaxial and true-triaxial stress states to assess the influence of joint geometry and stress ratios on deformational behaviour of rock mass. The physical models were composed of three continuous orthogonal joint sets in which joint set-I was inclined at angle θ=0°, 20°, 40°, 60°, 80° and 90° with x-axis, joint set-II was produced at staggering s=0.5 and joint set-III was kept always vertical. Thus, rock mass models with medium interlocked smooth joints (ϕ _j =36.8°) were simulated under true triaxial compression (σ₁>σ₂>σ₃). Modulus of rock mass shows anisotropy with joint inclination θ which diminishes with increase in σ₂/σ₃ ratio. The rock mass at θ=60° shows the highest modulus enhancement (599.9%) whereas it is minimum (32.3%) at θ=90°. Further two empirical expressions for estimation of deformation modulus were suggested based on experimental results, which were developed by incorporating two basic concepts, e.g. Janbu’s coefficients and joint factor, J _f.     

Thermoelastic model of minerals: application to Al2O3

 A thermoelastic model for calculating the high-pressure and high-temperature properties of isotropic solids is presented by extending the formalism by Thomsen and combining the resulting one with the Vinet model for static lattice and the Debye model for lattice vibration. Applying it to polycrystalline corundum, we have shown that the calculated values of entropy and heat capacity at constant pressure are in agreement with literature values to 2325 K at zero pressure and that the calculated values of thermal expansivity agree reasonably with experimental data to 1100 K at zero pressure. The model reproduces experimental data of sound velocities v _p and v _s of compressional and shear waves to 1825 K at zero pressure and those to 62 GPa at room temperature, and it reproduces also experimental shock-wave equation of state to 150 GPa. The velocity correlation (∂ln v _s /∂ln v _p ) _S was found to have weak pressure and temperature dependences and the results under lower mantle conditions are compared with those of magnesian and calcium silicate perovskites and magnesiowüstite, and the PREM values of the Earth's lower mantle. Received: 12 February 2000 / Accepted: 15 July 2000     

三峡库首区现今构造应力场的形成体制分析

本文从地质、地震、形变、地应力测量等方面对三峡库首区现今构造应力场进行了系统的分析和论证,并用数值模拟进行了验证,认为三峡库首区现今构造应力场属于纯剪切变形体制,即:在来自西部NE-SW方向主压应力挤压的基础上,同时叠加有因江汉-洞庭盆地拉张而引起的NWW-SEE向主张应力的作用,这两种力源近于直交,可以分别作为研究区现今构造应力场的主压应力(σ₁)和主张应力(σ₃).      

The Gibbs energy formulation of the α, β, and γ forms of Mg2SiO4 using Grover, Getting and Kennedy's empirical relation between volume and bulk modulus

 The empirical linear relation between volume and logarithm of bulk modulus of a material, discovered by Grover, Getting and Kennedy is taken as the basis for our equation of state. Using the latest experimental information on the adiabatic bulk modulus, the equation of state is applied to the three polymorphs of Mg₂SiO₄ to develop a consistent dataset of their thermodynamic properties in the temperature range of 200–2273 K and a pressure range of 0.1 MPa–30 GPa. The results imply that the bulk sound velocity contrast (v ^β−v ^α)/v ^α increases with temperature along the α–β phase boundary and reaches the value 8.9% at 13.5 GPa, a pressure equivalent to 410 km depth in the Earth. The bulk sound velocity contrast (v ^γ−v ^β)/v ^β decreases with temperature along the β–γ phase boundary and becomes less than 0.7% at temperatures and pressures equivalent to those associated with the 520-km seismic discontinuity in the Earth. Received: 1 August 2000 / Accepted: 1 March 2001     

Practical Estimates of Tensile Strength and Hoek–Brown Strength Parameter m i of Brittle Rocks

By applying the Griffith stress criterion of brittle failure, one can find that the uniaxial compressive strength (σ_c) of rocks is eight times the value of the uniaxial tensile strength (σ_t). The Griffith strength ratio is smaller than what is normally measured for rocks, even with the consideration of crack closure. The reason is that Griffith’s theories address only the initiation of failure. Under tensile conditions, the crack propagation is unstable so that the tensile crack propagation stress (σ_cd)_t and the peak tensile strength σ_t are almost identical to the tensile crack initiation stress (σ_ci)_t. On the other hand, the crack growth after crack initiation is stable under a predominantly compressive condition. Additional loading is required in compression to bring the stress from the crack initiation stress σ_ci to the peak strength σ_c. It is proposed to estimate the tensile strength of strong brittle rocks from the strength ratio of R = \fracs_\textc | s_\textt | = 8\fracs_\textc s_\textci . R = {\frac{{\sigma_{\text{c}} }}{{\left| {\sigma_{\text{t}} } \right|}}} = 8{\frac{{\sigma_{\text{c}} }}{{\sigma_{\text{ci}} }}}. The term \fracs_\textc s_\textci {\frac{{\sigma_{\text{c}} }}{{\sigma_{\text{ci}} }}} accounts for the difference of crack growth or propagation in tension and compression in uniaxial compression tests. \fracs_c s_ci {\frac{{\sigma_{c} }}{{\sigma_{ci} }}} depends on rock heterogeneity and is larger for coarse grained rocks than for fine grained rocks. σ_ci can be obtained from volumetric strain measurement or acoustic emission (AE) monitoring. With the strength ratio R determined, the tensile strength can be indirectly obtained from | s_\textt | = \fracs_\textc R = \fracs_\textci 8. \left| {\sigma_{\text{t}} } \right| = {\frac{{\sigma_{\text{c}} }}{R}} = {\frac{{\sigma_{\text{ci}} }}{8}}. It is found that the predicted tensile strengths using this method are in good agreement with test data. Finally, a practical estimate of the Hoek–Brown strength parameter m _i is presented and a bi-segmental or multi-segmental representation of the Hoek–Brown strength envelope is suggested for some brittle rocks. In this fashion, the rock strength parameters like σ_t and m _i, which require specialty tests such as direct tensile (or Brazilian) and triaxial compression tests for their determination, can be reasonably estimated from uniaxial compression tests.     

Influence of different strain rates on hydro-mechanical behaviour of reconstituted unsaturated soil

The hydro-mechanical behaviour of a reconstituted unsaturated soil under different suctions and strain rates was studied through various rate-controlled unsaturated/undrained triaxial tests. The fully saturated reconstituted specimens were desaturated to four different initial suctions (s₀?=?0, 100 kPa, 200 kPa and 300 kPa) and then triaxially sheared (conventional triaxial compression) at three different strain rates in undrained conditions (\(\dot{\varepsilon }_{1} = 0.001\) h^?1, 0.01 h^?1, and 0.1 h^?1). The observed hydro-mechanical behaviour during shearing including the volumetric strain, deviatoric stress, degree of saturation and suction is presented and discussed in this paper. The results indicate that when the strain rate rises at the given initial suctions (or pore water pressures), the maximum deviatoric stress (q_max), critical net stress ratio (M) and critical state suction (s_c) increase but the degree of saturation (S_rc) and volumetric strain at the critical state (ε^c_v ) reduce. The critical effective stress ratio (M′) is not dependent on the strain rate for saturated and unsaturated samples. The critical state lines for unsaturated soils with the constant strain rates are parallel with each other in the e???lnp′ space.