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.     

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.     

X-ray diffraction study of arsenopyrite at high pressure

The high-pressure X-ray diffraction study of a natural arsenopyrite was investigated up to 28.2 GPa using in situ angle-dispersive X-ray diffraction and a diamond anvil cell at National Synchrotron Light Source, Brookhaven National Laboratory. The 16:3:1 methanol–ethanol–water mixture was used as a pressure-transmitting medium. Pressures were measured using the ruby-fluorescence method. No phase change has been observed up to 28.2 GPa. The isothermal equation of state (EOS) was determined. The values of K ₀, and K′ ₀ refined with a third-order Birch–Murnaghan EOS are K ₀ = 123(9) GPa, and K′ ₀ = 5.2(8). Furthermore, we confirm that the linear compressibilities (β) along a, b and c directions of arsenopyrite is elastically isotropic (β _a  = 6.82 × 10⁻⁴, β _b  = 6.17 × 10⁻⁴ and β _c  = 6.57 × 10⁻⁴ GPa⁻¹).     

Ion tracks in apatite at high pressures: the effect of crystallographic track orientation on the elastic properties of fluorapatite under hydrostatic compression

Static elasticity measurements at high pressures were carried out on oriented fluorapatite single crystals, some of which contained oriented amorphous ion tracks (ITs) implanted with relativistic Au ions (2.2 GeV) from the UNILAC linear accelerator at GSI, Darmstadt. High-pressure experiments on irradiated and non-irradiated crystal sections were carried out in diamond-anvil high-pressure cells under hydrostatic conditions. In situ single-crystal diffraction was performed to determine the high-precision lattice parameters, simultaneously monitoring the widths of X-ray diffraction Bragg peaks. High-pressure Raman spectra were analyzed with respect to the frequency shift and widths of bands, which correspond to the Raman-active vibrational modes of the phosphate tetrahedra. Swift heavy ion irradiation was found to induce anisotropic lattice expansion and tensile strain within the host lattice dependent on the ion-track orientation. The relatively low Grüneisen parameter for the ν _1b(A _g) mode, which has been assigned to originate from the volume fraction of the amorphous tracks, and the γ(ν _1a)/γ(ν _1b) ratio reveals compressive strain on the amorphous ITs. The comparative compressibilities for the host lattice reveal approximately equivalent bulk moduli, but significantly different pressure derivatives (K _T = 88.4 ± 0.7 GPa, ∂K/∂P = 6.3 ± 0.3 for non-irradiated, K _T = 90.0 ± 1.7 GPa, ∂K/∂P = 3.8 ± 0.5 for irradiated samples). The axial compressibility moduli β ⁻¹ reveal significant differences, which correlate with the ion-track orientation [b_a ^{- 1} \beta_{a}^{ - 1}  = 240 ± 5 GPa, b_c ^{- 1} \beta_{c}^{ - 1}  = 361 ± 14 GPa, ∂( b_a ^{- 1} ) \left( {\beta_{a}^{ - 1} } \right) /∂P = 11.3 ± 1.2, ∂( b_c ^{- 1} ) \left( {\beta_{c}^{ - 1} } \right) /∂P = 11.6 ± 3.4 for irradiation ⊥(100); 246 ± 9 GPa, 364 ± 57 GPa, 9.5 ± 2.9, 14.7 ± 14.1 for irradiation ⊥(001), 230.7 ± 3.6 GPa, 373.5 ± 5.1 GPa, 19.2 ± 1.4, 20.1 ± 1.8 for no irradiation]. Line widths of XRD Bragg peaks in irradiated apatites confirm the strain of the host lattice, which appears to decrease with increasing pressure. By contrast, the bandwidths of Raman modes increase with pressure, and this is attributed to increasing strain gradients on the length scale of the short-range order. The investigations reveal considerable deviatoric stress on the [100]-oriented tracks due to the anisotropic elasticity, while the compression is uniform for the directions perpendicular to the tracks, which are aligned parallel to the c-axis. This difference might be considered to control the diffusion properties related to the annealing kinetics and its observed anisotropy, and hence to cause potential pressure effects on track-fading rates.     

Synchrotron X-ray analysis of norbergite, Mg2.98Fe0.01Ti0.02Si0.99O4(OH0.31F1.69) structure at high pressure up to 8.2?GPa

The natural norbergite, Mg_2.98Fe_0.01Ti_0.02Si_0.99O₄(OH_0.31F_1.69) is examined by synchrotron X-ray diffraction analysis at pressures up to 8.2 GPa. The measured linear compressibilities of the crystallographic axes are β _a  = 2.18(4) × 10⁻³, β _b  = 2.93(7) × 10⁻³, and β _c  = 2.77(7) × 10⁻³ (GPa⁻¹), respectively and the calculated isothermal bulk modulus of the norbergite is K _T = 113(2) GPa based on the Birch–Murnaghan equation of state assuming a pressure derivative of K′ = 4. The crystal structures of norbergite are refined at room temperature and pressures of 4.7, 6.3, and 8.2 GPa, yielding R values for the structure refinements of 4.6, 5.3, and 5.3%, respectively. The bulk moduli of the polyhedral sites are 293(15) GPa for the tetrahedron, 106(5) GPa for the M2 octahedron, 113(2) GPa for the M3 octahedron, and 113(3) GPa for the total void space. The bulk modulus exhibits a good linear correlation with the filling factor for polyhedral sites in structures of the humite minerals and forsterite, reflecting the Si⁴⁺ + 4O²⁻ ⇔ □ + 4(OH, F)⁻ substitution in the humite minerals. Moreover, two simply linear trends were observed in the relationship between bulk modulus and packing index for natural minerals and dense hydrous magnesium silicate minerals. This relationship would reflect that the differences in compression mechanism were involved with hydrogen bonding in these minerals. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

(Na,Ca)(Ti3+,Mg)Si2O6-clinopyroxenes at high pressure: influence of cation substitution on elastic behavior and phase transition

A compressional study of (Na,Ca)(Ti³⁺,Mg)Si₂O₆-clinopyroxenes was carried out at high pressures between 10⁻⁴ and 10.2 GPa using in situ single-crystal X-ray diffraction, Raman spectroscopy and optical absorption spectroscopy. Compressional discontinuities accompanied by structural changes, in particular, the appearance of two distinct Ti³⁺–Ti³⁺ distances within the octahedral chains at 4.37 GPa, provide evidence for the occurrence of a phase transition in NaTi³⁺Si₂O₆. Equation-of-state parameters are K ₀ = 115.9(7) GPa with K′ = −0.9(3) and K ₀ = 102.7(8) GPa with K′ = 4.08(5) for the low- and high-pressure range, respectively. The transition involves a C2/c–P [`1] \overline{1} symmetry change, which can be confirmed by the occurrence of new modes in Raman spectra. Since no significant discontinuity in the evolution of the unit-cell volume with pressure has been observed, the transition appears to be second-order in character. The influence of the coupled substitution Na⁺Ti³⁺↔Ca²⁺Mg²⁺ on the static compression behavior and the structural stability has been investigated using a sample of the intermediate composition (Na_0.54Ca_0.46)(Mg_0.46Ti_0.54)Si₂O₆. No evidence for a deviation from continuous compression behavior has been found, neither in lattice parameter nor in structural data and the fit of a third-order Birch–Murnaghan equation-of-state to the pressure–volume data yields a bulk modulus of K ₀ = 109.1(5) GPa and K′ = 5.02(13). Raman and polarized absorption spectra have been compared to NaTiSi₂O₆ and reveal major similarities. The main driving force for the phase transition in NaTi³⁺Si₂O₆ is the localization of the Ti³⁺ d-electron and the accompanying distortion, which is suppressed in the (Na,Ca)(Ti³⁺,Mg)Si₂O₆-clinopyroxene.     

High-pressure X-ray diffraction study of ε-FeOOH

An in situ synchrotron X-ray diffraction study was carried out on ε-FeOOH at room temperature up to a pressure of 8.6 GPa using the energy-dispersive method. The linear compressibility was determined to be β _a  = 1.69(3) × 10⁻³ GPa⁻¹, β _b  = 2.86(6) × 10⁻³ GPa⁻¹, and β _c  = 1.73(5) × 10⁻³ GPa⁻¹. The b-axis of the unit cell is more compressible than the a and c axes. The pressure–volume data were fitted to a third-order Birch–Murnaghan equation of state. The best fit was found using a room temperature isothermal bulk modulus of K ₀ = 126(3) GPa and its pressure derivative K′ = 10(1).     

Macrofaunal Spatial Patterns in Relationship to Environmental Variables in the Richibucto Estuary,New Brunswick,Canada

Estuarine macrobenthos respond to a variety of environmental gradients such as sediment type and salinity, and organic enrichment. A relatively new influence, organic loading from suspended bivalve culture, has the potential to alter this response. A study on soft-bottom macrobenthic communities was carried out in the Richibucto estuary (46°40′N, 64°50′W), New Brunswick, Canada, with samples collected from 18 stations in late September and early October 2006. The site consisted of a large tidal channel originating upstream in a small river. The channel was punctuated by bag culture of oysters along its length. A total of 88 species were recorded. The mean values of abundance, species richness, and diversity (H′) of macrofauna were 11,199 ind. m⁻² (ranged from 4,371 to 19,930 ind. m⁻²), 23.4 species grab⁻¹ and 3.29 grab⁻¹, respectively. In general species richness and H′ increased from the upper estuary to the estuarine mouth. Multivariate analyses clearly exhibited the spatial distribution in community structure, which coincided with the locations along the estuary (the upper, the lower and the mouth), as well as inside and outside the channel. Species richness and diversity H′ showed strong positive correlations with salinity (21.2–25.2 ppt), and abundance was positively correlated with water depth (1.0–4.5 m). Abundance and species richness were negatively correlated with both of silt–clay fraction (3.3–24.8%) and sorting (σ_I). Species richness was also negatively correlated with organic content (1.9–12.7%). The BIO-ENV analyses identified silt–clay fraction, σ_I and salinity as the major environmental variable combination influencing the macrofaunal patterns, and silt–clay fraction as the single best-correlated variable.     

Behavior of epidote at high pressure and high temperature: a powder diffraction study up to 10 GPa and 1,200 K

The thermo-elastic behavior of a natural epidote [Ca_1.925 Fe_0.745Al_2.265Ti_0.004Si_3.037O₁₂(OH)] has been investigated up to 1,200 K (at 0.0001 GPa) and 10 GPa (at 298 K) by means of in situ synchrotron powder diffraction. No phase transition has been observed within the temperature and pressure range investigated. P–V data fitted with a third-order Birch–Murnaghan equation of state (BM-EoS) give V ₀ = 458.8(1)ų, K _T0 = 111(3) GPa, and K′ = 7.6(7). The confidence ellipse from the variance–covariance matrix of K _T0 and K′ from the least-square procedure is strongly elongated with negative slope. The evolution of the “Eulerian finite strain” vs “normalized stress” yields Fe(0) = 114(1) GPa as intercept values, and the slope of the regression line gives K′ = 7.0(4). The evolution of the lattice parameters with pressure is slightly anisotropic. The elastic parameters calculated with a linearized BM-EoS are: a ₀ = 8.8877(7) Å, K _T0(a) = 117(2) GPa, and K′(a) = 3.7(4) for the a-axis; b ₀ = 5.6271(7) Å, K _T0(b) = 126(3) GPa, and K′(b) = 12(1) for the b-axis; and c ₀ = 10.1527(7) Å, K _T0(c) = 90(1) GPa, and K’(c) = 8.1(4) for the c-axis [K _T0(a):K _T0(b):K _T0(c) = 1.30:1.40:1]. The β angle decreases with pressure, β_P(°) = β_P0 −0.0286(9)P +0.00134(9)P ² (P in GPa). The evolution of axial and volume thermal expansion coefficient, α, with T was described by the polynomial function: α(T) = α₀ + α₁ T ^−1/2. The refined parameters for epidote are: α₀ = 5.1(2) × 10⁻⁵ K⁻¹ and α₁ = −5.1(6) × 10⁻⁴ K^1/2 for the unit-cell volume, α₀(a) = 1.21(7) × 10⁻⁵ K⁻¹ and α₁(a) = −1.2(2) × 10⁻⁴ K^1/2 for the a-axis, α₀(b) = 1.88(7) × 10⁻⁵ K⁻¹ and α₁(b) = −1.7(2) × 10⁻⁴ K^1/2 for the b-axis, and α₀(c) = 2.14(9) × 10⁻⁵ K⁻¹ and α₁(c) = −2.0(2) × 10⁻⁴ K^1/2 for the c-axis. The thermo-elastic anisotropy can be described, at a first approximation, by α₀(a): α₀(b): α₀(c) = 1 : 1.55 : 1.77. The β angle increases continuously with T, with β_T(°) = β_T0 + 2.5(1) × 10⁻⁴ T + 1.3(7) × 10⁻⁸ T ². A comparison between the thermo-elastic parameters of epidote and clinozoisite is carried out.     

The influence of the Jahn–Teller effect at Fe<Superscript>2+</Superscript> on the structure of chromite at high pressure

The crystal structure of chromite FeCr₂O₄ was investigated to 13.7 GPa and ambient temperature with single-crystal X-ray diffraction techniques. The unit-cell parameter decreases continuously from 8.3832 (5) to 8.2398 (11) Å up to 11.8 GPa. A fit to the Birch–Murnaghan equation of state (EoS) based on the P–V data gives: K ₀ = 209 (13) GPa, K′ = 4.0 (fixed), and V ₀ = 588 (1) ų. The FeO₄ tetrahedra and CrO₆ octahedra are compressed isotropically with pressure with their Fe–O and Cr–O bond distances decreasing from 1.996 (6) to 1.949 (7) Å and from 1.997 (3) to 1.969 (7) Å, respectively. The tetrahedral site occupied by the Fe²⁺ cation is more compressible than the octahedral site occupied by the Cr³⁺ cation. The resulting EoS parameters for the tetrahedral and the octahedral sites are K ₀ = 147 (9) GPa, K′ = 4.0 (fixed), V ₀ = 4.07 (1) ų and K ₀ = 275 (24) GPa, K′ = 4.0 (fixed), V ₀ = 10.42 (2) ų, respectively. A discontinuous volume change is observed between 11.8 and 12.6 GPa. This change indicates a phase transition from a cubic (space group Fd-[`3]{\overline{3}} m) to a tetragonal structure (space group I4₁ /amd). At the phase transition boundary, the two Cr–O bonds parallel to the c-axis shorten from 1.969 (7) to 1.922 (17) Å and the other four Cr–O bonds parallel to the ab plane elongate from 1.969 (7) to 1.987 (9) Å. This anisotropic deformation of the octahedra leads to tetragonal compression of the unit cell along the c-axis. The angular distortion in the octahedron decreases continuously up to 13.7 GPa, whereas the distortion in the tetrahedron rises dramatically after the phase transition. At the pressure of the phase transition, the tetrahedral bond angles along the c-axis direction of the unit cell begin decreasing from 109.5° to 106.6 (7)°, which generates a “stretched” tetrahedral geometry. It is proposed that the Jahn–Teller effect at the tetrahedrally coordinated Fe²⁺ cation becomes active with compression and gives rise to the tetrahedral angular distortion, which in turn induces the cubic-to-tetragonal transition. A qualitative molecular orbital model is proposed to explain the origin and nature of the Jahn–Teller effect observed in this structure and its role in the pressure-induced phase transition.     

Electronic absorption by Ti3+ ions and electron delocalization in synthetic blue rutile

Polarized absorption spectra, σ and π, in the spectral range 30000–400 cm⁻¹ (3.71–0.05 eV) were obtained on crystal slabs // [001] of deep blue rutile at various temperatures from 88 to 773 K. The rutile crystals were grown in Pt-capsules from carefully dried 99.999% TiO₂ rutile powder at 50 kbar/1500 °C using graphite heating cells in a belt-type apparatus. Impurities were below the detection limits of the electron microprobe (about 0.005 wt% for elements with Z≥13). The spectra are characterized by an unpolarized absorption edge at 24300 cm⁻¹, two weak and relatively narrow (Δν_1/2≈3500–4000 cm⁻¹), slightly σ-polarized bands ν₁ at 23500 cm⁻¹ and ν₂ at 18500 cm⁻¹, and a complex, strong band system in the NIR (near infra red) with sharp weak peaks in the region of the OH stretching fundamentals superimposed on the NIR system in the σ-spectra. The NIR band system and the UV edge produce an absorption minimum in both spectra, σ and π, at 21000 cm⁻¹, i.e. in the blue, which explains the colour of the crystals. Bands ν₁ and ν₂ are assigned to dd transitions to the Jahn-Teller split upper E_g state of octahedral Ti³⁺. The NIR band system can be fitted as a sum of three components. Two of them are partly π-polarized, nearly Gaussian bands, both with large half widths 6000–7000 cm⁻¹, ν₃ at 12000 cm^–1 and the most intense ν₄ at 6500 cm⁻¹. The third NIR band ν₅ of a mixed Lorentz-Gaussian shape with a maximum at 3000 cm⁻¹ forms a shoulder on the low-energy wing of ν₄. Energy positions, half band widths and temperature behaviour of these bands are consistent with a small polaron type of Ti³⁺Ti⁴⁺ charge transfer (CT). Polarization dependence of CT bands can be explained on the basis of the structural model of defect rutile by Bursill and Blanchin (1983) involving interstitial titanium. Two OH bands at 3322 and 3279 cm⁻¹ in σ-spectra show different stability during annealing, indicating two different positions of proton in the rutile structure, one of them probably connected with Ti³⁺ impurity. Total water concentration in blue rutile determined by IR spectroscopy is 0.10 wt-% OH. The EPR spectra measured in the temperature interval 20–295 K show the presence of an electron centre at temperatures above 100 K and Ti³⁺ ions in more than one structural position, but predominantly in compressed interstitial octahedral sites, at lower temperatures. These results are in good agreement with the conclusions based on the electronic absorption data. Received: 24 March 1997 / Revised, accepted: 14 October 1997     

The thermoelastic behavior of clintonite up to 10?GPa and 1,000°C

The thermoelastic behavior of a natural clintonite-1M [with composition: Ca_1.01(Mg_2.29Al_0.59Fe_0.12)_Σ3.00(Si_1.20Al_2.80)_Σ4.00O₁₀(OH)₂] has been investigated up to 10 GPa (at room temperature) and up to 960°C (at room pressure) by means of in situ synchrotron single-crystal and powder diffraction, respectively. No evidence of phase transition has been observed within the pressure and temperature range investigated. P–V data fitted with an isothermal third-order Birch–Murnaghan equation of state (BM-EoS) give V ₀ = 457.1(2) ?³, K _T0 = 76(3)GPa, and K′ = 10.6(15). The evolution of the “Eulerian finite strain” versus “normalized stress” shows a linear positive trend. The linear regression yields Fe(0) = 76(3) GPa as intercept value, and the slope of the regression line leads to a K′ value of 10.6(8). The evolution of the lattice parameters with pressure is significantly anisotropic [β(a) = 1/3K _T0(a) = 0.0023(1) GPa⁻¹; β(b) = 1/3K _T0(b) = 0.0018(1) GPa⁻¹; β(c) = 1/K _T0(c) = 0.0072(3) GPa⁻¹]. The β-angle increases in response to the applied P, with: β_P = β₀ + 0.033(4)P (P in GPa). The structure refinements of clintonite up to 10.1 GPa show that, under hydrostatic pressure, the structure rearranges by compressing mainly isotropically the inter-layer Ca-polyhedron. The bulk modulus of the Ca-polyhedron, described using a second-order BM-EoS, is K _T0(Ca-polyhedron) = 41(2) GPa. The compression of the bond distances between calcium and the basal oxygens of the tetrahedral sheet leads, in turn, to an increase in the ditrigonal distortion of the tetrahedral ring, with ∂α/∂P ≈ 0.1°/GPa within the P-range investigated. The Mg-rich octahedra appear to compress in response to the applied pressure, whereas the tetrahedron appears to behave as a rigid unit. The evolution of axial and volume thermal expansion coefficient α with temperature was described by the polynomial α(T) = α₀ + α₁ T ^−1/2. The refined parameters for clintonite are as follows: α₀ = 2.78(4) 10⁻⁵°C⁻¹ and α₁ = −4.4(6) 10⁻⁵°C^1/2 for the unit-cell volume; α₀(a) = 1.01(2) 10⁻⁵°C⁻¹ and α₁(a) = −1.8(3) 10⁻⁵°C^1/2 for the a-axis; α₀(b) = 1.07(1) 10⁻⁵°C⁻¹ and α₁(b) = −2.3(2) 10⁻⁵°C^1/2 for the b-axis; and α₀(c) = 0.64(2) 10⁻⁵°C⁻¹ and α₁(c) = −7.3(30) 10⁻⁶°C^1/2for the c-axis. The β-angle appears to be almost constant within the given T-range. No structure collapsing in response to the T-induced dehydroxylation was found up to 960°C. The HP- and HT-data of this study show that in clintonite, the most and the less expandable directions do not correspond to the most and the less compressible directions, respectively. A comparison between the thermoelastic parameters of clintonite and those of true micas was carried out.     

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     

Experimental Investigation of Cement Treated Sand Behavior Under Triaxial Test

In this paper, an experimental investigation of cement treated sand is performed under triaxial tests in order to quantify the effects of cementation on the stress–strain behavior, stiffness and shear strength. Samples were cured up to 180 days. The results show that the stress–strain behavior of cemented sands is nonlinear with contractive–dilative stages. The stress–strain response is strongly influenced by effective confining pressure and cement content. Stiffness and strength are greatly improved by an increase in binder content. An increase of the angle of shearing resistance and cohesion intercept with increasing cement content is observed consistently. Brittle behavior is observed at low confining pressure and high cement content. After yielding, the increase in the dilatancy accelerates. Two competing related processes determine the peak strength: Bond breakages cause a strength reduction but the associated dilatancy leads to a strength increase. This finding and the experimental observation that the dilatancy at the peak state increases with increasing cement content explain why the measured peak-state strength parameters, c′ and φ_p′, are relevant to the binder content.     

Elasticity and equation of state of Li<Subscript>2</Subscript>B<Subscript>4</Subscript>O<Subscript>7</Subscript>

A single crystal X-ray diffraction study on lithium tetraborate Li₂B₄O₇ (diomignite, space group I4₁ cd) has been performed under pressure up to 8.3 GPa. No phase transitions were found in the pressure range investigated, and hence the pressure evolution of the unit-cell volume of the I4₁ cd structure has been described using a third-order Birch–Murnaghan equation of state (BM-EoS) with the following parameters: V ₀  = 923.21(6) ų, K ₀  = 45.6(6) GPa, and K′ = 7.3(3). A linearized BM-EoS was fitted to the axial compressibilities resulting in the following parameters a ₀  = 9.4747(3) Å, K _0a  = 73.3(9) GPa, K′ _a  = 5.1(3) and c ₀  = 10.2838(4) Å, K _0c  = 24.6(3) GPa, K′ _c  = 7.5(2) for the a and c axes, respectively. The elastic anisotropy of Li₂B₄O₇ is very large with the zero-pressure compressibility ratio β _0c /β _0a  = 3.0(1). The large elastic anisotropy is consistent with the crystal structure: A three-dimensional arrangement of relatively rigid tetraborate groups [B₄O₇]²⁻ forms channels occupied by lithium along the polar c–axis, and hence compression along the c axis requires the shrinkage of the lithium channels, whereas compression in the a direction depends mainly on the contraction of the most rigid [B₄O₇]²⁻ units. Finally, the isothermal bulk modulus obtained in this work is in general agreement with that derived from ultrasonic (Adachi et al. in Proceedings-IEEE Ultrasonic Symposium, 228–232, 1985; Shorrocks et al. in Proceedings-IEEE Ultrasonic Symposium, 337–340, 1981) and Brillouin scattering measurements (Takagi et al. in Ferroelectrics, 137:337–342, 1992).     

Location and quantitative analysis of OH in coesite

 The incorporation of hydrogen (deuterium) into the coesite structure was investigated at pressures from 3.1 to 7.5 GPa and temperatures of 700, 800, and 1100 °C. Hydrogen could only be incorporated into the coesite structure at pressures greater 5.0 GPa and 1100 °C . No correlation between the concentration of trace elements such as Al and B and the hydrogen content was observed based on ion probe analysis (1335 ± 16 H ppm and 17 ± 1 Al ppm at 7.5 GPa, 1100 °C). The FTIR spectra show three relatively intense bands at 3575, 3516, and 3459 cm⁻¹ (ν₁ to ν₃, respectively) and two very weak bands at 3296 and 3210 cm⁻¹ (ν₄ and ν₅, respectively). The band at 3516 cm⁻¹ is strongly asymmetric and can be resolved into two bands, 3528 (ν_2a) and 3508 (ν_2b) cm⁻¹, with nearly identical areas. Polarized infrared absorption spectra of coesite single-crystal slabs, cut parallel to (0 1 0) and (1 0 0), were collected to locate the OH dipoles in the structure and to calibrate the IR spectroscopy for quantitative analysis of OH in coesite (ɛ _{i ,tot}=190 000 ± 30 000 l mol⁻¹ _H2O cm⁻²). The polarized spectra revealed a strong pleochroism of the OH bands. High-pressure FTIR spectra at pressures up to 8 GPa were performed in a diamond-anvil cell to gain further insight into incorporation mechanism of OH in coesite. The peak positions of the ν₁, ν₂, and ν₃ bands decrease linearly with pressure. The mode Grüneisen parameters for ν₁, ν₂, and ν₃ are −0.074, −0.144 and −0.398, respectively. There is a linear increase of the pressure derivatives with band position which follows the trend proposed by Hofmeister et al. (1999). The full widths at half maximum (FWHM) of the ν₁, ν₂, and ν₃ bands increase from 35, 21, and 28 cm⁻¹ in the spectra at ambient conditions to 71, 68, and 105 in the 8 GPa spectra, respectively. On the basis of these results, a model for the incorporation of hydrogen in coesite was developed: the OH defects are introduced into the structure by the substitution Si^4+(Si2)+4O²⁻= ^[4]□^(Si2) + 4OH⁻, which gives rise to four vibrations, ν₁, ν_2a, ν_2b, and ν₃. Because the OH(D)-bearing samples do contain traces of Al and B, the bands ν₄ and ν₅ may be coupled to Al and/or B substitution. Received: 19 December 2000 / Accepted: 23 April 2001     

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.     

New thermoelastic parameters of natural <Emphasis Type="Italic">C</Emphasis>2/<Emphasis Type="Italic">c</Emphasis> omphacite

The compressibility at room temperature and the thermal expansion at room pressure of two disordered crystals (space group C2/c) obtained by annealing a natural omphacite sample (space group P2/n) of composition close to Jd₅₆Di₄₄ and Jd₅₅Di₄₅, respectively, have been studied by single-crystal X-ray diffraction. Using a Birch–Murnaghan equation of state truncated at the third order [BM3-EoS], we have obtained the following coefficients: V ₀ = 421.04(7) Å³, K _T0 = 119(2) GPa, K′ = 5.7(6). A parameterized form of the BM3 EoS was used to determine the axial moduli of a, b and c. The anisotropy scheme is β _c  ≤ β _a  ≤ β _b , with an anisotropy ratio 1.05:1.00:1.07. A fitting of the lattice variation as a function of temperature, allowing for linear dependency of the thermal expansion coefficient on the temperature, yielded α_V(1bar,303K) = 2.64(2) × 10⁻⁵ K⁻¹ and an axial thermal expansion anisotropy of α _b  ≫ α _a  > α _c . Comparison of our results with available data on compressibility and thermal expansion shows that while a reasonable ideal behaviour can be proposed for the compressibility of clinopyroxenes in the jadeite–diopside binary join [K _T0 as a function of Jd molar %: K _T0 = 106(1) GPa + 0.28(2) × Jd_(mol%)], the available data have not sufficient quality to extract the behaviour of thermal expansion for the same binary join in terms of composition.     

Comparing Reservoir and Outcrop Specimens for Mixed Mode I–II Fracture Toughness of a Limestone Rock Formation at Various Conditions

Summary A fracture toughness study was conducted on a limestone rock formation from a petroleum reservoir in Saudi Arabia, and results were compared with those for outcrop specimens from the same geological formation. The objective was to investigate the possibility of using outcrop specimens to estimate the fracture toughness behavior of reservoir rock at in-situ conditions of temperature and confining pressure. The study was made on reservoir specimens from a depth of about 3.5 km, at both ambient and reservoir conditions. Mixed mode I–II fracture toughness at reservoir conditions of high temperature and confining pressure was studied using straight notched Brazilian disk (SNBD) specimens under diametrical compression. Tests were conducted at ambient conditions, at an effective confining pressure (σ₃) of 28 MPa (4000 psi), and at a temperature of 116^°C. The results showed a substantial increase in fracture toughness under confining pressure. Under σ₃=28 MPa, the pure mode-I fracture toughness (K _IC), increased by a factor of about 3.2, and the pure mode-II fracture toughness (K _IIC) increased by a factor of 4.4, compared to those under ambient conditions. On the other hand, K _IC at 116^°C was only 25% more than that at ambient conditions. These results were compared with recent results for outcrop specimens from the same geological formation. The results reveal that outcrop specimens can be successfully used to predict the fracture behavior of reservoir specimens at in-situ conditions, in spite of some differences at ambient conditions. Additionally, fracture toughness envelopes were obtained for reservoir specimens at ambient and high pressure conditions, in both positive and negative regions. Received September 14, 2000; accepted February 22, 2002 Published online September 2, 2002     

In-situ geotechnical experimentation and stability evaluation of an instrumented 180 m×70 m×12.5 m fill dike constructed on laminated soft ground

 An instrumented trial-fill dike was constructed on soft, laminated soils of the Lisan Peninsula foreshore of the Dead Sea. The earthwork had base dimensions of 180 m by approximately 70 m wide and was raised in two stages to a maximum height of 12.5 m above original ground level. The geotechnical data of the dike were monitored in order to: assess the short- and long-term strength of the foundation, obtain and analyze the pore-pressure response of the foundation soils for potential use in construction control, obtain data on embankment settlement in order to refine end-of-construction and post-construction settlement assessments, and optimize the height of the dike to be constructed by providing information on the construction sequence for use in calculation of capital costs and alternative layouts and dike heights. The successful completion of the trial dike has demonstrated that steep-side dikes up to 12.5 m high can be constructed rapidly on soft soils. The construction of the trial dike has therefore proved a very substantial benefit to the evaluation of the likely performance of a dike constructed along the Lisan shore. The key factor which made this fast construction possible was the unexpected, very rapid consolidation of the majority of the foundation soil which has been shown to occur. The principal observations from the trial dike were: (1) end of construction settlements may be calculated using drained stiffnesses where E′/s_{u initial} has a value of around 65; (2) post-construction settlements can be calculated using a coefficient of secondary compression, Cα equal to 0.015; (3) a rapid increase in undrained shear strength occurred when loading the soil up to a value of s_u equal to around 30 kPa. The value of s_u/σ_v′ was as high as 0.5 at this stage. With further loading the strength increase was more modest and s_u/σ_v fell to around 0.25 for a vertical effective stress of 160 kPa; (4) for the undrained stability analyses of the trial dike, the mean vane shear-strength profile provided an appropriate assessment of the short-term factor of safety against failure, 5) For the drained stability analyses of the trial dike, lower bound effective strength parameters for the foundation and embankment fill (c′=0, φ′=30° and c′=2 kN/m², φ′=33°, respectively), combined with field measurements of end of construction pore water pressures provided an analysis which was broadly compatible with the undrained analysis; and (6) the trial dike has been stable, pre- and post-construction, because of the well drained nature of its foundation which prevented the build up of high pore water pressures and led to rapid consolidation. Received: 22 June 1998 · Accepted: 30 October 1998