Experimental Investigation into Hydraulic Fracture Network Propagation in Gas Shales Using CT Scanning Technology

Multistage fracturing of the horizontal well is recognized as the main stimulation technology for shale gas development. The hydraulic fracture geometry and stimulated reservoir volume (SRV) is interpreted by using the microseismic mapping technology. In this paper, we used a computerized tomography (CT) scanning technique to reveal the fracture geometry created in natural bedding-developed shale (cubic block of 30 cm × 30 cm × 30 cm) by laboratory fracturing. Experimental results show that partially opened bedding planes are helpful in increasing fracture complexity in shale. However, they tend to dominate fracture patterns for vertical stress difference Δσ _v  ≤ 6 MPa, which decreases the vertical fracture number, resulting in the minimum SRV. A uniformly distributed complex fracture network requires the induced hydraulic fractures that can connect the pre-existing fractures as well as pulverize the continuum rock mass. In typical shale with a narrow (<0.05 mm) and closed natural fracture system, it is likely to create complex fracture for horizontal stress difference Δσ _h  ≤ 6 MPa and simple transverse fracture for Δσ _h  ≥ 9 MPa. However, high naturally fractured shale with a wide open natural fracture system (>0.1 mm) does not agree with the rule that low Δσ _h is favorable for uniformly creating a complex fracture network in zone. In such case, a moderate Δσ _h from 3 to 6 MPa is favorable for both the growth of new hydraulic fractures and the activation of a natural fracture system. Shale bedding, natural fracture, and geostress are objective formation conditions that we cannot change; we can only maximize the fracture complexity by controlling the engineering design for fluid viscosity, flow rate, and well completion type. Variable flow rate fracturing with low-viscosity slickwater fluid of 2.5 mPa s was proved to be an effective treatment to improve the connectivity of induced hydraulic fracture with pre-existing fractures. Moreover, the simultaneous fracturing can effectively reduce the stress difference and increase the fracture number, making it possible to generate a large-scale complex fracture network, even for high Δσ _h from 6 MPa to 12 MPa.     

3-D Mohr circle analysis of vein opening,Indarama lode-gold deposit,Zimbabwe: implications for exploration

The Indarama lode gold deposit is hosted by vertically-dipping basalt in the Late Archaean Midlands Greenstone Belt of Zimbabwe. Major deformation events at 2.68 and 2.58 Ga established a complex array of fractures. A limited range of orientations of this fracture network opened towards the end of the younger deformation event, creating a lode pattern where 92% of mineralised veins dip at less than 50°, mainly to the E and W, and most strike directions are represented. A clustered distribution of poles to the quartz–carbonate veins indicates a constrictional stress field at the time of vein opening where σ₁ and σ₂ were near horizontal, (directed NNW–SSE and ENE–WSW, respectively), and σ₃ was near vertical. 3-D Mohr circle analysis demonstrates that σ₂ was approximately 67% of σ₁ (the stress ratio) and that the driving pressure ratio (R′) was approximately 0.4, reflecting the role of fluid pressure, mean stress, and the maximum shear stress in controlling conditions of fracture opening.     

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.     

Interpretation of strains in torsion shear tests

The normal and shear strains obtained in torsion shear tests may be interpreted in two different ways to gain insight into (1) the type of plastic potential to be employed in hardening plasticity stress–strain models, and (2) the coincidence in physical space of the plastic strain increment direction with the stress direction during principal stress rotation. Thirty-four drained torsion shear tests were performed on hollow cylinder specimens of Santa Monica Beach sand deposited by dry pluviation. Twenty-six tests were performed on tall specimens with height of 40 cm, and eight tests were performed on short specimens with height of 25 cm to investigate the effect of the specimen height on the soil behavior in hollow cylinder specimens. Each test was conducted with the same, constant inside and outside confining pressure, σ_r, thus tying the value of b = (σ₂–σ₃)/(σ₁– σ₃) to the inclination, β, of the major principal stress. The directions of strain increment vectors at failure are compared with the directions corresponding to associated and non-associated flow. The relation between the directions of major principal strain increment and major principal stress during rotation of principal stress axes in physical space are investigated.     

Influences of loading direction and intermediate principal stress ratio on the initiation of strain localization in cross-anisotropic sand

Since cross-anisotropic sand behaves differently when the loading direction or the stress state changes, the influences of the loading direction and the intermediate principal stress ratio (b = (σ ₂ ? σ ₃)/(σ ₁ ? σ ₃)) on the initiation of strain localization need study. According to the loading angle (angle between the major principal stress direction and the normal of bedding plane), a 3D non-coaxial non-associated elasto-plasticity hardening model was proposed by modifying Lode angle formulation of the Mohr–Coulomb yield function and the stress–dilatancy function. By using bifurcation analysis, the model was used to predict the initiation of strain localization under plane strain and true triaxial conditions. The predictions of the plane strain tests show that the major principal strain at the bifurcation points increases with the loading angle, while the stress ratio decreases with the loading angle. According to the loading angle and the intermediate principal stress ratio, the true triaxial tests were analyzed in three sectors. The stress–strain behavior and the volumetric strain in each sector can be well captured by the proposed model. Strain localization occurs in most b value conditions in all three sectors except for those which are close to triaxial compression condition (b = 0). The difference between the peak shear strength corresponding to the strain localization and the ultimate shear strength corresponding to plastic limit becomes obvious when the b value is near 0.4. The influence of bifurcation on the shear strength becomes weak when the loading direction changes from perpendicular to the bedding plane to parallel. The bifurcation analysis based on the proposed model gives out major principal strain and peak shear strength at the initiation of strain localization; the given results are consistent with experiments.     

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.     

Quantitative analysis of the shallow crustal tectonic stress field in China mainland based on in situ stress data

The latest hydraulic fracturing and stress relief measurement data in the Chinese mainland were collected. The total of 3856 data entries are measured at 1474 locations. The measured area covers 75–130°E and 18–47°N, and the depth range varies from surface to 4000 meters depth, which generally includes each active tectonic block of China and each segment of North–South seismic belt. We investigated the tectonic stress field by removing the effect of gravity. For this, we assume lateral constraints and Heim’s rule. The gravity contribution is removed by using the assumption of lateral constraint and Heim’s rule. Our results show: (1) the maximum and the minimum horizontal principal stress σ_H, σ_h and the vertical stress σ_V in the shallow crust of China all increase linearly with depth: σ_H = 0.0229D + 4.738, σ_h = 0.0171D + 1.829, σ_V = 0.0272D. Maximum and minimum horizontal tectonic stress varies as a function of depth D linearly 4.738 < σ_T < 0.0139D + 4.738 and 1.829 < σ_t < 0.0162D + 1.829. The horizontal tectonic differential stress is σ_T − σ_t = 0.0058D + 2.912. (2) The intermediate value of σ_T1 (regression value of tectonic stress inferred from the assumption of lateral constraint at 2000 m depth) changes in different areas, the maximum value of which is 45.6 MPa, while the minimum value of which is 26.8 MPa. Horizontal tectonic differential stress σ_T − σ_t increases linearly with depth and the maximum and minimum of σ_T − σ_t is 25.3 MPa and 13.0 MPa, respectively. In general, the stress magnitude is much higher in western than in eastern China. This indicates that the strong Indo-Eurasian collision dominates the present tectonic stress field in Chinese mainland. (3) Compared with other study regions, the northward crustal compression to the Qinghai-Tibet block is relatively lower in magnitude in the shallow subsurface and higher at deeper depth. (4) The orientations of σ_T in China mainland generally form a radial scattering pattern centered in Tibetan Plateau. From western to eastern China, they rotate gradually clockwise from NS to NNE, NE, NEE, and SE, which is consistent with the result of focal mechanism solutions.     

Critical state framework for liquefaction of fine grained soils

A consistent methodology based on the critical state framework to characterize the different regimes of fine-grained soil behavior under earthquake loads is put forward. Shear strength and deformation behavior of soils depend in a major way on the combination of volume and confining stress. Depending on their combination, a soil aggregate may fracture into clastic debris, fail with fault planes, or yield plastically. This characterization of the class of limiting soil behavior is used to analyze the potential for large deformation and liquefaction in fine grained soils. The central piece of the proposed characterization is the (η, LI₅) stability diagram where η = q/p′ and LI₅ = LI + 0.5 log (p′/5). This diagram captures the effects of soil plasticity through liquidity index LI, confinement through mean normal effective stress p′, and shear stress q through the stress ratio η. The three regions of behavior; fracture, fault, and fold/yield are identified. Soils become susceptible to liquefaction when they shift into the fracture zone (LI₅ ≤ 0.4), or if they plot outside of the stable yielding region.Under earthquake loading, the initial soil states will migrate into different regions in the stability diagram depending on their initial location, shear stress increment, and, pore pressure response. The final position of the soil state would dictate the type of limiting behavior expected in the field; fracture, rupture or yield. The final states which fall into the fracture region have the potential for catastrophic failures including “liquefaction”; the ones which fall onto the rupture region would experience the attainment of a peak stress ratio followed by softening along failure planes; the ones in the yield region would continue to yield in a stable manner. The latter two types of deformations while resulting in large deformation may not be of a catastrophic nature. The proposed characterization is used to examine the liquefaction susceptibility of fine grained soils from China, Taiwan, and Turkey. Use of simplified empirical criteria based on parameters such as plasticity index and fines contents may not capture the true nature of the type of undrained limiting behavior of fine grains soils in the field including liquefaction.     

A Criterion for Brittle Failure of Rocks Using the Theory of Critical Distances

This paper presents a new analytical criterion for brittle failure of rocks and heavily over-consolidated soils. Griffith’s model of a randomly oriented defect under a biaxial stress state is used to keep the criterion simple. The Griffith’s criterion is improved because the maximum tensile strength is not evaluated at the boundary of the defect but at a certain distance from the boundary, known as half of the critical distance. This fracture criterion is known as the point method, and is part of the theory of critical distances, which is utilised in fracture mechanics. The proposed failure criterion has two parameters: the inherent tensile strength, σ ₀, and the ratio of the half-length of the initial crack/flaw to the critical distance, a/L. These parameters are difficult to measure but they may be correlated with the uniaxial compressive and tensile strengths, σ _c and σ _t. The proposed criterion is able to reproduce the common range of strength ratios for rocks and heavily overconsolidated soils (σ _c/σ _t = 3–50) and the influence of several microstructural rock properties, such as texture and porosity. Good agreement with laboratory tests reported in the literature is found for tensile and low-confining stresses.     

Evolution of fault zones in carbonates with mechanical stratigraphy – Insights from scale models using layered cohesive powder

We present analogue models of the formation of dilatant normal faults and fractures in carbonate fault zones, using cohesive hemihydrate powder (CaSO₄·½H₂O). The evolution of these dilatant fault zones involves a range of processes such as fragmentation, gravity-driven breccia transport and the formation of dilatant jogs. To allow scaling to natural prototypes, extensive material characterisation was done. This showed that tensile strength and cohesion depend on the state of compaction, whereas the friction angle remains approximately constant. In our models, tensile strength of the hemihydrate increases with depth from 9 to 50 Pa, while cohesion increases from 40 to 250 Pa. We studied homogeneous and layered material sequences, using sand as a relatively weak layer and hemihydrate/graphite mixtures as a slightly stronger layer. Deformation was analyzed by time-lapse photography and Particle Image Velocimetry (PIV) to calculate the evolution of the displacement field. With PIV the initial, predominantly elastic deformation and progressive localization of deformation are observed in detail. We observed near-vertical opening-mode fractures near the surface. With increasing depth, dilational shear faults were dominant, with releasing jogs forming at fault-dip variations. A transition to non-dilatant shear faults was observed near the bottom of the model. In models with mechanical stratigraphy, fault zones are more complex. The inferred stress states and strengths in different parts of the model agree with the observed transitions in the mode of deformation.     

Experimental investigation of shear strength of sands with inherent fabric anisotropy

Loading direction-dependent strength of sand has been traditionally characterized in the principal stress space as a direct extension of the Mohr–Coulomb criterion. A recent study found that it is more appropriate to define anisotropic strength of sand on failure/shear planes, but this proposition has only been demonstrated with discrete element method (DEM) simulations. The present study experimentally investigates anisotropic shear strength of sands in this new framework. Three granular materials with distinct grain characteristics ranging from smooth and rounded particles to flaky and angular particles are tested with the bedding plane inclination angle ψ _b varying over the full range of 0°–180°. The main objective is to study how the peak friction angle ? _p of sand is affected by the ψ _b angle and how the ψ _b–? _p relationship evolves with the change of characteristics of constituent sand particles. We find that the general trend of ψ _b–? _p curves for real sands resembles what was predicted by DEM in a previous study, whereas rich anisotropic strength behavior is revealed by the laboratory data. The effects of normal stress and initial density, as well as shear dilation behavior at different shear directions, are also studied.     

3-D Mohr circle construction using vein orientation data from Gadag (southern India) – Implications to recognize fluid pressure fluctuation

In this paper orientations of quartz veins from the Archaean age lode-gold bearing region of Gadag (southern India) are used to determine the relative stress and fluid pressure (P_f) conditions by constructing 3-D Mohr circle. Anisotropy of magnetic susceptibility (AMS) analysis of the host massive metabasalt reveals that the magnetic foliation is NW–SE striking, which is related to early NE–SW compression (D1/D2 deformation) that affected the region. The quartz veins have a wide range of orientations, with NW–SE striking veins (steep northeasterly dips) being the most prominent. Vein emplacement is inferred to have taken place under NW–SE compression that is known to have caused late deformation (D3) in the region. It is argued that the NW–SE fabric defined the pre-existing anisotropy and channelized fluid flow during D3. The permeability was initially low, which resulted in high P_f (>σ₂). 3-D Mohr circle analysis indicates that the driving pressure ratio (R′) was 0.94, a condition that favoured fracturing and reactivation of fabric elements (foliations and fractures) having a wide range of orientations. This led to an increase in permeability and fluid flowed (burped) into the fractures. Resulting vein emplacement and sealing of fractures led to a reduction of P_f (<σ₂). It is argued that at this low P_f, NW–SE oriented structures continued to remain susceptible to reactivation and vein emplacement, while fractures of all other orientations were inactive and remained sealed. As a consequence, the study area has a cluster of NW–SE oriented veins. R′ is calculated to be 0.07 from 3-D Mohr circle analysis at low P_f, when fractures with NW–SE orientation only were susceptible to dilation. However, it is envisaged that any emplacement of veins in these fractures would have sealed them, thus reducing the permeability and initiating the next cycle of rise in P_f (>σ₂). Thus, it is concluded that the quartz veins in the Gadag region are a consequence of an interplay between conditions that fluctuated from P_f > σ₂ to P_f < σ₂.     

Static stress drop inferred from near-fault parameters for the 1999 Chi–Chi earthquake in Taiwan

In 2001, a special issue of the Bulletin of the Seismological Society of America (BSSA) featured seismological research for the 1999 Chi–Chi Taiwan earthquake. This study uses source parameters suggested by the first author in this special issue to estimate static stress drop associated with the Chi–Chi earthquake. The waveform simulation method was used to carefully examine these source parameters. The simulation results indicate that source parameters, inferred from near-fault observations, are well determined. According to the rupture area and slip, the static stress drops (Δσ_s) obtained were distributed between a small value of 47 bars near the epicentral region and a much larger value (>200 bars) to the north. Similar trends in dynamic stress drop (Δσ_d) were also recognized by the first author in his paper published in 2001 BSSA special issue. Comparing the Δσ_s with Δσ_d, satisfies the relation Δσ_s/Δσ_d ≈ 1. This relation suggests that fault motion is mostly spent releasing seismic wave energy during the rupture process of the Chi–Chi earthquake. The consistency between static and dynamic stress drops thus provides a measure of energy-moment (E_s/M₀) ratios, which range from 9.0 × 10⁻⁵ to 6.5 × 10⁻⁴. The average E_s/M₀ ratio estimated for the northern portions of the fault is 3.4 × 10⁻⁴, which is about 3 times that of the south. Such a high E_s/M₀ ratio can be interpreted as having low strength in the rupture for the northern portions of the fault, where the fault would release less energy per unit rupture surface to create the new rupture.     

Displacement velocity effects on rock fracture shear strengths

Triaxial shear tests are performed to assess the effects of displacement velocity and confining pressure on shear strengths and dilations of tension-induced fractures and smooth saw-cut surfaces prepared in granite, sandstone and marl specimens. A polyaxial load frame is used to apply confining pressures between 1 and 18 MPa with displacement velocities ranging from 1.15 × 10⁻⁵ to 1.15 × 10⁻² mm/s. The results indicate that the shearing resistances of smooth saw-cut surfaces tend to be independent of the displacement velocity and confining pressure. Under each confinement the peak and residual shear strengths and dilation rates of rough fractures increase with displacement velocities. The sheared-off areas increase when the confining pressure increases, and the displacement rate decreases. The velocity-dependent shear strengths tend to act more under high confining pressures for the rough fractures in strong rock (granite) than for the smoother fractures in weaker rocks (sandstone and marl). An empirical criterion that explicitly incorporates the effects of shear velocity is proposed to describe the peak and residual shear strengths. The criterion fits well to the test results for the three tested rocks.     

Rock interface strength influences fluid-filled fracture propagation pathways in the crust

Rock interface strengths have often been assumed to be zero in numerical and analogue models of fracture propagation and magma intrusion in the crust. Rock strength tests were performed to explore the role that rock interfaces have on the geometry and propagation dynamics of fluid-filled fractures in the crust. We used a 1 kN test machine to study 5 mm thick cuboidal specimens cut from a sandstone-siltstone rock core, where the strata were known to host magma intrusions and the rock interface between the units was intact. By measuring the load required to grow a crack running along the lithological contact between the layers we calculate its fracture toughness K_c. The siltstone had an average K_c of 0.56 ± 0.03 MPa m^1/2 compared to the sandstone at 0.42 ± 0.02 MPa m^1/2. The rock interface had intermediate average fracture toughness to the parent units at 0.45 ± 0.03 MPa m^1/2. These results have important implications on fracture propagation pathways through rocks, as well as for the geometry and propagation dynamics of magma intrusions in the crust.     

Scaling the 3-D Mohr circle and quantification of paleostress during fluid pressure fluctuation – Application to understand gold mineralization in quartz veins of Gadag (southern India)

In this study, orientations of 157 quartz veins occurring in metabasalts of the Gadag region (Dharwar craton, southern India) are used to plot the 3-D Mohr stress circle, which provides information about relative stress/fluid pressure (P_f) conditions, as well as stress state during P_f fluctuation. To scale the 3-D Mohr circle, vein orientation data are integrated with (a) available estimates from fluid inclusions of highest recorded P_f (390 MPa) and lowest recorded P_f (50 MPa) and (b) intrinsic rupture criterion that empirically quantify rock properties. Based on the scaled 3-D Mohr circle, the absolute magnitudes of the three principal stresses are quantified for high and low P_f. Of 157 veins investigated here, 14 veins are identified as having favourable orientation for dilation at high as well as low P_f. These 14 veins have a mean strike of 150°, which is similar to the orientation of the gold-bearing quartz lodes reported in the region. The effective normal stress (σ′_n = σ_n−P_f) prevalent during dilation of fracture/fabric anisotropy with 150° strike is calculated to be −11.5 MPa at high P_f, and −1.0 MPa at low P_f. Thus, it is interpreted that in the Gadag region, a change in σ′_n of 10.5 MPa prevailed during P_f fluctuation and associated separation of gold from the fluid.     

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.     

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.     

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.     

Residual and Fully Softened Strength Evaluation of Soils using Artificial Neural Networks

A backpropagation artificial neural network (ANN) model is developed to predict the secant friction angle of residual and fully softened soils, using data reported by Stark et al. (J Geotech Geoenviron Eng ASCE 131:575–588, 2005). In the ANN model, index properties such as liquid limit, plastic limit, activity, clay fraction and effective normal stress are used as input variables while secant residual friction angle is used as output variable. The model is verified using data that were not used for model training and testing. The results also indicate that the secant residual friction angle of cohesive soils can be predicted quite accurately using liquid limit, clay fraction and effective normal stress as input variables with R ² = 0.93. The sensitivity analysis results indicate that plastic limit and activity have no appreciable effect on ANN predicted secant friction angles. The secant friction angle predictions of the ANN model were also compared with those of Stark’s et al. (2005) curves and the empirical formulas suggested for the same data sets by Wright (Evaluation of soil shear strengths for slope and retaining wall stability with emphasis on high plasticity clays, 2005). The comparison shows that the ANN model predictions are very close to those suggested by the Stark et al. (2005) curves but much better than the prediction of Wright’s (2005) empirical equations. The results also show that ANN is an alternative powerful tool to predict the secant friction angle of soils.