Prediction of longitudinal dispersion coefficient using multivariate adaptive regression splines

In this paper, multivariate adaptive regression splines (MARS) was developed as a novel soft-computing technique for predicting longitudinal dispersion coefficient (D_L) in rivers. As mentioned in the literature, experimental dataset related to D_L was collected and used for preparing MARS model. Results of MARS model were compared with multi-layer neural network model and empirical formulas. To define the most effective parameters on D_L, the Gamma test was used. Performance of MARS model was assessed by calculation of standard error indices. Error indices showed that MARS model has suitable performance and is more accurate compared to multi-layer neural network model and empirical formulas. Results of the Gamma test and MARS model showed that flow depth (H) and ratio of the mean velocity to shear velocity (u/u^?) were the most effective parameters on the D_L.     

Prediction of an environmental issue of mine blasting: an imperialistic competitive algorithm-based fuzzy system

Ground vibration resulting from blasting is one of the most important environmental problems at open-cast mines. Therefore, accurately approximating the blast-induced ground vibration is very significant. By reviewing the previous investigations, many attempts have been done to create the empirical models for estimating ground vibration. Nevertheless, the performance of the empirical models is not good enough. In this research work, a new hybrid model of fuzzy system (FS) designed by imperialistic competitive algorithm (ICA) is proposed for approximating ground vibration resulting from blasting at Miduk copper mine, Iran. For comparison aims, various empirical models were also utilized. Results from different predictor models were compared by using coefficient of multiple determination (R ²), variance account for and root-mean-square error between measured and predicted values of the PPVs. Results prove that the FS–ICA model outperforms the other empirical models in terms of the prediction accuracy. In other words, the FS–ICA model with R ² of 0.942 can forecast PPV better than the USBM with R ² of 0.634, Ambraseys–Hendron with R ² of 0.638, Langefors–Kihlstrom with R ² of 0.637 and Indian Standard with R ² of 0.519.     

Upscaling of transmissivity,derived from specific capacity: a hydrogeomorphological approach applied to the Doon Valley aquifer system in India

Transmissivity (T) is one of the most important parameters in groundwater studies, and is generally estimated from pumping tests. T can also be deduced from abundantly available specific-capacity (Q/s) data by using analytical and/or empirical approaches, further upscaled by geostatistical methods. A different, remote sensing based, hydrogeomorphological approach is proposed, to upscale T from point- or well-scale to aquifer-scale, and it is applied to the piedmont alluvial aquifer system of Doon Valley in India. In the first step, Q/s and T data-pairs available from aquifer tests were used to establish an empirical, logarithmic relation. Subsequently, satellite imagery along with available data from published and unpublished maps, literature sources and ground surveys were used to divide the aquifer system into major hydrogeomorphological domains that control the groundwater occurrence and flow. Then, the T data derived from Q/s (using the empirical relation) and that available from pumping tests at well-scale were upscaled to aquifer-scale by averaging the T values within each hydrogeomorphological domain. Such a stratification approach is especially useful in areas where availability of only a few data-pairs of known Q/s and T limit the use of geostatistical techniques. A comparative study of the published empirical relations between Q/s and T in various hydrogeologic settings revealed that the relation obtained for Doon Valley aquifer system is close to that found for a similar alluvial aquifer system in Morocco.     

Effect of foliation orientation on the P- and S-wave velocity anisotropies and dynamic elastic constants of the quartz-micaschists metamorphic rocks,Angouran mine,Iran

Laboratory measurements are required to study geophysical properties of the subsurface because of lacking direct observation of Earth’s crust. In this research, compressional (P) and shear (S) wave velocity measurements have been conducted on cylindrical specimens of Quartz-micaschist cored using rock blocks taken from the zinc and lead Angouran mine, Zanjan, northwest of Iran. Cylindrical rock specimens were prepared from the blocks by coring in 0°, 30°, 45°, 60°, and 90° into the foliation direction. P- and S-wave velocities were measured along the cylindrical specimens with different foliation orientations. Percent variations of the P- and S-wave velocities (Thomsen’s anisotropic parameters ε and γ) and constant dynamic modulus of test results have been determined. Percent variations of the P-wave velocity (ε) increase with an increase of the foliation angle with respect to the propagating waves direction by a parabolic function as it shows P-wave velocity differences up to a maximum value of 50 %. Thomsen’s anisotropic parameter of γ has also the same function with the foliation angle. Meanwhile, foliation orientation has a much greater influence on ε than γ for foliation angle from 45° to 90° as \( \frac{\varepsilon }{\gamma } \) ratio increases with an increase of foliation angle. Values of dynamic elastic modulus (E), Poisson’s ratio (ν), shear modulus (μ), bulk modulus (K), and Lamé’s constant (λ) increase with the increase of foliation angle with the parabolic function. The results show that dynamic elastic modulus, Poisson’s ratio, shear modulus, bulk modulus, and Lamé’s constant have anisotropic behavior in relation with the foliation orientation.     

Prediction of blasting-induced fragmentation in Meydook copper mine using empirical,statistical, and mutual information models

One of the most important aims of blasting in open pit mines is to reach desirable size of fragmentation. Prediction of fragmentation has great importance in an attempt to prevent economic drawbacks. In this study, blasting data from Meydook mine were used to study the effect of different parameters on fragmentation; 30 blast cycles performed in Meydook mine were selected to predict fragmentation where six more blast cycles are used to validate the results of developed models. In this research, mutual information (MI) method was employed to predict fragmentation. Ten parameters were considered as primary ones in the model. For the sake of comparison, Kuz-Ram empirical model and statistical modeling were also used. Coefficient of determination (R ²), root mean square error (RMSE), and mean absolute error (MAE) were then used to compare the models. Results show that MI model with values of R ², RMSE, and MAE equals 0.81, 10.71, and 9.02, respectively, is found to have more accuracy with better performance comparing to Kuz-Ram and statistical models.     

Debris flow density determined by grain composition

Density is one of the most important parameters of debris flows. Because observing an active debris flow is very difficult, finding a method to estimate debris flow density is urgently needed for disaster mitigation engineering. This paper proposes an effective empirical equation in terms of grain size distribution (GSD) parameters based on observations in Jiangjia Gully, Yunnan Province, China. We found that the GSD follows P(D) = KD ^-μ exp(? D/Dc), with μ and Dc representing the fine and coarse grains, respectively. In particular, μ is associated with some characteristic porosity of soil in the natural state and increases with increased porosity. Dc characterizes the grain size range of the flow and increases with the grain concentration. Studies show that flow density is related to both parameters in power law. Here, we propose an empirical equation for estimating flow density: ρ = 1.26μ ^-0.132 + 0.049Dc^0.443, which provides not only an estimation of the density for a flow, but also describes the variation in density with the GSD of material composition; this provides important information related to the design of debris flow engineering structures.     

Three-dimensional numerical and analytical study of horizontal group of square anchor plates in sand

In this paper, numerical and analytical methods are used to evaluate the ultimate pullout capacity of a group of square anchor plates in row or square configurations, installed horizontally in dense sand. The elasto-plastic numerical study of square anchor plates is carried out using three-dimensional finite element analysis. The soil is modeled by an elasto-plastic model with a Mohr–Coulomb yield criterion. An analytical method based on a simplified three-dimensional failure mechanism is developed in this study. The interference effect is evaluated by group efficiency η, defined as the ratio of the ultimate pullout capacity of group of N anchor plates to that of a single isolated plate multiplied by number of plates. The variation of the group efficiency η was computed with respect to change in the spacing between plates. Results of the analyses show that the spacing between the plates, the internal friction angle of soil and the installation depth are the most important parameters influencing the group efficiency. New equations are developed in this study to evaluate the group efficiency of square anchor plates embedded horizontally in sand at shallow depth (H = 4B). The results obtained by numerical and analytical solutions are in excellent agreement.     

Prediction of strength parameters of sedimentary rocks using artificial neural networks and regression analysis

Accurate laboratory measurement of geo-engineering properties of intact rock including uniaxial compressive strength (UCS) and modulus of elasticity (E) involves high costs and a substantial amount of time. For this reason, it is of great necessity to develop some relationships and models for estimating these parameters in rock engineering. The present study was conducted to forecast UCS and E in the sedimentary rocks using artificial neural networks (ANNs) and multivariable regression analysis (MLR). For this purpose, a total of 196 rock samples from four rock types (i.e., sandstone, conglomerate, limestone, and marl) were cored and subjected to comprehensive laboratory tests. To develop the predictive models, physical properties of studied rocks such as P wave velocity (V_p), dry density (γ_d), porosity, and water absorption (A_b) were considered as model inputs, while UCS and E were the output parameters. We evaluated the performance of MLR and ANN models by calculating correlation coefficient (R), mean absolute error (MAE), and root-mean-square error (RMSE) indices. The comparison of the obtained results revealed that ANN outperforms MLR when predicting the UCS and E.     

Orthogonal test and regression analysis of the strain on silty soil in Shanghai under metro loading

Cyclic triaxial test by means of the geotechnical digital system is conducted for the soil near the Guoquan Road Station of Metro Line 10 in Shanghai to analyze the strain characteristics and the variation law of saturated silty soil under subway loading. Orthogonal design method is used to arrange the experiment, considering the following factors: frequency ratio f _R, cyclic stress ratio σ _R, vibration time ratio N _R, and the interaction function among them. Results show that the cyclic stress ratio σ _R, the frequency ratio f _R, the vibration time ratio N _R, and the interaction between the cyclic stress ratio σ _R and the vibration time ratio N _R have a significant effect on the axial strain of the subway tunnel. The effect of the interaction between the cyclic stress ratio σ _R and the vibration time ratio N _R is also significant. From the analysis of variance and regression theory, the nonlinear regression equation of the cumulative plastic strain of silty soil under subway loading is established. Residual analysis proves that the equation is ideal and credible. The results have important value for the design of subway tunnels.     

Evaluation of ground vibrations and the effect of air blast in open-pit phosphate mines

Blasting constitutes a beneficial industrial technology, used in quarries and mining production processes, which ensures the achievement of the expected results in a short period of time with relatively low cost. Nevertheless, a significant part of the used blasting energy is wasted in the form of ground vibration and air blast. Hence, blasting-induced ground vibrations are one of the fundamental problems in the mining industry which may cause severe damage to structures and plants nearby. Therefore, a vibration control study plays an important part in the minimization of the environmental effects of blasting in mines. This study represents an investigation reporting ground motion (measured in terms of peak particle velocity (mm/s)) and air blast overpressure measurements around the open-pit phosphate mine near Metlaoui area (southwestern Tunisia). It aimed to calculate the site’s constants: K (ground transmission coefficient) and n (site attenuation curve slope). The obtained site parameters allowed determining the propagation equation of the blast-induced seismic waves in the study area. The scope of this study was to predict the peak particle velocity when the amount of explosive charge and/or the distance were altered with minimum spoil to the environment. Also, a frequency overview of the study area revealed the dominance of low frequencies (>?40 Hz). Such values can cause damage to the nearby structures when a specific peak particle velocity value is reached by blasting. Moreover, this study demonstrated that all overpressure magnitudes were less than 134 dB, which is the safe limit of air blast level.     

Masses of the visual components and black holes in X-ray novae: Effects of proximity of the components

It is shown that the approximation of the complex, tidally distorted shape of a star as a circular disc with local line profiles and a linear limb-darkening law, which is usually applied when deriving equatorial stellar rotation velocities from line profiles, leads to overestimation of the equatorial velocity V _rot sin i and underestimation of the component mass ratio q = M _x /M _v . A formula enabling correction of the effect of these simplifying assumptions on the shape of a star is used to re-determine the mass ratios q and the masses of the black holes M _x and visual components M _v in low-mass X-ray binary systems containing black holes. Taking into account the tidal–rotational distortion of the stellar shape can significantly increase the mass ratios q = M _x /M _v , reducing M _v , while M _x changes only slightly. The resulting distribution of M _v attains its maximum near M _v ? 0.35M _⊙, in disagreement with the results of population synthesis computations realizing standard models for Galactic X-ray novae with black holes. Possible ways to overcome this inconsistency are discussed. The derived distribution of M _x also differs strongly from the mass distribution for massive stars in the Galaxy.     

Timescales for mechanisms for the dynamical evolution of open star clusters

We have obtained the stellar velocity dispersion in three mutually perpendicular directions in the halos and cores of clusters as a function of time for several non-stationary open-cluster models. During the dynamical evolution of the open-cluster models, the velocity dispersions undergo oscillations that do not decay during 5–10 violent-relaxation timescales, τ _vr . We estimated the time for synchronization of the rotation of the open-cluster models and their motion around the center of the Galaxy, t _s , which, depending on the model parameters, is t _s ? (5–27)τ _vr . Synchronization mechanisms for the models are discussed. The disruption of the systems in the force field of the Galaxy is strongly affected by tidal friction. We have also estimated the time for the formation of a spherical stellar-velocity distribution in the cluster models, t _σ ? (6 ? 25)τ _vr . The impact of instability in the stellar motions in a cluster on the formation of a spherical velocity distribution in the open-cluster models is discussed. We have noted a tendency for a weakening of the dependence of the coarse phase density of the cluster on small initial perturbations of the stellar phase coordinates in the model cluster cores for times about five times longer than the violent-relaxation time.     

Determination of Cosmological Parameters with a Sample of Quasars

We use a sample of 808 quasars selected by Risaliti and Lusso to estimate two important cosmological parameters: the percentage of matter in the Universe Ωm and the Hubble constant. The method is based on an auxiliary experimental correlation between the luminosity of quasars in the Xray band and UV band in the form log L_X = β + γ log L_UV. For the flat ΛCDM model our fit gives Ω _m = 0.21 ± 0.12. Our main results are the following: firstly, the fraction of matter (baryonic + dark) contained in the Universe is 21% according to our estimate and is smaller than the one found by other authors using Type Ia Supernovae (though, considering the large error, our result is consistent with the supernova data). Secondly, the Einstein–de Sitter model is outside the 95% confidence interval of our best fit curve. In order to determine also the Hubble constant, we were compelled to fix one of the free parameters (β, γ,H₀,Ω _m ) and to determine the others with the non-linear least square method. We have proceeded in two different ways. Increasing h₀ = H₀/100 with a step of 0.01 in the range from 0.65 to 0.95, we obtain a Hubble constant H₀ = 74.6± 2.4 (km/s)/Mpc in agreement with the values found using CMB, supernovae and cepheids. On the other hand, increasing the parameter m = β/γ with a step of 0.03 in the range from 13.4 to 14.4, we obtain the same result (but with a greater statistical error), and hence a self-consistentmodel, only assuming β ≥ 8.21.     

Shear wave velocity as function of cone penetration resistance and grain size for Holocene-age uncemented soils: a new perspective

For feasibility studies and preliminary design estimates, field measurements of shear wave velocity, V _s, may not be economically adequate and empirical correlations between V _s and more available penetration measurements such as cone penetration test, CPT, data turn out to be potentially valuable at least for initial evaluation of the small-strain stiffness of soils. These types of correlations between geophysical (Vs) and geotechnical (N-SPT, q _c-CPT) measurements are also of utmost importance where a great precision in the calculation of the deposit response is required such as in liquefaction evaluation or earthquake ground response analyses. In this study, the stress-normalized shear wave velocity V _s1 (in m/s) is defined as statistical functions of the normalized dimensionless resistance, Q _tn-CPT, and the mean effective diameter, D ₅₀ (in mm), using a data set of different uncemented soils of Holocene age accumulated at various sites in North America, Europe, and Asia. The V _s1–Q _tn data exhibit different trends with respect to grain sizes. For soils with mean grain size (D ₅₀) < 0.2 mm, the V _s1/Q _tn ^0.25 ratio undergoes a significant reduction with the increase in D ₅₀ of the soil. This trend is completely reversed with further increase in D ₅₀ (D ₅₀ > 0.2 mm). These results corroborate earlier results that stressed the use of different CPT-based correlations with different soil types, and those emphasized the need to impose particle-size limits on the validity of the majority of available correlations.     

Towards a better understanding of the evolution of the flood risk in Mediterranean urban areas: the case of Barcelona

Dam failure constitutes a grave threat to human life. However, there is still a lack of systematic and comprehensive research on the loss of life (L) caused by dam break in China. From the perspective of protecting human life, a new calculation method for L occurred in dam break floods is put forward. Fourteen dam failure cases in China are selected as the basic data by three-dimensional stratified sampling, balancing spatial, vertical elevation and temporal representations, as well as considering various conditions of the dam collapse. The method includes three progressive steps: Firstly, some impact factors of loss of life (IFL) are selected by literature survey, i.e., severity of dam break flood (S _F), population at risk (P _R), understanding of dam break (U _B), warning time (T _W) and evacuation condition (E _C). And the other IFL of weather during dam break (W _B), dam break mode (M _B), water storage (S _W), building vulnerability (V _B), dam break time (T _B) and average distance from affected area to dam (D _D) are also taken into account to get a more comprehensive consideration. According to disaster system and disaster risk, these eleven IFL are divided into four categories. Through the improved entropy method, eight key IFL are further selected out of the eleven. Secondly, four L modules are built based on four categories, which are L-causing factor module (M ₁), L-prone environment module (M ₂), affected body module (M ₃) and rescue condition module (M ₄). Eventually, by using two methods of multivariate nonlinear regression and leave-one-out cross-validation in combination with coupled four modules, the calculation method for L is established. Compared with the results of Graham method and D&M method, the result of the proposed one is much closer to the actual value and performs better in fitting effect and regional applicability. In the application, L calculation and consequence assessment are carried out in the example of Hengjiang reservoir that has already broken down. At the same time, L calculation and risk prediction are used in the analysis of Yunshan reservoir, which is under planning. The proposed method can not only be applied to estimate L and its rate (f _L ) under various types of dam break conditions in China, but also provide a reliable consequence assessment and prediction approach to reduce the risk of L.     

Possible reasons for the frequency splitting of the harmonics of type II solar radio bursts

AIA/SDO data in the 193 Å channel preceding a coronal mass ejection observed at the solar limb on June 13, 2010 are used to simultaneously identify and examine two different shock fronts. The angular size of each front relative to the CME center was about 20°, and their propagation directions differed by ≈25° (≈4° in position angle). The faster front, called the blast shock, advanced the other front, called the piston shock, by R ≈ (0.02-0.03)R⊙ (R⊙ is the solar radius) and had a maximum initial speed of V_B ≈ 850 km/s (with V_P ≈ 700 km/s for the piston shock). The appearance and motion of these shocks were accompanied by a Type II radio burst observed at the fundamental frequency F and second harmonic H. Each frequency was split into two close frequencies f₁ and f₂ separated by Δf = f₂ - f₁ ? F, H. It is concluded that the observed frequency splitting Δf of the F and H components of the Type II burst could result from the simultaneous propagation of piston and blast shocks moving with different speeds in somewhat different directions displaying different coronal-plasma densities.     

Mathematical expression of discharge capacity of compound open channels using MARS technique

In this paper, analytical methods, artificial neural network (ANN) and multivariate adaptive regression splines (MARS) techniques were utilised to estimate the discharge capacity of compound open channels (COC). To this end, related datasets were collected from literature. The results showed that the divided channel method with a coefficient of determination (R ²) value of 0.76 and root mean square error (RMSE) value of 0.162 has the best performance, among the various analytical methods tested. The performance of applied soft computing models with R ²=0.97 and RMSE = 0.03 was found to be more accurate than analytical approaches. Comparison of MARS with the ANN model, in terms of developed discrepancy ratio (DDR) index, showed that the accuracy of MARS model was better than that of MLP model. Reviewing the structure of the derived MARS model showed that the longitudinal slope of the channel (S), relative flow depth (H _r ) and relative area (A _r ) have a high impact on modelling and forecasting the discharge capacity of COCs.     

Chesnokovite,Na<Subscript>2</Subscript>[SiO<Subscript>2</Subscript>(OH)<Subscript>2</Subscript>] · 8H<Subscript>2</Subscript>O,the first natural sodium orthosilicate from the Lovozero alkaline pluton,Kola Peninsula: Description and crystal structure of a new mineral species

Chesnokovite, a new mineral species, is the first natural sodium orthosilicate. It has been found in an ussingite vein uncovered by underground mining at Mt. Kedykverpakhk, Lovozero alkaline pluton, Kola Peninsula, Russia. Natrolite, sodalite, vuonnemite, steenstrupine-(Ce), phosinaite-(Ce), natisite, gobbinsite, villiaumite, and natrosilite are associated minerals. Chesnokovite occurs as intergrowths with natrophospate in pockets up to 4 × 6 × 10 cm in size consisting of chaotic segregations of coarse lamellar crystals (up to 0.05 × 1 × 2 cm in size) flattened along [010]. The crystals are colorless and transparent. The aggregates are white to pale brownish yellowish, with a white streak and a vitreous luster. The cleavage is perfect parallel to (010) and distinct to (100) and (001). The fracture is stepped. The Mohs’ hardness is 2.5. The measured density is 1.68 g/cm³; the density calculated on the basis of an empirical formula is 1.60 g/cm³ and 1.64 g/cm³ on the basis of an idealized formula. The new mineral is optically biaxial, positive, α = 1.449, β = 1.453, γ = 1.458, 2V _meas = 80°, and Z = b. The infrared spectrum is given. The chemical composition (Si determined with electron microprobe; Na, K, and Li, with atomic emission analysis; and H₂O, with the Alimarin method) is as follows, wt %: 21.49 Na₂O, 0.38 K₂O, 0.003 Li₂O, 21.42 SiO₂, 54.86 H₂O, total is 98.153. The empirical formula calculated on the basis of O₂(OH)₂ is as follows: (Na_1.96K_0.02)_Σ1.98Si_1.005O₂(OH)₂ · 7.58H₂O. The simplified formula (Z = 8) is Na₂[SiO₂(OH)₂] · 8H₂O. The new mineral is orthorhombic, and the space group is Ibca. The unit-cell dimensions are: a = 11.7119, b = 19.973, c = 11.5652 Å, and V = 2299.0 ų. The strongest reflections in the X-ray powder pattern [d, Å (I, %)(hkl)] are: 5.001(30)(211), 4.788(42)(022), 3.847(89)(231), 2.932(42)(400), 2.832(35)(060), 2.800(97)(332, 233), and 2.774(100)(341, 143, 114). The crystal structure was studied using the Rietveld method, R _p = 5.77, R _wp = 7.77, R _B = 2.07, and R _F = 1.74. The structure is composed of isolated [SiO₂(OH)₂] octahedrons and the chains of edge-shared [Na[H₂O)₆] octahedrons. The Si and Na polyhedrons are linked only by H-bonds, and this is the cause of the low stability of chesnokovite under atmospheric conditions. The new mineral is named in memory of B.V. Chesnokov (1928–2005), an outstanding mineralogist. The type material of chesnokovite is deposited in the Fersman Mineralogical Museum, Russian Academy of Sciences, Moscow.     

Atmospheric chemical abundances of the components of the quadruple system ADS 11061. 40 Draconis

As part of our study of the components of the hierarchic quadruple system ADS 11061, we acquired spectroscopic observations of the binary 40 Dra. Echelle spectra showing the separation of the components’ lines were obtained in the spectral range 3700–9200 Å. Effective temperatures and surface gravities were derived for the components from BV photometry and the hydrogen-line profiles. The components of the 40 Dra system have parameters close to T _eff ^a = 6420 K, log g _a = 4.17, T _eff ^b = 6300 K, and log g _b = 4.20. We find the microturbulence velocity in the component atmospheres to be V _t = 2.6 km/s. The abundances of iron, carbon, nitrogen, and oxygen in the atmospheres of both components are estimated to be log N(Fe)^a = 7.50, log N(Fe)^b = 7.46, log N(C)^a = 8.39, log N(C)^b = 8.45, log N(N)^a = 8.12, log(N)^b = 8.15, log N(O)^a = 8.77, log N(O)^b = 8.74.     

Reconstruction of the metamorphic <Emphasis Type="Italic">P–T</Emphasis> path from the garnet zoning in aluminous schists from the Tsogt Block,Mongolian Altai

The paper presents original authors’ data on aluminous schists in the Tsogt tectonic plate in the Southern Altai Metamorphic Belt. The nappe includes a medium-temperature/medium-pressure zonal metamorphic complex, whose metamorphic grade varies from the greenschist to epidote-amphibolite facies. The garnet and garnet–staurolite schists contain three garnet generations of different composition and morphology. The P–T metamorphic parameters estimated by mineralogical geothermometers and geobarometers and by numerical modeling with the PERPLEX 668 software provide evidence of two successive metamorphic episodes: high-gradient (of the andalusite–sillimanite type, geothermal gradient approximately 40–50°/km) and low-gradient (kyanite–sillimanite type, geothermal gradient approximately 27°/km). The P-T parameters of the older episode are T = 545–575°C and P = 3.1–3.7 kbar. Metamorphism during the younger episode was zonal, and its peak parameters were T = 560–565°C, P = 6.4–7.2 kbar for the garnet zone and T = 585–615°C, P = 7.1–7.8 kbar for the staurolite zone. The metamorphism evolved according to a clockwise P–T path: the pressure increased during the first episode at a practically constant temperature, and then during the second episode, the temperature increased at a nearly constant pressure. Such trends are typical of metamorphism related to collisional tectonic settings and may be explained by crustal thickening due to overthrusting. The regional crustal thickening reached at least 15–18 km.