A phase-by-phase upstream scheme that converges to the vanishing capillarity solution for countercurrent two-phase flow in two-rock media

We discuss the convergence of the upstream phase-by-phase scheme (or upstream mobility scheme) towards the vanishing capillarity solution for immiscible incompressible two-phase flows in porous media made of several rock types. Troubles in the convergence were recently pointed out by Mishra and Jaffré (Comput. Geosci. 14, 105–124, 2010) and Tveit and Aavatsmark (Comput. Geosci. 16, 809–825, 2012). In this paper, we clarify the notion of vanishing capillarity solution, stressing the fact that the physically relevant notion of solution differs from the one inferred from the results of Kaasschieter (Comput. Geosci. 3, 23–48, 1999). In particular, we point out that the vanishing capillarity solution depends on the formally neglected capillary pressure curves, as it was recently proven in by Andreianov and Cancès (Comput. Geosci. 17, 551–572, 2013). Then, we propose a numerical procedure based on the hybridization of the interfaces that converges towards the vanishing capillarity solution. Numerical illustrations are provided.     

Reply to ‘Comment on “The beginnings of hydrous mantle wedge melting” by Till et al.’ by Green, Rosenthal and Kovacs

The comment of Green et al. debates the interpretation of the temperature of the H₂O-saturated peridotite solidus and presence of silicate melt in the experiments of Till et al. (Contrib Mineral Petrol 163:669–688, 2012) at <1,000?°C. The criticisms presented in their comment do not invalidate any of the most compelling observations of Till et al. (Contrib Mineral Petrol 163:669–688, 2012) as discussed in the following response, including the changing minor element and Mg# composition of the solid phases with increasing temperature in our experiments with 14.5?wt% H₂O at 3.2?GPa, as well as the results of our chlorite peridotite melting experiments with 0.7?wt% H₂O. The point remains that Till et al. (Contrib Mineral Petrol 163:669–688, 2012) present data that call into question the H₂O-saturated peridotite solidus temperature preferred by Green (Tectonophysics 13(1–4):47–71, 1972; Earth Planet Sci Lett 19(1):37–53, 1973; Can Miner 14:255–268, 1976); Millhollen et al. (J Geol 82(5):575–587, 1974); Mengel and Green (Stability of amphibole and phlogopite in metasomatized peridotite under water-saturated and water-undersaturated conditions, Geological Society of Australia Special Publication, Blackwell, pp 571-581, 1989); Wallace and Green (Mineral Petrol 44:1–19, 1991) and Green et al. (Nature 467(7314):448–451, 2010).     

Applicability of different ground-motion prediction models for northern Iran

A total of 163 free-field acceleration time histories recorded at epicentral distances of up to 200 km from 32 earthquakes with moment magnitudes ranging from M _w 4.9 to 7.4 have been used to investigate the predictive capabilities of the local, regional, and next generation attenuation (NGA) ground-motion prediction equations and determine their applicability for northern Iran. Two different statistical approaches, namely the likelihood method (LH) of Scherbaum et al. (Bull Seismol Soc Am 94:341–348, 2004) and the average log-likelihood method (LLH) of Scherbaum et al. (Bull Seismol Soc Am 99:3234–3247, 2009), have been applied for evaluation of these models. The best-fitting models (considering both the LH and LLH results) over the entire frequency range of interest are those of Ghasemi et al. (Seismol 13:499–515, 2009a) and Soghrat et al. (Geophys J Int 188:645–679, 2012) among the local models, Abrahamson and Silva (Earthq Spectra 24:67–97, 2008) and Chiou and Youngs (Earthq Spectra 24:173–215, 2008) among the NGA models, and finally Akkar and Bommer (Seism Res Lett 81:195–206, 2010) among the regional models.     

Paleogeographical restoration and ramp tectonic evidence in Tunisian Tellian domain: Ain El Bey-Bou Awen area

The imbrication’s area in northern Tunisia is the most external segment of Alpine range, where several associated folds types with thrust ramps are recognized within imbricate units beneath Numidian front slope. Their presence help to understand thrusting mechanisms installation through studied area. In fact, this zone was considered as a result of Paleogene gravitary slop (Kujawski (Ann Miner Géol Tunis (24):281, 1969); Caire (Ann Min Géol Tunis 26:87–110, 1973); Rouvier 1977), which is proved to be affected by major deep decollement, given rise to various structures, some are propagation folds, specific of foreland front, limited to this area, and those in more external position: Tunisian Atlas (Creusot et al. (C R Acad Sci Paris 314(Sér II):961–965, 1992); Ouali and Mercier (PII: S0191-8141(97):00048-5, 1997); Ouali 1984; Ahmadi et al. (J Struct Geol 28:721–728, 2006)). Various categories of fold ramps could be identified: frontal folds ramp NE–SW and others as lateral or oblique ramp with NW–SE trend (Aridhi et al. (C R Geosci 343:360–369, 2011)). The relation between various structures has been used as recognition tools of thrusting sequences and to propose a new deformation chronology. Delimited outcropping of these structures between two both parallel faults strikes with regional displacement, leads to interpret these faults as cogenetic tear faults of propagation thrusts; this fault separates two domains with different deformation styles from each other side.     

Oxygen fugacity control in piston-cylinder experiments: a re-evaluation

Jakobsson (Contrib Miner Petrol 164(3):397–407, 2012) investigated a double capsule assembly for use in piston-cylinder experiments that would allow hydrous, high-temperature, and high-pressure experiments to be conducted under controlled oxygen fugacity conditions. Using a platinum outer capsule containing a metal oxide oxygen buffer (Ni–NiO or Co–CoO) and H₂O, with an inner gold–palladium capsule containing hydrous melt, this study was able to compare the oxygen fugacity imposed by the outer capsule oxygen buffer with an oxygen fugacity estimated by the AuPdFe ternary system calibrated by Barr and Grove (Contrib Miner Petrol 160(5):631–643, 2010). H₂O loss or gain, as well as iron loss to the capsule walls and carbon contamination, is often observed in piston-cylinder experiments and often go unexplained. Only a few have attempted to actually quantify various aspects of these changes (Brooker et al. in Am Miner 83(9–10):985–994, 1998; Truckenbrodt and Johannes in Am Miner 84:1333–1335, 1999). It was one of the goals of Jakobsson (Contrib Miner Petrol 164(3):397–407, 2012) to address these issues by using and testing the AuPdFe solution model of Barr and Grove (Contrib Miner Petrol 160(5):631–643, 2010), as well as to constrain the oxygen fugacity of the inner capsule. The oxygen fugacities of the analyzed melts were assumed to be equal to those of the solid Ni–NiO and Co–CoO buffers, which is incorrect since the melts are all undersaturated in H₂O and the oxygen fugacities should therefore be lower than that of the buffer by 2 log $a_{{{\text{H}}_{ 2} {\text{O}}}}$ .     

Reworking and resisting globalising influences: Cape Town hip-hop

Global cultural flows have emerged as key influences in driving changes in local consumer behaviour, identities and social relations. These flows are negotiated and contested in the local context. This article considers how local hip-hop artists in Cape Town, South Africa, challenge and disrupt the dominant images of success linked to consumerism and individualism in popular American music imports. Drawing on Katz’s (Signs 26(4):1213–1234, 2001a, Antipode 33(4):709–728, 2001b) thinking around topographies and counter-topographies, this article suggests that local political hip-hop can be used to develop powerful critiques of the outcomes of globalisation.     

Geology and geochemistry of Tertiary basalt in south Wadi Hodein area, South Eastern Desert, Egypt

Tertiary basalt is widespread in the area south of Wadi Hodein, south Eastern Desert, Egypt. It is the youngest unit in the basement rocks of the Central Eastern Desert classification of El Shazly (Proc 22nd Intl Geol Congr, New Delhi 10:88–101, 1964) and El Ramly (Ann Geol Surv Egypt II:1–17, 1972), traversed all the previous succession of the basement rocks as well as the Nubia Sandstone of Cretaceous age, forming sheets, small hills, ridges, and dikes. This Tertiary basalt is strongly associated with the opening of the Red Sea. Geologic, petrographic, and petrochemical studies as well as microprobe and X-ray analyses were performed on samples from Wadi Hodein Tertiary basalt. Field and petrographic studies classified the Tertiary basalt in south Wadi Hodein into porphyritic olivine basalt, plagiophyric basalt, and doleritic basalt. Opaque minerals (magnetite and ilmenite) constitute 6–7.5% of this basalt. Petrochemical studies and microprobe analyses reveal that they are low-TiO₂ basalt with low uranium and thorium contents, classified as being basaltic andesite to andesite, originated from calc-alkaline magma, and developed in within-plate tectonic environment. Scanning electron microscopy shows that magnetite and ilmenite are the prevalent opaque minerals in this Tertiary basalt. Field radiometric measurements of the Tertiary basalt in south Wadi Hodein reveals low uranium and thorium contents. Uranium contents range from 0.5 to 0.9 ppm, while thorium contents range from 1.2 to 3.2 ppm. Fractional crystallization and mass balance modeling indicate that the most-silica low-TiO₂ Tertiary basalt in south Wadi Hodein can be derived from the relatively less-silica low-TiO₂ Tertiary basalt of south Quseir and Gabal Qatrani through fractional crystallization of plagioclase, olivine, augite, and titanomagnetite oxides. Tertiary basalts in south Wadi Hodein and south Quseir have nearly the same age, 25 Ma (Sherif, The Fifth International Conference on the Geology of Africa, 2007), 24 Ma (Meneisy and Abdel Aal, Ain Shams Sci Bull 25(24B): 163–176, 1984), and 27 Ma (El Shazly et al., Egypt J Geol 1975), respectively. Finally, the fractionation modeling and geochemical characteristics of these basalts suggested their origination from one basaltic magma emplaced in late Oligocene.     

Convergence of iterative coupling for coupled flow and geomechanics

In this paper, we study solving iteratively the coupling of flow and mechanics. We demonstrate the stability and convergence of two widely used schemes: the undrained split method and the fixed stress split method. To our knowledge, this is the first time that such results have been rigorously obtained and published in the scientific literature. In addition, we propose a new stress split method, with faster convergence rate than known schemes. These results are specially important today due to the interest in hydraulic fracturing (Dean and Schmidt SPE J. 14:707–714, 2009; Ji et al. SPE J. 14:423–430, 2009; Samier and De Gennaro 2007; Settari and Maurits SPE J. 3:219–226, 1998), in oil and gas shale reservoirs.     

Flow rule in a high-cycle accumulation model backed by cyclic test data of 22 sands

The flow rule used in the high-cycle accumulation (HCA) model proposed by Niemunis et al. (Comput Geotech 32: 245, 2005) is examined on the basis of the data from approximately 350 drained long-term cyclic triaxial tests (N = 10⁵ cycles) performed on 22 different grain-size distribution curves of a clean quartz sand. In accordance with (Wichtmann et al. in Acta Geotechnica 1: 59, 2006), for all tested materials, the “high-cyclic flow rule (HCFR)”, i.e., the ratio of the volumetric and deviatoric strain accumulation rates \(\dot{\varepsilon}_{\rm{v}}^{{\rm acc}}/\dot{\varepsilon}_{\rm{q}}^{{\rm acc}}\) , was found dependent primarily on the average stress ratio η ^av = q ^av/p ^av and independent of amplitude, soil density and average mean pressure. The experimental HCFR can be fairly well approximated by the flow rule of the modified Cam-clay (MCC) model. Instead of the critical friction angle \(\varphi_{\rm{c}}\) which enters the flow rule for monotonic loading, the HCA model uses the MCC flow rule expression with a slightly different parameter \(\varphi_{\rm{cc}}\) . It should be determined from cyclic tests. \(\varphi_{\rm{cc}}\) and \(\varphi_{\rm{c}}\) are of similar magnitude but not always identical, because they are calibrated from different types of tests. For a simplified calibration in the absence of cyclic test data, \(\varphi_{\rm{cc}}\) may be estimated from the angle of repose \(\varphi_{\rm{r}}\) determined from a pluviated cone of sand (Wichtmann et al. in Acta Geotechnica 1: 59, 2006). However, the paper demonstrates that the MCC flow rule with \(\varphi_{\rm{r}}\) does not fit well the experimentally observed HCFR in the case of coarse or well-graded sands. For an improved simplified calibration procedure, correlations between \(\varphi_{\rm{cc}}\) and parameters of the grain-size distribution curve (d ₅₀,   C _u) have been developed on the basis of the present data set. The approximation of the experimental HCFR by the generalized flow rule equations proposed in (Wichtmann et al. in J Geotech Geoenviron Eng ASCE 136: 728, 2010), considering anisotropy, is also discussed in the paper.     

Assessment of Liquefaction Potential of Guwahati City: A Case Study

The liquefaction potential of saturated cohesionless deposits in Guwahati city, Assam, was evaluated. The critical cyclic stress ratio required to cause liquefaction and the cyclic stress ratio induced by an earthquake were obtained using the simplified empirical method developed by Seed and Idriss (J soil Mech Found Eng ASCE 97(SM9):1249–1273, 1971, Ground motions and soil liquefaction during earthquakes. Earthquake Engineering Research Institute, Berkeley, CA, 1982) and Seed et al. (J Geotech Eng ASCE 109(3):458–483, 1983, J Geotech Eng ASCE 111(12):1425–1445, 1985) and the Idriss and Boulanger (2004) method. Critical cyclic stress ratio was based on the empirical relationship between standard penetration resistance and cyclic stress ratio. The liquefaction potential was evaluated by determining factor of safety against liquefaction with depth for areas in the city. A soil database from 200 boreholes covering an area of 262 km² was used for the purpose. A design peak ground acceleration of 0.36 g was used since Guwahati falls in zone V according to the seismic zoning map of India. The results show that 48 sites in Guwahati are vulnerable to liquefaction according to the Seed and Idriss method and 49 sites are vulnerable to liquefaction according to the Idriss and Boulanger method. Results are presented as maps showing zones of levels of risk of liquefaction.     

Melting phase relations of a mica–clinopyroxenite from the Milk River area, southern Alberta, Canada

Melting experiments were conducted on a mica–clinopyroxenite xenolith brought up in a minette dyke in southern Alberta, Canada, near Milk River. Both the minettes and mica–clinopyroxenite xenoliths were studied by Buhlmann et al. (Can J Earth Sci 37:1629–1650, 2000), who hypothesized that the minettes formed by partial melting of a mantle source containing clinopyroxene + phlogopite ± olivine, at pressures ≥1.7 GPa. In liquidus experiments performed on the most primitive minette in our previous study (Funk and Luth in Contrib Mineral Petrol 164:999–1009, 2012), we found a multiple saturation point where olivine and orthopyroxene coexisted with liquid at 1.77 GPa and 1,350 °C. We argued that the minette originally formed by partial melting of clinopyroxene + phlogopite, but had re-equilibrated with a harzburgite during ascent. In the current study, we wanted to test both the source region hypothesis of Buhlmann et al. and our re-equilibration hypothesis by studying the near-solidus phase equilibria of a mica + clinopyroxene assemblage. We found the solidus for our xenolith has a steep slope in P–T space and lies at temperatures above those of a normal cratonic geotherm, implying that this mica–clinopyroxenite is stable in the cratonic mantle. Melting could occur at greater depths, where the solidus is extrapolated to cross the geotherm or must be induced either by raising the temperatures of the surrounding rocks or by introducing hydrous fluids into the source. Our melts are in equilibrium with clinopyroxene and olivine. The compositions of the liquids derived from melting this xenolith are similar to madupitic lamproites from the Leucite Hills, Wyoming, studied by Carmichael (Contrib Mineral Petrol 15:24–66, 1967) and Barton and Hamilton (Contrib Mineral Petrol 66:41–49, 1978; Contrib Mineral Petrol 69:133–142, 1979). Barton and Hamilton (Contrib Mineral Petrol 69:133–142, 1979) proposed that the madupitic lamproites may have come from a source containing mica and pyroxene. This study supports their hypothesis. The composition of the most primitive minette from southern Alberta lies between our experimental melt and a population of representative mantle orthopyroxenes. We conclude from our study that the Milk River minettes were likely derived from a source containing phlogopite, clinopyroxene and trace amounts of apatite, which formed olivine upon melting. During ascent, the melts changed composition by reacting with orthopyroxene.     

Fully coupled generalized hybrid-mixed finite element approximation of two-phase two-component flow in porous media. Part I: formulation and properties of the mathematical model

This paper is a prequel to that of Marchand et al. (Comput Geosci 16:691–708, 2012), where an efficient and accurate hybrid-mixed finite element approximation for a system of time-dependent nonlinear conservation equations has been formulated, implemented, and tested, which are general enough to represent most of the existing formulations for two-component liquid–gas flow in porous medium with phase exchange, also allowing for any (dis)appearance of one of the phases. Temperature variation is neglected, but capillary effects are included by extended Darcy’s law, and Fickian diffusion is taken into account. The efficiency and stability of the numerical method of Lake (1989) relies on an equivalent reformulation of the otherwise commonly used model in terms of new principal variables and subsequent static (flash) equations allowing more generally for any (dis)appearance of one of the phases without the need of variable switching or unphysical quantities. In particular, the formulation in terms of complementarity conditions allows for an efficient and stable solution by the semismooth Newton’s method.     

High-temperature and high-pressure equation of state for the hexagonal phase in the system NaAlSiO4 – MgAl2O4

Thermal equation of state of an Al-rich phase with Na_1.13Mg_1.51Al_4.47Si_1.62O₁₂ composition has been derived from in situ X-ray diffraction experiments using synchrotron radiation and a multianvil apparatus at pressures up to 24 GPa and temperatures up to 1,900 K. The Al-rich phase exhibited a hexagonal symmetry throughout the present pressure–temperature conditions and the refined unit-cell parameters at ambient condition were: a=8.729(1) Å, c=2.7695(5) Å, V ₀=182.77(6) Å³ (Z=1; formula weight=420.78 g/mol), yielding the zero-pressure density ρ₀=3.823(1) g/cm³ . A least-square fitting of the pressure-volume-temperature data based on Anderson’s pressure scale of gold (Anderson et al. in J Appl Phys 65:1534–543, 1989) to high-temperature Birch-Murnaghan equation of state yielded the isothermal bulk modulus K ₀=176(2) GPa, its pressure derivative K ₀ ^′ =4.9(3), temperature derivative (?K _T /?T) _P =?0.030(3) GPa K^?1 and thermal expansivity α(T)=3.36(6)×10^?5+7.2(1.9)×10^?9 T, while those values of K ₀=181.7(4) GPa, (?K _T /?T) _P =?0.020(2) GPa K^?1 and α(T)=3.28(7)×10^?5+3.0(9)×10^?9 T were obtained when K ₀ ^′ was assumed to be 4.0. The estimated bulk density of subducting MORB becomes denser with increasing depth as compared with earlier estimates (Ono et al. in Phys Chem Miner 29:527–531 2002; Vanpeteghem et al. in Phys Earth Planet Inter 138:223–230 2003; Guignot and Andrault in Phys Earth Planet Inter 143–44:107–128 2004), although the difference is insignificant (<0.6%) when the proportions of the hexagonal phase in the MORB compositions (～20%) are taken into account.     

Assessment of social vulnerability to natural disasters: a comparative study

The purpose of this study is to examine and compare the methodologies being developed in assessing social vulnerability to natural disasters. Existing vulnerability literature shows that two methods have been used in developing social vulnerability indexes: (1) a deductive approach based on a theoretical understanding of relationships and (2) an inductive approach based on statistical relationships (Adger et al. in New indicators of vulnerability and adaptive capacity. Tyndall Centre for Climate Change Research, Norwich, 2004). Two techniques were also utilized in aggregating social vulnerability indicators: (1) a deductive approach using standardization techniques such as z scores or linear scaling (Wu et al. in Clim Res 22:255?C270, 2002; Chakraborty et al. in Nat Hazards Rev 6(1):23?C33, 2005) and (2) an inductive approach using data-reduction techniques such as factor analysis (Clark et al. in Mitig Adapt Strateg Glob Change 3(1):59?C82, 1998; Cutter et al. Soc Sci Quart 84(2):242?C261, 2003). This study empirically compares deductive and inductive index development and indicator aggregation methods in assessing social vulnerability to natural disasters in the Gulf of Mexico and Atlantic coastal areas. The aggregated social vulnerability index is used to examine a relationship with disaster losses in the Gulf of Mexico and Atlantic coastal areas. The results show that coastal counties with more vulnerability in terms of social achieved status are positively associated with disaster damages, while variations in the development of the index using deductive and inductive measurement approaches produce different outcomes.     

Newania carbonatites, Western India: example of mantle derived magnesium carbonatites

The key mineralogical features of the Newania carbonatites, that illustrate their derivation from primary mantle melts (Gruau et al. Terra Nova, Abstract Suppl 1:336, 1995; Viladkar Petrology 6(3):272–283, 1998; Basu and Murty Abstracts of Goldschmidt Conference A40, 2006), are the presence of magnesite, graphite and Cr-rich magnetite. Magnesite is an early crystallizing phase. Cr-rich magnetite and graphite coexist with carbonatite minerals and precipitated from carbonate magma. Graphite, as well as gaseous CO₂ and carbonate minerals such as dolomite and magnesite, can be stable in peridotite mantle. Coexistence of these minerals is controlled by fO ₂ and PT-conditions. Mineral geothermometers for the Newania carbonatite give temperatures from 463 to 950°C. The parental source for Newania carbonatites was characterized by a relatively high log (fHF/fH₂O) level which increased during the crystallization history of Newania. The estimated oxygen fugacity (for ilmenite–magnetite pairs) varies from ?1.5 to +3.5 (log-bar unit deviation from FMQ buffer), which is supported by the presence of Fe-columbite, and the composition of phlogopite, amphibole and pyroxene that have an elevated concentration of Fe³⁺. However, the oxygen fugacity range represented by co-existing early-crystallized graphite and magnesite is below that of the FMQ buffer and lies on the CCO buffer.     

Chromite alteration processes within Vourinos ophiolite

The renewed interest in chromite ore deposits is directly related to the increase in Cr price ruled by international market trends. Chromite, an accessory mineral in peridotites, is considered to be a petrogenetic indicator because its composition reflects the degree of partial melting that the mantle experienced while producing the chromium spinel-bearing rock (Burkhard in Geochim Cosmochim Acta 57:1297–1306, 1993). However, the understanding of chromite alteration and metamorphic modification is still controversial (e.g. Evans and Frost in Geochim Cosmochim Acta 39:959–972, 1975; Burkhard in Geochim Cosmochim Acta 57:1297–1306, 1993; Oze et al. in Am J Sci 304:67–101, 2004). Metamorphic alteration leads to major changes in chromite chemistry and to the growth of secondary phases such as ferritchromite and chlorite. In this study, we investigate the Vourinos complex chromitites (from the mines of Rizo, Aetoraches, Xerolivado and Potamia) with respect to textural and chemical analyses in order to highlight the most important trend of alteration related to chromite transformation. The present study has been partially funded by the Aliakmon project in collaboration between the Public Power Corporation of Greece and Institute of Geology and Mineral Exploration of Kozani.     

Comment on “A Comparison of Modified Fuzzy Weights of Evidence,Fuzzy Weights of Evidence,and Logistic Regression for Mapping Mineral Prospectivity” by Daojun Zhang,Frits Agterberg,Qiuming Cheng,and Renguang Zuo Math Geosci DOI 10.1007/s11004-013-9496-8

Despite a missing definition of equivalence of mathematical models or methods by Zhang et al. (Math Geosci, 2013), an “equivalence” (Zhang et al., Math Geosci, 2013, p. 6,7,8,14) of modified weights-of-evidence (Agterberg, Nat Resour Res 20:95–101, 2011) and logistic regression does not generally exist. Its alleged proof is based on a previously conjectured linear relationship between weights of evidence and logistic regression parameters (Deng, Nat Resour Res 18:249–258, 2009), which does not generally exist either (Schaeben and van den Boogaart, Nat Resour Res 20:401–406, 2011). In fact, an extremely simple linear relationship exists only if the predictor variables are conditionally independent given the target variable, in which case the contrasts, i.e., the differences of the weights, are equal to the logistic regression parameters. Thus, weights-of-evidence is the special case of logistic regression if the predictor variables are binary and conditionally independent given the target variable.     

The Use of Rock Mass Classification Systems to Estimate the Modulus and Strength of Jointed Rock

Three-dimensional, elastic and elasto-plastic finite element (FE) programs have permitted calculation of the displacements and the factor of safety (FOS) for the excavation for a tower, 132.70 m high (above foundation) on the island of Tenerife. The tower is supported by a 2 m thick reinforced concrete slab on jointed, vesicular and weathered basalt and scoria. The installation of rod extensometers at different depths below the slab has permitted comparison between measured and calculated displacements and the estimation of in situ deformation modulus. The moduli deduced from the simple empirical equations proposed by Hoek et al. (In: NARMS-TAC, 2002) and Gokceoglu et al. (Int J Rock Mech Min Sci 40:701–710, 2003) as a function of GSI, and Nicholson and Bieniawski (Int J Min Geol Eng 8:181–202, 1990) as a function of RMR, provide an acceptable fit with the measured settlements in this type of rock. Good correlation is also obtained with the empirical equation presented by Verman et al. (Rock Mech Rock Eng 30(3):121–127, 1997) that incorporates the influence of confining stress in the deformation modulus. The FOS obtained from different correlations with geomechanical classifications is within a relatively narrow range. These results increase our confidence in the use of classification schemes to estimate the deformation and stability in jointed rock.     

Infiltration effects on a two-dimensional molecular dynamics model of landslides

We propose a two-dimensional computational model for deep landslides triggered by rainfall, based on interacting particles or grains. The model describes a vertical section of a fictitious granular material along a slope, in order to study the behavior of a wide-thickness landslide. The triggering of the landslide is caused by the exceeding of two conditions: a threshold speed and a condition on the static friction of the particles, the latter based on the Mohr–Coulomb failure criterion (Coulomb in Mem Acad R Div Sav 7:343–387, 1776; Mohr in Abhandlungen aus dem Gebiete der Technischen Mechanik. Ernst, Berlin, 1914). The interparticle interactions are represented as a potential that, in the absence of suitable experimental data and due to the arbitrariness of the grain dimension, is modeled similarly to the Lennard-Jones’ one (Lennard-Jones in Proc R Soc Lond A 106(738):463–477, 1924), i.e., with an attractive and a repulsive part. For the updating of the particle positions, we use a molecular dynamics method, which is quite suitable for this type of systems (Herrmann and Luding in Continuum Mech Thermodyn 10:189–231, 1998). An infiltration scheme is introduced for modeling the increasing pore pressure due to the rainfall. Finally, we also introduce the viscosity in the dynamical equations of motion. The statistical characterization and dynamical behavior of the results of simulations are quite satisfactory relative to real landslides: We obtain a power law distribution of landslide triggering times, and the velocity patterns are typical of real cases, including the acceleration progression. Therefore, we can claim that this type of modeling can represent a new method to simulate landslides triggered by rainfall.