A Finite Element Analysis of the Brindisi di Montagna Scalo Earthflow (Basilicata, Southern-Italy) 217 Vincenzo De Luca, Bentivenga Mario, Giuseppe Palladino, Salvatore Grimaldi, and Giacomo Prosser Abstract In this paper a general Finite Element Method (FEM) analysis is presented for the investigation of landslide mechanics behavior, including a non-linear constitutive model of soils. Landslide body is modeled using FEM with 3D volume elements, with large strains assumptions, and the soil mass properties are adopted according to the non-linear DruckerPrager material formulation. The remaining soil region is assumed as boundary constrains. A special attention is devoted to the geometrical deﬁnition of the volume of the landslide body and of the boundary surfaces, particularly the landslide sliding surface, and to the applied loads. To this aim a speciﬁc pre-processor code is employed which is able to generate the mesh and the input ﬁle for the FEM code. The performances of the approach have been checked by using the test case of Brindisi di Montagna Scalo landslide. In this ﬁrst approach the results show that the methodology is powerful and can be used efﬁciently for the numerical analysis of complex landslide conﬁguration. Keywords Landslide 217.1 Brindisi M.S.-Italy Introduction Soil mechanics and landslide problems involve large displacements and strains and elastic–plastic or elastic–viscoplastic behavior of soil materials. Most common numerical approaches, such as the Finite Element Method (FEM) (Zenkievicz 1967) or derived methods, apply discretization methods to analyze a continuum of a soil body. FEM can produce numerical instability due to excessive distortion of meshing. Other numerical methods have been proposed, formulated in a Lagrange and/or arbitrary Lagrange–Euler description of motion (Cuomo et al. 2013), such as point or meshless approaches (Idelsohn et al. 2003). We have adopted the ﬁnite element method with a Lagrange V. De Luca B. Mario (&) G. Palladino S. Grimaldi G. Prosser Dipartimento di Scienze, Università degli Studi della Basilicata, Via Ateneo Lucano, 10, 85100 Potenza, Italy e-mail: [email protected] FEM Slope stability formulation and by considering large strains and a non-linear constitutive Drucker-Prager law for soil materials. This framework was applied to the clayey Brindisi di Montagna Scalo Landslide (BMSL). The main objective of the work is to analyze the landslide mechanical behavior, using elastic and inelastic numerical models of soil, under a critical load, when the magnitude of unit mass of the soil body increases by changing water content from natural values to saturation. 217.2 Geological and Geomorphologic Setting The BMSL is located in Southern Apennine chain on the left side of the Basento River (Figs. 217.1, 217.2). In particular, this area shows a meso-cenozoic succession derived from the deformation of a deep-sea mesozoic palaeodomain identiﬁed as the Lagonegro Basin (Scandone 1972). These deposits are unconformably covered by siliciclastic ﬂysch deposits belonging to the mid-Miocene Irpinian Units. In the studied area the succession of the G. Lollino et al. (eds.), Engineering Geology for Society and Territory – Volume 2, DOI: 10.1007/978-3-319-09057-3_217, © Springer International Publishing Switzerland 2015 1239 1240 V. De Luca et al. Fig. 217.1 Panoramic view of the BMSL Lagonegro Basin starts with yellow and brown marls belonging to the Early Cretaceous Galestri Formation, followed upwards by the argillaceous deposits of the “Argille Varicolori” (Auct.) of Cretaceous age. The Lagonegro succession ends with an alternation of turbiditic limestone and red marls related to the Flysch Rosso Formation of Late Cretaceous—Eocene age. White cherty limestones, red clays and thick calcareous breccias may be related to a preNumidian interval. The Irpinian Units are exclusively represented in the studied area by the arenaceous deposits belonging to “Gorgoglione Flysch” (Auct.) (Fig. 217.2). In the BMS area a widespread geomorphologic instability has been observed in correspondence of argillaceous deposits belonging to the Lagonegro Units. In particular, a large complex landslide developing from Tempa Pizzuta hill down to Basento River has been recently described. The BMSL shows moderately deep slide characteristics in the upper part, where “Flysch Rosso” crops-out, while, downward, an earthﬂow evolution has been detected in correspondence of the “Argille Varicolori” (Bentivenga et al. 2012). 217.3 Materials and Methods To analyze the BMSL, according to the framework of the FEM by the code ADINA (ADINA 2012), some preliminary elaborations are carried out: (i) the interpolation into grids, using a MatLab biharmonic spline routine (MATLAB 2009b), of the irregularly distributed terrain points of the topography and of the boundaries; (ii) the automatic generation of the mesh into a certain number of discrete solid elements, eight nodes—“hexahedron”, with speciﬁc material properties and point displacement boundary conditions. For soil materials we have adopted the constitutive law of Drucker-Prager. The soil’s characteristics are assumed from the geotechnical investigations carried out by Cotecchia et al. (1986). The physical properties and the geotechnical parameters of those soils are listed in Tables 217.1 and 217.2 respectively. As constitutive law for soil material we have adopted the Drucker-Prager elasto-plasticity yield function (Swan and Seo 1999): 217 A Finite Element Analysis of the Brindisi di Montagna Scalo 1241 Fig. 217.2 Geological map (after Bentivenga et al. 2006, modiﬁed) Table 217.1 Soil physical properties (after Cotecchia et al. 1986) Porosity1 Water content1 Saturation1 Dry unit mass1 Natural unit mass2 Saturation unit mass2 (adim.) (adim.) (adim.) (kN/m3) (kN/m3) (kN/m3) Bedrock 0.316 0.155 0.976 16.17 18.68 19.33 Sliding soil 0.373 0.212 0.981 16.17 19.60 19.90 Soil type 1 2 after Cotecchia et al. 1986 calculated Table 217.2 Soil geotechnical properties (after Cotecchia et al. 1986) Soil type Cohesion Friction angle (kPa) (°) Table 217.3 FEM Drucker-Prager constants, derived from MohrCoulomb constants Soil type Material constant pffiffi 2$sin u 3$ð3#sin uÞ Material constant u ffi k ¼ pffi36$c$cos $ð3#sin uÞ Bedrock soil 80.00 34.0 a¼ Sliding soil 12.00 (residual strength) 10.0 (residual strength) (adim.) (kPa) Bedrock soil 0.2645 94.1285 Sliding soil 0.0709 14.484 pffiffiffiffi f ¼ aJ1 þ J2 # k whose model parameters are derived from the soil material constants, cohesion c and internal friction angle φ, where: J1 J2 is the ﬁrst invariant of the stress tensor; is the second invariant of the deviatoric stress tensor No dilatation and no cap hardening have been considered; the tension cut off has been ﬁxed to zero. From soil geotechnical properties (Cotecchia et al. 1986) (Table 217.2), the FEM Drucker-Prager constants are derived (Table 217.3). The elastic properties of the bedrock soil and of the sliding mass are reported in Table 217.4. We have to note that the yield model of the soil was applied only to the sliding soil, whereas the bedrock was considered simply elastic. A linear increase of gravitation loads has been accounted as a time function, which is introduced as input in the analysis code, in a transient approach to the problem. An important consideration is that 1242 V. De Luca et al. Table 217.4 Soil elastic model Soil type Oedometer consolidation ratio1 Undrained Poisson’s ratio2 Void ratio1 Effective vertical stress1 Undrained elastic modulus3 (adim.) (adim.) (kPa) (kPa) Bedrock soil 0.10 0.20 0.462 400 15159 Sliding soil 0.10 0.25 0.595 100 3675 1 2 3 after Cotecchia et al. (1986) assumed calculated Fig. 217.3 Isometric view in 3D of BMSL model: displacements magnitude ﬁeld often the numerical analysis collapses when an element encounters an excessive distortion. In this case, we have decided to remove the large displacements hypothesis. This operative choice habilitates us to complete successfully numerical run, and to recognize the incipient yielding state of the landslide body. 217.4 Results and Discussion The numerical results are reported in 3D isometric views. The Fig. 217.3 shows the displacement magnitude map of the soil mass. The maximum movement is detected in the upper region of the slope. The preliminary results can help us to recognize the incipient yielding state and incoming failure mechanism of the soil of the landslide body. 217.5 Conclusions The results of the numerical analysis show that displacements of the BMSL are efﬁciently modeled for an arbitrary monitoring time interval. Some numerical problems in severe distortion of element geometry have been encountered when we have included large displacements assumption. Further work is needed to solve this problem. However, this preliminary work shows some promising results useful for the mechanical analysis of landslides. References ADINA (2012) Version 8.8.0, 64-bit, License n. 10.6.36.52 Bentivenga M, Grimaldi S, Palladino G (2006) Caratteri geomorfologici della instabilità del versante sinistro del Fiume Basento 217 A Finite Element Analysis of the Brindisi di Montagna Scalo interessato dalla grande frana di Brindisi di Montagna Scalo (Potenza, Basilicata). Giornale di Geologia Applicata 4:123–130 Bentivenga M, Palladino G, Caputi A (2012) Development of pietra maura landslide and interactions with the marsico nuovo dam (Basilicata, Italy). Geogr Fis Dinam Quat 35:13–22 Cotecchia V, Del Prete M, Federico A, Fenelli GB, Pellegrino A, Picarelli L (1986) Studio di una colata attiva in formazioni strutturalmente complesse presso Brindisi di Montagna Scalo (PZ). AGI—XVI Conv. Naz. Geotecnica., pp 253–264, Bologna 14–16 maggio 1986 Cuomo S, Prime N, Iannone A, Dufour F, Cascini L, Darve F (2013) Large deformation FEMLIP drained analysis of a vertical cut. Acta Geotech 8:125–136 1243 Idelsohn SR, Oñate E, Del Pin F (2003) A lagrangian meshless ﬁnite element method applied to ﬂuid-structure interaction problems. Comput Struct 81:655–671 MATLAB (2009) MathWorks Inc., Version 7.9.0.529 (R2009b), 64bit, License n. 610405 Scandone P (1972) Studi della geologia lucana: carta dei terreni della serie calcareo-silico-marnosa e note illustrative. Ist. di Geol., Università di Napoli Swan CC, Seo YK (1999) Limit state analysis of earthen slopes us-ing dual continuum/FEM approaches. Int J Numer Anal Methods Geomech 23:1359–1371 Zenkievicz OC (1967) The ﬁnite element method. McGraw-Hill Publishing Company, New York

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