A Finite Element Analysis of the Brindisi di

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.
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