Scholarly article on topic 'Three-dimensional Finite Element Analysis of the Senise Landslide'

Three-dimensional Finite Element Analysis of the Senise Landslide Academic research paper on "Earth and related environmental sciences"

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{"progressive failure" / "numerical modelling" / plasticity / slopes / "strain localisation"}

Abstract of research paper on Earth and related environmental sciences, author of scientific article — Antonello Troncone, Enrico Conte, Antonio Donato

Abstract The results of a three-dimensional (3D) analysis concerning the Senise landslide are presented. This landslide occurred after deep excavations had been carried out at the toe of the slope for constructing several buildings. The soils involved in the landslide were characterized by a pronounced strain-softening behaviour. The analysis is performed using a finite element approach in which an elasto-viscoplastic constitutive model is incorporated. The strain-softening behaviour of the soils is simulated reducing the strength parameters from peak to residual, with the accumulated deviatoric plastic strain. The results from this analysis account for the occurrence of a 3D progressive failure process in the slope.

Academic research paper on topic "Three-dimensional Finite Element Analysis of the Senise Landslide"

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Procedía Engineering 158 (2016) 212 - 217

Procedía Engineering

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VI ITALIAN CONFERENCE OF RESEARCHERS IN GEOTECHNICAL ENGINEERING -Geotechnical Engineering in Multidisciplinary Research: from Microscale to Regional Scale,

CNRIG2016

Three-dimensional finite element analysis of the Senise landslide

Antonello Tronconea *, Enrico Contea, Antonio Donatoa

aDepartment of Civil Engineering, University of Calabria, Rende, Italy

Abstract

The results of a three-dimensional (3D) analysis concerning the Senise landslide are presented. This landslide occurred after deep excavations had been carried out at the toe of the slope for constructing several buildings. The soils involved in the landslide were characterized by a pronounced strain-softening behaviour. The analysis is performed using a finite element approach in which an elasto-viscoplastic constitutive model is incorporated. The strain-softening behaviour of the soils is simulated reducing the strength parameters from peak to residual, with the accumulated deviatoric plastic strain. The results from this analysis account for the occurrence of a 3D progressive failure process in the slope.

© 2016 The Authors.Published by ElsevierLtd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.Org/licenses/by-nc-nd/4.0/).

Peer-review under the responsibility of the organizing and scientific committees of CNRIG2016

Keywords: progressive failure; numerical modelling; plasticity; slopes; strain localisation

1. Introduction

On 26 July 1986, a landslide of great dimensions occurred at Senise which is a village located about 70 km from Potenza, in Southern Italy. Owing to this disastrous event, eight people died and several buildings were destroyed or badly damaged. The Senise landslide was studied by several authors who provided a detailed documentation of the event [1-5]. Before the occurrence of the landslide, deep excavations had been performed at the slope toe for allowing the construction of the above-mentioned buildings. The soils involved in the landslide were characterised by a pronounced strain-softening behaviour. As is known, a progressive failure may occur in these soils when an excavation

Corresponding author.

E-mail address: antonello.troncone@unical.it

1877-7058 © 2016 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Peer-review under the responsibility of the organizing and scientific committees of CNRIG2016 doi:10.1016/j.proeng.2016.08.431

is performed at the slope toe [6]. Such a failure process can be successfully analysed using a numerical approach which is able to simulate reliably the formation and development of the shear zones in which strain localises. An approach with these characteristics was proposed by Troncone [4] and Conte et al. [7] to perform a slope stability analysis under two-dimensional conditions. In this approach, an elasto-viscoplastic constitutive model is used in which the soil strength parameters are reduced from peak to residual with the accumulated deviatoric plastic strain. As an extension of the study performed by Troncone [4], the above-mentioned approach is applied in the present paper to analyse the Senise landslide under three-dimensional conditions. The results from this analysis have confirmed that a progressive failure occurred at Senise, owing to the deep excavations carried out at the slope toe, and have highlighted the 3D nature of this process.

Fig. 1. (a) Plan of the landslide area with an indication of the buildings involved (adapted from Del Prete and Hutchinson [1]); (b) geological cross section (adapted from Viggiani and Di Maio [3]).

2. A brief description of the Senise landslide

The landslide occurred at a site denominated Timpone hill. The dimensions of the landslide were about 150 m in width and 230 m in length. The thickness of the landslide body varied from 10 m to 15 m. A plan of the landslide is shown in Figure 1 a. The landslide involved the buildings indicated by the numbers from 1 to 13. A detailed description of the damage caused to these buildings can be found in the studies previously cited [1-4]. The buildings were constructed in the period from 1983 to 1986 [1]. Before their construction, excavations with different depth were performed. The depth of excavation, as estimated by Del Prete and Hutchinson [1], is specified in Figure 2 in which the date of the permission for the construction of each building is also shown. On the basis of these data it can be asserted that some excavations of small depth were first performed for constructing buildings 8 and 10. Afterwards, important excavations (with a maximum depth of about 10 m) were carried out in the shared zone indicated in Figure 1 a, where some high reinforced concrete retaining walls with shallow foundations were constructed at the back of buildings 5-7 and 3-4, respectively (Fig. la). In addition, Figure 2 shows that the landslide occurred at least two years after the construction of the buildings 3-4. The outcropping geological formation consists of yellowish sand with

interbedded thin layers of clayey silt (Aliano formation). These layers, with a dip prevalently South-West, have a thickness ranging from some centimetres to several decimetres, and an average inclination (downslope) of about 18° with respect to the horizontal plane. The sand is very dense and is characterised by a significant degree of cementation. The Aliano formation overlies a formation of blue-grey clay (Fig. lb). The former formation can be dated back to the Lower Pleistocene, and the latter to the Lower Pleistocene or Upper Pliocene [2]. After the landslide, a site investigation consisting of boreholes, standard penetration tests and laboratory tests was performed. The laboratory tests showed that both the sand and silt are characterised by a pronounced strain-softening behaviour [1,4]. Several piezometers and inclinometers were also installed. Inclinometer readings revealed that the main slip surface was located at a depth of about 14 m from the ground surface in the central part of the landslide body. This slip surface only involved the Aliano formation and developed essentially within a thin layer of clayey silt, where plastic strain localised [1,3]. Lastly, as asserted in all the previous studies [1-3], groundwater was not found in the piezometers installed in the landslide area.

Ü S 9 J

E ® 3 S

§ o 6 X S

CO ffi

11 Building number

Landslide

^ N# ^ ^ ^

x- 'J rP'

^ ^ 0d" ^ ^

, 0>- q<b<

Date of construction permission

Fig. 2. Date of the construction permission for the buildings involved by the landslide with an indication of the maximum depth of excavation performed for each building (from Troncone [4]).

3. Finite element analysis of the Senise landslide

The numerical analysis of the Senise landslide is performed in this study using the finite element code Tochnog [8]. A mesh consisting of tetrahedral solid elements with four nodes and one Gauss point is adopted to represent the slope where the landslide occurred (Fig. 3). The stratigraphy of the subsoil is also indicated in Figure 3, from which it is evident the presence of a thin layer of clayey silt (with slope of about 18°) at an average depth of about 14 m from the ground surface, where the slip surface was found [1,3]. Truss-beam elements with linear elastic behaviour are used for discretizing the retaining walls located at the back of the buildings. The base of the slope is fully fixed, while the back, the front and the lateral sides are constrained by vertical rollers. According to the results from the site investigation, no groundwater is considered in the analysis. In addition, it is assumed that the effects of partial saturation are negligible. Considering the uncertainties for defining the geologic history of the site and the lack of specific geotechnical data, the initial stress state of the slope (i.e., before excavation) is reproduced by increasing progressively the gravity acceleration up to 9.81 m/s2, under the assumption that the soil behaves as an elastic-perfectly plastic medium with Mohr-Coulomb failure criterion. At the end of the gravity loading, the associated displacements and strains are reset to zero. Subsequently, the excavations are simulated by a progressive removal of the soil elements in front of the retaining walls, which were preventively installed without affecting the stress state in the slope. To account for the strain-softening behaviour of both the yellow sand and the clayey silt, the elasto-viscoplastic constitutive model described in detail by Troncone [4] is used. In this model, a Mohr-Coulomb plastic law with a flow rule of non-associated type is adopted. The strain-softening behaviour of the soils is simulated reducing the strength parameters from peak to residual, with the accumulated deviatoric plastic strain [9-11].

Fig. 3. Mesh adopted for the 3D finite element analysis.

In the present study, this latter strain is expressed by the parameter few which is defined as:

k shear ={ k shear dt (1)

where t is time and

kshear =V0.56? 6? (2)

is an invariant of the deviatoric plastic strain rate tensor ejj . The expression of this tensor is:

eH = eH - | eSkSij (3)

where 8$ is Kronecker's delta, and efj is the plastic strain rate tensor. Figure 4 shows the relationship considered in this study to relate the mobilised strength parameters of the soil to few. As can be seen, this relationship is defined by the thresholds k^hear and krshear. A relationship similar to that shown in Figure 4 can also be adopted for the angle ofdilatancy y/ [5].

<p; c'

Fig. 4. Relationship between the soil strength parameters, <p 'and cand the plastic strain invariant, kshear with an indication of the strain thresholds, kpshear and krshear .

The material parameters required by the constitutive model are Young's modulus E', Poisson's ratio v', the angle of dilatancy y/, the parameters defining the peak 'p ; c 'p) and residual ; c 'r) strength of the soil, and the above-specified strain thresholds. The values assumed for these parameters are shown in Table 1 and their validation was performed by Troncone [4] by simulating some experimental results from triaxial tests. The viscous component of the model describes a material whose response is delayed with time, and requires two additional constitutive parameters, Y and a [12]. In particular, y influences the velocity with which a strain process occurs owing to a given stress change. Therefore, if different values of y are assumed the material response is delayed or anticipated with time. Although the viscous component is often used as a device to regularise the numerical solution [13], the values of the viscous parameters are chosen in the present study also with the objective of delaying the slope failure of over two years respect to the excavations carried out for the construction of the buildings 3-4 (Fig. 2). Specifically, the values assumed in the analysis for these parameters are y =10"6 day"1 and 810"7 day"1 for the sand and the clayey silt respectively, and a= 61 for both soils. Lastly, considering that the failure process did not involve the formation of blue-grey clay, the behaviour of this formation is simulated by an elastic-perfectly plastic Mohr-Coulomb model. The respective constitutive parameters are also indicated in Table 1.

Table 1. Soil parameters used in the analyses (after Troncone [4]).

Soil Y (kN/m3) E' (kPa) v' c'p (kPa) <P'p (°) c ' (kPa) <f'r (°) W (°) ^shear ^shear

sand 20 70000 0.25 37 43 0 35 0 0 0.04

silt 20 25000 0.25 15 30 0 12 0 0 0.04

clay 20 70000 0.25 150 31 0

Excavations performed for the construction of buildings 8 and 10 are first simulated. Then, the effects of the excavations for buildings 5, 6 and 7 are analyzed. The depth of these latter excavations ranges from 5 to 7 m. Due to space limitations, the associated results are not shown in the present paper. Anyway, the calculated displacements were of relatively small magnitude and affected a restricted portion of the slope. In addition, significant deviatoric plastic strain was not accumulated within the slope. This implies that no failure process develops in the slope owing to these excavations. Lastly, excavations of different depth are simulated for the construction of buildings 3 (maximum depth of 10 m) and building 4 (maximum depth of 9 m). Figure 5a shows the displacement field calculated at the end of these excavations. As shown, the displacement amplitude is still scarcely significant. However, this amplitude increases with time (Fig. 5b-c), and attains very high values at t= 800 days (Fig. 5d), i.e. over two years after completing all the excavations (as probably it occurred). Considering the magnitude of these displacements, it can be asserted that a general failure of the slope occurs. The area affected by movement enlarges both in the upward and westward directions involving a large portion of the slope where buildings 8 and 10 are located. By comparing this zone to the area really involved by the landslide the contour of which is indicated in Fig. 1 a, it can be noted that there is a reasonable agreement between simulation and observation.

4. Concluding remarks

A 3D analysis concerning the Senise landslide has been performed using a finite element approach in which an elasto-viscoplastic strain-softening model is incorporated. The results from this analysis show that a progressive failure occurred in the slope owing to the deep excavations carried out for the construction of buildings 3 and 4 indicated in Fig. la. Specifically, failure initiated at the toe of the slope in the area where these excavations were performed and propagated in the upward and westward directions, up to cause the collapse of the slope. The extent of the area affected by movements and their spatial and temporal evolution resulting from the numerical simulation under 3D conditions, are in fairly good agreement with what observed in field.

¡mem (cm) 0

3 6 9 2 5 8 1

Fig. 5. Displacement field calculated at (a) the end of all excavations; (b) t= 300 days; (c) t= 500 days; (d) t= 800 days after completing the excavations.

References

[1] M. Del Prete, J.N. Hutchinson, La frana di Senise del 26-7-1986 nel quadro morfologico del versante meridionale della collina Timpone.

Italian Geotechnical Journal 22 (1988) 7-34.

[2] A. Guerricchio, G. Melidoro, Urbanizzazione e franosita delle formazioni sabbiose plio-pleistoceniche in Basilicata: il caso di Senise. Memorie

della Societa Geologica Italiana 37 (1988) 745-774.

[3] C. Viggiani, C. Di Maio, Resistenza a taglio mobilitata nella frana di Senise. Gruppo Naz. di Coord, per gli Studi di Ingegneria Geot., CNR

Convegno sul tema: Deformazioni in prossimita della rottura e resistenza dei terreni naturali e delle rocce 1, Ravello, Italy, 1991, 133-158.

[4] A. Troncone, Numerical analysis of a landslide in soils with strain-softening behaviour. Geotechnique 55 (2005) 585-596.

[5] A. Troncone, E. Conte, A. Donato, Two and three-dimensional numerical analysis of the progressive failure that occurred in an excavation-

induced landslide. Engineeering Geology 183 (2014) 265-275.

[6] L. Bjerrum, Progressive failure in slopes of overconsolidated plastic clays and clay shales. Journal of Soil Mechanics and Foundation Engineering Division, ASCE 93 (1967) 1-49.

[7] E. Conte, F. Silvestri, A. Troncone, Stability analysis of slopes in soils with strain-softening behaviour. Computers and Geotechnics 37 (2010)

710-722.

[8] D.G. Roddeman, TOCHNOG, Professional user's manual. Heerlen: FEAT, The Netherlands, 2013.

[9] D.V. Griffiths, Computation of collapse loads in geomechanics by finite elements. Ingenieur-Archiv 59 (1989) 237-244.

[10] D.M. Potts, G.T. Dounias, P.R. Vaughan, Finite element analysis of progressive failure of Carsington embankment. Geotechnique 40 (1990) 79-101.

[11] E. Conte, A. Donato, A. Troncone, Progressive failure analysis for shallow foundation on soils with strain-softening behaviour. Computers and Geotechnics 54 (2013) 117-124.

[12] C. di Prisco, S. Imposimato, Time dependent mechanical behaviour of loose sands. Mech. of Cohesive-Frictional Materials 1 (1996) 45-73.

[13] O.C. Zienkiewicz, I.C. Cormeau, Vis co-plasticity—plasticity and creep in elastic solids—a unified numerical solution approach. International Journal for Numerical Methods in Engineering 8 (1974) 821-845.