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    Seismic Analysis of a Limestone Rock Slope through Numerical Modelling: Pseudo-Static vs. Non-Linear Dynamic Approach

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    In the present work, a seismic analysis was performed in advance on a limestone rock slope (height = 150 m) outcropping along the Tagliamento River valley, in the Friuli Venezia Giulia Region, north-eastern Italy. The analysed slope is characterised by strong rock mass damage, thus resulting in a critical stability condition (unstable volume = 110,000-200,000 m3). The seismic analysis was performed adopting the 2D finite difference method (FDM) and employing both a pseudo-static approach and a non-linear dynamic approach. Model outcomes demonstrate that the seismic motion induces internal, localised ruptures within the rock mass. Some important differences in the mechanical behaviour of the rock slope were highlighted, depending on the specific modelling approach assumed. When adopting a pseudo-static approach, the slope failure occurs for PGA values ranging between 0.056 g and 0.124 g, depending on the different initial static stability condition assumed for the slope (Strength Reduction Factor SRF = 1.00-1.15). According to the non-linear dynamic approach, the slope failure is achieved for PGA values varying between 0.056 g and 0.213 g. Pre-collapse slope displacements calculated with the pseudo-static approach (12-15 cm) are much more greater than those obtained through the non-linear dynamic approach (0.5-3 mm). The modelling results obtained through the non-linear dynamic analysis also testify that the seismic topographic amplification is 1.5 times the target acceleration at the slope face and 2.5 times the target acceleration at the slope toe

    The 1963 Vajont Landslide: 50th Anniversary

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    This editorial is intended to bring to our minds the 50th 8 Anniversary of the Vajont Landslide occurred on 9 October 9 1963 at 10.39 pm in Italy, in the Dolomites of Friuli, on the 10 borders of the Veneto Region and about 100 km north of 11 Venice. A mass of approximately 270–300 million m3 of 12 rock and debris collapsed into the reservoir generating a 13 wave that over-topped the 261.6 m high double curved 14 arch dam built across a V-shaped gorge (Fig. 1). The flood 15 wave dropped into the Piave Valley destroying the town of 16 Longarone and other villages nearby. More than 2,000 17 people (the real number is not known) were killed. 18 The Vajont landslide is considered to be one of the most 19 catastrophic slope failures and is an outstanding and 20 valuable reference case history for the study and back 21 analysis of the complex instability mechanisms which 22 generally characterize deep-seated landslides and rock 23 slopes. This dramatic event is also of particular importance 24 for the understanding of the influence of mountainside 25 reservoirs on the stability of the adjacent slopes, when 26 deep-seated landslides are present which were not dis- 27 closed or fully investigated at the design stage. 28 At the same time, interest stems from the need to find 29 the most appropriate investigation techniques to be adopted 30 at the design stage, including suitable numerical modelling 31 methods to be used for the analysis of instability modes and 32 simulation of the interaction between the rock mass and the new infrastructures to be built. Also the re-analysis of the 33 available database on the triggering and subsequent prop- 34 agation of the landslide may shed light on monitoring 35 methods—with conventional and advanced technologies— 36 used as key components of hazard assessment. This is of 37 particular relevance for those countries where the need for 38 energy and development leads to the construction of new 39 infrastructures, including dams, of unprecedented sizes. 40 It is noted that this editorial is only intended to remind 41 us what is considered to be the starting point for the 42 development of modern Rock Mechanics and Rock Engi- 43 neering, when in rock as well as in soil, according to 44 Terzaghi ‘we were over-stepping the limits of our ability to 45 predict the consequences of our actions’ (Hoek 2007). 46 With the intent to account for the most recent and updated 47 studies on the Vajont landslide, the Editor has asked the 48 help of Professor Paolo Paronuzzi from the University of 49 Udine who, together with his research group, has been and 50 is carrying out a comprehensive research project on dif- 51 ferent aspects and debated questions still posed on the 52 Vajont catastrophic landslid

    UCS field estimation of intact rock using the Schmidt hammer: A new empirical approach

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    In the present work we discuss the results of a number of Schmidt hammer tests (total number of impacts N > 2,400) that were performed in situ on rock outcrops of different lithology (marl, calcareous marl, limestone, sandstone, quartz sandstone and rhyolite) that occur in Italy. Firstly, a specific field procedure to choose the reference value of the rebound index adopted to calculate UCS of intact rock is suggested. A relationship between L and N hammer rebound index values (RL and RN, respectively) is subsequently assessed. Considering the experimental datasets provided by a Schmidt hammer construction company and other research available in literature, a new exponential equation for the correlation between RL and UCS of intact rock has been derived. Considering the here-proposed RL-RN relationship, a new exponential correlation between RN and UCS has also been defined. The newly proposed procedure and relationships were successfully utilised to determine the intact rock strength of different rocks. The calculated UCS values are very similar when using both types of Schmidt hammer (L and N) and are generally in line with previous determinations from experimental data available in literature

    Numerical Investigation of the Pre-collapse Behavior and Internal Damage of an Unstable Rock Slope

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    This paper describes the results of a 2D and 3D numerical modeling carried out on an unstable natural rock slope (volume = 110,000–335,000 m3) located in north-eastern Italy (Friuli Venezia Giulia Region). It was aimed at investigating the mechanical behavior and internal rock mass damage of the unstable slope before the collapse. The numerical simulations testify that the stability condition of the slope is close to the limit equilibrium (strength reduction factor, SRF = 1.03–1.13), as demonstrated by the considerable rock mass damage observed on the field. The overall mechanical behavior of the slope is mainly governed by the kinematic conditions of the secondary internal blocks, which, in turn, depend on the geometry and mechanical properties of the major discontinuities that delimit the adjacent blocks. Slope failure is achieved through internal rock mass damage represented by internal shear and tensile ruptures localized in correspondence with over-stressed zones. The failure mechanism is characterized by sliding along pre-existing discontinuities and inner damage in the form of the enucleation of shear bands that originate internal secondary failure surfaces and/or damaged rock mass zones. The stress–strain modeling predicts intense slope deformations in zones where rock mass damage actually occurred. This paper emphasizes the decisive connection between the geomechanical field survey and numerical modeling. The comparison of surface geological data acquired on the field with the mechanical indicators obtained from the numerical analyses can significantly improve knowledge of the rock mass damage process that involves unstable slopes approaching failure condition

    Geomechanical Field Survey to Identify an Unstable Rock Slope: The Passo della Morte Case History (NE Italy)

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    In this work, a geomechanical study performed on a natural rock slope located in north-eastern Italy (Tagliamento River valley, Friuli Venezia Giulia Region) is presented. The detailed geomechanical survey has provided a large bulk of field data proving that the investigated limestone slope is characterized by strong rock mass damage, thus resulting in a critical stability condition. Field evidence includes: (1) local faults crossing the rock mass and representing internal sliding surfaces; (2) slickensides and fault slips within the rock mass; (3) fracture joints of gravity-induced origin; (4) strong rock mass damage in over-stressed zones of the slope; and (5) slope monitoring data recorded by some installed devices. Three failure scenarios have been identified: a wedge failure involving a limestone block of 110,000 m3 (failure scenario 1: BLOCK1); a larger wedge failure involving an assembled limestone block of 200,000 m3 (failure scenario 2: BLOCK1-2-3); and a retrogressive failure involving a rear dolomitic block possibly triggered by the collapse of the limestone slope, mobilizing a maximum volume of 335,000 m3 (failure scenario 3: DOLOMITIC BLOCK). This paper shows that to comprehensively study stability problems involving natural rock slopes we must consider the interaction between pre-existing discontinuities, internal sub-blocks subdividing the unstable slope, rock mass strength and gravity-induced fractures that form during the delicate phase preceding slope collapse. Gravity-induced joints can be differentiated on the field from those of tectonic origin on the basis of some geometrical features, in particular their lower persistence and higher joint roughness

    3D Stress–Strain Analysis of a Failed Limestone Wedge Influenced by an Intact Rock Bridge

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    This paper presents a back-analysis of a rock wedge failure (volume = 25–30 m3) that involved a limestone scarp in the Rosandra valley (Trieste karst, NE Italy). Thanks to the mechanical survey of the detachment surface, a single rock bridge having a size of about 15 cm × 30 cm has been ascertained. A 3D stress–strain analysis has been performed to examine the influence of the rock bridge on the block stability (initial unweathered condition: strength reduction factor SRF equal to 1.14). The shear strength provided by the basal and lateral joints represents the main contributing factor for the wedge stability (about 60–75 % of the whole resisting system). However, the equilibrium of the wedge was temporarily attained thanks to the strength contribution provided by the rock bridge (25–40 %) until the acting forces locally exceeded the resisting forces, thus determining the bridge rupture and, as a consequence, the wedge collapse. The mean shear stress acting on the rock bridge at failure ranges from about 3.5 to 5 MPa. Calculated block displacements up to failure vary from 0.6 to 1.5 mm, depending on the different elastic modulus assumed for the wedge (E = 30, 10, and 4 GPa). Pre-collapse block displacements increase as a result of the shear strength decrease that was initially caused by the weathering of the delimiting rock joints and, further, by the progressive failure of the rock bridge. The cohesion at failure of the rock bridge ranges from 2.1 to 2.6 MPa (friction angle of intact rock φ = 40°). © 2016, Springer-Verlag Wien

    Rainfall infiltration and slope stability of alpine colluvial terraces subject to storms (NE Italy)

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    In the alpine environment, rainfall-induced shallow landslides can involve thin covers of colluvial soil (50–300 cm) on terraced belts that were formed as a result of fill-and-cut sedimentary processes that followed the deglaciation of the alpine valleys. Notably, research on shallow slope failures involving alpine terraces consisting of a near-flat upper ground surface (“tread”) and a moderately steep scarp (“riser”) is lacking in the literature. This paper describes the engineering geological characteristics and failure mechanisms of a large number of shallow landslides (soil slips or slide-debris flows) that were activated on alpine stratified colluvial terraces due to a rainstorm that hit the mountain area of the Friuli Venezia Giulia Region (NE Italy) on 21–22 June 1996. The paper reports data on the geomorphological and engineering geological characteristics of the soil slips acquired through extensive fieldwork and shows the outcomes of some two-dimensional seepage and slope stability analyses that were carried out in order to investigate the critical hydrological conditions and mechanisms that were responsible for the soil slip activation during and after rainfall. The soil slip activation can occur at two different stages during the infiltration process, based on the interacting water flows through the terrace tread and riser. The first critical stability condition is reached during the phases of greater precipitation intensity or at the end of the rainstorm because of the saturation of the top soil layer on the terrace riser and the subsequent formation of an ephemeral water table accompanied by a seepage sub-parallel to the slope face. The second critical condition is achieved some hours after the end of rainfall as a result of a tread-to-riser water outflow that is supplied by the water amount stored within the near-flat terrace tread during the peak rainfall stages (reservoir-like effect). This study also shows that a critical value of rainfall intensity of about 40–45 mm/h can cause the activation of soil slips in mountain basins characterised by a humid continental climate and by the occurrence of colluvial deposits with a high content of fine fraction. This critical value of rainfall intensity should be considered as a rainfall threshold for a basin-scale under geomorphological and geological conditions similar to those investigated in this paper

    On integer and bilevel formulations for the k-vertex cut problem

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    The family of critical node detection problems asks for finding a subset of vertices, deletion of which minimizes or maximizes a predefined connectivity measure on the remaining network. We study a problem of this family called the k-vertex cut problem. The problem asks for determining the minimum weight subset of nodes whose removal disconnects a graph into at least k components. We provide two new integer linear programming formulations, along with families of strengthening valid inequalities. Both models involve an exponential number of constraints for which we provide poly-time separation procedures and design the respective branch-and-cut algorithms. In the first formulation one representative vertex is chosen for each of the k mutually disconnected vertex subsets of the remaining graph. In the second formulation, the model is derived from the perspective of a two-phase Stackelberg game in which a leader deletes the vertices in the first phase, and in the second phase a follower builds connected components in the remaining graph. Our computational study demonstrates that a hybrid model in which valid inequalities of both formulations are combined significantly outperforms the state-of-the-art exact methods from the literature
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