Stress state analysis of a collapsed overhanging rock slab: A case study

Engineering Geology 108 (2009) 65–75

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Engineering Geology j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / e n g g e o

Stress state analysis of a collapsed overhanging rock slab: A case study Paolo Paronuzzi ⁎, Walter Serafini Dipartimento di Georisorse e Territorio, Università degli Studi di Udine, via Cotonificio 114 - 33100 Udine, Italy

a r t i c l e

i n f o

Article history: Received 13 November 2008 Received in revised form 29 May 2009 Accepted 25 June 2009 Available online 5 July 2009 Keywords: Rockfall Flexural failure Cantilevered slab Rock bridge 3D finite element model

a b s t r a c t This paper describes the geomechanical back-analysis of the flexural failure of an overhanging limestone slab (volume = 68 m3) that collapsed on 26/01/1999 on the abandoned Cellina Valley state road SS 251 (western Friuli, NE Italy). The survey carried out on site examining the contact surfaces between the block and the slope has ascertained that the rock slab was connected to the stable rock mass by means of a single great rock bridge. The detailed reconstruction of the slab geometry and of the actual restraint conditions acting before the rockfall permitted an estimation of the stress state by using a 3D finite element code (Strand7). The finite element numerical model, referred to the restrained cross-section measured on site (Ares = 2.82 m2), gives a maximum value of σt = 5.19 MPa for the tensile stress, which is in good agreement with the estimated value for the characteristic strength mobilized at rupture by the intact rock material (T0 = 3.5–5.5 MPa). Considerably lower maximum tensile stress (σt = 2.25 MPa), smaller than one half, is obtained if the whole contact surface is assumed as resisting surface (Ares = 10.50 m2) and the rock bridge is neglected. © 2009 Elsevier B.V. All rights reserved.

1. Introduction Many sub-vertical rock scarps can be subject to dangerous localised failures characterised by the sudden detachment of overhanging blocks in the shape of cantilevered rock masses (rock brackets) limited by pre-existing joints and protruding when compared to the average scarp orientation. These particular cases, highly conditioned by the orientation of the joint systems penetrating the rock mass as well as by the cantilevered block size, are very dangerous because they can involve people in transit or stationary under the scarps, often in the absence of warning signs denoting the close-to-failure critical condition of the block. Despite the obvious danger that characterises these particular conditions, only some recent research has analysed the failure mode involving a single rock slab subject to flexural load and laterally constrained by intact rock connections (Cravero and Iabichino, 2004). Indeed, this rupture mode is quite a different condition from the more common failure types affecting jointed rock masses (planar, wedge, toppling and circular failure: Norrish and Wyllie, 1996) because in this case the characteristic strength of the intact rock constituting the rock bridges (Paronuzzi and Serafini, 2005) plays a fundamental role. Rotation of rigid blocks and deformation of the rock slabs subject to flexure are usually analysed with different methods within the scope of more general toppling problems. This particular form of instability involving heavily jointed rock masses, identified in 1973 ⁎ Corresponding author. Dipartimento di Georisorse e Territorio, Università di Udine, via Cotonificio 114 - 33100 Udine, Italy. Tel.: +39 0432 558718; fax: +39 0432 558700. E-mail address: [email protected] (P. Paronuzzi). 0013-7952/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.enggeo.2009.06.019

(de Freitas and Watters) and classified for the first time in 1976 (Goodman and Bray), has been the subject of many specific studies and falls into one (topple) of the five main landslide types recognised worldwide (Varnes, 1978; Cruden and Varnes, 1996). Traditionally (Hoek and Bray, 1981) two types of primary toppling can be considered: a group of blocks totally isolated from three joint sets and dipping outwards to the slope (block toppling) or a rock slab system strongly dipping upslope and mutually interacting (flexural toppling), although in real rock slopes there are various combinations of processes and configurations — both primary and secondary— that can determine toppling (Tommasi, 1996). In the last twenty years, different approaches have been used for the geomechanical analysis of toppling, and they involve closed-form analytical solutions based on the limit equilibrium criterion (Aydan and Kawamoto,1992; Bobet, 1999) as well as numerical methods based on finite element (Adhikary et al., 1995, 1996) or distinct element codes (Pritchard and Savigny, 1990; Barla et al., 1995). All these analyses mostly take into consideration a significant process of deformation of the rock slope caused by rotation and/or slip of single blocks or by rock slab flexure. Major slope deformation can be followed by the failure on a critical inclined surface or the phenomenon can be limited to an outstanding continuous rotation of blocks and slabs. As opposed to block toppling, collapse of single rock brackets does not entail major displacement in the phase preceding the failure since the block behaves as a brittle material with little or no displacements before the collapse which takes place when the stress level overcomes the maximum tensile strength of the rock bridge. Failure of single rock slabs has been taken into account in analysing the mechanism of flexural toppling, a sub-category that includes the toppling resulting from flexural loading on rock slabs restrained at the

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base. The stress induced on the single constrained slab has been analysed by Aydan and Kawamoto (1992) based on the theory of elasticity (Timoshenko, 1974) making reference to the columnar model of a rock beam clamped at one extreme. This model has also been used by the same authors to evaluate the influence on the beam stress state of a crack of variable size localised at the clamped cross-section (Aydan and Kawamoto, 1992). The examination of an overhanging rock bracket with a discontinuity or joint located along the constrained resisting cross-section allows taking into account those cases, quite common in reality, where the unstable block is bounded by intermittent joints (Einstein et al., 1983; Gehle and Kutter, 2003) and the contact surface between the block and stable rock mass is characterised by intact rock bridges. In similar cases, the actual rock bridge areas are the only resisting surfaces of the slab subject to flexural load. This paper describes the geomechanical back-analysis of the flexural failure of an overhanging limestone slab which collapsed on January 26, 1999 on the abandoned Cellina Valley state road SS 251 (Carnic Prealps, western Friuli). The survey, carried out on site, examining the contact surfaces between the block and the slope has ascertained that the rock slab was connected to the rock mass by means of a wide rock bridge. The detailed reconstruction of the slab geometry and of the actual restraint conditions before the rockfall permitted an estimation of the stress state by using a 3D finite element code. The adopted approach is particularly useful in understanding the basic role played by the intact rock parts acting on the contact surfaces between potentially unstable block and slope. The use of a 3D finite element numerical model permits the verification the real stress state acting on the rock bridge and to compare it with the characteristic tensile strength of the intact rock. 2. Cantilevered rock slabs on real slopes On real slopes, there are various situations that can form cantilevered rock slabs potentially subject to flexural failure (Fig. 1). In general, they are single rock layers made by a specific rock type and limited by very continuous joints such as stratification surfaces. Lateral plane faces of cantilevered rock slabs are generally due to vertical or very inclined fractures, which are quite frequent in the Alpine regions involved in complex tectonic processes. Typically, bracket-patterned rock slabs correspond to single layers having a thickness ranging from 0.2 to 0.3 m up to 2 to 3 m, in most cases. The size of failed rock brackets are quite variable and collapsed slabs have cantilever lengths ranging from 1 to 2 m up to 10 to 12 m often corresponding to block volumes that go from a few cubic meter to 50–100 m3. Among the most frequent and recurrent situations are those of wellstratified rock masses formed by compact lithotypes (for instance, limestone and dolomitic rocks) that have been artificially cut to build roads on benched slopes intersecting vertical rock scarps (Fig. 1). This kind of engineering work, usually performed through blasting and reprofiling of the slope, was frequently adopted in the past (second half of 1800 and first half of 1900) for the construction of roads and railway tracks in conditions of difficult access and in the presence of hard rocks and steep slopes. Therefore, suspended rock volumes and overhanging rock brackets can be identified frequently in older mountain roads with poor construction methods. They are almost always plate rock slabs, bounded on the top by bedding surfaces and at the bottom by the artificial profile made through blasting. In other cases, the overhanging blocks can simply result from selective erosion processes on the scarp induced by the occurrence of materials with very different geomechanical properties (strong rocks alternating to weak rocks or with inter-bedded loose sediments) or by the joint orientation. On a generic rock slope, the shape of cantilevered blocks can be, therefore, very varied and can include sub-horizontal or inclined slabs (both upslope and downslope). Cantilevered rock masses can also be originated as a consequence of excavating operations for tunnels and for quarries or open mines if the structural pattern and the

Fig. 1. Typical geological and structural conditions isolating cantilevered rock slabs subjected to flexure and/or toppling: A) natural rock slab dipping against rock face, B) horizontal rock slab due to blasted slope profile of a mountain road, C) inclined rock slab isolated by a tunnel excavation work, D) overhanging rock layer formed by sea erosion. Triangular diagrams (on the right) indicate the characteristic stress distribution acting on the restrained cross-section: tensile stress (+) and compressive stress (-).

joints orientation make it possible. The presence of overhanging rock volumes over a scarp in general has major implications on the safety of vehicle and/or railway traffic eventually present, therefore, their stability condition must be conveniently evaluated. Suspended rock brackets can also be formed in environments very different from that of the mountains, for example, where there are steep coastal scarps (cliffs) formed by rock beds alternated with loose sediments (Fig. 1). In this case, cantilevered blocks result from wave erosion of weaker materials and finer soils. Typical examples are the stratified Pleistocene sequences formed by calcareous breccias alternating with loose sediments (clay, terra rossa, sandy silt and sand). Weathering phenomena and selective sea erosion give rise to horizontal rock brackets corresponding to stronger materials (breccia, pebbly sandstone, etc.). Progressive erosion of weaker soil strata with time increases the size of suspended blocks, until these reach a critical cantilever size and the flexural failure occurs. Such coastal processes are very frequent and they have to be taken into account as they can give rise to sudden rock falls that in the summer can cause fatal accidents to any people on the beach underneath. 3. The rockfall at the Glescana Tunnel (26/01/1999) The analysed rockfall involved an overhanging rock wall located at the eastern entrance of Galleria Glescana, at an elevation of about 360 m a.s.l. in the northern part of Cellina Valley gorge (Carnic Prealps in western Friuli, north-eastern Italy) (Fig. 2). The rockfall, which took place early in the morning of January 26, 1999, caused the sudden failure of a limestone slab above the old state road 251 of Cellina

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Fig. 2. General setting of the northern part of the Val Cellina gorge with the location of the Galleria Glescana rockfall occurred on the 26/01/1999: the topographical base derived by CTR (Friuli Venezia Giulia technical map) at the scale 1:5000 (on the left) and the orto-photo image taken in 1998 (on the right).

Valley, which at present is closed to ordinary vehicle traffic as it was decommissioned in 1994. Since 1994 the traffic on the SS 251 road was admitted only to the Enel staff (presently Edipower) working at the hydro-electrical station of Diga Vecchia site. As a consequence of the 1999 collapse, the traffic on the road connecting the Ponte Antoi's dam (Barcis' Reservoir) and the Molassa Stream confluence was interrupted. At present, the road that runs along Molassa Stream gorge is used to reach the hydro-electrical station near the Vecchia Diga site. The old Cellina Valley state road, whose construction dates back to the first half of the last century, presents a very suggestive gorge section, but several exposed rock slope areas denoted in the past a high rockfall activity due to the considerable extent of sub-vertical and steep rock walls. This particular condition has caused numerous road accidents due to the sudden detachment of rock masses and rock fragments onto the road, the last of which, with fatal consequences (June 3, 1990), involved a cyclist who was passing along the stretch of the road located immediately downstream the Cellina-Molassa Stream confluence. In order to eliminate the considerable rockfall risk affecting the state road S.S. 251 within Cellina Valley gorge, an alternative tunnel was built and since 1994, it has replaced the old road and conveniently communicates the towns of Montereale Valcellina and Barcis, eliminating the dangerous stretch within the Cellina gorge. The rockfall of January 26, 1999 caused the detachment of approximately 68 m3 of limestone rocks, modifying the pre-existing cross-

section obtained through rock blasting required for the road construction. The rupture involved a great rock “bracket” with a cantilever of about 11 m over the road. The collapsed slab, part of a limestone layer with a dip of about 28–30°, was 11.4 m long, 5 m wide and about 1.3 m thick. The slab had the shape of an irregular prism: two faces (top face and western margin) match the flat surfaces of pre-existing joints, while the bottom is convex and results from the man-made profile of the slope which was blasted to construct the road (Fig. 3). Before the rockfall, the slab presented its maximum thickness (2.4 m) at the SE extremity of the eastern border, while it decreased progressively, until disappearing, both to the N and to the NW. As a result of the detachment and the impact on the road, the rock mass was broken and sub-divided into various blocks, some of which as big as 3–4 m3. Collapsed rock mass was mainly accumulated on the road, except for some blocks that, after having broken the parapet, rolled down onto the alluvial bottom of the Cellina Stream valley (Fig. 4). On the detachment niche, the pre-existing contact surfaces between collapsed block and stable rock mass can be clearly identified by a field survey and are represented by two main discontinuities: a very continuous stratification surface (coded as ST joint and constituting the “roof” of the failed slab: see Figs. 3 and 5) and a vertical fracture joint characterised by a wide rock bridge (coded as KK2 joint in Fig. 3 and forming the lateral constraint of the rock bracket). The rock bridge is well recognisable on the contact surface by the grey-

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Fig. 3. Front view and axonometric projection of the limestone slab collapsed on the Val Cellina state road SS 251. The road was abandoned after 1994 and substituted by the actual tunnel path. For symbols: Aj = KK2 joint area; Ab = rock bridge area.

pale brown colour of the intact rock that has undergone the failure, quite different from the yellowish colour of the weathered joint (Fig. 5). Moreover, in the bridge area, there is a marked concave surface strong differentiating from the flat appearance of the KK fracture joint. The stratification ST has a 330/30° orientation (dip direction/dip) while the fracture KK, characterising the south-western edge of the slab, has a 240/90° orientation. In the upper part of the overhanging rock slope, other bedding joints which have the same orientation can be observed. Immediately upslope respect to the detachment niche, another very continuous layer can clearly be seen. This stratification surface is subject to progressive weathering, which causes the isolation of other cantilevered rock slabs with a flexural failure mechanism analogous to the preceding one (Fig. 3). The failure took place in January, a winter month characterised — together with February — by frequent below-zero temperatures and it was surely favoured by the freezing/thawing phenomenon that typically triggers winter rockfalls. The data supplied by the nearest meteorological stations (Diga Cellina and Barcis) reveal some particular climatic circumstances that may have induced the final failure phenomenon, both because of the low temperatures and the preceding heavy rainfalls. An episode of intense rainfall was recorded 14 days before the rockfall at the Cellina Dam station, on January 13, 1999 with 98.2 mm of total rainfall, while there were no precipitations

recorded on the following days. Short intense rainfalls (P N 10 mm/h) and daily precipitations greater than 50 mm can be considered critical for rockfall triggering in Friuli alpine region (Paronuzzi and Gnech, 2007) but the failure can occur even 1–2 weeks after the heavy rainfall event, depending on the specific water flow conditions within the rock mass and along the joints. Therefore, the storm that took place on January 13, 1999 could have favoured the rockfall, by itself or in combination with the freezing/thawing cycles. Also, the daily temperature ranges recorded in the month before the rupture by Barcis station reveal the possibility of freeze/thaw cycles, particularly in the week before the collapse, with daily temperatures ranging from −6° (Tmin) and +5° (Tmax) (Fig. 6). Both factors — the heavy rainfall episode of January 13, 1999 as well as the strong daily temperature variation with minimum values below zero recorded in the week before the rockfall — could have played a decisive role in the final rupture of the limestone slab whose geostatic equilibrium, after the road construction work, depended only on the flexural strength mobilised by the intact rock bridge. During the period immediately preceding the rockfall occurred on 26/01/1999, no significant earthquake events were recorded by the seismic monitoring system of the Friuli–Venezia Giulia region. From a general seismological viewpoint, the Glescana site is located 15 km towards east and north-east from the Alpago-Cansiglio area which is characterised by a certain seismicity well documented by the

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Fig. 6. Trend of the maximum and minimum daily temperature measured during the 30 days preceding the rockfall (Barcis meteorological station). In the diagram is reported also the heavy rain event occurred on 13 January 1999 with a daily precipitation of 98.2 mm.

4. Geological setting and intact rock characterisation

Fig. 4. Blocks and limestone angular fragments mobilized by the rockfall occurred on January 1999 near the Galleria Glescana tunnel. On the top it is evident the yellowish surface of the pre-existing stratification joint ST forming the “roof” remained after the collapse of the rock volumes.

historical earthquakes occurred on 29/6/1873 (Alpago earthquake: magnitude = 6.3) and on 18/10/1936 (Cansiglio earthquake: magnitude = 5.9) (seismological data are reported by D. Slejko in Carulli 2006).

The 1999 rockfall occurred in proximity of the northern entrance of the Glescana Tunnel and involved a stratified limestone sequence known in the geological literature as “Calcare del M. Cavallo” (Cuvillier et al., 1968) or “Calcari di M. Cavallo” Formation (Carulli, 2006). This formation can be dated to the Upper Cretaceous (Cenomanian– Campanian: about 100–70 million years ago) and widely outcrops in the northern area of Cellina gorge. It is a characteristic carbonate platform succession that reaches a total thickness of about 400 m. At the outcrop scale, the rock mass is characterised by compact bioclastic limestone, fine-grained limestone and calcareous sandstone, sometimes rich in fossil fragments, particularly Rudistae. Layering is evidenced by intercalations of finer limestone (micritic limestone) sometimes containing rests of plankton. Fresh fractured rock material is generally of pale brown or light brown-greyish colour.

Fig. 5. Detail of the great rock bridge (on the left, grey coloured), located at the SSE end of the contact between the cantilevered slab and the rock mass, which has been broken at the instant of the slab collapse.

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Fig. 7. Aerial view taken from helicopter (19/04/1999) of the Val Cellina area between the Old Dam and the confluence with the Molassa stream (on the left, in the shade). On the rock slopes one can note the regular dipping of the limestone layers, locally interrupted by extensive fractures belonging to the KK3 system.

The Monte Cavallo geological unit is a well-stratified rock mass, with limestone strata 1–2 m thick that can sometimes reach 10–15 m of thickness. In the zone between the confluence with Molassa Stream and Vecchia Diga site, limestone layers form a very regular isoclinalic succession with medium-to-low dipping (30–45°) and constant dip direction toward NNW (Fig. 7). The average orientation of stratification ST is 340 ± 26°/ 37 ± 8°/ (dip direction ± st. dev./dip ± st. dev.). The collapsed material of the 1999 rockfall is made up of fine grained compact limestone (micritic limestone) with a greyish-pale brown colour. The Schmidt hammer tests (Type L, Proceq® manufactured) carried out on the biggest fallen blocks have given a mean value of RL = 55± 7 (N = 300 measurements on 15 different rock surfaces) for the rebound number. By using different empirical relationships (Aydin and Basu, 2005), these measured values can be used to estimate a uniaxial compressive strength (UCS) of about 70–100 MPa for the intact rock material. Various limestone rock fragments (N = 51) having an adequate size (30 mmb d b 80 mm) have been subject to point load test (PLT) in the laboratory giving values of IS(50) index ranging from 2.09 to 5.64 MPa (3.58 ± 0.85 MPa). Some rock fragments were tested in the laboratory to measure the dry density γd of the intact rock and a mean value γd = 26.07 ± 0.1 kN/m3 was determined. Taking into consideration that the normalised point load index IS(50) corresponds to about 0.8 times the Brazilian tensile strength (ISRM, 1985), the characteristic tensile strength T0 of the intact rock can be estimated as ranging from 2.61 to 7.05 MPa with an average value of about 4.5 MPa (4.48 ± 1.07 MPa). In the area close to the 1999 rockfall, numerous orientation measurements have been made regarding both the stratification joints (N = 27) and the fracture joints (N = 75). The limestone rock mass is extensively crossed by 4 main sub-vertical fracture sets (dip range: 50–90°) of which one is clearly predominant (KK1 joint set), with approximate 290–300° strike and 74 ± 12° dipping. The average strike of the other fracture systems recognised with the field survey is 330° (KK2), 190° (KK3) and 220° (KK4) (Fig. 8). The three fracture systems KK1–KK3 are very important as regards diffusion and persistence. They often constitute the major macrojoints visible on the rock walls and they are able to condition the slope morphology itself. For instance, many discontinuities belonging to the KK1 set characterise the northern rock slopes of Cellina Valley immediately downstream of the confluence with Molassa Stream. The

KK2 fracture system, having a strike of 330°, very often influences slope morphologies determining frequent straight rock scarps on the southern side of Cellina Valley, immediately after the confluence with Molassa Stream. The western margin of the collapsed limestone slab coincides with a fracture joint belonging to the KK2 system (dip direction/dip: 240°/90°). Sometimes, the fracture systems KK1 and KK2 are open, with joint apertures ranging from 10 to 60 cm and filling materials made up of angular debris and blocks. Finally, well extended fractures with N–S direction (KK3 system: 190°), developed for many hundreds of meters and of outstanding continuity, can be recognised near the old dam site, on the left slope of Cellina Valley (Fig. 7). 5. Flexural failure and rock bridge breaking The collapsed rock slab is a part of a calcareous layer which was originally 2.5 m thick, but the layer thickness was very much reduced by slope re-profiling required for road construction. The significant modification of the natural rock slope has determined a thinning of the layer and the formation of an overhanging rock slab parallel to the road axis. On the rock slope, there is a very continuous stratification joint dipping against the slope, that forms an artificial “roof” over the road (Fig. 4). The original contact surfaces between the slab and the rock mass coincide with two discontinuities belonging to joint systems ST and KK2, characterised by a strong yellowish colour resulting from the considerable weathering and the frequent condition of water saturation affecting the joints. The stability of the rock bracket has depended all this time on the strength contribution given by the single rock bridge located at the SSE extreme of the western slab margin. The geometrical features of the collapsed block have been reconstructed based on the topographical survey, the elaboration of photographic images and the volume estimation of the failed rock masses. The rock bridge occupies an area of 2.82 m2 equivalent to over 26% of the whole lateral contact surface (10.50 m2) and coincides with the fracture system KK2 (Fig. 3). From the failure's mode point of view, the rockfall is due to a flexural failure of a sub-rectangular limestone slab, inclined about 30° above the horizontal and laterally restrained by the effect of the rock bridge. Considering the stress state, the maximum tensile stress on the rock slab was located on the top side of the rock bridge while the lower half was subject to a compressive state. The rupture critical

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Fig. 9. Characteristic values of tensile strength for limestone and dolomitic rocks according to various authors.

Fig. 8. On the top: Rose diagram showing the directions of the KK1–KK4 fracture joints (N = 75). On the bottom: polar diagram of the joints measured in the area near the 1999 rockfall, including the fractures KK (N = 75) and the layering surfaces ST (N = 27) — Schmidt stereographical projection, lower hemisphere.

condition was caused by the over-passing of the maximum tensile strength mobilised by the intact rock, with bridge fracturing in the upper part and immediate propagation of the fracture toward the bottom due to the reduction of the resisting section. The progressive concentration of the stress toward the lower part of the rock bridge determined an intense fracturing of the resisting intact rock, emphasized by the small dimensions of rock fragments produced by the bridge's crushing. On the contrary, the other parts of the slab are subdivided into rock pieces that, in spite of being small, reach the dimensions of the blocks (1–4 m3). The tensile strength characteristic of limestone and dolomite rocks, as obtained from various lab tests on intact rock specimens, is generally within the 1–10 MPa range (Fig. 9), with values that are generally around 5 ± 2 MPa according to what is reported in literature (Miller, 1965; Szechy, 1966; Farmer, 1968; Hardy and Jayaraman, 1970;

Ippolito et al., 1975). When cantilevered rock slabs are subject to a tensile stress greater than the maximum tensile strength of the intact rock, the failure takes place and the propagation of the fracture triggers the final collapse. Therefore, in the absence of external loads, the stability condition of the rock brackets basically depends on: a) geometrical characteristics (thickness and cantilever length) and slab orientation, b) rock bridge dimension and location, and c) characteristic tensile strength of the intact rock. Recurrent external factors, such as intense rainfalls or freezing/thawing cycles, are just the ultimate cause (triggers) of the collapse of the block that had been for some time in a poor stability condition. In real conditions, the main difficulty in evaluating the potential instability of suspended rock volumes is mainly related to the hypotheses on the block-rock mass connection and on the rock bridge location. As slabs are often delimited by joints (layering and fractures) developed inside the rock mass, their presence is determinant in a priori evaluations, but it can never be determined with accuracy from outside. This fact always causes significant restrictions regarding the hypothesis on the resisting section: fully resisting intact section or section with single or multiple rock bridges. The back-analysis of the collapse of actual overhanging rock slabs, as in the case of the Glescana Tunnel, allows us to better understand the key role of the rock bridges that almost always are the determinant resisting elements that ensures the stability of blocks delimited by systems of continuous and intermittent joints. 6. Stress state analysis 6.1. Simplified 2D model The stress state analysis of the constrained section supporting the cantilevered slab can be performed a priori with a 2D model by examining the case of a rectangular rock beam, restrained at one extreme and subject to straight flexure, according to the approach proposed by Aydan and Kawamoto (1992). In this case, symmetrical stress distribution is obtained with the maximum tensile stress on the most external fibre at the top of the clamped side and the maximum compression at the bottom extreme, according to the well-known bi-triangular stress pattern (“butterfly” diagram) (Fig. 1). With the same approach, always in the hypothesis of regular rectangular sections, it is possible to calculate through closed-form equations the stress state in the presence of a crack that reduces the resisting cross-section (Aydan and Kawamoto, 1992). The crack simulates the presence of an intermittent joint (Gehle and

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Kutter, 2003) and therefore, allows the evaluation of the influence of a rock bridge based on a simple geometry and for a two-dimensional model. In fact, to face the problem with this approach, it is still necessary to sketch the slab in a very simplified way assuming an idealized rectangular rock beam. 6.2. 3D finite element model Closed-form equations related to the simplified calculation mode are not used for the real rockfall case of the Glescana Tunnel as they cannot take into account the very irregular 3D geometry of the slab and, above all, they do not allow for the analysis of the stress state of the rock bridge. In similar cases, it is necessary to use a 3D finite element numerical model that allows reproducing both the slab geometry and the presence of eventual restraints related to irregularly shaped rock bridges. The geometry of the contact cross-section and of the rock bridge have been determined on the basis of the field evidence, while the collapsed block has been reconstructed taking into account the dimensions of the collapsed rock volumes and the shape of the detachment niche. For the elastic properties of the limestone slab material the following parameters have been assumed: γd = 26 kN/m3, E = 40 GPa, ν = 0.25. Once the rock slab geometrical model was obtained (V = 68 m3, P = 1768 kN), the 3D analysis of the stress state acting on the restrained cross-section was carried out through the Strand7 software (G+D Computing Pty Ltd., 2004). This is a 3D finite element code widely used to analyse the stress state for different engineering problems (structural, mechanical, aeronautical, naval, etc.). The finite element model is formed by brick-type tetrahedral elements (N = 122554) with 10 nodes in which the restraint condition has been assigned to the rock bridge nodes. The model mesh is generated automatically through a specific auto-meshing module (Fig. 10) and the elaboration of calculations is quicker due to the use of sparse solver procedure. Before examining the bracket of Glescana Tunnel, the Strand7 code was tested on simple geometries of cantilevered rock slabs that can be analysed even through closed-form equations, with results that can be totally matched regarding the calculated stresses. In the first model, the stresses were analysed assuming there was a fully-resisting contact cross-section (Ares = 10.50 m2), without considering the KK2 fracture. In this case, for maximum tensile and compressive stresses the following values σt = 2.25 MPa and σc = −2.58 MPa are obtained, if we consider the σzz axis (Fig. 11). Owing to

Fig. 10. Lateral cross-section of the collapsed rock slab (V = 68 m3; P = 1768 kN) illustrating the mesh of the tetrahedral elements (N = 122554) of the 3D finite element model for analyzing the stress state. Blue coloured area indicates the KK2 joint surface whereas red area corresponds to the rock bridge surface.

Fig. 11. Calculated stresses (σzz) obtained by the 3D numerical model assuming a fully resisting constrained section. For the signs: tensile stress (+) and compressive stress (−).

the geometry of the resisting surface, the main inertial axis of the slab and the Z axis of the local reference system are practically coincident. The calculated maximum value of the tensile stress is lower than the characteristic tensile strength estimated for the intact rock and therefore, in the absence of joint KK2, and due to the weight itself, the slab is stable and quite far from the failure condition. For this simplified model, the stress level can be calculated using the analytical equations if we consider a cantilevered slab with a rectangular-shaped cross-section, having the same inertial axis of the actual slab, 30° inclined above the horizontal and subject to deviated flexure. The maximum tensile stress calculated with this simplified scheme is σt = 2.25 MPa, a value very close to that given by the 3D finite element model for the irregularly-shaped rock slab. On the other hand, in the second model the real geometry of the rock bridge was taken into account, thus assuming a considerable reduction in the resisting area (Ares = 2.82 m2) located according to the rock bridge on-site evidence. The stress state calculated with the numerical model is dramatically different from the precedent situation, with clearly higher maximum stress values equivalent to σt = 5.19 MPa e σc = −8.10 MPa (Fig. 12). Fig. 12 shows the most significant stresses, the main maximum stress σ11 and the minimum stress σ33 (being σ11 N σ22 N σ33), acting on the restrained crosssection. In this case, the stress distribution shows a wide bridge area characterised by tensile stress values higher than 3.0 MPa (Fig. 12a), whereas the zone subjected to strong compression is more limited and only in two restricted bridge areas a compressive stress value of 6.0 MPa is over-passed (Fig. 12c). The calculated deformation is small with a maximum displacement of about 2.3 mm located at the far end of the slab and furthest from the constrained section.

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state that has led to the flexural failure of the overhanging block. Otherwise, it is only possible to explain how the failure condition was reached by hypothesizing the application of external loads (water pressure, seismic acceleration, etc.) that can hardly ever be verified and, above all, simulated in a rough way with simplified calculation methods. If the geometry of the slab and of the rock bridges is ascertained, the reconstruction of the stress state allows us to determine the maximum tensile stress that has determined the final rupture of intact rock connections. Therefore, the back-analysis of the collapse of overhanging rock slabs is very useful to evaluate the characteristic flexural strength of the rock materials under real conditions, taking into account the fundamental role of the joints and of the parts still connected to the rock mass (rock bridges). The so-calculated maximum tensile stress can be compared to the characteristic flexural strength of the intact rock determined through traditional laboratory tests. 6.3. Influence of rock bridge

Fig. 12. Calculated stresses obtained by the 3D numerical model assuming a partially resisting section with the fracture KK2 and the rock bridge. Reported values are referred to the main maximum stress σ11 (Fig. 12a and b) and to the main minimum stress σ33 (Fig. 12c). For the signs: tensile stress (+) and compressive stress (−).

Particularly relevant is the tensile stress that reaches a critical value, over two times higher (2.3) than the previous value and considerably high as compared with the characteristic tensile strength of the intact rock (T0 = 3.5–5.5 MPa). Therefore, the presence of the intermittent joint KK2 is a key feature in provoking the instability of the rock slab and only considering the real resisting cross-section of the rock bridge, it is possible to reproduce the effective on-site stress

The analysed rockfall of the Glescana Tunnel highlights the decisive role of the rock bridges in assuring the stability of blocks delimited by totally persistent joints (generally, layer surfaces) and by intermittent joints (almost always, fracture surfaces). This is true both for flexural failure of overhanging rock slabs and for rockfalls with failure modes characterised by a prevalent sliding process (planar and wedge failure) (Paronuzzi and Serafini, 2003). The limestone bracket rupture of Cellina Valley has taken place at a minimum resisting crosssection area coinciding with a highly persistent fracture joint (persistence: 0.74) (Fig. 3). On the other hand, on natural rock scarps, overhanging slabs are formed by plate-shaped blocks that are always subdivided by various fracture systems characterised by different persistence, whose location is very often decisive in determining the rupture surface. The back-analysed case indicates that a stress state analysis of cantilevered rock slab requires the evaluation of the effectively resisting section and therefore, the presence of an eventual intermittent fracture separated by rock bridges. In the hypothesis of completely resisting cross-section, the resulting levels of stress are significantly lower than the real ones (Fig. 11), when the resisting section is reduced by highly persistent fracture joints. For this reason, the back-analysis focused on the reconstruction of the stress state at the failure should be based on the on-site detailed observation of the detachment surfaces in order to identify the geometrical characteristics of pre-existing intact rock connections (rock bridges). Only in this way is it possible to make a realistic reconstruction of the restraint conditions of the cantilevered slab before the failure and thus calculate a stress state close to the actual on-site stress state (Fig. 12). Otherwise, the resisting surface is overestimated and the calculated stresses at the failure are lower, even far lower than the characteristic flexural strength of the intact rock. In this case, the failure condition is justified hypothesising external loads due to water in the joints or to seismic actions. Unfortunately, the described calculation procedure happens to be difficult to apply a priori because the information about any rock bridges (number, shape, area and location) is never exactly known and therefore, it has to be limited to statistical evaluations on the persistence of the different joint systems based on the traditional geomechanical survey. On a conceptual level, the importance of the topic role of rock bridges on block stability still remains: rock bridges guarantee the stability condition of rock masses for a long time until small increments of stress, resulting from processes of different nature, determine the final sudden failure that triggers the rockfall. 7. Fatigue behaviour and rockfall triggering Similarly to most rock slope failures, the Glescana rockfall can be analysed considering the preparatory processes acting on the

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cantilevered slab over a long time before the final collapse. According to this approach, the preparatory factors have to be clearly distinguished from external triggers which cause the ultimate sudden failure. Rock slopes typical triggers are: water over-pressures along rock joints induced by heavy or persistent rainfall, stress changes caused by intense frost-thaw sequences, earthquake-induced ground accelerations, rock fracturing generated by blasting. Rockfall triggering can occur contemporarily to a sudden stress state change (strong earthquakes) or some time — ranging from hours to several days — after a critical meteorological event as noted for slope failures induced by storms or by intense frost–thaw cycles. As a consequence, rockslide triggers represent only the final factor causing the block rupture but very often important fatigue phenomena have occurred over a long time interval determining a considerable weakening of the rock material. The most important process causing rock fatigue is microfracturing induced by cyclic loading caused by external forces such as strong seismic events or intense frost–thaw cycles (dynamic fatigue) but static fatigue also has to be considered for cantilevered rock slabs. Rock fatigue is a progressive deterioration of the rock material properties over a certain period of time due to the growth of new cracks or to the widening of pre-existing joints or micro-fractures. Rock fatigue, both dynamic and static, causes a progressive decrease in rock material strength reducing the strength contribution due to the intact rock connections (rock bridges) thus favouring the final block collapse. For this reason, rock fatigue is a decisive mechanical process in preparing rock slope failures but it is generally poorly considered due to the obvious difficulty in identifying the complex phenomenon of rock micro-fracturing which precedes the failure. Progressive microfracturing induced by rock fatigue processes is the main cause of rock material softening. The 1999 Glescana rockfall was the conclusive event of many distinct successive man-made and natural processes. The original rock slope profile was strongly modified by man through blasting in the early years of 1900 to insert the old Cellina Valley state road (SS 251). In this circumstance, the rock mass suffers severe damage caused by rough blasting procedures and it is presumable that at this time some pre-existing joints were opened and widened together with the appearance of diffuse micro-fracturing. The stress state of the man-made overhanging rock slab changed considerably from previous natural slope conditions due to the modification of the slope geometry and the irreversible rock damage caused by blasting. However, the cantilevered rock slab did not fail because the mobilised tensile strength of the rock bridge was sufficient to sustain the suspended block although this came close to the failure condition. In the successive period, after the road construction, the cantilevered rock slab experienced many cyclic loading sequences essentially due to vehicular traffic and frost–thaw alternating episodes denoting an annual recurrence period, typical of an alpine stream gorge. Other occasional dynamic cyclic loading on the slab was induced by a medium–strong earthquake (magnitude: 5.9) which occurred on 18 October 1936 in the Cansiglio plateau area, located about 15 Km SW of the Glescana site. Both recurrent cyclic loading (frost–thaw, traffic) and occasional dynamic loading due to the severe seismic episode (18/10/1936) contributed to the progressive damage and micro-fracturing of the rock slab. The continuous process of rock weakening was also favoured by static fatigue induced by the selfweight of the cantilevered block which determined a flexural deformation of the slab. These fatigue processes, both static and dynamic, acted over a time period of about 100 years determining a progressive deterioration of the rock material strength before the final 1999 collapse. The specific trigger of the rockfall which occurred on January 26, 1999 was probably the intense frost–thaw cycle measured the day before, with extreme temperature values ranging from −6° to +5 °C (Fig. 6). However, also the storm (total rainfall event: 98.2 mm) which

occurred 14 days before the collapse (13/01/1999) could have greatly contributed to generate some water over-pressures within the joints. For rainfall-triggered rockfalls, the delay time between the critical precipitation and the failure instant only depends on the hydraulic conditions of the joint network crossing the rock mass. In any case, both factors — the frost–thaw cycle and the heavy rainfall episode — are to be considered as possible triggers for the 1999 Glescana rupture and the role played by the single factor cannot be distinguished. The adopted 3D finite element model cannot be used to reproduce complex time-dependent phenomena involving rock fatigue, thermalinduced stresses, growth of micro-fractures within the intact rock and rock mass weakening. These fatigue processes, both static and dynamic, are difficult to simulate and require also a dynamic approach considering cyclic loading and fracture mechanics which is out of the scope of this work. The employed numerical model considers only the static case (load due to self-weight, only) and all problems related to cyclic loading and progressive fracture mechanics are neglected. Nevertheless, the reconstruction of the stress state acting on the isolated great rock bridge, helps us to understand the fundamental role played by the intact rock connection for ensuring a precarious stability condition to the overhanging block. Because the stability condition of the cantilevered rock slab was very close to the limit equilibrium, fatigue processes determined the progressive deterioration of the rock material strength since small cyclic frost–thaw loading or water over-pressures caused the final collapse. Rockfall triggering constitutes only the ultimate phase of a long-term fatigue process involving progressive deterioration (micro-fracturing) of the intact rock material. 8. Conclusions Overhanging blocks can form on the rock slopes which are both natural (coastal cliffs, Karst caves, steep mountain slopes) and artificial (re-profiled rock walls, quarry slopes, excavation fronts in tunnels, etc.), and very often have the shape of plate cantilevered slabs. In sedimentary rock masses, these rock slabs are defined mainly by stratification joints, while in the case of metamorphic rocks the main discontinuity surfaces are due to foliation or schistosity. In both situations, fracture joints are decisive in defining the unstable block and in conditioning the shape, the total volume and the orientation of the rock slab. Overhanging rock slabs are subject to flexural failure when the tensile stress induced on the constrained cross-section overcomes the maximum tensile strength of the intact rock. In real cases, the rock brackets that suffer flexural failure have variable thickness that range from 0.3 to 3 m and cantilevers often from 0.5–1 m to 10–12 m. The size of the collapsed slabs mainly depends on the geomechanical characteristics of the intact rock material (tensile strength) and on the eventual presence of defects due to cracks and/or fracture inside the bracket. In the natural rock scarps exposed to atmospheric agents, preexisting fractures may be widened, and even extended in depth, due to the action of plant roots. The 3D finite element analysis performed on a limestone slab which collapsed on January 26, 1999 on the old state road 251 of the Cellina Valley, presently out of use, has allowed us to reconstruct the stress state existing before the failure. For the purposes of the geomechanical analysis, the identification of an isolated wide rock bridge was fundamental as it determined the slab connection to the stable rock mass. Taking into account the constrained cross-section (Ares = 2.82 m2) corresponding to the real rock bridge examined on site, the 3D finite element model supplied a maximum tensile stress σt = 5.19 MPa, comparable with the characteristic flexural strength estimated for the intact rock (T 0 = 3.5–5.5 MPa). Instead, a considerably lower value (σt = 2.25 MPa) was obtained considering the whole contact area as resisting surface (Ares = 10.50 m2). Such results show the usefulness and effectiveness of three-dimensional numerical finite element models in the stress state analysis of rock

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slabs subject to flexural load. This approach is necessary if the effect of localised constraints (rock bridges) and of irregular block geometries are to be considered as in real cases the overhanging blocks never have a regular shape. References Adhikary,, D.P., Dyskin,, A.V., Jewell,, R.J., 1995. Analysis of failure and deformation process during flexural toppling in foliated rock slopes. 2nd Int. Symp. Mech. Jointed and Faulted Rock, Rossmanith Ed., Wien (Au), pp. 611–616. Adhikary,, D.P., Dyskin,, A.V., Jewell,, R.J., 1996. Numerical modelling of the flexural deformation of foliated rock slopes. Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 33 (6), 595–606. Aydan,, O., Kawamoto,, T., 1992. The stability of slopes and underground opening against flexural toppling and their stabilization. Rock Mech. Rock Eng. 25, 143–165. Aydin,, A., Basu,, A., 2005. The Schmidt hammer in rock material characterization. Eng. Geol. 81, 1–14. Barla,, G., Borri-Brunetto,, M., Devin,, P., Zaninetti,, A., 1995. Validation of a distinct element model for toppling rock slopes. Proceedings of the Int. Congress on Rock Mechanics, Tokyo, pp. 417–421. Bobet,, A., 1999. Analytical solution for toppling failure. Technical Note: Int. J. Rock Mech. and Min. Sci., vol. 36, pp. 971–980. Carulli, G.B., 2006. Carta geologica del Friuli Venezia Giulia, scala 1:150,000: Note Illustrative (Geological map of Friuli Venezia Giulia region, scale 1:150,000. Illustrative notes). Regione Autonoma Friuli Venezia Giulia, Direzione Centrale Ambiente e Lavori Pubblici, Edizioni S.EL.CA. s.r.l., Firenze, Italy, 2006, 44 pp. Cravero,, M., Iabichino,, G., 2004. Analysis of the flexural failure of an overhanging rock slab. SINOROCK2004 Symposium — Paper 2B 24: Int. J. Rock Mech. and Min. Sci., vol. 41(3), p. 475. Cruden, D.M., Varnes, D.J., 1996. Landslides types and processes. In: Turner A.K. and Schuster R.L. (eds) Landslides Investigation and Mitigation. TRB Transportation Research Board, National Research Council, Washington, D.C., Special Report 247:36–75. Cuvillier, J., Foury, G., Pignatti Morano, A., 1968. Foraminifères nouveaux du Jurassique supérieur du Val Cellina (Frioul Occidental, Italie) (New foraminifers from Upper Jurassic of Cellina Valley, western Friuli). Geol. Rom. 7, 141–156. De Freitas,, M.H., Watters,, R.J., 1973. Some field examples of toppling failure. Geotechnique 23 (4), 495–514. Einstein,, H.H., Veneziano,, D., Baecher,, G.B., O'Reilly,, K.J., 1983. The effect of discontinuity persistence on rock slope stability. Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 20 (5), 227–236. Farmer,, I., 1968. Engineering properties of rocks. E. and F. N. Spon, Ltd., London, United Kingdom. 57 pp.

75

Gehle,, C., Kutter,, H.K., 2003. Fracture and shear behaviour of intermittent rock joints. Int. J. of Rock Mech. Min. Sc. 40, 687–700. Goodman,, R.E., Bray,, J.W., 1976. Toppling of rock slopes: Proc. of ASCE Spec. Conf. on Rock Engineering for Foundations and Slopes, Boulder, Colorado, vol. 2, pp. 201–234. G+D Computing Pty Ltd. 2004. Strand7, Suit 1, level 7, 541 Kent St, Sydney NSW 2000, Australia. Hardy, H.R., Jayaraman, N.I., 1970. An investigation of methods for determination of the tensile strength of rock: Proc 2nd Cong. Int. Soc. Rock Mech., Belgrade, Serbia, vol. 3, pp. 85–92. Hoek,, E., Bray,, J.W., 1981. Rock Slope Engineering3rd Ed. Institution of Mining and Metallurgy, London. 402 pp. Ippolito,, F., Nicotera,, P., Lucini,, P., Civita,, M., de Riso,, R., 1975. Geologia tecnica per ingegneri e geologi (Engineering geology for engineers and geologists). ISEDI, Milano, Italia. 449 pp. ISRM, 1985. Suggested method for determining point load strength. I nt. J. Rock Mech. Min. Sci. Geomech. Abstr. 22 (2), 53–60. Miller, R.P., 1965. English classes and index properties for intact rock, Ph.D. Thesis, University of Illinois, USA. Norrish,, N.J., Wyllie,, D.C., 1996. Rock slope stability analysis. In: Turner, A.K., Schuster, R.L. (Eds.), Landslides Investigation and Mitigation: TRB, Transportation Research Board, National Research Council, Washington, D.C., Special Report, vol. 247, pp. 391–425. Paronuzzi,, P., Serafini,, W., 2003. Analisi di stabilità per la valutazione del fattore di sicurezza di blocchi interessati da processi di crollo (Stability analysis to estimate the factor of safety of blocks affected by rockfall processes). Geol. Tec. Ambientale 4, 21–37. Paronuzzi,, P., Serafini,, W., 2005. The influence of rock bridges in block fall processes. Ital. J. Eng. Geol. Environ. 1, 37–55. Paronuzzi,, P., Gnech,, D., 2007. Frane di crollo indotte da piogge intense: la casistica del Friuli-Venezia Giulia (Italia NE) (Rock falls triggered by heavy rainfalls: case histories from Friuli Venezia Giulia region, NE Italy). G. Geol. Applicata 6, 55–64. Pritchard,, M.A., Savigny,, K.W., 1990. Numerical modelling of toppling. Can. Geotech. J. 27, 823–834. Szechy, K., 1966. The art of tunnelling. Budapest: Akkadémiai Kiadò Budapaest, Budapest, Hungary, 76 pp. Timoshenko,, S.P., 1974. Strength of Materials, Advanced theory and problems3rd Edition. Van Nostrand Reinhold Ed., New York. Tommasi,, P., 1996. Stabilità di versanti naturali ad artificiali soggetti a fenomeni di ribaltamento (Stability of natural and man-made slopes subject to toppling phenomena). Riv. Ital. Geotec. 30 (4), 5–34. Varnes,, D.J., 1978. Slope movement types and processes. In: Schuster, R.L., Krizek, R.J. (Eds.), Landslides Analysis and Control: TRB, Transportation Research Board, National Research Council, Washington, D.C. Special Report, vol. 176, pp. 11–33.