Stress-strain Numerical Modelling Research Articles

Piuro Landslide: 3D Hydromechanical Numerical Modelling of the 1618 Event

The Piuro 1618 landslide represents a well-known case history of a large Alpine landslide. It destroyed the ancient village of Piuro (Italian Bregaglia Valley), renowned as an important trading center between the Mediterranean region and Northern Europe. The event had a significant impact among communities of all Alpine regions and was well documented by chronicles and paintings during subsequent decades. However, some aspects, such as the geometry reconstruction of the landslide body, the location of the landslide scarp, and its dynamics, remained undefined in previous studies, and a geomechanical characterization of the failure area is completely missing. Using field and laboratory analysis followed by stress–strain numerical modelling, this work develops a 3D conceptual geomechanical model of the slope considering its complex geological framework. The aim is to back-analyze the 1618 event, defining predisposing and triggering factors of the sliding event, and providing verifications on the geometry and location of the failure scar, as well as on the landslide dynamics. A coupled hydro-mechanical analysis with a 3D numerical approach is presented, assuming a rainfall scenario as a possible triggering factor. Simulated displacement and the development of a deep region of shear strain localization at a depth roughly corresponding to that of the detected Piuro sliding surface, allow us to highlight the mechanical role of geological elements outcropping along the slope and to validate the proposed scenario as a likely triggering factor for the 1618 event.

The Cimaganda Rockslide (Italian Alps): geomechanical characterization and hydro-mechanical numerical modelling

San Giacomo Valley (Sondrio, Italy) as many alpine areas, is quite frequently affected by rock slope landslides at different scales. This work deals with the study of the Cimaganda rockslide, occurred in September 2012 after four days of persistent rainfall. It involved a volume of about 20.000 m3 of massive crystalline rock, blocking the main road (SS36) and isolating the upper Valley for a few days. The event developed at the right flank of the historical Cimaganda rock-avalanche, which had mobilized some Mm3 of rock, irreversibly changing the morphology of the valley. Using field and laboratory analysis followed by stress-strain numerical modelling, this work develops a solid conceptual geomechanical model of the area and the back-analysis of the 2012 event, exploring instability-forecasting scenarios.

Time-dependent modelling of a mountain front retreat due to a fold-to-fault controlled lateral spreading

The Eastern Betic Cordillera (Spain) exemplifies at the Sierra de Aitana an impressive case of lateral spreading which involves a mountain anticline ridge dislodged by a post-orogenic extensional tectonic. The deep trenches testify the ongoing gravitational slope deformation featured by a rock mass lateral spreading. The Sierra de Aitana anticline ridge was dislodged along a normal fault zone which generated a scarp with a kilometric lateral continuity. The lateral spreading originated because Eocene limestone overlays Eocene marls, inducing a continuous evolution over time due to visco-plastic deformations and isolating huge prismatic blocks. To quantify the creep-driven stress-strain effects at Sierra de Aitana ridge, the mechanical and rheological parameter values of the involved rocks were quantified through field and laboratory tests which allowed to constrain an engineering-geological model based on equivalent-continuum approach. A stress-strain numerical modelling aimed at back-analysing the sequential morpho-structural evolution of the Sierra de Aitana anticline-ridge was performed by reproducing the retreat of the ridge front and the time succession of faults (re)activations. A time-dependent solution was approached by assuming a time-dependent creep configuration of the modelling and a parametric solution adopted to calibrate rock mass rheology, also taking into account: tectonic displacement due to the Aitana normal fault system by simulating these element as interface in the discretized domain; influence of pre-existing joint sets by assuming a main anisotropy in the elasto-plastic failure solution; admissible variations of the regional stress-field related to compressive and extensional phases and a generalised visco-plastic behaviour representing the ductile marls. The numerical modelling outputs that the lateral spreading mainly evolved as a creep-driven process while stress-release induced by tectonic activity is not sufficient to justify the observed landforms. The obtained results highlight a not negligible role of inherited structural elements for regulating the time evolution of the ongoing gravitational process at the Sierra the Aitana anticline.

Comprehensive analysis of the local seismic response in the complex Büyükçekmece landslide area (Turkey) by engineering-geological and numerical modelling

Multi-risk management requires a strong comprehension of possible effects induced by natural hazardous events. In this regard, landslides triggering due to earthquakes results from complex interactions between seismic waves and slopes. Multidisciplinary approaches can significantly contribute to better understand such interactions. The large Büyükçekmece landslide (about 1500m wide and 1830m long) located in Turkey (Avcilar peninsula), about 15km northward from the North Anatolian Fault Zone (NAFZ), was selected as case-study in the framework of the European project “MARSite – Marmara Supersite: new directions in seismic hazard assessment through focused Earth observation in the Marmara Supersite”. The Avcilar area was recently affected by the 17th August 1999 Mw 7.4 Kocaeli and by the 12th November Mw 7.2 Düzce earthquakes. The Büyükçekmece landslide involves upper Oligocene to lower Miocene deposits, consisting of silty clays, tuffs and sands. No earthquake-induced re-activations are testified so far but the landslide area was interested by a very intense urbanization during the last decade. A detailed engineering-geological model for the local seismic response of the Büyükçekmece landslide slope was constructed based on geophysical measurements, data from a multisensor in-hole monitoring system and stress-strain numerical modelling. Several tens of earthquakes were recorded from October 2014 to May 2015 in the landslide site by considering in-hole and surface data. The reliability of the local seismic response obtained by numerical modelling respect to the empirically derived one was checked in terms of both site-to-reference spectral ratios and transfer function between surface and downhole sites inside the landslide mass. The 2D numerical amplification functions confirm that the local seismic response is a consequence of the complex geological setting of the landslide slope while no relevant amplification effects can be referred to topographic features. Based on these results, the interaction between seismic waves and the Büyükçekmece landslide slope cannot be neglected to evaluate the possibility of future landslide re-activations.

Time-dependent evolution of rock slopes by a multi-modelling approach

This paper presents a multi-modelling approach that incorporates contributions from morpho-evolutionary modelling, detailed engineering-geological modelling and time-dependent stress-strain numerical modelling to analyse the rheological evolution of a river valley slope over approximately 102kyr. The slope is located in a transient, tectonically active landscape in southwestern Tyrrhenian Calabria (Italy), where gravitational processes drive failures in rock slopes. Constraints on the valley profile development were provided by a morpho-evolutionary model based on the correlation of marine and river strath terraces. Rock mass classes were identified through geomechanical parameters that were derived from engineering-geological surveys and outputs of a multi-sensor slope monitoring system. The rock mass classes were associated to lithotechnical units to obtain a high-resolution engineering-geological model along a cross section of the valley. Time-dependent stress-strain numerical modelling reproduced the main morpho-evolutionary stages of the valley slopes. The findings demonstrate that a complex combination of eustatism, uplift and Mass Rock Creep (MRC) deformations can lead to first-time failures of rock slopes when unstable conditions are encountered up to the generation of stress-controlled shear zones. The multi-modelling approach enabled us to determine that such complex combinations may have been sufficient for the first-time failure of the S. Giovanni slope at approximately 140ka (MIS 7), even without invoking any trigger. Conversely, further reactivations of the landslide must be related to triggers such as earthquakes, rainfall and anthropogenic activities. This failure involved a portion of the slope where a plasticity zone resulted from mass rock creep that evolved with a maximum strain rate of 40% per thousand years, after the formation of a river strath terrace. This study demonstrates that the multi-modelling approach presented herein is a useful tool for estimating the progressive development of slope failures because it can highlight time-dependent continuous deformations as the major processes that drive rocky slopes to failure. This type of approach can be devoted to the best selection of risk mitigation strategies with respect to both human life and anthropic infrastructure.

Thermomechanical stress–strain numerical modelling of deglaciation since the Last Glacial Maximum in the Adamello Group (Rhaetian Alps, Italy)

Deglaciated areas in the valleys of the Italian Alps have recently exhibited a high potential for geomorphologic hazards from diffuse deep-seated gravitational deformations (DSGSDs), caused by rock-mass creep processes that can evolve into rock falls and rock avalanches. A multidisciplinary approach that integrated geomorphologic surveys and stress–strain numerical simulations was used to investigate the effects of the stress release that was induced by the Last Glacial Maximum (LGM) in the Adamè Valley (Italian Alps). No evidence of DSGSDs has been found in this area; however, data are available to develop a well-constrained evolutionary model of the valley deglaciation. The extent and thickness of the southern extension of the Adamello glacier (the widest glacier in Italy) during its primary growth phases, including those of the LGM, three Late Glacial stages and the Little Ice Age (LIA) were reconstructed using glacial geological surveys and were reproduced using a finite-difference stress–strain sequential model spanning from the LGM to the present. A thermomechanical numerical configuration was developed based on geomechanical field measurements that were collected from rock outcrops and data from laboratory tests, specifically performed on intact rock samples. The numerical simulations demonstrate that thermomechanical viscous behaviour cannot be neglected because the resulting strains on the slopes are significantly higher than those resulting from conventional elastoplastic behaviour. The last major thermal effect in the rock masses reproduced using the model occurred from 11.5ka until the LIA; the resulting displacement rates are as much as several tens of mm/ka, which are consistent with the absence of DSGSDs in the Adamè Valley, as these rates are significantly lower than those previously obtained from DSGSDs and other large landslides in the Alps. Based on thermomechanical numerical solutions, these rates should persist for the next 1000years assuming that no variations in current climatic conditions occur.

Potential rockfalls and analysis of slope dynamics in the Palatine archaeological area (Rome, Italy)

The Palatine Hill is among the main archaeological sites of Roman antiquity. Today, this place requires continuous care for its safeguarding and conservation. Among the main problems, slope instabilities threaten the southwestern border of the hill flanked by the Velabrum Valley, as also testified by historical documents. The upper part of the investigated slope is characterized by Middle Pleistocene red-brownish tuffs known as “Tufo Lionato”. The rock mass is affected by two jointing belts featuring the slope edge and its internal portion with different joint frequency and distribution. The analysis of the geometric relationship between the joint systems and the slope attitude evidenced possible planar sliding and toppling failure mechanisms on the exposed tuff cliffs. Potential rock block failures threatening the local cultural heritage were contrasted with preliminary works for site remediation. In addition, stress-strain numerical modelling verified the hypothesis of a tensile origin for the jointing belts, suggested by fracture characteristics and orientation. A first modelling was limited to the southwestern edge of the Palatine Hill and analysed the present stress-strain condition of the slope, proving the inconsistency with the observed deformation. A second modelling was extended to the Palatine-Velabrum slope-to-valley system to consider the role played by the geomorphological evolution of the area on the local slope dynamics during the late Pleistocene-Holocene. Results demonstrate how original conditions of slope instability, deformation and retreat along the Palatine western edge were determined by deep valley incision, and controlled by deformability contrasts within the slope. Slope instability influenced the site occupation and development during the Roman civilization, as also indicated by the remnants of retaining walls of different ages at the slope base.

Back analysis of a rock landslide to infer rheological parameters

On 30 January 2009, a rock slide involving approximately 0.23Mm3 of highly jointed gneiss from the local Ercinic substratum was recorded in southern Italy. The landslide occurred after exceptional autumnal rainfalls and involved a quarry whose activity has been documented over the past 10years by aerial images.An engineering-geology model of the slope involved in the landslide was developed based on the geomechanical classification of the outcropping rock masses, the ISRM (2007) indexes Ib (the block size index) and Jv (the volumetric joint count), and the observed geological setting of the slope. An equivalent continuum approach was adopted to attribute strength and stiffness parameter values to the different classes of jointed rock masses.A simplified evolutionary model of the slope was developed, starting from 300ka (i.e., from the erosional phase following the deposition of the 300-m-a.s.l. marine terrace deposits overlaying the gneiss substratum) to 30 January 2009. The model took into account the main depositional phases as indicated by the Pleistocene marine terrace deposits and the documented stages of quarry activity.Time-dependent stress–strain numerical modelling was performed by the FDM software FLAC 6.0. A visco-plastic Burger model was used to back-analyse the landslide event and to define the values of the rheological parameters for the jointed gneiss.The results, which were strongly constrained by the geomorphological evidences and by the displacement field observed before and after the landslide, demonstrated a combination of i) time-dependent gravitational slope deformation and ii) anthropogenic release due to quarry activity, which induced a progressive failure process and an increase in the jointing within the gneissic rock mass located behind the cut-wall of the quarry. Failure was ultimately triggered by intense rainfalls that occurred in the 3months before the landslide.The stress–strain numerical modelling demonstrated the reliability of visco-plastic rheology for simulating the rock mass creep in this case history: viscosity values in the range of 1019–1023Pa·s were derived.

Earthquake triggering of landslides in highly jointed rock masses: Reconstruction of the 1783 Scilla rock avalanche (Italy)

The Scilla rock avalanche occurred on 6 February 1783 along the coast of the Calabria region (southern Italy), close to the Messina Strait. It was triggered by a mainshock of the “Terremoto delle Calabrie” seismic sequence, and it induced a tsunami wave responsible for more than 1500 casualties along the neighbouring Marina Grande beach. Based on subaerial and submarine surveys, a 5×106m3 subaerial landslide was identified together with a 3×106m3 submarine scar area, whereas block deposits are present in both the subaerial and submerged regions. A detailed geological reconstruction of the slope was obtained and a geomechanical characterisation of the metamorphic rocks involved in the landslide was performed. Based on this reconstruction, intense jointing conditions of the rock mass can be related to main fault zones parallel and normally oriented to the actual coastline. An engineering geology model of the landslide was devised according to an equivalent continuum approach to evaluate both stiffness and strength of the rock mass within the slope. A finite difference stress–strain numerical modelling of the Scilla landslide was performed under dynamic conditions to back-analyse the landslide trigger as well as local seismic amplifications.This modelling gave new insights into the physical interactions between seismic inputs and slopes, as it demonstrated the fundamental role played by i) the interaction between the seismic input and geological setting of unsheared rock slopes (i.e., without preexisting landslide masses), ii) cumulated strain effects due to seismic sequences, and iii) jointing conditions of the involved rock masses responsible for the seismic amplification of the landslide-prone volume, driving it toward failure conditions.

Stress–strain history from the geological evolution of the Orvieto and Radicofani cliff slopes (Italy)

The study proposes geological evolution models for the cliff slopes of the two Italian towns of Orvieto (Umbria) and Radicofani (Tuscany). The models were validated by the use of a stress–strain numerical modelling, implemented by the finite-difference code FLAC 5.0. The numerical modelling was approached in a sequential way, by assuming specific stiffness values related to the evolutionary stages. For this purpose, unconventional laboratory tests were performed aiming at reproducing the stress path related to the geological evolution model, using standard equipment for CID triaxial testing. The geological evolution models infer that deformation in both cases is driven by stress reduction. At the Orvieto plateau, stress reduction is induced by stress relief involving a tuff plate; in the case of Radicofani, stress reduction is due to stress release in consequence of lateral erosion of clay. Numerical simulations refine the lithotechnical zoning of the two investigated slopes, introducing a stress–strain criterion in addition to the conventional geological and geomechanical ones.