Читать книгу Instabilities Modeling in Geomechanics - Jean Sulem - Страница 16

Landslides are the most common consequence of soil and rock instabilities at the field scale. In addition, they more common than earthquakes, and may claim many victims per occurrence in populated areas. Classically, shallow sliding is considered separately from deep rotational slope failures. Here, only the latter are considered. The traditional factor of safety (FOS) is understood as a ratio of resisting resultant moment to driving resultant moment the FOS approaching unity is considered as a condition of failure in classical geotechnics. However, as will be seen in what follows, in several historical landslides, failure occurred at a FOS substantially higher than 1, 2 or even 3. Incorrect evaluation of several variables, material properties or contributing processes led to misleading assessment of FOS.

A recent (February 2010) well-documented landslide is that of Maierato (Vibo Valentia), Calabria, which occurred at a site of paleo-landslides of 1783 and 1932. A rare, dramatic, but very instructive video by Patrizia Venturino (2010) has documented (https://www.youtube.com/watch?v=oWHjBsvmyLc) the event in detail. The most important thing to note in this video a succession of localized rotational collapses of individual scarps, intercalated with a mass flow. The general trigger of the landslide was a protracted period of rainfalls. As in so many similar cases, there were numerous precursors of the final event; in this case, a day to several hours prior to generalized failure consisting of minor local strikes, one of them toppling a high voltage powerline. Because of those warning signs, no fatalities occurred. The area affected was 0.3 km², with a front of about 800 m, depth of 60–70 m and involving about 10 Mm³ (Figure 1.11). The geological structure, shown in a cross-section in Figure 1.12, points out to two particularities of relevance: the presence of two particularly weak permeable rocks: evaporitic limestone and Miopcene sandstone, intercalated by two layers of clay, roughly 10 m thick. Prior to the main collapse, a substantial swelling was observed, suggesting a rotational collapse of a part of mass. It is believed (Gattinoni et al. 2012) and confirmed by laboratory experiments that evaporitic limestone transformed from plastic to semifluid behavior. Such a transformation is suggested to explain the rapid change from a mode of sliding to the flowing debris mass observed in the videos.

Figure 1.11. General view of the Maierato landslide site (Borrelli et al. 2014). For a color version of this figure, see www.iste.co.uk/stefanou/instabilities.zip

The most surprising finding from preliminary finite element (FE) calculations (Gattinoni et al. 2012) is that when dry the slope has FOS equal to 3.36, with slip surface within the evaporitic limestone, while with the water table up by a maximum of 10–15 m there is a reduction of FOS by 40% (about 2). Thus, the conventional understanding of slope stability highly overestimates FOS. Among the possible causes of failure not given proper consideration until now, the authors list penetration and pressurization of pore water along the contact between Miocene sandstone and Miocene clay, as well as the presence (and evolution upon inundation) of evaporitic limestone and Miocenic sandstone. They also suggest that autobrecciation induced by dissolution of halite and gypsum due to weathering and diagenesis might have played a role (Gattinoni et al. 2012; Borelli et al. 2014).

Figure 1.12. A geological profile across the area prior to the landslide. The green line denotes post-event topography (from Gattinoni et al. 2012). For a color version of this figure, see www.iste.co.uk/stefanou/instabilities.zip

These findings from the preliminary analyses of the Maierato landslide (Gattinoni et al. 2012; Borrelli et al. 2014) interestingly connect to observations made about the instability of slopes made by Terzaghi (1950) in his paper on “Mechanism of landslides”. Analyzing “landslide producing processes”, he emphasizes the difference between the “causes” and the “contributing factors” of landslides. He defines the latter through an example as follows: “if a slope is old, heavy rainstorms (...) can hardly be the sole cause of a slope failure, because it is most unlikely that they are without any precedent in the history of the slope. They can only be considered contributing factors”. In the same paper, in Table 1.1, Terzaghi (1950) introduces causes or “acting agents”, among which there is water from heavy rainstorms or snow melting. Among several “modes of action of agent” linked to water, he lists in ninth place chemical weathering, which “weakens inter- granular bonds” and leads to a decrease of cohesion. For an “old slope” slide of Mount Turtle in Alberta (1903), he then shows after McConnell and Brock (2004) a progressive decrease in FOS over 15 years, with some variations corresponding to dry and wet spells, eventually reaching reaching 1, in conjunction with “a contributing factor” of high pore water pressure (Figure 1.13). He returns to this mechanism in the case of loess, where water from external reservoirs is listed as removing soluble binders, destroying intergranular bond(s), with the same macroscopic effect of a decreasing cohesion.

Figure 1.13. Evolution of factor of safety of the slope at Mount Turtle along the process of soil weathering (from Terzaghi 1950)

Sensitivity of basic mechanical properties to chemical processes in the environment has been seen as a critical factor of the stability of slopes and coastal structures due to several processes. These include: cyclic changes in the salinity and acidity of pore water, heat effect due to frictional slip during a creep phase of slope instability, oxidation and dissolution of sandstone, dissolution of calcite, dissolution of silica in aging sediments and dissolution of gypsum in abandoned mines, to mention just a few examples.

The conclusion from the above considerations, in slightly more modern terms, is that a proper approach to a realistic evaluation of FOS would be to view the stability as a scenario composed of several processes coupled between them. These processes would be solid and fluid mechanical as well as geochemical, coupled through both balance equations (including exchanges) and constitutive (phenomenological) coupling, i.e. reactions versus porosity (permeability) versus elasticity or softening. The processes may be either simultaneous or sequential. Hence, the evaluation of the instability of such processes or the differential equations describing them should be approached accordingly, as instability either of the whole process or of any element of the sequence.

An example of such an approach proposed by Veveakis et al. (2007) is an analysis of Vajont dam landslide of 1963 in Northern Italy (Figure 1.14). This was one of the largest disasters of this sort in the previous century, killing nearly 2,000 people in a town below the dam (which survived). In their analysis, Veveakis et al. postulated that 2–3 years prior to the collapse, creep of the rock mass localized in a clay-rich layer was self-alimented by shear-generated heat, pressurizing and possibly vaporizing water within the layer, and thus leading to thermal softening of clay and accelerating the creep, eventually leading to the massive landslide.

Figure 1.14. Top left: view of the landslide scarp (2014). Top right: a crack (50–100 cm across, 2 km long) that developed parallel to the reservoir shore a few months before the collapse. Bottom: the town of Longarone 2 km below the dam, before (left) and after (right) the tragedy

They calibrated their model against the data from the site at 35°C temperature and 2.5 MPa increase in pore pressure, which were sufficient to produce a creep of velocity 20 cm/day, prior to the failure (Figure 1.15).

The model has subsequently been generalized to a thermo-plasticity simulation by Cecinato et al. (2011).

Figure 1.15. Top: predicted tempearture and excess pore pressure arising in the shear band during sliding against time (seconds). Bottom: calculated velocity of creep against time in months, compared to other assessments (from Veveakis et al. 2007)

In a similar spirit, a case study of two landslide slip surfaces at Diao Jiao Zui and Qian Jiang Ping sites in the Three Gorges area, China, has been undertaken using a multiphysics approach. Geochemical testing revealed that due to acid rain (with pH between 5.4 and 3.45), potassium ions at the slide surface were released, the cementation was reduced and the ratio of interlayer clay minerals evolved. Accordingly, illite or montmorillonite–illite mixtures were transformed first into kaolinite and subsequently into montmorillonite associated with a complex chemical softening evolution, including a 30% drop in shear strength at the slide surface, but not at a close vicinity (Zhao et al. 2011). Interestingly, both effective internal friction angle and cohesion appear for remolded smectite samples to be non- monotonic functions of time (Figure 1.16).

Figure 1.16. Evolution with time of the effective internal friction angle and cohesion during laboratory-simulated chemical transformation due to increase in the pore water pH of a model smectite soil corresponding to the slip surface at Diao Jiao Zui and Qian Jiang Ping sites in the Three Gorges area, China (from Zhang et al. 2015)

In a similar direction of chemo-mechanical coupling at the slide surface, an interesting extension of their thermal runaway creep instability developed for Vajont simulation was proposed by Veveakis et al. (2010). They postulated that the aforementioned frictional motion is affected by not only the generated heat, but also the strain rate. It appears that steady-state heat diffusion across the shear band may be unstable and lead to localization of heat dissipation (and hence thermal softening) at the center of the band. Hence, the authors consider the effect of localized dissipation on endothermic chemical reactions, leading to a variety of possibilities depending on the nature of the specific chemical reaction.

In an analogous spirit, Stefanou and Sulem (2015) investigated the conditions of chemically induced compaction band instability via a chemo-plasticity model.