Seismic stability of the excavation fronts in the ancient Roman city of Pompeii

Introduction

The ancient Roman city of Pompeii, close to Napoli, at the foot of Mount Vesuvius, was completely buried after the Plinian volcanic eruption in 79 AD. This catastrophic event destroyed the city, killing about two thousands of inhabitants but, at the same time, paradoxically, preserved its buildings and their contents for many centuries, until the beginning of the excavation works, during the Reign of Bourbon King Carlo III, in 1748. Nowadays, after more than 250 years of archaeological excavations, with long periods of interruption, almost two-thirds of the urban agglomerate within the city walls have already been excavated, as shown in Fig. 1. The boundary of the excavated area is constituted by steep artificial slopes, approximately 8 m high. The definition of the profile of these excavation fronts represents a relevant problem since from the archaeological point of view it is suggested to proceed with sub-vertical excavations, for the preservation of the archaeologic ruins that are still buried, while from the geotechnical point of view such steep slopes might not satisfy the safety requirements. As a matter of fact, many sliding events have already occurred, indicating that, actually, these artificial slopes are not stable enough. As it will be shown, the re-profiling interventions needed to avoid the occurrence of slope failure under static conditions do not meet the safety requirements under earthquake actions. Therefore, in order to follow as close as possible the archaeological criteria, more detailed studies should be carried out when the seismic stability of the excavation fronts is being investigated.

Fig. 1. Plan view of the ancient town of Pompeii, the white area has not yet excavated (modified from de Sanctis et al., 2019).

The focus is set primarily on the importance of a proper simulation of surface (topography) and morphology amplification effects for a reliable prediction of the seismic demand in the excavation fronts. Second, emphasis is placed on the need of exploring strategies of analysis other than the classical pseudo-static approach for a sustainable definition of slope-stabilizing interventions in the ancient city. For the purposes of this work, the attention is focused on the case study of the Insula dei Casti Amanti, a block of masonry buildings in the city centre, partly brought to light because of some archaeological excavations. This choice comes from the availability of two boreholes alignments along the lanes on the lateral sides of the Insula, consisting of three boreholes for each side. From a geotechnical standpoint, this is a fortunate circumstance, as the chance to carry out subsoil investigations in the ancient city is today very limited, due to the severe restraints imposed by the Archaeological Park of Pompeii, a local body of the Italian Ministry of Cultural Heritage and Activity and Tourism (MiBACT). At the same time, a few number of boreholes have been executed elsewhere within the walls of the ancient city.

The Insula dei Casti Amanti takes its name from a fresco (Fig. 2) on a wall in one of the houses located in this block (named Insula from the Latin), in which two lovers (Amanti in Italian) are kissing in a chaste way (Casto in Italian), in comparison with the subjects of other Pompeii frescos. The Insula is also referred to as Regio IX-12, where the Latin number indicates the part (Regio in Latin) of ancient Pompeii in which the block is located. As shown in Fig. 1, this Regio is delimited along the North and South sides by respectively Via Nola and Via dell’Abbondanza, two of the main roads called decumani, and, on the East, by the Caius Julius Polibius mansion. The Insula has been recently involved in restoration works financed by the European Commission in the framework of a major project referred to as ‘Grande Progetto Pompei’ and consisting of: (a) the stabilization of the artificial slopes realized during archaeological excavation; (b) the replacement of the actual roofing system with a single-span covering; (c) the conservative restoration of the archaeological ruins. The main geotechnical aspects of the restoration works have been already discussed by de Sanctis et al. (2019).

Fig. 2. The fresco of the Chaste Lovers.

In this paper, the attention is solely focused on the seismic stability of the excavation fronts. In order to carry out such type of analyses, a detailed study of seismic amplification effects has been carried out by means of bi-dimensional wave propagation analysis, to account in a realistic way for surface (topography) amplification effects and the morphological depression of the Lava bedrock detected in the area of the Insula. The input signals selected for seismic site response analysis were applied on outcropping rock, propagated downward until the base of the reference model and then upward, through the layered subsoil by the equivalent linear approach. Emphasis is placed on the so-called ‘aggravation’ factor (Ashford et al., 1997, Bouckovalas and Papadimitriou, 2005, Assimaki et al., 2005), defined as the ratio of the maximum ground motion acceleration occurring at the crest of the slope over that evaluated through a reference 1D model. The above study allowed to evaluate in a reliable way the seismic demand in the artificial slopes. At this point, the problem is first tackled by the classical pseudo-static approach, in which the acceleration is supposed to be constant in space and in time and is represented through an equivalent seismic coefficient. In the second stage, a displacement based approach derived from the formulation originally developed by Newmark (1965) is employed. Unlike the classical Newmark’s block rigid model, the seismic performance in this case is evaluated in terms of accumulated rotation of the unstable soil mass. Under both situations, the asynchronism of the ground motion is taken into account in a simplified manner, as explained in the ensuing. The re-profiling interventions of the excavation fronts coming from the two methods of analysis are finally compared and discussed.

From a conceptual standpoint, the ‘decoupled’ approach suggested in this work is a ‘two-stage’ analysis, in which the seismic demand is first evaluated by the equivalent linear method and slope permanent displacements are then computed via the Newmark model. It is the same approach suggested by Makdisi and Seed, 1978, Bray and Rathje, 1998, Rathje and Antonakos, 2011. As an alternative, a ‘fully coupled’ approach may be adopted by evaluating simultaneously ground motion and slope permanent displacements (Fotopoulou and Pitilakis, 2015). In this last case, however, the availability of both advanced laboratory tests and constitutive models capable to simulate with sufficient approximation the cyclic and dynamic behaviour of soil under seismic conditions is mandatory. Overall, the approach proposed in this paper represents a good compromise between complex methods of analysis and the classical pseudostatic analysis. It is therefore particularly suited for engineering applications. From a methodological point of view, the ‘decoupled procedure’ followed in this example can be applied elsewhere in the ancient city of Pompeii, in the context of future restoration works.

Subsoil conditions and soil properties in the area of the Insula dei Casti Amanti

A detailed subsoil investigation in the area of the Insula dei Casti Amanti was carried out in 2002, as a part of a geotechnical study commissioned by the Archaeological Park of Pompeii. It included boreholes with Standard Penetration Tests (SPTs), retrieval of undisturbed soil samples for laboratory testing and a down-hole test. More details on this investigation can be found in de Sanctis et al. (2019).

The boreholes were located along the lateral sides of the Insula, as schematically depicted in Fig. 3. The stratigraphy of the site, illustrated in Fig. 4, can be summarised as follows:

  • Made ground from the soil surface until a depth of 1.3 m;
  • Volcanic ashes, produced by the so called Surge of the Plinian eruption in 79 AD, up to a depth between 1.6 and 3.7 m;
  • Pumices deposit, representing the first phase of the same eruption, the so-called Pyroclastic Fall, until a depth of 4.7–6.8 m;
  • Paleosoil with varying thickness, up to a depth varying from 8.0 and 9.7 m, interbedded with pyroclastic gravelly sand originated from the explosion of the previous eruptive cycle;
  • A transition zone consisting of lava slags and sand gravel, representing the alteration of the underlying layer of Lava;
  • A Lava layer, until the maximum investigated depth;
Fig. 3. Plan view of Insula dei Casti Amanti and available in situ investigations (modified from de Sanctis et al., 2019).
Fig. 4. Subsoil profile along the lateral lanes of the Insula.

The Altered Lava has a regular thickness along the western alignment (S4-S5-S6), and an irregular profile along the opposite side (S1-S2-S3), due to a morphological depression at the position of borehole S2. The groundwater table was not intercepted by the boreholes. Fig. 5 shows a schematic subsoil profile together with the results of the down-hole test, the profile of SPT blow counts and the geotechnical parameters obtained from all the available in situ and laboratory investigations carried out in the neighbouring Regiones in previous investigations.

Fig. 5. Subsoil properties (from de Sanctis et al., 2019).

With regard to strength parameters, the relative density was first obtained from the SPT blow counts using the correlation by Skempton (1986), and the friction angle was finally derived through the correlation by Schmertmann (1975). Such values are meaningful for the Pumices and the Pyroclastic gravelly sand layers, as in the case of volcanic ashes the indirect relationship with the SPT blow counts is not applicable. Laboratory investigations consisted of direct shear stress on relatively undisturbed soil sample retrieved from both the Pyroclastic gravelly sand and the layer of volcanic ashes. The values of the angle of shearing resistance obtained for the Pyroclastic gravelly sand, not presented here for sake of brevity, compare well with those coming from the SPT blow counts. With regard to the volcanic ashes, the angle of shearing resistance was determined from the direct shear tests. At this point, it is worth mentioning that the cohesion of the volcanic ashes in Fig. 5 is partly an ‘apparent’ term, due to the partial saturation of the soil. This cohesion was back-figured from the stability analysis of the steeper excavation front in the ancient roman city carried out by means of limit equilibrium and adopting a safety factor equal to 1. Such front, located in Regio I and labelled as Section FF in the plan view of Fig. 1, is schematically depicted in Fig. 6. The cohesion back-figured under this assumption is therefore a conservative determination.

Fig. 6. Excavation front located in Regio I.

The shear wave velocity profile shown in Fig. 5 comes from the Down-Hole test. From the roof of the Altered Lava downward, the average value of the shear wave velocity exceeds 800 m/s. Therefore, this formation can be idealized as the reference bedrock. Fig. 7 shows the decay of normalized shear modulus, G/G0, and the variation of damping ratio, D, with the level of shear strain, γ, as obtained from literature on pyroclastic soils in the eastern area of Napoli (Vinale, 1988, Bilotta et al., 2015). Data for sand were available until a shear strain of 0.5%, and so they were extrapolated up to 1% by interpolating laboratory results through the model proposed by Stokoe et al. (2004). The curves plotted in Fig. 7 were adopted for equivalent linear (EL) analysis of wave propagation in the site of the Insula. Particularly, modulus reduction and damping ratio curves pertaining to volcanic ashes were also attributed to made ground, while those related to sands were attributed to both the pumices and the pyroclastic gravelly sand layers. Worthy of note, the volcanic ashes in the eastern area of Napoli originated from the Phlaegrean Fields, and not from Somma-Vesuvio. However, the shape of the modulus reduction and damping ratio curves should not be affected by the originating volcano, so as the assumption made can be considered acceptable from an engineering standpoint. On the other hand, sands investigated by Vinale (1988) in the eastern area of Napoli are of alluvial origin, while pumices and gravelly sand in the reference city are of pyroclastic origin. The assumption made in this case is certainly more questionable. In any case, extending data in Fig. 7 to the materials in the reference site of Pompeii may be considered acceptable for the complexity of the ‘decoupled’ analysis approach employed in this paper.

Fig. 7. Decay of G and variation of D with the level of shear strain.

Excavation fronts

The excavation fronts surrounding the Insula dei Casti Amanti, whose actual profiles are represented in Fig. 4, Fig. 8, have suffered many sliding events, indicating that they are not stable. Moreover, the ancient masonry walls on the boundary of adjacent Insula (IX-11) act improperly as retaining walls, because of the different height on the retained and rear sides after the excavation of the lateral lane on the west side (Fig. 8). Not surprisingly, these walls suffered severe damages, such as the collapse depicted in Fig. 8a which brought to light the colonnade of the adjacent Insula IX-11 and the very pronounced tilting shown in Fig. 8b. Another noteworthy point is the perfect correspondence between the soil stratigraphy re-constructed from the boreholes and the profile of ground surface in Fig. 8a after the collapse of the elevator wall, characterised in the lower part by a slope equal to the angle of shearing resistance of the pumices.

Fig. 8. Excavation fronts along cross sections parallel to Via dell’Abbondanza: (a) ground profile after the collapse of the elevator wall; (b) tilting of the elevator wall.

Fig. 4, Fig. 8 also show the profiles of the excavation fronts defined on the basis of the stability analyses presented in this paper and referred to as ‘design profiles’. As a general rule, the slope angle of the excavation fronts was set equal to 34° for the layer of pumices and to 55° for the overlying deposit of ashes, taking advantage in this last case from the condition of partial saturation.

Ground motion amplification

Selection of natural recordings

The seismic hazard is affected by far-field tectonic earthquakes, originating from the Apennine chain, and the activity of the two volcanic districts surrounding the city of Napoli, the Phlaegrean Fields and the Somma-Vesuvio. The Mw 6.9 Irpinia earthquake in 1980 originated from the tectonic faults belonging to seismogenic zone SZ 927 of the Apennines (Meletti et al., 2008). A detailed representation of the main seismogenic sources in Campania Region has been recently reported by Ebrahimian et al. (2019). From data collected in the Parametric Catalogue of Italian Earthquake (Rovida et al., 2016), it is argued that the background area has been struck by 10 events with Mw in the range 6.1–7.2 over the period 1349–1980. Further details can be found in Licata et al., 2019, Ebrahimian et al., 2019.

According to the recommendation of the MiBACT, a life span of 50 years and a class of use IV are considered. This is a reasonable choice, because the boundary of the excavated area will certainly expand in the near future. The return period for the seismic action of the life-safety limit state (ULS) is therefore 949 years. Since the depth of the Lava’s roof is lower than 30 m, according to the Italian Building Code (NTC, 2018), adopting similar soil classification criteria as Eurocode 8 EN-1998–1 (CEN 250, 2003), the subsoil is classifiable as type E. For the problem under examination, the maximum acceleration on the crest of the slope will be:

where Ss is the soil amplification factor and ar the peak acceleration on outcropping rock.

The same set of outcropping recordings already selected by de Sanctis et al. (2019) was considered for seismic site response analysis (SRA). In particular, the design earthquakes (magnitude Mw = 5·5–7, epicentral distance R = 25–70 km) were defined by a preliminary de-aggregation (partitioning) of the seismic hazard into selected magnitude and distance, so as to identify the modal contributions to the overall site hazard. Table 1 summarises the main characteristics of the input signals selected to define the response spectrum of the horizontal acceleration for slope stability analysis. Fig. 9 shows the response spectra of the selected accelerograms, scaled to 0.168 g, the average spectral function and the spectrum specified by the Italian code for the life-safety limit state (SLV). Obviously, the spectral compatibility is satisfied at T = 0, since recordings were scaled to the same peak acceleration. In any case, the average curve compares well with the code specified design spectrum over the entire range of structural periods of interest.

Table 1. Input signals and scaling factors.
Fig. 9. Average spectral function and spectrum specified by the Italian code on outcropping rock.

One and two-dimensional wave propagation analyses

Site amplification effects are evaluated by two-dimensional analyses of wave propagation, using the equivalent linear approach. The code LSR-2D (Local Seismic Response 2D rel. 4.3.1, Stacec Srl, Reggio Calabria, Italy) based on the finite element (FE) approach developed by Hudson et al. (1993) is adopted to this aim. Fig. 10, Fig. 11 illustrate the FE domains defined for sections A-A and B-B, respectively. The natural recordings are applied to all nodes belonging to the lower boundary of the mesh, taking into account the change due to wave propagation from the outcropping surface to the reference lower boundary. The energy dissipation due to radiation through the lower boundary is accounted for by means of viscous dampers characterised by the following properties:

Fig. 10. Section A-A: amplification factors in 1D (out of brackets) and 2D analyses (in brackets).
Fig. 11. Section B-B: amplification factors in 1D (out of brackets) and 2D analyses (in brackets).

where ρb, Vsb and Vpb are density, shear (s) and compression-dilation (p) wave velocities of the underlying Lava layer. Theoretically, the displacement of the lateral boundaries of the FE mesh should be equal to those under free-field of an isolated soil column with the same stratigraphy. However, in case of low soil damping, the distance of the lateral boundaries should be too high to match the above conditions. The lateral boundaries are therefore coupled with the 1D response through a series of viscous dashpots, so as to avoid the re-introduction into the model of reflected waves.

Fig. 10, Fig. 11 show the amount of amplification at ground surface at some locations. For any point, the reference peak acceleration has to be intended as the mean value of the maximum accelerations at ground surface corresponding to the selected natural recordings. The results of 1D propagation analyses are also reported for comparison at the toe and behind the crest of the slope. They have been carried out with the local soil stratigraphy corresponding to the reference point at ground surface, so as to decouple soil (1D) effects from surface (topography) and morphology (valley) amplification. Following Ashford et al., 1997, Bouckovalas and Papadimitriou, 2005, the above effects may be expressed through the ‘aggravation’ factors, defined as:

where amax is the maximum acceleration of the reference point at ground surface from the two-dimensional analysis, abff the maximum acceleration at the base of the slope and atff the maximum acceleration on the top of the slope, behind the crest; both abff and atff are estimated by 1D ground response analyses and are not equal to one another. For section A-A, the overall amplification on the crest of the slope is 5.42, while the same factor is 1.85 at the toe of the slope (point 16) and 2.68 on the boundary of the domain (point 27). The value of 5.42 on the crest of the slope is worthy of note and, what is more, is much greater than the overall amplification of 1.539 based on conventional subsoil classification (Eq. (1)). The situation is similar in section B-B; in this case the amplification factor is 4.32 on the crest of the slope, 1.37 on the toe and 2.38 on the boundary of the domain. Such results indicate that the simplified method suggested by the Italian code, based on conventional subsoil classification, is unable to predict the amplitude of the ground motion behind the slope. The amount of amplification in section A-A is generally more pronounced than in section B-B. This is due to the additional amplification caused by the morphological depression of the Lava roof in section A-A.

It is also very interesting to express the results in terms of aggravation factors. The aggravation factor At on the crest of the slope is 1.75 for section A-A and 1.78 for section B-B. According to Bouckovalas and Papadimitriou (2005), who provided a deep insight into the phenomenon of aggravation in proximity of a slope under the assumption of homogenous soil, the same factor lies in the range [1.15, 1.45]. The greater aggravation detected from the two dimensional analyses, compared to the above literature range, is due to the intense interference between surface and soil effects occurring in case of a very shallow bedrock. The same Authors suggest also that the aggravation factor Ab at the base of the slope is about unity. This finding is fully consistent with the results of the wave propagation analysis carried out in this paper, indicating a value of Ab equal to 0.92 at the toe of the slope.

Summing up, the very pronounced peak of ground acceleration on the crest of the slope is due not only to the combination of surface (topography) and morphological effects, but also to the intense interaction between topographic amplification and soil effects. This last interference originates from the very shallow compliant rock. As a final comment, a proper modelling of local soil condition and geomorphological properties is mandatory for a reliable estimation of the seismic demand in the excavation fronts of Pompeii.

Seismic stability of excavation fronts

General

The most widespread approach in geotechnical engineering for slope stability analysis is the limit equilibrium method. It allows to identify the factor of safety (SF) of any potential failure surface. Many works in the literature deal with this approach, such as Janbu, 1954, Bishop and Morgenstern, 1960, Morgenstern and Price, 1965, Sarma, 1975. In all these methods, the earthquake action is idealized by a seismic coefficient (kh) constant in space and time (pseudo-static analysis). The critical slip surface is defined as the slip line associated with the minimum safety factor. It may be defined under both static and pseudo-static assumptions, with the two critical surfaces not necessarily equal to one another. The value of the seismic coefficient bringing the soil mass above the critical sliding line to a status of incipient failure (SF = 1) is also referred to as ‘critical’ (khc) (and the corresponding acceleration as critical acceleration ac).

According to the Italian building code the seismic coefficient can be evaluated as:

where amax is the maximum acceleration within the potentially unstable soil mass, while α is a reduction factor accounting for the amount of tolerable displacement of the slope. In case of excavation fronts, for the earthquake action of the life-safety limit state the above reduction factor is equal to 0.38. Therefore, evaluating the maximum acceleration at soil surface through the conventional subsoil classification would lead to kh = 0.10. According to draft of EN-1998–5 revision (CEN 250, 2019), the equivalent seismic coefficient shall be taken as:

where β is a reduction coefficient reflecting the ground motion asynchrony and χ a reduction coefficient reflecting the amplitude of acceptable residual displacement for the considered limit state. As a matter of fact, χ is equivalent to the inverse of reduction factor α in Eq. (4). For the life-safety limit state this coefficient shall be taken equal to 2. The reduction factor reflecting the spatial variability of ground motion may be evaluated as:

where H is the height of the slope, Tm the average period of the seismic action (Rathje et al., 1998) and Vs the mobilized shear wave velocity over the height of the slope. This simplified approach yields β = 0.85 for section A-A and β = 0.83 for section B-B, indicating about an additional 16% reduction for the asynchrony of the motion as an average. Therefore, according to the above draft, the equivalent seismic coefficient would be about 0.11 for both the examined sections. As anticipated in the introduction, the seismic coefficient for the problem at hand is derived from the results of 2D wave propagation analysis.

The stability analyses are preliminary carried out by the pseudostatic approach following the method of Sarma (1975), which allows to evaluate the seismic coefficient corresponding to any prescribed value of the safety factor and vice versa. Even if the Sarma method is applicable to irregular surfaces, for sake of simplicity reference is only made to circular slip lines.

The selected method of analysis can be also adopted under static conditions, by setting the seismic coefficient equal to zero. In this case, the critical slip lines represented in Fig. 12 are obtained. The corresponding factors of safety are 1.342 and 1.463. According to NTC (2018), under static conditions the partial factor for soil parameters (γM) is equal to 1.25, while the partial factor for resistance (γR) is 1.1. Since the slopes under examination are not subjected to variable load, the minimum allowable safety factor is SFmin = γR∙γM = 1.375. Although the SF of section A-A is slightly smaller than SFmin, the excavation fronts can be considered stable enough under static conditions.

Fig. 12. Critical surfaces for section A-A and B-B (distances and elevations above sea level are in m).

Pseudo-static analysis and its implication on slope-stabilizing interventions

A problem arises from the definition of the seismic coefficient equivalent to the earthquake induced inertial forces, variable both in space and time. Fig. 13 illustrates the contour plot of horizontal accelerations evaluated under earthquake No. 1 (EQ1) at the instant time where the acceleration at the crest of the slope is minimum. Noticeably, while there is a remarkable variation of the calculated acceleration within the soil domain along with the vertical direction, the variation of the acceleration along with the horizontal direction is almost negligible. The results obtained for earthquakes other than EQ1 are very similar and not reported here for sake of brevity. Based on results like those shown in Fig. 13, the asynchronism of ground motion is taken into account in a simplified manner, as explained in the following. First, reference is only made to points at ground surface from the toe to the crest of the slope. Second, for each input signal, the acceleration profile corresponding to points at ground surface on the slope is evaluated at any instant time. The instant time at which the integral of the acceleration profile is minimum (section A-A) or maximum (section B-B) is finally identified. The profiles obtained by this approach are represented in Fig. 14 for both the examined sections, by projecting horizontally target points at ground surface on the y-axis (16–26 for section A-A and 11–17 for section B-B). Noticeably, they do not occur at same time. The mean profile and the corresponding average value, is shown schematically in Fig. 14. This procedure leads to an average acceleration of 0.4 g for section A-A and 0.37 g for section B-B. The corresponding seismic coefficients (kh), evaluated by taking the above equivalent accelerations in conjunction with a reduction factor α = 0.38, are 0.152 and 0.140. They include soil surface (topography), morphology and ground motion asynchrony effects. A noteworthy point is that they are much greater than the seismic coefficient obtained through the simplified approach suggested by either the Italian code (kh = 0.10) or the draft of EN-1998–5 revision (kh = 0.11). The effect of the spatial variability of the ground motion may be roughly estimated by relating the average acceleration to the average maximum acceleration on the crest of the slope. The ratio of these two quantities, which is equivalent to reduction factor β in Eq. (5), is equal to 0.44 for Section A-A and 0.51 for Section B-B. Therefore, the simplified approach recommended by draft of EN-1998–5 revision underestimates the effect of ground motion asynchrony in a remarkable way.

Fig. 13. Contour plots of acceleration in slope section A-A at the instant time where the acceleration at the crest is minimum (earthquake EQ1).
Fig. 14. Acceleration profiles from two-dimensional wave propagation analyses.

The critical slip lines under pseudo-static assumption are identical to those identified in static conditions (Fig. 12). The safety factors obtained by this approach are 1.05 (section A-A) and 1.17 (section B-B). They are both smaller than the minimum value imposed by the Italian code for the excavation fronts under the earthquake action of the life-safety limit state (SFmin = 1.2). The distance from SFmin is particularly relevant for section A-A, characterised by the morphological depression of the Lava layer. Summing up, according to the pseudo-static approach, the slopes are not sufficiently stable.

A possible option would be that of re-profiling them as shown in Fig. 15, where the profiles defined under static conditions are also shown for comparison. However, this intervention would involve more extensive archaeological excavations. Moreover, in the occasion of intense rainfall events, a flatter slope like that in Fig. 15 would imply much greater infiltration, a reduction of suction in unsaturated soils and a decrease of the shear strength of the soil. This design option is therefore in contrast with the need of preserving the archaeological ruins that are still buried. As a matter of fact, it was rejected by the Archaeological Park of Pompeii.

Fig. 15. Slope profiles after conventional pseudostatic analysis.

Dynamic analysis by the rigid block theory

The stability of engineered earth slopes may be evaluated in several ways. The pseudo-static approach can only check whether or not slope instability will occur by judging the safety factor. An alternative, more elegant option is the dynamic analysis by the rigid block theory as originally formulated by Newmark (1965), in which the landslide is modelled as a rigid-plastic friction block having a known critical acceleration. The analysis calculates the displacements of the block as it is subjected to the effects of an earthquake; the significance of the accumulated displacement is then judged. Compared to more sophisticated finite element calculations, the Newmark’s model is a workable means, yielding much more useful information than the conventional pseudo-static approach (e.g. Jibson, 1993). Permanent displacement analysis begins exactly when pseudo-static analysis ends, at the point where the critical acceleration, ac, is exceeded. The block continues to move until the relative velocity between the soil mass and the base reaches zero and will slip again if the acceleration exceeds again ac. The process continues until the relative velocity drops to zero for the last time. While the classical Newmark theory was developed for translational sliding mechanisms, the critical surface of the examined slopes is circular shaped. For such slopes, the damage or failure mechanism is represented by the accumulation of permanent rotations. A modification of the classical Newmark theory was therefore developed in this work to calculate the rotational displacement of slopes. A similar approach has been proposed for example by Zeng and He (2013).

The first step is the evaluation of the critical acceleration of the unstable soil mass. For the problem at hand, the pseudo-static analysis yields a critical seismic coefficient of 0.18 in case of section A-A and 0.24 for section B-B. The second step is the selection of ground input motion. In this case, an artificial earthquake is generated from each input signal, by averaging at any instant time the spatial distribution of acceleration over the slope height as calculated from 2D analyses. Therefore, for both the sections, a specific set of recordings is defined by taking into account the asynchronism of ground motion. Unlike the classical Newmark’s theory, reference is made in this application to the rotation ϑ of the rigid friction block. Particularly, for instant time at which the seismic coefficient exceeds the critical one, the equation of dynamic rotational equilibrium of the sliding soil mass yields:

where Ip is the polar moment of inertia of the unstable soil mass, W is the weight of the same mass and yG the distance between the horizontal inertial action and the centre of rotation. Cumulated rotations are calculated by double integrating those parts of the artificial ground motion that lie above critical acceleration using the rigorous algorithm of Wilson and Keefer (1983). A Matlab code has been developed to this aim, available on a repository at www.ingegneria.uniparthenope.it. Usually, Wilson and Keefer algorithm takes into account explicitly the asymmetrical resistance to downslope and upslope sliding. The program developed for calculation of cumulated rotations has been modified to prohibit upslope rotations. This is a reasonable assumption in many engineering problems, since the critical acceleration in the upslope direction is much greater than the peak ground acceleration.

The rotation time histories evaluated by this approach for the two examined sections are plotted in Fig. 16. According to the Italian provisions, reference can be made to the mean effect of the selected earthquakes for seismic performance evaluation of geotechnical systems. The average permanent displacements of the two examined slopes are:

Fig. 16. Permanent rotations for section A-A and B-B.

where ϑpA and ϑpB are the average accumulated rotations, while RA and RB are the radii of the critical circular surfaces of Fig. 12. The median displacements for the above reference sections are instead 26 and 5 mm.

The main practical problem related to the application of sliding block method of analysis is how to define tolerable permanent displacements. The limits on calculated values could be related to (Matasovic, 1991): (a) functionality of structures on the crest, or at the toe, of the slope; (b) the stability of the slope itself after the earthquake. As outlined in the introduction, this work is focused on the stability of the excavation fronts, rather than on the functionality of the archaeological ruins intersected by the critical slip lines. With regard to point (b), the main problem related to excessive slope movements comes from earthquake-triggered macroscopic ground cracking, as water percolation in earthquake opened cracks can significantly reduce the static stability. Ideally, the dilemma about whether calculated displacements are tolerable or not may be overcome through database in which observed earthquake-triggered slope movements are correlated to measures of damage. The first attempt set for slope in this direction is the one established by the State of Alaska’s Geotechnical Evaluate Criteria Committee (Idriss, 1985). According to these criteria, for earthquake events with a probability of exceedance of 10% in 100 years, as those considered in this work, earthquake triggered movements must not exceed ‘12 in.’. Wilson and Keefer (1983) used a value of 100 mm as a conservative estimate of the critical displacement required for macroscopic ground failure. Jibson and Keefer (1993) used the 5 to 10 cm range as the level of critical displacement leading to ground cracking and general failure of landslides in Mississippi Valley. The Guidelines for Analyzing and Mitigating Landslide Hazard in California (Blake et al., 2002) claim that under circumstances where the critical slip surface may affect a building that is likely to be occupied by people during an earthquake, the ‘median’ displacement should be maintained at less than 50 mm. Finally, the Guidelines for Evaluating and Mitigating Seismic Hazard in California (California Geological Survey, 2008) recommend that calculated displacements do not exceed 100 mm. Based on the above review about tolerable earthquake triggered slope movements, the calculated displacements for the problem under examination can be considered compatible with the life-safety limit state. Therefore, the design profiles in Fig. 15 labelled as ‘static’ were finally adopted for the stabilization of the excavation fronts.

Discussion and conclusions

This work has examined the problem of the seismic stability of the excavation fronts in the ancient Roman city of Pompeii. Reference was made to the case study of the Insula dei Casti Amanti, a block of masonry buildings partly brought to light because of archaeological excavations. The excavation fronts surrounding the Insula have suffered many sliding events, indicating that they are actually not stable enough. For this reason, the restoration works of the Insula included the stabilization of the above fronts.

The seismic demand in the artificial slope was evaluated by means of two-dimensional analysis of wave propagation using the equivalent linear approach. This study allowed to isolate the amount of amplification due to surface (topography) and morphology effects. Particularly, the irregularity of the ground slope and the morphology of the bedrock roof induce significant aggravation of horizontal acceleration. Another noteworthy point is the intense interference between soil and topographic amplification due to the very shallow depth of the reference bedrock. The asynchronism of ground motion was taken into account by averaging at any instant time the spatial distribution of acceleration over the slope height. The reduction factor of inertial actions evaluated by this approach was significantly smaller than that predicted by the simplified method recommended by draft of EN-1998–5 revision. Overall, the equivalent seismic coefficient coming from two dimensional wave propagation analysis is much greater than that evaluated through conventional subsoil classification. Thus, a proper modelling of wave propagation is crucial for a safe and reliable prediction of the seismic demand in the artificial slopes of the archaeological site.

The stability of the excavation fronts was evaluated by the Sarma method, based on limit equilibrium. The design profile of these slopes was preliminary identified so as to meet the requirements imposed by the Italian code under static conditions. The same profile was then examined under pseudo-static assumption with the equivalent seismic coefficient evaluated by two-dimensional wave propagation analysis. In this case, the safety factor is lower than the minimum allowable value, especially where the morphology of the underlying rock layer is irregular. A new re-profiling of the artificial slope was exploited at this stage as a design option, but this intervention would have not been compatible with the need of preserving the archaeological remnants surrounding the Insula.

The stability of the artificial slope was finally examined by a Newmark type approach, thus idealizing the unstable soil mass as a rigid-plastic material; in this case, no displacement occurs below the critical acceleration, and displacement occurs at constant shearing resistance when the critical acceleration is exceeded. Unlike the classical Newmark theory, the problem is tackled in terms of cumulated rotation. The average permanent displacement was finally judged compatible with the reference ULS. Therefore, the alternative, dynamic analysis by the rigid block theory was proved to be a sustainable approach for slope stability analysis in the archaeological site.

The approach followed in this work may be conveniently applied elsewhere in the archaeological site of Pompeii for future restoration works. Finally, the aggravation factors detected by these analyses can be taken into account for preliminary seismic slope stability analyses of other excavation fronts in the ancient city.

Source:

Seismic stability of the excavation fronts in the ancient Roman city of Pompeii

Lucade Sanctis, Maria Iovino, Rosa Maria Stefania Maiorano, Stefano Aversa

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