1. Background
The historical 23 November 1980 Irpinia–Basilicata (Southern Italy) earthquake (Ms = 6.9) showed the importance of assessing seismic risk for Italian communities. In particular, earthquake vulnerability depends on the mechanisms occurring inside the superficial layers that filter the input motion from the bedrock. Many parameters may drive these mechanisms, such as soil properties, bedrock characteristics, layers depth, stratification and water level. In particular, the effects caused by water level may modify the vertical pressures on the soil layers, as observed and discussed by [
1,
2]. Other contributions showed the importance of controlling the water table as a soil improvement [
3,
4]. In addition, the correlation between shallow groundwater levels and liquefaction occurrence is proposed by [
5] for the May 2006 earthquake at Yogyakarta (Indonesia). In addition, [
6] showed the effects of water level on analytical indexes for liquefaction susceptibility, while [
7] investigated the effects of water table level during the recent Emilia Romagna earthquake, where the oscillations were shown to be limited to less than 2 m.
In this regard, there are many approaches to measure the depth of the water table. One of the most common consists of applying piezometers that are typically inserted into the soil at different depths below the surface with measurements made manually or automatically with a continuous registration [
8]. As shown in [
9], other interesting issues are the density, the frequency of measurement sites, the spatially interpolating point data and the extrapolating of the water table depth procedures. In this regard, interpreting redoximorphic features [
10] is another common methodology in routine soil surveys. More extended approaches that allow for the prediction of the variation of shallow water table are based on climatic records, field evidences from soil morphology and properties, outputs of physically based water balance models and combinations of the different approaches. Soil morphology is particularly valuable for interpreting water table dynamics in the soil profile [
11], and simulation models were recently proposed (e.g., [
12]).
After the 23 November 1980 Irpinia–Basilicata earthquake, several contributions considered the various mechanisms of rupture [
13,
14,
15,
16,
17] and estimated damages [
18], which focused on the effects of spectral accelerations [
19,
20,
21] or quantified the consequences [
22,
23,
24], and proposed several models [
25,
26]. Even with such extended literature, information regarding the level of the water table was not registered; this paper proposes numerical simulations of 3D models with different water levels in order to investigate the role of this parameter on the seismic vulnerability of the structure, which was previously investigated [
27]. In particular, the effects of water level are relevant especially in the case of shallow foundations, since they are more sensitive to the change of the vertical stresses due to changing water level. For example, [
28] showed that structures with shallow foundations on soft soils are expected to experience big damages and losses due to soil–structure interaction (SSI), which can be beneficial, detrimental or uninfluential on the seismic vulnerability. In addition, [
29] showed that considering SSI for unreinforced masonry (URM) buildings with shallow foundations is non-negligible and that taking into account the inelastic behaviour of the soil foundation system may lead to smaller structural displacements. Furthermore, [
30] focused on the mechanisms at the base of the permanent deformation of the soil to conclude that buildings founded on shallow foundations are particularly vulnerable to seismically induced settlements.
With this background, the present paper aims firstly at covering the lack of information regarding the position of the water level during the Irpinia–Basilicata earthquake by presenting a case study to assess the most detrimental water level conditions under which the earthquake may have occurred. Secondly, this paper proposes an attempt to generalize the outcomes presented to other seismic assessments by accounting the water level position, which is an important source of uncertainty, and sometimes underestimated or even neglected. The methodology applied in this paper consists of performing advanced 3D finite element models of the entire system (soil + foundation + structure) that allow consideration of the soil nonlinear mechanisms of shear deformation. In particular, different positions of water level were considered in order to assess several saturated conditions among the homogenous 20 m layer selected in the previous work [
27]. The structural configuration performed is representative of the Italian residential buildings that were mainly damaged during the Irpinia–Basilicata earthquake, and consists of a reinforced concrete (RC) structure with infilled masonry walls. In particular, the documentary sources are based on two main typologies of technical data preserved in local archives: the “Scheda A” and “Scheda B” (
Figure 1), which report the damages to the buildings and were fundamental tools to detect the level of damage to the buildings, [
31,
32]. These were used to summarize the data from the surveys that were carried out in two phases: the first, to evaluate the conditions of the entire building (Scheda A) and the second, to verify the effects on each housing unit (Scheda B) [
18]. Other important documents are the recovery plans (named “Piani di Recupero”) of the historical centres, and sources used to analyse the outcomes of the earthquake at the urban scale. For an extended literature review, please refer to [
27]. Results in terms of settlements, accelerations, base shear forces and floor displacements are calculated in order to assess the most detrimental positions of the water level.
2. The Irpinia–Basilicata Earthquake
The 23 November 1980 Irpinia–Basilicata earthquake (
Figure 2) may be considered one of the strongest earthquakes recorded in Italy [
18,
24,
33,
34,
35,
36,
37], causing profound changes in communities and extended damages to civil structures and infrastructures. In particular, [
18] conducted an extended literature review showing that the knowledge of the damages focused on some of Campania’s and Basilicata’s most heavily damaged towns, but without a systematic study. In particular, estimations assessed that approximately 1.85 million buildings were involved in the event, with 75,000 destroyed, 275,000 seriously damaged and 480,000 slightly damaged. In addition, the environmental effects induced by the 23 November 1980 Irpinia–Basilicata earthquake were also significantly severe since primary and secondary effects (such as hydrological variations and liquefaction-induced mechanism) brought important natural modifications to the natural conditions [
27], such as ground deformations, slopes, landslides, lateral displacements and settlements, which were extensively documented by several contributions [
37,
38,
39,
40,
41,
42,
43].
The damaged buildings consisted mostly of reinforced concrete (RC) structures characterised by infilled masonry walls (IMWs), the object of this paper (see next section). Specific studies were carried on as recovery plans (named “Piani di Recupero”) and described the procedures to recover the historical centres. These plans are useful as sources of information regarding the seismic effects at the urban scale [
27,
44,
45,
46,
47,
48,
49].
3. Methodology
SSI consists of several mechanisms that define the mutual behaviour of the soil, the foundation and the building, and consequently affect the structural performance. The water level depth modifies the vertical pressures in the soil and thus the shear mechanisms that cause soil deformations and settlements at foundation levels, and, consequently, stresses in the superstructures that affect the whole behaviour of the system. The proposed 3D finite element models (
Figure 3) aim to reproduce these complex nonlinear mechanisms to represent realistically the behaviour of the entire system (soil + foundation + structure). This goal is particularly challenging because of the mutual effects of two sources of nonlinearity: the shear mechanisms in the soil and the structural behaviours. The study proposed here is based on the previous contribution [
27], here extended to consider the role of water level depth.
The input motion performed (
Figure 4), selected from the Italian Accelerometric Archive [
50], consists of the registration at the Sturno (STN) station (latitude: 41.0183°, longitude: 15.1117°) in Avellino, Campania, which is defined on soil B (following the Eurocode 8 classification); more details are available in [
27].
The tridimensional (3D) models performed are based on the
u–p formulation (
u is the displacement of the soil skeleton and
p is the pore pressure), defined in detail in [
51] and [
52]. The
Pressure Depend Multi Yield02 model [
53,
54], selected to represent the soil layer, consists of a multi-yield-surface plasticity framework that may reproduce the mechanism of cycle-by-cycle permanent shear strain accumulation in incoherent soil materials, as shown in [
55]. The model is based on the definition of several parameters, such as the low-strain shear modulus, the friction angle, shear wave velocity and permeability, shown in
Table 1. In particular, an equivalent uniform linear layer was adopted in order to calculate the soil fundamental periods [
56]. Note that the paper aims to reproduce a historical event and geotechnical parameters for superficial layers are currently not available for the Irpinia–Basilicata earthquake, as specified in [
27]. The data that are necessary to be implemented in a numerical model require material characterizations with in situ tests that are impossible 40 years after the earthquake occurred, since soil materials and hydraulic conditions have changed significantly. Therefore, the values in
Table 1 were defined on the available information (mainly [
20]) and the free-field study that was carried out in [
27].
Figure 5 shows the water levels performed, corresponding to the six numerical models that were performed in this study. The dimensions of the mesh were calibrated with a calibration procedure [
27] and the final ones were 118.4 × 124.4 × 20.5 m. A total of 31,860 nodes and 35,868 20-node
BrickUP elements were applied, following the previous contributions [
57,
58,
59]. As explained in [
27], S2 is implemented amongst the soil materials that were considered in
Table 1.
Boundary conditions are fundamental when SSI analyses are carried out, especially to represent correctly the development of pore pressures. The penalty method with a tolerance value of 10
−4 was chosen to ensure strong constrain conditions without computational problems associated with conditioning of the system of equations (more details in [
60,
61]). Base boundaries (20.5 m depth) were considered rigid and all the directions were constrained. In order to allow shear deformations, longitudinal and transversal directions were left unconstrained in correspondence with the lateral boundaries, while the vertical direction (described by the third Degree of Freedom (DOF) of the nodes) was constrained. Hydraulic conditions were defined on the fourth DOF of each node that were blocked during the gravity analyses (step 1) and then released when hydraulic conditions were applied (more details in [
60,
61]).
The structure consists of an RC building with infill masonry walls (RCIMW) as a benchmark, in order to represent the Italian residential buildings that were mostly damaged during the 1980 Irpinia–Basilicata earthquake, and already studied in [
27].
Figure 6 shows the structural scheme consisting of 4 × 2 columns (4 columns in the transversal direction (spaced 8 m apart) and 2 columns in the longitudinal direction (spaced 10 m apart) and 3 floors (a 3.4 m-storey height, 10.2 m total height). RCMIW is a typical Italian system based on two schemes (
Figure 6): RC concrete columns and beams are superposed on vertical masonry walls. It is worth noting that the structural configuration performed here is a simplified version of frame-type buildings because detailed information should have required material characterizations with in situ tests that are almost impossible after 40 years from the earthquake, since the conditions of the materials could have changed significantly. Both vertical and horizontal elements are composed by RC concrete columns and beams, respectively, and characterized by fibre section models.
Concrete02 material (
Figure 7a,b [
27]) is chosen to model the core and the cover portions. A total of 30 bars are used and represented by
Steel02 material (
Figure 7c [
27]). The masonry walls are modelled as equivalent diagonal
elastic Beam Column elements [
53,
54], in both longitudinal and transversal directions. The masonry walls properties are selected based on the Italian code provisions, as shown in [
27].
Table 2 shows the vibration periods of the structure with and without the infill masonry walls, related to the fixed-base condition (no SSI effects included). It is worth seeing that the masonry walls affect the structural natural period (from 0.3012 to 0.2085 s), since they increase the lateral stiffness of the whole structure (as shown in [
27]).
The foundation is modelled as a 0.50 m-deep rectangular concrete raft foundation (28.4 × 34.4 m) in order to represent recurring shallow foundation typologies for residential buildings. The foundation considered is assumed to be rigid, by tying all the columns base nodes together with those of the soil domain surface, using
equalDOF [
53,
54]. The foundation is modelled with an equivalent concrete material, by applying the
Pressure Independent Multi-Yield model [
53,
54] (
Table 3). The first 0.5 m-deep soil layer around the foundation is modelled with a backfill defined by the
Pressure Depend Multi Yield model [
53,
54] and
Table 4 shows the adopted parameters, such as the low-strain shear modulus, the friction angle and the permeability. The number of yield surfaces is equal to 20.