Vibrations during TBM excavation. Details and analyses of real cases 
Due to its non-invasive approach and considerable speed, excavation with TBM is the preferred choice for building tunnels in urban contexts where disturbances must be contained as much as possible. Despite these advantages, the rotating head that performs the excavation generates periodic stress on the face, which propagates underground causing vibrations. The effects of those vibrations can be environmental (people perception) or structural (building integrity) on which we will focus in this paper. Depending on their importance, the damages on buildings can be classified in cosmetic (merely aesthetic alteration), minor or major (damage of structural elements). In order to correctly evaluate and predict the effects, it’s important to characterise the examined vibratory phenomenon. In particular, an excavating TBM excitates surrounding buildings with what can be represented as a motion induced at their base: the elastic waves generated by the machine (source) pass through the ground which transmits them to the foundations by modifying their spectral content. In terms of duration, the phenomenon can be considered continuous. The distinction between a continuous response (long duration excitation) and a transitory response (short duration) of a certain structure is based on its intrinsic characteristics. The discriminating reference period is, in fact, 5 times the “time constant of the building” (􀄲0), which depends on the first period of vibration, on the structure geometry, on the dampening factor and on the structure type. For normal constructions, it assumes a value of a few seconds, clearly much lower than the average duration of underground work cycles. For the measurements, it is necessary to establish the nature of the phenomenon. In the case of excavations with a TBM, although the presence of sources other than the main one (such as street traffic) can create an inevitable aleatory “disturbance”, the acting force presents a mostly deterministic nature with a periodic tendency over time; this makes it possible to carry out a study in terms of frequency with a Fourier analysis. Analysing the spectre of the vibratory phenomena associated to the TBM excavation, the frequency field in which it is concentrated is between 10 and 70 Hz. Comparing the highest harmonic components of the acting force to the frequencies of the construction (both estimated and measured), the last appear lower scattering any critical condition (resonance). The methods used to measure vibrations are generally chosen on the basis of distinctive elements of excitation and in function of the purpose of measurement. In general, data can be collected in terms of displacements (d), velocity (v) or acceleration (a) vs time, depending on the frequency range: the representation in terms of displacements accentuates the low frequencies components rather than the high frequency ones that are accentuated in the representation in terms of acceleration. Considering the field of frequencies typically associated with the excavation process of a TBM (>100Hz) and the availability of efficient accelerometers on the market, it is common practice to measure acceleration. Data collection must be followed up by the processing necessary to obtain parameters which can be compared with normative values, that normally refer to threshold velocities: PPV (peak particle velocity): defined as the maximum value of the velocity vector modulus. PCPV (peak component particle velocity): defined as the maximum value of a modulus of one of three orthogonal components of the velocity vector. Some of the regulations on this subject differentiate the limit values on the dominant frequency range that can be evaluated by means of the Fourier analysis. The main documents, which indicate threshold values under which it isn’t expected for constructions to suffer even aesthetic damage, are the following: [1] DIN 4150 – Erschütterungenim Bauwesen - Einwirkungen aufbaulichen Anlagen; [2] BS 7385-1 - Evaluation and measurement for vibration in buildings - Guide for measurement of vibrations and evaluation of their effects on buildings; [3] SN 640312a - Effet des ébranlements sur les constructions. Granting that: Measurements must be taken according to three mutually orthogonal axes. The reference values only take into account the direct effect of vibrations. Excess of the indicated limits does not necessarily imply damage, but indicates the need for deeper analysis. The vibrations caused by a TBM are classifiable as a continuous phenomenon. Tables 3, 4 and 5 report a summary of the reference values of PPV or PCPV for the vibrations induced on different types of constructions. The complex of experimental surveys carried out during TBM mechanical excavation for different metro lines in different geographic contexts, has pointed out very different vibrational level values. They depend on the type of grounds present in the sites, and on the type of examined receptor (in terms of structure, geometry and mass) as well as on the altimetric plane distance between the source of the vibrations and the receptor point. In general, it was observed that the levels are quite contained in the presence of alluvial grounds with gravels and poorly or averagely gathered sands and in absence of cementing elements on the superficial layer. Whilst in the presence of conglomerates or more gathered/compact formations, there is usually an increase of the vibrational levels, which is also in function of the consistency of the excavated material. The presence of constructions in the immediate vicinity, which reshapes the superficial portion of the ground by compacting it (e.g. the surveys carried out for the Milan Metro), as well as medium-large boulders, generally intensifies the phenomenon. Where the grounds are sufficiently homogeneous and the distance between the source of the vibrations and the receptor point is limited, the presence of a building with its own geometry and mass causes a decrease of the vibrational levels compared to those observed on the ground (due to the cushioning effect of the mass). In the absence of other parameters, it’s expected that an increase of the mass of the construction will cause an indicatively proportional decrease of the recorded vibrational levels. In absence of other ground characteristics, the depth of excavation significantly influences the vibrations. Indeed, a deeper source reaches the surface engaging a wider portion of ground and therefore a greater mass; this factor, as mentioned before, contributes to cushion partially the vibrational effects. Quantitatively, with reference to the examples given, the values summarised in Figure 13 show a PCPV value equal to around 1.5 mm/s at a frequency of 40 Hz. If interpreted in the light of the BS 7385-1, this data should be compared to the threshold value of 25 mm/s (see Table 4), and be therefore acceptable. The maximum values deduced from the Brescia Metro show PPV values equal to 4.00 mm/s at the foundations and 1.90 mm/s at the elevations. The first factor, if interpreted according to BS 7385-1 (foundation values), is acceptable; the second, if interpreted according to SN 640312a (the elevation areas being considered the most vulnerable), is acceptable regardless of the associated frequency value.