The assessment of possible effects on built environment resulting from tunnelling operations for the
micrometropolitana of Florence
M. Severi, G. Vannucchi
Dept. of Civil Engineering, University of Florence, Italy
Keywords: shallow tunnel, masonry, interaction, subsidence
ABSTRACT: Protecting and maintaining the urban heritage against the impact of underground construction has become an essential part of the design process. The case study of the ‘feasibility project of the micrometropolitana of Florence’ is presented. Both empirical and numerical methods have been used to achieve an appropriate estimation of excavation induced effects and the relative risk of damage to the structures. Particular emphasis is put on masonry building response to tunnelling. The advantages and limitations of both methods are discussed and the results are compared.
1 Introduction
The design process of relatively shallow tunnels close to important buildings must include procedures to estimate the probable extent of settlement-induced damage to the buildings. An assessment of potential damage is particularly important when the buildings are made of masonry, in which case relatively small differential settlements can lead to unsightly cracking in the walls and façades.
The surface settlements caused by shallow tunnel construction at a greenfield site, usually approximated empirically by a Gaussian curve in a direction perpendicular to the tunnel axis, have been the subject of much research.
Current semi-empirical methods are generally based on a multi-stages process: preliminary assessment; second stage assessment; detailed evaluation. Burland and Wroth (1974) describe a general procedure for the prediction of settlement-induced damage to masonry buildings. Boscardin and Cording (1989), however, applied the method to the particular case of settlements caused by tunnelling, and included the effect of horizontal movements at the ground surface. Burland (1995) illustrate a method in which individual façades of a building are modelled as elastic deep beams. To estimate the extent of likely damage to a masonry building, it is assumed that the cracking is related to the magnitude of the tensile strains developed within the structure. The greenfield tunnel-induced settlements are imposed on the building façades and approximate expressions are used to estimate the induced maximum tensile strain. In this approach, the lateral strain at the ground surface is taken to be zero, and different analytical approaches are used to deal with portions of the building deforming in hogging and sagging modes.
In Literature many other relationships for tunneling induced ground movement and associated structure damage can be found, using either empirical or analytical methods such as those proposed by Peck (1969), Polshin & Tokar (1957), O’Reilly and New (1982), and Sagaseta (1989).
All the mentioned papers neglect the influence of the building stiffness in the interaction process, thus leading in general to an overestimation of the potential damage to buildings.
Potts and Addenbrooke (1997) used a coupled 2D finite element model to study the influence of a surface structure on the ground movement due to tunneling. Their numerical results showed that
the presence of the surface structure significantly influences the ground settlements.
Although assessment methods such as these that are based on the assumption of elastic structural behaviour are convenient to use, it should be noted that a masonry building is unlikely to behave elastically, particularly once significant cracking occurs.
Burd et al. (2000) describe a full three dimensional coupled modeling that takes into account the presence of existing structures and the tunnelling procedure employed to analyse the interaction between the construction of an unlined tunnel and a masonry building. Their studies noted a significant influence of the tunneling–building interaction on the distribution of damage in the building. Such complex analyses, including the non-linear behaviour of geomaterials and materials involved, allow for a good comprehension of the phenomenon but must be limited to specific case of study, due to the high computational effort required.
On the other hand, the availability of simplified computational models afford the designer to perform fast numerical analyses that are suitable for preliminary stage of assessment.
In the present paper this approach has been applied within the framework of the feasibility project of a subway system for the city of Florence. Both empirical and numerical methods have been used to achieve an appropriate estimation of excavation induced effects and the relative risk of damage to the structures. Particular emphasis is put on masonry building response to tunnelling. The advantages and limitations of both methods are discussed and the results are compared.
2 Components of the numerical procedure
In order to avoid extensive and detailed analyses at the preliminary stage, the potential damage to structures can be evaluated in term of building typology response. The aim is to supply different scenarios for further steps of investigation.
As reported by Liu et al. (2000), the use of parametric numerical analysis can efficiently provide an
“easy to read” insight of the building response to tunneling operations. Varying the characteristic parameters of the problem, such as the relative horizontal distance between tunnel and the façade, the mechanical properties and/or the geometry of the structure, it is possible to define a set of patterns at which an existing structure can be compared to.
2.1 Description of the adopted method
The first step of the proposed procedure is to investigate the main parameters of the building environment by means of a statistical analysis over the constructions along the layout. It is therefore possible to identify one or more representative structures lying in the settlement trough.
Fundamental parameters that must be investigated are:
− Geometry of the facade: length (L) and height (H)
− Percentage of openings, such as windows and doorways, and their position with respect to the façade.
− Mechanical/physical properties of the masonry in order to define a model that reflects the behaviour of brick and mortar combined.
Considering the presence of openings is of particular importance, because of the high local stress increase induced in the structure that causes the cracking.
The study presented here uses some simple tunnel-façade configuration, considering the relative position that maximize sagging and hogging deformation modes. The façade is placed normal to the tunnel axis, and its horizontal location with respect to the tunnel is altered by the eccentricity e (the horizontal distance between the tunnel axis and the centre of the structure L/2). A minimum of three different location are to be investigated (Fig. 1):
A. symmetric layout with sagging deformation mode: e=0;
B. asymmetric layout with sagging/hogging deformation mode: e=i (point of inflection);
C. asymmetric layout with hogging deformation mode: e=i+L/2.
The choice of constitutive model for both masonry and soil is of prime importance, but, as reported above, has to be reconciled with the required simplicity. The soil behaviour is assumed to be
governed by an elastic perfectly-plastic constitutive relation based on the Mohr–Coulomb criterion.
For the masonry we consider that at this stage the same model with an additional tension cut-off criterion is suitable for the interaction analysis.
C B
A
L
H
i
Z
L
H
i
Z Z
i
H
L
Figure 1. Facade positions considered in the analysis
The reference parameter for crack opening is the ultimate tensile strain that develops in the building during the excavation.
The magnitude of the ground movements is determined principally by volume loss (VL), thus it is noticeable the importance this parameter plays in the interaction phenomenon. Because of the geotechnical variabilità and other factors we consider a varying value for VL between a minimum for the excavtion at regime and a maximum as alarm level, in terms of safety of operations.
The method outlined can result in a certain usefulness if considering that many cities present district that are homogeneous from a typological and constructive point of view.
3 Settlement and damage to building assessment
3.1 Project overview
The feasibility project of the “Micrometropolitana concerns the construction of a light underground subway for the town of Florence (Severi & Vannucchi, 2002, 2004). With regard to civil and geotechnical aspects, the main characteristics can be summarized as follow:
− Excavation driven in saturated non-cohesive soil by closed shield Tunnel Boring Machines (TBM);
− Circular cross-section with external diameter of 5,00 m (excavation diameter);
− Tunnel axis at depth varying between 9.50 and 22.00 meters below the ground level;
− Tunnel longitudinal profile of “catenary like” shape, rising in correspondence of stations, while descending down to a minimum in between two contiguous stations.
Although all the described characteristics are aimed to minimize the effects deriving from the excavation, the tunnel induced subsidence are to be estimated in order to avoid any potential damage to the structures.
With reference to the longitudinal sections (Fig. 2), the stratigraphical succession is the following:
R: is formed of heterogeneous antropic filling soils of a more or less recent epoch. The layer consists mainly of silts ranging from weakly sandy often with pebbles, from medium dense to dense.
Ag: is formed of alluvial soils consisting mainly of well-graded gravel, sand and pebbles in a mainly silty-clayey matrix with intercalations of sandy silt to clayey silt, mostly sporadic and with a variable thickness.
A: mainly made up of consistent over-consolidated clay or clayey silt, at times with inclusions or intercalations of gravel and sand.
S: Bedrock (flyschoide), formed of marls, argillites, marly and sandy calcareous rock. The rock shows a dense network of discontinuities. In particular, the upper part of the formation is very fractured and weak.
Figure 2. geological profile of the central part of the layout
The geotechnical properties for the numerical analyses are summarized in Table 1.
Table 1. principal geotechnical parameters.
Unit R Ag S
(fractured) normal Thickness [m] 4.70 11.60 4.50 -
γ [kN/m3] 19.5 21.0 23.0 23.0 IP [%] 15.2 17.3 21.5 -
φ [°] 27.8 39.0 43.3 43.3 c’ [kPa] - - - 100 E [MPa] 6.77 175 133 485 G0 [MPa] 2.67 70 104 170
k [m/s] 10-6 10-4 10-7 10-9
In the case of excavation with closed shield, the ground loss is mainly due to two separate mechanisms. Loss occurs at the tunnel heading by an amount that depends essentially on the pressure applied to the tunnel face (VLf); it also occurs by radial displacements of the soil after excavation has taken place, and before the tunnel liner is installed and grouted (VL
r). While the former may vary, depending on the back-pressure applied at the face, the latter remains almost constant, being defined by the geometry of the shield. For a TBM suitable for the case of study, the radial component of ground loss can be estimate to be VL
r= 0.5%. Different values for VL f are chosen in order to take into account the occurrence of unexpected events such as inclusions, or the block of TBM, etc. (Table 2)
Table 2. design ground loss for parametric analysis.
Working level Normal Critical Alert
VLf 0 0.5% 1.0%
VLr
0.5% 0.5% 0.5%
VL 0.5% 1.0% 1.5%
The “normal working level (NWL)” corresponds to an effective advancing of the TBM, while the critical and alert ones denote the attainment of a limiting and ultimate state, respectively.
Extensive multi-stage empirical method have been used for building along the whole layout. For sake of briefness, in the following we refer only to the results obtained in comparison with numerical analysis output.
3.2 Numerical analysis
In order to illustrate the procedure, in the following we refer to the analyses carried out for a part of the layout regarding the historical center of Florence (Fig. 2).
First, finite element (PLAXIS) and Lagrangian finite difference (FLAC) methods have been used to estimate ground movements due to a tunnel in free field condition, and the results have been compared with values obtained by empirical equations or experimental data (Attewell 1978, O’Reilly
&New 1982).
On the basis of the statistical study, it was found that a façade whose geometry is described in Table 3, is well representative of an almost homogeneous set of buildings.
Table 3. representative façade.
L (m) H (m) Openings
percentage Stories
15 15 18% 4
The mechanical properties of the investigate structures denote the presence of two prevailing type of masonry, described in Table 4, in terms of characteristic shear and compressive strenght (τk , σk), and elastic and shear moduli (E, G). All values are in MPa.
Table 4. representative facade.
Masonry type σk τk E G
M1: Multiple leaf masonry 1.5 0.040 264 44
M2: Squared stone masonry 2.0 0.070 462 77
Analysis of the tunneling–structure interaction problem is performed in two stages. The first stage is concerned with the determination of initial stresses in the soil mass prior to the tunnel construction.
It is performed using a calculation considering the self-weight of the soil and after the construction of the structure. Displacements are reset to zero at the end of this stage; consequently, results referred to hereafter are due to the tunnel construction. The second stage deals with the numerical simulation for the excavation of the tunnel in presence of the structure.
4 A comparison of empirical and numerical damage to building assessment Standing the geometry, for each position (A, B, C), and each masonry type (M1 to M3), the interaction analysis has been performed for the values of VL reported in Table 2. The tunnel depth
is kept constant to the minimum value of the project, equal to 9.50m below ground surface, since the settlement trough produced becomes wider and flatter as depth increases, thus reducing the differential settlement and the consequent interaction.
The resulting tensile strain for the facades (Table 5) is compared to critical strain, obtained by empirical method, and the category of damage is then achieved using the relationship after Boscardin & Cording (1989).
The FE and FD Analyses confirm that for VL
0.5 all the representative façades fall in negligible risk category, validating the choice of the excavation technique.
Table 5. representative facade.
Position / masonry
type VL ∆εtens
Category
(Numerical) εcrit
Category (Empirical)
0.5 0.049 0 0.042 0 1 0.168 3 0.284 3 A & M1 1.5 1.368 4 0.426 4 0.5 0.016 0 0.042 0 1 0.060 1 0.284 3 A & M2 1.5 0.229 3 0.426 4 0.5 0.032 0 0.081 1 1 0.042 0 0.467 4 B & M1 1.5 0.081 2 0.701 4 0.5 0.021 0 0.081 1 1 0.047 0 0.467 4 B & M2 1.5 0.082 2 0.701 4 0.5 0.025 0 0.013 0 1 0.118 2 0.027 0 C & M1 1.5 0.157 3 0.040 0 0.5 0.018 0 0.013 0 1 0.014 0 0.027 0 C & M2 1.5 0.068 1 0.040 0
-40 -35 -30 -25 -20 -15 -10 -5 0 5
-30 -25 -20 -15 -10 -5 0 5 10 15 20 25 30
Distance (m)
Settlement (mm)
c=0,5% greenfield c=0,5% parete piena c=0,5% parete finestrata c=1,0% greenfield c=1,0% parete piena c=1,0% parete finestrata c=1,5% greenfield c=1,5% parete piena c=1,5% parete finestrata
Building
-45 -40 -35 -30 -25 -20 -15 -10 -5 0 5
-30 -25 -20 -15 -10 -5 0 5 10 15 20 25 30
Distance (m)
Settlement (mm)
piena c=0,5%
forata c=0,5%
piena c=1,0%
forata c=1,0%
piena c=1,5%
forata c=1,5%
green-field c=0,5%
green-field c=1,0%
green-field c=1,5%
Building
-45 -40 -35 -30 -25 -20 -15 -10 -5 0 5
-30 -20 -10 0 10 20 30
Distance (m)
Settlement (mm)
green-field c=0,5%
piena c=0,5%
forata c=0,5%
green-field c=1,0%
piena c=1,0%
forata c=1,0%
green-field c=1,5%
piena c=1,5%
forata c=1,5%
Building
Figure 3. Settlement profiles for façade of type M1 in positions A, B, and C (VL = 1,5%).
Results show that the stiffness is found to have a strong influence on the damage in the façade: for all the analyses, the type M1 attain a higher category than the type M2. More uniform contact pressures can be observed for the weaker masonry M1. This means that a more flexible structure will experience more serious damage, from the greater differential settlements.
If comparing the results of numerical and empirical model, it can be noted that the latter is not always more conservative than the former. In fact, for position C the numerical outputs denote a higher risk level, while the empirical ones indicate no damage for the structure.
%
-0.100 -0.075 -0.050 -0.025 0.000 0.025 0.050 0.075 0.100 0.125 0.150 0.175 0.200 0.225 0.250 0.275 0.300 0.325 0.350 0.375 0.400
Figure 4. Tensile strain for façade of type M1 in positions A, B, at VL = 1,5%.
5 Conclusions
Within the framework of the ‘feasibility project of the micrometropolitana of Florence’ empirical and numerical methods have been used to estimate the excavation induced effects and the relative risk
of damage to the structures.
The main advantage of the semi-empirical method is the capability to detect the most sensitive buildings to tunnelling in terms of geometry, while nothing can be said about the influence of the actual stiffness of the structure on the settlement trough and the risk level associated to a specific type of masonry.
In most case, interaction analyses predict less damage than applying the greenfield trough to the building. However, when the facade is positioned in the overall hogging area it can be observed to show high tensile strain from the base that can lead to cracks.
It is to note the numerical methods, even using simple model as those described, provide an insight of the local behaviour of the structure, thus allowing from the very beginning the planning of the measures for the mitigation of damage.
In general, although the details of a model of a real structure might be different from the one considered representative, uncoupling the soil and the structural behaviour can lead to an unrealistic assessment of damage.
6 References
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