1. Background
Structural vulnerability to earthquakes may be significantly reduced by the application of base isolation, as demonstrated since the first studies by Kelly [
1,
2]. However, when isolation technique is applied on structures founded on deformable soil, its benefits may be reduced, as shown in [
3,
4,
5,
6,
7]. Moreover, the role of Soil Structure Interaction (SSI) on base isolation has been assessed by experimental studies [
8]. In this regard, SSI effects has been demonstrated [
9,
10,
11] to consist of two important mechanisms: lengthening the structural periods and increasing the damping of the system. Moreover, [
12] analyzed the interaction between SSI and base isolation (BI) by performing numerical analyses, ref. [
13] studied the multi-story buildings with and without sliders in the cases of ground shock due to tunnel explosions. Spyrakos et al. [
14,
15] investigated the effect of SSI on the response of base-isolated buildings by considering equivalent fixed-base systems. In addition, ref. [
16] assessed the local site conditions of the soil and their effects in the isolated structures.
In addition, since the first contribution by [
17], seismic resilience has been applied as a parameter to assess the seismic performance of buildings. Moreover, ref. [
18] defined resilience as the capacity to reduce the consequences of events, and to recover quickly from a damaged to an operational state. More recently, the resilience-based earthquake design initiative (REDi) rating system proposed a methodology to design resilient structures based on several criteria [
19]. Many applications have been developed from this framework for assessing the seismic resilience of single structural configurations [
20,
21,
22]. In particular, ref. [
23] proposed an integrated approach to assess the seismic resilience of acute-care facilities with fragility functions.
In this background, there are still few contributions that assess the resilience of base isolated configurations. In particular, ref. [
24] proposed a methodology to assess the seismic resilience of conventional and base-isolated steel structures by considering the aspects of sustainability (economic, social and environmental).
However, the assessment of the role of SSI on base isolated buildings by considering a resilience-based approach is still a hole in literature and thus the principal goal of this paper is to propose a framework that may calculate resilience of based-isolated structures founded on deformable soil.
In this regard, numerical simulations are performed with Opensees, enabling to consider the mutual effects of structural properties and soil deformations. In particular, the soil is represented with non-linear hysteretic materials and advanced plasticity models as to assess the mutual effects of BI and soil non-linearity at the same time. The models have been implemented in Opensees that may reproduce soil hysteretic elasto-plastic shear response, foundation impedances, realistic boundary conditions and advanced interface between the soil and the structure. The main objective is to assess these two dynamic mechanisms by investigating the cases where BI becomes detrimental. In particular, isolated structures on rigid soil are compared with the same structural schemes on soil with decreasing deformability showing the effects on the periods and on the damping of the performed systems.
In this regard, historically, ref. [
25] showed that period elongation depends mainly on the so-called structure to soil stiffness ratio (depending on the height and the shear velocity of the flexible layer). Later, ref. [
26] extensively investigated the formulas in ASCE 7-05 for several buildings by considering over 800 fundamental periods. Moreover, ref. [
27] proposed an empirical formula for assessing the fundamental period of reinforced concrete structures by performing 3D numerical simulations of SSI effects. Additionally, ref. [
28] investigated the effects of SSI on several residential RC buildings with different capacity design principles founded on four different soil conditions and applying 20 acceleration records. Other studies, such as refs. [
29,
30] proposed analytical surveys on the effects of SSI in terms of fundamental period and damping ratio. In addition, ref. [
31] considered both experimental and numerical results and ref. [
32] investigated the effects of SSI with a 1/4-scale steel-frame structure by reproducing 34 scenarios under fixed-base and flexible-base conditions. Moreover, the interaction between SSI and BI has been relatively studied in the literature. In this regard, ref. [
12] analyzed the interaction between SSI and BI by performing numerical analyses, ref. [
6] studied the multi-story buildings with and without sliders in the cases of ground shock due to tunnel explosions. Spyrakos et al. [
14,
15] investigated the effect of SSI on the response of base-isolated buildings by considering equivalent fixed-base systems.
This paper aims to overcome the previous literature, by proposing several novelties. (1) The interaction between base isolation (BI) and SSI effects are considered with advanced 3D numerical simulations, to capture the highly non-linear mechanisms between the soil, the foundation, the isolators and the superstructure. (2) The paper proposes a novel framework that consider resilience as the reference parameter. (3) The comparisons of the behaviour of the different configurations may be helpful for code provisions.
The paper is structured with the presentation of the case studies (
Section 2), followed by the definition of the seismic resilience calculation (
Section 3).
Section 4 show the results and their discussion.
3. Resilience Calculation
Assessing the resilience of buildings is fundamental for the community itself, since if residential buildings are damaged in a non-operational way, people cannot stay in their houses and they need to find temporary housing in the same area or move or other areas, creating troubles within or between the communities. The same problem occurs when a business structure of a factory is damaged, there is a need to move shift staff and operations to other locations. In particular, realizing the balance between resilient structures and the necessary services is a duty for civil engineers in order to maintain post-earthquake functionality of communities.
In this paper the traditional formulation by [
17] was used to calculate the seismic resilience of the structural configurations:
where:
t0E is the time of occurrence of the earthquake E,
RT is the repair time (RT) that is necessary to recover the original functionality;
Q(
t) is the recovery function that describes the recovery process necessary to return to the pre-earthquake level of functionality (see
Figure 3).
Figure 3 shows that the formulation depends on several parameters:
- (1)
L = losses (calculated as: L = 1 − Q0, where Q0 is the initial functionality)
- (2)
RT: repair time to return to the original functionality.
These quantities are calculated with the Loss model and the Recovery model, proposed in the next subsections.
3.1. Loss Model
The paper proposes to calculate the losses on the definition of various limit states. In particular, four limit states (slight, moderate, extensive, complete) were selected by the technical literature [
43] and by the previous contribution [
37]. These limit states are based on the calculation of the longitudinal drifts of the structures. In particular, Slight, Moderate, Extensive and Complete damage states correspond with 0.30%, 0.60%, 1.50% and 4.00% (named LS1, LS2, LS3 and LS4), respectively. In correspondence with the exceedance of one LS, a specific value of L was assigned, as shown in
Table 4. For example, if the calculated exceeds LS2, the assigned loss is 0.50, meaning that the functionality of the structure is reduced to a half of its original value.
3.2. Recovery Model
The recovery model is necessary in the calculation of resilience [
17,
44,
45], but may be quite challenging to be realistically defined since it requires sufficient information from previous earthquakes. Analytical formulations are generally assumed and calibrated on the database of previous earthquakes. In this paper, two hypotheses were considered:
- (1)
mobilization time [
46] (that includes building inspection, site preparation, providing engineering services…) was neglected and thus the recovery function starts at the time of occurrence (
t0
E).
- (2)
a linear recovery function was considered, as suggested by [
17], when no sufficient information is available.
These two hypotheses may be considered the principal limitations of the model and may be object of future work.
Then, the calculation of repair time has been proposed in literature by several contributions. In particular, ref. [
47] proposed a RT model consisting of two components: (1) Repair Scheduling and (2) Resource Scheduling. In addition, ref. [
48] proposed a procedure to calculate RT, by considering the worker allocation and repair sequencing procedure. Both these approaches were introduced in order to overcome the well-established FEMA P-58 methodology [
49]. Herein RT was calculated by following the simplified assumption that repair time is proportional with the drift ratio (the ratio between the maximum drift due to the seismic loads (
) and the design drift under static load conditions (
)).
It is worth noting that the coefficient needs to be calibrated in order to represent the conditions that range between the case that the building is not repairable or uneconomical to repair the building (RT equal to replacing time) and the case of minor damage that does not compromise the structural operability (RT = 0).
3.3. Seismic Scenario
The seismic scenario consists of ten input motions selected from the NGA database in order to verify that the mean of the spectrum values of the sets of accelerograms is located between the −10% and +30% of the code-based spectrum, following the Eurocode 8 (2004) prescriptions, by considering the life-safety limit state (return period of 475 years, lat.: 42.333 N, 14.246 E, S = 1.50714, Tb = 0.257 s, Tc = 0.770 s, Td = 2.538, Cc = 2.02847), as shown in
Figure 4.
Table 5 shows the characteristics of the selected input motions in terms of peak ground acceleration (PGA).
4. Results and Discussion
The results of the performed models for the four soil conditions are shown in
Figure 5,
Figure 6,
Figure 7 and
Figure 8 in terms of maximum longitudinal drifts for the considered seismic scenario. The limit states (LS1, LS2, LS3, LS4) are shown with horizontal lines in order to define the occurrence of exceedance. This condition is fundamental to derive the L on the basis of
Table 4. In particular,
Table 6 shows the state limits exceeded (for every configuration) deduced from the results (
Figure 5,
Figure 6,
Figure 7 and
Figure 8). In particular, the columns represent the condition of exceeding the four limit states for the selected models (models B1, B2 and B3 and for the foure soil conditions: F1, F2, F3 and F4).
Table 7 shows the calculation of the losses, while
Table 8 shows the RT resulted from the application of (2) by using a γ equal to 1. It is possible to see how RT increases with the intensities and how it varies for the 3 models. It is worth noticing that soil deformability plays an important role for increasing RT in case of model 1 (fixed case), white its effects are not linear for the other two models. It is also significant to consider that RT values for model 2 (linear model) are bigger than those obtained for model 3, since the role of non-linearity reduce the damage. Therefore, neglecting the non-linear mechanisms that occur in the bearings, is conservative, if compared with model 3, as previously demonstrated in [
13,
50].
Table 9 shows the results in terms of Seismic Resilience (SR), and same observations regarding the dependency on the seismic intensity, the role of soil deformability and non-linear mechanisms of bearings in the quantification of SR.
Figure 9 plots the last line of
Table 9 in order to show the dependency of the SR with the soil deformability (in terms of Vs) for the most intense input motion (RRS) and by comparing the three models. It is worth noting that (1) isolation technique has beneficial effects in increasing the Seismic Resilience of the system (even if RT are bigger) and (2) the value of resilience does not significantly vary for model 1, while the trends for the isolated models differ significantly between each other. In particular, the best performance in terms of resilience seems to occur for model 2 (linear isolation) for deformable soils. However, this outcome is affected by the fact that non-linear mechanisms of the bearings are considered. Therefore, the more realistic model 3 shows that the isolation technique performs well at higher values of Vs (rigid soil). Smaller values of resilience at low intensities for model 3 are due to the interaction between the soil deformability and the isolator, that may become unconservative, as previously demonstrated in [
13,
50].