Seismic performance of bridge piers: caisson vs pile foundations

Soil Dynamics and Earthquake Engineering 130 (2020) 105985

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Seismic performance of bridge piers: caisson vs pile foundations Riccardo Conti a, Raffaele Di Laora b, *, Valeria Licata c, Maria Iovino d, Luca de Sanctis d a

Niccol� o Cusano University, Rome, Italy Universit� a della Campania Luigi Vanvitelli, Department of Engineering, Aversa, Italy c Italian Government Institution for Highways (Anas S.p.A.), Roma, Italy d Universit� a di Napoli Pathenope, Department of Engineering, Napoli, Italy b

A R T I C L E I N F O

A B S T R A C T

Keywords: Seismic performance Soil-structure interaction Bridge pier Kinematic interaction Inertial interaction Foundation impedances Caisson foundation Pile foundation Finite element modelling

This work investigates the role of foundation type and layout on the seismic response of a bridge pier. Reference is made to an Italian case study of a bridge pier to be founded on a well-characterized subsoil. Both a caisson and a 3�3 pile foundation are considered as suitable design options. For each foundation type, three different geometrical layouts satisfying Ultimate Limit State (ULS) checks are analysed. Equivalent-linear ground response analyses are preliminary performed to derive the mobilized soil stiffness and damping ratio. FE analyses of the complete soil-foundation-bridge pier model are then carried out. Results indicate that consideration of SoilStructure Interaction effects strongly reduces the pier acceleration, especially for pile foundations, which allow for a higher dissipation of energy due to radiation damping. Further, the role of foundation type and layout is discussed by separating the kinematic and inertial components of interaction, with reference to both frequency and time domain response. Some considerations about possible simplifying assumptions to account for these effects in routine engineering are finally reported.

1. Introduction Bridge piers in soft soil deposits are usually supported by pile or caisson foundations, characterized by different load transfer mecha­ nisms, which essentially rely on the lateral soil shear stresses in the former case, and also on soil normal stresses at the base in the latter case. This main difference, which affects the overall behaviour and design of the foundation under both static (essentially vertical) and seismic loads, stems from the different length-to-width ratio (i.e. slenderness), which is typically in the range of 0.5–4 for caisson foundations and larger than 8 for piles [1,2]. The seismic performance of multi-span bridges is usually analysed under fixed-base conditions, thus neglecting any possible interaction between the deck-pier system and the underlying soil-foundation sys­ tem. This approach typically leads to an over-estimation of the seismic demand in the bridge and, consequently, to an over-design of both the structure and the foundation [3,4]. As a matter of fact, Soil-Structure Interaction (SSI) can modify sub­ stantially the dynamic response of the bridge pier because of: (i) the change of seismic motion due to kinematic interaction, (ii) the energy dissipation into the soil by radiation and hysteretic damping, (iii) the

lengthening of the fundamental period of the fixed-base model [5,6]. With reference to point (i), the available evidence demonstrates that embedded and deep foundations may reduce substantially the hori­ zontal component of the free-field motion [7–11], even if the kinemat­ ically induced rotation may lead sometimes to an overall increase of the seismic demand in the structure, compared to the case where the change of input motion is not taken into account [12,13]. Not surprisingly, Eurocode 8 Part-5 [14] makes explicit reference to the modification of the foundation input motion of flexibly-supported structures, possibly including an important rocking component. On the other hand, the dissipation of energy into the supporting medium (point (ii)) leads invariably to a reduction of internal forces and displacements in the bridge pier. With this regard, Maravas et al. [15] have shown that the radiation mechanism for piles is entirely different from that for shallow foundations, leading generally to a greater amount of energy dissipation. Finally, the lengthening of the structural period (point (iii)) may be beneficial or detrimental depending on the input motion and the dy­ namic properties of the coupled system [16]. This work is focused on the dynamic behaviour of a single bridge pier founded on either caisson or piled foundations. The main goal is to

* Corresponding author. E-mail addresses: [email protected] (R. Conti), [email protected] (R. Di Laora), [email protected] (V. Licata), maria.iovino@ uniparthenope.it (M. Iovino), [email protected] (L. de Sanctis). https://doi.org/10.1016/j.soildyn.2019.105985 Received 2 August 2019; Received in revised form 18 November 2019; Accepted 21 November 2019 Available online 5 December 2019 0267-7261/© 2019 Elsevier Ltd. All rights reserved.

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interaction between the network of rivers in marine environment as well as manmade interventions. The soil media formed by these complex geological activities are divided into two depositional systems. The lower geological system is associated to the alluvial facies, typically characterized by the presence of sands and silty sands, while the upper system is associated to the deltaic activities, with resulting deposits made of sandy and clayey silts. The shallowest part of the upper system is characterized by the presence of high amounts of organic material, indicating that the geological process was developed in a lagoonal and marshy environment. In order to characterize the mechanical behaviour of the soils, a wide geotechnical investigation campaign was executed, including 25 bore­ holes, 20 piezocone penetration tests (CPTU), 15 vane tests, 20 downhole tests (DH) and 12 Nakamura tests (HVSR). During the campaign, standard laboratory tests were carried out on undisturbed and disturbed soil samples. Moreover, two resonant column tests (RC) were performed to define the dissipative and non-linear properties of the soils. Fig. 1a illustrates the geological setting below the bridge examined in this study. The soil layering is approximately horizontal. From ground surface until 20–25 m there is a layer of very soft clayey silt interbedded with peat layers; then, up to about 30 m, the subsoil consists of alter­ nating layers of silty sands and sandy silt; this last formation is underlain by a unit of clayey silt which extends until the maximum investigated depth. A noteworthy point is that the cone resistance qc is less than 1 MPa in the upper clayey silt. The geotechnical soil model adopted in the analyses is represented in Fig. 1b, while all the physical and mechanical properties assumed for each soil layer are summarised in Table 1. The shear wave velocity data were collected from all the available DH tests, following the criterion proposed by Licata et al. [18]. The resulting VS0 profile matched in a satisfactory way the shear wave velocity coming from HVSR tests, which also suggested that the seismic bedrock is located at a depth of about 100 m from the surface [17].

quantify the change of seismic demand in the bridge pier system due to SSI, depending on type and properties of the foundation system. To this aim, the central piers of a highway multi-span bridge founded on soft soils [17,18] are used as a case study. The response of the coupled soil-foundation-bridge pier model is first examined by means of a complete FE model. Then, foundation impedances and the kinematic-induced modification of the free-field motion are evaluated under separate numerical analyses of the sole soil-foundation system, in order to identify the relative importance of kinematic and inertial interaction for both the caisson and the piled foundations. 2. Case study The case study under investigation refers to a highway multi-span bridge in the Po plain region, Northern Italy, the morphology of which is strictly related to a dense network of rivers and rivulets. Due to the presence of several crossing rivers, the layout of the road foresees many bridges of different length. Fig. 1 shows the longitudinal profile of the main bridge of the highway, together with the soil stratigraphic model reconstructed on the basis of available in situ and laboratory in­ vestigations. The geometrical features of this bridge were defined to satisfy both the flood limits over the riverbed and the minimum requirement for highway gradients. The study presented in this work is referred to the transversal section of the two central piers displayed in Fig. 2, falling in the floodplain of the river bank. 2.1. Subsoil layout and characterization The reconstruction of the buried setting was based on an accurate site investigation carried out in the area of the highway bridge. From a geological point of view, the highway bridge lies on soil deposits belonging to the Holocene period, which are the products of the

Fig. 1. (a) Longitudinal profile of the geological setting underlying the bridge (length scales are not isometric); (b) geotechnical soil model and shear wave velocity profile adopted in the analyses (modified after Licata et al. [17]). 2

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Fig. 2. Section and plan view of the foundations: (a) pile group foundations and (b) circular caisson foundations. Table 1 Geotechnical soil model: physical and mechanical properties of the soil layers (after Licata et al. [17]). Layer

z [m]

γ [kN/ m3]

VS0 [m/s]

cu [kPa]

φ [� ]

PI [%]

OCR

K0

MG CS P CS

0–5 5–14 14–16 16–20 20–24 24–29 29–40 40–60 60–80 80–100 100- …

18 16 12 16 16 18 18 18 18 18 20

125 130 97 170 200 235 250 350 450 500 800

40 50 32 120 120 – 180 290 400 520

23 20 28 20 20 30 22 22 22 22

10 30 50 30 30 5 30 30 30 30

1 1 1 1 1 1 1 1 1 1

0.61 0.66 0.53 0.66 0.66 0.50 0.63 0.63 0.63 0.63

SS CS

Bedrock

Two RC tests were performed on soil samples retrieved from the peat and the clayey silt layers. The experimental data are shown in Fig. 3, in terms of normalized shear modulus, G/G0, and damping ratio, D, curves. For the manmade ground and the silty sand layers, for which no labo­ ratory data were available, the empirical curves proposed by Darendeli [19] were adopted. Finally, the undrained shear strength profile of fine grained soils was defined from available vane and cone penetration tests. Fig. 3. Geotechnical soil model: (a) shear modulus degradation and (b) damping curves (modified after Licata et al. [17]). 3

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2.2. Structural bridge-pier-foundation model

of 10% in a reference life of 100 years, is 0.23g. Seven spectrum-compatible natural seismic inputs recorded on outcropping rock were selected from Italian ITACA [23], and European ESM [24], databases, using REXEL code [25]. They were defined by a preliminary disaggregation of the seismic hazard into selected magnitude and dis­ tance (M ¼ 4.5�6.5, R ¼ 0�30 km), so as to identify the modal con­ tributions to the overall site hazard. Fig. 4 shows the scaled acceleration time histories (a) and the corresponding elastic response spectra (b), together with the average and the soil class ‘A’ target spectra. Table 3 summarizes the main features of the selected signals. One-dimensional seismic site response analyses were carried out to compute both the free-field surface accelerations and the average mobilized soil properties, under the seven design earthquakes. Equiva­ lent linear analyses were performed in the frequency domain and in terms of total stress, using the code Strata (Kottke & Rathje 2009). Fig. 5 shows the main results of the site response analyses, in terms of vertical profiles of: (a) maximum shear strain, γmax; (b) maximum ac­ celeration, amax; mobilized values of (c) shear wave velocity, VS, and (d) damping ratio, D. The results illustrated in Fig. 5a show a progressive increase of the mobilized strain level from the base to the top of the soil column, with a concentration of shear strains within the peat layer, at the depth of 14–16 m. Correspondently, the peat reduces locally the acceleration, from an approximate value of 0.3 g–0.2 g, while the average accelera­ tion increases again up to 0.28 g in the shallower layers (0–5 m). Similar results were also obtained by Bilotta et al. [26] and Scarfone et al. [27] for the subsoil of the Directional Centre of Napoli, characterised by the presence of a soft peaty layer close to the soil surface. Fig. 5c and d il­ lustrates that the higher levels of non-linearity and dissipation are attainted at 25–30 m below surface, in the silty sand layer, and at 5 m depth, at the interface between the made-ground and the clayey silt layers. Fig. 6 shows the transfer functions between surface and outcrop accelerations (a), and the elastic response spectra at 5% damping of the free-field surface accelerations (b). The dotted line in Fig. 6a is the linear amplification function of the soil deposit, i.e. referring to the smallstrain soil properties, while the thick grey line in Fig. 6b is the average elastic spectrum of the applied outcrop signals. As expected, Fig. 6a shows that soil non-linearity reduces the first fundamental frequency of the soil deposit from the value of 1.0 Hz to an average value of about 0.7 Hz. The shifting of the frequency content of the soil deposit towards higher periods is also evident in Fig. 6b.

As illustrated in Fig. 1, the bridge is composed by 10 spans with variable lengths. The two central piers consist in a single hammerhead reinforced concrete column of height Hstr ¼ 11 m and diameter dstr ¼ 3.0 m. The total vertical load transferred by the deck is 16000 kN, while the weights of the pier cap and of the pier are 1400 kN and 1950 kN, respectively. Different design solutions were considered for the foundation sys­ tem, including three 3�3 pile group foundations, capped by a 2 m thick reinforced concrete raft (Fig. 2a) and three hollow cylindrical caissons (Fig. 2b). All the foundations were designed under static loads, in order to guarantee virtually the same ratio Rd/Ed, where Rd and Ed are the design capacity and action, respectively, with reference to the bearing capacity failure mechanism. Specifically, the undrained bearing capac­ ity of the foundations was computed using standard plasticity formulae for both the piles and the caissons [20]. Table 2 summarizes the relevant geometrical properties of the six foundation systems considered in this study, together with the corre­ sponding ratios Rd/Ed. The top of the foundation is always located 6 m below the ground level, due to an excavation foreseen around the pier (Fig. 2). In all the calculations, an equivalent unit weight of γeq ¼ 20 kN/ m3 was adopted for the hollow caissons. 2.3. Analysis methodology The response of the coupled bridge pier-foundation system is eval­ uated in the frequency domain by means of 2D axisymmetric and fully 3D numerical FE analyses. Soil properties are preliminary defined so as to be compatible with the shear strain level mobilized by the propaga­ tion of seismic waves in 1D equivalent linear analyses. The frequencydomain results are then transferred to the time domain by FFT/IFFT algorithms and the seismic response of the pier-deck system under real earthquakes is assessed. The seismic demand in the bridge pier, expressed in terms of both maximum absolute acceleration and maximum displacement of the structural mass relative to the base, is finally compared to that in the fixed base model, to elucidate the importance of SSI for both the foundation types. Foundation impedances and the modification of free-field motion are also evaluated under separate numerical analyses of the sole soilfoundation system, so as to isolate the effect of foundation compliance and kinematic interaction on the seismic demand of the bridge pier. To this end, the coupled model is idealized in the framework of the sub­ structure method [21] and reduced to an equivalent Single Degree Of Freedom (SDOF) structure resting on frequency dependent springs and dashpots.

4. Dynamic FE analysis of the SSI system Soil-Foundation-Structure Interaction analyses were performed via the FE code ANSYS [28]. These analyses allowed to derive the frequency-dependent complex transfer functions relating the motion of the structure and the foundation to the free-field motion at ground surface. For each coupled system, the following set of analyses has been performed:

3. Selection of natural recordings and seismic site response analyses Following the Italian Building code [22], the seismic inputs were selected using a probabilistic seismic hazard approach. The peak ground acceleration, PGA, of the reference site, with a probability of exceedance

(1) A kinematic interaction analysis, where the model involves the soil and the foundation, with their actual properties (including mass density), subjected to a horizontal acceleration gravity field; (2) An inertial interaction analysis, to evaluate the three dynamic impedances of the foundation, where the same model used for the kinematic interaction problem is subjected to forces applied atop the foundation; (3) A complete 3-component interaction analysis, where the whole system is excited by an acceleration gravity field. In this case, the pier is modelled as a cantilever beam with the top free to rotate, which is appropriate for modelling the dynamic response of the pier-deck system in the transversal direction [3].

Table 2 Selected caisson and piled foundations: geometrical properties and static safety factor. d [m]

L [m]

Hraft [m]

Spacing

Rd/Ed

Caissons

6 9 10

13 9 6

– – –

– – –

1.01 1.00 1.02

3�3 pile groups

0.8 1.2 2.0

40 33 29

2.0 2.0 2.0

3d 3d 2.5d

1.03 1.01 1.02

4

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Fig. 4. Selected input earthquakes: (a) acceleration time histories and (b) elastic response spectra at 5% damping (modified after Licata et al. [17])>. Table 3 Selected input earthquakes. ID

Earthquake

Station ID

Comp.

Date

Mw

Fault Mechanism

REPI [km]

EQ1 EQ2 EQ3 EQ4 EQ5 EQ6 EQ7

Bingol Lazio Abruzzo Sicilia-Orientale Mt. Vatnafjoll South Iceland (as) South Iceland South Iceland

ST539 ST143 ST296 ST2487 ST2483 ST2486 ST2486

N–S E-W E-W E-W E-W E-W N–S

01/05/2003 07/05/1984 13/12/1990 25/05/1987 21/06/2000 17/06/2000 17/06/2000

6.3 5.9 5.6 6.0 6.4 6.5 6.5

strike slip normal strike slip oblique strike slip strike slip strike slip

14 22 50 24 6 5 5

Fig. 5. Seismic site response analyses: profiles of maximum shear strain (a) and maximum acceleration (b), together with the maximum mobilized shear wave velocity (c) and damping (d).

4.1. Numerical FE model

equal to 0.25 m up to 40 m from the soil surface, increasing to 0.5 m from 40 m to 60 m and to 1 m from 60 m until the lower boundary set at 100 m. The element width was set at 0.25 m, from the symmetry axis up to the caisson boundary, and then increased up to 2.5 m at the lateral boundary; the latter was set at a very large distance (¼600 m) to allow attenuation of reflected waves even for low values of soil hysteretic damping. Nodes at the base of the model were fixed both in the hori­ zontal and vertical direction, while only vertical displacements were restrained for nodes on the axis of symmetry and on the lateral boundary of the mesh.

For caisson foundations, the original three-dimensional system was reduced to a two-dimensional one, taking advantage of the axisym­ metric geometry and the anti-symmetric load, following the method proposed by Wilson [29]. Four-noded axisymmetric 2D elements were used to model both the soil and the caisson (Fig. 7a). The element size along the vertical direction was selected in order to ensure propagation of the frequencies of interest throughout the soil mass. Given the very low shear modulus of the peat layer, the height of the elements was set 5

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Fig. 6. Seismic site response analyses: (a) surface to bedrock amplification functions and (b) 5% elastic response spectra of surface accelerations.

Fig. 7. Finite Element Analyses: (a) axisymmetric model for caissons and (b) three-dimensional model for piles foundations.

For the pile foundations, a more computationally expensive 3D model with 8-noded brick elements was adopted (Fig. 7b). One fourth of the soil-foundation system was modelled, taking advantage of the dou­ ble geometrical symmetry. Vertical size of the elements was set at 1 m at any depth, while the size in the horizontal plane varies from 1 m, close to the foundation, to 6 m, at the lateral boundaries, located at 100 m from the symmetry axes. Such model still provides quite accurate results, the difference from the ones obtained by the previous 2D densely meshed model being negligible for the frequencies of interest. Nodes at the base were fully restrained, the ones on the symmetry plane X (direction of shaking) – Z (vertical direction) were restrained against displacement along Y, and the nodes laying on the other three boundaries were restrained against displacement along Z. In both models, the height of the pier elements is kept at 0.25 m to ensure accurate modelling of the flexural behaviour, while the pier plan dimensions and Young’s modulus were selected to obtain the same lateral stiffness of the original cylindrical pier. The structural mass at the top of the pier, comprising the deck and the pier cap, was simulated by properly attributing mass density of the top 2 element layers. All materials were modelled using a complex elastic modulus, so as to simulate a constant hysteretic (frequency-independent) damping ratio. The latter was set equal to 5% for the structural elements and variable with depth for soil elements, according to the average mobilized values obtained from 1D site response analyses. The load, consisting of a horizontal acceleration, was applied in the form of a body force imposed to the elements at 1000 frequency values

ranging from 0.24414 to 24.414 Hz. 4.2. Kinematic interaction The kinematic response of the selected foundations is illustrated in Fig. 8 in terms of translational (Iu ¼ uFIM/uff0) and rotational (Iθ ¼ θFIMHstr/Uff0) interaction factors, where uFIM and θFIM are the swaying and rocking components, respectively, of the Foundation Input Motion (FIM), both computed at the top of the foundation. The dashed curve in Fig. 8(a,c) represents the ratio of the free-field horizontal displacement at the excavation level, Uff,z¼6m, over that at soil surface, Uff0. Note that the rotational interaction factor is defined herein using the height of the pier, Hstr, as the scaling length, to allow for a direct comparison between caisson and pile foundations. Moreover, according to this definition, the interaction factor physically represents the ratio between the structural displacement due to the rigid rotation imposed by the FIM and the freefield surface displacement. Two aspects are noteworthy: (1) the translational interaction factor exhibits marginal differences among the analysed foundations. This evidence, which could come in surprise at first sight, is just related to the major effect of free-field soil amplification between the top of the foundation and the ground surface. In other words, although from a general viewpoint the filtering effect strongly depends on the size and type of foundation, in this case the interplay between soil and foundation plays a minor role when compared with the reduction 6

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Fig. 8. Kinematic interaction factors for the horizontal displacement (a, c) and rocking (b, d) of the foundation.

of the free-field motion merely associated to the foundation embedment. (2) The rotational component of the FIM is always negligible in piled foundations, due to the large axial stiffness of piles [12]. On the contrary, caisson rotation can be much larger and increases with slenderness L/d [10,13].

averages the free-field soil motion [11]. As a result, for a given value of d, increasing L will result in a larger rotation due to a larger average free-field shear strain along the caisson length. Similarly, for a given L, decreasing d will clearly provide a larger rotation [10]. This behaviour does not necessarily hold for the inertial interaction phenomenon, where the rotational stiffness of the foundation-soil system is strictly related the portion of soil interacting with the caisson, and generally increases with the total caisson-soil contact area. Consistently, for a given L, a smaller d will result in higher rotational compliance of the foundation, whereas for a given d the caisson length definitely provides a higher stiffness. Therefore, the effect of slenderness on foundation compliance does not follow a general rule. (4) As opposed to the rotational compliance, the swaying (Chh) and swaying-rocking (Chm) components for the three caissons slightly reduce with increasing the ratio L/d. However, this result cannot be generalised, as it strongly depends on the peculiar soil stiffness profile under examination.

4.3. Foundation impedances The impedance functions of the soil-foundation system reflect the effect of foundation compliance and energy dissipation, the latter due to wave scattering from the foundation and hysteretic damping into the soil. Figs. 9 and 10 show, for all the foundation types, the swaying (Chh), rocking (Cmm) and cross swaying-rocking (Chm) components of the complex compliance matrix, i.e. the inverse of the impedance matrix. The reason behind the choice of this alternative representation relates to a more straightforward interpretation of the results reported in the ensuing. By inspection of the graphs, the following conclusions may be drawn:

From the above, it is expected that pile foundations will provide a lower shift in the fundamental frequency of the above structure, espe­ cially for large-diameter piles. The effect of the caisson slenderness on the structural period shift is not straightforward, as increasing L/ d within the three examined cases will provide higher translational and swaying-rocking compliance but lower rotational compliance.

(1) The translational compliance of pile foundations, Chh, is very sensitive to the slenderness ratio L/d (Fig. 9a, d, g). In fact, given that a pile does not exploit its whole length to provide lateral stiffness, large diameter piles are always stiffer even if shorter. (2) In a similar fashion as for the kinematic interaction, piles generally provide higher rotational stiffness as compared to caissons (Fig. 9b, e, h and Fig. 10b, e, h). Moreover, the same conclusion holds for the swaying-rocking compliance of the foundation (Chm), i.e. a force applied at the top of the pile foun­ dation will produce a lower rotation (Fig. 9c, f, i and Fig. 10c, f, i). (3) Contrary to kinematic interaction, squatter caissons result in larger rotations (higher Cmm) (Fig. 10b,e,h). This result reflects the sharp difference between kinematic and inertial interaction, related to the different role played by the foundation length in conjunction with the different nature of the dynamic excitation. In the kinematic interaction phenomenon, the caisson essentially

4.4. Complete SSI analysis The dynamic response of all the pier-foundation systems is shown in Fig. 11 in terms of dimensionless transfer functions, relating the deck (ustr) and foundation (ufnd, θfnd) motion to the free-field motion at sur­ face (uff0). For comparison, Fig. 11a and b also show the transfer func­ tion of the fixed-base structure (i.e. neglecting SSI altogether), characterised by a fundamental frequency f0,FIX ¼ 1.92 Hz. As expected, dynamic SSI induces an increase of both the compliance (f0,SSI < f0,FIX) and damping (DSSI > DFIX) of the system, the latter being 7

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Fig. 9. Compliance functions of the pile foundations: (a, d, g) swaying, (b, e, h) rocking and (c, f, i) coupled swaying-rocking components.

in inverse proportion to the peak values of ustr/uff0 (Fig. 11a and b). The increase in compliance is more evident in caisson foundations (f0,SSI � 1.06 Hz), compared to pile foundations (f0,SSI ¼ 1.15–1.71 Hz), con­ firming that inertial effects are more pronounced in the former cases. Moreover, the higher Chh and Chm and the lower Cmm, obtained for the three caisson configurations with increasing L/d, tend to counterbalance each other and result in almost identical flexible-base fundamental frequency. The reduction in the structural response is more evident in the case of pile foundations. For the case of large diameter piles (d ¼ 1.2–2.0 m), the SSI transfer function of the structure is below the corresponding fixed-base curve in most of the frequency range, thus indicating that SSI is always beneficial for the dynamic response of the pier. This evidence results from two concurrent phenomena, i.e.: (i) the higher capability of the piled foundation to increase the damping of the SSI system and (ii) the negligible rotation induced by the kinematic interaction with the surrounding soil. A further insight into the problem can be obtained by observing the dynamic response of the foundations, which is affected by both inertial and kinematic effects. As shown in Fig. 11b,e, the interaction with the pier is concentrated around the fundamental frequencies of the structure (f0,FIX and f0,SSI), where the rotation is maximum (Fig. 11c,f), while ki­ nematic effects clearly dominate at higher frequencies. Again, the foundation rotation is smaller in the case of pile foundations, due to their higher rotational stiffness and lower coupling between swaying and rocking modes of vibration. It can be also noted that there is a peculiar

frequency, lower than f0,FIX, where the horizontal motion of the foun­ dation is minimized with respect to the free-field one. This has been named in Rovithis et al. [30,31] as the ‘pseudo-natural SSI frequency’ and was later identified by means of centrifuge tests in Hussien et al. [32]. The time domain response of the pier, under the seven design earthquakes, is illustrated synthetically in Figs. 12 and 13, for the caisson and piled foundations, respectively. The figures show the most relevant information from the seismic design viewpoint, i.e. the maximum absolute acceleration (on the left) and the maximum relative displacement at the top of the pier (on the right). Both types of foun­ dation reduce the absolute acceleration transmitted to the pier, with a stronger attenuation for squatter caissons (Fig. 12a–c) and largediameter piles (Fig. 13a–c). This result was partly anticipated by comparing the elastic response spectra of the free field surface acceler­ ations (Fig. 6b) with the fundamental frequencies f0,FIX and f0,SSI, which appear in the descending branch of the average spectrum. Radiation damping and kinematic interaction contribute in reducing further the inertial forces in the pier, even though their individual contribution cannot be isolated by looking at the time domain response of the coupled system. As evident by inspection of Fig. 12a, the above trend holds for all the earthquakes except one (earthquake EQ6 in Table 3), corresponding to which the ascending branch of the acceleration spectrum is located between f0,SSI and f0,FIX and hence SSI induces a larger acceleration atop the pier. As far as the horizontal displacement of the deck relative to the base 8

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Fig. 10. Compliance functions of the caisson foundations: (a, d, g) swaying, (b, e, h) rocking and (c, f, i) coupled swaying-rocking components.

is concerned, this is given by two contributions: (1) the flexural displacement of the pier, induced by the inertial forces in the structure, and (2) the rotation of the foundation due to the compliance of the soilfoundation system. As SSI effects reduce the inertial forces, while introducing the foundation rotation, the final displacement of the deck strictly depends on the relative importance of these two contributions. Specifically, an average increase of 104% (d ¼ 6 m), 63% (d ¼ 9 m) and 56% (d ¼ 10 m), compared to the fixed-base model, was computed for the caisson foundations, while piled foundations were characterised by an increase of 24% (d ¼ 0.8 m) and a reduction of 23% (d ¼ 1.2 m) and 36% (d ¼ 2.0 m). Further insight is gained in Fig. 14, reporting the SSI and the fixedbase transfer functions of the pier, in terms of absolute acceleration, astr/aff0 (Fig. 14a,c) and relative displacement, urel,str/uff0 (Fig. 14b,d), along with the Fourier amplitude acceleration and displacement spectra of the seven free-field surface motions. For pile foundations with d ¼ 1.2 m and 2.0 m, the compliant-base transfer functions are below the fixedbase ones essentially in the whole relevant frequency range, thereby leading to an enhanced seismic performance of the system in terms of both maximum inertia forces and relative displacements. For the other foundations, the SSI transfer functions move towards the low-frequency range, where the Fourier amplitude spectra of the free-field displace­ ments are located, thus resulting in larger relative displacements. Moreover, the acceleration transfer functions are smoothened but move towards higher free-field motion amplitudes, and thereby, in principle, SSI could be either beneficial or detrimental in terms of inertia forces.

However, for the cases under examination the beneficial effect of the smoothened amplification function prevails over the slight increase in the free-field signal amplitudes. 4.5. Relative importance of inertial and kinematic interaction This section provides a deeper understating of the role of SSI on the seismic response of the pier, isolating kinematic from inertial effects and highlighting possible consequences of neglecting one of the two con­ tributions. To this end, five different models have been considered, as outlined in Fig. 15: (1) the compliant-base structure subjected to the FIM (considering both kinematic and inertial interaction); (2) the compliant-base structure subjected to the free-field surface motion (considering inertial and neglecting kinematic interaction); (3) the fixed-base structure subjected to both translational and rotational component of the FIM (neglecting inertial and considering entirely the kinematic interaction); (4) the fixed-base structure subjected to the horizontal component of the FIM (i.e. neglecting inertial interaction and considering partially the kinematic effects); (5) the fixed-base structure subjected to the free-field surface motion, that is neglecting both kinematic and inertial interaction

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Fig. 11. Non-dimensional steady-state transfer functions relating the horizontal displacement of the pier (a, d), the horizontal displacement of the foundation (b, e) and the rotation of the foundation (c, f) to the free field motion at surface.

To separate the different contributions, numerical analyses were carried out by means of a Matlab script considering a SDOF structure resting on impedance functions derived by the FEM analyses. The input motion is either the free-field one, derived by the ground response analysis, or the latter modified by the kinematic interaction factors derived by the FEM analyses. It is worth mentioning that, as the kinematic interaction analyses include the foundation mass in the numerical model, both in the case of caisson and pile foundations, the input motion at foundation level does not match exactly the definition of the FIM adopted in the classical substructure approach. The same consideration applies for the computed values of the impedance functions, which also take into ac­ count the inertial response of the foundation. Nonetheless, the sub­ structure approach can still be applied rigorously in a hybrid form, in which the foundation mass is taken into account in the computation of both the FIM and the impedance functions, and not employed in the model of the compliant-base structure. Moreover, including the foun­ dation mass in the kinematic interaction problem has, at least, two ad­ vantages in the analysis of caisson foundations, as it allows: (i) to isolate clearly the possible strong contribution of the foundation mass on the filtering effect [10]; and (ii) to avoid the issue of how to consider the

inertia of the soil-foundation system when using a lumped-parameters model for evaluating the dynamic interaction of the compliant-base structure see e.g. Refs. [33,34]. The response of the above models is shown in Fig. 16 with reference to a caisson (d ¼ L ¼ 9m) and a pile foundation (d ¼ 1.2m). As far as the caisson foundation is concerned (Fig. 16a), it is noted that for the fixedbase case (systems 3, 4 and 5) considering the filtering effect (system 3) does not alter significantly the pier response as compared to the mere free-field signal (system 5). However, this result stems from the com­ bination of a relevant beneficial effect of the horizontal component of the filtered motion (system 4) and a significant detrimental effect of the rotational component of the FIM. With regard to the compliant-base structures (systems 1 and 2), the natural frequency is severely reduced with respect to system 5 and, most important, the resonant response is much attenuated, due to the addi­ tional energy dissipation associated to radiation of waves in the soil medium. It is also observed that kinematic interaction seems to play a negligible role when the inertial interaction is accounted for. However, although the decrease in the natural frequency of the system leads to weaker filtering effect (see e.g. Fig. 8), still one should expect some difference in the structural response when excited by either the FIM or 10

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Fig. 12. Time domain analyses for the caisson foundations: comparison of the maximum absolute accelerations and maximum relative displacements between the systems with and without SSI.

the free-field signal. The irrelevance of the kinematic interaction is due to the mere coincidence that the beneficial filtering effect of the hori­ zontal motion (Iu < 1) is cancelled out by the detrimental effect – of the same magnitude – provided by the rotational component of FIM. Given that Iu is essentially independent of the caisson size, while Iθ rapidly increases with L/d, neglecting the kinematic interaction altogether will be conservative for squat caissons, but could lead to unconservative results for slender ones. Pile foundations (Fig. 16b) also provide a beneficial effect on the seismic response of the pier due to both kinematic and inertial interac­ tion. Compared to the caisson foundation, the following differences are detected:

(2) kinematic effects are always beneficial due to the limited detri­ mental effect of the kinematic rotation; (3) kinematic effects are as important as the inertial ones, i.e. neglecting one of the two interactions will lead to a conservative error of similar magnitude. Summarising, it may be concluded that SSI effects are more relevant for caisson foundations in terms of increase in structure flexibility, while pile foundations provide higher radiation damping. This is in agreement with the time-domain results reported in the previous section. 5. Simplified modelling for practical SSI applications

(1) the reduction in the natural frequency of the structure is lower, due to the high rotational stiffness, and the reduction in resonant response is higher, due to the higher radiation damping provided by the piles. This behaviour may be explained considering that, due to the high rotational stiffness, the foundation tends to oscillate according to the swaying vibration mode, characterised by larger radiation damping as compared to rocking [35], which is predominant, instead, in the caisson behaviour. This is also consistent with the study of Maravas et al. [15], according to which piles induce larger radiation damping with respect to shallow foundations;

Even though accounting for SSI effects is proven to be mandatory for a rational seismic design of bridge piers, carrying out complex FE ana­ lyses, such as the ones employed in this study, is very demanding for routine engineering. Therefore, a good compromise for practical appli­ cations could be that of modelling SSI using simpler approaches, typi­ cally developed under strong simplifying assumptions. With this regard, the substructure approach still provides a powerful tool for the seismic design of relevant structures, such as bridges. Ac­ cording to this method, the free-field soil response can be evaluated by means of standard ground response analyses using a linear equivalent method. Then, kinematic interaction effects can be assessed using 11

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Fig. 13. Time domain analyses for the piles foundations: comparison of the maximum absolute accelerations and maximum relative displacements between the systems with and without SSI.

simplified formulae available in the literature for the frequencydependent kinematic interaction factors, such as those proposed by Di Laora et al. [12] for rigidly capped pile groups, Iovino et al. [11] for fixed-head piles into inhomogeneous soils and Elsabee and Morray [36] and Conti et al. [10] for embedded foundations. Analogously, inertial interaction effects are taken into account using simplified formulae for the dynamic impedance functions of the soil-foundation system [1,4]. Both set of functions are described by simple expressions only in the case of homogeneous or continuously inhomogeneous soil and when the top of the foundation is located at the ground surface. In order to investigate the accuracy of the above simplifying as­ sumptions, two sets of FE analyses were further performed: (1) neglecting the soil layers above the foundation (i.e. considering a total depth of Z ¼ 94 m for the soil deposit); and (2) retaining this reduced depth, while considering an equivalent homogeneous soil deposit. Clearly, in both cases the top of the foundation results to be virtually located at the ground surface. With regard to the definition of the equivalent homogeneous soil layer, the average soil properties (density, mobilized shear wave velocity and damping) were considered within either the caisson length or up to 10 diameters (roughly the active length) for the pile foundation. The main results are summarised in Fig. 17 for both the caisson (d ¼ 9 m) and the pile (d ¼ 1.2 m) foun­ dation, in terms of: the kinematic interaction factors (a, e) |Iu| and (b, f) | Iθ|, relating the motion atop the foundation to the free-field motion at

surface; (c, g) the transfer functions of the compliant-base structure subjected to the free-field surface motion (system 2 in Fig. 15, consid­ ering only the inertial interaction); and (d, h) the transfer functions of the compliant-base structure subjected to the FIM (system 1 in Fig. 15, considering both kinematic and inertial interaction). Specifically, the results obtained under the two simplifying assumptions are compared with those provided by the reference cases discussed in the previous sections (continuous black lines). For the kinematic interaction problem, neglecting the soil layers above the foundation leads to an overestimation of the horizontal foundation motion (Fig. 17 a,e), while no relevant effects are observed in terms of foundation rocking (Fig. 17 b,f). As discussed before (see x 4.2), this result stems from the reduction of the free-field soil motion between the surface and the depth corresponding to the top of the foundation. On the other hand, the assumption of homogeneous soil deposit does not have remarkable effects on the kinematic interaction factors, as the layered and the homogeneous assumptions lead to similar trends of |Iu| and |Iθ|. In the inertial interaction problem, the presence of the upper soil strata does not alter significantly the foundation impedances and, therefore, the two layered cases do provide comparable results (Fig. 17 c,g). The homogeneous assumption is also proven to be effective for the caisson foundation, while leading to a slightly softer response of the pile foundation. In this respect, it is worth mentioning that the 12

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Soil Dynamics and Earthquake Engineering 130 (2020) 105985

Fig. 14. Comparison between the SSI and fixed-base transfer functions of the pier with the Fourier amplitude spectra of the free-field surface acceleration (a, c) and displacements (b, d).

Fig. 15. Schematic representation of the five systems analysed to evaluate the relative contribution of kinematic and inertial interaction to SSI.

Fig. 16. Non-dimensional steady-state transfer functions considering different contributions of kinematic and inertial interaction (systems 1 to 5): (a) caisson foundation (d ¼ 9 m, L ¼ 9 m) and (b) piles foundation (d ¼ 1.2 m, L ¼ 33 m).

homogenization criterion has been selected, in the case of piles, with the attempt of matching the response of the foundation to lateral loads. This assumption leads necessarily to an underestimation of the foundation

rocking stiffness, given that the axial pile stiffness is strongly affected by the shear modulus of soil layers well below 10 pile diameters. Finally, similar conclusions can be drawn for the whole dynamic 13

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Soil Dynamics and Earthquake Engineering 130 (2020) 105985

Fig. 17. Caisson (d ¼ 9 m, L ¼ 9 m) and piles (d ¼ 1.2 m, L ¼ 33 m) foundation. Comparison of simplified and rigorous modelling of the SSI problem, in terms of: (a, d) Iu; (b, e) Iθ; (c, f) inertial interaction; (d, h) complete dynamic interaction.

interaction problem (Fig. 17 d,h), where the simplified analyses still provide a reasonable prediction of SSI effects, on the conservative side, due to the underestimation of the filtering action exerted by the foundation.

� the consideration of soil-foundation-structure interaction alters significantly the dynamic behaviour of the pier, resulting in a decrease of the natural frequency and an increase of the overall damping; � any layout of caisson and pile foundations, designed to barely satisfy ULS checks for avoiding a bearing capacity failure, leads to a sig­ nificant reduction of pier acceleration; � slender caissons provide a smaller beneficial effect (about 20% reduction of acceleration), as compared to squatty ones (about 40%), due to the higher kinematically-induced rotational component of

6. Conclusions This work focused on the role of foundation type and layout on the seismic performance of a bridge pier, with reference to an Italian case study. The main conclusions may be summarised in the following points: 14

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Soil Dynamics and Earthquake Engineering 130 (2020) 105985

motion. Moreover, displacements are larger and increase with increasing caisson slenderness; pile foundations lead to a higher reduction of the pier acceleration, and reduce displacements, even compared to the fixed-base model. This double beneficial effect is more evident for large-diameter piles and can be attributed to an increase in foundation stiffness and ra­ diation damping; neglecting kinematic effects can be either beneficial or detrimental for caisson foundations, as the beneficial effect of reduction of hor­ izontal motion may be counterbalanced by the detrimental effect of the rotational component of the FIM; on the contrary, kinematic interaction is always beneficial for pile foundations due to the limited rotational compliance; inertial interaction effects dominate over the kinematic ones for caisson foundations; on the contrary, for pile foundations the two components of SSI have similar impact on the pier behaviour; while inertial interaction effects may be assessed by means of simplified assumptions (i.e. considering an equivalent homogeneous soil and neglecting the portion of soil above the foundation) without appreciable loss in accuracy, kinematic effects cannot neglect the change of motion from the foundation level to soil surface. However, even large inaccuracies in deriving the FIM are much smoothened in the overall seismic response of the pier. Rough assumptions and simplifications still lead to conservative results, yet more accurate than the crude fixed-base assumption.

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As a final remark, it is of prominent importance to highlight that while the trends observed in this work keep their general validity, the quantitative conclusions may vary according to the pier layout and soil properties. Author contribution statement Conti: Conceptualization, Supervision, Methodology, Software, Validation, Writing - Original Draft, Writing - Review & Editing. Di Laora: Conceptualization, Supervision, Methodology, Software, Validation, Writing - Original Draft, Writing - Review & Editing. Licata: Conceptualization, Investigation, Resources, Methodology, Software, Validation, Writing - Original Draft, Writing - Review & Editing. Iovino: Methodology, Software, Validation, Writing - Original Draft, Writing - Review & Editing. de Sanctis: Methodology, Validation, Writing - Original Draft, Writing - Review & Editing. Acknowledgment Part of this research was funded by the Department of Civil Protec­ tion through the ReLUIS (University Network of Seismic Engineering Laboratories) Consortium. References [1] Gerolymos N, Gazetas G. Winkler model for lateral response of rigid caisson foundations in linear soil. Soil Dyn Earthq Eng 2006;26(5):347–61. [2] Karapiperis K, Gerolymos N. Combined loading of caisson foundations in cohesive soil: finite element versus Winkler modeling. Comput Geotech 2014;56:100–20. [3] Mylonakis G, Nikolaou A, Gazetas G. Soil–pile–bridge seismic interaction: kinematic and inertial effects. Part I: soft soil. Earthq Eng Struct Dyn 1997;26(3): 337–59. [4] Mylonakis G, Nikolaou S, Gazetas G. Footings under seismic loading: analysis and design issues with emphasis on bridge foundations. Soil Dyn Earthq Eng 2006;26 (9):824–53.

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