# Effects of Soil-Foundation-Interaction on the Seismic Response of a Cooling Tower by 3D-FEM Analysis

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Case Study

#### 2.1. Geology and Seismicity of Area

_{W}= 5.4), it caused deaths, injuries, and widespread damage due to the soft-soil conditions and construction deficiencies [23].

#### 2.2. Geotechnical Soil Properties

- -
- S1: backfill (0.00–2.00 m depth), calcarenites (2.00–2.40 m depth), yellow quartz sand (2.40–2.80 m depth), sandy silty clay (2.80–5.00 m depth), clayey sand (5.00–5.80 m depth), calcarenites (5.80–7.40 m depth), yellow quartz sand (7.40–9.70 m depth), and marly clay (9.70–30.00 m depth).
- -
- S2: backfill (0.00–1.00 m depth), sandy calcarenites and quartz sand (1.00–4.00 m depth), sandy clay (4.00–6.00 m depth), clayey sand (6.00–8.50 m depth), sandy clay (8.50–9.70 m depth), sandy silty clay (9.70–15.50 m depth), and marly clay (15.50–30.00 m depth).
- -
- S3: backfill (0.00–1.00 m depth), calcarenites (1.00–1.40 m depth), calcarenite sands and gravel sand (1.40–2.90 m depth), calcarenites and yellow calcarenite sands (2.90–4.40 m depth), brown silty clayey sand (4.40–8.50 m depth), yellow gravel sand (8.50–10.00 m depth), calcarenites (10.00–10.50 m depth), yellow gravel sand (10.50–12.00 m depth), clayey sand (12.00–12.60 m depth), sandy clay (12.60–13.50 m depth), and marly clay (13.50–30.00 m depth).
- -
- S4: backfill (0.00–3.00 m depth), brown sandy-silty alluvial deposits (3.00–8.00 m depth), sandy alluvial deposits with included volcanic and calcarenite stones (8.00–18.00 m depth), and blue-grey clay (18.00–30.00 m depth).

_{S}values ranged from 160 to 360 m/s. Higher values were reported for depths between 11 and 19 m.

#### 2.3. Petrochemical Facilities

## 3. Model Geometry and Boundary Conditions of Soil

_{0}) and gave indications about the average shear wave velocity and the depth of seismic bedrock. The analysis of the noise measurements using the spectral ratios HVSR (Horizontal to Vertical Spectral Ratio) showed the lowest values of f

_{0}(0.69–1.37 Hz) along the coastal area under consideration (Figure 5). Moreover, the results indicated that the most important geotechnical unit in terms of soil response is the blue clay with an average shear wave velocity of 600 m/s. The same value of V

_{S}is also reported by Tortorici [35]. Finally, the results allowed us to identify the surface that generates the amplifications at the base of the blue-grey clays, which constitutes the seismic bedrock [33,34]. The thickness of the blue-grey clay is equal to 73 m in the studied area [36]. The soil model is shown in Table 3, where V

_{S}values are obtained from D-H tests and from previous considerations. The values of the unit weight have been provided by the laboratory tests. Finally, the water head has been imposed at a depth of 11 m.

_{S}is the shear wave velocity in the soil deposit of thickness H. The fundamental natural frequency of the soil deposit is equal to 1.37 Hz.

_{S,min}is the lowest wave velocity and f

_{max}is the maximum frequency component of the input wave. The number of elements is 308,703.

## 4. Full-Coupled FEM Model

#### 4.1. Mohr-Coulomb Model

#### 4.2. Structural Elements and Loads

_{s}) at a particular point is given by:

_{max}is the equivalent local skin resistance at that point.

_{pile}, is given by:

_{max}is the base resistance and F

_{skin}is the axial skin resistance [46,47].

_{p}= base area of pile, c

_{u}= undrained cohesion at the base of the pile, N

_{c}= bearing capacity factor, assumed to equal 9, and ${\mathsf{\sigma}}_{\mathrm{v}0,\mathrm{p}}$ = vertical total stress at the base of the pile.

_{i}is the local shear stress resistance of the interface, φ

_{i}and c

_{i}are the friction angle and the cohesion of the interface, φ

_{soil}and c

_{soil}are the friction and the cohesion of the correspondent soil layer, R

_{inter}is the strength reduction factor, and σ’

_{n}= (σ’

_{2}+ σ’

_{3})/2 is the normal stress.

_{inter}has been assumed to be 2/3.

_{1}, Young’s modulus in the second axial direction E

_{2}, in-plane shear modulus G

_{12}, out-of-plane shear modulus related to shear deformation over the first direction G

_{13}, out-of-plane shear modulus related to shear deformation over the second direction G

_{23}and Poisson’s ratio ν

_{12}. The material behavior has been considered as orthotropic. Therefore:

^{2}, ν = 0.2, γ = 25kN/m

^{3}).

_{o}, is the empty weight of equipment plus the maximum weight of contents (fluid load) during a normal operation [5]. It has been simulated as a cylindrical column with a total weight of 294 kN.

_{W}= 6.1 struck the Emilia Romagna Region of Italy and a small portion of the Lombardia region caused 27 deaths and considerable damage [52]. The MRN station is located at an epicentral distance of 13 km and is classified as a C site [42]. Therefore, a deconvolution analysis has been performed to obtain the appropriate input motion at the bedrock (PGA = 0.30 g, f

_{p}= 1.93 Hz) (Figure 23).

#### 4.3. Results

_{e,max}= 1.94 g at T = 0.25 s is obtained, while, for the SSI alignment (Figure 26b), the maximum spectral acceleration S

_{e,max}= 1.21 g at T = 0.24 s is found. A second less important period T = 0.58 s can be observed in the SSI condition.

_{e,max}= 1.46 g at T = 0.25 s is obtained for the free-field condition (Figure 26a), while, for the SSI alignment (Figure 26b), the maximum spectral acceleration S

_{e,max}= 1.20 g at T = 0.25 s is found. A second less important period T = 0.05 s can be observed in FF and SSI conditions.

_{e,max}= 0.41 g at T = 0.23 is obtained, while, for the SSI alignment, the maximum spectral acceleration S

_{e,max}= 0.32 g at T = 0.25 is found.

_{FF}(I) = f

_{SSI}(I) = 2.1 Hz and f

_{FF}(II) = f

_{SSI}(II) = 3.7 Hz. Therefore, A(f) peaks move toward greater frequencies in comparison with the fundamental natural frequency of the soil (f

_{0}= 1.37 Hz). These results are due to the higher predominant frequencies of the input motions.

_{STRU,FB}) can computed by the following expression [5]:

_{STRU, SSI}, is equal to 0.95 s (f

_{STRU,SSI}= 1.05 Hz). In this case, a spectral acceleration of 0.65 g has been obtained, according to NTC 2018 [51], while lower values of 0.37 g (FF alignment) and 0.40 g (SSI alignment) have been found from FEM numerical analysis. SSI has beneficial effects because the spectral accelerations are lower than those required for the period of the fixed-base structure.

- (a)
- inertia forces on the superstructure transmitted on the heads of the piles in the form of axial and horizontal forces and moment;
- (b)
- soil deformations arising from the passage of seismic waves, which impose curvatures and, thereby, a lateral strain on the piles along their whole length.

_{1}+ σ

_{2}+ σ

_{3})/3, where σ

_{1}is the largest compressive principal stress and σ

_{3}is the smallest compressive principal stress (σ

_{1}≤ σ

_{2}≤ σ

_{3}). The variation of the stress state in the area close to the pile tips is likely related to a more pronounced interaction effect of the piles in the group with respect to the fixed connection of the top.

## 5. Conclusions

- to better understand the intent behind certain provisions of seismic design codes, so that they can be more properly and uniformly applied to structures and systems typically found in petrochemical facilities;
- to provide background information on technical areas that are related to the seismic evaluation of petrochemical facilities;
- to provide specific guidance to the seismic evaluation of petrochemical facilities;
- to provide practical analytical guidance specifically applicable to petrochemical facilities.

- The FEM analyses show a strong amplification in the last 20 m up to ground level for both Free-Field (FF) and soil-structure interaction (SSI) alignments using the 2012 and 1693 seismic inputs. The 1990 accelerogram induces a larger amplification in the upper 10 m of soil. Moreover, the presence of the structure generates a lower amplification as compared to the free-field condition;
- The influence of the soil-structure interaction is also indicated by reducing the maximum spectral acceleration at the main period of T = 0.25 s. However, a second, less important, period T = 0.58 s, corresponding to a spectral acceleration of 1.0 g, can be observed in the SSI condition using the 1693 seismogram;
- Taking into account the SSI effects, a beneficial effect can be observed. The spectral accelerations obtained when considering the structure resting on the soil are lower than what is required for fixed-base structure’s period;
- The main resulting frequencies for the SSI condition are equal to: f
_{SSI}(I) = 2.1 Hz and f_{SSI}(II) = 3.7 Hz. They are far from the frequency of the structure f_{STRU,SSI}= 1.05 Hz. - The soil amplification factors R derived for SSI and FF alignments using the 1990 and 1693 input motions are greater than the amplification value provided by the Italian Technical Code [51]. Instead, lower values are obtained using the 2012 accelerogram. The comparison between the elastic response spectra obtained by numerical analyses using the 1693 and 2012 seismic inputs and the same provided by NTC 2018 shows that FEM spectral accelerations are lower than those given by NTC 2018 for periods greater that 0.30 s. In particular, for the period of the structure under consideration (T
_{STRU,SSI}= 0.95 s), the spectral acceleration given by NTC 2018 is equal to 0.65 g. - To investigate the effect of the kinematic and inertial interaction on pile bending moments, the distribution of the peak pile bending moments has been studied. It can be observed that the maximum bending moments occur at a depth of about 12.5 m, and it can result in a kinematic interaction effect between the piles and the surrounding soil.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Geological sketch map of the Hyblean Plateau and adjacent fore deep area (After Di Martire et al. [16], modified).

**Figure 2.**Timeline of earthquakes in the city of Augusta (After Locati et al. [17], modified, INGV database).

**Figure 8.**(

**a**) G [MPa] versus γ [%] curves. (

**b**) D [%] versus γ [%] curves (for the S1C1 soil sample).

**Figure 9.**(

**a**) G [MPa] versus γ [%] curves. (

**b**) D [%] versus γ [%] curves (for the S4C1 soil sample).

**Figure 20.**Embedded beam element (After Brinkgreve et al. [45], modified).

**Figure 21.**Seismogram of 1693 scaled to the value of 0.350 g corresponding to a return period of 975 years in the actual Italian seismic code [51].

**Figure 22.**Accelerogram recorded at Sortino during the earthquake on 13 December 1990 [53].

**Figure 25.**Maximum accelerations along SSI and FF alignments: using the 1990, 2012, and 1693 seismic inputs.

**Figure 26.**Comparison between the elastic response spectra obtained by numerical analyses and the same provided by NTC 2018 [51]: (

**a**) FF alignment. (

**b**) SSI alignment.

**Figure 27.**Amplification functions for each seismic input: (

**a**) FF alignment, and (

**b**) SSI alignments.

**Figure 28.**Uniform cylindrical column (After Reference [5], modified).

**Figure 29.**Bending moments along the plate at the end of the dynamic phase using the 1693 seismic input.

**Figure 31.**Kinematic bending of a free-head pile in a two-layer profile (After Castelli et al. [12], modified).

**Figure 32.**Mean total stresses p = (σ

_{1}+ σ

_{2}+ σ

_{3})/3 at the end of the dynamic phase (for the 1693 seismic input), σ

_{1}being the largest compressive principal stress and σ

_{3}being the smallest compressive principal stress (σ

_{1}≤ σ

_{2}≤ σ

_{3}).

N. | Borehole | Name | Depth [m] |
---|---|---|---|

1 | S1 | C1 | 4.50–5.00 |

2 | S1 | C2 | 13.00–13.50 |

3 | S2 | C1 | 11.40–11.90 |

4 | S2 | C2 | 20.00–20.50 |

5 | S3 | C1 | 14.00–14.50 |

6 | S3 | C2 | 20.40–20.90 |

7 | S4 | C1 | 2.00–2.50 |

8 | S4 | C2 | 4.00–4.50 |

9 | S4 | C3 | 18.00–18.50 |

10 | S4 | C4 | 22.00–22.60 |

Samples | γ [kN/m ^{3}] | γ_{s}[kN/m ^{3}] | w_{n}[%] | w_{l}[%] | w_{p}[%] | I_{P}[%] | I_{C} | c’ [kPa] | ϕ‘ [°] | c_{u}[kPa] |
---|---|---|---|---|---|---|---|---|---|---|

S1C1 | 18.44 | 25.12 | 29.27 | 66.18 | 32.20 | 33.99 | 1.09 | - | - | - |

S1C2 | 18.74 | 25.00 | 34.28 | 57.15 | 28.03 | 29.12 | 0.79 | - | - | - |

S2C1 | 18.84 | 25.02 | 31.22 | 66.84 | 30.32 | 36.52 | 0.98 | - | - | - |

S2C2 | 18.64 | 25.11 | 32.71 | 72.33 | 31.05 | 41.28 | 0.96 | - | - | - |

S3C1 | 18.74 | 26.09 | 24.34 | 37.24 | 23.37 | 13.88 | 0.93 | - | - | - |

S3C2 | 18.93 | 25.11 | 31.14 | 59.44 | 24.89 | 34.55 | 0.82 | - | - | - |

S4C1 | 17.9 | 24.5 | 29.3 | 61.7 | 32.2 | 29.5 | 1.1 | - | - | - |

S4C2 | 17.9 | 25.4 | 43.2 | 54.0 | 32.8 | 21.2 | 0.5 | 24 | 21 | 35 |

S4C3 | 18.4 | 24.4 | 32.6 | 69.4 | 38.3 | 31.1 | 1.2 | 58 | 24 | 114 |

S4C4 | 18.7 | 26.5 | 33.7 | 69.5 | 27.9 | 41.6 | 0.9 | 44 | 25 | 159 |

Layers | From [m] | To [m] | Thickness [m] | V_{S} [m/s] | γ [kN/m^{3}] |
---|---|---|---|---|---|

Backfill | 0 | 2.5 | 2.5 | 202 | 17.9 |

Alluvial Deposits | 2.5 | 12 | 9.5 | 222 | 17.9 |

Sandy Clay | 12 | 17 | 5 | 639 | 18.4 |

Blue-Grey Clay | 17 | 90 | 73 | 600 | 18.7 |

Layers | γ [kN/m^{3}] | E [kN/m^{2}] | ν [[–] | φ’ [°] | c’ [kN/m^{2}] | Ψ [°] | V_{p} [m/s] | V_{p}/V_{s} |
---|---|---|---|---|---|---|---|---|

Backfill | 17.9 | 220,099 | 0.478 | 21 | 24 | 0 | 986 | 4.88 |

Alluvial Deposits | 17.9 | 268,089 | 0.490 | 21 | 24 | 0 | 1634 | 7.36 |

Sandy Clay | 18.4 | 2,227,231 | 0.454 | 24 | 58 | 0 | 2203 | 3.45 |

Blue-Grey Clay | 18.7 | 1,990,245 | 0.450 | 25 | 44 | 0 | 1992 | 3.32 |

Parameter | Symbol | Pile Foundation | Unit |
---|---|---|---|

Young’s modulus | E | 32,587,468 | kN/m^{2} |

Unit weight | γ | 25 | kN/m^{3} |

Beam type | - | Massive circular beam | - |

Diameter | D | 0.5 | m |

Axial skin resistance | T_{skin} | Layer dependent | kN/m |

Strength reduction factor | R_{inter} | 0.67 | - |

Base resistance | F_{max} | 1061 | kN |

Parameter | Symbol | Plate Foundation | Unit |
---|---|---|---|

Thickness | d | 1.2 | m |

Unit weight | γ | 25 | kN/m^{3} |

Type of behavior | - | Elastic, orthotropic | - |

Young’s Modulus | E_{1} = E_{2} | 32,587,468 | kN/m^{2} |

Poisson’s ratio | ν_{12} | 0.2 | - |

Shear Modulus | G_{12} = G_{13} = G_{23} | 13,578,111 | kN/m^{2} |

FF, 1990 | SSI, 1990 | FF, 2012 | SSI, 2012 | FF, 1693 | SSI, 1693 | |
---|---|---|---|---|---|---|

PGA_{input} | 0.10 g | 0.10 g | 0.30 g | 0.30 g | 0.35 g | 0.35 g |

PGA_{output} | 0.16 g | 0.14 g | 0.35 g | 0.32 g | 0.52 g | 0.46 g |

R = PGA_{output}/PGA_{input} | 1.60 | 1.40 | 1.17 | 1.07 g | 1.49 | 1.31 |

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## Share and Cite

**MDPI and ACS Style**

Castelli, F.; Grasso, S.; Lentini, V.; Sammito, M.S.V. Effects of Soil-Foundation-Interaction on the Seismic Response of a Cooling Tower by 3D-FEM Analysis. *Geosciences* **2021**, *11*, 200.
https://doi.org/10.3390/geosciences11050200

**AMA Style**

Castelli F, Grasso S, Lentini V, Sammito MSV. Effects of Soil-Foundation-Interaction on the Seismic Response of a Cooling Tower by 3D-FEM Analysis. *Geosciences*. 2021; 11(5):200.
https://doi.org/10.3390/geosciences11050200

**Chicago/Turabian Style**

Castelli, Francesco, Salvatore Grasso, Valentina Lentini, and Maria Stella Vanessa Sammito. 2021. "Effects of Soil-Foundation-Interaction on the Seismic Response of a Cooling Tower by 3D-FEM Analysis" *Geosciences* 11, no. 5: 200.
https://doi.org/10.3390/geosciences11050200