# Comparative Experiment and Analysis of a Base-Isolated Structure with Small Aspect Ratio on Multi-Layered Soft Soil Foundation and Rigid Foundation

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Shaking Table Test Design

#### 2.1. Similitude Ratio of SSI System

#### 2.2. Model Structure and Isolation Bearing

#### 2.3. Model Pile Foundation and Model Soil

^{3}and a water content ranging from 8.2% to 9.0%. The middle layer, which is 40 cm thick, is clay with a density of 1933 kg/m

^{3}and a water content ranging from 27.2% to 30.0%. The bottom layer, which is 60 cm thick, is saturated dense sand with a density of 1920 kg/m

^{3}and a water content ranging from 26.2% to 27.0%. This stratified soil constitutes a multi-layered soft soil foundation. The physical and mechanical parameters of the soil layers in the model are shown in Table 3. The preparation of the model soil involves controlling the water content and compactness, with the water sinking method and manual layer filling employed. Prior to the loading tests, the average shear wave velocity of the soil was measured using an SDMT wave velocity tester, and was about 35–40 m/s, indicating that the model soil meets the requirements for simulating flexible foundation tests. The model soil box has a net size of 3.5 m (vibration direction) × 2 m (lateral direction) × 1.7 m (height), with a layered shear deformation soil box configuration developed by the Institute of Geotechnical Engineering of Nanjing Tech University [27]. The model box is constructed with 15 layers of rectangular planar steel frames, with grooves placed between each layer of steel frames to accommodate steel balls that form support points capable of free sliding. This design allows for the generation of horizontal relative deformation between the layers of the model soil box, thus allowing for almost unconstrained shear deformation of the soil. As a result, the reflection of waves from the boundary is greatly reduced, leading to better simulation of soil boundary conditions.

#### 2.4. Measurement Points and Loading Method

## 3. Analysis of Test Results

#### 3.1. Dynamic Characteristics of the Isolated Structure

#### 3.2. Seismic Acceleration Response of Isolated Structures

#### 3.3. Interstory Displacement Response of Isolated Structures

#### 3.4. Hysteresis Curve of Seismic Isolated Structure Lead Rubber Bearing

#### 3.5. Rotational Effects of Foundation and Isolation Layer

_{1}is the horizontal distance between accelerometers V1 and V2, L

_{2}is the horizontal distance between accelerometers V3 and V4. ${\ddot{V}}_{1}~{\ddot{V}}_{4}$ are the vertical peak accelerations recorded by accelerometers V1, V2, V3, and V4.

^{2}, while the PRA of the cap with rigid foundation is very small and can be neglected [22]. This indicates that the softer the foundation soil, the more significant the rotational effect on the isolated structure system’s pile cap.

#### 3.6. Energy-Based Structural Response Analysis

#### 3.6.1. Energy Response Equation of Isolated Structures Considering SSI Effect

#### 3.6.2. Parameters for Calculating Model Energy Dissipation

#### 3.6.3. Energy Dissipation Analysis of Isolated Structures on Rigid Foundations and Multi-Layered Soft Soil Foundations

_{k}(R

_{k}= E

_{K}/E

_{i}), R

_{s}(R

_{s}= E

_{s}/E

_{i}), R

_{c}(R

_{c}= E

_{c}/E

_{i}), and R

_{d}(R

_{d}= E

_{d}/E

_{i}) represent the ratios of kinetic energy, structural deformation energy, damping energy, and energy dissipated by hysteretic behavior of the isolation layer, respectively. The portion of the total energy input to the model system that is converted into kinetic energy and elastic strain energy is not dissipated. The energy dissipation of the model system mainly occurs in the form of damping and hysteretic energy dissipation. A comprehensive analysis of Figure 13, Figure 14 and Figure 15 reveals that the energy dissipation of the isolated structure models on rigid and multi-layered soft soil foundations is not the same and follows certain rules.

- The seismic input energy of isolated structures on rigid foundations is primarily absorbed by the hysteresis energy dissipation (E
_{d}) of the isolation layer, and during the strong seismic motion, the hysteresis energy dissipation of the isolation layer exceeds 0.8. The kinetic energy of the isolated structure is relatively small compared to the energy dissipation of the isolation layer’s hysteresis (R_{k}) and damping (R_{c}). The deformation energy dissipation (R_{s}) of the upper structure of the isolation system is minimal and can be ignored. The energy dissipation distribution of the isolated structure system on a multi-layered soft soil foundation is different from that on a rigid foundation. The hysteresis energy dissipation of the isolation layer (R_{d}) still accounts for a large proportion, but there is a significant change in the kinetic energy of the isolated structure compared to the energy dissipation of the isolation layer’s hysteresis (R_{k}) and damping (R_{c}). The deformation energy dissipation (R_{s}) of the upper structure of the isolation system is relatively small. - The dynamic kinetic energy ratio R
_{k}of an isolated structure on a rigid foundation decreases with increasing PGA of the input seismic motion, while the variation pattern of R_{k}for an isolated structure model system on the multi-layered soft soil foundation is significantly different from that on a rigid foundation, mainly manifested as follows: the dynamic kinetic energy ratio R_{k}of the isolated structure system on the multi-layered soft soil foundation increases with increasing PGA of the El-Centro motion and the Kobe motion, and decreases with increasing PGA of the Nanjing motion. This phenomenon is consistent with the experimental results in Table 5, which show that the ratio of the PRA of the isolation layer to the pile cap increases with increasing PGA of the El-Centro motion and the Kobe motion, while the ratio of the PRA of the isolation layer to the pile cap decreases with increasing PGA of the Nanjing motion. The above analysis indicates that the dynamic kinetic energy ratio R_{k}of the isolated structure model system on the multi-layered soft soil foundation is related to the strength of the isolation layer rotation effect. When the rotation effect of the isolation layer is enhanced, the dynamic kinetic energy ratio R_{k}of the isolated model system increases, while it decreases when the rotation effect of the isolation layer is weakened. - The damping energy ratio R
_{c}of the isolated structure on the multi-layered soft soil foundation is not equivalent to that on the rigid foundation, and it is dependent on the damping ratio of the isolated structure. The damping energy ratio R_{c}of the isolated structure under different input motion ranges from 0.045 to 0.076 on the rigid foundation, whereas it ranges from 0.073 to 0.154 on the multi-layered soft soil foundation. This indicates that the damping energy ratio R_{c}of the isolated structure on the multi-layered soft soil foundation is significantly greater compared to that on the rigid foundation. The main reason for this discrepancy is that the damping ratio of the isolated structure on the multi-layered soft soil foundation increases significantly due to the influence of soil–structure interaction (SSI) effects, resulting in an increase in the damping energy ratio R_{c}of the isolated structure. - The hysteretic deformation energy dissipation ratio R
_{d}of the isolation layer on the multi-layered soft soil foundation is lower than that on the rigid foundation during the strong seismic motion, with values ranging from 0.624 to 0.801 and 0.835 to 0.874, respectively, under different seismic motions. Two factors contribute to this phenomenon. Firstly, the energy response equation of the isolated structure on the multi-layered soft soil foundation differs significantly from that on the rigid foundation, with kinetic energy components that include the translation of the foundation and the rotation of the isolation layer. Experimental results from Section 3.5 demonstrate that the rotational acceleration response of the isolation layer on the multi-layered soft soil foundation is significant (as shown in Table 5), and the kinetic energy of the isolated structure is closely related to the strength of the rotational effect of the isolation layer. Secondly, the SSI effect greatly influences the dynamic characteristics of the isolated structure on the multi-layered soft soil foundation. The damping ratio of the isolation system on the multi-layered soft soil foundation is significantly higher than that on the rigid foundation, resulting in an increase in the damping energy dissipation of the isolated structure. This indirectly reduces the proportion of hysteretic deformation energy dissipation of the isolation layer, which is particularly evident during the strong seismic motion. Therefore, the hysteretic deformation energy dissipation ratio R_{d}of the isolation layer on the multi-layered soft soil foundation is lower than that on the rigid foundation during the strong seismic motion, under a certain total input energy of seismic motion. - The energy dissipation allocation pattern of the isolated structure on the multi-layered soft soil foundation may be the same or opposite to that on the rigid foundation, which depends on the characteristics and peak value of the seismic motion applied. When the El-Centro motion and the Kobe motion are applied on the multi-layered soft soil foundation, the ratio of hysteretic deformation energy dissipation R
_{d}of the isolation layer decreases with the increasing PGA of the input seismic motion, while the corresponding damping energy dissipation ratio R_{c}and kinetic energy ratio R_{k}increase. That is, the greater the peak value of the input seismic motion, the worse the energy dissipation performance of the isolation layer, which is completely opposite to the variation law of R_{d}on the rigid foundation. On the other hand, when the Nanjing motion is applied on the multi-layered soft soil foundation, the R_{d}ratio of hysteretic deformation energy dissipation of the isolation layer increases with the increasing PGA of the seismic motion applied, while the corresponding damping energy dissipation ratio R_{c}and kinetic energy ratio R_{k}decrease. That is, the greater the PGA of the input seismic motion applied, the better the energy dissipation performance of the isolation layer, which is the same as the variation law of R_{d}on the rigid foundation.

## 4. Conclusions

- Due to the SSI effect, the first-order natural frequency of the isolated structure on the multi-layered soft soil foundation is reduced compared to that on the rigid foundation, while the damping ratio is significantly increased compared to that on the rigid foundation. The magnitude of this effect is closely related to the stiffness of the foundation soil and the aspect ratio of the isolated structure.
- On the site of multi-layered soft soil foundation, the SSI effect can either increase or decrease the acceleration response of the isolated structure, depending on the characteristics and peak value of the input earthquake motion.
- The isolated structure system’s pile cap on multi-layered soft soil foundations has significant rotational acceleration response, and the isolation layer has a certain amplification effect on the rotational acceleration response of pile cap.
- The equation has a clear concept, and the energy response analysis of the model test system shows that it effectively reflects the energy distribution law of each part of soil-isolated structure dynamic interaction system.
- Isolated structures on the rigid foundation primarily dissipate energy by the hysteresis deformation energy of the isolation layer, and as the input seismic motion increases, the hysteresis energy ratio of the isolation layer also increases. This indicates that the stronger the seismic motion, the better the isolation efficiency. However, for the isolated structures on the multi-layered soft soil foundation, although the energy dissipation is still mainly by the hysteresis deformation energy of the isolation layer, the hysteresis deformation energy of the isolation layer on the multi-layered soft soil foundation is reduced during strong seismic motion compared to that on the rigid foundation. This indicates that the isolation efficiency of the isolation layer on a soft soil foundation is reduced.
- The effect of SSI on the energy dissipation of isolated structures on the multi-layered soft soil foundation is related to the characteristics and peak values of the seismic motion applied. Under the action of seismic motion with mainly low-frequency components, the SSI effect has a significant impact on the energy dissipation of the isolation layer, leading to a continuous decrease in the hysteresis energy ratio of the isolation layer, an increase in the damping energy ratio and kinetic energy ratio of the isolated structure, and a significant decrease in the seismic isolation efficiency of the isolation layer. On the other hand, under the action of seismic motion with mainly high-frequency components, the SSI effect has a smaller impact on the energy dissipation of the isolated structure system, resulting in a continuous increase in the hysteresis energy ratio of the isolation layer and a decrease in the damping energy ratio and kinetic energy ratio.

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 2.**Lead-rubber isolation bearing model. (

**a**) Geometric dimensions of lead–rubber bearing; (

**b**) appearance of lead–rubber bearing.

**Figure 6.**Original time histories of the earthquake waves used as input motions. (

**a**) El-Centro wave; (

**b**) Kobe wave; (

**c**) Nanjing wave.

**Figure 7.**Fourier spectra of the accelerations used as input motions. (

**a**) El-Centro wave; (

**b**) Kobe wave; (

**c**) Nanjing wave.

**Figure 8.**Comparison of the AMFs of the isolated structure on a multi-layered soft soil foundation and a rigid foundation. (

**a**) El-Centro motion; (

**b**) Kobe motion; (

**c**) Nanjing motion.

**Figure 9.**Comparison of maximal interstory displacements of isolated structure on multi-layered soft soil foundation and rigid foundation. (

**a**) El-Centro motion; (

**b**) Kobe motion; (

**c**) Nanjing motion.

**Figure 10.**Hysteresis curve of lead−rubber bearings on multi-layered soft soil foundation and rigid foundation. (

**a**) El−Centro motion; (

**b**) Kobe motion; (

**c**) Nanjing motion.

**Figure 11.**Calculation model for non-isolated structure with SSI effect. (

**a**) Mechanical model; (

**b**) Multi-particle simplified analysis model.

**Figure 12.**Calculation model for isolated structure with SSI effect. (

**a**) Mechanical model; (

**b**) Multi-particle simplified analysis model.

**Figure 13.**Comparison of energy dissipation distribution for isolated structure models on rigid foundation and multi-layered soft soil foundation when El-Centro motion is applied.

**Figure 14.**Comparison of energy dissipation distribution for isolated structure models on rigid foundation and multi-layered soft soil foundation when Kobe motion is applied.

**Figure 15.**Comparison of energy dissipation distribution for isolated structure models on rigid foundation and multi-layered soft soil foundation when Nanjing motion is applied.

**Figure 16.**Fourier spectra of test point A6 on multi-layered soft soil foundation. (

**a**) El Centro motion; (

**b**) Kobe motion; (

**c**) Nanjing motion.

**Figure 17.**Fourier spectra of test point A12 on multi-layered soft soil foundation. (

**a**) El Centro motion; (

**b**) Kobe motion; (

**c**) Nanjing motion.

Types | Physical Quantity | Similitude Relationship | Similitude Ratio | |
---|---|---|---|---|

Model Structure | Model Foundation | |||

Geometric characteristics | Length, l | ${S}_{l}$ | 1/20 | 1/20 |

Displacement, r | ${S}_{x}={S}_{l}$ | 1/20 | 1/20 | |

Material properties | Elastic modulus, E | ${S}_{E}$ | 1 | 1/4 |

Equivalent density, ρ | ${S}_{\rho}$ | 20 | 1 | |

Mass, m | ${S}_{m}={S}_{\rho}{S}_{l}^{3}$ | 1/400 | 1/8000 | |

Stress, σ | ${S}_{\sigma}={S}_{E}{S}_{\epsilon}^{}$ | 1 | 1/4 | |

Shear modulus, G | ${S}_{G}$ | 1 | 1/4 | |

Dynamic characteristics | Time, t | ${S}_{t}=\sqrt{{S}_{l}/{S}_{a}}$ | 1/4.47 | 1/4.47 |

Frequency, ω | ${S}_{f}=1/{S}_{t}$ | 4.47 | 4.47 | |

Acceleration, a | ${S}_{a}$ | 1 | 1 |

Physical Quantity | Value | Physical Quantity | Value |
---|---|---|---|

Shear modulus of rubber G (N/mm) | 0.6 | First form factor S_{1} | 19.2 |

Bulk modulus of rubber E _{b} (N/mm^{2}) | 1960 | Second form factor S_{2} | 3.48 |

Vertical elastic modulus of rubber E_{0} (N/mm^{2}) | 1.8 | Diameter of pencil lead (mm) | 8 |

Rubber hardness correction factor K | 0.77 | Diameter of bearing (mm) | 100 |

Soil Layer | Thickness (m) | Density, ρ (kg/m ^{3}) | Shear Modulus, G (MPa) | Friction Angle (°) |
---|---|---|---|---|

Top sand layer | 0.3 | 1760 | 11.3 | 27 |

Soft clay | 0.4 | 1933 | 3.91 | 18 |

Bottom sand layer | 0.6 | 1920 | 27.6 | 28 |

Test Sample No. | Loading No. | Seismic Wave | Peak Bedrock Acceleration of the Input Motion (G) |
---|---|---|---|

1 | JTWN1 | White noise | 0.05 |

2 | JTEL1 | El-Centro | 0.05 |

3 | JTNJ1 | Nanjing | 0.05 |

4 | JTKB1 | Kobe | 0.05 |

5 | JTEL2 | El-Centro | 0.15 |

6 | JTNJ2 | Nanjing | 0.15 |

7 | JTKB2 | Kobe | 0.15 |

8 | JTEL3 | El-Centro | 0.3 |

9 | JTNJ3 | Nanjing | 0.3 |

10 | JTKB3 | Kobe | 0.3 |

11 | JTEL4 | El-Centro | 0.5 |

12 | JTKB4 | Kobe | 0.5 |

13 | JTWN2 | White noise | 0.05 |

Test Condition | Type of Foundation | |||
---|---|---|---|---|

Multi-Layered Soft Soil Foundation | Rigid Foundation | |||

Frequency (Hz) | Damping Ratio (%) | Frequency (Hz) | Damping Ratio (%) | |

Before test | 2.4 | 14.8 | 2.65 | 8.3 |

After test | 2.27 | 18.4 | 2.62 | 8.8 |

**Table 6.**Rotational acceleration amplitude of pile cap and isolation layer with multi-layered soft soil foundation.

Input Motion | PGA (g) | ${\mathit{\theta}}_{1,\mathbf{m}\mathbf{a}\mathbf{x}}^{\u2033}$ (rad/s^{−2})
| ${\mathit{\theta}}_{2,\mathbf{m}\mathbf{a}\mathbf{x}}^{\u2033}$ (rad/s^{−2})
| ${\mathit{\theta}}_{2,\mathbf{m}\mathbf{a}\mathbf{x}}^{\u2033}/{\mathit{\theta}}_{1,\mathbf{m}\mathbf{a}\mathbf{x}}^{\u2033}$ |
---|---|---|---|---|

El-Centro | 0.1 | 0.347 | 0.418 | 1.200 |

Nanjing | 0.356 | 0.435 | 1.220 | |

Kobe | 0. 414 | 0. 432 | 1.04 | |

El-Centro | 0.2 | 0.459 | 0.716 | 1.56 |

Nanjing | 0.556 | 0.659 | 1.190 | |

Kobe | 0.810 | 0.980 | 1.210 | |

El-Centro | 0.3 | 1.113 | 1.762 | 1.580 |

Nanjing | 0.940 | 0.920 | 0.980 | |

Kobe | 1.129 | 1.502 | 1.330 |

Horizontal Equivalent Stiffness of Isolation Layer (N/mm) | Equivalent Viscous Damping Ratio of Isolation Layer (%) | Vertical Stiffness of Isolation Layer (N/mm) |
---|---|---|

1111 | 8.3 | 791,600 |

Floor Location | Density (kg) | Stiffness (N/mm) | Story Height (m) |
---|---|---|---|

4 | 800 | 23,040 | 0.5 |

3 | 800 | 23,040 | 0.5 |

2 | 800 | 23,040 | 0.5 |

1 | 800 | 16,000 | 0.6 |

**Table 9.**Analysis of energy dissipation composition of isolated structures on multi-layered soft soil foundation and rigid foundation when El-Centro motion is applied.

Type of Foundation | Actual PGA (g) | Total Input Energy E _{i} (N·m) | Kinetic Energy E_{k} (N·m) | Deformation Energy E _{s} (N·m) | Viscous Damping Energy E_{c} (N·m) | Hysteresis Energy of Isolation Layer E_{d} (N·m) |
---|---|---|---|---|---|---|

Rigid foundation | 0.131 | 15.9 | 1.5 | 0.2 | 1.0 | 13.3 |

0.235 | 55.2 | 4.6 | 0.6 | 2.9 | 47.1 | |

0.344 | 123.6 | 9.0 | 1.0 | 5.6 | 108.0 | |

Multi-layered soft soil foundation | 0.112 | 13.4 | 1.6 | 0.2 | 1.4 | 10.3 |

0.203 | 46.0 | 6.4 | 0.9 | 6.4 | 32.4 | |

0.327 | 127.3 | 25.5 | 2.8 | 19.6 | 79.4 |

**Table 10.**Analysis of energy dissipation composition of isolated structures on multi-layered soft soil foundation and rigid foundation when Kobe motion is applied.

Type of Foundation | Actual PGA (g) | Total Input Energy E _{i} (N·m) | Kinetic Energy E _{k} (N·m) | Deformation Energy E _{s} (N·m) | Viscous Damping Energy E_{c} (N·m) | Hysteresis Energy of Isolation Layer E_{d} (N·m) |
---|---|---|---|---|---|---|

Rigid foundation | 0.094 | 9.3 | 2.2 | 0.1 | 0.9 | 6.1 |

0.187 | 34.4 | 5.4 | 0.6 | 2.7 | 25.8 | |

0.274 | 86.1 | 9.0 | 1.1 | 5.8 | 70.2 | |

Multi-layered soft soil foundation | 0.118 | 16.2 | 1.4 | 0.2 | 1.2 | 13.5 |

0.220 | 60.9 | 6.7 | 1.3 | 6.8 | 46.1 | |

0.390 | 193.3 | 38.9 | 5.0 | 25.3 | 124.1 |

**Table 11.**Analysis of energy dissipation composition of isolated structures on multi-layered soft soil foundation and rigid foundation when Nanjing motion is applied.

Type of Foundation | Actual PGA (g) | Total Input Energy E _{i} (N·m) | Kinetic Energy E _{k} (N·m) | Deformation Energy E _{s} (N·m) | Viscous Damping Energy E_{c} (N·m) | Hysteresis Energy of Isolation Layer E_{d} (N·m) |
---|---|---|---|---|---|---|

Rigid foundation | 0.113 | 14.9 | 1.8 | 0.3 | 1.1 | 11.7 |

0.237 | 79.8 | 7.3 | 1.8 | 4.9 | 65.8 | |

0.321 | 117.7 | 9.8 | 1.6 | 6.7 | 99.6 | |

Multi-layered soft soil foundation | 0.072 | 5.6 | 0.8 | 0.1 | 0.6 | 4.1 |

0.132 | 20.6 | 2.7 | 0.3 | 2.0 | 15.6 | |

0.260 | 84.6 | 8.3 | 0.8 | 7.8 | 67.8 |

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**MDPI and ACS Style**

Yu, X.; Shan, Z.; Zhuang, H.; Chen, G.
Comparative Experiment and Analysis of a Base-Isolated Structure with Small Aspect Ratio on Multi-Layered Soft Soil Foundation and Rigid Foundation. *Sustainability* **2023**, *15*, 8693.
https://doi.org/10.3390/su15118693

**AMA Style**

Yu X, Shan Z, Zhuang H, Chen G.
Comparative Experiment and Analysis of a Base-Isolated Structure with Small Aspect Ratio on Multi-Layered Soft Soil Foundation and Rigid Foundation. *Sustainability*. 2023; 15(11):8693.
https://doi.org/10.3390/su15118693

**Chicago/Turabian Style**

Yu, Xu, Zhicheng Shan, Haiyang Zhuang, and Guoxing Chen.
2023. "Comparative Experiment and Analysis of a Base-Isolated Structure with Small Aspect Ratio on Multi-Layered Soft Soil Foundation and Rigid Foundation" *Sustainability* 15, no. 11: 8693.
https://doi.org/10.3390/su15118693