Dynamic Performance of Soil–Tunnel System under Transverse Sinusoidal Excitations
Abstract
:1. Introduction
2. Test Design
2.1. Prototype of a Site
2.2. Similitude Ratios
2.3. Model Ground
2.4. Refined Lining Ring of Model Tunnel
2.4.1. Stiffness Ratio of Prototype
2.4.2. Stiffness of Model Tunnel
2.4.3. Similarity of Stiffness Ratio and Validation
2.5. Scheme of the Experiment
2.5.1. Preparation of Free-Field Model
2.5.2. Model Tunnel and Its Instrumentation
2.5.3. Input Motions and Testing Cases
3. Fundamental Frequency Responses of Two Model Grounds
4. Response of FF Ground under Sinusoidal Excitation
4.1. Acceleration along Depths
4.1.1. Time Histories
4.1.2. Amplification Coefficients of Acceleration along Depth
4.1.3. Response Spectrum
4.2. Deformation of the Ground
5. Responses of Segmental Tunnel
5.1. Acceleration Responses of the ST Ground
5.1.1. Time Histories
5.1.2. Differences of Amplification of Acceleration along Depth
5.2. Acceleration Responses of Model Tunnel
5.3. Cross-Sectional Deformations of Model Tunnel
5.4. Extension/Closure of Longitudinal Joints of Model Tunnel
5.5. Dynamic Normal Earth Pressures of Model Tunnel
5.6. Dynamic Strain of Segments of Model Tunnel
5.7. Relationship between Sinusoidal Excitations and Maximum Tunnel Responses
6. Summary
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Number | Type of Soil | Thickness (m) | Depth (m) | Weight (kN/m3) | Density (kg/m3) | Shear Velocity (m/s) |
---|---|---|---|---|---|---|
1 | Backfill | 1.8 | 1.8 | 17.0 | 1730 | 137 |
2 | Yellow/gray-yellow silty clay | 7.2 | 9.0 | 18.1 | 1846.94 | 140 |
3 | Gray muddy silty clay | 3.3 | 12.3 | 17.6 | 1795.92 | 133 |
4 | Gray clay | 4.7 | 17.0 | 17.4 | 1775.51 | 161 |
5 | Gray silty clay | 10.0 | 27.0 | 17.8 | 1816.33 | 179 |
6 | Dark green silty clay | 2.8 | 29.8 | 19.6 | 2000.00 | 311 |
7 | Yellow-gray sandy silt with clay | 9.4 | 39.2 | 19.0 | 1938.78 | 289 |
8 | Gray silty fine sand | 2.8 | 42.0 | 18.9 | 1928.57 | 346 |
Physical Quantities | Symbol | Dimensions | Expression | Similarity Ratio (Model/Prototype) |
---|---|---|---|---|
Geometrical dimension | L | 1/15 | ||
Density | M | 1/2.7 | ||
Shear modulus | ML−1T−2 | 1/39.2 | ||
Elastic modulus | ML−1T−2 | 1/39.2 | ||
Acceleration | LT−2 | 1/1 | ||
Time | T | 1/3.92 | ||
Frequency | T−1 | 3.92/1 |
Parameters | Prototype | Model |
---|---|---|
Shear stiffness of grounds (N/mm) | 914,083 | 2926 |
Radial stiffness of linings (N/mm) | 7022 | 23.10 |
Transverse stiffness of linings (N/mm) | 994 | 3.15 |
Stiffness ratio | 920 | 929 |
Types | Accelerometer (Tunnel) | Accelerometer (Soil) | Displacement Gauge | Inductive Displacement Transducer | Earth Pressure Gauge |
---|---|---|---|---|---|
Resolution | 0.1% | <5% | 0.3% | 0.25% | 0.25% |
Range | ±8 g | ±5 g | 0~0.6 mm | 0~10 mm | 0~30 kPa |
Maximum sampling frequency | 570 Hz | 1000 Hz | 1000 Hz | 1000 Hz | 5000 Hz |
Test ID | Input Motions | Frequency (Hz) |
---|---|---|
WN-1 | White noise | 0–50 |
Sin-2 | Sinusoidal Wave | 2 |
Sin-3 | Sinusoidal Wave | 3 |
Sin-6 | Sinusoidal Wave | 6 |
Sin-9 | Sinusoidal Wave | 9 |
Sin-11 | Sinusoidal Wave | 11 |
Sin-14 | Sinusoidal Wave | 14 |
Sin-17 | Sinusoidal Wave | 17 |
WN-2 | White noise | 0–50 |
Model | Test ID | Input Motions | Fundamental Frequency (Hz) | Relative Difference (%) |
---|---|---|---|---|
FF | WN-1 | White noise | 4.99 | 0.81 |
WN-2 | 4.95 | |||
ST | WN-1 | White noise | 5.00 | 1.20 |
WN-2 | 4.94 |
Mode Order | Modal Participating Mass Ratios | Total Ratio |
---|---|---|
n = 1 | 81.1% | 95.0% |
n = 2 | 9.0% | |
n = 3 | 3.2% | |
n = 4 | 1.7% |
Modal Amplitude (Absolute Peak Value) | Frequency of Sinusoidal Excitation | |||||||
---|---|---|---|---|---|---|---|---|
2 Hz | 3 Hz | 6 Hz | 9 Hz | 11 Hz | 14 Hz | 17 Hz | ||
Mode order | 1 | 9.66 | 7.78 | 2.64 | 2.17 | 1.84 | 1.51 | 1.38 |
2 | 2.80 | 1.59 | 0.95 | 0.96 | 0.74 | 0.59 | 0.57 | |
3 | 1.90 | 1.15 | 0.51 | 0.57 | 0.53 | 0.51 | 0.46 | |
4 | 1.45 | 0.83 | 0.50 | 0.44 | 0.40 | 0.39 | 0.31 |
Case | A-Top (g) | A-Bottom (g) | Difference (%) | Phase Difference |
---|---|---|---|---|
Sin-2 | 0.120 | 0.119 | 0.83 | 1/64π |
Sin-3 | 0.210 | 0.158 | 24.76 | 3/64π |
Sin-6 | 0.117 | 0.054 | 53.85 | 3/5π |
Sin-9 | 0.057 | 0.093 | −63.16 | 1π |
Sin-11 | 0.065 | 0.099 | −52.31 | 3/7π |
Sin-14 | 0.113 | 0.150 | −32.74 | 1/3π |
Sin-17 | 0.085 | 0.144 | −69.41 | 1/4π |
Cases | Label | Absolute Maximum (με) | Cases | Label | Absolute Maximum (με) |
---|---|---|---|---|---|
Sin-2 Hz | SW1 | 9.70 | Sin-3 Hz | SW1 | 22.63 |
SW2 | 12.94 | SW2 | 25.88 | ||
SW3 | 11.30 | SW3 | 20.99 | ||
SW4 | 8.91 | SW4 | 13.76 | ||
Sin-6 Hz | SW1 | 12.12 | Sin-9 Hz | SW1 | 7.27 |
SW2 | 12.13 | SW2 | 7.28 | ||
SW3 | 10.49 | SW3 | 4.85 | ||
SW4 | 8.90 | SW4 | 8.09 | ||
Sin-11 Hz | SW1 | 8.89 | Sin-14 Hz | SW1 | 7.27 |
SW2 | 7.28 | SW2 | 5.66 | ||
SW3 | 5.65 | SW3 | 6.46 | ||
SW4 | 6.47 | SW4 | 4.86 | ||
Sin-17 Hz | SW1 | 6.46 | Sin-17 Hz | SW3 | 5.65 |
SW2 | 4.85 | SW4 | 8.09 |
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Zhang, S.; Yuan, Y.; Yang, Y.; Li, C.; Mang, H.A. Dynamic Performance of Soil–Tunnel System under Transverse Sinusoidal Excitations. Appl. Sci. 2021, 11, 5097. https://doi.org/10.3390/app11115097
Zhang S, Yuan Y, Yang Y, Li C, Mang HA. Dynamic Performance of Soil–Tunnel System under Transverse Sinusoidal Excitations. Applied Sciences. 2021; 11(11):5097. https://doi.org/10.3390/app11115097
Chicago/Turabian StyleZhang, Shaohua, Yong Yuan, Yusheng Yang, Chong Li, and Herbert A. Mang. 2021. "Dynamic Performance of Soil–Tunnel System under Transverse Sinusoidal Excitations" Applied Sciences 11, no. 11: 5097. https://doi.org/10.3390/app11115097