Author Contributions
Conceptualization, W.H. and Y.Y.; methodology, M.J.; software, Y.Y.; validation, R.P.; formal analysis, Y.Y.; investigation, R.P.; resources, R.P.; writing—original draft preparation, W.H.; writing—review and editing, Y.Y.; visualization, M.J.; supervision, R.P.; project administration, R.P.; funding acquisition, R.P. All authors have read and agreed to the published version of the manuscript.
Figure 1.
Flowchart of the framework of this study.
Figure 1.
Flowchart of the framework of this study.
Figure 2.
The establishment process of source–path–site mechanism.
Figure 2.
The establishment process of source–path–site mechanism.
Figure 3.
Dependent representative point set. (a) Relationship between variables and (b) Relationship between variables and .
Figure 3.
Dependent representative point set. (a) Relationship between variables and (b) Relationship between variables and .
Figure 4.
Schematic diagram of ground motion simulation.
Figure 4.
Schematic diagram of ground motion simulation.
Figure 5.
Four examples of acceleration time history of stochastic earthquake sequences. (a) Sample #1 of acceleration time history of seismic sequence. (b) Sample #2 of acceleration time history of seismic sequence. (c) Sample #3 of acceleration time history of seismic sequence. (d) Sample #4 of acceleration time history of seismic sequence.
Figure 5.
Four examples of acceleration time history of stochastic earthquake sequences. (a) Sample #1 of acceleration time history of seismic sequence. (b) Sample #2 of acceleration time history of seismic sequence. (c) Sample #3 of acceleration time history of seismic sequence. (d) Sample #4 of acceleration time history of seismic sequence.
Figure 6.
Comparison between simulation data and real data of stochastic seismic sequences. (a) Comparison of mean values. (b) Comparison of standard deviation. (c) Comparison of acceleration response spectrum.
Figure 6.
Comparison between simulation data and real data of stochastic seismic sequences. (a) Comparison of mean values. (b) Comparison of standard deviation. (c) Comparison of acceleration response spectrum.
Figure 7.
Sampling points on the projected subspace. (a) Initial independent scattered points. (b) Independent representative point set (Color is only for distinguishing).
Figure 7.
Sampling points on the projected subspace. (a) Initial independent scattered points. (b) Independent representative point set (Color is only for distinguishing).
Figure 8.
Principle of stochastic dynamic analysis. (a) Flowchart of dynamic reliability analyses. (b) Evolution of probability information (Color is only for distinguishing).
Figure 8.
Principle of stochastic dynamic analysis. (a) Flowchart of dynamic reliability analyses. (b) Evolution of probability information (Color is only for distinguishing).
Figure 9.
Nonlinear SDOF dynamic system.
Figure 9.
Nonlinear SDOF dynamic system.
Figure 10.
Restoring force hysteresis loop.
Figure 10.
Restoring force hysteresis loop.
Figure 11.
The PDF of the displacement of SDOF at representative times. (a) PDF at 10 s. (b) PDF at 50 s. (c) PDF at 90 s.
Figure 11.
The PDF of the displacement of SDOF at representative times. (a) PDF at 10 s. (b) PDF at 50 s. (c) PDF at 90 s.
Figure 12.
The CDF of the absorbing condition of displacement.
Figure 12.
The CDF of the absorbing condition of displacement.
Figure 13.
Dynamic reliability of SDOF under various thresholds.
Figure 13.
Dynamic reliability of SDOF under various thresholds.
Figure 14.
Main cross-section of the studied dam (1:1000).
Figure 14.
Main cross-section of the studied dam (1:1000).
Figure 15.
Finite element model of the dam (1:1000) (Different colours represent different material partitions).
Figure 15.
Finite element model of the dam (1:1000) (Different colours represent different material partitions).
Figure 16.
Dynamic response after mainshock of a single sample. (a) Horizontal deformation. (b) Vertical deformation.
Figure 16.
Dynamic response after mainshock of a single sample. (a) Horizontal deformation. (b) Vertical deformation.
Figure 17.
Dynamic response after aftershock of a single sample. (a) Horizontal deformation. (b) Vertical deformation.
Figure 17.
Dynamic response after aftershock of a single sample. (a) Horizontal deformation. (b) Vertical deformation.
Figure 18.
Dynamic response time history of single sample. (a) Horizontal deformation. (b) Vertical deformation.
Figure 18.
Dynamic response time history of single sample. (a) Horizontal deformation. (b) Vertical deformation.
Figure 19.
Comparison of deformation (amplified 30 times).
Figure 19.
Comparison of deformation (amplified 30 times).
Figure 20.
Vertical deformation of 34 groups which .
Figure 20.
Vertical deformation of 34 groups which .
Figure 21.
Mean and standard deviation of dynamic response. (a) Mean of dynamic response. (b) Standard deviation of dynamic response.
Figure 21.
Mean and standard deviation of dynamic response. (a) Mean of dynamic response. (b) Standard deviation of dynamic response.
Figure 22.
PDF surfaces of response at typical times. (a) PDF surface of horizontal displacement at 20–40 s. (b) PDF surface of horizontal displacement at 60–80 s. (c) PDF surface of settlement at 20–40 s. (d) PDF surface of settlement at 60–80 s.
Figure 22.
PDF surfaces of response at typical times. (a) PDF surface of horizontal displacement at 20–40 s. (b) PDF surface of horizontal displacement at 60–80 s. (c) PDF surface of settlement at 20–40 s. (d) PDF surface of settlement at 60–80 s.
Figure 23.
PDF contour map at 60–80 s. (a) PDF contour of horizontal displacement. (b) PDF contour of settlement.
Figure 23.
PDF contour map at 60–80 s. (a) PDF contour of horizontal displacement. (b) PDF contour of settlement.
Figure 24.
PDFs at typical time instants.
Figure 24.
PDFs at typical time instants.
Figure 25.
CDFs at typical time instants.
Figure 25.
CDFs at typical time instants.
Figure 26.
CDF of the absorbing condition of permanent settlement.
Figure 26.
CDF of the absorbing condition of permanent settlement.
Figure 27.
Dynamic reliabilities under various thresholds.
Figure 27.
Dynamic reliabilities under various thresholds.
Figure 28.
Dynamic reliability at threshold = 0.6 m.
Figure 28.
Dynamic reliability at threshold = 0.6 m.
Figure 29.
Reliability and difference at different thresholds.
Figure 29.
Reliability and difference at different thresholds.
Table 1.
Distribution and statistics of seismic characteristics.
Table 1.
Distribution and statistics of seismic characteristics.
Variable | Mainshocks | Aftershocks |
---|
Type | | | Type | | |
---|
| Lognormal | −2.85 | 1.26 | Lognormal | −4.54 | 1.32 |
| Lognormal | −1.75 | 1.24 | Lognormal | −2.15 | 1.71 |
a | Lognormal | 1.32 | 0.56 | Lognormal | 1.83 | 0.49 |
b | Lognormal | 1.89 | 0.55 | Lognormal | 1.95 | 0.50 |
c | Weibull | 1.33 | 1.22 | Weibull | 1.76 | 1.66 |
d | Weibull | 1.23 | 1.20 | Weibull | 1.44 | 1.35 |
Table 2.
Distribution and statistics of site characteristics.
Table 2.
Distribution and statistics of site characteristics.
Variable | Type | | |
---|
| Weibull | 0.49 | 4.674 |
| Weibull | 12.63 | 1.26 |
Table 3.
The best Copula type and parameter.
Table 3.
The best Copula type and parameter.
Best Copula | | | | | | |
---|
| Plackett | Student | Plackett | Clayton | Clayton | Student |
Parameters | | | | | | |
| 20.172 | 0.233 | 4 | 3.199 | 1.330 | 0.523 | 0.212 | 4 |
Table 4.
Errors and calculation time.
Table 4.
Errors and calculation time.
Methods | Sample Size | Errors | Calculation Time (s) |
---|
DPIM | 200 | 0.10% | 4.51 |
MCS | 5 × 104 | - | 1059.04 |
Table 5.
Rockfill parameters for generalized plastic model.
Table 5.
Rockfill parameters for generalized plastic model.
| G0 | K0 | Mg | Mf | | | H0 | HU0 |
---|
2250 | 1130 | 1440 | 1.75 | 1.60 | 0.35 | 0.35 | 1500 | 2000 |
ms | mv | ml | mu | rd | | | | |
0.40 | 0.40 | 0.20 | 0.30 | 180 | 70 | 7 | 35 | 0.038 |
Table 6.
Transition parameters for generalized plastic model.
Table 6.
Transition parameters for generalized plastic model.
| G0 | K0 | Mg | Mf | | | H0 | HU0 |
---|
2365 | 1330 | 1540 | 1.70 | 1.40 | 0.20 | 0.32 | 1000 | 1800 |
ms | mv | ml | mu | rd | | | | |
0.20 | 0.20 | 0.25 | 0.10 | 120 | 50 | 7 | 30 | 0.021 |
Table 7.
Core wall parameters for generalized plastic model.
Table 7.
Core wall parameters for generalized plastic model.
| G0 | K0 | Mg | Mf | | | H0 | HU0 |
---|
2460 | 1000 | 800 | 1.70 | 1.60 | 0.45 | −0.80 | 800 | 2000 |
ms | mv | ml | mu | rd | | | | |
0.50 | 0.50 | 0.10 | 0.20 | 220 | 70 | 7 | 10 | 0.01 |
Table 8.
Parameters for linear-elastic model.
Table 8.
Parameters for linear-elastic model.
Material | | E/(GPa) | |
---|
Bed rock | 2650 | 13 | 0.250 |
Concrete base | 2450 | 30 | 0.167 |
Table 9.
Time when reliability begins to decrease.
Table 9.
Time when reliability begins to decrease.
Thresholds | 0.8 m | 0.7 m | 0.6 m | 0.5 m |
---|
Mainshock | 14.4 s | 12.7 s | 12.0 s | 10.9 s |
Aftershock | 71.7 s | 69.3 s | 66.9 s | 60.8 s |