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There are few systematic studies on the risk probability assessment, although embankment seismic damages are extremely serious. Meanwhile, retaining walls and other retaining structures play positive roles in improving the embankment seismic performance, but relevant quantitative study is rarely reported. In particular, there are few existing studies on the seismic damage characteristics of the embankment fill-soil foundation system and the retaining structure-embankment fill-soil foundation system under different seismic actions. In view of this, the Xi’an-Baoji expressway K1125 + 470 embankment was taken as the research object, the risk probability assessment of the embankment seismic damage was conducted on the basis of the seismic fragility and seismic hazard assessment, the positive role of the retaining wall in improving the embankment seismic performance was verified, and the seismic damage evolution processes of the retaining wall-embankment fill-soil foundation system and the embankment fill-soil foundation system were analyzed. The research results show that the risk probabilities of the severe damage and destruction of the embankment fill-soil foundation system are 29.07% and 7.62% in the next 50 years, while of the retaining wall-embankment fill-soil foundation system are 19.30% and 3.46% and are reduced by 33.61% and 54.60%, respectively. The influence of the retaining wall on the embankment seismic performance mainly occurs at the middle stage of a violent earthquake, but the seismic damages of the retaining wall itself are also very serious, and the engineering disturbance of the retaining wall is reduced greatly or even lost completely at the final stage of the violent earthquake.

Embankment is one of the most common structural forms of highway subgrade [

Due to the increasing in frequencies and losses of earthquakes, researches on the risk probability assessment of the embankment seismic damage have attracted attention from many scholars [

There are few systematic studies on the hazard, fragility, and risk probability assessment, although the embankment seismic damages are extremely serious [

According to the differences in data acquisition and calculation method, the seismic fragility assessment is divided into empirical method and theoretical method [

This method applies computer loading and can select different types and intensities of the seismic ground-motion records, thus completely reflecting the uncertainties of the ground-motions and reducing the influences of the subjective factors on the assessment results.

Seismic damage levels can be output through software, avoiding the errors in judging the seismic damage levels by manual surveys, thus realizing quantitative control of the seismic damage.

Finite difference model of a monomer structure can be established by computer automatically, thus completely reflecting the antiseismic capacity of different structures and realizing accurate study on a monomer structure.

By referencing on Castaldo et al. [

Finite difference model of the embankment fill-soil foundation system.

In modeling the embankment fill-soil foundation system, an elastoplastic constitutive relationship was employed, and the Mohr–Coulomb criterion was used as the yield criterion [^{3} and 1630.00 kg/m^{3}, respectively, elastic modulus was 48.00 MPa and 42.00 MPa, respectively, Poisson’s ratio was 0.34 and 0.36, respectively, bulk modulus was 50.00 MPa and 43.75 MPa, respectively, internal friction angle was 33.00° and 28.00°, respectively, and cohesive force was 34.00 KPa and 31.00 KPa, respectively [

Under the action of the ground acceleration _{max} was selected as the seismic damage parameter, as shown in the following:_{max} is the maximum lateral permanent displacement on the embankment surface and _{max} are as follows: (1) _{max} cannot only characterize the damage to the whole embankment, but also characterize the most vulnerable parts; (2) _{max} can reflect the seismic effect on traffic capacity: the larger the _{max} the more serious seismic damage and, therefore, the lower the traffic capacity. The corresponding relationship between the seismic damage level and _{max} was established on the basis of the displacement damage criterion, as shown in Table

Relationship between the seismic damage level and _{max}.

Seismic damage level | Basically intact | Slight damage | Moderate damage | Severe damage | Destruction |
---|---|---|---|---|---|

_{max} | 0 ≤ _{max} ＜ 0.20 | 0.20 ≤ _{max} ＜ 0.40 | 0.40 ≤ _{max} ＜ 0.80 | 0.80 ≤ _{max} ＜ 1.20 | _{max} ≥ 1.20 |

10 seismic ground-motion records provided by PEER for IDA analysis were selected [_{d}) of these records ranges from 11.7 km to 50.9 km, the magnitude (

Selected seismic ground-motion records.

Sequence number | Earthquake | _{d} | Original PGA (g) | |
---|---|---|---|---|

1 | Kobe_Japan | 49.9 | 6.9 | 0.094 |

2 | Landers | 50.9 | 7.3 | 0.117 |

3 | San Simeon_CA | 38.0 | 6.5 | 0.132 |

4 | Duzce_Turkey | 34.3 | 7.1 | 0.138 |

5 | Chalfont Valley-1 | 16.2 | 6.0 | 0.248 |

6 | Cape Mendocino | 18.5 | 7.1 | 0.385 |

7 | Chalfont Valley-2 | 11.7 | 6.0 | 0.447 |

8 | Cape Mendocino | 13.5 | 7.1 | 0.591 |

9 | Chi-Chi, Taiwan-1 | 26.0 | 7.6 | 0.639 g |

10 | Chi-Chi, Taiwan-2 | 18.8 | 7.6 | 0.724 g |

Due to the limited space, the time-history curves of acceleration of the No. 1–No. 3 seismic ground-motion records are listed in Figure

Time-history curves of acceleration of the No. 1–No. 4 seismic ground-motion records.

The PGA of each record was adjusted to 0.1 g, 0.2 g, 0.3 g, 0.4 g, 0.5 g, 0.6 g, 0.7 g, 0.8 g, 0.9 g, 1.0 g, 1.1 g, and 1.2 g, respectively [

The 120 seismic ground-motion records were input to the finite difference model shown in Figure _{max} of each analysis as well as their mean value and standard deviation was computed, as shown in Table

Dynamic response analysis results.

PGA (g) | _{max} | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Sequence number of the seismic ground-motion records | Mean value | Standard deviation | ||||||||||

No. 1 | No. 2 | No. 3 | No. 4 | No. 5 | No. 6 | No. 7 | No. 8 | No. 9 | No. 10 | |||

0.1 | 0.0795 | 0.0774 | 0.0751 | 0.0695 | 0.0754 | 0.0681 | 0.0622 | 0.0574 | 0.0702 | 0.0635 | 0.0698 | 0.0072 |

0.2 | 0.1579 | 0.1629 | 0.1964 | 0.1854 | 0.1788 | 0.1763 | 0.1844 | 0.1924 | 0.1605 | 0.1864 | 0.1781 | 0.0136 |

0.3 | 0.2549 | 0.2678 | 0.2845 | 0.2789 | 0.2657 | 0.2458 | 0.2987 | 0.2697 | 0.2784 | 0.2567 | 0.2701 | 0.0156 |

0.4 | 0.3568 | 0.3459 | 0.4103 | 0.3746 | 0.4472 | 0.3521 | 0.3854 | 0.4086 | 0.3795 | 0.4187 | 0.3879 | 0.0328 |

0.5 | 0.4983 | 0.4909 | 0.4352 | 0.4651 | 0.5029 | 0.4901 | 0.5418 | 0.5065 | 0.4587 | 0.4952 | 0.4885 | 0.0294 |

0.6 | 0.5868 | 0.5698 | 0.5717 | 0.5329 | 0.5324 | 0.6487 | 0.5349 | 0.6173 | 0.5551 | 0.5837 | 0.5733 | 0.0381 |

0.7 | 0.7964 | 0.7542 | 0.7781 | 0.7045 | 0.7954 | 0.7745 | 0.7542 | 0.7267 | 0.7524 | 0.7854 | 0.7622 | 0.0299 |

0.8 | 0.7534 | 0.8637 | 0.8525 | 0.7201 | 0.7968 | 0.7716 | 0.8055 | 0.7784 | 0.7738 | 0.7719 | 0.7888 | 0.0433 |

0.9 | 0.9027 | 1.0587 | 0.9627 | 0.9984 | 0.9578 | 0.9057 | 0.9254 | 0.9742 | 0.9781 | 1.0485 | 0.9712 | 0.0535 |

1.0 | 1.2694 | 1.1458 | 1.3694 | 1.1129 | 1.2287 | 1.1567 | 1.3042 | 1.1964 | 1.2023 | 1.0894 | 1.2075 | 0.0877 |

1.1 | 1.3695 | 1.3384 | 1.3145 | 1.3075 | 1.2827 | 1.2984 | 1.2645 | 1.3064 | 1.3275 | 1.2287 | 1.3038 | 0.0393 |

1.2 | 1.5843 | 1.4134 | 1.5436 | 1.5756 | 1.5149 | 1.5084 | 1.4371 | 1.6294 | 1.5555 | 1.5156 | 1.5278 | 0.0657 |

Total energy dissipations of the embankment fill-soil foundation system.

The logarithms of the PGA and _{max} were taken according to the dynamic response analysis results of the embankment fill-soil foundation system so as to obtain the probabilistic seismic demand model [

Formula (_{j} refers to the exceeding probability of the embankment seismic damage level _{j} refers to the structural performance level shown in Table _{2} = 0.20 when _{3} = 0.40 when _{4} = 0.80 when _{5} = 1.20 when

Seismic fragility curves of the embankment fill-soil foundation system.

The exceeding probability of each seismic damage level of the embankment fill-soil foundation system was calculated according to Figure

Seismic fragility assessment results of the embankment fill-soil foundation system.

PGA | Exceeding probability | |||
---|---|---|---|---|

Slight damage | Moderate damage | Severe damage | Destruction | |

0.1 | 0.024792 | 0.000404 | 0.000000 | 0.000000 |

0.2 | 0.372665 | 0.043532 | 0.000976 | 0.000005 |

0.3 | 0.736894 | 0.225876 | 0.016226 | 0.001590 |

0.4 | 0.905566 | 0.471158 | 0.072330 | 0.011616 |

0.5 | 0.967225 | 0.675516 | 0.175902 | 0.040752 |

0.6 | 0.988473 | 0.812256 | 0.308519 | 0.094932 |

0.7 | 0.995818 | 0.894475 | 0.446065 | 0.171937 |

0.8 | 0.998425 | 0.941370 | 0.571457 | 0.264071 |

0.9 | 0.999384 | 0.967470 | 0.676721 | 0.362276 |

1.0 | 0.999750 | 0.981867 | 0.760416 | 0.458867 |

1.1 | 0.999895 | 0.989810 | 0.824583 | 0.548568 |

1.2 | 0.999954 | 0.994215 | 0.872583 | 0.628452 |

1.3 | 0.999979 | 0.996678 | 0.907898 | 0.697420 |

1.4 | 0.999990 | 0.998070 | 0.933597 | 0.755594 |

1.5 | 0.999995 | 0.998865 | 0.952167 | 0.803811 |

1.6 | 0.999998 | 0.999325 | 0.965531 | 0.843247 |

1.7 | 0.999999 | 0.999594 | 0.975128 | 0.875180 |

1.8 | 0.999999 | 0.999753 | 0.982016 | 0.900841 |

1.9 | 1.000000 | 0.999848 | 0.986963 | 0.921346 |

2.0 | 1.000000 | 0.999905 | 0.990522 | 0.937663 |

2.1 | 1.000000 | 0.999940 | 0.993087 | 0.950610 |

2.2 | 1.000000 | 0.999962 | 0.994940 | 0.960862 |

2.3 | 1.000000 | 0.999976 | 0.996284 | 0.968971 |

2.4 | 1.000000 | 0.999984 | 0.997260 | 0.975379 |

2.5 | 1.000000 | 0.999990 | 0.997973 | 0.980444 |

2.6 | 1.000000 | 0.999993 | 0.998495 | 0.984448 |

Risk probability of the embankment seismic damage numerically equals the convolution between the seismic hazard of the site and the embankment seismic fragility, that is, the integral of exceeding probabilities of all damage levels under all seismic events in the next _{max} in the next _{max} under any given

Seismic ground-motion distribution model includes the probability distribution model of the site seismic intensity and transformational relationship between the seismic intensity and PGA.

Liu and Zhang [

According to (

Taking the derivative of (

The transformational relationship between the seismic intensity and PGA proposed by Liu and Zhang [

According to (

MATLAB software was used to conduct _{j-} ≤ _{i}) = 1 when _{j-} ≤ _{i} and _{j-} ≤ _{i}) = 0 when _{j-}＞_{i}.

According to the seismic hazard assessment results along the Xi’an-Baoji expressway, PGAs with certain exceeding probabilities in the next 50 years were calculated [

Seismic intensities in the next 50 years.

Exceeding probability (%) | 2 | 10 | 63 |
---|---|---|---|

PGA (g) | 0.3155 | 0.2106 | 0.0851 |

Seismic intensity | 8.293 | 7.705 | 6.385 |

According to Table

Structure form of the retaining wall-embankment fill-soil foundation system.

The solution is

Probability distribution of the seismic intensity of the embankment site in the next 50 years’ embankment.

Taking the derivative of Formula (

Probability density of the seismic intensity of the embankment site in the next 50 years’ embankment.

In consideration of the calculation accuracy and model applicability, the best results can be obtained when the number of simulations is 100000 when the Monte Carlo method is conducted [_{1}, _{2}, _{3}, ……, _{100000} were selected, which indicated the 100000 possibilities of the seismic intensities; besides, the above random numbers complied with the seismic hazard assessment results. After inputting _{1}, _{2}, _{3}, ……, _{100000} to Formula (_{1}, PGA_{2}, PGA_{3}, ……, PGA_{100000} were calculated.

According to Figure _{2}(PGA_{1}), _{2}(PGA_{2}), _{2}(PGA_{3}),…, _{2}(PGA_{100000}) are defined as the exceeding probabilities of the slight damage under the actions of PGA_{1}, PGA_{2}, PGA_{3},…, PGA_{100000}, respectively. The risk probability exceeding the slight damage in the next 50 years _{2,50} was calculated according to Formula (

_{j,50} refers to the risk probability of each seismic damage level in the next 50 years.

Risk probability assessment results.

Seismic damage level | Basically intact | Slight damage (%) | Moderate damage (%) | Severe damage (%) | Destruction (%) |
---|---|---|---|---|---|

Risk probability exceeding each damage level | 100.00 | 98.22 | 68.03 | 29.07 | 7.62 |

Risk probability of each damage level | 1.78 | 30.19 | 38.96 | 21.45 | 7.62 |

In order to verify the positive influences of the retaining wall on the risk probability of the embankment seismic damage, a retaining wall was assumed to be built at the left side of the research object. An isotropic elastic constitutive relationship was used to model the retaining wall, and the mechanical properties were: elastic modulus 3000.00 MPa, Poisson’s ratio 0.17, bulk modulus 1515.15 MPa, shear modulus 1282.05 MPa, and density 2300.00 kg/m^{3} (Yin et al. [

120 dynamic response analysis were conducted on the retaining wall-embankment fill-soil foundation system. The total energy dissipation of each analysis is shown in Figure

Total energy dissipation of the retaining wall-embankment fill-soil foundation system fill-soil foundation system.

Fragility curves of the retaining wall-embankment fill-soil foundation system fill-soil foundation system.

Fragility assessment results of the retaining wall-embankment fill-soil foundation system.

PGA (g) | Exceeding probability | |||
---|---|---|---|---|

Slight damage | Moderate damage | Severe damage | Destruction | |

0.1 | 0.139971 | 0.006817 | 0.000005 | 0.000001 |

0.2 | 0.610763 | 0.134583 | 0.006364 | 0.000480 |

0.3 | 0.859458 | 0.378886 | 0.045066 | 0.006112 |

0.4 | 0.949815 | 0.601322 | 0.129339 | 0.026162 |

0.5 | 0.981304 | 0.756522 | 0.244740 | 0.066540 |

0.6 | 0.992649 | 0.853909 | 0.369587 | 0.126337 |

0.7 | 0.996951 | 0.912481 | 0.487993 | 0.200165 |

0.8 | 0.998671 | 0.947226 | 0.591822 | 0.281397 |

0.9 | 0.999394 | 0.967838 | 0.678544 | 0.364183 |

1.0 | 0.999713 | 0.980153 | 0.748769 | 0.444208 |

1.1 | 0.999859 | 0.987589 | 0.804517 | 0.518719 |

1.2 | 0.999928 | 0.992135 | 0.848216 | 0.586239 |

1.3 | 0.999962 | 0.994950 | 0.882201 | 0.646219 |

1.4 | 0.999980 | 0.996716 | 0.908513 | 0.698721 |

1.5 | 0.999989 | 0.997838 | 0.928839 | 0.744174 |

1.6 | 0.999994 | 0.99856 | 0.944531 | 0.783204 |

1.7 | 0.999996 | 0.99903 | 0.956652 | 0.816515 |

1.8 | 0.999998 | 0.99934 | 0.966029 | 0.844818 |

1.9 | 0.999999 | 0.999547 | 0.973296 | 0.868787 |

2.0 | 0.999999 | 0.999685 | 0.978942 | 0.889042 |

2.1 | 1.000000 | 0.99978 | 0.983341 | 0.906131 |

2.2 | 1.000000 | 0.999844 | 0.986778 | 0.920537 |

2.3 | 1.000000 | 0.999889 | 0.989471 | 0.932676 |

2.4 | 1.000000 | 0.999921 | 0.991589 | 0.942905 |

2.5 | 1.000000 | 0.999943 | 0.993259 | 0.951526 |

2.6 | 1.000000 | 0.999958 | 0.994580 | 0.958797 |

2.7 | 1.000000 | 0.999969 | 0.995629 | 0.964932 |

2.8 | 1.000000 | 0.999977 | 0.996464 | 0.970115 |

2.9 | 1.000000 | 0.999983 | 0.997131 | 0.974497 |

3.0 | 1.000000 | 0.999988 | 0.997665 | 0.978206 |

Risk probability assessment results of the retaining wall-embankment fill-soil foundation system.

Seismic damage level | Basically intact (%) | Slight damage (%) | Moderate damage (%) | Severe damage (%) | Destruction (%) |
---|---|---|---|---|---|

Risk probability exceeding each damage level | 100.00 | 59.37 | 52.79 | 19.30 | 3.46 |

Risk probability of each damage level | 10.63 | 36.58 | 33.49 | 15.84 | 3.46 |

It can be seen that the risk probability of the embankment seismic damage can be significantly reduced through the retaining wall; for example, the risk probabilities of the severe damage and destruction of the retaining wall-embankment fill-soil foundation system are 29.07% and 7.62%, while risk probabilities of the embankment fill-soil foundation system are 19.30% and 3.46% and there is a reduction of 33.61% and 54.60%, respectively.

Figure

Embankment seismic damages. (a) Embankment fill-soil foundation system, PGA = 0.2 g, _{max} = 0.1579, and crack length is 2.38 m. (b) Retaining wall-embankment fill-soil foundation system, PGA = 0.2 g, _{max} = 0.1195, and crack length is 1.92 m. (c) Embankment fill-soil foundation system, PGA = 0.4 g, _{max} = 0.3568, and crack length is 3.71 m. (d) Retaining wall-embankment fill-soil foundation system, PGA = 0.4 g, _{max} = 0.2954, and crack length is 3.08 m. (e) Embankment fill-soil foundation system, PGA = 0.6 g, _{max} = 0.5868, and crack length is 6.49 m. (f) Retaining wall-embankment fill-soil foundation system, PGA = 0.6 g, _{max} = 0.4938, and crack length is 4.18 m. (g) Embankment fill-soil foundation system, PGA = 0.8 g, _{max} = 0.7534, and crack length is 12.86 m. (h) Retaining wall-embankment fill-soil foundation system, PGA = 0.8 g, _{max} = 0.6382, and crack length is 10.34 m. (i) Embankment fill-soil foundation system, PGA = 1.0 g, _{max} = 1.2694, and crack length is 16.32 m. (j) Retaining wall-embankment fill-soil foundation system, PGA = 1.0 g, _{max} = 0.9541, and crack length is 12.21 m. (k) Embankment fill-soil foundation system, PGA = 1.2 g, _{max} = 1.5843, and crack length is 24.84 m. (l) Retaining wall-embankment fill-soil foundation system, PGA = 1.2 g, _{max} = 1.3548, and crack length is 20.33 m.

It can be seen from Figure _{max} is reduced by 18.11% and the crack length is shortened by 21.83% on average. However, the seismic damages of the retaining wall itself are also very serious; especially after a violent earthquake, the engineering disturbance of the retaining wall is reduced greatly or even lost completely.

Figure

Seismic damage evolution processes. (a) Embankment fill-soil foundation system, _{max} = 0.0927, and crack length is 1.24 m. (b) Retaining wall-embankment fill-soil foundation system, _{max} = 0.0854, and crack length is 1.19 m. (c) Embankment fill-soil foundation system, _{max} = 0.3264, and crack length is 5.37 m. (d) Retaining wall-embankment fill-soil foundation system, _{max} = 0.3004, and crack length is 5.12 m. (e) Embankment fill-soil foundation system, _{max} = 0.5846, and crack length is 9.67 m. (f) Retaining wall-embankment fill-soil foundation system, _{max} = 0.4237, and crack length is 7.51 m. (g) Embankment fill-soil foundation system, _{max} = 0.8064, and crack length is 15.85 m. (h) Retaining wall-embankment fill-soil foundation system, _{max} = 0.5932, and crack length is 11.24 m. (i) Embankment fill-soil foundation system, _{max} = 1.2982, and crack length is 20.37 m. (j) Retaining wall-embankment fill-soil foundation system, _{max} = 0.9567, and crack length is 16.58 m. (k) Embankment fill-soil foundation system, _{max} = 1.5843, and crack length is 24.84 m. (l) Retaining wall-embankment fill-soil foundation system, _{max} = 1.3548, and crack length is 20.33 m.

The Xi’an-Baoji expressway K1125 + 470 embankment was taken as the research object, the risk probability assessment of the embankment seismic damage was conducted on the basis of the seismic fragility and seismic hazard assessment, the positive role of the retaining wall in improving the embankment seismic performance was verified, and the seismic damage evolution processes of the retaining wall-embankment fill-soil foundation system and the embankment fill-soil foundation system were analyzed.

The risk probabilities of the severe damage and destruction of the embankment fill-soil foundation system are 29.07% and 7.62% in the next 50 years, while those of the retaining wall-embankment fill-soil foundation system are 19.30% and 3.46% and are reduced by 33.61% and 54.60%, respectively. The influence of the retaining wall on the embankment seismic performance mainly occurs at the middle stage of a violent earthquake, but the seismic damages of the retaining wall itself are also very serious, and the engineering disturbance of the retaining wall is reduced greatly, or even lost completely at the final stage of the violent earthquake.

The research results can be used as the theoretical basis of the embankment antiseismic design, and the proposed risk probability assessment method can also be applied to similar structures. However, some aspects of this paper can be further improved; for example, the study on the dynamic coupling mechanism of the embankment and the seismic ground-motion can continue to be developed in the future.

The data used to support the findings of this study are available from the corresponding author upon request.

The authors declare that they have no conflicts of interest with respect to the research, authorship, and publication of this article.

This research was supported by the National Natural Science Foundation of China (Grant no. 51808327) and Natural Science Foundation of Shandong Province (Grant no. ZR2019PEE016).