# Durability-Aimed Design Criteria of Cement-Stabilized Loess Subgrade for Railway

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## Abstract

**:**

## 1. Introduction

_{u}as the strength index in China and other countries [7,8,9]. The actual experience of railway departments in China shows that it is safer to choose 7-day saturation strength as the strength of stabilized soil [10]. As for the durability of subgrade, many countries refer to the loss rate of mass or strength after 12 times of wet–dry and freeze–thaw cycling, according to the ASTM (American Society for Testing Material). However, the loss rate of strength after only 5 times of wet–dry and freeze–thaw cycling is used to control the durability of subgrade in China [11], and long-term stability under influences of wet–dry and freeze–thaw cycling is less considered. The strength design criteria of stabilized soil of subgrade bottom and embankment below the subgrade of all grades of the railway are shown in Table 1, which is provided by “Code for Design of Railway Earth Structure” [12].

_{u}] is the strength considering the impact of the environment and train load on the subgrade filling, kPa;

_{u}is the strength without the impact of the environment and train load on the subgrade filling, kPa;

_{dmax}is the maximum dynamic stress of subgrade, kPa;

_{f}is the fatigue reduction coefficient of the subgrade filling under repeated train load;

_{G}is the strength reduction coefficient of the subgrade filling under wet–dry cycling;

_{D}is the strength reduction coefficient of the subgrade filling under freeze–thaw cycling.

_{u}of subgrade filling can be obtained by substituting Equation (2) into Equation (1).

_{dmax}, and the other is η

_{G}and η

_{D}. For dynamic stress, Zhu et al. investigate dynamic compressive stress characteristics and related influencing factors in the permafrost site along Qinghai-Tibet Railway [13]. Yao et al. presented a full vehicle-track-ground coupling model to evaluate the dynamic response of subgrade due to high-speed trains [14]. Wang et al. compared the dynamic responses of the earth structures constructed using stabilized cinders and traditional geomaterials [15]. Ma et al. conducted the dynamic triaxial tests on cement- and lime-improved loess specimens to study the cyclic shear strain threshold and critical dynamic stress [16]. Fang et al. established a new track-multilayer ground model to investigate railway subgrade dynamic responses induced by moving train load [17]. Moreover, dynamic responses of high-speed railway and heavy-haul railway were studied by some scholars [18,19,20,21,22,23,24]. In China, Ye et al. studied the subgrade design indices of improved soil and found that the cumulative deformation rate of stabilized soil was less than 0.5% when the strength of improved soil was 5 times the critical dynamic strength of filling [25]. Based on theoretical calculation and field measurement data, the strength design criteria of filling can be 250 kPa of the top surface of the subgrade bottom and 125 kPa of embankment below the subgrade bottom when the design values of dynamic stress are 50 kPa and 25 kPa, respectively, and the actual design criteria are 416 kPa and 208 kPa because of the differences between field and laboratory, which is basically consistent with Table 1 [26,27,28,29,30,31,32,33,34,35,36].

## 2. Experimental Design

#### 2.1. Materials

#### 2.1.1. Loess

#### 2.1.2. Cement

#### 2.2. Specimens Preparation

#### 2.3. Test Methods

#### 2.3.1. Fatigue Test

#### 2.3.2. Wet-Dry Cycling

_{u}, and the unconfined compressive strength with n times of wet–dry cycling was denoted by q

_{G}.

#### 2.3.3. Freeze-Thaw Cycling

_{u}, and the unconfined compressive strength with n times of freeze–thaw cycling was denoted by q

_{Du}.

## 3. Results and Discussion

#### 3.1. Fatigue Performance of Cement-Stabilized Loess

Cement Dosage, P _{s} (%) | Compaction Level (K) | The Fatigue Life N of Cement-Stabilized Loess Specimens under the Following Stress Levels S (Time) | ||||
---|---|---|---|---|---|---|

0.80 | 0.75 | 0.70 | 0.65 | 0.60 | ||

3 | 0.92 | 239 | 568 | 1326 | 4825 | 8143 |

344 | 782 | 2072 | 6843 | 11,629 | ||

656 | 996 | 2945 | 8848 | 14,401 | ||

897 | 1453 | 4177 | 10,268 | 19,955 | ||

1121 | 1882 | 5584 | 12,851 | 26,785 | ||

0.95 | 416 | 1645 | 4060 | 9061 | 19,320 | |

688 | 3098 | 7345 | 16,453 | 34,396 | ||

935 | 4552 | 8840 | 23,697 | 46,005 | ||

1210 | 6009 | 11,285 | 32,078 | 54,720 | ||

1720 | 7946 | 13,865 | 42,153 | 72,153 | ||

0.97 | 578 | 3177 | 6835 | 13,645 | 51,421 | |

896 | 4945 | 9275 | 22,787 | 76,553 | ||

1427 | 6362 | 12,951 | 30,597 | 85,648 | ||

2166 | 7761 | 15,784 | 35,780 | 100,990 | ||

3439 | 9581 | 17,896 | 49,668 | 121,764 | ||

4 | 0.92 | 389 | 895 | 2846 | 8815 | 10,524 |

536 | 1539 | 3781 | 10,629 | 13,066 | ||

861 | 2262 | 4974 | 13,815 | 17,251 | ||

1062 | 3122 | 5655 | 15,993 | 21,892 | ||

1413 | 4528 | 7523 | 18,651 | 24,145 | ||

0.95 | 575 | 3628 | 7225 | 15,729 | 40,548 | |

906 | 5043 | 9356 | 28,955 | 53,526 | ||

1288 | 6215 | 13,023 | 35,726 | 67,262 | ||

1662 | 8149 | 14,898 | 44,830 | 81,049 | ||

2141 | 9352 | 17,653 | 56,004 | 89,553 | ||

0.97 | 810 | 5682 | 11,617 | 36,299 | 78,219 | |

1621 | 7427 | 18,528 | 54,473 | 90,316 | ||

2577 | 8932 | 26,743 | 60,338 | 99,886 | ||

3705 | 10,055 | 34,622 | 72,455 | 114,190 | ||

5106 | 11,947 | 43,850 | 81,637 | 130,925 | ||

6 | 0.92 | 541 | 1676 | 4571 | 11,259 | 82,150 |

809 | 3587 | 7033 | 18,215 | 101,583 | ||

1168 | 4633 | 9124 | 31,945 | 134,783 | ||

1382 | 5684 | 13,086 | 39,661 | 159,745 | ||

2033 | 7590 | 17,258 | 50,157 | 181,738 | ||

0.95 | 763 | 4781 | 10,273 | 61,235 | 125,681 | |

1256 | 6955 | 15,831 | 97,650 | 165,240 | ||

1864 | 9271 | 20,773 | 116,042 | 228,132 | ||

3295 | 11,352 | 23,896 | 158,123 | 273,185 | ||

4136 | 13,161 | 31,652 | 195,635 | 325,160 | ||

0.97 | 970 | 7195 | 21,453 | 101,887 | 162,293 | |

1954 | 10,862 | 32,612 | 145,064 | 230,919 | ||

2766 | 14,276 | 43,965 | 204,692 | 292,588 | ||

4081 | 21,016 | 51,432 | 287,654 | 345,067 | ||

4852 | 26,422 | 60,100 | 346,950 | 423,740 |

_{f}of cement-stabilized loess could be expressed as:

_{e}is the accumulated times of axle load within the design life.

_{e}is 1.05 ${\times \text{}10}^{8}$ times. The fatigue reduction coefficient k

_{f}of cement-stabilized loess is 0.262 when m

_{0.95}, n

_{0.95}and N

_{e}are substituted into Equation (8). This result is overall consistent with the principle that the critical strength of improved soil is 5 times the dynamic stress [25]. Therefore, the fatigue reduction factor k

_{f}of cement-stabilized loess is 0.26 in this study.

#### 3.2. Strength Reduction under Wet-Dry Cycling

**Table 6.**The 28-day compressive strength test results of cement-stabilized loess under wet–dry cycling.

Cement Dosage, P_{s} (%) | Compaction Level (K) | The Compressive Strength (MPa) of Cement-Stabilized Loess under the Following Cycling N (Time) | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

0 | 1 | 3 | 5 | 7 | 9 | 12 | 15 | 20 | 25 | ||

2 | 0.92 | 1.03 | 0.73 | 0.68 | 0.58 | 0.53 | 0.48 | 0.44 | 0.43 | 0.43 | 0.43 |

0.95 | 1.34 | 1.06 | 0.91 | 0.80 | 0.72 | 0.66 | 0.60 | 0.58 | 0.58 | 0.56 | |

0.97 | 1.65 | 1.32 | 1.14 | 1.01 | 0.91 | 0.83 | 0.76 | 0.73 | 0.73 | 0.71 | |

3 | 0.92 | 1.30 | 1.03 | 0.88 | 0.75 | 0.69 | 0.64 | 0.57 | 0.55 | 0.55 | 0.55 |

0.95 | 1.60 | 1.28 | 1.10 | 0.99 | 0.86 | 0.82 | 0.74 | 0.70 | 0.69 | 0.69 | |

0.97 | 2.03 | 1.68 | 1.44 | 1.28 | 1.12 | 1.08 | 0.95 | 0.89 | 0.89 | 0.89 | |

4 | 0.92 | 1.49 | 1.21 | 1.04 | 0.94 | 0.83 | 0.76 | 0.69 | 0.64 | 0.64 | 0.63 |

0.95 | 1.90 | 1.58 | 1.39 | 1.24 | 1.08 | 0.99 | 0.91 | 0.84 | 0.84 | 0.84 | |

0.97 | 2.26 | 1.90 | 1.74 | 1.56 | 1.29 | 1.24 | 1.11 | 1.02 | 1.01 | 1.01 | |

6 | 0.92 | 2.03 | 1.68 | 1.42 | 1.30 | 1.14 | 1.04 | 0.95 | 0.87 | 0.87 | 0.87 |

0.95 | 2.44 | 2.03 | 1.78 | 1.63 | 1.39 | 1.27 | 1.17 | 1.07 | 1.06 | 1.05 | |

0.97 | 2.80 | 2.38 | 2.18 | 1.96 | 1.62 | 1.60 | 1.34 | 1.26 | 1.25 | 1.25 |

#### 3.3. Strength Reduction under Freeze-Thaw Cycling

_{Du}is the compressive strength of specimens after N times of freeze–thaw cycling;

_{u}is the compressive strength of specimens before freeze–thaw cycling.

**Table 7.**The 28-day compressive strength test results of cement-stabilized loess under freeze–thaw cycling.

Cement Dosage, P_{s} (%) | Compaction Level (K) | The Compressive Strength (MPa) of Cement-Stabilized Loess under the Following Cycling N (Time) | ||||||||
---|---|---|---|---|---|---|---|---|---|---|

0 | 1 | 3 | 5 | 7 | 9 | 12 | 15 | 20 | ||

2 | 0.92 | 1.03 | 0.71 | 0.61 | 0.46 | 0.31 | 0.24 | - | - | - |

0.95 | 1.34 | 0.96 | 0.81 | 0.62 | 0.43 | 0.29 | - | - | - | |

0.97 | 1.65 | 1.22 | 1.01 | 0.80 | 0.57 | 0.39 | - | - | - | |

3 | 0.92 | 1.30 | 0.95 | 0.81 | 0.64 | 0.49 | 0.42 | 0.39 | 0.37 | 0.37 |

0.95 | 1.60 | 1.19 | 1.04 | 0.81 | 0.71 | 0.64 | 0.60 | 0.58 | 0.57 | |

0.97 | 2.03 | 1.53 | 1.32 | 1.05 | 0.93 | 0.84 | 0.78 | 0.75 | 0.75 | |

4 | 0.92 | 1.49 | 1.13 | 0.98 | 0.76 | 0.64 | 0.58 | 0.53 | 0.52 | 0.52 |

0.95 | 1.90 | 1.44 | 1.28 | 1.02 | 0.90 | 0.83 | 0.77 | 0.75 | 0.74 | |

0.97 | 2.26 | 1.76 | 1.55 | 1.30 | 1.11 | 1.02 | 0.96 | 0.93 | 0.93 | |

6 | 0.92 | 2.03 | 1.56 | 1.37 | 1.05 | 0.91 | 0.83 | 0.76 | 0.74 | 0.74 |

0.95 | 2.44 | 1.89 | 1.61 | 1.32 | 1.16 | 1.05 | 0.99 | 0.98 | 0.98 | |

0.97 | 2.80 | 2.18 | 1.87 | 1.59 | 1.38 | 1.23 | 1.16 | 1.14 | 1.14 |

## 4. The Design Criteria Aiming at Subgrade Durability

#### 4.1. Determination of Dynamic Stress

_{dmax}transferred to filling through the subgrade bed under the train load must be less than the allowable strength of filling.

_{max}of subgrade surface was given in “Code for Design of Intercity Railway” [69] and “Code for Design of High Speed Railway” [70]. In addition to the criteria, some scholars calculated the dynamic stress by finite element simulation [31,32]. It was found that the calculated values are in good agreement with the measured values. It can verify the possibility of finite element analysis. The measured and theoretical data showed that the dynamic stress of the subgrade decreases rapidly with depth [26,27,28,29,30,31,32,33,34,35,36]. As for the reduction law of dynamic stress along the depth, it can be known that the calculated value of dynamic stress of subgrade is generally greater than the measured value according to the above research results. Based on the existing research results, it was determined that the dynamic stress of the subgrade bottom is 20–50 kPa, and the dynamic stress of embankment below the subgrade bottom is 10–25 kPa under a certain guaranteed rate.

_{d}] using foundation coefficient K

_{30}or critical static strength [σ

_{0}] was obtained [32] by analyzing the field data of subgrade of Da-Qin Line, which is shown in Equation (13) and Table 8. It can be seen that the calculated value is basically consistent with the measured value. According to the respective requirements of K

_{30}for the filling at the subgrade bottom and the embankment below the subgrade bottom in “Code for Design of Railway Earth Structure” [12], the critical dynamic strength of filling at the subgrade bottom and the embankment below the subgrade bottom is, respectively, 147 kPa and 104 kPa.

_{dmax}of the subgrade bottom is 50 kPa, and the dynamic stress of embankment below the subgrade is 25 kPa.

#### 4.2. The Design Criteria

_{f}, η

_{G}, η

_{D}and σ

_{dmax}into Equation (3):

## 5. Conclusions

- (1)
- The effects of cement dosage and compaction level on the fatigue characteristics of cement-stabilized loess were investigated in this study. Taking into account the most unfavorable conditions, the strength fatigue reduction coefficient of 0.26 was obtained.
- (2)
- The effect of wet–dry cycling on the strength reduction of cement-stabilized loess was investigated in this study. The results show that the strength decreases continuously with the increase of the time of wet–dry cycling, and the strength became to be stable after 15 times. Taking into account the most unfavorable conditions, the strength reduction coefficient of cement-stabilized loess under wet–dry cycling of 0.40 was obtained.
- (3)
- The effect of freeze–thaw cycling on the strength reduction of cement-stabilized loess was investigated in this study. The results show that the strength decreases continuously with the increase of the time of freeze–thaw cycling, and the strength became to be stable after 12 times. Taking into account the most unfavorable conditions, the strength reduction coefficient of cement-stabilized loess under freeze–thaw cycling of 0.30 was obtained.
- (4)
- The dynamic stress level of the railway subgrade was analyzed in this study. Moreover, it was obtained that the dynamic stress σ
_{dmax}of subgrade bottom is 50 kPa, and the dynamic stress σ_{dmax}of the embankment below the subgrade is 25 kPa. - (5)
- The 7-day strength design criteria were presented based on durability: 7-day unconfined compressive strength of cement-stabilized loess saturated with water of the subgrade bottom should be higher than 1100 kPa, and 7-day unconfined compressive strength of cement-stabilized loess saturated with water of embankment below the subgrade should be higher than 550 kPa.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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The Grade of Railway | Design Speed (km/h) | 7-Day Unconfined Compressive Strength Saturated with Water (kPa) | ||
---|---|---|---|---|

Subgrade Bottom | Embankment below the Subgrade | |||

Passenger and freight railway, Inter-city railway | Ballast track | 120, 160 | ≥350 (550) | ≥200 |

200 | ≥350 (550) | ≥250 | ||

Ballastless track | - | ≥350 (550) | ≥250 | |

High-speed railway, Heavy-haul railway | - | ≥350 (550) | ≥250 |

Technical Indices | Particle Density (g/cm ^{3}) | Liquid Limit (%) | Plastic Limit (%) | Plasticity Index | Percentage Passing (%) of Sieve Sizes (mm) | ||||
---|---|---|---|---|---|---|---|---|---|

0.25~0.075 | 0.075~0.05 | 0.05~0.01 | 0.01~0.005 | ≤0.005 | |||||

Test value | 2.74 | 26.4 | 15.7 | 10.7 | 2.47 | 7.22 | 53.43 | 13.83 | 23.05 |

Technical Indices | Fineness (%) | Soundness | Ignition Loss (%) | Initial Setting Time (min) | Final Setting Time (min) |
---|---|---|---|---|---|

Testing standard | $\le $10 | Qualified | $\le $5 | $\ge $45 | $\le $600 |

Test value | 1.2 | Qualified | 1.02 | 265 | 320 |

P_{s} (%) | 3 | 4 | 6 | Average | ||||||
---|---|---|---|---|---|---|---|---|---|---|

K | 0.92 | 0.95 | 0.97 | 0.92 | 0.95 | 0.97 | 0.92 | 0.95 | 0.97 | |

m | 0.571 | 1.062 | 0.780 | 0.823 | 1.125 | 0.890 | 0.591 | 0.679 | 0.883 | 0.823 |

n | 14.393 | 13.667 | 17.253 | 14.543 | 15.368 | 18.426 | 17.864 | 19.806 | 19.666 | 16.776 |

R^{2} | 0.9662 | 0.9706 | 0.9378 | 0.9356 | 0.9378 | 0.9268 | 0.9663 | 0.9540 | 0.9542 |

The Type of Data | K_{30} (MPa/m) | 90 | 110 | 130 | 150 | 170 | 190 |
---|---|---|---|---|---|---|---|

The calculated value | $\left[{\sigma}_{0}\right]$ (kPa) | 231 | 279 | 327 | 375 | 425 | 471 |

$\left[{\sigma}_{\mathrm{d}}\right]$ (kPa) | 104 | 126 | 147 | 169 | 190 | 212 | |

The measured value | $\left[{\sigma}_{\mathrm{d}}\right]$ (kPa) | 118 | 134 | 150 | 166 | 182 | 199 |

The Grade of Railway | 7-Day Unconfined Compressive Strength Saturated with Water (kPa) | |
---|---|---|

Subgrade Bottom | Embankment Below the Subgrade | |

Passenger and freight railway, Inter-city railway High-speed railway, Heavy-haul railway | $\ge $1100 | $\ge $550 |

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## Share and Cite

**MDPI and ACS Style**

Wang, F.; Pang, W.; Qin, X.; Han, L.; Jiang, Y.
Durability-Aimed Design Criteria of Cement-Stabilized Loess Subgrade for Railway. *Appl. Sci.* **2021**, *11*, 5061.
https://doi.org/10.3390/app11115061

**AMA Style**

Wang F, Pang W, Qin X, Han L, Jiang Y.
Durability-Aimed Design Criteria of Cement-Stabilized Loess Subgrade for Railway. *Applied Sciences*. 2021; 11(11):5061.
https://doi.org/10.3390/app11115061

**Chicago/Turabian Style**

Wang, Fuyu, Weichen Pang, Xingyuan Qin, Leilei Han, and Yingjun Jiang.
2021. "Durability-Aimed Design Criteria of Cement-Stabilized Loess Subgrade for Railway" *Applied Sciences* 11, no. 11: 5061.
https://doi.org/10.3390/app11115061