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Unbound granular material is an important construction material that is used for flexible pavement. As one of the most important indices used for describing the properties of unbound granular material, the deformation characteristic is significantly influenced by the compaction method used. However, the effects of the compaction method on the deformation behaviour are neglected in the existing studies. Hence, we investigate the deformation characteristics of unbound granular material produced by the vertical vibration compaction method (VVCM) and the modified Proctor compaction method (MPCM) via repeated triaxial load tests and reveal the effect of loading conditions and aggregate gradations. The results show that (a) the deformation of unbound granular material decreases as the stress level and confining pressure are increased; (b) the deformation resistance of unbound granular material produced by the VVCM is superior to that produced by the MPCM; (c) the difference of deformation resistance arising between using the VVCM and MPCM decreases as confining pressure increases and is not significant with changes in the stress level; (d) the extent of various factors on deformation characteristics from greatest to least is as follows: stress level > aggregate gradation > compaction method > confining pressure; and (e) increasing the content of coarse aggregates is conducive to enhancing the deformation resistance of unbound granular material, particularly for the VVCM. Finally, a simple approach for modelling and predicting deformation is established.

It is well known that flexible pavements with composite bases have desirable structural and functional capacities [

Rahman and Erlingsson [

Among these factors, the compaction density, which has a direct relationship with the compaction method, is regarded as one of the most important indices of pavement properties of unbound granular material [

Existing studies [

The objective of this study is to investigate the deformation characteristics of unbound granular material produced by different compaction methods. Specifically, the following two cases are considered:

The effect of various compaction methods on the deformation behaviour of unbound granular material

The sensitivity of loading conditions (e.g., deviator stresses and confining presses) and aggregate gradations to the effect of compaction methods

This is achieved by running repeated triaxial load tests on unbound granular material produced by the VVTM and MPCM for a range of loading conditions and aggregate gradations. All tests in accordance with Chinese specification “

The unbound granular material is composed of four types of aggregates with different size ranges: 31.5–19 mm, 19–9.5 mm, 9.5–4.75 mm, and 0–4.75 mm. The aggregates are obtained from Shaanxi province of China, and their technical properties are shown in Table

Technical properties of aggregates.

Aggregate size (mm) | Bulk volume relative density (g/cm^{3}) | Water absorption (%) | Crushing value (%) | Los Angeles abrasion (%) | Content of needle-like (%) | Firmness (%) | Sand equivalent (%) | Liquid limit (%) | Plasticity index (%) |
---|---|---|---|---|---|---|---|---|---|

31.5∼19 | 2.725 | 0.3 | — | 19.4 | 6.6 | 5.4 | — | — | — |

19∼9.5 | 2.721 | 0.6 | 19.5 | 20.5 | 8.4 | 5.8 | — | — | — |

9.5∼4.75 | 2.633 | 0.6 | — | 20.9 | 5.8 | 6.3 | — | — | — |

<4.75 | 2.645 | 0.7 | — | — | — | 6.2 | 71.5 | 17 | 2.8 |

Two types of aggregate gradations are selected in this study, as shown in Table

Aggregate gradation.

Diameter (mm) | Pass percent (%) | |
---|---|---|

Strong skeleton gradation | Specification gradation | |

31.5 | 100 | 100 |

19 | 64 | 84 |

16 | 58 | 76 |

13.2 | 52 | 68.5 |

9.5 | 46 | 56.5 |

4.75 | 36 | 35 |

2.36 | 28 | 23.5 |

1.18 | 23 | 16 |

0.6 | 19 | 11 |

0.3 | 15 | 7.5 |

0.15 | 11 | 5 |

0.075 | 8 | 3.5 |

In this study, the VVCM and MPCM are both adopted to produce the unbound granular material samples according to the Chinese specification “

Step 1: the aggregates and water are mixed according to the target moisture content.

Step 2: the samples (Φ152 mm ×

Step 3: the dry density of the sample prepared in Step 2 is measured.

Step 4: Steps 1–3 are repeated, and the optimum moisture content and the maximal dry density are determined.

Step 5: the final cylindrical samples (Φ100 mm ×

Step 1: the aggregates and water are mixed according to the target moisture content.

Step 2: the samples (Φ152 mm ×

Step 3: the dry density of the sample prepared in Step 2 is measured.

Step 4: Steps 1–3 are repeated, and the optimum moisture content and the maximal dry density are determined.

Step 5: the final cylindrical samples are compacted to a size of Φ100 mm ×

The maximum dry density and the optimum moisture content of different unbound granular materials are shown in Table

Physical parameters of unbound granular materials.

Abbr. | Aggregate gradation | Compaction method | Maximum dry density (g/cm^{3}) | Optimum moisture content (%) |
---|---|---|---|---|

GM | Strong skeleton gradation | VVCM | 2.425 | 3.8 |

GF | Specification gradation | VVCM | 2.401 | 4.0 |

LX1 | Strong skeleton gradation | MPCM | 2.390 | 4.2 |

LX2 | Specification gradation | MPCM | 2.376 | 4.4 |

In addition, a sampling inspection shows that the errors of the dry density and the moisture content of the final formed samples are both less than 5%, compared to the maximum dry density and the optimal moisture content. Hence, we consider that the samples that are finally formed are corresponding to the maximum dry density and the optimal moisture content under the molding method.

The repeated triaxial load test is generally considered to be the most appropriate tool for characterizing the deformation properties of unbound granular material [

Repeated triaxial load test apparatus.

The repeated triaxial load tests are implemented according to the Chinese specification “

The repeated load triaxial tests are employed under a stress-controlled mode at a loading frequency of 1 Hz. The controlled stress, namely, the deviator stress _{d}, is applied in the axial direction and is constant during the experimental process. The confining pressure stress _{c} (equal to the minor principal stress _{3}) is applied by pressurizing the cell water surrounding the cylindrical sample of unbound granular material. Hence, the axial stress _{a} (equal to the maximum principal stress _{1}) acting on the sample is equal to the sum of the deviator stress _{d} and the confining press _{c}.

In this study, three types of confining stress (50, 100, and 150 kPa) are selected because the horizontal stress of the pavement structure under loads of moving vehicles ranged, in general, from 50 kPa to 150 kPa [_{a}, _{d}, and _{c} can be expressed as equation (_{d} is the deviator stress, and _{s} is the ultimate strength of the tested sample measured via the static triaxial test according to the Chinese specification “

Testing conditions.

Confining press _{c} (kPa) | Deviator stress _{d} (kPa) | Axial stress _{a} (kPa) | Ultimate strength _{s} (kPa) | Stress level |
---|---|---|---|---|

50 | 85 | 135 | 853 | 0.1 |

100 | 128 | 228 | 1281 | 0.1 |

150 | 170 | 320 | 1698 | 0.1 |

50 | 256 | 306 | 853 | 0.3 |

100 | 384 | 484 | 1281 | 0.3 |

150 | 509 | 659 | 1698 | 0.3 |

50 | 427 | 477 | 853 | 0.5 |

100 | 641 | 741 | 1281 | 0.5 |

150 | 849 | 999 | 1698 | 0.5 |

50 | 597 | 647 | 853 | 0.7 |

100 | 897 | 997 | 1281 | 0.7 |

150 | 1189 | 1339 | 1698 | 0.7 |

50 | 768 | 818 | 853 | 0.9 |

100 | 1153 | 1253 | 1281 | 0.9 |

150 | 1528 | 1678 | 1698 | 0.9 |

The loading number and the axial strain measured in the repeated triaxial load tests are the most important indices that characterize the deformation behaviour of unbound granular material [

The loading number exceeds 10000 times, and the sample has not failed, as shown in Figure

The loading number does not reach 10000 times, but the sample has failed, as shown in Figure

Failed sample.

Accordingly, the deformation resistance can be evaluated through

The permanent strain when the loading number reaches 10000 times and the sample has not failed

The ultimate loading number when the sample has failed

The relationship between the loading number and the axial strain of unbound granular material is plotted in Figure

Relationship between the axial strain and loading number under different compaction methods. (a) (s) = 0.1, _{3} = 50 kPa, (b) (s) = 0.1, _{3} = 100 kPa, (c) (s) = 0.1, _{3} = 150 kPa, (d) (s) = 0.3, _{3} = 50 kPa, (e) (s) = 0.3, _{3} = 100 kPa, (f) (s) = 0.3, _{3} = 150 kPa, (g) (s) = 0.5, _{3} = 50 kPa, (h) (s) = 0.5, _{3} = 100 kPa, (i) (s) = 0.5, _{3} = 150 kPa, (j) (s) = 0.7, _{3} = 50kP, (k) (s) = 0.7, _{3} = 100 kPa, (l) (s) = 0.7, _{3} = 150 kPa, (m) (s) = 0.9, _{3} = 50 kPa, (n) (s) = 0.9, _{3} = 100 kPa, and (o) _{3} = 150 kPa.

As shown in Figure

Moreover, the difference in deformation resistance arising from using the VVCM and MPCM decreases as confining pressure increases, particularly for the strong skeleton gradation. For instance, when the stress level ranges from 0.1 to 0.5, the differences of ultimate axial strain in the case of using the strong skeleton gradation are, on average, 18.75%, 11.11%, and 8.72% at the confining pressure of 50 kPa, 100 kPa, and 150 kPa, respectively, while those for the case of using the specification gradation are 14.16%, 13.91%, and 13.23%, respectively. When the stress level exceeds 0.7, a similar phenomenon also can be found, as in Figures

Relations between the axial strain and loading number under different stress levels. (a) _{3} = 50 kPa, GM, (b) _{3} = 50 kPa, GF, (c) _{3} = 50 kPa, LX1, (d) _{3} = 50 kPa, LX2, (e) _{3} = 100 kPa, GM, (f) _{3} = 100 kPa, GF, (g) _{3} = 100 kPa, LX1, (h) _{3} = 100 kPa, LX2, (i) _{3} = 150 kPa, GM, (j) _{3} = 150 kPa, GF, (k) _{3} = 150 kPa, LX1, and (l) _{3} = 150 kPa, LX2.

The relationship between the axial strain and loading number is plotted in Figure

As shown in Figure

The relationship between axial strain and loading numbers is plotted in Figure

Relations between the axial strain and loading number under different confining pressures. (a) (s) = 0.1, GM, (b) (s) = 0.1, GF, (c) (s) = 0.1, LX1, (d) (s) = 0.1, LX2, (e) (s) = 0.3, GM, (f) (s) = 0.3, GF, (g) (s) = 0.3, LX1, (h) (s) = 0.3, LX2, (i) (s) = 0.5, GM, (j) (s) = 0.5, GF, (k) (s) = 0.5, LX1, (l) (s) = 0.5, LX2, (m) (s) = 0.7, GM, (n) (s) = 0.7, GF, (o) (s) = 0.7, LX1, (p) (s) = 0.7, LX2, (q) (s) = 0.9, GM, (r) (s) = 0.9, GF, (s) (s) = 0.9, LX1, and (t) (s) = 0.9, LX2.

As shown in Figure

The prediction equation of the deformation behaviour provides the basis for further study on the design standards of unbound granular material [

Puppala et al. [_{1}, _{2}, and _{3} are the coefficients.

Korkiala-Tanttu [

Chow [_{1}, _{2}, and _{3} are the coefficients.

Lu et al. [_{1} and _{2} are the coefficients.

Zhang et al. [_{1}–_{5} are the coefficients.

In this study, the prediction equation is established according to the relationship of the axial deformation, loading number, confining stress, and stress level, which can be expressed as the following equation:_{1}, _{2}, _{3}, and _{4} are the coefficients.

The prediction equations for different aggregates and compaction methods are listed in Table

Prediction equations.

Aggregate gradation | Compaction method | Prediction equation | ^{2} |
---|---|---|---|

Strong skeleton gradation | VVCM | 0.982 | |

Specification gradation | VVCM | 0.966 | |

Strong skeleton gradation | MPCM | 0.953 | |

Specification gradation | MPCM | 0.951 |

It can be found that the correlation coefficients all have high levels (

The objective of this study is to investigate the deformation behaviour of unbound granular material produced by different compaction methods and to reveal the effects of loading conditions and aggregate gradations.

The deformation of unbound granular material decreases as the stress level and confining pressure are increased.

The deformation resistance of unbound granular material produced by the VVCM is superior to the MPCM.

The difference in deformation resistance resulting from using the VVCM and MPCM decreases as confining pressure is increased, particularly for the strong skeleton gradation. The effect of the stress level is not significant.

The extent that different factors affect the deformation resistance of unbound granular materials is as follows: stress level > aggregate gradation > compaction method > confining pressure.

Increasing the content of coarse aggregates is conducive to enhancing the deformation resistance of unbound granular material, particularly for the VVCM.

A simple approach for modelling the deformation prediction of unbound granular material is established.

The data used to support the findings of this study are included within the article.

The authors declare that they have no conflicts of interest.

This study was sponsored in part by the National Natural Science Foundation of China under grant no. 51808326, to which the authors are very grateful. In addition, the authors would like to thank Editage (