# Investigation of Resilience Characteristics of Unbound Granular Materials for Sustainable Pavements

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## Abstract

**:**

## 1. Introduction

_{r}) is used in the designing process and selection of unbound granular materials (UGMs) for unbound pavement layers. There are many factors which affect the resilient modulus of unbound granular material, including stress level, moisture content, density, material gradation, aggregate type and shape, number of load cycles, load duration frequency, and load sequence. Among the other factors, moisture content, material gradations, and stress levels are the most important factors which affect the resilient modulus of unbound granular materials. Therefore, it is important to understand and quantify the changes that take place in the resilient modulus with changes in moisture content, material gradations, and stress levels, and to develop understanding of the relationship between these factors and resilient modulus of unbound granular material for indigenous material.

## 2. Experimental Program

#### 2.1. Materials and Samples

_{max}is the maximum particle size, and ‘n’ is the grading coefficient, describing the shape of the curve. Four types of gradation were selected on the basis of the grading coefficient (n). Gradation coefficient values of 0.6, 0.5, 0.4, and 0.3 were selected for this study to find the effect of variation in gradation on the resilient behavior of UGM. Figure 1 shows gradation curves for different gradation coefficients.

#### 2.2. Material Properties

#### 2.3. Specimen Preparation

#### 2.4. Resilient Modulus Test

#### 2.5. Results and Discussion

#### 2.5.1. Effect of Moisture Content on the Resilient Modulus

_{r}values shown in Figure 4 were at gradation coefficient n = 0.6 compacted at a moisture contents of 5.03%, 4.03%, 3.03%, 2.03%, and oven-dry conditions, i.e., (mc%). It can be observed that M

_{r}at an OMC of 4.03% shows significantly lower values than at 3.03%, 2.03%, and oven-dry conditions, and the value of M

_{r}at 5.03% moisture content is lower than that at OMC 4.03%. Thus, increasing the percentage moisture content at the wet side of OMC significantly reduces the M

_{r}.

_{r}values shown in Figure 5 were measured at a gradation coefficient (n) of 0.5 and compacted at moisture contents of 5.30%, 4.30%, 3.30%, 2.30%, and oven-dry conditions, i.e., (mc%). It can be observed that the M

_{r}at an OMC of 4.30% showed significantly lower values than at 3.30%, 2.30%, and oven-dry condition, and the value of Mr at 5.30% moisture content was lower than at OMC 4.30%. Thus, increasing the moisture content at the wet side of OMC significantly reduces the M

_{r}.

_{r}values shown in Figure 6 were measured at a gradation coefficient (n) of 0.4 and compacted at moisture contents of 5.80%, 4.80%, 3.80%, 2.80%, and oven-dry conditions, i.e., (mc%). It can be observed that M

_{r}at an OMC of 4.80% shows significantly lower values than at 3.80%, 2.80%, and oven-dry conditions, and the value of M

_{r}at 5.80% moisture content is lower than at an OMC of 4.80%. Thus, increasing the moisture content at the wet side of OMC significantly reduces the M

_{r}.

_{r}values shown in Figure 7 were measured at a gradation coefficient (n) of 0.3 and compacted at moisture contents of 6.42%, 5.42%, 4.42%, 3.42%, and oven-dry conditions, i.e., (mc%). It can be observed that M

_{r}at an OMC of 5.42% shows significantly lower values than at 4.42%, 3.42%, and oven-dry conditions, and the value of Mr at a 6.42% moisture content is lower than at an OMC of 5.42%. Thus, increasing the moisture content at the wet side of OMC significantly reduces the Mr.

_{r}at high moisture decreases because with a lower water content, the material becomes stiffer and rigid, which gives a higher M

_{r}. By increasing the water content, the friction between the particles reduces, which reduces the rigidity and stiffness of the particles. Moisture works as a lubricant between aggregate particles, making it easier for the particles to relatively slide/roll; thus, M

_{r}decreases.

_{r}with respect to moisture. It was also investigated that with increasing moisture for different gradations, the gradation behaves differently.

_{r}has been observed at a gradation of 0.5 at moisture (OMC + 1) %, as shown in Figure 8. Fine and very coarse gradation at a higher moisture content, above OMC, shows a smaller resilient modulus. Gradation n = 0.6 contain 3% fine content. Gradation n = 0.6 at (OMC + 1) % shows the smallest M

_{r}, which is because of the instability of the sample, compromising the resilience and rigidity of the material. The other factor is due to the small number of fine particles in n = 0.6: the pore water pressure is so high that the material just starts to flow, and the friction between the aggregates is reduced. Increasing water with less fine content, the erosion of particles has been observed, which decreases the rigidity. The finer gradation becomes softer when additional moisture is added above OMC.

_{r}has been observed from 0.3 to 0.6. This shows that by increasing the gradation coefficient at moisture OMC%, the resilient modulus has been observed to increase. The maximum dry density from the proctor test was also observed to increase, from 0.3 to 0.6. This is because at OMC, the gradation of 0.6 has the maximum dry density. At (OMC − 1), gradation 0.6 shows a higher M

_{r}than other gradations. In dry conditions, the material becomes stiffer, which increases the resilient modulus. At moisture (OMC − 2), the graph shows that gradation between 0.4 and 0.5 shows higher M

_{r}than the other gradations.

#### 2.5.2. Effect of Moisture Stresses on Resilient Modulus

#### 2.5.3. Effect of Material Gradation on the Resilient Modulus

_{r}and 0.3 shows the smallest M

_{r}value; therefore, it has been observed from testing that a coarser gradation shows higher M

_{r}than finer gradation. When the gradation becomes coarser, the workability of the material decreases, increasing the rigidity and stiffness in the sample. This has been observed in the literature [24,25,26,27], that the coarser gradations exhibit better pavement performance characteristics.

## 3. Statistical Model

#### 3.1. Statistical Model Evaluation

^{2}, p-value, F-value, and RMSE, were calculated and are presented in Table 6, Table 7 and Table 8. The p-value is used for assessing the predictive capability of the regression model, i.e., whether the proposed model fits the data well. The p statistic is a ratio of the variance explained by the regression model (regression mean square) to the unexplained variance (residuals mean square). It is frequently thought of as a refinement of the more general likelihood ratio test (LR). The p-value is employed to determine whether all the predictors are jointly significant.

^{2}is a measure of how much variance in the dependent variable is explained by the model’s explanatory (independent) variables. It is calculated by multiplying the “cumulative difference in the total sum of squares (TSS) and residual sum of squares (RSS) by the total sum of squares (TSS)”. An R

^{2}of 0.8 and above shows a strong correlation between predicted and observed values.

^{2}is better and commonly preferred. For calculating the adjusted R

^{2}, the estimated variance (MST) and residuals (MSE) are determined by dividing the respective sum of squares by the degree of freedom.

#### 3.2. Relationship of Resilient Modulus and Moisture Content

_{r}’ (kPa) is the resilient modulus, ‘p

_{o}’ (kPa) is the atmospheric pressure, k

_{1}and k

_{2}are regression constants, and m is the moisture content.

^{2}’ is shown in the table for specified stresses (theta) and also advocates the results.

_{r}values, come from normal distributions with the same variance. A p-value of ‘0’ shows that null hypothesis (variances are equal) cannot be rejected at the 5% significance level; a p-value of ‘1’ shows that the null hypothesis can be rejected at the 5% level. To say that our model is a good fit, the p-value should be equal to ‘0’. From Table 6, all p-values are ‘0’ showing a good fit.

#### 3.3. Improved Relationship for Resilient Modulus, Stresses, and Moisture

_{r}’ (kPa) is the resilient modulus, ‘p

_{o}’ (kPa) is the atmospheric pressure (100 kPa), and k

_{1}, k

_{2}, k

_{3}, and k

_{4}are regression constants, $\theta $ is the sum of confining and deviator stress, and d is the deviator stress.

^{2}, adjusted R

^{2}, F-test, F-test values, and RMSE values for training and testing data are shown in Table 7 and Table 8. The coefficient of determination, R

^{2}, along with adjusted R

^{2}, shows that the model predicts the trained values well and also performs well with the testing data. All p-values show that the null hypothesis is true, exhibiting a ‘0’ value. The higher values of F and lower relative values of RMSE also show that the model fitness is acceptable.

## 4. Conclusions

- The resilient modulus decreases with an increase in the moisture content of unbound granular material, and vice versa. This is because at the dry side of optimum moisture content, the materials behave more stiffly, resulting in an increase in the resilient modulus, and at the wet side of optimum moisture content, the material becomes saturated and pore water pressure develops, resulting in a reduction in the stiffness.
- The resilient modulus increases significantly with the increase in both deviator and confining stresses of unbound granular material. It is shown in Figure 9b that by increasing the confining stress from 103 kPa to 137 kPa, the resilient modulus increases from 585 Mpa to 691 Mpa.
- The resilient modulus also decreases with an increase in finer gradation and increases with an increase in coarser gradation in unbound granular materials. A lower resilient modulus value is observed at (n) 0.3 and 0.4, and a higher resilient modulus value is seen at (n) 0.5 and 0.6. This is because the coarser gradations are stiffer than the finer gradation.
- A new relationship has been proposed in Equation (2), which depicts that the moisture content and resilient modulus of unbound granular material can be predicted through a linear relationship. However, the accuracy is better if Equation (3) is applied.
- The new relationship has been trained on three-fifth of the dataset, and regression parameters were calculated. The model was tested on the rest of the data with the trained parameters. It can be concluded that resilient modulus values predicted by the new relationship are in good agreement with repeated load triaxial test data. Therefore, new relationships can be used in the design process with greater confidence compared with the previous relationships, which only consider the stress tensors for the prediction of resilient modulus.

_{r}values are indicative of greater stiffness and strength of unbound granular materials, as well as their increased resistance to shear failure under traffic loading, thereby improving pavement durability. To conclude, the structural behavior of the pavement against traffic loading can be reliably determined by knowing the resilient modulus of various pavement materials. The resilient modulus of unbound granular material obtained in this study can be helpful for engineers and scientists for sustainable pavement design.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 9.**Resilient modulus and confining stress values at different moisture contents. (

**a**) n = 0.6 (

**b**) n = 0.5 (

**c**) n = 0.4 (

**d**) n = 0.3.

**Figure 11.**Stress and strain curve of unbound granular material under repeated load triaxial testing.

Model | Author | Equation | Variable | Remarks |
---|---|---|---|---|

(Uzan Model) [44] | Uzan | ${M}_{r}$ = k_{1} P_{a} (θ/P_{a})^{k}^{2} * (σ_{d}/P_{a})^{k}^{3} | k_{1}, k_{2} = Material constantsPa = Atmospheric pressure | More precisely models the nonlinearity of granular soils |

AASHTO Model [5] | ${M}_{r}$ = k_{1}σ_{d} ^{k}^{2} | k_{1}, k_{2} = Material constants | Uses least square regression analysis | |

Universal Model (Modified Uzan model) (Uzan et al. 1992) [45] | Uzan | ${M}_{r}$ = k_{1}P_{a} (θ/P_{a})^{k}^{2} * (${\tau}_{oct}$/P_{a})^{k}^{3} | k_{1}, k_{2} = Material constantsPa = Atmospheric pressure | Bulk stress and deviator stress effects are considered |

K-Θ Model [44] | Uzan | ${M}_{r}$ = A(3p_{max})^{B} | A,B = Material constants Pmax = Max atmospheric pressure | Poisson’s ratio is assumed to be constant. No effect of dev. stress is considered |

Boyce Model [5] | Boyce (1980) | ε_{v} = p^{A}*(1/k_{1}) [1 − β (q^{2}/p^{2})]ε _{s} = (p^{B}/3C)*(q/p) | A, C = Material constants controlled by B | The model is nonlinear elastic and isotropic |

Gradation Coefficients (n) | Max Dry Density kg/m³ | Optimum Moisture Content % |
---|---|---|

0.6 | 2432.40 | 4.03 |

0.5 | 2406.93 | 4.3 |

0.4 | 2395.72 | 4.8 |

0.3 | 2381.46 | 5.42 |

Gradation Coefficient | OMC% | OMC + 1% | OMC − 1% | OMC − 2% | Dry |
---|---|---|---|---|---|

0.6 | 4.03 | 5.03 | 3.03 | 2.03 | mc = 0 |

0.5 | 4.3 | 5.3 | 3.3 | 2.3 | mc = 0 |

0.4 | 4.8 | 5.8 | 3.8 | 2.8 | mc = 0 |

0.3 | 5.42 | 6.42 | 4.42 | 3.42 | mc = 0 |

S. No | Description | Designation | Result | Allowable Limits |
---|---|---|---|---|

1 | Aggregate Abrasion Value % [49] | C 131 | 21 | <40 |

2 | Aggregate Impact Value % [50] | BS 812–112 | 14 | <40 |

3 | Water Absorption of Coarse Aggregates % [51] | C 128 | 0.57 | <2 |

4 | Specific Gravity of Coarse Aggregate [52] | C 127 | 2.63 | 2.5–2.9 |

Sequence Number | Confining Pressure, σ_{3} (kPa) | Maximum Axial Stress, σ_{d} (kPa) | Cyclic Stress, σ_{cd} (kPa) | Contact Stress, σ_{contact} (kPa) | Number of Load Applications |
---|---|---|---|---|---|

Conditioning | 103.4 | 103.4 | 93.1 | 1.5 | 500–1000 |

1 | 20.7 | 20.7 | 18.6 | 2.1 | 100 |

2 | 20.7 | 41.4 | 37.3 | 4.1 | 100 |

3 | 20.7 | 62.1 | 55.9 | 6.2 | 100 |

4 | 34.5 | 34.5 | 31.0 | 3.5 | 100 |

5 | 34.5 | 68.9 | 62.0 | 6.9 | 100 |

6 | 34.5 | 103.4 | 93.1 | 10.3 | 100 |

7 | 68.9 | 68.9 | 62.0 | 6.9 | 100 |

8 | 68.9 | 137.9 | 124.1 | 13.8 | 100 |

9 | 68.9 | 206.8 | 186.1 | 20.7 | 100 |

10 | 103.4 | 68.9 | 62.0 | 6.9 | 100 |

11 | 103.4 | 103.4 | 93.1 | 10.3 | 100 |

12 | 103.4 | 206.8 | 186.1 | 20.7 | 100 |

13 | 137.9 | 103.4 | 93.1 | 10.3 | 100 |

14 | 137.8 | 137.9 | 124.1 | 13.8 | 100 |

15 | 137.9 | 275.8 | 248.2 | 27.6 | 100 |

**Table 6.**Regression constants and goodness-of-fit test results for the moisture model (Equation (2)).

Effect of Moisture on UGM by Changing Theta and Gradation | |||||||
---|---|---|---|---|---|---|---|

Theta | n | k_{1} | k_{2} | ${\mathit{R}}^{2}(1-\frac{\mathbf{MSE}}{\mathbf{MST}})$ | p-$\mathbf{Value}=\left(1-\frac{\mathbf{RSS}}{\mathbf{TSS}}\right)$ | F-$\mathbf{Value}=\mathbf{MSR}/\mathbf{MSE}$ | $\mathbf{RMSE}=\sqrt{\frac{{{\displaystyle \sum}}_{\mathit{i}=1}^{\mathit{N}}{\Vert \mathit{y}\left(\mathit{i}\right)-\stackrel{\wedge}{\mathit{y}}\left(\mathit{i}\right)\Vert}^{2}}{\mathit{N}}}$ |

196.5 | 0.3 | 5705.8 | −712.35 | 0.94 | 0 | 0.94 | 41,092 |

392.7 | 0.3 | 7128.4 | −907.1 | 0.93 | 0 | 0.93 | 53,360 |

496.2 | 0.3 | 7956.9 | −986.01 | 0.98 | 0 | 0.98 | 33,749 |

661.7 | 0.3 | 8581.4 | −963.76 | 0.97 | 0 | 0.97 | 37,130 |

196.5 | 0.4 | 3709.3 | −319.99 | 0.93 | 0 | 0.93 | 17,324 |

392.7 | 0.4 | 5057.3 | −448.19 | 0.93 | 0 | 0.93 | 23,958 |

496.2 | 0.4 | 5961.9 | −585.82 | 0.94 | 0 | 0.94 | 28,193 |

661.7 | 0.4 | 7404 | −774.95 | 0.92 | 0 | 0.92 | 45,509 |

196.5 | 0.5 | 4433.8 | −528.15 | 0.95 | 0 | 0.95 | 20,986 |

392.7 | 0.5 | 5434 | −575.46 | 0.95 | 0 | 0.95 | 23,711 |

496.2 | 0.5 | 5886.9 | −527.86 | 0.94 | 0 | 0.94 | 23,396 |

661.7 | 0.5 | 6949.2 | −602.11 | 0.94 | 0 | 0.94 | 26,509 |

196.5 | 0.6 | 4422.6 | −526.41 | 0.91 | 0 | 0.91 | 29,166 |

392.7 | 0.6 | 6093.8 | −768.35 | 0.91 | 0 | 0.91 | 41,358 |

496.2 | 0.6 | 6095.1 | −683.1 | 0.86 | 0 | 0.86 | 47,719 |

661.7 | 0.6 | 7430.4 | −872.65 | 0.91 | 0 | 0.91 | 46,875 |

Model Training Regression Parameters and Goodness-of-Fit Tests | |||||||||
---|---|---|---|---|---|---|---|---|---|

n | k_{1} | k_{2} | k_{3} | k_{4} | R^{2} | adj R^{2} | p-Value | F-Value | RMSE |

0.3 | 5191.7 | 0.0691 | 0.1652 | −714.36 | 0.89 | 0.88 | 0.00 | 0.89 | 73,667 |

0.4 | 3687.7 | 0.1530 | 0.1654 | −410.53 | 0.80 | 0.78 | 0.00 | 0.81 | 64,009 |

0.5 | 3448.6 | 0.0616 | 0.2667 | −433.28 | 0.91 | 0.91 | 0.00 | 0.93 | 39,910 |

0.6 | 4918.6 | 0.2397 | −0.0061 | −551.76 | 0.78 | 0.76 | 0.00 | 0.79 | 71,683 |

Model Testing Regression Parameters and Goodness-of-Fit Tests | |||||||||
---|---|---|---|---|---|---|---|---|---|

n | k_{1} | k_{2} | k_{3} | k_{4} | R^{2} | adj R^{2} | p-Value | F-Value | RMSE |

0.3 | 5191.7 | 0.0691 | 0.1652 | −714.36 | 0.76 | 0.73 | 0.00 | 1.23 | 50,008 |

0.4 | 3687.7 | 0.1530 | 0.1654 | −410.53 | 0.76 | 0.72 | 0.00 | 0.90 | 48,587 |

0.5 | 3448.6 | 0.0616 | 0.2667 | −433.28 | 0.88 | 0.86 | 0.00 | 0.93 | 36,376 |

0.6 | 4918.6 | 0.2397 | −0.0061 | −551.76 | 0.55 | 0.47 | 0.00 | 0.90 | 65,674 |

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**MDPI and ACS Style**

Ullah, S.; Jamal, A.; Almoshaogeh, M.; Alharbi, F.; Hussain, J.
Investigation of Resilience Characteristics of Unbound Granular Materials for Sustainable Pavements. *Sustainability* **2022**, *14*, 6874.
https://doi.org/10.3390/su14116874

**AMA Style**

Ullah S, Jamal A, Almoshaogeh M, Alharbi F, Hussain J.
Investigation of Resilience Characteristics of Unbound Granular Materials for Sustainable Pavements. *Sustainability*. 2022; 14(11):6874.
https://doi.org/10.3390/su14116874

**Chicago/Turabian Style**

Ullah, Salamat, Arshad Jamal, Meshal Almoshaogeh, Fawaz Alharbi, and Jawad Hussain.
2022. "Investigation of Resilience Characteristics of Unbound Granular Materials for Sustainable Pavements" *Sustainability* 14, no. 11: 6874.
https://doi.org/10.3390/su14116874