# Using Resilient Modulus to Determine the Subgrade Suitability for Forest Road Construction

^{1}

^{2}

^{*}

## Abstract

**:**

_{r,CBR}. The results of the statistical analysis showed a large variability of M

_{r,CBR}values and wide intervals of its occurrence for individual types of subgrade. The variability was subjected to analysis and the influence of basic geotechnical parameters on the values of M

_{r,CBR}was analyzed. A fundamental correlation was found between the value of M

_{r,CBR}and the value of the plunger stress, which reached values exceeding the bearing capacity of the soil types using the Delft University method. It is necessary to limit the plunger stress during cyclic loading up to the failure limit or even better to the expected traffic load. The modified procedure results show a more consistent behavior of the modulus.

## 1. Introduction

_{r}) of the subgrade for the design pavement layers. For the first design level, where high transport loads are expected, the modulus M

_{r}, of the subgrade is determined by the triaxial cyclic test [10]. For the second and third design levels where the daily intensity is a maximum of 400 heavy vehicles, this test is not recommended for its complexity and it is possible to replace M

_{r}with the so-called design modulus E

_{D}, determined from other soil characteristics, e.g., the CBR [7]. However, this pavement layers design based on the subgrade CBR has gradually become insufficient even for the second and third design levels, because it does not describe the real deformation behavior of the material, does not allow using new materials, assessing the layer thickness, and using numerical analyses and thus minimizing the consumption of natural nonrenewable resources [11,12]. Last but not least, this design method does not allow including climatic conditions in the design [13]. Additionally, the use of conversions between the CBR and the design modulus E

_{D}, brings a number of inaccuracies to the road design [14]. Therefore, the present MEPDG methodology recommends replacing these conversions by the resilient modulus M

_{r}, or at least by its estimation based on the laboratory cyclic tests.

_{r,eff}, was used, employing the standard CBR test equipment for cyclic loading. This method of estimating the resilient modulus was tested and innovated in the laboratories of Mendel University in Brno (MENDELU) and the geotechnical laboratory GEOSTAR s.r.o. Within the project, software P 304642 has been developed for the automated test implementation, which was patented in 2014 [16]. It controls the cyclic loading procedure and determines the parameters for the resilient modulus calculation, which is labelled M

_{r,CBR}.

_{r,CBR}obtained from cyclic testing. The determination of the modulus was based on the Dutch theory of the effective resilient modulus for unbound materials [15]. The statistical analysis of the obtained results for the basic subgrade soil types according to the Unified Soil Classification System [20] is presented.

## 2. Materials and Methods

#### 2.1. Study Area, Samples, and Geotechnical Analysis

- eluvial rocks:
- ○
- metamorphic rocks—gneiss from the Bohemian-Moravian Highlands—siSa, grsiSa, siGr;
- ○
- igneous rocks—granites from the Bohemian-Moravian Highlands—csaCl, sagrSi, siSa, clGr;
- ○
- diagenetic lithificated sediments of sandstone, greywacke from the Nízký Jeseník Mts.—Cl, siCl, csaCl, sagrSi, grsaCl;
- ○
- Devonian limestone from the Moravian Karst—csaCl,sagrSi, clSa, siSa, siGr;
- ○
- Paleogenic diagenetic lithificated sediments of the flysch belt from the Beskydy Mts.—Cl, grsaCl;

- sediments:
- ○
- cretaceous clays and sands from the Drahanská Highland—Cl, siCl, saclSi;
- ○
- Neogenic and Quarternary clays of the Lower Morava Valley—saciSi, csaCl, grsaCl.

_{r,CBR}values. Six samples were produced from each sampling. The samples were compacted into test mold for the CBR test with a diameter of 152 mm and a height of 117 mm using the Proctor Standard energy and they were conditioned to the optimum humidity and maximum dry density according to [22]. The samples thus prepared were subjected to the appropriate cyclic test for the determination of M

_{r},

_{CBR}value and a set of six values was statistically evaluated. In total, 276 samples for nine soil types were tested. After the cyclic test, the maximum dry density and the humidity of each sample were measured and their average values for each class were determined.

#### 2.2. Laboratory Analysis—Cyclic CBR Tests

_{i}− w

_{(i−1)}= 0 (condition A), where i is the cycle number. This was achieved in approximately 50 cycles. To calculate the resilient modulus M

_{r,eff}, deformation w and stress σ from the last test cycle of the selected sample was used according to condition A and Equation (1):

_{r,CBR}, the effect of friction was modified using the mean values of constants C

_{1}, C

_{2}, C

_{3}[14]. To calculate the modulus deformation value w′ and stress σ from the last test cycle were used according to condition B and Equation (2)

_{r}, is not a constant property of materials, but depends on many factors and, depending on the material tested, it is most affected by the maximum dry density, water content, and the load size given by the applied stress. Therefore, given their variability, it cannot be assumed that one value of modulus M

_{r}can be assigned to one soil type, as there are an infinite number of values depending on the test conditions.

_{r,CBR}, for basic soil type with a uniform preparation of samples at optimum humidity, determined by the Proctor Standard test. The minimized influence of different water content values was assumed to reduce the variability of M

_{r,CBR}due to different conditions of the sample and to allow monitoring the effect of granulometry—from different locations of the Czech Republic—for one soil type by USCS, thus providing representative occurrence intervals of the resilient modulus for efficient LVRs designs.

#### 2.3. Statistical Analysis

_{r,CBR}can be expected; the standard deviation and the coefficient of variation indicate the expected dispersion of values from the mean; the minimum and maximum values show the estimated interval where the values can be expected. The 0.05 quantile is a value of M

_{r,CBR}for which we can expect with a 5% probability that the values will be smaller, or with a 95% probability that they will be greater than the 0.05 quantile. The 0.95 quantile case is analogical. In addition, the difference between the two quantiles determines the interval where the values will occur with a 90% probability.

## 3. Results

#### 3.1. Statistical Results M_{r,CBR} from the Cycle Test

_{r,CBR}mean, and 0.05 and 0.95 quantiles are listed. These statistical quantities are also given for the whole soil type.

- Soil N°1—Cl

_{r,CBR}mean of the whole soil type (obtained from the statistical evaluation of all 60 samples) is 123.35 MPa. The coefficient of variation of the whole soil type is 0.83. The minimum value is 36.9 MPa, the maximum value is 429.9 MPa. The 0.05 quantile is 39.0 MPa, the 0.95 quantile is 371.7 MPa for the entire soil type. The results show two distinct subgroups of the values of M

_{r,CBR}. In the first subgroup, the values of M

_{r,CBR}reach to about 150 MPa; in the second up to a value of about 420 MPa.

- Soil N°2—siCl

_{r,CBR}mean of the entire soil type (obtained from the statistical evaluation of all 18 samples) is 140.8 MPa. The coefficient of variation of the entire soil type is 1.08. The minimum value is 14.9 MPa, the maximum value is 375.9 MPa. The 0.05 quantile is 18.7 MPa, the 0.95 quantile is 299.4 MPa for the entire soil type. The results show two distinct subgroups of the values of M

_{r,CBR}. In the first subgroup, the values of M

_{r,CBR}reach to about 30 MPa; in the second, up to a value of about 380 MPa.

- Soil N°3—saclSi

_{r,CBR}mean of the entire soil type (obtained by statistical evaluation of all 12 samples) is 122.7 MPa. The coefficient of variation of the entire soil type is 0.59. The minimum value is 46.9 MPa, the maximum value is 261.3 MPa. The 0.05 quantile is 48.8 MPa, the 0.95 quantile is 235.3 MPa for the entire soil type. The results show two distinct subgroups of the values of M

_{r,CBR}. In the first subgroup, the values of M

_{r,CBR}reach up to about 65 MPa; in the second, up to a value of about 260 MPa.

- Soil N°4—csaCl

_{r,CBR}mean of the entire soil type (obtained by statistical evaluation of all 30 samples) is 106.9 MPa. The coefficient of variation of the entire soil type is 0.46. The minimum value is 44.2 MPa, the maximum value is 250.8 MPa. The 0.05 quantile is 51.8 MPa, the 0.95 quantile is 205.7 MPa for the entire soil type. The results show three distinct subgroups of the values of M

_{r,CBR}. In the first subgroup, the values of M

_{r,CBR}reach up to about 55 MPa; in the second, up to a value of about 150 MPa; in the third, up to a value of about 250 MPa.

- Soil N°5—sagrSi

_{r,CBR}mean of the entire soil type (obtained by statistical evaluation of all 36 samples) is 101.8 MPa. The coefficient of variation of the entire soil type is 0.78. The minimum value is 20.8 MPa, the maximum value is 330.7 MPa. The 0.05 quantile is 24.1 MPa, the 0.95 quantile is 271.3 MPa for the entire soil type. The results show three distinct subgroups of the values of M

_{r,CBR}. In the first subgroup, the values of M

_{r,CBR}reach up to about 90 MPa; in the second, up to a value of about 140 MPa, in the third, up to 380 MPa.

- Soil N°6—grsaCl

_{r,CBR}mean of the entire soil type (obtained by statistical evaluation of all 24 samples) is 107.9 MPa. The coefficient of variation of the entire soil type is 0.82. The minimum value is 41.8 MPa, the maximum value is 374.9 MPa. The 0.05 quantile is 44.0 MPa, the 0.95 quantile is 310.7 MPa for the entire soil type. The results show two distinct subgroups of the values of M

_{r,CBR}. In the first subgroup, the values of M

_{r,CBR}reach up to about 90 MPa; in the second, up to a value of about 560 MPa.

- Soil N°7—siSa

_{r,CBR}mean of the entire soil type (obtained by statistical evaluation of all 60 samples) is 153.4 MPa. The coefficient of variation of the entire soil type is 0.67. The minimum value is 23.1 MPa, the maximum value is 451.3 MPa. The 0.05 quantile is 29.9 MPa, the 0.95 quantile is 357.6 MPa for the entire soil type. The results show four distinct subgroups of the values of M

_{r,CBR}. In the first subgroup, the values of M

_{r,CBR}reach up to about 55 MPa; in the second, up to about 180 MPa; in the third, up to 245 MPa; and in the fourth, up to 675 MPa.

- Soil N°8—grsiSa

_{r,CBR}mean of the entire soil type (obtained by statistical evaluation of all 12 samples) is 116.9 MPa. The coefficient of variation of the entire soil type is 0.24. The minimum value is 67.4 MPa, the maximum value is 168.7 MPa. The 0.05 quantile is 74.6 MPa, the 0.95 quantile is 159.3 MPa for the entire soil type.

- Soil N°9—siGr

_{r,CBR}mean of the entire soil type (obtained by statistical evaluation of all 24 samples) is 32.2 MPa. The coefficient of variation of the entire soil type is 0.60. The minimum value is 9.0 MPa, the maximum value is 79.9 MPa. The 0.05 quantile is 10.7 MPa, the 0.95 quantile is 64.0 MPa for the entire soil type. The results show two distinct subgroups of the values of M

_{r,CBR}.

_{r,CBR}. Moreover, intervals of possible values overlap each other, see Figure 10. As result, the representative estimates of M

_{r,CBR}for the individual soil types cannot be determined.

_{r,CBR}was analyzed and the essential parameters of individual samples, such as humidity, maximum dry density, and plunger stress during the cyclic test, were monitored within individual soil types. The real humidity and the maximum dry density did not differ much from the set optimum humidity and the maximum dry density according to Proctor Standard energy. These parameters were therefore not further examined. On the contrary, the influence of the plunger stress values from the last cycle on variability of M

_{r,CBR}was found interesting.

#### 3.2. Results of Plunger Stress in CBR Cyclic Test Analysis

- Soil N°1—Cl

_{r,CBR}, which at the same time correspond to the stress limit of 500 kPa. The first subgroup, which was cycled at stresses up to 500 kPa, shows lower values of the moduli, the mean of M

_{r,CBR}equal to 77.2 MPa, as well as a smaller variability. The second subgroup, where the samples were cycled at a stress higher than 500 kPa, shows high variability in values of the moduli. The maximum stress was observed in sample 4/19; it was 2202.8 kPa and M

_{r,CBR}reached 300.2 MPa.

- Soil 2—siCl

_{r,CBR}, which in this soil type correspond to the stress limit of 500 kPa. The first subgroup, which was cycled at stresses up to 500 kPa, shows lower values of the moduli, the mean of M

_{r,CBR}equal to 21.9 MPa, as well as a smaller variability of their occurrence. The second subgroup, where the samples were cycled at a stress higher than 500 kPa, shows high variability in values of the moduli. The maximum stress was observed in sample 12/11; it was 1986.3 kPa and M

_{r,CBR}reached 285.9 MPa.

- Soil 3—saclSi

_{r,CBR}, which correspond to the stress limit up to 800 kPa. The first subgroup, which was cycled at stresses up to 800 kPa, shows lower values of the moduli, the mean of M

_{r,CBR}equal to 65 MPa, and there is a smaller variability. The second subgroup, where the samples were cycled at a stress higher than 900 kPa, shows high variability in the values of the moduli; the standard deviation was 38.62. The maximum stress was observed in sample 14/5; it was 3514.1 kPa and M

_{r,CBR}reached 214 MPa.

- Soil 4—csaCl

_{r,CBR}, which also here correspond to the stress limit. The first subgroup, which was cycled at stresses up to 630 kPa, shows lower values of the moduli, the mean of M

_{r,CBR}equal to 51.8 MPa, and there is a smaller variability. The second subgroup, where the samples were cycled at a stress from 630 to 850 kPa, shows higher variability in the values of the moduli. The mean of M

_{r,CBR}in the second subgroup is 101.9 MPa. The third subgroup, where the samples were cycled at a stress over 850 kPa, shows the highest variability in the values of the moduli. The maximum stress was observed in sample 16/9; it was 1229.0 kPa and M

_{r,CBR}reached 244.8 MPa.

- Soil 5—sagrSi

_{r,CBR}, and this division is reflected in the groups defined by these stresses. The first subgroup, which was cycled at stresses up to 600 kPa, shows the lowest values of the moduli, the mean of M

_{r,CBR}equal to 48.6 MPa, as well as smaller variability in the case of three out of four samplings. The second subgroup, where the samples were cycled at a stress from 600 to 950 kPa, shows smaller variability of the moduli. The mean of M

_{r,CBR}in the second subgroup is 105.4 MPa. The third subgroup, where the samples were cycled at a stress over 950 kPa, shows the highest variability in the values of the moduli. The maximum stress was observed in sample 27/31; it was 1211.3 kPa and M

_{r,CBR}reached 257.3 MPa.

- Soil 6—grsaCl

_{r,CBR}, which also here approximately corresponds to the stress limit. The first subgroup, which was cycled at stresses up to 700 kPa, shows lower values of the moduli, the mean of M

_{r,CBR}equal to 69.26 MPa, and there is a smaller variability. The second subgroup, where the samples were cycled at a stress over 700 kPa, shows higher variability in the values of the moduli. The maximum stress was observed in sample 29/8; it was 999.1 kPa and M

_{r,CBR}reached 512.8 MPa.

- Soil 7—siSa

_{r,CBR}, which also here approximately correspond to the stress limit. The first subgroup, which was cycled at stresses up to 550 kPa, shows lower values of the moduli, the mean of M

_{r,CBR}equal to 43.0 MPa, and there is a smaller variability. The second subgroup, where the samples were cycled at a stress from 550 to 1000 kPa, shows higher variability in the values of the moduli. The mean of M

_{r,CBR}in the third subgroup is 244.8 MPa. The fourth subgroup, where the samples were cycled at a stress over 1500 kPa, shows the highest variability in the values of the moduli. The mean of M

_{r,CBR}in the fourth subgroup is 541.6 MPa. The maximum stress was observed in sample 33/2; it was 1935.3 kPa and M

_{r,CBR}reached 324.7 MPa.

- Soil 8—grsiSa

_{r,CBR}. The mean of M

_{r,CBR}is 116.9 MPa.

- Soil 9—siGr

_{r,CBR}, which also here correspond to the stress limit. The first subgroup, which was cycled at stresses up to 200 kPa, shows lower values of the moduli, the mean of M

_{r,CBR}equal to 16.8 MPa, and there is a smaller variability. The second subgroup, where the samples were cycled at a stress from 200 to 500 kPa, shows higher variability in the values of the moduli. The maximum stress observed was 495.1 and M

_{r,CBR}reached 64.0 MPa.

_{r,CBR}values were determined in individual soil types is shown in Figure 11.

_{r,CBR}on the applied plunger stress is shown for each soil type in Figure 12.

_{r,CBR}as well as its mean value increased. After the reduction, the values of M

_{r,CBR}fell into realistic limits. This behavior can be observed in all soil types analyzed.

## 4. Discussion

^{−3}and clay Cl were published [15]. The results valid for both of these materials are comparable to the moduli obtained at Mendel University. The moduli obtained for grSa at Delft University of Technology ranged in intervals from 210 to 900 MPa; MENDELU research found moduli from 100 to 900 MPa. Clay was only tested using one sample with a modulus value of 40 MPa; the occurrence interval of the modulus for Cl ranged from 14 to 429 MPa at MENDELU. Comparing the results, a similar variability of the M

_{r,CBR}values obtained from the corresponding test on a cyclic CBR device, can be observed. Despite the small size of the sample and incomplete information on the tests of the Delft research, a good match was found. These values are valid for the state before the plunger stress reduction, i.e., in samples with stress higher than the load bearing capacity limit. The Dutch research did not present the values of the plunger stress applied. With regard to the test methodology going to a depth of 2.5 mm in both studies, high values of plunger stress can be expected.

_{r}ranged in an interval of 76–159 MPa for soil type clSa, in an interval of 32–111 MPa for siSa, in an interval of 57–148 MPa for grsiSa, and in an interval of 88–141 MPa for siGr. The mean values of M

_{r}from this study and M

_{r,CBR}from cyclic CBR after the reduced stress range, were 117 and 67 MPa, respectively, for clSa; 71 and 51 MPa, respectively, for siSa; 102 and 115 MPa, respectively, for grsiSa; 114 and 45 MPa, respectively, for siGr. In all cases, the mean values of the modulus from the cyclic CBR ranged within the interval obtained using the triaxial device.

_{r}: 20–134 MPa for Cl, 90–150 MPa for siCl, and 11–84 MPa for csaCl. The occurrence intervals of M

_{r,CBR}from cyclic CBR ranged from 37 to 66 MPa for Cl, from 15 to 28 MPa for siCl, and from 44 to 80 MPa for csaCl.

_{r,CBR}estimates can be considered satisfactory.

_{r,CBR}variability. It also reflects the effect of highly plastic clays on flexible behavior as well as the differences between soil types.

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 12.**Dependence of the mean values of resilient modulus M

_{r,CBR}on the applied plunger stress.

Locality Number N° | Soil Type USCS | Sampling Number | Sample Number | Mean Density kg·m^{−3} | Mean Humidity % |
---|---|---|---|---|---|

1 | Cl | 10 | 60 | 1598.8 | 23.8 |

2 | siCl | 3 | 18 | 1655.9 | 20.7 |

3 | saclSi | 2 | 12 | 1748.3 | 18.6 |

4 | csaCl | 5 | 30 | 1813.7 | 15.7 |

5 | sagrSi | 6 | 36 | 1858.5 | 13.4 |

6 | grsaCl | 4 | 24 | 1635.5 | 21.5 |

7 | siSa | 10 | 60 | 1796.0 | 14.7 |

8 | grsiSa | 2 | 12 | 1827.3 | 13.6 |

9 | siGr | 4 | 24 | 1929.6 | 12.7 |

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## Share and Cite

**MDPI and ACS Style**

Ševelová, L.; Florian, A.; Hrůza, P.
Using Resilient Modulus to Determine the Subgrade Suitability for Forest Road Construction. *Forests* **2020**, *11*, 1208.
https://doi.org/10.3390/f11111208

**AMA Style**

Ševelová L, Florian A, Hrůza P.
Using Resilient Modulus to Determine the Subgrade Suitability for Forest Road Construction. *Forests*. 2020; 11(11):1208.
https://doi.org/10.3390/f11111208

**Chicago/Turabian Style**

Ševelová, Lenka, Aleš Florian, and Petr Hrůza.
2020. "Using Resilient Modulus to Determine the Subgrade Suitability for Forest Road Construction" *Forests* 11, no. 11: 1208.
https://doi.org/10.3390/f11111208