Stress Response of Graded Gravel Under Triaxial Compression Test Conditions Haiqing Li School of Geosciences and Info-Physics, Central South University, Changsha, 410083, China Corresponding author; e-mail: [email protected]

Ziqiang Zhu School of Geosciences and Info-Physics, Central South University, Changsha, 410083, China

ABSTRACT A graded gravel base mainly improves the stability and humidity conditions of the soil base and ensures the strength and stability of the base and surface. The grading of the gravel base plays an important role in the influence of the stress and deformation of the pavement and soil base structures. Three types of graded gravel are selected in this study to investigate the influence of grading on the strength, modulus, and deformation of the gravel base. The related characteristics of the different gravel types are analyzed based on the actual gravel base grading of a road. In this study, the mechanical properties of gravel base and the static mechanical influence of loading velocity on gravel base are analyzed based on triaxial test.

KEYWORDS: loading velocity; graded gravel; triaxial test; mechanical properties

INTRODUCTION A graded gravel base mainly improves the stability and humidity conditions of the soil base and ensures the strength and stability of the base and surface[1,2]. The vertical wheel loads can also be diffused by the gravel base. Besides, a gravel base can prevent the soil base from infiltrating into the pavement structure under the action of water to reduce the influence on the pavement structure. The grading of the gravel base plays an important role in the influence of the stress and deformation of the pavement and soil base structures[3-5]. Three types of graded gravel are selected in this study to investigate the influence of grading on the strength, modulus, and deformation of the gravel base. The related characteristics of the different gravel types are analyzed based on the actual gravel base grading of a road. Current research mainly focuses on the deformation and strength stability of graded gravel[68]. Several scholars have utilized direct shear test or static triaxial test to study the mechanical properties of graded gravel[9,10]. The triaxial test is one of the most commonly utilized tests in studying rock and soil mechanical properties and plays an irreplaceable role in the analysis of rock and soil mechanical properties [11-13]. In his experimental study, Knight [14] reported that reducing the porosity of gravel leads to a better result and recommended the use of coarse - 6809 -

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aggregate graded gravel. Wang et al. [15] employed high-precision static triaxial test to study the effect of vibration and compaction molding method on the shear strength of a graded gravel base material. Janoo et al. [16] studied the influence of grading the material peak strength. These studies mainly focused on the mechanical response of graded gravel under static loads. However, in practical engineering, the velocity of loading affects graded gravel significantly. Current research in this area is still rare. Therefore, the mechanical properties of gravel base and the static mechanical influence of loading velocity on gravel base are analyzed in this study based on triaxial test.

GRADING SELECTION AND ANALYSIS OF GRAVEL MATERIAL 100

100 90 82.6

90

Content / %

80 70

69.9 64.2 58.3 49.5

60 50 40 30 20 10

8

0 0.01

0.1

10.2 13.1

16.8

21.3

27.3

1 Particle Diameter/mm

1-3

35

10

100

Figure 1: Grading curved graph of graded gravel 1-3 The maximum particle diameter of the gravel base material was set to 37.5 mm. According to the actual grading of the gravel base, three types of graded gravel were selected as the objects of study to investigate the influence of grading on strength, modulus, and deformation of the gravel base. The properties of the different types of gravel were analyzed to determine the mechanical influence of gravel grading on the gravel base. Moreover, the different types of graded gravel were compared. Grading was classified into three classes after the analysis of different particle diameter contents. Fig. 1 shows the curved graph of grading class 1. The maximum particle diameter in class 1 is 37.5 mm. The content of particles whose diameters are greater than 4.75 mm is 65.0% of the total. The contents of particles whose diameters are in the range of 37.5 mm to 31.5 mm, 31.5 mm to 26.5 mm, 26.5 mm to 19 mm, 19 mm to 16 mm, 16 mm to 13.2 mm, 13.2 mm to 9.5 mm, and 9.5 mm to 4.75 mm are 10%, 7.4%, 12.7%, 5.7%, 5.9%, 14.5%, and 14.5%, respectively. Fig. 2 shows the grading curved graph of graded gravel class 2. The maximum particle diameter in gravel class 2 is 37.5 mm. The content of particles whose diameters are greater than 4.75 mm is 70.0% of the total. The contents of particles whose diameters are in the range of 37.5 mm to 31.5 mm, 31.5 mm to 26.5 mm, 26.5 mm to 19 mm, 19 mm to 16 mm, 16 mm to 13.2 mm, 13.2 mm to 9.5 mm, and 9.5 mm to 4.75 mm are 10%, 8.6%, 14.3%, 6.4%, 6.4%, 9.4%, and 14.9%, respectively. Fig. 3 shows the grading curved graph of graded gravel class 3. The maximum particle diameter in gravel class 3 is 31.5 mm. The content of particles whose diameters are greater than

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4.75 mm is 75.0% of the total. The contents of particles in the range of 37.5 mm to 31.5 mm, 31.5 mm to 26.5 mm, 26.5 mm to 19 mm, 19 mm to 16 mm, 16 mm to 13.2 mm, 13.2 mm to 9.5 mm, and 9.5 mm to 4.75 mm are 0%, 19.9%, 16.2%, 7.0%, 7.0%, 9.9%, and 15.0%, respectively. 100

100

90

90

80

81.4

Content/ %

70

67.1 60.7 54.3

60 50

44.9

40 30 20 10

8

12.4

10

15.5

19.2

24

2-3

30

0 0.01

0.1

1 Particle Diameter / mm

10

100

Figure 2: Grading curved graph of graded gravel 2-3

100

100 100

90 80

80.1

content / %

70

63.9 56.9 49.9

60 50 40

40

30 20 10

8

0 0.01

0.1

9.7

17.1 11.7 14.2

20.6

1 Particle Diameter/ mm

3-3

25

10

100

Figure 3: Grading curved graph of graded gravel 3-3 The following observations were obtained from the comparison of the three classes. The maximum particle diameters of classes 1 and 2 are 37.5 mm, whereas that of class 3 is 31.5 mm. The content of graded gravel whose particle diameters are in the range of 26.5 mm to 31.5 mm is considerably higher in gravel class 3 than in gravel classes 1 and 2. The content of gravel whose particle diameters are smaller than 0.15 mm is approximately 10%, whereas that of gravel whose particle diameters are larger than 26.5 mm is approximately 20%. After analyzing the content of gravel whose particle diameters are in the range of 0.6 mm to 26.5 mm, the content law in this range is as follows: gravel class 1 > gravel class 2 > gravel class 3.

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TEST CONDITIONS AND EQUIPMENT ① Apparatus The equipment utilized is a type YS30-3 stress path controlling triaxial testing machine. The main technical parameters are as follows: specimen size of φ300 mm × 600 mm, maximum compression of 750 kN. ② Specimen preparation

The specimen is 300 mm in diameter and 600 mm in height. ③ Filling and saturation tests The sample filling was divided into three layers. Prior to filling, a rubber membrane was tied to the base and the forming barrel was installed. Then, the rubber membrane was turned outward on the forming barrel to make it straight and cling to the in-wall of the forming barrel. Every time a portion of the sample was filled, vibrated casting method was implemented to allow the soil to meet the required height. The surface was leveled after filling. The porous disc and sample cap were positioned, and the rubber membrane was tied tightly.

The press machine was initiated to allow for contact between the sample and the force transmission piston, dynamometer, and so on. When the pointer of the dynamometer moved slightly, the machine was shut down immediately and the axial displacement meter and dynamometer pointer were adjusted to zero. A servo mechanism was utilized during the test to control the loading velocity and apply confined pressure around the specimen. Static loads were applied on the top of the specimen until the graded gravel specimen lost its stability. The stress–strain curve was then obtained. The graded gravel modulus was obtained through calculation after compiling the stress–strain curves and the data obtained from the test.

DETERMINING THE TEST PARAMETERS ① Initial modulus (shown in Fig. 4) as defined by the typical stress–strain curve and parameters is considered linear and elastic in this study when the axial strain is less than 0.5%. Linear regression is established in the corresponding stress–strain part, the slope of which is the initial modulus. ② Peak strength is

qf

,

and failure strain is

εf

.

③ Residual strength is qr . When axial strain reaches 10%, the corresponding deviatory stress is considered the residual strength.

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Figure 4: Typical stress–strain curve and parameter definitions The gravel stress–strain curve (shown in Figure 5) obtained from the test indicates that the axial pressure the gravel can tolerate increases with the increase in axial strain. When the axial strain reaches a certain value, the gravel reaches its ultimate strength. When the axial strain is greater than that strain, the gravel strength decreases rapidly with the increase in axial strain. When the axial strain continues to increase, the gravel strength basically remains unchanged; at this time, the gravel strength is the residual strength.

Figure 5: Graded gravel stress–strain curve

INFLUENCE OF STATIC TRIAXIAL TEST LOADING VELOCITY WITH DIFFERENT GRADED GRAVEL This study focused on the influence of loading velocity on graded gravel strength, graded gravel modulus, and so on. Loading velocity was divided into six, namely, 0.5, 1.0, 2.0, 4.0, 8.0, and 16.0 kPa/s. The stress–strain curves of the three classes of graded gravel under different loading velocities were obtained by tests and then analyzed.

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After analyzing the stress–strain curve of graded gravel class 1-3 under different loading velocities (Figure 6), we found that with the increase in loading velocity, the strength of gravel class 1-3 increases significantly; the peak and residual strengths of gravel increase continually. When the gravel reach their peak strength, the corresponding axial strain differs. With the change in loading velocity, the axial strain that corresponds to the peak strength follows a certain law: the corresponding axial strain increases with the increase in loading velocity. 1.60E+07 1.40E+07

Axial Stress/pa

1.20E+07 1.00E+07

0.5 kPa/s 1kPa/s

8.00E+06

2kPa/s 4kPa/s

6.00E+06

8kPa/s

4.00E+06

16kPa/s

2.00E+06 0.00E+00 0%

2%

4%

6%

8%

10%

12%

14%

16%

18%

Strain

Figure 6: Stress–strain curve of graded gravel 1-3 under different loading velocities 1.60E+07 1.40E+07

Axial Stress/Pa

1.20E+07 1.00E+07

0.5kta/s 1kta/s

8.00E+06

2kta/s

6.00E+06

4kta/s 8kta/s

4.00E+06

16kta/s

2.00E+06 0.00E+00 0%

2%

4%

6%

8%

10%

12%

14%

16%

18%

Strain

Figure 7: Stress–strain curve of graded gravel 2-3 under different loading velocities After analyzing the stress–strain curve of graded gravel class 2-3 under different loading velocities (Figure 7), we found that with the increase in loading velocity, the strength of gravel class 2-3 increases significantly. The peak strengths of gravel increase continually. Residual strength also increases. The elastic modulus of gravel class 2-3 increases with the increase in loading velocity. Meanwhile, when the gravel reach their peak strength, the corresponding axial strain differs. With the change in loading velocity, the axial strain that corresponds to the peak strength follows a certain law: the corresponding axial strain increases with the increase in loading velocity. In addition, when the loading velocity reaches 16 kPa/s, the axial strain of graded gravel class 2-3 reaches 18%, which is not the peak strength.

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After analyzing the stress–strain curve of graded gravel class 3-3 under different loading velocities (Figure 8), we found that with the increase in loading velocity, the strength of gravel class 3-3 increases significantly. The peak strengths of gravel increase continually. Residual strength also increases. By contrast, we found that the elastic modulus of gravel class 3-3 increases with the increase in loading velocity. When the gravel reach their peak strength, the corresponding axial strain differs. With the change in loading velocity, the axial strain that corresponds to the peak strength follows a certain law: the corresponding axial strain increases with the increase in loading velocity. In addition, when the loading velocity reaches 16 kPa/s, the axial strain of graded gravel class 3-3 reaches 18%; the bearing capacity does not decline.

1.60E+07 1.40E+07

Axial Stress/Pa

1.20E+07 0.5kPa/s

1.00E+07

1kPa/s

8.00E+06

2kPa/s

6.00E+06

4kPa/s 8kPa/s

4.00E+06

16kPa/s

2.00E+06 0.00E+00 0%

2%

4%

6%

8%

10%

12%

14%

16%

18%

Strain

Figure 8: Stress–strain curve of graded gravel 3–3 under different loading velocities

INFLUENCE OF LOADING VELOCITY ON GRAVEL PEAK STRENGTH AND RESIDUAL STRENGTH q

Figure 9 shows the change trend in the three classes of graded gravel peak strength f under different loading velocities (v). Gravel peak strength increases linearly with the increase in loading velocity. The relationship between loading velocity and graded gravel peak strength can be described by the formula,

q= a2 + b2 v f

where a2 and b2 are undetermined coefficients.

(2)

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6816 y = a + b*x

Equation

No Weightin Weight Residual 250514.1435 Sum of 7 Squares 0.99895 Pearson's r 0.99737 Adj. R-Squar

Peak Strength/ kPa

Value

10000

Intercept Slope

B B

Standard Err

853.4825 821.8763

142.31307 18.87053

8000 6000 4000 2000 0 0

2

4

6

8

10

12

14

16

18

14

16

18

Loading Velocity / kPa/s

(a) 1-3 16000 14000

Peak Strength/ kPa

12000 10000

Equation

y = a + b*x

Weight Residual Sum of Squares Pearson's r

No Weightin 111703.340 44 0.99956 0.9989

Adj. R-Squar

Value

Standard Err

C

Intercept

724.8756

95.03022

C

Slope

850.8173

12.60088

8000 6000 4000 2000 0 0

2

4

6

8

10

12

Loading Velocity / kPa/s

(b) 2-3 14000 12000

Peak Strength/ kPa

10000 8000 y = a + b*

Equation

No Weight Weight Residual 98833.17 Sum of 129 Squares Pearson's r 0.99957 Adj. R-Squ 0.99892

6000 4000 2000

Value

0 0

2

4

6

8

Standard E

D

Intercept

708.248

89.38816

D

Slope

807.603

11.85276

10

12

14

16

18

Loading Velocity / kPa/s

(c) 3-3

Figure 9: Graded gravel peak strength under different loading velocities

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The fitting correlation coefficient exceeds 0.99 and thus indicates high correlation. Figure 10 shows the law of gravel residual strength with the change in loading velocity. The three classes of graded gravel follow the same law with the change in loading velocity: the residual strength of graded gravel increases continually with the increase in loading velocity. Moreover, the relationship between residual strength qr and loading velocity v is linear and can also be fitted by the linear equation,

q= a3 + b3v r

(3)

where a3 and b3 are undetermined coefficients. The fitting correlation coefficient exceeds 0.99 and thus indicates high correlation. The differences in gravel residual strength are small under different loading velocities, but the maximum gravel grading of residual strength are classes 1-3 and 2-3. 14000 12000

Equation

y = a + b*x

Weight

No Weightin

Residual Sum 387893.808 1 of Squares 0.99851 Pearson's r

Residual Strength/ kPa

Adj. R-Square

10000

0.99627

B

Intercept

B

Slope

Value Standard Erro 96.01493 177.08635 858.1876

23.48142

8000 6000 4000 2000 0 0

2

4

6

8

10

12

14

16

18

14

16

18

Loading Velocity / kPa/s

(a) 1-3 14000 12000

Equation

y = a + b*x

Weight Residual Sum of Squares Pearson's r

No Weightin 16742.0042 6 0.99994

Residual Strength/ kPa

Adj. R-Squar

0.99984 Value

10000 C

Intercept

C

Slope

Standard Err

-8.8806

36.79022

870.9296

4.87834

8000 6000 4000 2000 0 0

2

4

6

8

10

12

Loading Velocity / kPa/s

(b) 2-3

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Residual Strength/ kPa

12000

6818

y = a + b*x Equation No Weightin Weight Residual 123444.705 Sum of 05 Squares 0.99949 Pearson's r 0.99872 Adj. R-Squa

10000 8000

Value

Standard Er

D

Intercept

-123.308

99.89986

D

Slope

828.0270

13.24659

6000 4000 2000 0 0

2

4

6

8

10

12

14

16

18

Loading Velocity / kPa/s

(c) 3-3 Figure 10: Gravel residual strength under different loading velocities

CONCLUSIONS The peak strength of graded gravel increases with the increase in loading velocity; the residual strength of graded gravel also increases with the increase in loading velocity. Furthermore, the relationship between peak strength and loading velocity is linear, similar to the relationship between residual strength and loading velocity; they can be fitted with formulae a3 + b3v respectively, and their results are also highly correlated. q= a2 + b2 v and q= r f

REFERENCES [1] Gray, J. (1962) "Characteristics of graded base course aggregates determined by triaxial tests," National Crushed Stone Association, 7, 61-64. [2] White, W., Day, T. (1982) "Transport of graded gravel bed material," Gravel-Bed Rivers, Fluvial Processes, Engineering and Management, 181-223. [3] Arellano-Aguilar, R., Burciaga-Díaz, O., Gorokhovsky, A., Escalante-García, J.I. (2014) "Geopolymer mortars based on a low grade metakaolin: Effects of the chemical composition, temperature and aggregate:binder ratio," Construction and Building Materials, 50, 642-648. [4] Hamidi, A., Azini, E., Masoudi, B. (2012) "Impact of gradation on the shear strengthdilation behavior of well graded sand-gravel mixtures," Scientia Iranica, 19, 393402. [5] Shon, C.S., Jung, Y.s., Saylak, D. (2013) "Evaluation of synthetic aggregates using off-ASTM specification ashes as road base course materials," Construction and Building Materials, 38, 508-514.

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[6] Fragaszy, R.J., Su, J., Siddiqi, F.H., Ho, C.L. (1992) "Modeling strength of sandy gravel," Journal of Geotechnical engineering, 118, 920-935. [7] Haeri, S.M., Hamidi, A. (2005) "Steady state and liquefaction characteristics of gravely sands," Geotechnical & Geological Engineering, 23, 141-156. [8] Kokusho, T., Hara, T., Hiraoka, R. (2004) "Undrained shear strength of granular soils with different particle gradations," Journal of Geotechnical and Geoenvironmental Engineering, 130, 621-629. [9] Vallejo, L.E. (2001) "Interpretation of the limits in shear strength in binary granular mixtures," Canadian Geotechnical Journal, 38, 1097-1104. [10] Yagiz, S. (2001) "Brief note on the influence of shape and percentage of gravel on the shear strength of sand and gravel mixtures," Bulletin of Engineering Geology and the Environment, 60, 321-323. [11] Cai, K. (2012) "Numerical analysis for the excavation of geotechnical material in tunnel and grouting effect," in: Du, X.L., Zheng, J.J., Yan, W.M., Li, Y., Zhang, J.W. (Eds.), Trends in Civil Engineering, Pts 1-4, pp. 1581-1584. [12] Lin, H., Cao, P., Wang, Y. (2013) "Numerical simulation of a layered rock under triaxial compression," International Journal of Rock Mechanics and Mining Sciences, 60, 12-18. [13] Lu, G.Y., Zhu, Z.Q., Liu, Q.Y., He, X.Q. (2009) "Failure mode and strength anisotropic characteristic of stratified rock mass under uniaxial compressive situation," Journal of Central South University of Technology, 16, 663-668. [14] Knight, J.A. (1935) "Gradation of aggregate as applied to stabilization of gravel roads," Canadian Engineer, 69, 9-13. [15] Wang, L., Xie, X.G., Feng, D.C. (2007) "Characteristics of the modulus and distortion of the graded aggregate material," Journal of Harbin Institute of Technology, 6, 1265-1268. [16] Janoo, V.C., Bayer, I., John, J. (2001) "The Effect of Aggregate Angularity on Base Course Performance." DTIC Document.

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Editor’s note. This paper may be referred to, in other articles, as: Haiqing Li and Ziqiang Zhu: “Stress Response of Graded Gravel under Triaxial Compression Test Conditions” Electronic Journal of Geotechnical Engineering, 2016 (21.20), pp 6809-6919. Available at ejge.com.