Laboratory testing and analysis of dynamic and static resilient modulus of subgrade soil under various influencing factors

Construction and Building Materials 195 (2019) 178–186

Contents lists available at ScienceDirect

Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat

Laboratory testing and analysis of dynamic and static resilient modulus of subgrade soil under various influencing factors Xiaolan Liu a, Xianmin Zhang a,b,⇑, Hao Wang c, Baiyu Jiang c a

College of Civil Aviation, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China College of Airport Engineering, Civil Aviation University of China, Tianjin 300300, China c Rutgers, The State Univ. of New Jersey, Piscataway, NJ 08854, USA b

h i g h l i g h t s
The influence of compaction degree on static and dynamic modulus is investigated.
The influence of loading frequency on dynamic modulus is investigated.
The prediction model of dynamic resilient modulus is developed with various factors.
The relationship of dynamic and static resilient modulus is developed.

a r t i c l e

i n f o

Article history: Received 17 August 2018 Received in revised form 17 October 2018 Accepted 7 November 2018

Keywords: Dynamic resilient modulus Static resilient modulus Moisture content Compaction degree Loading frequency Stress level

a b s t r a c t In this study, dynamic and static resilient modulus of subgrade soil were conducted for six types of subgrade soil using the stress level and loading range on top of subgrade under moving vehicle loading. The influences of loading frequency, stress level, compaction degree, and moisture content on dynamic and static modulus were investigated. The prediction models of nonlinear parameters of dynamic resilient modulus and the relationship of dynamic and static resilient modulus were developed. Results showed that dynamic resilient modulus of different soils were significantly affected by loading frequency at the loading frequency range of 0.5–3 Hz. Dynamic and static resilient modulus were both positively related with confining pressure and compaction degree, but negatively related to the moisture content of subgrade soil. The nonlinear parameters of dynamic resilient modulus prediction models had the similar form for different types of subgrade soil, while the coefficients of nonlinear parameters varied with the type of subgrade soil. The parameters of the relationships between dynamic and static resilient modulus for different types of soil were also similar in the equation format with different parameter values. The research findings provide valuable information for using realistic subgrade soil modulus in pavement design and analysis. Ó 2018 Elsevier Ltd. All rights reserved.

1. Introduction Subgrade soil provides the important foundation support for the upper layers in pavement structure. Static modulus of soil is usually used in traditional pavement design and analysis and in many specifications. However, dynamic testing method is recommended for pavement material testing because this method can capture the stress state in the pavement under moving vehicle loading. Therefore, it is needed to investigate the relationship

⇑ Corresponding author at: College of Civil Aviation, Nanjing University of Aeronautics and Astronautics, No.29 Jiangjun Road, Nanjing City, Jiangsu Province, 210016, China. E-mail address: [email protected] (X. Zhang). https://doi.org/10.1016/j.conbuildmat.2018.11.061 0950-0618/Ó 2018 Elsevier Ltd. All rights reserved.

between dynamic and static modulus in order to compare and conduct pavement design and analysis using different methods. A number of studies have investigated dynamic and static resilient modulus for different types of soil. Xenaki et al. [20] and Yang and Woodsrichard [21] investigated the influences of confining pressure, moisture content, and cyclic strain amplitude on dynamic and static resilient modulus of clay soil. They found that the resilient modulus increased with the increase of confining pressure and the decrease of moisture content. Ling et al. [11] and Christ and Park [6] studied the response patterns of maximum dynamic resilient modulus and static resilient modulus with different soil types, temperatures, confining pressures, and moisture contents for frozen soil, respectively. They discovered that both dynamic and static resilient modulus decreased with the increase

179

X. Liu et al. / Construction and Building Materials 195 (2019) 178–186

of temperature, but the moisture content had little effect on dynamic resilient modulus when the moisture content was more than 21%. Navarrete et al. [13] studied dynamic resilient modulus of clay soil in Mexico area using resonant column test and laser ultrasonic test, and found that resilient modulus remarkably depended on frequency and strain ratio. Zheng et al. [24] conducted the triaxial test on the typical clay and found that dynamic resilient modulus of saturated clay declined with the addition of strain and the decrease of frequency. Guo et al. [7] found that confining pressure and cyclic tress ratio had significantly influence on resilient modulus of soft clay. Li et al. [10] investigated dynamic resilient modulus of saturated muddy clay with step cyclic loading. Meanwhile, they took freezing temperature and loading frequency into account to build the hyperbolic model of resilient modulus. Wichtmann et al. [19] used resonant column test to analyze quartz sand soil samples with different relative densities, and proved that dynamic resilient modulus decreased largely with the increase of fine particle content. Salour and Erlingsson [15] studied the effect of subgrade soil suction on resilient modulus using repeated load triaxial tests, and provided an enhanced approach to predict resilient modulus of subgrade muddy soil. Zhang et al. [25] conducted dynamic triaxial experiments of frozen aeolian soil, and indicated that its resilient strain and modulus significantly depended on temperature and dynamic stress amplitude. Naji [12] considered seasonal variations in moisture content and soil type for the resilient modulus of subgrade soil. Pereira et al. [14] established nonlinear parameters of resilient modulus model based on seventeen gravel bases, sandy subgrades, and clay subgrades. Sas et al. [16] utilized triaxles test to study the influence of effective stress and loading characteristics on resilient modulus of subgrade cohesive soil. Yao et al. [22] measured dynamic resilient modulus of subgrade soil under different stress conditions, water contents, and traffic loading. The review of previous work indicates that the influential factors of compaction degree and loading frequency on nonlinear dynamic resilient modulus were seldom studied for subgrade soil, which were the important parameters affected by construction quality and vehicle speed. The quantitative relationship between dynamic and static resilient modulus of subgrade soil is still missing. Therefore, this study focused on investigating dynamic and static resilient modulus under the range of loading frequency and stress level experienced on subgrade under moving vehicle loading, along with other influencing factors. The prediction model of nonlinear dynamic resilient modulus and the relationship of converting static resilient modulus to dynamic resilient modulus were established with various influencing factors. 2. Laboratory tests In the testing, six different fine-grained soils obtained from different suburbs in China were dried naturally and removed from impurities. Then, the liquid limit (wL), plasticity index (Ip), optimum moisture content (OMC), and maximum dry density (MDD)

were measured following test specifications [2].The physical parameters of six soils are shown in Table 1. According to the preparation method of remolded soil in the test methods of soils for highway engineering [1], the cylindrical specimens with the diameter of 61.8 mm and the length of 125 mm were prepared. The triaxles test machine utilized in this study has the maximum axial load of 1kN and the maximum confining pressure of 0.3 MPa. The range of testing frequency is 0–20 Hz. The influences of moisture content, compaction degree, stress level and loading frequency on dynamic and static resilient modulus were investigated. The level of moisture content (x) was OMC2%, OMC, and OMC + 2% and the level of compaction degree (K) included 90%, 93%, and 96%, which corresponded to the requirements of compaction for the roadways having different functional classifications [3]. The levels of confining pressure (r) were 15 kPa, 30 kPa, 45 kPa, 60 kPa, and the level of deviator stress (rd) were 30 kPa, 55 kPa, 75 kPa, 105 kPa, respectively. These stress levels were selected following the test methods of soils for highway engineering, which were determined based on the subgrade stress level under vehicle loading [8]. A numerical model was developed to simulate moving vehicle loading on pavement and calculate the loading frequency in the pavement. The typical pavement structure in China was used, which was composed of 16-cm asphalt layer, 32-cm semi-rigid base layer, and soil subgrade. The resilient modulus of asphalt layer, base layer, and subgrade were assumed 1500 MPa, 1200 MPa, and 60 MPa, respectively, following pavement design specification in China. The finite dimension of the model was selected to be 16  16  3.2 m (length  width  depth). The element thicknesses were selected at 32 mm for the subgrade, and 16 mm for asphalt and base layers through sensitivity analysis. The bottom of subgrade was restricted for all degrees of freedom. The both sides of subgrade and base layer were constrained in the horizontal directions. The widths and lengths of the elements in the loading area were respectively selected at 16 mm and 32 mm depending on the widths of the tire ribs and grooves based on the practice used in the literature [4,17]. A dual-tire assembly was simulated with a spacing of 122 mm between the two tires. The load applied on each tire was 25kN and tire pressure was 0.7 MPa, which represented typical truck loading. The loading area depended on the tire load and tire pressure. The moving load was simulated by changing the loading area on pavement surface at the specific interval depending on the speed. A wide range of speeds (18–144 km/h) were simulated. The frequency range of dynamic vehicle loading was shown in Fig. 1. The results showed that the loading frequency (f) on top of subgrade varied from 0.5 Hz to 3 Hz. This range of loading frequency was selected in the dynamic resilient modulus test of soil. In order to simulate the stress history experienced in subgrade during construction, the confining pressure, deviator stress, and cycle number were selected at 30 kPa, 55 kPa, 1000 loading cycles respectively in the pre-conditioning stage [8,7]. For the purpose of

Table 1 Physical parameters of soil sample.

a b

Sample number

Sample location

USCS classa

wL/%

Ip

OMCb/%

MDDb/(g/cm3)

S1 S2 S3 S4 S5 S6

Tianjin Shijiazhuang Cangzhou Xuanhua Mohe Nanjing

CL CL SM SM ML ML

49.8 42.93 38.39 34.91 21.75 18.8

25.02 20.90 21.26 16.85 10.08 7.81

19.67 18.72 14.89 15.86 11.98 10.85

1.69 1.66 1.75 1.70 1.92 1.88

USCS, unified soil classification system. Maximum dry weight and optimum moisture content based on standard proctor compaction test (ASTM D698).

180

X. Liu et al. / Construction and Building Materials 195 (2019) 178–186

Fig. 1. Load frequency on top of subgrade at different vehicle speeds.

considering the effect of dynamic vehicle loading on subgrade, a haversine- shaped loading pulse was applied on the soil specimen with 100 loading cycles for each stress state [15]. The specific loading sequences of different stress states were listed in Table 2. In the static triaxles test, the value of moisture content, compaction degree, and stress level was similar to those of dynamic triaxles tests; while the loading time was kept at 60 s.

3. Results and discussion 3.1. Dynamic resilient modulus The dynamic resilient modulus was defined as shown in Eq. (1):

Ed ¼

rd er

ð1Þ

where, Ed is dynamic resilient modulus. rd is the applied deviator stress. er is the recoverable strain during each loading cycle. The average values of dynamic resilient modulus in the last five loading cycles were calculated for analysis. The measured dynamic resilient modulus of S1 soil at different stress sequences with different influencing factors (moisture content, compaction degree, and loading frequency) were shown in Fig. 2.

Table 2 Testing sequence. Stress sequence

Confining pressure

Deviator stress

Cycle number

Pre-conditioning 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

30 kPa 60 kPa 60 kPa 60 kPa 60 kPa 45 kPa 45 kPa 45 kPa 45 kPa 30 kPa 30 kPa 30 kPa 30 kPa 15 kPa 15 kPa 15 kPa 15 kPa

55 kPa 30 kPa 55 kPa 75 kPa 105 kPa 30 kPa 55 kPa 75 kPa 105 kPa 30 kPa 55 kPa 75 kPa 105 kPa 30 kPa 55 kPa 75 kPa 105 kPa

1000 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100

Fig. 2. Dynamic resilient modulus results measured at different (a) moisture contents; (b) compaction degrees; and (c) loading frequencies.

Fig. 2 shows that when moisture content, compaction degree, and frequency are the same, the dynamic resilient modulus increases as the confining pressure increases or the deviator stress

181

X. Liu et al. / Construction and Building Materials 195 (2019) 178–186 Table 3 Relationship between Ed and Edref. Sample number

Ed = f(x, Edref)

S1

Ed = (0.0922x+2.7586) R2 = 0.9342 Ed = (0.0740x+2.3500) R2 = 0.9548 Ed = (0.0805x+2.2080) R2 = 0.9151 Ed = (0.0837x+2.3084) R2 = 0.9398 Ed = (0.0619x+1.7334) R2 = 0.9079 Ed = (0.0535x+1.5747) R2 = 0.9612

S2 S3 S4 S5 S6

Ed = f(K, Edref) Edref Edref Edref Edref Edref Edref

Ed = (0.0613K4.8804) R2 = 0.9274 Ed = (0.0472K3.5265) R2 = 0.9643 Ed = (0.0356K2.4112) R2 = 0.9314 Ed = (0.0420K3.0271) R2 = 0.9248 Ed = (0.0432K3.1486) R2 = 0.9457 Ed = (0.0369K2.5411) R2 = 0.9338

Ed = f(f, Edref) Edref Edref Edref Edref Edref Edref

Ed = (0.1502f+0.8179) R2 = 0.9523 Ed = (0.1242f+0.8573) R2 = 0.9146 Ed = (0.1294f+0.8426) R2 = 0.9047 Ed = (0.1052f+0.8725) R2 = 0.9152 Ed = (0.1425f+0.8318) R2 = 0.9220 Ed = (0.2055f+0.7533) R2 = 0.9137

Edref Edref Edref Edref Edref Edref

Edref is dynamic resilient modulus with the testing parameter of 19.67% for moisture content 96% for compaction degree, and 1 Hz for loading frequency; x is moisture content; K is compaction degree; and f is loading frequency.

decreases. In Fig. 2(a), when the compaction degree and loading frequency keep the same, the dynamic resilient modulus decreases with the increase of moisture content. The dynamic resilient modulus increases by 9%–20% when the moisture content increases from OMC-2% to OMC and 24%–30% when the moisture content increases from OMC to OMC +2%. Because the increase of moisture content reduces the cohesion strength of soil with more lubrication effect, this leads to the decrease of modulus. Hence, making the moisture content of subgrade soil close to the optimum moisture content is beneficial to increase the modulus of subgrade soil. In Fig. 2(b), when moisture content and loading frequency stay the same, the dynamic resilient modulus increases with the increase of compaction degree. The dynamic resilient modulus increases by 21%–26% when the compaction degree increases from 90% to 93% and 20%–24% when the moisture content increases from 93% to 96%. Since the growth of compaction degree reduces the air voids and increases the density of soil, this causes the increase of modulus. The density is usually used as the control parameter in most quality control and quality assurance specifications for pavement construction. However, modulus concept is used in pavement design and analysis. Therefore, the discovered relationships between density and resilient modulus can be used to determine the suitable compaction degree for subgrade soil based on the modulus requirement used in the pavement design. In Fig. 2(c), when the moisture content and compaction degree remain the same, the dynamic resilient modulus increases with the increase of loading frequency. This conclusion is consistent with the findings from Zhang et al. [25] and Zheng et al. [24]. The dynamic resilient modulus increases by 7%–14% when the frequency increases from 0.5 Hz to 1 Hz. When the frequency is in the range of 1–3 Hz, the dynamic resilient modulus grows by 9%–14% with the frequency increasing by 1 Hz. This clearly indicates the frequency-dependency of soil modulus. In other words, the subgrade soil modulus may vary depending on vehicle speeds. Previous researches have focused on the effect of vehicle speed on asphalt pavement response considering viscoelastic properties of asphalt layer [18]. The findings here indicate that the frequencydependency of soil modulus should be considered in pavement response analysis. In order to further analyze the effect of individual factor on dynamic resilient modulus (Ed) measured at different stress sequences, the reference modulus (Edref) was defined as the modulus with the testing parameter of 19.67% for moisture content, 96% for compaction degree, and 1 Hz for loading frequency. The relationships between Ed and Edref at different stress sequences were shown in Table 3, respectively, for each influencing factor. The results show that linear relationships exist between dynamic resilient modulus and each individual influencing factor as the stress

level changes. In general, the relationships between Ed and Edref were similar for six types of soils, although the slope coefficients of linear regression models varied with moisture content, compaction degree, or loading frequency. 3.2. Prediction model of dynamic resilient modulus Many prediction models have been proposed incorporating the influence of various factors on the resilient modulus (such as bilinear model, hyperbolic model, power exponent model, etc.). The power exponent model is the most widely used one among them and is shown in Eq. (2) [9,17].

Ed ¼ k1 rkd2

ð2Þ

where, k1 and k2 are regression coefficient. The relationships of k1 and k2 were plotted with different moisture contents, compaction degrees, loading frequencies, and confining pressures, as shown in Figs. 3 and 4, respectively. Multivariate regression analysis was conducted to obtain k1 and k2, which was influenced by moisture content, compaction degree, loading frequency and stress level, as shown in Table 4. Generally, the regression models of k1 and k2 were similar for six types of soils, but the coefficients of confining pressure in the models of k2 for S3 and S4 was different from those of S1, S2, S5 and S6. This is because the coefficients of k1 and k2 vary with the type of subgrade soils. In other words, nonlinear parameters of dynamic resilient modulus, named k1 and k2, are influenced by physics parameters of subgrade soil, such as liquid limit, plasticity index, optimum moisture content, and maximum dry density. For the purpose of verifying the accuracy of the prediction model of dynamic resilient modulus, previous laboratory measurements from Bao and Mohajerani [5] were used to compare with the prediction results of different subgrade soils, as shown in Table 5. The results show that the discrepancies between the measured values and the calculated values from the prediction models are less than 30% for S1 and S3, while the discrepancy between the measured values and the calculated values from the prediction model was less than 15% for S5. This is because the performance of subgrade soil is complex and the properties of soil specimens are affected by regional effect. 3.3. Relationship between dynamic and static resilient modulus The static resilient modulus is defined as the ratio of deviator stress to resilient strain when the loading time is kept for 60 s [23]. Ideally, the static modulus should be measured at very long loading time or very small loading frequency. The 60-second loading time is used because the resilient modulus of soil has negligible

182

X. Liu et al. / Construction and Building Materials 195 (2019) 178–186

Fig. 3. Regression models between k1 and (a) moisture content; (b) compaction degree; and (c) loading frequency.

Fig. 4. Regression models between k2 and (a) moisture content; (b) compaction degree; and (c) loading frequency.

183

X. Liu et al. / Construction and Building Materials 195 (2019) 178–186 Table 4 Regression models of dynamic resilient modulus. Sample number

k1 = f(x, K, f, r)

k2 = f(x, K, f, r)

S1

k1 = (0.0666x+0.0636K0.0998f3.5014)r +(19.2200x+6.0553K+15.9670f98.8288) R2 = 0.9852 k1 = (0.0665x+0.0484K0.0554f2.2577)r +(18.4125x+6.3880K+14.7235f147.2356) R2 = 0.9147 k1 = (0.0456x0.0075K0.0476f+1.8949)r +(9.1650x0.8830K5.5679f339.3912) R2 = 0.9642 k1 = (0.0828x+0.3165K0.1068f27.8142)r +(14.4875x+0.1528K+16.0648f344.6577) R2 = 0.9351 k1 = (0.0186x+0.0062K+0.0906f1.4824)r +(11.2825x+3.8611K+5.689f7.7586) R2 = 0.9515 k1 = (0.1305x0.0238K+0.4156f+1.0573)r +(21.8250x+13.8931K21.7052f867.6848) R2 = 0.9135

k2 = (0.0001f0.0010)r +(0.0071x+0.0017K+0.0158f0.4569) R2 = 0.9612 k2 = (0.0001f0.0024)r +(0.0096x0.0012K+0.0064f0.1940) R2 = 0.9353 k2 = (0.0002K0.0001f0.0023)r +(0.0101x+0.0930K+0.0456f1.0869) R2 = 0.9575 k2 = (0.0006K+0.0002f+0.0535)r +(0.0039x+0.0120K+0.0014f1.3204) R2 = 0.9179 k2 = (0.0002f+0.0028)r +(0.0035x+0.0072K+0.0281f1.0556) R2 = 0.9642 k2 = (0.0002f+0.0032)r +(0.0096x0.0009K+0.0438f0.5836) R2 = 0.9257

S2

S3

S4

S5

S6

Table 5 Comparison between previous findings and prediction models. Regression models

rd /kPa

r/kPa

x/%

K/%

f/Hz

Measured values/MPa [5]

Calculated values/MPa

Error/%

S1

24.8 12.4 24.8 37.3 49.7 62 12.4 24.8 37.3 49.7 62 12.4 24.8 37.3 49.7 62 24.8 12.4 24.8 37.3 49.7 62 12.4 24.8 37.3 49.7 62 12.4 24.8 37.3 49.7 62 24.8 12.4 24.8 37.3 49.7 62 12.4 24.8 37.3 49.7 62 12.4 24.8 37.3 49.7 62

41.4 41.4 41.4 41.4 41.4 41.4 27.6 27.6 27.6 27.6 27.6 13.8 13.8 13.8 13.8 13.8 41.4 41.4 41.4 41.4 41.4 41.4 27.6 27.6 27.6 27.6 27.6 13.8 13.8 13.8 13.8 13.8 41.4 41.4 41.4 41.4 41.4 41.4 27.6 27.6 27.6 27.6 27.6 13.8 13.8 13.8 13.8 13.8

20.4 20.4 20.4 20.4 20.4 20.4 20.4 20.4 20.4 20.4 20.4 20.4 20.4 20.4 20.4 20.4 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 11.5 11.5 11.5 11.5 11.5 11.5 11.5 11.5 11.5 11.5 11.5 11.5 11.5 11.5 11.5 11.5

99.87 99.87 99.87 99.87 99.87 99.87 99.87 99.87 99.87 99.87 99.87 99.87 99.87 99.87 99.87 99.87 99.88 99.88 99.88 99.88 99.88 99.88 99.88 99.88 99.88 99.88 99.88 99.88 99.88 99.88 99.88 99.88 98.29 98.29 98.29 98.29 98.29 98.29 98.29 98.29 98.29 98.29 98.29 98.29 98.29 98.29 98.29 98.29

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

105.30 119.26 105.30 97.86 92.95 89.33 110.44 98.36 91.87 87.57 84.39 100.93 90.67 85.12 81.42 78.69 136.34 157.01 136.34 125.47 118.34 113.13 148.20 129.80 120.05 113.64 108.94 138.67 122.50 113.88 108.18 103.99 99.68 118.74 99.68 89.93 83.64 79.10 112.28 91.95 81.74 75.25 70.60 106.05 84.71 74.21 67.62 62.94

125 130 123 120 118 117 117 114 112 116 118 108 110 109 112 114 112 134 110 98 93 90 120 104 95 92 87 107 95 90 88 84 102 127 101 95 90 84 105 89 83 82 80 92 80 76 74 72

16 8 14 18 21 24 6 14 18 25 28 7 18 22 27 30 22 17 24 28 27 26 23 25 26 24 25 30 29 27 23 24 2 7 1 5 7 6 7 3 2 8 12 15 6 2 9 13

S3

S5

184

X. Liu et al. / Construction and Building Materials 195 (2019) 178–186

Comparing the fitting results of using power function, exponential function, logarithmic function, and linear function, linear function was adopted to build the relationship between dynamic resilient modulus (at 1 Hz) and static resilient modulus, as shown in Eq. (4).

E0d ¼ aEs þ b

ð4Þ

where, a and b are regression coefficients (fitting parameters). The variations of fitting parameters a and b with different moisture contents, compaction degrees, and confining pressures, were plotted in Figs. 6 and 7, respectively. It was found that the parameter a was in the range of 1.8–2.3; while the parameter b was in the range of 2–14. In general, the dynamic resilient modulus at 1 Hz was more than twice the corresponding static resilient modulus at the same moisture content, compaction degree, and confining pressure. The regression equations of parameters a and b with different influencing factors are listed in Table 6, respectively, for each type of soil. These regression models are in the similar form for six types of soils, while the coefficients of confining pressure in the models of parameter a for S3 and S4 are different from those for S1, S2,

Fig. 5. Static resilient modulus curve at different (a) moisture contents and (b) compaction degrees.

changes as the loading time increases further based on previous literature [23]. The static resilient modulus was measured for the same six types of soils with different moisture contents, compaction degrees, and stress levels, as shown in Fig. 5. It was found that the influences of moisture content, compaction degree, and stress level on static resilient modulus was similar to those of dynamic resilient modulus. The increase of moisture content and deviator stress caused the reduction of static resilient modulus, while the increase of compaction degree and confining pressure are beneficial to the increase of static resilient modulus. As compared to dynamic resilient modulus, the corresponding static modulus is much smaller at the same moisture content, compaction degree, and confining pressure. Because the influences of moisture content, compaction degree, and stress level on dynamic and static resilient modulus are similar, the relationship between dynamic and static resilient modulus can be established, as shown in Eq. (3).

E0d ¼ f ðEs ; r; x; K Þ

ð3Þ

where, Ed’ is dynamic resilient modulus measured at 1 Hz, and Es is static resilient modulus.

Fig. 6. Regression models between parameter a and confining pressure at different (a) moisture contents; and (b) compaction degrees.

X. Liu et al. / Construction and Building Materials 195 (2019) 178–186

185

S5 and S6. Although the above analysis was based on the dynamic resilient modulus at 1 Hz, the effect of loading frequency as shown in Table 3 can be used. Therefore, the relationship between dynamic and static resilient modulus can be established with different loading frequencies, confining pressures, compaction degrees, and moisture contents.

4. Conclusions

Fig. 7. Regression models between parameter b and confining pressure at different (a) moisture contents; and (b) compaction degrees.

Dynamic and static triaxial tests for six types of subgrade soil were conducted to study the resilient modulus of subgrade soil considering the effects of loading frequency (dynamic loading), stress level, compaction degree, and moisture content. The prediction models of nonlinear parameters of dynamic resilient modulus and the relationship of dynamic and static resilient modulus were investigated. The dynamic triaxial test results showed that loading frequency had significant influence on dynamic resilient modulus for six types of subgrade soil. The dynamic resilient modulus increased as loading frequency increased. The increasing amplitude of dynamic resilient modulus was obvious at the frequency range of 0.5–3 Hz. In addition, dynamic resilient modulus of soil were positively related with confining pressure and compaction degree, but negatively related to moisture content. However, the changes of dynamic resilient modulus under different influencing factors varied with the type of subgrade soil. In the prediction models of dynamic resilient modulus, the nonlinear parameters of prediction models were related to loading frequency, stress level, compaction degree, and moisture content. In static triaxial tests, the effects of confining pressure, compaction degree, and moisture content on static resilient modulus was similar to those of dynamic resilient modulus for six types of subgrade soils. The parameters of the quantitative relationship between dynamic and static resilient modulus were influenced by loading frequency, stress level, compaction degree, and moisture content. The model formats were similar for six types of subgrade soils, but the parameters varied for different type of soils. In the future work, more soil samples should be tested to build the large database. This will improve the accuracy of prediction models of nonlinear dynamic resilient modulus and the quantitative relationships of dynamic and static resilient modulus for practical application in pavement design and analysis.

Table 6 Regression models of parameters a and b relating dynamic and static resilient modulus. Sample number

a = f(x, K, r)

b = f(x, K, r)

S1

a = (0.0029x0.0005K0.0061)r +(0.0719x0.0018K+3.4002) R2 = 0.9712 a = (0.0022x0.0003K0.0161)r +(0.0590x+0.0088K+2.3375) R2 = 0.9147 a = (0.0001x+0.005)r +(0.0105x0.0001K+1.8014) R2 = 0.9649 a = (0.0002x+0.0017)r +(0.0056x0.0011K+2.0153) R2 = 0.9345 a = (0.0002x+0.0001K0.0163)r +(0.0183x+0.0021K+2.1207) R2 = 0.9549 a = (0.0002x+0.0003K0.0258)r +(0.0152x0.0176K+3.4877) R2 = 0.9253

b = (0.0781x+0.0235K0.8621)r +(1.7668x0.1878K2.1918) R2 = 0.9564 b = (0.0863x+0.0142K+0.3615)r +(2.3758x0.4436K+4.7535) R2 = 0.9305 b = (0.0036x0.0007K0.006)r +(0.3416x+0.056K+10.9474) R2 = 0.9781 b = (0.0045x+0.0009K0.1428)r +(0.2375x+0.0220K+11.6075) R2 = 0.9078 b = (0.0040x0.0024K+0.2970)r +(0.5111x0.1200K+13.2526) R2 = 0.9474 b = (0.0043x0.0053K+0.4579)r +(0.5100x+0.3535K17.5076) R2 = 0.9149

S2

S3

S4

S5

S6

186

X. Liu et al. / Construction and Building Materials 195 (2019) 178–186

Conflict of interest None. Acknowledgement The authors gratefully acknowledge the National Natural Science Foundation of China (No. 51178456) for providing the funding that made this study possible. References [1] AASHTOT307-99 (2012) Standard method of test for determining the resilient modulus of soils and aggregate materials. Washington, D. C. [2] ASTM D698 (2000) Standard test methods for laboratory compaction characteristics of soil using standard effort. Washington, D. C. [3] AASHTO (2002) Guide for design of pavement structures. Washingto, D. C. [4] I.L. Al-Qadi, H. Wang, Impact of wide-base tires on pavements: results from instrumentation measurements and modeling analysis, Transp. Res. Rec. 2304 (2012) 169–176. [5] T.N. Bao, A. Mohajerani, Resilient modulus of fine-grained soil and a simple testing and calculation method for determining an average resilient modulus value for pavement design, Transp. Geotech. 7 (5) (2016) 59–70. [6] M. Christ, J.B. Park, Ultrasonic technique as tool for determining physical and mechanical properties of frozen soils, Cold Reg. Sci. Technol. 58 (3) (2009) 136–142. [7] L. Guo, J. Wang, Y. Cai, et al., Undrained deformation behavior of saturated soft clay under long-term cyclic loading, Soil Dyn. Earthquake Eng. 50 (7) (2013) 28–37. [8] JTG E40-2007 (2007) Test methods of soils for highway engineering. Beijing, China. [9] D. Kim, J.R. Kim, Resilient behavior of compacted subgrade soils under the repeated triaxles test, Constr. Build. Mater. 21 (7) (2007) 1470–1479. [10] J. Li, Y. Tang, P. Yang, et al., Dynamic properties of freezing–thawing muddy clay surrounding subway tunnel in Shanghai, Environ. Earth Sci. 74 (6) (2015) 5341–5349.

[11] X.Z. Ling, Z.Y. Zhu, F. Zhang, et al., Dynamic elastic modulus for frozen soil from the embankment on Beiluhe Basin along the Qinghai-Tibet Railway, Cold Reg. Sci. Technol. 57 (1) (2009) 7–12. [12] K. Naji, Resilient modulus–moisture content relationships for pavement engineering applications, Int. J. Pavement Eng. 7 (12) (2016) 1–10. [13] M. Navarrete, F.A. Godínez, M. Villagrán-Muniz, Elastic properties of compacted clay soils by laser ultrasonics, Int. J. Thermophys. 33 (8) (2013) 1810–1816. [14] C. Pereira, S. Nazarian, A.G. Correia, Extracting damping information from resilient modulus tests, J. Mater. Civ. Eng. 29 (12) (2017) 54–69. [15] F. Salour, S. Erlingsson, Resilient modulus modelling of unsaturated subgrade soils: laboratory investigation of silty sand subgrade, Road Mater. Pavement Des. 16 (3) (2015) 553–568. [16] W. Sas, A. Głuchowski, K. Gabrys´, et al., Resilient modulus characterization of compacted cohesive subgrade soil, Appl. Sci. 7 (370) (2017) 1–20. [17] L.N. Wang, Train-Induced Dynamic Response and Permanent Deformation of Embankment in Permafrost Region Alone Qinghai-Tibet Rail Way Ph. D. Thesis, Harbin Institute of Technology, Harbin, 2013. [18] H. Wang, I.L. Al-Qadi, The importance of nonlinear anisotropic modeling of granular base for predicting maximum viscoelastic pavement responses under moving vehicular loading, J. Eng. Mech. 139 (1) (2013) 29–38. [19] T. Wichtmann, M.A.N. Hernández, T. Triantafyllidis, On the influence of a noncohesive fines content on small strain stiffness, modulus degradation and damping of quartz sand, Soil Dyn. Earthquake Eng. 69 (2) (2015) 103–114. [20] V.C. Xenaki, G.A. Athanasopoulos, Dynamic properties and liquefaction resistance of two soil materials in an earth-fill dam—Laboratory test results, Soil Dyn. Earthquake Eng. 28 (8) (2008) 605–620. [21] L.L. Yang, D. Woodsrichard, Shear stiffness modeling of cemented clay, Can. Geotech. J. 52 (2014) 1–11. [22] Y.S. Yao, Z.L. Zheng, J.H. Zhang, et al., Model for predicting resilient modulus of unsaturated subgrade soils in South China, KSCE J. Civ. Eng. 22 (6) (2018) 2089–2098. [23] Y.J. Zhang, The Research of the Loess Subgrade Modulus of Resilience in Shanxi Province, Chang’an University, Xi’an, China, 2015. [24] G. Zheng, H.F. Huo, H.Y. Lei, et al., Contrastive study on the dynamic characteristics of saturated clay in different vibration frequencies, J. Tianjin Univ. (Sci. Technol.) 46 (1) (2013) 38–43. [25] S. Zhang, C.A. Tang, P. Hu, et al., Reversible and irreversible strain behavior of frozen aeolian soil under dynamic loading, Environ. Earth Sci. 75 (3) (2016) 1– 11.