Evaluating the influence of moisture on settling velocity of road embankment constructed with recycled construction wastes

Construction and Building Materials 241 (2020) 117988

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Evaluating the influence of moisture on settling velocity of road embankment constructed with recycled construction wastes Lulu Liu a,b, Zhe Li b, Guojun Cai a,⇑, Surya S.C. Congress c, Xiaoyan Liu a, Baosen Dai b a

Institute of Geotechnical Engineering, Southeast University, Nanjing, Jiangsu 211189, China School of Highway, Chang’an University, Xi’an, Shaanxi 710054, China c Zachry Department of Civil and Environmental Engineering, Texas A&M University, College Station, TX 77843-3136, USA b

h i g h l i g h t s
Change in moisture and settling velocity of recycled construction waste are analyzed.
Influence of moisture on the settling velocity is mainly within a depth of 3 m.
Settling velocity of the arc-shaped protective slope section contains two peaks.
Prediction model for settling velocity of recycled construction waste is obtaind.

a r t i c l e

i n f o

Article history: Received 25 August 2019 Received in revised form 26 December 2019 Accepted 30 December 2019

Keywords: Embankment Recycled construction wastes Change in moisture Settling velocity

a b s t r a c t Variation in moisture can influence the mechanical performance of embankments, and affect the bearing capacity of pavement structures. Therefore, it is necessary to constrain the relationship between the moisture and the settling velocity of embankments, to assess the safety and stability of highways built on the embankments. This research includes a long-term study of monitoring the moisture and deformation of an embankment on the Xi’an-Xianyang Highway, China. The influence of moisture on the settling velocity of barricade and arc-shaped protective slope sections were analyzed in detail. The results show that changes to the moisture and settling velocity followed similar trends. The influence of moisture on the settling velocity were mainly observed within a depth of 3 m from the road surface. The settling velocity of the arc-shaped protective slope section was bimodal. A model to predict the influence of moisture on the settling velocity of embankments made from recycled construction wastes was developed, based on the probability density function defined by the Weibull distribution. A formula to describe the cumulative effects of moisture on the settling velocity was devised, based on data measured at the barricade sections. Ó 2019 Elsevier Ltd. All rights reserved.

1. Introduction With rapid economic developments and the progress of urbanization, abundant construction waste has been produced in urban–rural reconstruction and urban construction projects [1,2]. Currently, China is among the top countries generating construction waste, where the annual production exceeds 0.4 billion tons and occupies a significant amount of spatial resources causing serious environmental pollution. Recently, the demand for sands and gravels increased due to the rapid development of infrastructure including highways and railways in China [3,4]. As a sustainable solution, it is suggested that construction waste should be treated ⇑ Corresponding author. E-mail address: [email protected] (G. Cai). https://doi.org/10.1016/j.conbuildmat.2019.117988 0950-0618/Ó 2019 Elsevier Ltd. All rights reserved.

appropriately and used in the engineering construction of embankments. This can not only resolve supply–demand conflicts for construction materials but can also reduce environmental pollution caused by construction waste and conform to the national sustainability development strategy [5]. The subsidence deformations of embankments, especially from uneven settlements, can induce various pavement distresses that can affect traffic safety [6,7]. Subsidence deformation (especially the long-term deformation) of embankments constructed with recycled construction waste is a new challenge for the transportation infrastructure industry. Dahlberg [8] summarized the details of selected subgrade settlement models, including Japanese models [9,10], US models [11,12], European models [13–16], South African models [17] and Australian models [18]. However, these models did not account for the subgrade moisture. Road slopes,

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shoulders, and pavements in arid and semi-arid regions are the most vulnerable structures to atmospheric precipitation. For high-class highways with strong water resistances, water ingress into the pavement is relatively low. Hence, precipitation mainly penetrates into the embankment through the shoulder and slope. This penetrated moisture may further infiltrate into the embankment and accelerate its settling. Moisture changes within the embankment can significantly influence its settlement, which affects the bearing capacity of the pavement structure to some extent. Therefore, evaluating the influence of embankment

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moisture on its settling velocity is significant to accurately assess the safety and stability of highways. Investigations on recycled construction wastes have mainly focused on characteristics that include durability [19–21], shear behavior and compressive strength [22–25], resilient modulus and load bearing capacity [4,22,23], pore pressure and particle distributions [3,26,27], and stress–strain relationships [28–30]. Most of these studies were based on laboratory test results. Only few datasets are available from field tests conducted on subgrades constructed with recycled construction wastes. Past studies have been conducted on measuring subgrade moisture using field tests and numerical methods, but they did not elucidate the relationship between changes in moisture and settling velocity of subgrade. For example, Qian et al. [31] showed that the groundwater depth, which changes with season and climate, is an important factor that influences subgrade water content [31]. Liu et al. [32] investigated changes to the moisture content of an upper embankment using numerical methods. Additionally, Hu et al. [33] and Liu et al. [32] used numerical data to suggest that the initial groundwater depth controls the subgrade moisture [32,33]. Cumulative settlement is strongly affected by the properties of the embankment materials, stress state, dynamic stress, and variations in the water level [34]. In addition, Hao et al. [35] showed that the level of river water affected the distribution of moisture and influenced settlement within a levee subgrade [35]. There is a need for further research to investigate the influence of moisture on the settling velocity of embankments constructed with recycled construction waste. To address this need, longterm monitoring of the moisture and settlement of a subgrade was conducted at the north ring of the Xi’an-Xianyang Highway, Shaanxi Province, China. The effects of moisture were analyzed in

Fig. 2. Vertical setup of the settlement monitoring points embedded in the embankment at the barricade section.

Fig. 3. Vertical setup for the settlement monitoring points embedded in the embankment at the arc-shaped protective slope section.

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Fig. 4. Distribution of the moisture sensors at the barricade section: (a) Vertical layout; (b) Plan layout.

detail for barricade and arc-shaped protective slope sections, and the extent of correlation between the moisture and the settling velocity of embankment was determined. Monitoring long-term deformations of embankments constructed with recycled construction waste and analyzing the relevant influential factors are conducive to provide traffic safety, improve the construction and design level, and promote sustainable practices.

2. Introduction to the construction project The north ring of Xi’an-Xianyang Highway, 34.5 m wide and 122.613 km long, was chosen as the monitoring site. It is a sixlane two-way highway with a speed limit of 120 km/h. It plays an important role in the highway network in Shanxi by assisting in the construction of the international metropolis in Xi’an. The entire section is composed primarily of embankment, bridges, and tunnels, where the filled subgrade accounts for the highest proportion. The project used a total of 6 million tons of construction waste and recovered more than 2000 km2 of construction waste yardage. Therefore, it achieved outstanding economic and social benefits [3,4]. A pavement test section with embankment constructed with recycled wastes located in the north ring between the standard mileage of K36 + 600 m ~ K36 + 300 m in Wanzi Town, Gaoling County, Xi’an City, Shanxi Province was considered for this study. Barricade sections are used at the transition joints between bridges and the fill subgrade. The arc protective slope section is applied after the transition section; therefore, the barricade and arc protective slope sections were chosen for field monitoring.

2.1. Properties of recycled construction wastes According to JTG E40-2007 [36], the particle size, California bearing ratio (CBR), water absorption, density and moisture content of recycled construction waste from the field were measured. Fig. 1 shows the grading curve of recycled construction wastes, and the coefficient of uniformity Cu and coefficient of curvature Cc were obtained as 4.1 and 0.81, respectively. The optimum moisture content and maximum dry density of recyclable construction waste considered in this study were obtained as 11.44% and 1.88 g/cm3, respectively. The water absorption capacities of concrete slag, mortar slag and brick slag were 2.4% 11.1% and 21.5%, respectively. The CBR value of recycled construction waste was 43%, meeting the minimum strength requirement of subgrade packing CBR. The expansion rate of the construction waste after immersion in water was found to be only 0.017%. Detailed characteristics of the construction waste materials can be found in the work conducted by Li et al. [4].

2.2. Settlement monitoring program and instruments In this study, field settlement monitoring was mainly focused on barricade and arc-shaped protective slope sections. The long-term deformation monitoring meter is equipped with YTDG-0320 hydrostatic leveling apparatus. Diameter, height, range, resolution, and working temperature limits of the instrument were 10 mm, 650 mm, 200 mm, 0.01 mm, and 20 ~ 80 °C, respectively. The device was buried under the road embankments at the monitoring sites. It performed automatic all-weather monitoring of the

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Fig. 5. Distribution of the moisture sensors at the arc-shaped protective slope section: (a) Vertical layout; (b) Plan layout.

embankment subsidence deformation by leveraging the supporting wireless transmission and the cloud storage systems [37]. Under the embankment at the barricade section, the hydrostatic leveling equipment were located under the road axis, the east and westbound traffic lanes, and shoulders, as shown in Fig. 2. A hydrostatic leveling reference point was set at a depth of 1.26 m and 6.86 m from the top of the pavement surface, as marked in the Fig. 2 (i.e. A, B, C, D, E, A’, B’, C’, D’ and E’). The long-term deformation of the internal road section was monitored at these points [36]. similarly, under the embankment at the arc-shaped protective slope section, the hydrostatic leveling was set at 1.26 m and 4.68 m from surface of the road (i.e. F, G, H, I, J, F’, G’, H’, I’, and J’). The distribution of the hydrostatic leveling is shown in Fig. 3 [37]. The settlement value of embankment constructed with recycled construction wastes is the difference of settlement value between top and bottom sensors. Based on the field monitoring program, the settlement monitoring data were collected in two stages. The first stage began after the completion of the basic construction of the monitoring section and ended before it was opened to traffic (early December 2015). During this time, data were collected manually every month. During the second stage, automatic data collection began from the opening of traffic to March 2018.

2.3. Moisture monitoring program and instrumentation Based on the needs of the monitoring protocol, the RS-485 soil moisture sensor was installed to measure the variation in embankment moisture. These sensors were buried at 1.26, 3.56, 5.76 and 7.16 m from surface of the road at the barricade section, and 1.26, 3.16 and 5.06 m from surface of the road at the arc-shaped

protective slope section, as shown in Figs. 4 and 5, respectively. Moisture monitoring data from the road embankment sections were collected and stored automatically in the combined data storage unit. During the early stage of monitoring, the data was recorded manually. Later, instrument was upgraded with a data acquisition device to automatically record data. The internal moisture of the road, which was measured with these sensors, is equal to the volume of the moisture content. Thus, temporal and spatial variations of internal moisture of the road were measured and monitored. The vertical and plan layouts of the moisture sensors at the barricade and arc-shaped protective slope sections are shown in Figs. 4 and 5 [37].

3. Results and analysis 3.1. Effects of moisture at the barricade section on settling velocity The embankment settlement was measured from the difference in the two sensor readings collected at the top and bottom of the embankment. This was measured over a period to calculate the settling velocity of the embankment. The settling velocities of the different monitoring points at the barricade section are shown in Fig. 6. The settling velocity was observed to peak during the monitoring duration. It began to increase gradually after 200 days and peaked at approximately 500 days before decreasing continuously and becoming stable at around 600 days. Hence, it can be observed that the variation trend of the settling velocity at the barricade section followed a skewed distribution. Plots depicting the relationship between the cumulative increment in moisture and the settling velocity at the barricade section are shown in Fig. 7. It can be observed that the moisture

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at the middle and upper parts of the embankment initially increased before decreasing gradually throughout the observation period. The variation in the moisture was nearly consistent with that of the settling velocity. This is mainly because the internal weight of the road changed in response to the moisture.

When the particle mass of the recycled material in the construction waste remained approximately constant, the road weight was positively correlated with the moisture. Changes in the mass led to a redistribution of the internal stress of the embankment, thus altering the settling velocity of the road. Variations in the

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Fig. 7. Relationship between the cumulative increment in moisture and the settling velocity at the barricade section: (a) Westbound shoulder (1.26 m from surface of the road); (b) Westbound lane (1.26 m from surface of the road); (c) Road axis (1.26 m from surface of the road); (d) Eastbound lane (1.26 m from surface of the road); (e) Eastbound shoulder (1.26 m from surface of the road); (f) Westbound shoulder (3.56 m from surface of the road); (g) Westbound lane (3.56 m from surface of the road); (h) Road axis (3.56 m from surface of the road); (i) Eastbound lane (3.56 m from surface of the road); (j) Eastbound shoulder (3.56 m from surface of the road).

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moisture at different monitoring points were different, which was accompanied by non-uniform changes in the settling velocity. Moreover, the correlation between the moisture and the deformation is found to be strong near the upper part of the embankment. At the barricade section, cumulative changes in the moisture at depths of 1.26 and 3.56 m from the road surface are shown in Fig. 8. With an increase in settling velocity, the moisture was found to be predominantly influenced closer to the surface of the barricade section, and the moisture at the eastbound side of barricade section changed more compared with the westbound side. The mean settling velocity at the barricade section and mean variation of the moisture at a depth of 1.26 m from surface of the road were

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calculated from Figs. 7 and 8. When the cumulative change of the moisture at the embankment top reached 1.9%, the maximum rate of settling velocity was 7.1 mm/month.

3.2. Effects of moisture at the arc-shaped protective slope section on settling velocity Plots depicting the temporal variation of settling velocity and moisture within the embankment located at the arc-shaped protective slope section are shown in Fig. 9. It can be seen from Fig. 9(a)-(e) that the monthly change rate of the settling velocities at different monitoring points on the surface of the arc-shaped protective slope section showed staged characteristics over the entire monitoring period. The cumulative variations in the settling velocities at different monitoring points on the arc-shaped protective slope section were 0 to 2 mm/month before the road was opened to traffic in December 2015. Until it was opened to traffic, the settling velocities of the embankment decreased continuously to zero and tended to be stable. The overall settling velocity of the arcshaped protective slope section began to increase after December 2015, showing that all the points under those five areas followed same fluctuating trend (see Fig. 9). The maximum rate of settling velocity reached 4.48 mm/month. The settling velocities of the monitoring points of arc-shaped protective slope section began to decline after September 2017, and its variation stabilized to<0.5 mm/month. In summary, the subsidence deformation of the arc-shaped protective slope section declined gradually, and the embankment deformation tended to be stable. Relationship between the moisture changes and settling velocities at the arc-shaped protective slope section are shown in Fig. 10. Over the entire observation period, the settling velocity of the arc-shaped protective slope section had two peaks. There is a certain regularity between the cumulative change in the moisture at different depths and variations of the settling velocities. At specific monitoring points, the moisture changes at 1.26 m from surface of the road for the westbound shoulder had two peaks. The presence of the two moisture peaks was relatively consistent with the two peaks for the settling velocity. The moisture at the road axis, eastbound lane, and eastbound shoulder changed suddenly before the second variation of the settling velocity. The moisture at different monitoring points at 3.16 m from surface of the road also showed two peaks. Besides, changes in the settling velocity were delayed to some extent relative to the moisture changes. Therefore, the influence of the moisture on the subsidence deformation for the arc-shaped protective slope section was mainly manifested at 3.16 m from surface of the road. At the arc-shaped protective slope section, variation in moisture during two stages at depths of 1.26 and 3.16 m from the road surface are shown in Fig. 11(a)-(b). In the first increment period, the variation of moisture in the westbound lane at 1.26 m from surface of the road was 0.66% of initial value of moisture, while the variation of moisture for the remaining four monitoring points at the same depth was < 0.5% of initial moisture. In the second increment period, the variation of moisture in the westbound shoulder and westbound lane was approximately 0.2% of initial moisture, whereas the moisture on the road axis, eastbound lane, and eastbound shoulder increased significantly. The largest change in moisture was observed in the eastbound shoulder, which was 10.45% of initial moisture. The variation of moisture of all monitoring points at 3.16 m from surface of the road was < 0.5% of initial moisture. Based on the time point of the first change in the settling velocity, the first peak was relatively large and only required a short duration to reach the peak. The second peak was smaller and required more time to reach the peak. These revealed that as time continued, the settling velocity of the road changed with a certain

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delay with changes in the internal moisture. However, the influence of the moisture on the subsidence deformation weakened. Based on the influence of the moisture on the settling velocity for the arc-shaped protective slope section, smaller the depth from

surface of the road, smaller is the influence of moisture change on settling velocity. And after opening to traffic, the change in embankment moisture at arc-shaped protective slope section has obvious influence on settlement.

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L. Liu et al. / Construction and Building Materials 241 (2020) 117988

Cumulative time (day) (h)

Fig. 10. Relationship between for the moisture change and settling velocity at the arc-shaped protective: (a) Westbound shoulder (1.26 m from surface of the road); (b) Westbound lane (1.26 m from surface of the road); (c) Road axis (1.26 m from surface of the road); (d) Eastbound lane (1.26 m from surface of the road); (e) Eastbound shoulder (1.26 m from surface of the road); (f) Westbound shoulder (3.16 m from surface of the road); (g) Westbound lane (3.16 m from surface of the road); (h) Road axis (3.16 m from surface of the road); (i) Eastbound lane (3.16 m from surface of the road); (j) Eastbound shoulder (3.16 m from surface of the road).

L. Liu et al. / Construction and Building Materials 241 (2020) 117988

0.4 3 0.3 2

0.2 0.1

1

0.0 0 Settling velocity Cumulative increment in moisture 0

150

300

450

600

750

-0.2 900 1050 1200

0.7

4 0.4

0.4 2 0.3 0.2

1

0.1 0 Settling velocity Cumulative increment in moisture 600

2

0.3

1 0

Westbound Westbound Road axis Eastbound Eastbound shoulder lane lane shoulder

750

0.0

-0.1 900 1050 1200

0.25

Variation in moisture (%)

0.5

3

450

3

0.2

Cumulative increment in moisture (%)

Settling velocity (mm/month)

0.6

300

5

(a)

4

150

6

0.5

(i)

0

8 7

0.6

Cumulative time (day)

-1

9 The first period of variation in moisture The second period of variation in moisture

0.50 The first period of variation in moisture The second period of variation in moisture

0.45 0.40

0.20

0.35 0.15

0.30 0.25

0.10 0.20

Variation in moisture (%)

-1

-0.1

0.8

Variation in moisture (%)

0.5

Variation in moisture (%)

Settling velocity (mm/month)

4

Cumulative increment in moisture (%)

10

0.15

0.05

0.10 Westbound Westbound Road axis Eastbound Eastbound shoulder lane lane shoulder

Cumulative time (day) (j)

(b)

Fig. 10 (continued)

Fig. 11. Two periods of variation in moisture at the arc-shaped protective slope section: (a) 1.26 m from surface of the road; (b) 3.16 m from surface of the road.

3.3. Correlation analysis between moisture and settling velocity of embankment According to Rinne [38], the morphology of the settling velocity can be fitted using a Weibull distribution, which is the theoretical basis for reliability analyses and lifetime testing. The physical mechanism for a Weibull distribution is the randomness of objective units. Settlement of roads is random to some extent; therefore, it is reasonable to describe these changes using a Weibull distribution. The probability density function of a Weibull distribution can be expressed as:

f ðxÞ ¼

n xn  xn1  eð u Þ u

ð1Þ

where u is the mean of n powers of the variable and n is the parameter in the Weibull distribution probability function. In actual observations, the variable  is generally positive; hence, Eq. (1) can be rewritten as: ðxaÞn n f ðxÞ ¼  ðx  aÞn1  eð u Þ u

ð2Þ

where a is the minimum of variable x. From Eq. (2), the settling velocity at different monitoring points conforms to the probability density function of the Weibull distribution. The calculated results under the road axis at the barricade section are shown in Fig. 12. Normalized time calculated as the ratio of the considered time and total monitoring time was used for better understanding. The probability density function of the Weibull distribution is reasonable to describe changes in the settling velocity at the road axis and can describe the variation trends and peak state of the subsidence deformation at the westbound shoulder. The fitting results for

Fig. 12. Comparison of the fitting results under the road axis at the barricade section.

the settling velocity of measuring points under the westbound lane, road axis, eastbound lane, and eastbound shoulder at the barricade section are shown in Table 1. It can be seen from Table 1 that changes in the settling velocity at the barricade section conform to the Weibull probability distribution. The maximum settling velocity was achieved at approximately 500 days. Subsequently, the settling velocity at different monitoring points began to decrease until finally becoming stable. The temporal variation in the settling velocity on the arc-shaped protective slope section are shown in Fig. 10. The

11

L. Liu et al. / Construction and Building Materials 241 (2020) 117988 Table 1 Fitting model for the settling velocity at the barricade section. Location

Fitting function

Westbound shoulder Westbound lane Road axis Eastbound lane Eastbound shoulder

Correlation coefficient

 14    ðxþ0:28Þ x þ 0:28 13 0:85 y ¼ 0:6 þ 16:5  e 0:85  7:5    ðx0:1Þ x  0:1 6:5 0:49 y ¼ 0:68 þ 15:25  e 0:49  13:5    ðxþ0:2Þ x þ 0:2 12:5 0:77 e y ¼ 0:83 þ 17:42  0:77  8    ðx0:03Þ x þ 0:28 7 0:54 y ¼ 0:77 þ 14:8  e 0:54  11    ðxþ0:1Þ x þ 0:1 10 0:67 e y ¼ 0:72 þ 16:41  0:67

0.92 0.91 0.86 0.91 0.89

observation period was divided into a first stage (From day 300 to day 700) and a second stage (From day 700 to day 1050) after opening to traffic, and the Weibull distribution was applied to the data (Fig. 13 and Tables 2-3). Changes in the settling velocity on the arc-shaped protective slope section in the different stages conformed to the Weibull distribution. The correlation coefficient after fitting was greater than 0.73. Long-term deformations at the barricade and arc-shaped protective slope sections are influenced by the moisture, while changes in the moisture of an embankment that is built with construction waste can be fit with a Weibull distribution. According to Eqs. (1) and (2), the Weibull distribution can be used to describe

Settling velocity (mm/month)

3

Table 2 Calculation model of the settling velocity at the arc-shaped protective slope section (First stage). Location

Fitting function

Correlation coefficient

 10   Westbound  ðx0:0025Þ x  0:0025 9 0:64 shoulder y ¼ 0:4 þ 15:63  e 0:64  150   Westbound  ðxþ12:17Þ x þ 12:17 149 12:81 lane e y ¼ 0:54 þ 11:71  12:81  10   Road axis  ðx0:0055Þ x  0:0025 9 0:68 e y ¼ 0:65 þ 14:71  0:68  9   Eastbound  ðx0:0025 x  0:0025 8 0:63 lane e y ¼ 0:63 þ 0:47  0:63  8   Eastbound  ðx0:043Þ x  0:043 7 0:66 shoulder y ¼ 0:36 þ 0:16  e 0:66

0.84 0.67 0.84 0.87 0.91

Table 3 Calculation model of the settling velocity at the arc-shaped protective slope section (Second stage). Location

Fitting function

Correlation coefficient

 15   Westbound  ðxþ1:16Þ x þ 1:16 14 1:56 shoulder y ¼ 0:26 þ 9:62  e 1:56  8   Westbound  ðxþ0:56Þ x þ 0:56 7 0:92 lane e y ¼ 0:21 þ 8:7  0:92  90   Road axis  ðxþ12:11Þ x þ 12:11 89 12:45 e y ¼ 0:05 þ 7:23  12:45  9   Eastbound  ðxþ0:35Þ x þ 0:35 8 0:75 lane e y ¼ 0:3 þ 12  0:75  20   Eastbound  ðxþ2:41Þ x þ 2:41 19 2:83 shoulder y ¼ 0:02 þ 7:07  e 2:83

0.77 0.83 0.85 0.74 0.73

2

1

Road axis Fitting curve 0 0.0

0.2

0.4

0.6

0.8

1.0

Normalized time (a)

Settling velocity (mm/month)

3.5 3.0 Fig. 14. Fitting curves for the moisture changes under the road axis at the barricade section.

2.5 2.0

Road axis Fitting curve

1.5

Table 4 Fitting model of the cumulative moisture changes at 1.26 m from surface of the road at the barricade section.

1.0 0.5 0.0 -0.5

0.0

0.2

0.4

0.6

0.8

Location

Fitting formula

Westbound shoulder Westbound lane

f i ðxÞ ¼ 0:94  9:83  ðx  1:18Þ3:03  e 

1.0

Normalized time (b) Fig. 13. Fitting results for the settling velocity at the arc-shaped protective slope section: (a) First stage (From day 300 to day 400); (b) Second stage (From day 700 to day 1050).

Road axis Eastbound lane Eastbound shoulder



f i ðxÞ ¼ 0:63  5:81  ðx  2:4Þ8:59  e

ðx1:18Þ4:03 0:41

ðx2:4Þ9:59 1:65







ðx46:33Þ153:49

45:65 f i ðxÞ ¼ 0:71  3:36  ðx  46:33Þ152:49  e   ðx0:57Þ2:45  0:05 f i ðxÞ ¼ 2:5 þ 49  ðx  0:57Þ1:45  e   2:01  ðx0:68Þ 0:03 f i ðxÞ ¼ 1:9 þ 67  ðx  0:68Þ1:01  e



12

L. Liu et al. / Construction and Building Materials 241 (2020) 117988

where f 2 ðxÞ is the fitting function of the cumulative changes in the internal moisture of the embankment and  is the number of observation days. According to the fitting formula regarding changes in the settling velocity of the embankment:

the cumulative variations in the internal moisture of the embankment: n

f 2 ðxÞ ¼ y02 þ

ðxa Þ 2 n2 ð u2 Þ 2  ðx  a2 Þn2 1  e u2

ð3Þ

Fig. 15. Distributions of the fitting parameters for the cumulative moisture changes of different monitoring points at the barricade section: (a) Parameter y02; (b) Parameter a2; (c) Parameter u2; (d) Parameter n2.

Table 5 Calculated and adjusted values of g(l) corresponding to the road width. Road width (m)

0

8.625

17.25

25.875

34.5

Calculated value Adjusted value

1.34 0.4

0.4775 0.1525

0.385 1.105

1.2475 3.7475

2.11 0.21

Table 6 Transformation parameters between the cumulative moisture change and the long-term deformation rate. Measuring Position

nn

nu

na

y0

Westbound shoulder Westbound lane Road axis Eastbound lane Eastbound shoulder

0.325 1.3959243 13.277682 0.323219 0.2180043

1.4642857 16.5 228.25 1.6666667 0.3

1.3882353 4.8979592 60.168831 1.0555556 1.0149254

1.5666667 0.9264706 0.8674699 3.246753 2.638889

L. Liu et al. / Construction and Building Materials 241 (2020) 117988 n

f 1 ðxÞ ¼ y01 þ

ðxa Þ 1 n1 ð u1 Þ 1  ðx  a1 Þn1 1  e u1

ð4Þ

Since the long-term deformation rate and cumulative moisture changes of the embankment are probability density functions of x. The parameters in the fitting formula for the long-term deformation rate correspond to those in the fitting formula for the cumulative moisture changes. There are certain proportional relations for the numerical values of the parameters in the two fitting formulas:

n1 u1 a1 y ¼ nn ; ¼ nu ; ¼ na ; 01 ¼ ny n2 u2 a2 y02 Therefore, Eq. (4) can be rewritten as:

ture change at the road axis was similar to the measured curve with a correlation coefficient of 0.96. This indicates that the Weibull distribution is feasible and reliable for curve fitting the cumulative moisture changes. The other fitting results are shown in Table 4. The fitting distributions for the cumulative moisture fitting parameters at different monitoring points at a depth of 1.26 m from surface of the road along the barricade section are shown in Fig. 15. The distributions for the fitting parameters present functional relations, which allow to calculate the cumulative moisture change with time and position (Eq. (6)):

f 2 ðxÞ ¼ gðlÞ þ

ðxa2 na Þnn n2 Þ ð Þ u2 nu

nn  n2 f 1 ðxÞ ¼ y02 þ ny þ  ðx  a2  na Þnn n2 1  e u2  nu

ð5Þ where y02 a2., u2, and n2 are the parameters of Eq. (5). Thus, the long-term deformation rate can be calculated using the parameters for the cumulative moisture changes. On the barricade section, the cumulative moisture changes for different monitoring points at a depth of 1.26 m from surface of the road were fit using Eq. (3). The fitting results under the road axis are shown in Fig. 14. The fitting curve of the cumulative mois-

13

ðxhðlÞkðlÞ Þ kðlÞ kðlÞ1 ð Þ jðlÞ e  ðx  hðlÞÞ jðlÞ

ð6Þ

where gðlÞ ¼ 1:34  0:1l is the function of y02 hðlÞ ¼ 16:31 þ 30:02  sinðp  l10:71 Þ is the function of a2. 12:98

jðlÞ ¼ 15:61 þ 30:04  sinðp  l257:45 Þ is the function of u2. 12:99

kðlÞ ¼ 54:51 þ 98:99  sinðp  l10:68 Þ is the function of n2. 13:01 l is the road width in m. The fitted value of g(l) has a certain error with the actual parameters, which must be accounted. The adjusted values of g(l) at different monitoring points are listed in Table 5. Then, the value of y02

Fig. 16. Distribution of the transformation parameters of different monitoring points at the barricade section: (a) Parameter ny; (b) Parameter na; (c) Parameter nu; (d) Parameter nn.

14

L. Liu et al. / Construction and Building Materials 241 (2020) 117988

Table 7 Calculated and adjusted values of G(l) corresponding to the road width. Road width (m)

0

8.625

17.25

25.875

34.5

Calculated value Adjusted value

2.01 0.44333

0.71625 0.21022

0.5775 1.44497

1.87125 1.3755

3.165 0.52611

can be determined by adding the calculated and adjusted values. The transformation parameters between the fitting function of the cumulative moisture change and the fitting function for the long-term deformation are listed in Table 6. The distribution for the change parameters in the fitting functions of the cumulative moisture change and the long-term deformation rate are shown in Fig. 16. The different parameters have different distribution laws for the road section, which possess certain functional relationships with the section. Therefore, changes in the transforming cumulative moisture change in the long-term deformation rate with time and position on the section are determined (Eq. (7)):

kðlÞ  KðlÞ kðlÞKðlÞ1 f 1 ðxÞ ¼ GðlÞ  gðlÞ þ  ðx  hðlÞ  HðlÞÞ jðlÞ  JðlÞ ðxhðlÞHðlÞkðlÞKðlÞ Þ ð Þ jðlÞJðlÞ

e

ð7Þ

where GðlÞ ¼ 2:01  0:15lis the function of ny.

hðlÞ ¼ 16:31 þ 30:02  sinðp 

l  10:71 Þ 12:98

HðlÞ ¼ 21:65 þ 38:54  sinðp  l10:61 Þis the function of na. 13:05

JðlÞ ¼ 79:25 þ 149:11  sinðp  l2:06 Þ is the function of nu. 0:65 Þis the function of nn. JðlÞ ¼ 4:87 þ 8:41  sinðp  l10:55 13:11

The fitted value of G(l) had a certain error compared with the actual parameter and must be adjusted. The adjusted values of G (l) at different monitoring points are listed in Table 7. According to the table, the values of y01 can be determined by adding the calculated and adjusted values. In summary, the settling velocity at different monitoring points can be calculated from the parameters of the cumulative moisture change. Moreover, the settling velocity that was calculated from the adjusted values was highly consistent with the actual value at different monitoring points. 4. Conclusions (1) The moisture at the middle and upper parts of the barricade section increased initially before decreasing gradually after reaching the peak. The variation in the moisture was nearly consistent with that of the settling velocity. The influence of moisture on the settling velocity of the road were mainly observed within a depth of 3 m from the road surface. In addition, the correlation between the moisture and deformation is strong near the road surface. (2) The settling velocity of the arc-shaped protective slope section contained two peaks. The occurrence of the two moisture peaks was relatively consistent with those of the settling velocity. The influence of the moisture at the arcshaped protective slope section on the deformation was primarily observed at a depth of 3.16 m from surface of the road. (3) A forecasting model for the moisture and settling velocity of the embankment, which was built with recycled construction waste, was established based on the probability density function of a Weibull distribution. In addition, the transfor-

mation formula for the cumulative moisture change into the settling velocity was obtained based on data collected at the barricade section. 5. Author construction statement Lulu Liu: Writing-original draft preparation; Zhe Li: Supervision; Guojun Cai: Supervision; Surya Sarat Chandra Congress: Reviewing and Editing; Xiaoyan Liu: Collecting data; Baosen Dai: Collecting data. Acknowledgements The authors are grateful for the financial and technical support provided by the National Key R&D Program of China (2016YFC0800200), the National Natural Science Foundation of China (41672294 and 41877231), Project of Jiangsu Provincial Transportation Engineering Construction Bureau (CX-2019GC02), Colleges and Universities in Jiangsu Province Plans to Graduate Research and Innovation (Grant No. KYCX19-0098) and Scientific Research Foundation of Graduate School of Southeast University (Grant No. YBPY1926). References [1] M. Safiuddin, M.Z. Jumaat, M. Salam, M. Islam, R. Hashim, Utilization of solid wastes in construction materials, Int. J. Phys. Sci. 5 (13) (2010) 1952–1963. [2] G.C. Ulubeyli, R. Artir, Sustainability for blast furnace slag: use of some construction wastes, Procedia-social and behavioral sciences 195 (2015) 2191–2198. [3] Z. Li, L. Liu, S. Yan, M. Zhang, J. Xia, Y. Xie, Effect of freeze-thaw cycles on mechanical and porosity properties of recycled construction waste mixtures, Constr. Build. Mater. 210 (2019) 347–363. [4] Z. Li, L. Liu, S. Yan, M. Zhang, Y. Xie, Properties of microscopic particle morphology and particle contact of renewable construction waste mixtures, Constr. Build. Mater. 207 (2019) 190–205. [5] P.M. Velasco, M.M. Ortíz, M.M. Giró, L.M. Velasco, Fired clay bricks manufactured by adding wastes as sustainable construction material–A review, Constr. Build. Mater. 63 (2014) 97–107. [6] Q. Xu, B. Li, H. Fan, Influence of uneven settlement of subgrade on dynamic characteristic of train-ballastless track on subgrade coupling system, J. Railway Sci. Eng. 9 (3) (2012) 13–19. [7] A.J. Puppala, P. Ruttanaporamakul, S.S.C. Congress, Design and construction of lightweight EPS geofoam embedded geomaterial embankment system for control of settlements, Geotext. Geomembranes 47 (3) (2019) 295–305. [8] T. Dahlberg, Some railroad settlement models—a critical review, P. I. Mech. Eng., Part F-J Rai. 215(4) (2001) 289-300. [9] Y. Sato, Japanese studies on deterioration of ballasted track, Vehicle Syst. Dyn. 24 (sup1) (1995) 197–208. [10] M. Shenton, Ballast deformation and track deterioration, Track Technology (1985) 253–265. [11] J. Alva-Hurtado, E. Selig, Permanent strain behavior of railroad ballast, in: Proceedings of the International Conference on Soil Mechanics and Foundation Engineering, 1981, pp. 543–546. [12] R. Ford, Differential ballast settlement, and consequent undulations in track, caused by vehicle-track interaction, Vehicle Syst. Dyn. 24 (sup1) (1995) 222– 233. [13] K. Demharter, Setzungsverhalten des Gleisrostes unter vertikaler Lasteinwirkung, Prüfamt für Bau von Landverkehrswegen der, Techn. Univ. (1982). [14] N. Guerin, Approche expérimentale et numérique du comportement du ballast des voies, ferrées (1996). [15] A. Hecke, Effects of future mixed traffic on track deterioration, Report TRITAFKT 30 (1998). [16] L. Mauer, An interactive track-train dynamic model for calculation of track error growth, Vehicle Syst. Dyn. 24 (sup1) (1995) 209–221. [17] S. Van As, E. Kearsley, Deterioration of rail track geometry, J. S. Afr. Inst. Civ. Eng. 37 (1) (1995) 1–5.

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