Ranking of influence factors and control technologies for the post-construction settlement of loess high-filling embankments

Computers and Geotechnics 118 (2020) 103320

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Research Paper

Ranking of influence factors and control technologies for the postconstruction settlement of loess high-filling embankments

T

Caihui Zhu , Ning Li ⁎

D.E., Institute of Geotechnical Engineering, Xi'an University of Technology, 5 South Jinhua Road, Xi'an, Shaanxi 710048, China State Key Laboratory of Eco-hydraulics in Northwest Arid Region, Xi’an University of Technology, Xi’an, China Shaanxi Provincial Key Laboratory of Loess Mechanics, Xi’an University of Technology, Xi’an, China

ARTICLE INFO

ABSTRACT

Keywords: Post-construction settlement (PCS) Loess high-filling embankment (LHFE) Influence factors Sensitivity analysis Creep model

Ground treatments and post-construction settlement (PCS) control technologies are hot topics within the loess high-filling embankment (LHFE) research area. Taking the test section of a high filling airport constructed on a thick loess foundation as an example, the creep behaviour of undisturbed loess and compacted loess under highpressure and different initial conditions are investigated using laboratory tests. The Mod-Burgers creep model of loess is proposed; a FLAC-3D simulation study is conducted to explore the PCS of high fill embankment under different influence factors. The research results show that the proposed Mod-Burgers model and equivalent creep modulus clearly reflect the long-term deformation characteristics of compacted and undisturbed loess. The filling height has the greatest impact on the PCS of high filling body, the compaction degree and water content are the second most important influence factors on the PCS of the high filling body. The pile length and pile spacing are the third important influence factors on the PCS of the original foundation. For the construction control of an LHFE in the gully, different treatment methods should be adopted according to different functional zones. It is recommended to adopt the dynamic compaction method for shallow loess foundation, and the collapsibility of loess should be eliminated. For thick loess foundation, the vibrating sinking gravel pile method is well-suited for treating an original foundation with low water content; cement-fly ash-gravel pile and lime-soil compaction pile are suitable for treating an original foundation with high water content.

1. Introduction With the expansion of transportation demands, the construction of airports and roads is on the rise. However, for the collapse loess areas in northwestern China, deep excavation and high filling projects must be carried out. Among them, the geotechnical engineering problems related to the design and operation of the high-filling construction, such as the filling technology, the treatment method of collapse loess in original foundation, and the post-construction settlement (PCS) control measures, are widely known issues in high-filling projects. High-filling engineering practices have shown that the PCS and stability time of a loess high-filling embankment (LHFE) are closely related to the type of original foundation, the reinforcement method of the original foundation, the thickness of the fill, the filling process, and the mechanical behaviour of the fill materials [1–7]. In the previous studies, in-situ monitoring, numerical methods, laboratory tests, model tests, etc. are often used to study the PCS law of the high-filling foundations. The insitu monitoring method is used to quickly obtain the stress-strain-time

⁎

law and the stability of high-filling foundations during and after construction [8,1,2,4,6,9,10]. However, as there are a relatively small number of reports available, the influence effect of different treatment methods of the original foundation and the filling method of the filling body on the PCS is less quantified. These limitations have hindered the proposal of a comprehensive PCS law of the high-filling embankment. Therefore, it is necessary to quantify the above problems by means of laboratory tests, theoretical models of long-term deformation, and numerical analysis methods [11–15,32,34,16,17], which provides a scientific way to study the PCS mechanism of the LHFE. It is well known that in the high-filling projects, in order to reduce the crest PCS and the differential PCS of the high fill embankment, the original foundation needs to be reinforced [18,19]. The goal of the reinforcement is to enhance the shear strength and increase the bearing capacity of the soil system. In recent years, there have been many ways to reinforce soft foundations, including dynamic compaction (DC), rolling, blasting, etc. [20–23] and pile-reinforced methods. The most common pile-reinforced methods include gravels pile, geogrid-

Corresponding author at: State Key Laboratory of Eco-hydraulics in Northwest Arid Region, Xi'an University of Technology, Xi’an 710048, China. E-mail addresses: [email protected] (C. Zhu), [email protected] (N. Li).

https://doi.org/10.1016/j.compgeo.2019.103320 Received 20 August 2019; Received in revised form 9 October 2019; Accepted 19 October 2019 0266-352X/ © 2019 Elsevier Ltd. All rights reserved.

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Fig. 1. Profile of the test region of LÜ-liang Airport.

compacted loess under high-pressure conditions are conducted. The creep properties of the fill materials are investigated, and the empirical creep model is established and introduced into a numerical analysis method. The sensitivity analysis of the different treatment methods of the original foundation and the influence of the filling technology on the PCS is carried out. The construction control method and recommendations for reducing the PCS of an LHFE are proposed, and can provide a scientific reference for the design and construction of similar high-filling projects.

reinforced pile, deep mixed columns, floating soil cement columns, lime-soil compaction pile, CFG pile, etc. [21,24–31]. Based on in-situ tests, numerical analysis, model tests, etc., the above published works have studied the different influence factors such as the pile materials, pile diameter, pile length, pile spacing, modulus ratio of soil-pile and arrangement shape (triangular, square) on the reducing effect of the crest PCS of high-filling embankments. These results play an important reference role in the reinforcement design methods for high-filling foundations. However, the research on the influence degree of different foundation reinforcement methods on long-term PCS is still lacking. The main reason is that the investigation of the long-term deformation properties and conducting experimental study periods of high-filling materials under different initial conditions is complex and time-consuming. In recent years, many scholars have carried out some creep laws research with laboratory tests for different fill materials. The unified hardening (UH) model [32], Merchant creep model [33], and anisotropic creep constitutive model named Creep-SCLAY1S [14] have been proposed to describe the long-term deformation of rock and soil mass. These models have been applied to predict the PCS of high-filling projects. With the increase of high-filling construction projects in loess regions, research on the creep properties of undisturbed loess has gradually developed [13,34,15,35]. In fact, the long-term settlement of compacted loess is also an important part of the PCS of high filling embankments. The crest PCS of high-filling embankments has a strong correlation with the filling construction process [2,3], but there are few studies on the long-term deformation of compacted loess under highpressure conditions. In addition to this, the numerical sensitivity analysis has also been used to study the different influencing factors on PCS [16,17,9,10,36–40], which provides the necessary scientific reference for the foundation treatment and filling technology of high-filling engineering. In summary, the PCS law of an LHFE is not only related to the treatment methods of the original foundation, but is also related to the long-term deformation characteristics of loess. This research embodies empirical data into a combination creep model of Burgers model and Kelvin model that is based on numerical analysis methods. This is accomplished by using the test section of the LHFE at the LÜ-liang Airport as an example; the uniaxial drainage creep tests of undisturbed and

2. Engineering background of LHFE 2.1. Project description of LÜ-liang Airport LÜ-liang Airport is located over the loess ridge in Shanxi province. The test section of the LHFE has been constructed over the thick loess foundation in a deep gully. The geographical location and project profile of the high-filling airport are shown in Fig. 1. The airport station and linking taxiway are constructed on the test region, which is located on the west side of the airstrip (width × length = 45 m × 2600 m). The deep loess gully (700 m long, 300 m wide, and 50–100 m deep) basically distributes in a north–south direction, and the longitudinal slope of the loess gully is 7.1%. The upstream and downstream cross-sections of the gully are shaped like the letters “V” and “U”, respectively; the slope angle is approximately 40–80°. 2.2. Physical and mechanical properties of original foundation soil The original foundation is composed of Q3 loess, Q2 loess, silty clay, and sandy shale. The fill material is mainly Q3 loess. The soil layers of the original foundation from the surface to the bottom of the gully can be classified as follows:①1-Q42ml plain fill (thickness is about 1.7–6.5 m), ①2-Q4dl loess-like soil (1.5–19.3 m), ②1-Q3eol Malan loess (6.5–17.8 m), ②2-Q3eol Malan loess (3.1–21.5 m), ③-Q2eol Lishi loess (2.9–14.6 m), ④1-N2b silty clay (17.1–23.5 m), ④2-N2b silty clay (13.5–24.6 m), and ⑤-C2b sandy shale (more than 12.2 m). The physical parameters of the soils over depth are shown in Fig. 2a. The location of boreholes are shown in Fig. 2b. 2

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Fig. 2. Soil properties of test region of the original foundation. (a) The physical parameters of the soils over depth. (b) The location of boreholes.

It can be seen that the water content is basically distributed between 7% and 25%, the average of which is 15%, the dry density is basically distributed between 1.4 and 2.1 g/cm3. Based on the heavy compaction test of the fill materials, the optimum water content of Q3 and Q2 loess is 13.3% and 12.2%, respectively; their maximum dry density is 1.88 g/ cm3 and 1.93 g/cm3, respectively. In order to obtain the mechanical parameters of the undisturbed soil, on-site sampling of Q3 and Q2 loess is carried out to conduct the laboratory experiments. The Q3 loess is taken from the top of the loess beam, the depth of the soil is 1.0–3.0 m. The Q3 loess has abundant macropores and a loose structure; it exhibits high compressibility, collapsibility, and disintegration. The Q2 loess is taken from the deep loess gully, and the depth of the soil is 0–18.0 m. The Q2 loess is relatively high in bearing capacity due to its low compressibility and low collapsibility. The photo of the on-site sampling is shown in Fig. 2.

Through the physical index test, compression test, and direct shear test, the statistical values of the physical and mechanical parameters of the Q3 and Q2 loess samples are obtained, as shown in Fig. 3 and Table 1. The test results show that the compression modulus of the original foundation soil increase nonlinearly with the axial load; the compression modulus of the fill material (undisturbed Q3 loess) varies from 7.0 MPa to 8.2 MPa, the cohesive force changes between 32 kPa and 37 kPa, and the average value of internal friction angle is 23.3°. The water content of the original foundation soil (silty clay) is obviously higher than the Q3 loess, and the compressibility of silty clay is lower than the Q3 loess, which indicates that the original foundation should be reinforced.

3

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vibration compaction method (VC), percussive compaction method (PC), and DC method (DCE is 3000 kN·m). The compaction methods and compaction degree standards of high filling are shown in Fig. 5 and Table 3. As mentioned above, the high filling body has been divided into three regions: fill slope, ordinary, and airstrip. For the airstrip region, the VC + PC and VC + DC methods have been adapted to the 20 m depth soil beneath the crest of the filling body. The loose laying thicknesses of the fill materials with the VC and PC methods are 0.35–0.50 m and 1.0–1.5 m, respectively. This achieves the highest compaction degree, which is 0.96–0.98. The single-point DC (DCE = 3000 kN·m) has been adapted to each 6 m of the fill materials between 20 m and the H-20 of the filling body. For the fill slope and ordinary region, the compaction degrees achieved in these regions are between 0.90 and 0.93.

Fig. 3. Compression modulus of undisturbed soil under different vertical stress.

3. Sensitivity analysis of the PCS and control technology of the LHFE

2.3. Construction methods of LHFE 1. Original foundation treatment with dynamic compaction methods

From the point of view of creep mechanics, the stress in the high fill embankment was kept constant after the filling process of LHFE was completed. The PCS of the LHFE can be calculated and simulated with the strain during creep stage. In order to simulate the creep deformation of the LHFE, the creep properties of loess should be obtained by using laboratory experiments, and the creep model of loess should be introduced into the simulation program in the numerical analysis.

Based on the collapsibility level of loess, the original foundation in the bottom of the loess gully has been divided into six zones (D1, D2-1, D2-2, D3, D4, D5), which are shown in Fig. 4a [41]. (1) D1 (the thickness of alluvial soil in zone D1 is about 4–6 m); (2) D2-1 (the thickness of alluvial soil in zone D2-1 is about 4–6 m); (3) D2-2 (zone D2-2 is the junction between the bottom of loess gully and the slope); (4) D3 (the thickness of the low collapsibility loess in zone D3 is less than 7 m); (5) D4 (the thickness of the moderate collapsibility loess in zone D4 is about 7–10 m); (6) D5 (the thickness of the high collapsibility loess in zone D5 is more than 10 m).

3.1. Creep properties of Q3 and Q2 loess 3.1.1. Materials and methods LÜ-liang Airport is a high-filling airport and built on the deep loess foundation in the gully. The monitoring results indicate that the original foundation and the filling body have undergone a long-term PCS [2,3]. In order to further explore the PCS law of the high filling embankment and construction control standards, it is necessary to investigate the long-term deformation characteristics of loess with creep tests. To this end, this paper has developed laboratory compression creep testing equipment. The sample tube has an inner diameter of 10 cm and a height of 12 cm; the equipment can test in both drained and undrained processes. The test process of loading and data recording can be automatically controlled by using the computer system, which is shown in Fig. 6. In order to obtain the creep properties of undisturbed Q3 loess, Q2 loess and compacted Q3 loess, the uniaxial drainage creep tests are carried out. The locations of the soil samples were secured and marked in Section 2.2. The creep experiments of soil samples were also taken from the same locations in the high fill embankment. The test scheme is as follows:

The six regions of the original foundation have been treated with a single-point DC method and an overlapping DC method, which are shown in Fig. 4b and c. The design of the DC method employed in the above six regions summarized in Table 2. The dynamic compact effort (DCE) of the single-point DC uses 3000, 6000 and 10,000 kN·m. The single-point DC is employed to further reinforce the original foundation, and is arranged squarely, the tamping distance (TD) is 3.5–5.5 m, and the number of tamping times (TT) is 10–12. After the single-point DC finishes, the overlapping DC begins. The DCE of the overlapping DC uses 1000 kN·m and 1500 kN·m. The TT of the overlapping DC is 3–6 and the overlapping length is TD/4. 2. filling body treatment with combined methods

(1) Creep tests of undisturbed Q3 and Q2 loess under high compression load are conducted, the maximal vertical load is 1.6 MPa.

The filling body has been compacted with the combination of the Table 1 Physical index and mechanical parameters of the undisturbed soil. Soils

W/(%)

ρd/(g/cm3)

ρdmax/(g/cm3)

wop/(%)

e

wL/(%)

wP/(%)

av0.1-0.2/(MPa−1)

ES0.1-0.2/(Mpa)

c/(kPa)

φ/(°)

①1 ①2 ②1 ②2 ③ ④1 ④2

23.66 15.65 15.84 16.97 21.36 22.00 21.53

1.60 1.44 1.63 1.56 1.65 1.64 1.67

– – 1.87 1.88 1.93 – –

– – 13.5 13.3 12.2 – –

0.696 0.882 0.663 0.741 0.647 0.663 0.628

25.2 24.72 24.98 24.87 29.29 29.91 30.13

15.89 15.75 16.21 16.08 17.49 17.53 17.66

0.396 0.249 0.269 0.228 0.231 0.238 0.229

4.65 7.48 7.00 8.23 7.57 7.20 7.21

19.3 49.4 31.7 36.6 70.2 114.9 126.6

20.5 26.6 23.1 23.6 23.5 21.3 22.8

In this table, w is the water content, ρd is the dry density, e is the void ratio, wL is the liquid limit, wp is the plastic limit, av0.1-0.2 is the coefficient of compressibility, ES0.1-0.2 is the compression modulus, c is the cohesive force, and φ is the internal friction angle. In addition, ρdmax and wop is the maximal dry density and optimal water content with the heavy compaction test, respectively. 4

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Fig. 4. Original foundation treatment with the DC method. (a) Planar graph of DC. (b) Section of single-point DC. (c) Design of overlapping DC. Table 2 Dynamic compaction of original foundation. Region

Compaction method

DCE/(kN.m)

TD/(m)

TT/(times)

Dynamic compactor

D1, D2-1, D3

Single-point DC Overlapping DC Single-point DC Overlapping DC Single-point DC Overlapping DC Single-point DC Overlapping DC

3000 1000 3000 1000 6000 1000 10,000 1500

4.0 D/4-overlapping 3.5 D/4-overlapping 5.0 D/4-overlapping 5.5 D/4-overlapping

10–12 3–4 10–12 3–4 10–12 4–5 10–12 4–6

① W200A-50 t (Hangzhou Heavy Machinary Co., Ltd.) ② QUY35A-35 t (FuWa Heavy Industry Machinary Co., Ltd.)

D2-2 D4 D5

(2) Creep properties of compacted Q3 loess with different water content are carried out when the compaction degree λ = 0.90. The water content of the five compacted Q3 loess samples are w = 12.0%, 14.5%, 17.0%, 19.0%, and 21.0%. (3) Creep characteristics of the compacted Q3 loess under five different compaction degrees are tested. The compaction degrees are λ = 0.80, 0.85, 0.90, 0.95, 0.98; the optimum water content value is used, i.e., w = 13.3%. (4) Loading and stability standards. After pre-loading 25 kPa, the

following eight loads are applied: σ = 0.1 MPa, 0.2 MPa, 0.4 MPa, 0.6 MPa, 0.8 MPa, 1.0 MPa, 1.2 MPa and 1.6 MPa. The stability criterion for adding the next load is that the cumulative compression increment of the vertical deformation each day is less than 0.002 mm, and the temperature is maintained at 20 ± 1 °C in the laboratory. 3.1.2. Results of creep tests According to the above test scheme, the creep curves for the vertical 5

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Fig. 5. Compaction standards for the test section of the high fill embankment. Table 3 Compaction methods and compaction degree standards for the test fill. Location

Below Airstrip

Compaction method

Thickness of loose laying

Compaction degree

Airstrip region

Y = 0–1 m Y = 1–20 m Y = 20 m–H-20

VC + PC VC + PC VC + DC

VC-4 × 0.35 m, PC-1.0 m VC-5 × 0.40 m, PC-1.5 m VC-20 × 0.40 m, DC-6.0 m

0.98 0.96

Fill slope region

Y = 0–20 m Y = 20 m–H-20 Y = 0–1 m Y = 1 m–H

VC (H represents the height of filling body in Fig. 5 and Table 3)

0.4 m 0.4 m 3 × 0.45 m 0.5 m

0.90 0.93 0.90

Ordinary region

Fig. 6. High pressure axial compression apparatus.

strain over time ε-t of the soil under different loads are obtained, as shown in Fig. 7. According to the above test results, the following conclusions can be drawn:

smaller. (3) The strain-time curve of undisturbed loess under similar loading conditions is similar to that of compacted soil. However, under the same load conditions, the creep strain of the undisturbed Q3 loess is obviously higher than that of the Q2 loess. This is mainly due to the Q3 loess belonging to the newly deposited soil, and it is mostly in the unconsolidated state. However, the Q2 loess belongs to the old loess, and it is mostly in the state of over-consolidation, so its creep behaviour is weak.

(1) Under the same compaction degree, the higher the soil water content (w) and the larger the axial load (σ), the larger the vertical strain (ε) of the soil. This indicates that the higher the soil water content, the bonding performance among the soil particles is deteriorated, and the soil structure is more likely to cause frictional slip or damage. (2) Under the same water content, the higher the compaction degree (λ) of the soil and the larger the axial load (σ), the smaller the vertical strain (ε) of the soil. This indicates that the higher the compaction degree of the soil, the larger the dry density (or the smaller the void ratio) and the stronger the bonding performance of the soil. As a result, it is more difficult for the soil structure to undergo further compaction or damage, and the deformation is

3.2. Creep model for loess 3.2.1. Mod-Burgers model and the calculation of creep parameters It can be seen from Fig. 7 that the creep curves of various kinds of loess are similar. Based on the Burgers model and the Kelvin model [42], the two models are connected in series to describe the creep properties of the soil; this new model is referred to as the Mod-Burgers model. As shown in Fig. 8. The mathematical equation of the Mod6

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Fig. 9. Comparison among the Burgers model, Kelvin model and Mod-Burgers model.

Burgers model is shown in Eq. (1).

(t ) =

1 t 1 + + 1 Em Ek1 m

exp

Ek1 k1

t

+

1 1 Ek2

exp

Ek2

t

k2

(1) where E represents a spring constant of the Hookean element, and η represents the viscosity of the dashpot element. Em, Ek1, Ek2 is the modulus of creep (MPa); ηm, ηk1, ηk2 is the viscous coefficient (MPa·h); σ is the axial load (MPa); ε(t) is the vertical strain; and t is the measuring time (h). Taking the compacted Q3 loess for example (the initial conditions: λ = 0.90, w = 12%, σ = 1.6 MPa), the fitted curves of creep strain-time with the Burgers model, Kelvin model and Mod-Burgers model are shown in Fig. 9. It shows that the Burgers model and Kelvin model are not suitable to simulate the creep behaviors of loess, and there are some convergence problems during the numerical solution; however, the Mod-Burgers model has much higher fitting precision, and the ModBurgers model has shown a good convergence characteristics. Based on the measured strain-stress-time curves of different loess, the parameters of Mod-Burgers model can be obtained by regression analysis with the Curve Fitting Toolbox in MATLAB [43]. Nonlinear regression algorithms such as robust method, nonlinear least squares, Levenberg-Marquardt method, and Gauss-Newton method have been used to fit the creep parameters. The process of the obtaining creep model parameters is shown in Fig. 10. The creep parameters of loess under different initial conditions are shown in Table 4. Fig. 11a–d illustrates the comparison between the measurements of different types of loess and the calculated results with the Mod-Burgers model, respectively. From Table 4 and Fig. 11, it can

Fig. 7. Creep curves of different loess conditions. (a) Compacted Q3 loess with different water content. (b) Compacted Q3 loess with different compaction degrees. (c) Undisturbed Q3、Q2 loess.

Fig. 8. Mod-Burgers model. Fig. 10. Procedures for obtaining creep parameters solutions. 7

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Table 4 Creep parameters of loess under different initial conditions. Loess

λ

w

Em/MPa

ηm/(MPa·h)

Ek1/MPa

ηk1/(MPa·h)

Ek2/MPa

ηk2/(MPa·h)

σ/(MPa)

R2

Compacted Q3 loess

0.90

12.0%

11.1 12.9 16.3 21.8 24.4 24.1

9041.6 8787.3 21204.4 27677.8 88968.0 64850.8

93.5 260.9 312.1 273.3 133.9 249.7

146.7 4.1 11.5 6.0 191.7 967.0

72.0 143.3 207.6 194.5 295.0 366.6

3.0 82.1 303.8 266.1 3.3 46.7

0.1 0.2 0.4 0.8 1.2 1.6

0.9975 0.9961 0.9541 0.9977 0.9963 0.9637

0.90

14.5%

8.0 9.5 13.3 19.1 21.7 22.9

4764.2 7369.2 16069.4 27012.4 67934.8 64766.8

54.8 141.5 278.5 204.1 131.0 377.5

27.2 115.6 6.2 271.6 146.7 52.3

61.3 195.9 179.4 379.2 1015.7 241.9

0.5 4.6 131.4 6.3 1553.6 966.4

0.1 0.2 0.4 0.8 1.2 1.6

0.9960 0.9172 0.9986 0.9940 0.9784 0.9990

0.90

17.0%

5.8 8.0 11.7 17.1 20.2 21.7

4430.7 15398.8 16069.4 29112.1 121036.1 73313.8

61.5 131.2 208.8 289.1 266.9 283.4

67.4 208.2 2.1 3.7 16.5 21.1

62.3 123.6 142.8 180.1 206.5 299.3

2.3 4.8 85.4 234.5 478.9 1311.6

0.1 0.2 0.4 0.8 1.2 1.6

0.9954 0.9895 0.9953 0.9950 0.9720 0.9820

0.90

19.0%

6.3 8.2 11.5 16.0 19.4 20.1

3552.4 7002.8 18178.5 101708.7 65061.8 155593.6

100.1 166.7 164.9 189.5 274.0 250.2

32.9 2.6 159.2 114.8 5.8 3306.3

47.3 85.3 219.6 215.7 127.2 251.3

15.6 51.1 5.9 1843.2 159.4 96.5

0.1 0.2 0.4 0.8 1.2 1.6

0.9960 0.9609 0.9570 0.9855 0.9965 0.9986

0.90

21.0%

3.9 5.9 9.0 13.7 15.8 16.9

3653.6 10438.4 12156.6 27412.3 71275.8 77700.1

86.2 91.6 142.6 164.8 170.4 267.7

99.9 52.6 0.7 1.2 274.1 1901.5

53.8 114.9 135.4 125.4 158.5 294.3

64.9 65.9 52.2 166.7 6.4 65.9

0.1 0.2 0.4 0.8 1.2 1.6

0.9345 0.9951 0.9931 0.9966 0.9975 0.9894

0.80

13.3%

10.0 10.3 11.0 11.6 13.5 14.9

6137.5 20277.7 20581.8 40116.6 70803.0 899749.5

58.1 90.5 72.5 158.6 205.4 306.8

73.0 130.7 11.5 149.8 229.3 484.7

51.9 76.4 58.8 98.5 136.5 278.0

1.3 2.5 1.2 2.3 3.8 21.2

0.1 0.2 0.4 0.8 1.2 1.6

0.9975 0.9934 0.9901 0.991 0.992 0.9957

0.85

13.3%

11.1 11.4 13.8 15.8 16.2 16.7

4058.2 7711.3 98080.0 31253.1 44277.8 97597.5

81.6 150.2 154.0 140.0 128.1 274.7

94.3 6.0 286.9 193.4 4.2 1195.6

71.2 142.1 111.8 79.3 164.4 282.2

2.1 167.3 7.1 2.2 192.1 59.6

0.1 0.2 0.4 0.8 1.2 1.6

0.9939 0.9916 0.9857 0.9882 0.992 0.9942

0.90

13.3%

10.9 13.0 18.2 24.0 29.1 34.6

5966.6 19669.6 37119.5 34554.3 60096.2 109733.3

118.5 216.3 175.6 551.3 733.1 441.9

16.0 56.9 18.6 623.0 3975.8 124.8

111.0 269.9 367.5 1706.2 2065.7 385.4

169.0 1671.2 1414.6 4949.8 309.2 3792.9

0.1 0.2 0.4 0.8 1.2 1.6

0.9702 0.9438 0.9960 0.9922 0.9938 0.9992

0.95

13.3%

8.5 15.1 15.7 21.9 27.5 34.8

7256.9 13798.8 31989.8 168918.9 233918.1 107066.4

74.5 149.5 364.6 925.9 1031.2 406.7

9.9 184.2 1583.0 352.7 38450.7 535.1

117.2 34.1 248.1 560.2 1975.5 8620.7

170.9 0.3 42.8 5240.6 4117.3 17172.7

0.1 0.2 0.4 0.8 1.2 1.6

0.9869 0.9852 0.9950 0.9829 0.9989 0.9975

0.98

13.3%

14.5 16.5 19.4 27.4 34.2 40.6

6858.7 12727.5 23380.9 55555.6 96711.8 263643.6

103.8 248.9 286.0 1115.7 2301.5 1205.8

243.2 515.1 159.8 135.7 209.4 12248.2

73.9 587.2 473.9 839.6 1232.3 1651.8

8.8 763.7 24594.4 2790.4 4151.9 933.2

0.1 0.2 0.4 0.8 1.2 1.6

0.9981 0.9951 0.9970 0.9975 0.9975 0.9847

3.7 3.2 3.2 4.5 5.5 6.9

6289.3 6711.4 7830.9 16007.7 190839.7 181488.2

20.9 20.9 43.4 95.1 274.0 177.0

1.9 0.9 5.2 243.2 2003.3 1229.3

25.9 38.8 77.2 83.6 380.1 215.9

32.7 48.9 226.8 15.2 478.8 228.7

0.1 0.2 0.4 0.8 1.2 1.6

0.9926 0.9949 0.9972 0.9991 0.9475 0.9575

Undisturbed Q3 loess

(continued on next page)

8

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Table 4 (continued) Loess

λ

w

Undisturbed Q2 loess

Em/MPa

ηm/(MPa·h)

Ek1/MPa

ηk1/(MPa·h)

Ek2/MPa

ηk2/(MPa·h)

σ/(MPa)

R2

8.5 10.9 14.1 17.0 19.8 23.1

25680.5 12779.6 17825.3 128008.2 91743.1 92421.4

102.6 100.1 158.0 435.7 429.7 350.8

409.0 6.2 10.3 234.6 4644.3 89.0

97.6 155.4 163.6 300.7 616.9 263.9

16.0 222.8 220.0 2027.4 845.2 1476.5

0.1 0.2 0.4 0.8 1.2 1.6

0.9939 0.9934 0.9968 0.9787 0.9909 0.9963

Fig. 11. Comparison between the measured data and the calculated results (Mod-Burgers model). (a) w = 17%, λ = 0.90. (b) λ = 0.95, w = 13.3%. (c) Undisturbed Q3 loess. (d) Undisturbed Q2 loess.

be seen that the R2 values for the goodness of fit often exceed 99%, which indicates that the Mod-Burgers model can clearly reflect the long-term deformation characteristics of compacted and undisturbed loess.

degradation characteristics of soil under long-term loading. In general, smaller E(t) values correspond to a larger the creep deformation and a longer the stabilization time. According to the test data, the deformation rate of soil samples can be controlled within 0.001 mm/d after 120 h under a certain load. It can be considered that the creep strain tends to be stable, and then the creep parameters Em, Ek1, Ek2, ηm, ηk1, and ηk2 are substituted into formula (3) to obtain the equivalent creep modulus of the soil in different initial states. These results are shown in Fig. 12 and Table 5. The conclusions can be drawn as follows:

3.2.2. Creep law analysis In order to facilitate the quantification of the creep behaviour of loess, the equivalent creep modulus E(t) is used to comprehensively reflect the creep properties of compacted loess under different initial conditions. According to formula (1), the relationship among stress–strain-time can be simplified to:

(t ) =

(1) Fig. 12a shows that when the water content increases from 12.0% to 21.0%, the equivalent creep modulus E(t) gradually decreases. Because of the increasing amount of free water among the soil particles, the friction between them is reduced, the fluidity is enhanced, and the stiffness degradation property is increased. Fig. 12b shows that with the increasing of vertical stress, E(t) increases rapidly when the load is low, and tends to be slow at high vertical stress values. This is because of the decrease of pores among the soil particles. Fig. 12c shows that when the compaction degrees increase from 0.80 to 0.98, the E(t) increases and the friction among the soil particles increases, which weakens the creep effect. Fig. 12d shows that the equivalent creep modulus E(t) increases non-linearly with the increase of the axial load σ.

(2)

E (t )

The equivalent creep modulus E(t) is also written as:

E (t ) =1

+

1 t 1 + + 1 Em Ek1 m 1 1 Ek2

exp

Ek2 k2

t

exp

Ek1

t

k1

(3)

where E(t) is the equivalent creep modulus, which reflects the stiffness 9

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Fig.12. The Equivalent creep modulus E(t) of different types of loess. (a) E(t) versus water content under different vertical stress. (b) E(t) versus vertical stress under different water content. (c) E(t) versus compaction degree under different vertical stress. (d) E(t) versus vertical stress under different compaction degree. (e) E(t) versus vertical stress of undisturbed Q3 and Q2 loess. (f) Comparison between measured data and calculated values of E(t).

increases. These results indicate the compacted Q3 loess is gradually hardening under the increasing load and softening after the humidification. (3) For the undisturbed Q3 and Q2 loess, E(t) of Q3 loess is obviously lower than that of the Q2 loess, indicating that the creep of the Q3 loess is higher, mainly because the Q3 loess belongs to the newly deposited soil layer, the structure is loose, the pores are large, and it has strong water sensitivity. The Q2 loess is an over/normallyconsolidated soil with low water sensitivity and small pores. In addition, the relationships between the E(t) of the undisturbed Q3 and Q2 loess, formula (5) and (6), are presented in the second column of Table 5.

Table 5 Empirical formula of equivalent creep modulus of different types of loess. Soil types

Empirical formula

Compacted Q3 loess Undisturbed Q3 loess Undisturbed Q2 loess

E (t ) = Ae

Bw + C

E (t ) = E e F (5)

E (t ) = G

H

(6)

Empirical coefficient D

(4)

A = 5.4–5.6, B = 4.8–5.0, C = 1.98–2.0, D = 0.45–0.48 E = 2.2831, F = 0.662 G = 16.372, H = 0.3843

(2) Considering the relationship among E(t), water content, compaction degree, and vertical stress, the E(t) is established as a function that relates the above-mentioned influence factors; this is formula (4) in Table 5. The measured E(t) with the calculated value by using Eq. (4) are compared. The results are shown in Fig. 12f, which indicate the calculated error does not exceed 10%. As the water content increases, E(t) decreases; however as the axial load increases, E(t)

3.3. Numerical simulation plan According to the reported research results, the main factors affecting the PCS of the LHFE could be summarized as follows: the filling height of the LHFE(H), the filling rate during construction (v), the 10

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Fig. 13. Different foundation treatment methods of high fill embankments. (a) Foundation treatment with dynamic compaction (DC) method. (b) Foundation treatment with VSGP method. Table 6 Numerical analysis schemes of single factor. Parameters of Influence factor

Method

Other influence factors

H v λ w h

35.0 0.3 0.80 12.0 1.0

50.0 0.5 0.85 14.5 2.0

65.0 0.8 0.90 17.0 3.0

80.0 1.0 0.95 19.0 4.0

100.0 1.5 0.98 21.0 5.0

DC

v = 0.8 m/d; λ = 0.90; w = 13.3%; h = 3.0 m H = 65.0 m; λ = 0.90; w = 13.3%; h = 3.0 m H = 65.0 m; v = 0.8 m/d; w = 13.3%; h = 3.0 m H = 65.0 m; v = 0.8 m/d; λ = 0.90; h = 3.0 m H = 65.0 m; v = 0.8 m/d; λ = 0.90; w = 13.3%

l d L

0.6 0.2 10.0

0.8 0.3 12.0

1.0 0.5 15.0

1.2 0.7 18.0

1.5 1.0 20.0

VSGP

H = 65.0 m; v = 0.8 m/d; λ = 0.90; w = 13.3%; d = 0.5 m; L = 15 m H = 65.0 m; v = 0.8 m/d; λ = 0.90; w = 13.3%; l = 1.0 m; L = 15 m H = 65.0 m; v = 0.8 m/d; λ = 0.90; w = 13.3%; l = 1.0 m; d = 0.5 m

Where v is the earth filling rate (m/d); H is the filling height (m); λ is the average compaction degree of filling materials; w is the water content of filling materials (%); h is the effective reinforcement depth with the DC method (m); l is the pile spacing with the VSGP method (m); d is the pile diameter of VSGP (m); and L is the pile length of the VSGP method (m).

average compaction degree of the fill materials (λ), and water content of the fill materials (w). The above four influence factors affecting the PCS will be used to conduct sensitivity analysis. During this parametric analysis, the value range of the above parameters is as follows: H = 35–100 m, v = 0.3–1.5 m/d, λ = 0.80–0.98, and w = 12–21%. The factors affecting the PCS of the original foundation are mainly reinforcement methods. The DC method and vibrating sinking gravel pile (VSGP) method are widely used to treat the collapse loess foundation. According to the in-situ tests of DC method, the effective reinforcement depth of the DC method (h) in original foundation is determined as 1–5 m in the numerical simulation. The schematic diagram of the DC method is shown in Fig. 13a. The VSGP method is mainly used in the middle of the original foundation when the upper filling height exceeds 30 m. The influence

factors of VSGP affecting the PCS are the pile length (L), pile spacing (l), and pile diameter (d). According to the engineering experiences, the pile parameters of VSGP are taken as L = 10–20 m, l = 0.6–1.5 m, and d = 0.2–1.0 m in the numerical simulation. A schematic diagram of the VSGP processing is shown in Fig. 13b. The local numerical sensitivity analysis of different influence factors on the crest PCS of high filling embankment will be carried out based on the above variables. The numerical analysis schemes are shown in Table 6. 3.4. Establishment of numerical model and parameters With the increase of the filling load, the lower layer soil is gradually compacted and the parameters are gradually hardened. In order to reflect this construction details, the filling body is divided into 10 layers 11

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Fig. 14. Finite element model of high fill embankment in a loess gully.

according to a certain thickness along the vertical direction, and a 3D numerical model is simulated by using FLAC-3D (Itasca. 2005). The 3D model and two profiles are shown in Fig. 14. The boundary conditions of the 3D model can be described as follows: the four side nodes of the 3D model are constrained by the normal direction, and the bottom nodes of the 3D model are constrained by three directions (X, Y, Z direction). The maximal height of the 3D model from the bottom of the LHFE is 80 m, the geometries of 3D model are X = 380 m, Y = 630 m, Z = 210 m. The initial conditions are concerned with the influence factors of fill materials and reinforcement methods of the original foundation. The filling body is mainly composed of compacted Q3 loess; the original foundation is mainly composed of undisturbed Q3 loess, Q2 loess, and sandy shale, which are all simulated by a brick solid element. During the numerical analysis, the initial soil parameters of each elements at different elevations should be taken based on the load of the upper fill, the compaction degree and the moisture content of the current soil layer. In the FLAC-3D program, the initial soil parameters of each soil element were given according to the vertical stress state, which are simulated according to the Fig. 12 and Tables 4 and 7. During the construction stage, the fill process was simulated according to the filling rate, and the filling duration time of each soil layer was considered to be instantaneous. When the filling process of the upper layer soil was completed, the mechanical parameters of lower layer of soil was updated to a new parameter by considering the gravity stress of the upper layers soil, the updated process continued until the filling process was completed. The Mohr-Coulomb criterion is mainly used to simulate soil deformation under the filling load [45]. The original foundation of sandy shale and reinforcement piles with the VSGP method are simulated by a linear elastic model; their creep and failure behaviour are ignored. In the FLAC-3D program, the relationships between the elastic modulus (E), shear modulus (G), and bulk modulus (K)

are:

G=

K=

E 2(1 + µ )

(7)

E 3(1

2µ )

(8)

where, μ is the Poisson ratio. The Poisson ratio values of the undisturbed Q3 loess, undisturbed Q2 loess, compacted Q3 loess, sandy shale, and VSGP are set to 0.33, 0.31, 0.30, 0.28, and 0.27, respectively. The elastic parameters and strength index of different types of soil, rock mass, and the VSGP reinforced soil are shown in Tables 1 and 7. The main research purpose of this work is to study the influence factors on PCS of the LHFE, therefore, the settlements during construction stage was excluded and the displacement field was set to zero in the 3D simulation. During the post-construction stage, both the fill and the original foundation are simulated with the Mod-Burgers model; the parameters of this model are shown in Table 4. The Mod-Burgers model has been compiled into the FLAC-3D program for simulation with the embedded FISH languages [44]. The users can set new variables or functions according to different requirements to realize the modification of element type, special boundary, mechanical parameters, node displacement, element stress and other characteristics based on the FISH languages. 3.5. Numerical analysis results 3.5.1. PCS variation with different influence factors Through the numerical sensitivity analysis of the above schemes, when the PCS rate is less than 0.02 mm/d, the calculation of creep deformation is stopped. The crest maximal PCS over time curves of the LHFE under different influencing factors are shown in Fig. 15. 12

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Table 7 Elastic parameters of different soils. Soil types

Parameters/(MPa)

Vertical stress σ/(MPa) 0.1

0.2

0.3

0.4

0.6

0.8

1.0

1.2

1.6

Undisturbed Q3 loess

Es K G

7.1 2.4 0.9

7.6 2.5 1.0

10.4 3.5 1.3

12.7 4.2 1.6

15.1 5.0 1.9

16.9 5.6 2.1

21.0 6.9 2.7

17.2 5.7 2.2

13.5 4.5 1.7

Undisturbed Q2 loess

Es K G

5.3 1.7 0.7

7.6 2.4 1.0

11.3 3.6 1.6

14.2 4.5 2.0

17.8 5.6 2.4

22.7 7.2 3.1

27.4 8.7 3.8

31.9 10.1 4.4

41.4 13.1 5.7

Silty clay N2b

Es K G

7.1 2.2 1.0

7.2 2.2 1.0

10.8 3.3 1.5

14.9 4.6 2.1

17.6 5.4 2.5

21.8 6.7 3.1

25.6 7.9 3.7

29.6 9.2 4.2

32.2 10.0 4.6

Compacted Q3 loess (λ = 0.80, w = 13.3%)

Es K G

2.0 0.6 0.3

2.5 0.8 0.4

5.6 1.7 0.8

8.4 2.6 1.2

15.0 4.7 2.1

14.9 4.6 2.1

18.5 5.7 2.6

23.5 7.3 3.4

27.4 8.5 3.9

Compacted Q3 loess (λ = 0.85, w = 13.3%)

Es K G

4.0 1.3 0.6

5.2 1.6 0.7

8.4 2.6 1.2

10.9 3.4 1.6

16.6 5.1 2.4

18.4 5.7 2.6

23.1 7.2 3.3

27.8 8.6 4.0

32.2 10.0 4.6

Compacted Q3 loess (λ = 0.90, w = 13.3%)

Es K G

7.2 2.2 1.0

8.4 2.6 1.2

11.9 3.7 1.7

14.0 4.3 2.0

18.4 5.7 2.6

21.2 6.6 3.0

26.0 8.1 3.7

30.2 9.4 4.3

34.4 10.7 4.9

Compacted Q3 loess (λ = 0.95, w = 13.3%)

Es K G

7.8 2.4 1.1

10.8 3.4 1.5

14.2 4.4 2.0

15.8 4.9 2.3

19.8 6.1 2.8

26.5 8.2 3.8

33.6 10.4 4.8

37.9 11.7 5.4

43.4 13.4 6.2

Compacted Q3 loess (λ = 0.98, w = 13.3%)

Es K G

10.1 3.1 1.4

12.5 3.9 1.8

16.2 5.0 2.3

17.8 5.5 2.5

20.9 6.5 3.0

26.8 8.3 3.8

33.5 10.4 4.8

37.3 11.5 5.3

42.2 13.1 6.0

Compacted Q3 loess (λ = 0.90, w = 12.0%)

Es K G

8.2 6.9 3.2

9.6 8.0 3.7

10.8 9.0 4.2

12.1 10.1 4.7

14.2 11.8 5.4

16.2 13.5 6.2

17.2 14.3 6.6

18.1 15.1 7.0

17.9 14.9 6.9

Compacted Q3 loess (λ = 0.90, w = 14.5%)

Es K G

5.9 5.0 2.3

7.1 5.9 2.7

8.5 7.1 3.3

9.9 8.2 3.8

12.0 10.0 4.6

14.2 11.8 5.5

15.2 12.6 5.8

16.1 13.4 6.2

17.0 14.2 6.5

Compacted Q3 loess (λ = 0.90, w = 17.0%)

Es K G

4.3 3.6 1.7

5.9 5.0 2.3

7.3 6.1 2.8

8.7 7.2 3.3

10.7 8.9 4.1

12.7 10.6 4.9

13.9 11.5 5.3

15.0 12.5 5.8

16.1 13.4 6.2

Compacted Q3 loess (λ = 0.90, w = 19.0%)

Es K G

4.7 3.9 1.8

6.1 5.1 2.3

7.3 6.1 2.8

8.5 7.1 3.3

10.2 8.5 3.9

11.9 9.9 4.6

13.1 11.0 5.1

14.4 12.0 5.5

14.9 12.4 5.7

Compacted Q3 loess (λ = 0.90, w = 21.0%)

Es K G

2.9 2.4 1.1

4.4 3.7 1.7

5.5 4.6 2.1

6.7 5.6 2.6

8.4 7.0 3.2

10.2 8.5 3.9

11.0 9.1 4.2

11.7 9.8 4.5

12.6 10.5 4.8

Sandy shale C2b

Es K G

2000.0 1185.2 611.1

VSGP

Es K G

15.0 8.7 4.7

From the above numerical analysis results, the following conclusions can be drawn:

from −0.38 m to −0.25 m. It can be seen that appropriately increasing the compaction degree greatly reduces the PCS. During the increase of fill materials’ water content from 12.0% to 21.0%, the PCS increases from −0.26 m to −0.38 m. As water content of the fill materials increases, the cohesive force and the compressive modulus of the soil particles decrease sharply, which causes an increase in the PCS. (3) After the original foundation is reinforced with the DC method, the average compaction degree of the soil is 0.96. When the treatment depth is gradually increased from 1.0 m to 5.0 m, the PCS linearly decreases from −0.42 m to −0.30 m. It can be seen that even if the treatment depth of the original foundation is shallow, it can effectively reduce the PCS. (4) When the VSGP reinforcement method is applied in the original foundation, the PCS linearly increases from −0.18 m to −0.30 m as

(1) Within 200 days after completion, the crest maximal PCS rate of the LHFE is relatively large. After 3.5 years of completion, the PCS rate gradually slows down, and becomes lower than 0.02 mm/d. At this point in time for a project, the PCS of the high fill embankment can be considered as being relatively stable. (2) During the increasing of the filling height from 35 m to 100 m, the PCS linearly increases from −0.17 m to −0.83 m. When the filling rate increases from 0.3 m/d to 1.5 m/d, the PCS linearly increases from −0.25 m to −0.46 m. This indicates that the fast filling rate generates a large PCS, and the unfinished deformation during the construction period is accumulated into the PCS. When the compaction degree increases from 0.85 to 0.98, the PCS linearly reduces 13

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Fig. 15. The maximal crest PCS over time curves under different influence factors. (a) PCS-t curves with different H. (b) PCS-t curves with different v. (c) PCS-t curves with different λ. (d) PCS-t curves with different w. (e) PCS-t curves with different h. (f) PCS-t curves with different l. (g) PCS-t curves with different d. (h) PCS-t curves with different L.

the pile spacing increases from 0.6 m to 1.4 m. When the pile diameter of the VSGP method is gradually increased from 0.2 m to 1.0 m, the PCS is linearly reduced from −0.35 m to −0.17 m. When the pile length used in the VSGP method increases from 10.0 m to 20.0 m, the PCS decreases from −0.30 m to −0.18 m. It can be seen that appropriate increases of the pile diameter and the pile length, in addition to reducing the pile spacing can effectively increase the

reinforcement area of the original foundation, which can significantly reduce the PCS of the original foundation. 3.5.2. Sensitivity analysis results In order to more accurately describe the influence of various factors on crest PCS of high fill, the sensitivity coefficient (M) is introduced to characterize the effect of various factors on the PCS. The sensitivity 14

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MF ≈ (MF1 + MF2 + MF3 + MF4)/4 to compare their relative importance. If there are great differences among the α1, α2, α3 and α4, the average sensitivity coefficient is not suitable for comprehensive sensitivity analysis. The absolute value of the average sensitivity coefficient is plotted as shown in Fig. 18, and the calculated results are shown as follows:

•M •M

H=

1.90 > Mλ = 1.68 > Mw = 0.73 > Mv = 0.36. > Ml = 0.57 > Md = 0.35 > Mh = 0.18.

L = 0.69

By comparison the slope of curves and the absolute value of average sensitivity coefficient in Fig. 16, it can be seen that the two methods to compare the relative importance of different influence factors are almost the same. It is suitable for using the absolute value of the average sensitivity coefficient to compare their relative importance. From the above-mentioned sensitivity coefficient curves of various influencing factors on the PCS, we can see:

Fig. 16. The explanation of sensitivity coefficient of MF. Table 8 Sensitivity index formulas of different influence factors of the PCS. MH=(ΔS/S)/(ΔH/H) Mλ=(ΔS/S)/(Δλ/λ) Mw=(ΔS/S)/(Δw/w) Mv=(ΔS/S)/(Δv/v)

(11) (12) (13) (14)

Mh=(ΔS/S)/(Δh/h) Md=(ΔS/S)/(Δd/d) Ml=(ΔS/S)/(Δl/l) ML=(ΔS/S)/(ΔL/L)

(1) Fig. 17 indicates that the variation ratio of the PCS (ΔS/S) has a linear relationship with the variation ratio of the influencing factors (ΔF/F). The filling height (H), filling rate (v), water content (w), and pile spacing (l) are positively correlated to the PCS; however, the filling compaction degree (λ), reinforcement depth (h), pile diameter (d), and pile length (L) are inversely related to the PCS. (2) Fig. 18a shows that the filling height has the greatest influence on the PCS (MH = 1.90). Since the fill height is often determined by the needs of the project itself, it is difficult to control it artificially. The comprehensive compaction degree (Mλ = 1.68) and water content (Mw = 0.73) has the second and the third largest effect on the PCS. Therefore, during the construction of the fill, the control of the compaction degree and the water content becomes the primary influence factors. The fill rate (Mv = 0.36) has the least influence on PCS, however, the fill rate impact on the PCS should not be neglected. In high fill projects, it is not necessary to monitor the construction progress of the filling body. After the DC method is applied, the fill process should be allowed to stop for a certain period of time, so that the high fill can be further compacted under the self-weight of the filling body. At this time in the project, the consolidation or creep settlement occurs, which is more conducive to the reduction of the PCS. (3) Fig. 18b shows that when the original foundation is reinforced by the VSGP method, the average sensitivity indices of pile length, pile spacing, and pile diameter are ML = 0.69, Ml = 0.57, and Md = 0.35, respectively. It can be seen that increasing the pile length is the most effective approach for controlling the PCS, followed by reducing the pile spacing and enlarging the pile diameter. When the DC method is used to treat the original foundation, the average sensitivity index of the effective reinforcement depth is Mh = 0.18, which has the least impact on the PCS. It can be seen that the reinforcement depth and effect of the DC method is limited, but is widely used. This is because the cost of using the DC method is low and the construction process is relatively simple. The VSGP method can be effectively used to reinforce the original foundation, however, due to the difficulty of construction, high requirements on the site and associated costs, it is actually less used to reinforce the soil in high fill projects involving massive volumes.

(15) (16) (17) (18)

index of a certain factor (F) to the PCS is MF: (9)

MF = ( S S ) ( F F )

According to Eq. (9), the sensitivity coefficient MF could be explained as shown in Fig. 16, when the influencing factor (F) changes from F1 to F5, the calculated crest PCS of high fill (S) changes from S1 to S5, and the sensitivity coefficient MH at each variation step can be written as:

MF =

MF 1 =

S1 F1 F1 S1

=

F1 S1

tan

1

MF 2 =

S2 F1 F2 S1

=

F1 S1

tan

2

MF 3 =

S3 F3

F1 S1

=

F1 S1

tan

3

MF 4 =

S4 F4

F1 S1

=

F1 S1

tan

4

(10)

where ΔS is the difference between the PCS of a certain influencing factor and its reference value F; S is the PCS under the reference influencing factor; ΔS/S is the variation ratio of the PCS; F is the reference value of the influencing factor; ΔF is the variation of the influencing factor F; and ΔF/F is the variation rate of the influencing factor. ΔSi and ΔFi is the difference value (i = 1, 2, 3, 4); tanαi is the slope of the curve of (ΔS/S)–(ΔF/F). When MF greater than 0, it means that the PCS is positively correlated with the influencing factors F; when MF < 0, it means that the PCS is inversely related to the influencing factors F. According to formula (9), the sensitivity coefficients of the factors mentioned above are defined as follows: MH, Mλ, Mv, Mw, Mh, Md, Ml, ML; these can be calculated according to the formulas (11)–(18) in Table 8. The curves of ΔS/S and ΔF/F are shown in Fig. 17. From Figs. 16 and 17, the slope of the curves S-F at different variation step is approximately equal, the relationship between ΔS/S and ΔF/F is almost linear, which is tanα1 ≈ tanα2 ≈ tanα3 ≈ tanα4, the sensitivity coefficient MF1 ≈ MF2 ≈ MF3 ≈ MF4. For comprehensive compare their relative importance of different influence factors on the crest PCS, it is suitable to use the average sensitivity coefficient

3.6. Controlling technologies of the LHFE For controlling the crest PCS and the differential PCS of the LHFE, according to engineering experiences in China’s civil airports [46], the

15

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Fig. 17. Curves between ΔS/S and ΔF/F. (a) Relationship between ΔS/S and ΔH/H. (b) Relationship between ΔS/S and Δv/v. (c) Relationship between ΔS/S and Δλ/ λ. (d) Relationship between ΔS/S and Δw/w. (e) Relationship between ΔS/S and Δh/h. (f) Relationship between ΔS/S and Δl/l. (g) Relationship between ΔS/S and Δd/ d (h) Relationship between ΔS/S and ΔL/L.

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4. Conclusions (1) Under long-term high-pressure conditions, the undisturbed loess and compacted loess exhibit creep behaviour. The creep deformation of the undisturbed Q3 loess is obviously higher than that of the Q2 loess. The higher the soil water content and the larger the axial load, the larger the creep deformation of the soil. The higher the compaction degree of the soil, and the larger the axial load, result in a smaller creep deformation of the soil. The proposed Mod-Burgers model and equivalent creep modulus can clearly reflect the longterm deformation characteristics of compacted and undisturbed loess. The further relationship between the creep parameters and other parameters (water content, dry density, initial saturation, shear strength) are also important to be seen in the engineering practice, and it will be obtained at next research stage. (2) The variation ratio of the PCS (ΔS/S) has an approximate linear relationship with the variation ratio of the influencing factors (ΔF/ F). The filling height, filling rate, water content, and pile spacing are positively correlated to the PCS; however, the filling compaction degree, reinforcement depth with DC, pile diameter, and pile length are inversely related to PCS. The sensitivity indices of influencing factors are sorted from high to low as follows: filling height (MH = 1.90), comprehensive compaction degree (Mλ = 1.68), water content (Mw = 0.73), pile length (ML = 0.69), pile spacing (Ml = 0.57), fill rate (Mv = 0.36), pile diameter (Md = 0.35), and treatment depth of original foundation with DC (Mh = 0.18). After the filling height, the compaction degree and water content are the next two important influence factors to be controlled for the high filling body; the pile length and pile spacing are the most important influence factors to be controlled for the reinforcement of the original foundation. (3) For the construction control of the LHFE in the gully, different treatment methods should be adopted according to different functional zones. For important or special building areas, the compaction degree of soil within 0.4 m below the crest of the high fill or excavation should be controlled more than 0.98. For the deep soil of the filling body, the compaction degree should be controlled above 0.93–0.96, water content should be strictly controlled close to the optimum water content, and the fill rate should not exceed 0.4 m/d. The fill should be allowed to stand for seven days or more after each DC. For general or non-construction areas, the compaction degree of the filling materials should exceed 0.90. By considering the economic efficiency of the treatment methods of the original foundation, it is recommended to adopt the DC method for shallow loess foundations. When the treatment depth is at least 5 m, the collapsibility of loess should be eliminated. For thick loess foundations, the VSGP method is more suitable for the original foundation with low water content; the CFG pile or lime-soil compaction pile method can be used in the original foundation with high water content. For the VSGP methods, the recommended pile length is not less than 10 m, pile diameter is more than 0.5 m, and pile spacing is controlled between 1.0 and 2.0 m.

Fig. 18. Average sensitivity coefficient of the PCS with different influence factors. (a) Sensitivity coefficient of the filling body. (b) Sensitivity coefficient of the original foundation reinforcement.

allowable values of the PCS within 20 years should not exceed the values as shown in Table 9. Table 9 shows that the crest PCS and the differential PCS of the building areas on the HFE should be limited within 200 mm and 1.5‰, respectively. Based on the control standards mentioned above and the sensitivity analysis results in Section 3.5, it is suggested that the filling parameters with DC method are controlled as follows: fill rate v ≤ 0.4 m/d, comprehensive compaction degree λ ≥ 0.93, soil water content w = wop ± 2%, effective reinforcement depth with the DC method h ≥ 5 m, and the standing time after each DC construction is T ≥ 7 d. If the original foundation is reinforced by using the VSGP method, the following parameter values are used: pile length L ≥ 10 m, pile diameter d ≥ 0.5 m, and the pile spacing l = 1.0–2.0 m. In the end, for controlling the PCS, the control method of the compaction process during filling and the reinforcement technologies of high fill embankments are suggested as shown in Table 10. Table 9 Allowable values of crest PCS and differential PCS of LHFE in loess gully. No.

Areas

PCS-S/(mm)

Differential PCS/(‰)

① ② ③ ④

Important or special building area: aircraft traffic link, airport station General building area: High fill slope region Traffic area Green area and other non-building area

100 200 300 500

1.0 1.5 2.0 –

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Table 10 Construction technologies of the LHFE in a loess gully. Areas of LHFE

Important or special building area

Fill

Treatment Range

Reinforcement method of fill body Compaction degree

Water content

Filling process

0–0.4 m 0.4–4.0 m

λ ≥ 0.98 H ≥ 20 m,λ ≥ 0.96 H < 20 m,λ ≥ 0.96 H ≥ 20 m,λ ≥ 0.96 H < 20 m,λ ≥ 0.93 λ ≥ 0.98 H ≥ 20 m, λ ≥ 0.93 H < 20 m, λ ≥ 0.90 λ ≥ 0.90

(1) w = 11–15%, can be directly compacted with DC method; (2) w ≥ 15%, remove and replaced with admixtures; (3) w ≤ 11%, water should be injected into the soil.

(1) v = 0.4 m/d, when using the combined methods of VC + DC; (2) Intermission time should be more than 7d after each DC; (3) Thickness of loose laying soil should be less than 0.4 m. with VC method

4.0 m–H General building area Non-building area

Excavation Fill Excavation

0–0.4 m H-20–H 0–H 0–0.4 m

Declaration of Competing Interest

Reinforcement method of Original foundation (1) DC method: shallow loess foundation,treatment thickness should be more than 5 m; (2) VSGP method: thick loess foundation with low water content; (3) CFG pile and lime-soil compaction pile: thick loess foundation with high water content; (4) Collapsibility soil of 3.5–4.0 m below the foundation must be eliminated.

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The authors declared that there is no conflict of interest. Acknowledgements The authors would like to extend their gratitude to the National Natural Science Foundation of China (No. 51678484), China Scholarship Council (No. 201808610061) and the Research Fund of the State Key Laboratory of Eco-hydraulics in Northwest Arid Region, Xi’an University of Technology (2019KJCXTD-12), who funded this research, as well as the graduate students for their hard work in carrying out the testing. The authors would like to express appreciation to the reviewers for their valuable comments and suggestions that helped improve the quality of our paper. The authors would like to express their gratitude to EditSprings (https://www.editsprings.com/) for the expert linguistic services provided. References [1] Liu H, Li P, Zhang Z. Prediction of the post-construction settlement of the high embankment of Jiuzhai-Huanglong airport. Chin J Geotech Eng 2005;27(1):90–3. [in Chinese]. [2] Zhu C, Li N, Liu M, et al. Spatiotemporal laws of post-construction settlement of loess-filled foundation of Lvliang Airport. Chin J Geotech Eng 2013;35(2):293–301. [in Chinese]. [3] Ge M, Li N, Zhang W, et al. Settlement behavior and inverse prediction of postconstruction settlement of high filled loess embankment. Chin J Rock Mech Eng 2017;36(3):745–53. [in Chinese]. [4] Yang X. Analysis of foundation deformation and stability of high fill of airport in mountainous area. Lanzhou University of Technology; 2017. [in Chinese]. [5] Zheng J, Cao J, Zhang J, et al. Analysis of influencing factors of high loess-filled foundations based on centrifugal model tests. Chin J Rock Mech Eng 2019;38(3):560–71. [in Chinese]. [6] Du W, Zheng J, Liu Z, et al. Settlement behavior of high loess-filled foundation and impact from exhaust conditions. Rock Soil Mech 2019;40(1):325–31. [in Chinese]. [7] Yao Z, Lian J, Zhang J, et al. On erosion characteristics of compacted loess during wetting procedure under laboratory conditions. Environ Earth Sci 2019;78(18). https://doi.org/10.1007/s12665-019-8588-2. [8] Yao Z, Huang X, Chen Z, et al. Comprehensive soaking tests on self-weight collapse loess with heavy section in Lanzhou region. Chin J Geotech Eng 2012;34(1):65–74. [9] Indraratna B, Baral P, Rujikiatkamjorn C, et al. Class A and C predictions for Ballina trial embankment with vertical drains using standard test data from industry and large diameter test specimens. Comput Geotech 2018;93:232–46. [10] Amavasai A, Sivasithamparam N, Dijkstra J, et al. Consistent Class A & C predictions of the Ballina test embankment. Comput Geotech 2018;93:75–86. [11] Jiang M, Li T, Hu H, et al. DEM analyses of one-dimensional compression and collapse behaviour of unsaturated structural loess. Comput Geotech 2014;60:47–60. [12] Liu Z, Liu F, Ma F, et al. Collapsibility, composition, and microstructure of loess in China. Can Geotech J 2016;53(4):673–86. [13] Zhao C. Study on post-construction settlement deformation laws and prediction of high fill embankment in mountainous areas. Wuhan 430074, PR China: China University of Geosciences; 2018. [in Chinese]. [14] Rezania M, Bagheri M, Nezhad MM, et al. Creep analysis of an earth embankment on soft soil deposit with and without PVD improvement. Geotext Geomembr 2017;45(5):537–47. [15] Zhi B, Wang P, Liu E, et al. Experimental study on deformation and strength characteristics of undisturbed loess foundation under high fill DEStech Transactions on Materials Science and Engineering International conference on transportation

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