J. Cent. South Univ. (2013) 20: 1368−1375 DOI: 10.1007/s11771-013-1624-6

Mechanical analysis of fixed geosynthetic technique of GRPS embankment

ZHANG Jun(张军)1, ZHENG Jun-jie(郑俊杰)2, MA Qiang(马强)2

1. Key Lab of Highway Construction and Maintenance Technology in Loess Region, Shanxi Transportation Research Institute, Taiyuan 030006, China;

2. Institute of Geotechnical and Underground Engineering, Huazhong University of Science and Technology, Wuhan 430074, China

© Central South University Press and Springer-Verlag Berlin Heidelberg 2013

Abstract: To overcome the deficiencies of conventional geosynthetic-reinforced and pile-supported (GRPS) embankment, a new improvement technique, fixed geosynthetic technique of GRPS embankment (FGT embankment), was developed and introduced. Based on the discussion about the load transfer mechanism of FGT embankment, a simplified check method of the requirement of geosynthetic tensile strength and a mechanical model of the FGT embankment were proposed. Two conditions, the pile cap and pile beam conditions are considered in the mechanical model. The finite difference method is used to solve the mechanical model owing to the complexity of the differential equations and the soil strata. Then, the numerical procedure is programmed. Finally, a field test is conducted to verify the mechanical model and the calculated results are in good agreement with field measured data. Key words: mechanical model; load transfer mechanism; fixed geosynthetic technique; GRPS embankment; field test 1 Introduction

Geosynthetic-reinforced and pile-supported (GRPS) embankment has been increasingly used to construct high embankment over soft soil [1−5]. As shown in Fig. 1, GRPS embankment contains embankment fill, piles, subsoil, firm soil, sand cushion and geosynthetic. However, in the wide applications on GRPS embankment, its deficiencies are exposed, i.e. low pile efficiency, low geosynthetic efficiency, intolerable settlement and differential settlement [6−8].

Fig. 1 Illustration of GRPS embankment

In the view of these deficiencies, a new

improvement technique, fixed geosynthetic technique of GRPS embankment (FGT embankment), is developed [9].

It fixes geosynthetic on the pile tops by a fixed system, which consists of steel bar fixed fulcrum and the concrete fixed top (Fig. 2). To ensure the stability of FGT embankment, rigid piles and high tensile geosynthetic must be applied, and the pile tip must be penetrated into the firm soil or locate at the top of the bedrock.

Fig. 2 Schematic of FGT structure

Several methods have been proposed for analyzing

the load transfer mechanism of conventional GRPS embankment. HEWLLET and RANDOLPH [10] proposed two-dimensional and three-dimensional soil arching models on the basis of the observed deformations in a series of tests. ZHANG et al [11] presented a simplified calculation method for the biaxially reinforced working system on the basis of the discussion about working mechanism of biaxially reinforced composite foundation. CHEN et al [12]

Foundation item: Project(51278216) supported by the National Natural Science Foundation of China; Project(20091341) supported by the Scientific

Research Foundation for Returned Overseas Chinese Scholars, Ministry of Education, China; Project(HF-08-01-2011-240) supported by the Graduates’ Innovation Fund of Huazhong University of Science and Technology, China

Received date: 2012−02−22; Accepted date: 2012−07−05 Corresponding author: ZHENG Jun-jie, Professor, PhD; Tel: +86−27−87557024; E-mail: zhengjj@hust.edu.cn

J. Cent. South Univ. (2013) 20: 1368−1375 1369

obtained a closed-form solution to evaluate the interactions among the pile cap, pile, soil and embankment fill under the one-dimensional condition. ABUSHARAR et al [13] proposed a simple two-dimensional method by the soil arching effect and the tensioned membrane effect. ZHAO et al [14] deduced a function of the horizontal reinforced cushion deflection and proposed a method to calculate the pile-to-soil stress ratio of GRPS embankment. ZHANG et al [15] developed a mechanical model with the consideration of the embankment and improved area as a whole. However, these studies either assumed the height of equal settlement plane as an invariable value or treated the geosynthetic and sand cushion as a whole.

In the conventional GRPS embankment, the invariable value of the height of equal settlement plane may be available in a certain condition. However, the rationality of this method for the FGT embankment is questionable owing to the difference of the structure and load transfer mechanism between the FGT embankment and conventional GRPS. In addition, the thickness and material properties of reinforced cushion are difficult to determine. In order to understand this new improvement technique, a simplified check method of the requirement of geosynthetic tensile strength and a mechanical model of FGT embankment are proposed according to the understanding of load transfer mechanism of FGT embankment. Finally, the measured results of a field test are used to verify the mechanical model in this work. 2 General information 2.1 Load transfer mechanisms

As shown in Fig. 3, the load transfer mechanisms of FGT embankment and conventional GRPS embankment are different. Figure 3(a) shows the load transfer mechanism of conventional GRPS embankment. Under embankment load, the deformation of geosynthetic in the conventional GRPS embankment is smaller than that at the plane of pile top owing to the geosynthetic yields compatible with sand cushion, which weakens the tensioned membrane effect. However, the deformation of geosynthetic in the FGT embankment is uniform with that at the plane of pile top owing to the rigid connection between the geosynthetic and pile top. In this way, the FGT embankment can mobilize the geosynthetic efficiency significantly. 2.2 Simplified check method

Due to the difference of the structures and load transfer mechanisms between the conventional GRPS embankment and FGT embankment, the requirement of geosynthetic tensile strength in the FGT embankment is higher than that in the conventional GRPS embankment.

Therefore, the tensile strength of geosynthetic must be checked. 2.2.1 At center of embankment

As shown in Fig. 4(a), the applied load on the geosynthetic is assumed as the average embankment load

Fig. 3 Load transfer mechanisms: (a) Conventional GRPS

embankment; (b) FGT embankment

Fig. 4 Diagram of simplified check model: (a) At center of

embankment; (b) At shoulder of embankment

J. Cent. South Univ. (2013) 20: 1368−1375 1370

H , and the checking formula is as follow:

s p g m( ) /A H S E (1) where H is the height of embankment; γ is the unit weight of embankment fill; As is the subsoil area contributed by a single pile; Sp is the perimeter of pile cap; εm is the maximum tolerable strain of geosynthetic; Eg is the tensile stiffness of geosynthetic. 2.2.2 At shoulder of embankment

As shown in Fig. 4(b), assume all of the lateral pressures in the shoulder area are resisted by the geosynthetic, and the checking formula can be obtained (the horizontal pressure is calculated by the active earth pressure):

a g m1

2p H E (2)

where pa is the active earth pressure. 3 Mechanical model

The mechanical performance of FGT embankment includes soil arching effect, tensioned membrane effect and interaction between the piles and soil. The mechanical model in this work is shown in Fig. 5. In this model, two equal settlement planes (equal settlement plane I and equal settlement plane II) exist in the embankment fill and subsoil, respectively. In the embankment fill, two vertical planes passing through the outer edges of the span are assumed and the embankment fill is divided into two parts, i.e., the supported fill mass and yield fill mass. Under the embankment load, the yield fill mass tends to settle relative to the stationary supported fill mass. The relative movement induces the friction between the moving and stationary fill mass and this friction transfers some load from the moving fill to the stationary fill. The geosynthetic is modeled as a square thin plate, and the pressure and deformation of the geosynthetic are calculated by the thin plate theory. Dissimilar to the conventional GRPS embankment, the geosynthetic is modeled as a thin plate owing to transferring the load from the subsoil to piles through the geosynthetic tension directly. The pile reinforced area is divided into two parts to consider the interaction between the piles and subsoil. Above the equal settlement plane II, the pile and surrounding subsoil below the pile cap (beam) are treated as a composite pile owing to the deformation compatibility of the two parts. Below the equal settlement plane II, the pile and subsoil are considered as two parts, respectively.

In addition, the pile cap and pile beam conditions are considered in the mechanical model. In the pile cap condition, the mechanical model is a three-dimensional problem. In the pile beam condition, the part above the equal settlement plane II is a two-dimensional problem

Fig. 5 Mechanical model of FGT embankment

and the part below the equal settlement plane II is a three-dimensional problem. 3.1 Analysis of soil arching effect

Based on the analysis of the yield fill mass element with the height of h, the soil arching effect in the embankment fill is considered (Fig. 6).

Fig. 6 Calculation diagram of yield fill mass element

3.1.1 Pile cap condition

The equilibrium equation in the vertical direction is given by

s s a a( d ) [( 2 ) tan ]dp p A S hk c k c h

s sdpA A h (3) where c is the cohesion of embankment fill; is the friction angle of the embankment fill; p is the mean vertical pressure acting on the top of the yield fill mass element; Ka is the coefficient of Rankine active earth pressure, and 2

a tan (45 / 2)K .

J. Cent. South Univ. (2013) 20: 1368−1375 1371

Solving Eq. (3), the vertical average pressure is given by

2 2a e p s( ) tan [ ( ) ] / 2p h h k h H h S A

a e p s(1 2 tan )( ) /c k h H h S A (4) where p(h) is the vertical pressure of yield fill mass at the height of h; H is the height of embankment fill; he is the height of equal settlement plane I.

By taking h=H, the vertical pressure below the yield fill mass element is given by

sem a e e p stan (2 ) / 2p H k H h h S A

a e p s(1 2 tan ) /c k h S A (5) where psem is the vertical pressure at the bottom of the yield fill mass.

The vertical equilibrium in embankment fill requires

p ( ) (1 ) ( ) /p h h m p h m (6)

where p ( )p h is the vertical pressure of supported fill mass at the height of h; m is the displacement ratio.

By taking h=H, Eq. (6) becomes

pem sem(1 ) /p H m p m (7)

where ppem is the vertical pressure at the bottom of supported fill mass.

The average differential settlement between the yield fill mass and the supported fill mass below the embankment fill is given by

e

pem sem p em ( ( ) ( )) / d

H

H hs S S p h p h E h

(8)

where Eem is the elastic modulus of embankment fill. 3.1.2 Pile beam condition

The equilibrium equation in the vertical direction is given by

a a( d ) 2 ( 2 ) tan d dp p b hk c k c z pb b h

(9)

where b is the clear spacing of pile beams. By solving Eq. (9), the vertical average pressure is

given by

2 2a e( ) tan [ ( ) ] /p h h k h H h b

a e2 (1 2 tan )( ) /c k h H h b (10)

By taking h=H, Eq. (9) becomes

em a e etan (2 ) /p H k H h h b

a e2 (1 2 tan ) /c k h b (11)

3.2 Analysis of tensioned membrane effect

Based on the thin plate theory, the tensioned

membrane effect is considered in the FGT embankment. The geosynthetic is modeled as a square thin plate. The area of square plate is equivalent to the area of yield fill mass. The average pressure transferred by the tensioned membrane effect is denoted as q0. 3.2.1 Pile cap condition

The calculation diagram of thin plate is shown in Fig. 7. By assuming the boundary of thin plate is constrained by the simple supports, the flexivity expression of the plate is given by

maxπ π

( , ) sin sinx y

w x y wd d

(12)

where d is the length of square thin plate, sd A ; wmax is the flexivity at the center of plate.

Fig. 7 Calculation diagram of thin plate

The basic differential equation of large deflection

bending problem of the square thin plate is given by

4

22 2 2

2 2

w w wf E

x y x y

(13)

where f is the stress function, and E is the elastic modulus of the thin plate.

Substituting Eq. (12) into Eq. (13) leads to 4

4 2max 4

π 2π 2πcos cos

2

E x yf w

d dd

(14)

The average in-plane load at x=0 and x=d is defined

as Px; the average in-plane load at y=0 and y=d is defined as Py. Solving Eq. (14), we have

22 2max 2π 2π 1 1

cos cos32 2 2x y

w x yf E P y P x

d d

(15)

According to Galerkin equation, we have

π πsin sin d d 0

x yX x y

d d (16)

where2 2 2 2 2

4g g g2 2 2 2

2f w f w f

X D w h h hx yy x x y

J. Cent. South Univ. (2013) 20: 1368−1375 1372

0

2wq

x y

; 3 2

g /12(1 )D Eh , and hg is the thickness

of thin plate; is Possion ratio of the thin plate.

By integrating and making Eq. (16) dimensionless, the pressure-flexivity expression of square thin plate is given by

6 2 3 60 0(π / 256) 4 2(3 ) 4(π /192) W W P (17)

where 0 0 g/W w h and 2 4g 0(1 )( / ) /P d h q E .

According to the equilibrium condition of volume, we have

s( , )d dw x y x y s A (18)

Substituting Eq. (10) into Eq. (18), the maximum differential settlement, wmax, is obtained. Then, by substituting wmax into Eq. (17), the average pressure transferred by the geosynthetic q0 is obtained. 3.2.2 Pile beam condition

By assuming the boundary of thin plate is restricted by the simple supports, the flexivity expression of plate is given by

maxπ

( ) sinx

w x wb

(19)

Similarly, the pressure-flexivity expression of thin plate is given by

5 5 3g g3

max max 02 4 2 4

π π0

16(1 ) 48(1 )

Eh Ehw w q

s s

(20)

3.3 Interaction between piles and soil

By considering the complexity of soil strata in the projects, and dividing the pile and subsoil into n segments, the length of each segment is nlz / . The serial number of each node from pile top to bottom is 0, 1, 2, …, n−1, n. The differential settlement at node i between the pile and subsoil can be expressed as

p( ) s( )( ) ( 1)

p( ) s( )

Δi ii i

i i

W W z zE E

(21)

where ( 1)iW is the differential settlement at node i−1 between the pile and subsoil; p( )i is the pressure at the top of pile element; p( )iE is the elastic modulus of pile element; s( )i is the pressure at the top of subsoil element; s( )iE is the elastic modulus of subsoil element.

Based on the practical conditions, the different load transfer models between the pile and the subsoil can be chosen. As shown in Fig. 8, the ideal perfect elasto-plastic model is used in this work and the skin friction at node i between the pile and subsoil can be expressed as

Fig. 8 Perfect elasto-plastic model

( ) ( ) u

( )u ( ) u

( )

, | |

, | || |

i i i

ii i

i

τ k W W

Wτ k W

W

(22)

where i is the skin friction at node i between the pile and subsoil; k is the stiffness coefficient of ideal elastic-plastic model; u is the limited relative displacement between the pile and subsoil. 3.3.1 Pile cap condition

Above the equal settlement plane II, the equilibrium equation in the vertical direction is given by

p( 1) p( ) p p

s( 1) s( ) p s

Δ /

Δ /

i i i

i i i

τ zS A

τ zS A

(23)

where Ap is the area of pile cap. 3.3.2 Pile beam condition

Above the equal settlement plane II, the equilibrium equation in the vertical direction is given by

p( 1) p( )

s( 1) s( )

2 Δ /

2 Δ /

i i i

i i i

τ z s

τ z b

(24)

where s is the width of pile beam. Below the equal settlement plane II, the pile cap and

pile beam conditions in the mechanical model both are the three-dimensional problems. The equilibrium equation in the vertical direction is given by

p( 1) p( ) p p

s( 1) s( ) p s

Δ /

Δ /

i i i

i i i

τ zS A

τ zS A

(25)

where pS is the perimeter of single pile; pA is the area of single pile; sA is the area of subsoil.

Based on Eq. (21), the differential settlement at the bottom of pile can be obtained. Then, the differential settlement at the bottom of pile can be also obtained based on the elastic foundation beam model:

c 1 p(n) s(n)( )S C (26)

where Sc is the differential settlement at the bottom of

J. Cent. South Univ. (2013) 20: 1368−1375 1373

pile; C1 is the differential settlement at the bottom of pile under the unit pressure and 2

1 0 0(1 )C μ ω b E , E0 is the deformation modulus of soil beneath the pile tip, 0 is Poisson ratio of soil beneath the pile tip, and ω is the settlement coefficient. 3.4 Calculation approach

By considering the complexity of the differential equations and soil strata, a numerical procedure for solving the calculation approach based on the finite difference method is programmed. The detailed flow chart of calculation is shown in Fig. 9. If (n) cW S δ (δ is the value of precision criterion), adjust the value of he and repeat calculation steps if (n) cW S δ , the height of equal settlement plane I he is determinated.

4 Verification

A field test of FGT embankment at a trial bridge approach in Chang-An Expressway is carried out to verify the proposed approach discussed above, as shown in Fig. 10. The trial embankment is located at the east of MCK+826 No. 0 Bridge in the southeast of Shanxi province, China. The embankment is 5.0 m high with a crown width of 34 m. The side slope is 1:1.5 (vertical: horizontal). The fill material consists mainly of loess with cohesion strength of 16.8 kPa, friction angle of 24.6°, and average unit weight of 19.0 kN/m3. The soil profile can be divided into six groups. The skin friction between the pile and the soil are obtained from the CPT

Fig. 9 Flow chart of calculation

J. Cent. South Univ. (2013) 20: 1368−1375 1374 test. The material properties of the embankment fill and the soil layers are obtained from the in-situ and laboratory tests (Table 1).

Fig. 10 Photo of trial embankment

Table 1 Material properties in field test

Material Es/MPa γ/(kN·m−3) c/kPa φ/(°) (H/L)/m

Fill 20.0 19.0 16.8 24.6 5

Silty clay 5.2 17.2 14.2 18.3 3.5

Silty soil 7.6 17.8 7.6 19.7 6.0

gravelly Sand 30.0 20.1 0 28.6 4.0

Clay 22.1 18.3 15.7 21.0 6.5

The bridge is supported on bored concrete piles,

which are installed into the weathered granite rock. The FGT embankment is used at bridge approach to accommodate the differential settlement between the bridge approach embankment and bridge abutment. The tips of the cast in-situ concrete piles at bridge approach are penetrated 0.5 m into the gravelly sand layer and spaced 3.5 m. The width of pile caps is 1.0 m. The concrete strength grade of concrete is C25. A layer of geosynthetic is used and the tensile stiffness of geosynthetic at 0.5% is 1 700 kN/m. The elastic modulus of geosynthetic is 20.0 GPa and the thickness is 1.5 cm. To validate of the mechanical model, the earth pressure cells are installed at the different depths along the centerline of FGT embankment. The cross-section view of the instrumentations is shown in Fig. 11.

Fig. 11 Cross-section view of instrumentations

Based on Eqs. (1) and (2), it can be found that the tensile strength of geosynthetic meets the requirement in this project. Table 2 shows the comparison between the measured pressures and calculated results based on the presented approach. The calculated results are basically in good agreement with the measurements, which is similar to the work of FGT embankment in engineering practice. Table 2 Measured and calculated results

Position Measured

result/kPa

Calculated

result/kPa

Difference/

%

Above

geosynthetic392.6 350.1 10.1

Pile capBelow

geosynthetic− 672.1 −

Above

geosynthetic68.6 72.3 5.4

SubsoilBelow

geosynthetic40.8 43.7 7.1

5 Conclusions

1) In the view of the deficiencies of conventional GRPS embankment, a new improvement technique, FGT embankment has been developed to construct an embankment over soft soil ground.

2) Based on the discussion about the difference between the conventional GRPS embankment and FGT embankment, a simplified check method of the requirement of geosynthetic tensile strength is proposed.

3) In this mechanical model, the pile cap and pile beam conditions are considered, respectively. The finite difference method is used to solve the mechanical model owing to the complexity of the differential equations and soil strata. Finally, a field test is conducted to verify the mechanical model and the calculated results are basically in good agreement with the measurements. References [1] LIU H L, NG C W W, FEI K. Performance of a geogrid-reinforced

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(Edited by HE Yun-bin)