Analysis of geosynthetic-reinforced pile-supported embankment with soil-structure interaction models

Computers and Geotechnics 121 (2020) 103438

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Research Paper

Analysis of geosynthetic-reinforced pile-supported embankment with soil-structure interaction models

T

Tuan A. Pham Department of Civil Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo, Japan Laboratory 3SR, University of Grenoble Alpes, CNRS UMR 5521, Grenoble Cedex 09, France Department of Geotechnical Engineering, The University of Danang, Danang, Viet Nam

ARTICLE INFO

ABSTRACT

Keywords: Piled embankment Subsoil Geosynthetic Arching Skin friction Membrane effect Consolidation

A geosynthetic-reinforced pile-supported (GRPS) embankment is a complex soil-structure system. The response of a GRPS system is affected by the interactions among its five linked elements, namely the geosynthetic (a synthetic product used in civil engineering to stabilise the terrain), foundation, granular platform, fill soil, and geological media underlying and surrounding the foundation. The key load transfer mechanism in a GPRS embankment is a combination of various phenomena that include arching in the fill layers, tensioned membrane effect of the geosynthetic, frictional interaction, and support of the soft subsoil. Referring to the current numerical and experimental studies, a new theory has been developed in this study by combining the arching theory for the soil layer and the tensioned membrane theory for the geosynthetic. The subsoil effect with both linear and non-linear models and the frictional interaction are also included in the proposed method, thereby providing a more comprehensive design approach than the earlier methods that considered only either the tensioned membrane theory or the arching theory. It is demonstrated in this work that the proposed method produces results that are in good agreement with the experimental observations.

1. Introduction Piled embankments have existed for a long time, but they have become more popular since the 1980s. Nowadays, embankments of granular soils supported by piles and high strength geosynthetic are often used for highways, railways and construction activities. This is known as a geosynthetic reinforced pile supported (GRPS) embankment. The techniques are increasingly used to overcome significant problems related to consideration of stability and deformation such as bearing capacity, durability, large differential settlements when construction is undertaken on very soft soil ground. The load transfer mechanism in GRPS is a combination of the following four phenomena: (1) stress transfer from the soft soil to the pile due to the difference in their stiffness and so-called soil arching, (2) tensioned membrane effect of the geosynthetic, (3) support of subsoil, and (4) frictional behaviour along interfaces of geosynthetic-soils. The design of GRPS embankment includes the design of a various number of parameters for the embankment fill, geosynthetic, piles, and the underlying foundation soil. Arching often occurs in soil, especially when there is a materially different structure, termed a rigid inclusion. Soil arching is a term used to describe a range of phenomena in which stresses within the soil between piles are redistributed as the earth tries to establish

equilibrium by transferring loads into stiffer elements and decrease loads on soft subsoil. As a result, different structural arrangements of the particles are created. Sometimes this arrangement and stress redistribution is such that the resistance provided by the soil is analogous to a structural arch. For evaluating the limit state requirements or studying the behaviour of a GRPS embankment, several commonly used approaches are available in the literature. The analysis of a GRPS embankment can be conducted using experimental investigations, numerical modelling techniques or theoretical methods. The experimental approach comprises a full-field test, scaled model test or true scale experiment. The numerical modelling provides a helpful and powerful tool to understand the complicated behaviour of GRPS embankments. In this approach, one of three methods, namely the finite element method, finite difference method, and discrete element method, is commonly used. Being as important as the design methods, these analysis approaches are an essential part of any geotechnical design. The three aforementioned approaches can be used separately or in combination with one another. The choice of the most relevant approach(es) depends on the needs of the designers in different applications scenarios. The first one is the experimental investigation. Experimental study on the performance of a geosynthetic reinforced pile-supported

E-mail address: [email protected]. https://doi.org/10.1016/j.compgeo.2020.103438 Received 20 August 2019; Received in revised form 12 November 2019; Accepted 2 January 2020 0266-352X/ © 2020 Elsevier Ltd. All rights reserved.

Computers and Geotechnics 121 (2020) 103438

T.A. Pham

Nomenclature A Ac As Bers c cs d Dact E Ea Em Ep Es E0 FGRsquare FGRstrip hg H KP Ks Pca Pcm

Psa Ps q qsu s′ sd SRR SRRa SRRm

T Tε

contributory area of one pile (m) area of a pile cap (m) area of soft subsoil between pile caps (m) equivalent width of a pile cap (m) cohesion of embankment soils (kPa) total cohesion of soils at upper and lower sides of the geosynthetic interface (kPa) diameter of a circular pile cap (m) active depth of subsoil (m) total efficacy (dimensionless) efficacy component from arching effect (dimensionless) efficacy component from the membrane effect (dimensionless) elastic modulus of pile (kPa) Oedometric modulus of subsoil (kPa) Young’s modulus (kPa) total vertical load exerted by the 3D hemispheres on square subsurface (kN) total vertical load on the GR strips (kN) arching height (m) Height of embankment (m) passive earth pressure coefficient (dimensionless) modulus of subgrade reaction (kPa/m) load component distributed on pile cap by arching effect (kN) load component transferred onto pile cap by geosynthetic tensioned membrane (kN) total load resting on geosynthetic and subsoil by soil arching (kN) load component received by soft subsoil (kN) surcharge (kPa) ultimate bearing capacity of the saturated soft subsoil (kPa) clear spacing (s′ = s – a) (m) diagonal pile spacing (m) stress reduction ratio (dimensionless) stress reduction ratio induced by the arching effect (dimensionless) stress reduction ratio induced by the membrane effect (dimensionless)

Tf TH y U W γ σup μs σc a s

GR

θ τ ϕp ϕs

αp, αs

maximum tension in geosynthetic (kN/m) component of GR tensile force induced by stretching under embankment pressure(kN/m) component of GR tensile force induced by skin friction (kN/m) horizontal component of the tensile force in the GR (kN/ m) maximum deflection of geosynthetic (m) degree of consolidation of the subsoil at any time t (dimensionless) total load of embankment fills and surcharge (kN) unit weight of embankment soils (kN/m3) upward counter pressure from subsoil (kPa) Poisson’s ratio of subsoil (dimensionless) total vertical stress acting on the pile cap by both arching and membrane effect (kPa) vertical stress distributed on subsoil by arching effect (kPa) vertical stress carried by geosynthetic (kPa) deflected angle of geosynthetic (degree) total shear stress along geosynthetic interfaces (kPa) friction angle of soil at the upper side of the geosynthetic interface (degree) friction angle of soil at the lower side of the geosynthetic interface (degree) interaction coefficients between the geosynthetic-soils (dimensionless)

Abbreviations BS CUR EBGEO

PWRC GRPS IAR CBR PLT CPT

embankment has been performed by many researchers (e.g., Terzaghi [1], Hewlett and Randolph [2], Liu et al. [3], Le Hello and Villard [4], Van Eekelen et al. [5], Blanc et al. [6], Huckert et al. [7], Hosseinpour et al. [8], Chen et al. [9], Cao et al. [10], Xu et al. [11], King et al. [12], Girout et al. [13], Fagundes et al. [14], Tano et al. [15], Shen et al. [16], Khansari and Vollmert [17]). Trapdoor test was developed by Terzaghi [1] to investigate soil arching. Based on the trapdoor tests, Terzaghi [1] found that the slip surfaces of the mobilized portion above the trapdoor were curved. Hewlett and Randolph [2] conducted a series of model tests on free-draining granular soil. It was observed that the region of sand between the pile caps comprised of a series of hemispherical domes having radius approximately equal to half the diagonal pile spacing. Liu et al. [3] described a case history of a geogrid-reinforced and pile-supported (GRPS) highway embankment with a low improvement area ratio (the improvement area ratio, defined as the percent coverage of the pile caps over the total foundation area), and field data showed that there was a significant load transfer from soil to the piles as a result of soil aching, Moreover, there is a sharp reduction of tension force in the geogrid from edge of pile toward the centre. This is because of the sharpest change in the settlement occurred near the edge of the pile. Le Hello and Villard [4] presented a series of four full

British Standard Centrum Uitvoering Research Empfehlungen für den Entwurf und die Berechnung von Erdkörpern mit Bewehrungen aus Geokunststoffen (Recommendations for design and analysis of earth structures using geosynthetic reinforcement) Public Works Research Centre Geosynthetic-Reinforced Pile-Supported improvement area ratio Californian Bearing Ratio plate loading test cone penetration test

scale instrumented experiments, and the membrane effect of geosynthetic was observed evidently over the pile. Van Eekelen et al. [5] presented a series of nineteen 3D model experiments on piled embankments, and have found that the calculated GR strains using current analytical models exceed the GR strains measured in the field. In addition, it was found that consolidation of the subsoil results in an increase of arching. In the small-scale centrifuge model conducted by Blanc et al. [6], a finding found that the efficiency increases linearly with subsoil settlement, except when full arching occurs. Huckert et al. [7] describe full-scale experiments specifically designed to integrate the progressive opening of six circular cavities. These experiments were interesting because it allows observing the tensile geosynthetic behaviour with the frictional interaction between the soil and the reinforcement. In the study of Hosseinpour et al. [8], the two-dimensional finite-element analysis was performed using an axisymmetric unit cell, and then the results were compared with field measurements for a fullscale test embankment. It was interesting to find that the decrease of the soil apparent stiffness from quasi undrained to drained stiffness led the soil arching to develop at a constant rate during consolidation. Chen et al. [9] modelled the consolidation of the subsoil in their 2D tests by permitting water to flow out gradually from water bags. No researchers 2

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chose to control or to measure the subsoil support. Xu et al. [10] confirmed the support of subsoil by performing a series of scaled model tests. Xu et al. [10] concluded that most of the applied load was transferred to the pile caps due to soil arching and the tensioned membrane of the geogrid but a portion of the load was transferred to the subsoil between the pile caps. Moreover, tensioned membrane and increase of subsoil modulus might have some effects on the reduction of the settlement rate. Cao et al. [11] presented a field test of floating piled embankment with a well-designed monitoring program. A worthy finding was that more counter support from the subsoil was developed as the pile settled. Thus, lesser soil arching effects and tensioned membrane effects were observed. King et al. [12] presented the field monitoring data of a GRPS embankment and found a strong relationship between the development of arching stresses and subsoil settlement. Girout et al. [13] conducted a series of 33 small scale models that were tested using a geotechnical centrifuge. The interesting finding of this work is the fact that, with a GRPS embankment, the membrane effect permits the improvement of the total load transfer toward the piles. The stiffer the geosynthetic is, the lower the deflection. Fagundes et al. [14] performed a series of twenty-eight centrifuge tests on piled embankments with basal geosynthetic reinforcement. An interesting finding was that the loss of contact of the geosynthetic with the soft soil identified at this point corresponded to the GR maximum deflection. Tano et al. [15] presented a new large-scale test to assess the efficiency of a geosynthetic reinforcement laid over cavity, and an interesting finding is that the geosynthetic strain not only contributed by load pressure but also by shear stress at both side of geosynthetic. Shen et al. [16] conducted three centrifuge model tests on GRPS embankments with side slopes to investigate the influence of pile end-bearing conditions. The results showed that the majority of the embankment load was transferred to the piles due to the combined contribution of soil arching, tensioned membrane effect, and stress concentration. Khansari and Vollmert [17] collected the field data for a geosynthetic-reinforced pile-supported structure, and comparison with three analytical models led to a conclusion that the models fail to accurately estimate the geogrid reinforcement deflection and overestimate the loads on the pile foundation. The second approach is numerical analysis. Numerical methods are nowadays also quite often used, but usually with some significant simplifications in the models in design practice for soil improvement analysis (Han and Gabr [18], Pham [19], Jenck et al. [20], Le Hello and Villard [5], Yapage et al. [21], Ariyarathne and Liyanapathirana [22], Zhuang and Wang [23], Mohapatra and Rajagopal [24]; Li & Espinoza [25], Esmaeili et al. [26], Almeida et al. [27], Wijerathna and Liyanapathirana [28]). Han and Gabr [18] performed a numerical study on reinforced piled embankments, including the underlying subsoil, however, an axisymmetric analysis was used. The numerical results demonstrated the effect of the geosynthetic stiffness and the pile modulus on the stress reduction ratio. Pham [19] have found that support of subsoil was mobilized under geosynthetic sheet while shear stress was mobilized along interfaces of geosynthetic and soils. Jenck et al. [20] presented three-dimensional numerical modelling of a piled embankment, using a finite-difference continuum approach, and the soft ground is explicitly taken into account in the numerical model using the modified Cam Clay model. The interesting finding is that arching governed by both the embankment and the soft deposit characteristics. Especially, the behaviour of subsoil is complex follows the consolidation. Le Hello and Villard [5] used a coupled finite-discrete element model to investigate the interaction between soils-structure in the piled embankment. Le Hello and Villard [5] observed that the membrane behaviour of geosynthetic has a specific effect on the load transfer mechanism and indirectly contributes to the value of total efficacy. From the numerical results, Yapage et al. [21] concluded that all the available methods yield uneconomical and over-conservative predictions for the geosynthetic reinforcement. The disagreement between the design methods and the finite element results is mainly due to the

disregard of some factors contributing to soil arching and membrane action of the geosynthetic in developing the design methods in comparison to the finite element modelling. Ariyarathne and Liyanapathirana [22] investigated the load transfer mechanism of GRPS embankments using finite element analyses. Based on these model results, the inconsistencies in the currently available design methods are identified. Moreover, it was interesting that the degrees of soil arching within geosynthetic reinforced and unreinforced pile-supported embankments are not the same. Alternatively, the vertical load transferred to the piles will be increased by the vertical component of the tension developed in the geosynthetic layer. Zhuang and Wang [23] presented a finite-element analysis of the effect of subsoil in a reinforced piled embankment. They showed that stiff subsoil can carry a significant portion of the embankment load, whereas very soft subsoil support may result in intolerable strain on the geogrid. Li and Espinoza [24] found that the tensile stiffness of geosynthetic has a great effect on the load transfer mechanism that can be explained through the tensioned membrane effect of geosynthetic reinforcement. Mohapatra and Rajagopal [25] performed a systematic series of stability analyses on column embankments and found that the undrained shear strength of soft clay had a strong effect on the deformation of a piled embankment. Esmaeili et al. [26] investigated the effect of geogrid on controlling the stability and settlement of high railway embankments using finite element modelling. The results showed that the value of the geogrid-soil interface coefficient has a minor effect on bearing capacity and settlement. Numerical and analytical modelling was performed to complement experimental data from 40 centrifuge tests of reinforced piled embankments in the study of Almeida et al. [27]. Numerical results showed that the maximum tensile forces with arching and membrane effects in full operation occur at the pile edge, and increase with embankment height, surface surcharge, and geosynthetic stiffness. Wijerathna and Liyanapathirana [28] investigated the mechanism of soil arching in an embankment supported by columns in a triangular grid, using 3D numerical models. Results show that the most influential parameters on the column efficacy are column spacing and diameter. Both the height and width of the soil arches were changed with column spacing while only the width of the arch was changed with column diameter. Lastly, the theoretical analysis approach is also very useful to engineers in designing a GRPS embankment. The design guidelines for calculating the vertical stresses applied on the piles and the subsoil, as well as the tension in the geosynthetic layer, are available in the literature (Terzaghi [2], Hewlett and Randolph [3], Low et al. [29], Kempfert et al. [30], Abusharar et al. [31], BS8006 [32], EBGEO [33], Van Eekelen et al. [34], Ng and Tan [35], Feng et al. [36], Zhuang et al. [37], Pham [38], PWRC [39]). However, until now, there has been no analytical approach that precisely describes the complex behaviour of a GRPS system consisting of the embankment, geosynthetic, platform, piles, and soft subsoil. There still exist several moot points in the available design methods. The first of these is the role of the subsoil. BS8006 [32] discussed the potential role of the subsoil support, but suggested that it should not be considered in the design. EBGEO [33] and Van Eekelen et al. [34] suggested that the subsoil would also contribute to the embankment load and furthermore, considered the subsoil effect in calculating the geosynthetic strain. Unfortunately, they had taken into account the effect of the soft subsoil with a simple approach using a linear model. In reality, the behaviour of the soft subsoil may be more complex and in addition, its consolidation and non-linear behaviour with time needs to be considered (Mirjalili et al. [40], Lu et al. [41]). The second point is that the deformation of the geosynthetic depends on the differential settlement between the pile cap and the subsoil in between; therefore it is indirectly affected by the consolidation of the subsoil. However, the effect of subsoil consolidation is totally neglected in the existing design methods. In addition, it should be noted that the skin friction generated along the interfaces, which increases the tension in the geosynthetic and decreases the differential settlement, is 3

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not dealt with adequately in the existing design methods. Furthermore, it has been observed that the inclusion of a geosynthetic enhances the load transfer mechanism and significantly reduces the differential settlement between the pile and the soft subsoil through the tensioned membrane effect. However, most current design methods do not clearly include this effect in the calculation through the concepts of efficacy or stress reduction ratio. Because the behaviour of these structures is generally understood, but not yet described and addressed in the analytical design methods adequately, a further study is warranted, and the same will be discussed in this study. The main objective of this work is to study the key load transfer mechanism in a complex soil–structure system of a GRPS embankment. The study focuses on the interactions between the five linked elements, i.e., the geosynthetic, foundation, granular platform, fill soil, and the geologic media underlying and surrounding the foundation. An analytical method has been developed through a combination of the arching theory for the soil layer, tensioned membrane theory for the geosynthetic, full support of the soft subsoil, and skin friction generated along the geo-interface. The support of the subsoil is considered under both linear and non-linear subsoil models. Thus this analytical method provides a more comprehensive design approach than the earlier approaches that considered only either the tensioned membrane theory or the arching theory. In addition, the results from this method applied to a GRPS embankment were compared to the experimental measurements, as well as the current design guidelines for three field test projects to investigate the validity of the analytical method. Finally, a parametric study was performed to assess the influence of several factors on the behaviour of the GRPS embankment.

geosynthetic, (iii) subgrade reaction model for the subsoil support, (iv) frictional interaction at the interface of the geosynthetic and the soil, and (v) consolidation of the soft subsoil. In principle, the design procedure of this analytical method is divided into two steps. In the first step, the stress distribution owing to the arching effect of the soil in the embankment, which results in a vertical stress on the top of the pile cap and on the soft subsoil in between, is calculated. In the second step, the deflection and strain of the geosynthetic are calculated. The support of the subsoil is considered under both linear and non-linear models. The load transfer mechanism adopted in this method is schematically outlined in Fig. 1. Some notations that are used throughout this work are as follows: y is the maximum geosynthetic deflection; a is the pile-cap width; s is the centre-to-centre pile spacing; s′ is the clearance spacing (s′ = s – a); and sa is the total vertical stress acting on the subsoil by the arching effect. In the development of the proposed method, the following are the underlying assumptions in the derivation of the mathematical equations: (a) The embankment material is homogeneous and isotropic. (b) The soft subsoil and the embankment fill deform only vertically. (c) The geosynthetic reinforcement is homogenous, isotropic, and is in tension only. (d) The geosynthetic strain is uniformly distributed in the considered cross-section. 2.2. Stress reduction ratio and efficacy As the starting point of the analysis, it is assumed that under the embankment fill and surcharge, a portion of the embankment load acts on the pile cap and the rest is distributed on the soft subsoil and the geosynthetic between the pile caps. It should be noted that because the subsoil is more compressible relative to the pile caps, the pressure on the subsoil is reduced and that on the pile caps is increased owing to the arching effect of the soil and the membrane effect of the geosynthetic. Hence, the vertical stress on the subsoil is less than γH, as illustrated in

2. Proposed method 2.1. Key load transfer mechanism The analytical method proposed in this study has been developed from a combination of the following five phenomena: (i) arching theory for the fill soil layer, (ii) tensioned membrane theory for the

Analysis of geosynthetic reinforced piled supported embankment

Geosynthetic Pile cap Pile

soft subsoil

Pile

=

Arching effect in fill soils and subsoil support

Pile cap

Tensioned membrane effect in geosynthetic and frictional interaction

T + dT

T

T Pile cap

+

Pile cap

ds

Pile

dz

s

a

s'

dx

a

Fig. 1. Analysis of load transfer mechanism in present method. 4

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T.A. Pham

Fig. 2. This concept will be considered through the concepts of stress reduction ratio (SRR) and efficacy (E). Taking into account the contribution area of one pile cap in a threedimensional plane, as shown in Fig. 3, the relationships governing the vertical equilibrium for both the load condition and the stress condition are as follows:

s

=

a s

c.

Ac +

s.

As

where

(1b) (2)

GR

E=

s

H+q

= SRRa

SRRm

Pca + Pcm = Ea + Em ( H + q) A

2K p

3

FGRsquare1 =

H+q H

FGRsquare2 =

H+q ( 1FGRsq2 + 2FGRsq2 + 3FGRsq2 + 4 FGRsq2) H

P3D L3D Kp 2

+

2 L Q3D 3D 3 2

where

where W = total load of embankment fills and surcharge; Pca = load component distributed directly on pile cap by arching effect; Pcm = load component transferred onto pile cap by tensioned membrane effect of geosynthetic; Ps = load component received by soft subsoil; γ = the unit weight of embankment soils; H = height of embankment; q = surcharge; σc = total vertical stress acting on the pile cap by both arching and membrane effect; sa = vertical stress acting on the subsoil and geosynthetic by arching effect; GR = vertical stress carried by geosynthetic; s = actual vertical stress received by subsoil; A = contributory area of one pile (A = sx.sy); Ac = area of a pile cap; As = area of soft subsoil between pile caps (As = A – Ac). The performance of a geosynthetic reinforced pile-supported embankment is assessed through the term of stress reduction ratio and efficacy. The stress reduction ratio is understood as the ratio of the average vertical stress on the soft subsoil to the average weight of the embankment and surcharge. The term efficacy is defined as the proportion of the embankment load carried by the pile caps.

SRR =

(5)

FGRsquare = FGRsquare1 + FGRsquare2 + FGRsquare3

(1a)

W = Pca + Pcm + Ps ( H + q). A =

by integrating the tangential stress of the 3D hemispheres over the area of the square.

1FGRsq2

=

2FGRsq2

=

3FGRsq2

=

+

(KP

4 FGRsq2

P3D Kp 1 L3D (2 ) Kp 2 2 Q3D (2 2 3

P3D .22

2KP .

3

L3D 2

(L3D )2KP 22

KP

1)(KP 2)(KP 42 =

1)

2KP

3)

+

Q3D (L3D )3 ( 2 (1 6

KP

(KP

KP

+1+

1)(KP

) + ln(1 +

(3)

KP = tan2 (45° + /2)

(4)

Hg 3D = 2 for H (partial arching) L3D = s a for s

where s = vertical stress received by the subsoil; SRR = final stress reduction ratio; SRRa = stress reduction ratio by the arching effect; SRRm = stress reduction ratio by the membrane effect; E = total efficacy; Ea = efficacy component from arching effect; Em = efficacy component from the membrane effect. SRRa = 0 represents the complete soil arching while SRRa = 1 represents no soil arching.

H<

s

a where 2

2KP .

s 2

H

Hg3D .

(

(KP

1)(KP 10

3)(KP

4)

for

L3D < s

a;

)

and Q3D =

2)(KP 216

+

2)

2 ))

FGRsquare3 = ( H + q)((s a ) 2 (L3D )2) FGRsquare3 = 0 for L3D s a where

P3D = . KP . (Hg3D )2

1 3

2KP 2KP

2 3

and

. KP 2KP 3

(full arching) and Hg 3D = H for H <

H

s

a 2

and

L3D =

2. Hg 3D

s 2

for

a (m) is the width of a square pile cap or the equivalent

width of a circular pile cap 2.3.2. Determine the total vertical load, FGRstrip FGRstrips (kN/pile) is the total vertical load exerted by the 2D arches on the strips. FGRstrips is derived by integrating the tangential load of the 2D arches over the area of the GR strips.

2.3. Arching theory

FGRstrip = FGRstrip1 + FGRstrip2

As mentioned earlier, the design of a piled embankment comprises two calculation steps. The first step involves calculating the arching behaviour in the fill. This step divides the total vertical load into two parts: (1) the load part Pca that is transferred to the piles directly by the arching effect and (2) the remaining portion of the load distributed on the geosynthetic and the subsoil (Pcm + Ps). The analysis of the first step presented here is based on the concentric arches model presented by Van Eekelen et al. [34]. The main refinements to the above model in the proposed method are (1) representing the design method for a square pile pattern with a reduced form, (2) inclusion of the fill soil cohesion, and (3) consolidation effect of the subsoil. It is assumed that the pile is installed in a square pattern with the same pile spacing in both the directions (s = sx = sy). As for the cohesion of the fill soil, it is assumed that the stress state in the arch is uniform around the semicircle and that the limit state occurs in the entire arch, which gives a tangential stress σθ equal to KP . r + 2. c. KP1/2 . Here, KP is the passive earth pressure coefficient and c is the cohesion of embankment soils. The derivation and integration procedure is similar to that presented by Van Eekelen et al. [34].

where

2.3.1. Determine the total vertical load, FGRsquare FGRsquare (kN/pile) is the total vertical load exerted by the 3D hemispheres on their square subsurface. This load FGRsquare is derived

Fig. 2. Stress re-distribution due to arching in embankment. 5

(6)

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T.A. Pham

2.4. Subsoil-geosynthetic interaction model In recent years, a number of studies [42–46] have been conducted in the areas of soil–structure interaction modelling and the underlying soil using sophisticated methodologies. The results of these studies combined with the experimental measurements suggest that the subsoil has a major influence on the load–deflection behaviour of geosynthetic reinforcements [38]. From this viewpoint, it is assumed that a part of the embankment load is borne by the subsoil (Fig. 4). This concept is considered in the presented method by introducing the upward counter pressure σup, as shown in Eq. (12).

SubsoilArea

s

As/4

GR

Pile cap area A c = a.a

a

s'

a

Fig. 3. Contributory area of one pile.

H + q 4aP2D L 2D H KP 2

FGRstrip1 =

KP

+

aQ2D (L 2D ) 2 2

FGRstrip2 = 2a. ( H + q)(s a L2D ) FGRstrip2 = 0 for H (s a)/2 where P2D = KP . (Hg 2D )1

=

. KP KP 2

Hg 2D =

s 2

KP .

for H

H + ptransferred s 2

for

Hg 2D.

2. c. KP . L2D KP 1 H < (s

( ) Kp

1

Kp

2

and

(full arching ) and Hg 2D = H for H <

(partial arching ) L 2D = s a for H s a for H < 2 (partial arching )

s

a 2

and

a)/2

s 2

Q2D

for

(full arching ) and L2D = 2Hg 2D

( H + q). (s a ) 2 FGRsquare H H+q a. (2L 2D + a)

ptransferred =

where a is the square pile-cap width, Kp is the passive earth pressure coefficient, c is the cohesion of embankment fills.

up

2.3.3. Determine the load distribution The total load resting on geosynthetic and subsoil with the effect of subsoil consolidation is:

Psa = Pce + Ps =

1 2

U

(FGRsquare + FGRstrip)

FGRsquare + FGRstrip 2

U

up

=

FGRsquare + FGRstrip Psa 1 = . As 2 U s 2 a2

SRRa =

a s

(8)

(9)

(10)

H+q

The efficacy component that represents the proportion of the embankment load transferred directly onto the pile caps by arching effect is:

Ea =

Pca =1 ( H + q) s 2

1

a2 . SRRa s2

(12)

= yKs / U

(13a)

=

yKs U [1 + yKs/ qsu]

(13b)

where σup is the upward counter pressure from subsoil; Ks is the modulus of the subgrade reaction; y is the maximum deflection of the geosynthetic; qsu is the ultimate bearing capacity of the saturated soft subsoil; U is the degree of consolidation of the subsoil at any time t; and U represents the state of consolidation (U = 0 means no consolidation, while U = 1 represents complete consolidation). There is a fundamental issue with the use of these models, i.e., with determining the stiffness of the elastic springs which are used to model the soil below the foundation. This issue becomes two-fold as the value of the modulus of the subgrade reaction depends on not only the nature of the subsoil but also the soil–structure interaction and the loaded area as well. Because the subgrade stiffness is the only parameter in the Winkler model that idealises the physical behaviour of the subgrade, care must be taken in determining the value of subgrade stiffness for use in practical problems. The modulus of subgrade reaction is the ratio of the pressures at any given point of the surface of contact and the settlement. The value of the reaction subgrade modulus Ks can be optimally obtained from the field experiments, such as a plate load test, consolidation test, tri-axial test, and CBR test. However, in some cases where suitable test data are not available, representative values for the same may be estimated from the ratio of the deformation modulus and the active depth of the soft subsoil, as shown in Eq. (14). It should be

(7)

The total vertical stress acting on the geosynthetic and subsoil, and the stress reduction ratio by soil arching is identified as follows: a s

up

For the non-linear subsoil model:

The loading part transferred onto the pile cap directly by arching therefore is:

Pca = ( H + q). s 2

a s

The soft subsoil possesses very complex force–displacement characteristics as it is heterogeneous, anisotropic, and non-linear. The presence of fluctuations of the water table further adds to its complexity. However, the mechanical behaviour of the subsoil is proven to be utterly erratic and complex, and it may be very difficult to establish any mathematical laws that would conform to the actual observations. In this context, the simplicity of the models often becomes a prime consideration and they often yield reasonable results. In this analysis, both linear and the non-linear models of soils are introduced to evaluate the support of the soft subsoil. The approach adopted in the linear model is similar to Winkler’s model, which idealises the soil medium as a system of identical but mutually independent, closely spaced, discrete, and linearly elastic springs [45]. This type of model was adopted in some design guidelines, such as EBGEO [34] and CUR226 [47]. A number of studies in the area of soil–structure interaction have been conducted on the basis of Winkler’s hypothesis in view of its simplicity. The other approach with the non-linear model was based on the consideration of the hyperbolic non-linear stress–displacement relation proposed by Kondner [48]. This model was developed on the basis of the relationship between the shear modulus and the settlement considering the ultimate bearing capacity of the saturated subsoil. In this study, the consolidation effect of the soft subsoil is applied using both the approaches. The pressure deflection relation at any point is given by the following expressions: For the linear subsoil model:

a

Ac = a2

=

(11) 6

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The strain component of geosynthetic induced by the pressure of embankment under soil arching is given as follows:

Vertical stress acting on upper surface of reinforcement

a

T

=

sin

=

a

s'

a

5

4y /(s

a

(14b)

Es1. D1 + Es 2. D2 + ...Esn. Dn D1 + D2 + ...Dn

16(y /(s

(20)

a))3

sin

+ (sin )3/6

(21)

a)

a))3

(22)

(16/3)(y /(s

Replace Eqs. (20), (22) back into (17) yields the following:

=

4y /(s a) 16/3(y /(s a))3 4y /(s a) 16(y /(s a))3

1

(23)

Using a classical approximation, Eq. (23) becomes: a

(24)

8/3(y / s ) 2

On the other hand, the tension in a geosynthetic is a function of the amount of strain. According to the tensioned membrane theory for the circular deformation model, the tension in a geosynthetic is determined by:

(15)

where E0 = Young’s modulus; μs = Poisson’s ratio of the subsoil. For multi-layers of soft subsoil, the assumption of a structure of infinite width is used and the equivalent oedometric modulus of the subsoil in the active depth is derived.

Es =

a)

Hence:

(14a)

2µs )]

4y /(s

= sin 1 (sin )

where Dact is the active depth of the subsoil under the vertical stress acting on the area of the subsoil; γs is the average unit weight of subsoil; and Es is the oedometric modulus of the subsoil, which can be derived from Young’s modulus and Poisson’s ratio, as shown in Eq. (15).

Es = E0/[(1 + µs )(1

(19)

Hence, the following truncated series expansion can be used:

noted that the value of Winkler's spring stiffness for most applications is often dependent on the type of the structure and its dimensions (e.g., size of the foundations). In the present study, Eq. (14) is the result of a simplification through the introduction of the concept of ‘active depth’ that includes the dimensional effect. a s/ s

(18)

1 2y s a + 4 s a 2y

sin

Fig. 4. Support model of soft subsoil.

Ks = Es/ Dact

1 2

Substitute Eq. (19) back into Eq. (18) and apply small strain method, a classical approximation is obtained:

s

Dact

=

Pile cap Upwards counter-pressure on lower surface of reinforcement

Pile

(17)

where θ is the deflected angle and is a function of y/(s − a), defined as follows:

T

Pile cap

1

sin

T=

1 4

GR

2y +

(s

a)2 where 2y

GR

is vertical stress carried by (25)

geosynthetic, and calculated by Eq. (12) (16)

where D1, D2,…Dn are the thicknesses of different soil layers in the active depth; and Es1, Es2,…Esn are the corresponding one-dimensional deformation moduli of the subsoil. The term “active depth” is defined as the depth at which the increment of the vertical stress produced by the embankment fill is less than 20% of the vertical geostatic stress. In a conventional analysis, the basic limitation of the hypothesis of subsoil models lies in the fact that the stiffness of the soil is constant and is independent of the depth and the vertical stress. Moreover, it does not account for the dispersion of the load over a gradually increasing area of influence as the depth increases. Therefore, the concept of active depth is introduced to overcome these drawbacks.

2.6. Frictional interaction between soil-geosynthetic The tension in the geosynthetic results from its stretching. Combined with the effect of skin friction along the soil–geosynthetic interfaces, this tension transfers the load onto the pile caps (Fig. 6). Therefore, the tension in the geosynthetic is considered as a function of two strain components, one due to the load and the other due to the skin friction. Thus, mathematically

r

2.5. Tensioned membrane theory of geosynthetic The geosynthetic layer is stretched as the soft ground settles and a portion of the geosynthetic strength is therefore mobilised. Consequently, the geosynthetic acts as a ‘tensioned membrane’, and the resulting hoop tension will reduce the net pressure on the soft ground. In this analysis, it is assumed that in the considered cross-section, the deflected geosynthetic has the shape of a smooth curve that can be described as an arc of a circle. It is pre-assumed that the geosynthetic strain is uniformly distributed in the considered cross-section. The geosynthetic is fixed at the edges of the pile caps, which are at the same level. Furthermore, it is assumed that the geosynthetic is initially flat. Therefore, its initial length is s (Fig. 5).

T Pile cap

T y

Pile cap

geosynthetic Pile

s-a s Fig. 5. Geometry of deformed geosynthetic.

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(26)

T = T + Tf

find the maximum tension in geosynthetic. Moreover, by using the strict equilibrium of vertical forces at the top of the pile cap, the vertical load transferred onto the pile cap by the tensioned membrane effect, is calculated as follows:

where T is the maximum tension in the geosynthetic; Tε is the component of tension in the geosynthetic induced by the stretching of the geosynthetic under the embankment pressure; and Tf is the component of tension in the geosynthetic induced by skin friction. The component of the tension in geosynthetic induced by stretching geosynthetic under embankment pressure is a function of the strain and stiffness of geosynthetic. The relation is given by the following expressions:

T = JGR .

=

a

where a is the width of the square pile cap, θ is the deflected angle that can be obtained using Eq. (10), and T is the maximum tension in the geosynthetic. The expression for the efficacy component contributed by membrane action is as follows:

2

8 y 3 s

JGR where JGR (kN

Em =

(27)

/m ) is tensile stiffness of geosynthetic.

In other words, the skin friction along with the interface between soil-geosynthetic also is a cause of the tension in geosynthetic. The deformation-friction relation is expressed as follows:

Tf = . (s

upper

+

lower

= 0.85(

a p tan p s

+

s tan s up

+ 0.1cs )

2

0.85 J+ ( 4

a p s

p tan

+

s tan s up

SRRm = Em

SRR =

(29)

+ 0.1cs ) s

(35)

The stress reduction ratio of a piled embankment with geosynthetic is determined from the relationship with efficacy.

where ϕp = friction angle of soil at the upper side of the geosynthetic interface; ϕs = friction angle of soil at the lower side of the geosynthetic interface; cs = total cohesion of soils at upper and lower sides of the geosynthetic interface; αp, αs = interaction coefficients between the geosynthetic-soils. Value αP varies within 0.65–0.85 while value αs varies from 0.60 to 0.75 ([49,50]). Substitute Eqs. (27)–(29) back into Eq. (26), an expression of total tension in geosynthetic is given:

8 y T= 3 s

A As

SRRa

(36a)

To validate the proposed method, several experimental studies were selected from the literature for comparison in this section. The results are presented in terms of efficacy, maximum deflection, and tension in the geosynthetic. 3.1. The field test case in Anhui, China (Cao et al. [10]) Cao et al. [10] presented field experiments of a high-speed railway embankment in Anhui province, China. The embankment was 2.4 m in height and 13.2 m in crown width. The backfill for surcharge was 3 m to provide a large surcharge load such that the monitoring results were

(30)

The problem of a piled embankment with geosynthetic is entirely solved by using Eqs. (25) and (30). Combination of Eqs. (12), (25) and (30), the equation involved in the maximum deflection of geosynthetic is derived. For the linear subsoil model: 3

+

2y

2

+

3y

+

4

a )2 ; where 2 = 1.7 s tan s K s (s 1 = 21.33JGR U + 4K s (s 4 sa. U (s a)2 ; a a)3 + Ks (s a) 4 + 0.17Ucs (s a)3 ; 3 = 1.7 p tan p s U (s a 4 a) 4 = s U (s For the non-linear subsoil model: 4 1y +

3 2y +

2 3y +

Embankment

4y +

5

a

arch

T

(31)

=0

(36b)

SRRm

3. Validation of the analytical method

2.7. Determination of design parameters

1y

(34)

E = Ea + Em

In which, s = centre-to-centre pile spacing; a = width of pile cap; τ = shear stress along geosynthetic interface. The total shear stresses are a result of skin friction along the upper and lower sides of the soilgeotextile interfaces as follows:

=

Pm ( H + q) s 2

The total efficacy of a piled embankment with geosynthetic is given as follows:

(28)

a)/4

(33)

Pcm = 8aT sin

T y

Pile cap

a )3

subsoil

Pile

and

Pile cap

s a

s'/2

a

s'/2

(32)

=0

where

b

T

= 21.33JGR UKs ; 4UKs sa (s a)2 + 4Ks qsu (s a)2 ; 2 = 21.33JGR Uqsu a a)3 + 1.7 s tan s Ks qsu (s a)3; 3 = 1.7 p tan p s UK s (s

1

+ 0.17UKs cs (s 4

5

= 1.7

=

p tan

a )3

a p s Uqsu (s

a s UK s (s

a s Uqsu (s

4

a s Uqsu (s

a)3 + 0.17Uqsu cs (s

a )2 a )3 + Ks qsu (s

+ dT

ds

a) 4 ; and

dz

a) 4

a) 4 .

dx

It should be noted that sa is estimated by using Eq. (9). Substitute value of maximum geosynthetic deflection back into Eqs. (25) or (30) to

Fig. 6. Membrane behavior and friction interaction of geosynthetic. 8

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obvious. The unit weight of surcharge fill was estimated to be 16 kN/ m3. In this field tests, the cement-fly ash-gravel (CFG) piles were used to support the embankment, which was arranged in a triangular pattern with a centre-to-centre spacing of 1.6 m, and 1 m of pile cap width. The soft subsoil is silty clay, and soil properties were determined by plate loading test (PLTs) and static cone penetration test (CPTs). The qsu of subsoil obtained from PLTs was 390 kPa. Soils at both upper side and lower side of geo-interface were gravel 0.1 m thick. Details of the site condition, construction, instrumentation, and monitoring are reported by Cao et al. [10]. A brief summary of the input parameters for the analytical methods is presented in Table 1. The active depth Dact is larger than or equal to 4.68 m. The elastic modulus of silty clay determined from the test is 8.81 Mpa and therefore yields a coefficient of subgrade reaction about 2000 kPa/m The results obtained from the proposed design procedure are compared with the experimental measurements and are summarised in Table 2. It should be noted that the proposed method produces a satisfactory agreement with the measured results in terms of maximum tension in the geosynthetic. CUR226 gives a similar prediction as the present method in terms of efficacy and maximum geosynthetic deflection. However, CUR226 significantly underpredicts the maximum tension in the geosynthetic compared to the field measurements by approximately 66%. The underprediction by CUR226 for the same pressure can be attributed to the fact that skin friction is ignored in the strain calculation of the geosynthetic by CUR226. On the other hand, EBGEO significantly overpredicts the geosynthetic deflection, while it underpredicts the maximum tension in the geosynthetic (by approximately 89%). It should be noted that in the design method of EBGEO, a triangular load distribution is assumed for the subsoil support. The strain component by skin friction is not taken into account in this design method as well. The strain value of the geosynthetic in EBGEO is an average value and not the maximum strain value. Therefore, the strain values from EBGEO result in the underprediction of the geosynthetic deflection. BS8006 significantly overestimates the maximum deflection and the tension in the GR. The subsoil support not being considered in the GR strain calculation is the reason for this underprediction. PWRC significantly overestimates the maximum geosynthetic deflection. This is evidently because PWRC overestimates the load acting on the geosynthetic. The calculation method of PWRC also does not consider the subsoil support, nor does it consider the membrane effect of the geosynthetic. It is also interesting to note that the difference in the results from the linear and non-linear subsoil models is negligible.

enrichment process, had an effective friction angle of 45°. It should be noted that a 1.3 m thick sand working was placed beforehand on the top of the natural clay soil platform, thus crossing the column, which also acted as a sand blanket below the embankment. The writer thinks that this sand layer with a friction angle of 40° has a significant effect on soil arching because the difference in stiffness between column and subsoil becomes lesser. Using the average equivalent method, the embankment material with a friction angle of 42° is recommended to use for arching analysis. Details of the site condition, construction, instrumentation, and monitoring are reported by Hosseinpour et al. [8]. A brief summary of the input parameters used for the analytical methods is presented in Table 3. The active depth is larger than or equal to 11 m. The average elastic modulus of 1.3 m sand (Es = 12 MPa) and 8.7 m soft clay (Es = 1.34 MPa) is 2.48 Mpa and therefore yields a modulus of subgrade reaction about 225 kPa/m. The qsu of subsoil from test did not provide in the paper of Hosseinpour et al. [9], but it can be derived from the relationship Es = 22.5qsu, is 110 kPa. A comparison of the proposed analytical method and field measurements is shown in Table 4. For efficacy by the arching effect, the proposed method produces an excellent agreement with CUR226, BS8006 and EBGEO. However, the prediction of efficacy by membrane effect is inconsistent with the above design methods, and consequently, the total efficacy is also inconsistent. It should be noted that the present method is in a better agreement with the measurements than the other design methods in predicting the deflection and tension in the geosynthetic. CUR226 overpredicts both maximum deflection and tension in the geosynthetic by approximately 35%. On the other hand, the German EBGEO over-estimates the GR deflection by approximately 25% and underpredicts the maximum tension in the geosynthetic slightly by 5%. The British BS8006 and the Japanese PWRC significantly over-estimate the maximum GR tensile force. It is also interesting to note that the results obtained from using the linear subsoil model are better than those from the non-linear subsoil model in this case. This could be explained by the fact that the accuracy of the nonlinear subsoil model depends considerably on the ultimate bearing capacity of the subsoil. Because the ultimate bearing capacity of the subsoil is derived from the elastic modulus rather than the field measurements, this may result in a significant difference in the results between the linear and non-linear subsoil models. 3.3. Full-scale field test case in Shanghai, China (Liu et al. [3]) Liu et al. [4] presented a case history of a geogrid-reinforced and piled supported highway embankment with a low area improvement ratio of 8.7%. This site is located in a northern suburb of Shanghai, China. The embankment was 5.6 m high and 120 m long with a crown width of 35 m. The fill material consisted mainly of pulverized fuel ash with cohesion of 10 kPa, an angle of friction of 30°, and an average unit weight of 18.5 kN/m3. The embankment was supported by cast-in-place annulus concrete piles that were formed from a low-slump concrete with a minimum of a compressive strength of 15 N/mm2. The ultimate bearing capacity of the subsoil is 300 kPa, and the undrained shear strength of the clay is about 15 kPa. The field monitoring program was terminated 180 days after the commencement of the construction of the embankment. The details of the experimental model, instrumentation, and properties of materials were reported in the paper of Liu et al. [3].

3.2. Full-scale load test case in Rio de Janeiro, Brazil (Hosseinpour et al. [8]) A full-scale test embankment was constructed on a soft deposit improved by geotextile-encased granular columns in Rio de Janeiro, Brazil and reported by Hosseinpour et al. [8]. The height of the embankment was 5.3 m. The fill material was sinter feed, a sub-product material obtained through the ore-enrichment process. The density of the fill material was determined by in situ density tests. A biaxial horizontal geogrid was placed at the base of the embankment. The settlement sensors place on the top of the encased columns and surrounding soil to measure both total and difference. The fill material was sinter feed, a sub-product material obtained through the oreTable 1 Input parameters from field test case of Cao et al. (2016).

H = 2.4 m, γ = 19.5 kN/m3, ϕ = 35°; q = 48 kN/m2 ϕp = 38°, c=0 kPa, αp = 0.8 (assumed) ϕs = 38°, c = 0 kPa, αs = 0.8 (assumed) γs = 19.5 kN/m3, Ks = 2000 kPa/m, qsu = 390 kPa; U = 1 a = 1 m; s = 1.6 m; Ep = 2 × 107 kPa (assumed) JGR = 300 kN/m

Embankment fill Upper side of geo-interface (gravel) Lower side of geo-interface (gravel) Soft subsoil Pile (square pile cap) Geosynthetic

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Table 2 Comparison of analytical methods with field measurement of Cao et al. (2016). Parameters

Present methods

Efficacy by arching effect, Ea (%) Efficacy by membrane effect Em(%) Total efficacy, E (%) Maximum GR deflection (mm) Maximum GR tension (kN/m)

Linear Model Eq.(31)

Non-linear Model Eq. (32)

90.4 0.39 90.79 7.27 2.47

90.4 0.41 90.81 7.54 2.47

CUR226 (2016)

BS8006 (2010)

EBGEO (2011)

PWRC (2007)

Measured result

90.4 0.54 90.94 7.0 0.85

87 13 100 96.7 20.77

92.54 1.48 94.02 18.59 0.256

62 – 62 27.7 –

– – 71.1 4.2 2.4

Table 3 Input parameters from field test case of Hosseinpour et al. (2015). H = 5.3 m, γ = 28 kN/m3, ϕ = 42°; c=0 kPa; q = 0 kN/m2 ϕp = 45°, c = 0 kPa, αp = 0.8 (assumed) ϕs = 45°, c = 0 kPa, αs = 0.8 (assumed) γs = 15.3 kN/m3, Ks = 225 kPa/m, qsu = 110 kPa; U = 1 a = 0.7 m; s = 2 m; Ep = 2 × 107 kPa (assumed) JGR = 2000 kN/m

Embankment fill Upper side of geo-interface (fill soils) Lower side of geo-interface (fill soils) Soft subsoil Pile (square pile cap) Geosynthetic

Table 4 Comparison of analytical methods with field measurement of Hosseinpour et al. (2015). Parameters

Present methods

Efficacy by arching effect, Ea (%) Efficacy by membrane effect Em(%) Total efficacy, E (%) Maximum GR deflection (mm) Maximum GR tension (kN/m)

Linear Model Eq. (31)

Non-linear Model Eq. (32)

81 8.1 89.1 84.19 33.65

81 9.3 90.3 89.65 36.23

The input data necessary for the analytical methods are summarized in Table 5. The subgrade reaction modulus of the subsoil is 550 kPa/m. A comparison of different design methods with field measurements is shown in Table 6. It is noted that the proposed method with the linear model of subsoil provides a better agreement with the measured results than with the non-linear model. As discussed earlier, the uncertainty in the ultimate bearing capacity of subsoil could be a reason for the significant difference between the two models. It should be noted that the influence of the 1.5 m thick coarse-grained fill is not included in the calculations. The layer of coarse-grained fill with a high stiffness decreases the deflection of the geosynthetic; however, this effect is not considered in the calculation of qsu. The uncertainty in the ultimate bearing capacity should be carefully borne in mind during the calculations. The present method and CUR226 produce a good agreement with field measurement in the prediction of total efficacy, while EBGEO overestimates it by approximately 7.5%. CUR226 agrees well with measured results in the estimation of maximum tension in the geosynthetic, but overpredicts the maximum geosynthetic deflection. The cohesion of the fill soils is not considered in CUR226. On the other hand, EBGEO overpredicts both maximum deflection and tension in the geosynthetic. The assumption of a triangular shaped load distribution on the geosynthetic appears to be not suitable in this situation. BS8006 and PWRC significantly overpredict the load distribution on the

CUR226 (2016)

BS8006 (2010)

EBGEO (2011)

PWRC (2007)

Measured result

81 8.8 89.8 109 45.41

81 19 100 193 118

81.5 10.86 94.02 100 31.7

41 – 41 112 –

– – 71.1 80 33.6

geosynthetic and the subsoil. The fact that the subsoil support is neglected could be considered as a reason for the highly conservative values for the tension in the geosynthetic, as calculated by these two methods. 4. Parametric study This section focuses on the parametric analysis of the piled embankment using the proposed method. The analyses have been conducted over a range of values to evaluate the effect of several parameters on the load-deflection behaviour of the piled embankment. The parameters considered in this analysis include the effect of subsoil consolidation, embankment height, friction angle of the fill soils, subgrade reaction modulus of the subsoil, ultimate bearing capacity of the subsoil, geosynthetic tensile stiffness, and improvement area ratio (IAR). The influence of each parameter has been investigated through efficacy, maximum geosynthetic deflection, and maximum tension in the geosynthetic. In this parametric study, the geometry of the embankment and the design parameters have been taken from the field test case of Liu et al. [3] as the baseline case values. In the field test case selected, the ultimate bearing capacity of the subsoil from the field measurement is available, and this facilitated a convenient comparison between the linear and non-linear subsoil models in the current

Table 5 Input parameters from full-scale field test case of Liu et al. (2007). H = 5.6 m, γ = 18.5 kN/m3, ϕe = 30°; q = 0 kN/m2 ϕp = 40°, c = 10 kPa, αp = 0.8 (assumed) ϕs = 10°, c = 8 kPa, αs = 0.65 (assumed) γs = 17 kN/m3, Ks = 550 kPa/m, qsu = 300 kPa; U = 1.0 a = 1 m; s = 3 m, Ep = 2 × 107 kPa, ν = 0.2 JGR= 1180 kN/m, ν = 0.2

Embankment fill Upper side of geo-interface (gravel) Lower side of geo-interface (subsoil) Soft subsoil Pile (square pile cap) Geosynthetic

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Table 6 Comparison of analytical methods with field measurement of Liu et al. (2007). Parameters

Efficacy by arching effect, Ea (%) Efficacy by membrane effect Em(%) Total efficacy, E (%) Maximum GR deflection (mm) Maximum GR tension (kN/m)

Present methods LinearModelEq. (23)

Non-linear Model Eq. (24)

61.6 2.65 64.25 75.73 20.54

61.6 3.21 64.81 86.34 21.85

CUR226 (2016)

BS8006 (2010)

EBGEO (2011)

PWRC (2007)

Measured result

57.9 5.3 63.2 89 21.3

61 39 100 497 195

55.6 11.67 67.27 268 47.6

18 – 18 306 –

– – 62.57 72 19.97

method. This further explains why this project was selected. The brief description of baseline case values that have been used in the proposed method are as follows: embankment—height = 5.6 m, unit weight = 18.5 kN/m3, internal friction angle = 30°; interface upper side—internal friction angle (ϕp) = 40°, cohesion = 10 kPa, αp = 0.8 (assumed); interface lower side—internal friction angle (ϕs) = 10°, cohesion = 8 kPa, αp = 0.65 (assumed); pile – cap width = 1 m, centre-to-centre pile spacing = 3 m; subsoil—unit weight = 17 kN/m3, subgrade reaction modulus = 550 kPa/m, ultimate bearing capacity = 300 kPa; geosynthetic – tensile stiffness = 1180 kN/m; and no surcharge load. In this study, these values are used throughout unless otherwise specified. No partial factors of safety are applied to the design parameters. The results of the present case study are shown in Figs. 7–27. 4.1. Influence of subsoil consolidation

Fig. 8. Effect of subsoil consolidation on geosynthetic deflection.

Fig. 7 shows the effect of subsoil consolidation on total efficacy. It should be noted that the total efficacy increases with an increase in the subsoil consolidation. With an increase in the subsoil consolidation, more shear resistance accumulates, which in turn, enhances the development of soil arching. In Fig. 7, the difference between the total efficacy and the efficacy by arching could be attributed to the tensioned membrane action of the geosynthetic. In addition, the present method, using both linear and non-linear subsoil models, gives a similar result for the total efficacy. Fig. 8 demonstrates the maximum geosynthetic deflection versus the subsoil consolidation. It is interesting to note that the maximum geosynthetic deflection increases with an increase in the subsoil consolidation; however, it approaches a constant value when the subsoil consolidation is continuously increased (in this analysis, this value was 80%). This finding is in agreement with experimental observation by some researchers (Hosseinpour et al. [8], Chen et al. [9], Xu et al. [10]). The development of arching becomes stronger as the subsoil consolidation is increased, and it becomes stable at a sufficiently large rate

of consolidation. As a result, the maximum geosynthetic deflection is approached at a constant rate. Moreover, it is also interesting to note that the difference in the results when using the linear and non-linear models of subsoil becomes more significant when the subsoil consolidation is increased. As shown in Fig. 9, the maximum tension in the geosynthetic increases slightly prior to the subsoil reaching 60% of consolidation; however, it decreases when the subsoil consolidation further increases. Furthermore, it can be seen that the subsoil consolidation has a significant effect on the difference in the result between using the linear and non-linear models of the subsoil in estimating the maximum tension in the geosynthetic. 4.2. Influence of ultimate bearing capacity of the subsoil

Max. tension in geosynthetic, T (kN/m)

As discussed, the parameter involved in the ultimate bearing 30 28 26 24 22 20 18 16 14

Linear subsoil model

12

Nonlinear subsoil model

10 0.2

Fig. 7. Effect of consolidation degree of subsoil on efficacy.

0.4 0.6 0.8 Consolidation degree of subsoil

Fig. 9. Effect of subsoil consolidation on tension in geosynthetic. 11

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Fig. 10. Effect of ultimate bearing capacity of subsoil on efficacy.

Fig. 12. Effect of ultimate bearing capacity of subsoil on tension in geosynthetic.

capacity of the subsoil, i.e., qsu is the basic difference in the pressuredeflection relations for linear and non-linear subsoil models. Fig. 10 describes the relationship between the total efficacy and the ultimate bearing capacity of the subsoil and a conclusion could be drawn that the efficacy by the tensioned membrane effect decreases with an increase in the ultimate bearing capacity of the subsoil. Additionally, the difference in the prediction of total efficacy using the linear and non-linear subsoil models decreases and the efficacy value with the non-linear model approaches that of the linear model when the ultimate bearing capacity of the subsoil is further increased. Figs. 11 and 12 show the variation of maximum deflection and tension in the geosynthetic when the ultimate bearing capacity of the subsoil is increased. The results show that the deflection and tension in the geosynthetic predicted by using the non-linear subsoil model decrease with an increase in the ultimate bearing capacity of the subsoil and both these values approach the corresponding values of the linear subsoil model.

m. Both linear and non-linear models of the subsoil behaviour agree very well with each other in terms of predicting the variation of the efficacy with subgrade reaction modulus. Fig. 14 indicates that the maximum geosynthetic deflection decreases with an increase in the subgrade reaction modulus of the subsoil. A similar trend can be also seen for the variation of maximum tension in the geosynthetic, as shown in Fig. 15. The higher the subgrade reaction modulus corresponding to the subsoil stiffness, the higher is the support from the subsoil, and the lower is the stretching of the geosynthetic. This can be considered a reason for the maximum deflection and tension in the geosynthetic decreasing with an increase in the subgrade reaction modulus of the subsoil. 4.4. Influence of geosynthetic tensile stiffness

Because the subgrade reaction modulus represents the stiffness of subsoil, this parameter is therefore important in recognizing the contribution of the subsoil to the load support. Hence, the effect of the subgrade reaction modulus of the subsoil is investigated next. Fig. 13 shows the effect of subgrade reaction modulus on the efficacy. The results indicate that the efficacy decreases with an increase in the subgrade reaction modulus of the subsoil and nearly approaches a constant value when the subgrade reaction modulus exceeds 500 kPa/

The existing design methods do not consider the stiffness effect of the geosynthetic. However, the geosynthetic tensile stiffness is involved in the tensioned membrane behaviour of geosynthetics; therefore, it should have an effect on the prediction of the total efficacy. As calculated by the proposed method, the effect of geosynthetic stiffness on the efficacy is shown in Fig. 16, from which it is seen that an increase in the geosynthetic tensile stiffness increases the efficacy by the membrane effect. However, the membrane effect increases significantly only when the geosynthetic stiffness is larger than 1000 kN/m. The increase in the load transferred onto the pile cap by the tensioned membrane of the geosynthetic explains why the total efficacy is greater for the reinforced case than that for the unreinforced case.

Fig. 11. Effect of ultimate bearing capacity of subsoil on geosynthetic deflection.

Fig. 13. Effect of subgrade reaction modulus of subsoil on efficacy.

4.3. Influence of subgrade reaction modulus of subsoil

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Fig. 14. Effect of subgrade reaction modulus of subsoil on geosynthetic deflection.

Fig. 17. Effect of geosynthetic stiffness on geosynthetic deflection.

Fig. 18. Effect of geosynthetic stiffness on tension in geosynthetic.

Fig. 15. Effect of subgrade reaction modulus of subsoil on tension in geosynthetic.

that the results obtained from the linear and non-linear subsoil models deviate more from each other as the geosynthetic stiffness increased.

Fig. 17 demonstrates the benefits of geosynthetics in reducing the geosynthetic deflection. As the geosynthetic reinforcement gets stiffer, the membrane action of the geosynthetic becomes stronger and therefore, the geosynthetic deflection becomes less. Fig. 18 indicates the variation of maximum tension in the geosynthetic with an increase in the geosynthetic stiffness. It can be observed

4.5. Influence of embankment height Fig. 19 shows the efficacy computed with both linear and non-linear subsoil models. With both the models the total efficacy increases with the embankment height; however, they approach a limiting value when

Fig. 16. Effect of geosynthetic stiffness on efficacy.

Fig. 19. Effect of embankment height on efficacy. 13

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Fig. 20. Effect of embankment height on geosynthetic deflection.

Fig. 22. Effect of friction angle of embankment soils on efficacy.

the embankment height is further increased. This finding confirms the existence of a critical height in mobilising the soil arching. The critical height is defined as the embankment height at which the plane of equal settlement occurs, and the embankment load above this plane will not participate in the arching mobilisation. Therefore, the critical height corresponds to the embankment height at which the efficacy by the arching starts to approach a limiting value. In this analysis, the critical height is observed at a height of 2 m that equals the clearance spacing (s′ = s – a). Fig. 19 also shows that the efficacy by the membrane effect increases with an increase in the embankment height. The effect of the geosynthetic is maximised with the tensioned membrane, with the result that it increases the load on the pile cap. Such an increase is estimated to be from 1.1% at an embankment height of 1 m to 2.9% at an embankment height of 5.6 m. It is also noted that no significant difference in the total efficacy is expected between the two subsoil models. The effect of the embankment height on the maximum deflection and tension in the geosynthetic is shown in Figs. 20 and 21. As can be seen from these figures, the maximum deflection and tension in the geosynthetic increase with an increase in the embankment height. It is interesting to note that the difference in the predicted results between the two subsoil models increases as the embankment height is increased.

the embankment and hence is considered for the parametric study in this work. Fig. 22 shows the variation of the efficacy with an increase in the friction angle of the embankment soils. It should be noted that the total efficacy represents the combination of the arching and membrane effects. Therefore, the difference between the value of total efficacy and that of the arching effect is the efficacy by the membrane effect. The results indicate that the total efficacy increases significantly with an increase in the friction angle of the fill soils. However, as the membrane effect becomes less, the value of the total efficacy moves towards that of the arching effect when the friction angle of the fill soil is increased. Fig. 23 shows the effect of friction angle of the embankment soils on the maximum geosynthetic deflection. The results indicate that the maximum geosynthetic deflection decreases with an increase in the friction angle of the embankment soils. The larger the friction angle of the embankment soils, the less is the load distributed on the geosynthetic, and the deflection is consequently reduced. Fig. 24 demonstrates the variation of maximum tension in the geosynthetic with the friction angle of the embankment soils. With both the subsoil models, the maximum tension in the geosynthetic decreases with an increase in the friction angle of the embankment soils. In addition, it is also noted that the prediction results between both models of the subsoil tend to be close when the friction angle of the embankment soils is increased. The difference between both models of the subsoil is estimated to be 10% and 2% at friction angles of 25° and 45°, respectively.

4.6. Influence of friction angle of embankment soils The friction angle of the embankment soils is one of the most important parameters that significantly affects the arching prediction in

Fig. 21. Effect of embankment height on tension in geosynthetic.

Fig. 23. Effect of friction angle of embankment soils on geosynthetic deflection. 14

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Fig. 26. Effect of improvement area ratio on geosynthetic deflection.

Fig. 24. Effect of friction angle of embankment soils on tension in geosynthetic.

4.7. Influence of improvement area ratio(IAR)

60

Max. tension in geosynthetic (kN/m)

Pile spacing, s, and pile-cap width are two of the most important design parameters in the design process of GRPS embankments because they control the IAR of the improved ground. IAR is defined as the ratio of the pile cap area to the influence area of that pile (i.e., IAR = Ac/ A = a2/s2). Therefore, in this work, the influence of IAR on the behaviour of GRPS embankments has been investigated by varying the pilecap width from 0.25 m to 1.25 m. For the range of values selected for the pile-cap width, the IAR is varied from 2.44% to 61%. In these analyses, s is not changed. As presented in Fig. 25, the total efficacy increases as the IAR is increased. However, the degree of improvement becomes smaller once the IAR exceeds 20%. Fig. 26 shows that the maximum geosynthetic deflection decreases with an increase in the IAR. A similar tendency can also be observed for the maximum tension in the geosynthetic, as shown in Fig. 27. As the IAR is increased, more load is distributed on the pile cap and less load is carried by the geosynthetic. This can be considered as a reason for the reduction of deflection and tension in the geosynthetic with an increase in the IAR. Additionally, it is interesting to note that the discrepancy in the results predicted by the two subsoil models is smaller when the IAR is increased.

50 40 30 20 10

Linear subsoil model Nonlinear subsoil model

0

0

10

20

30

40

50

60

Improvement area ratio (%) Fig. 27. Effect of improvement area ratio on tension in geosynthetic.

medium, and low. However, there is no widely accepted standard to classify these levels. Therefore, the significance of the degree of influence is presented in Table 7 based on a commonly used method in geotechnical engineering. For the deflection and tension in the geosynthetic, all the influencing factors have a high degree of influence. Therefore, in the design process of the geosynthetic reinforcement layer or geosynthetic reinforced platform, it is advisable to consider the influence of all these factors. Efficacy by the arching effect is governed by subsoil consolidation, embankment height, friction angle of fill soils and IAR. Efficacy by membrane effect is mainly governed by geosynthetic tensile stiffness, embankment height and subgrade reaction modulus of the subsoil. Therefore, these are the most important design factors to be considered for improving the load transfer to the columns.

4.8. Degree of Influence of factors on embankment performance The degree of influence of any of the influencing factors on the assessed parameters can be divided into three levels, namely high,

5. Conclusion A new analytical method that considers the geosynthetic–soil–pile interaction has been proposed for the analysis of a GRPS embankment. The support of the subsoil is taken into account for both linear and nonlinear models. The presented method provides a more complete design approach than the earlier methods that only considered either the tensioned membrane theory or the arching theory. The proposed method has an advantage over the other methods in that it is simple to obtain the solution of the developed equations and

Fig. 25. Effect of improvement area ratio on efficacy. 15

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Table 7 Influence degree of factors on GRPS embankment performance. Factors

Efficacy by arching effect

Efficacy by membrane effect

Total efficacy

Max. geosynthetic deflection

Max. tension in geosynthetic

Subsoil consolidation Ultimate bearing capacity of subsoil, qsu Subgrade reaction modulus of subsoil Geosynthetic stiffness Embankment height Friction angle of fill soils Improvement area ratio

High –

Low High (qsu < 200 kPa)

High High

High(U < 0.8) High (qsu < 200 kPa)

Medium High (qsu < 200 kPa)

–

High (Ks < 500 kPa/m)

High (Ks < 500 kPa/m)

High (Ks < 500 kPa/m)

High (Ks < 500 kPa/m)

– High High High

High (JGR > 1000 kN/m) Medium Low Low

High (JGR > 1000 kN/m) High High High

High (JGR > 1000 kN/m) High High High

High (JGR > 1000 kN/m) High High High

there is no need for trial values to obtain the solution, as is done in CUR226 and EBGEO. Using the proposed method, the influence of the membrane effect, skin friction, geosynthetic stiffness and consolidation of subsoil can be determined. A comparison of the proposed method with experimental measurements and the existing design methods has been carried out for three cases. It is shown that the results from the present method are in good agreement with the experimental results, as well as those from the other methods. The analysis of maximum deflection and tension in the geosynthetic indicates that the deflection obtained from using the non-linear subsoil model is higher than that obtained by using the linear subsoil model. However, the difference in the results between the two subsoil models becomes smaller with an increase in the subsoil consolidation, an increase in the ultimate bearing capacity of the subsoil, an increase in the friction angle of embankment soils, an increase in the IAR, and a decrease in the embankment height. The proposed method with the linear model of the subsoil is generally suitable for situations in which the subsoil support is significant and the ultimate bearing capacity of the soft soil is high. In addition, it should be also used in cases where the information of the soft subsoil from field measurements is not available or subsoil is inhomogeneous. The present method, when used with a non-linear model of the subsoil is more suitable for homogenous subsoils or if the ultimate bearing capacity of the subsoil is known. Furthermore, the analysis data indicates that the total efficacy increases with an increase in the consolidation degree of the subsoil, embankment height, friction angle of embankment soils, geosynthetic stiffness, and IAR. On the contrary, it increases with a decrease in the modulus of the subsoil. However, the current design/analysis methods have generally neglected the effect of geosynthetic stiffness, subsoil consolidation, and bearing capacity of the subsoil. The performance of a GPRS embankment is significantly affected by various factors to different degrees. The results show that the embankment height, friction angle of the fill soils, subsoil consolidation, and IAR have a large influence on the maximum geosynthetic deflection and tensile force. In addition, the effect of geosynthetic stiffness, subgrade reaction modulus, and ultimate bearing capacity of the subsoil on geosynthetic deformation is also relatively significant in the limiting value range.

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CRediT authorship contribution statement Tuan A. Pham: Conceptualization, Methodology, Validation, Formal analysis, Writing - original draft, Visualization, Writing - review & editing, Supervision, Funding acquisition. Declaration of Competing Interest The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: 16

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