J. Cent. South Univ. Technol. (2009) 16: 0857-0864

DOI: 10.1007/s11771-009-0142-z

Comparison between responses of reinforced and

unreinforced embankments due to road widening

HUANG Xiao-ming(黄晓明)¹, WANG Hao(汪 浩)²

(1. School of Transportation, Southeast University, Nanjing 210096, China;

2. Department of Civil and Environmental Engineering, University of Illinois at Urbana-Champaign, IL61866, USA)

Abstract: The objective of this work is to compare the responses of geosynthetically-reinforced embankment and unreinforced embankment due to road widening by using the centrifuge model tests and a two-dimensional (2D) finite element (FE) model. The measured and calculated responses of the embankment and foundation exposed to road widening include the settlement, horizontal displacement, pore water pressure, and shear stresses. It is found that the road widening changed the transverse slope of the original pavement surface resulting from the nonuniform settlements. The maximum horizontal movement is found to be located at the shoulder of the original embankment. Although the difference is small, it is clearly seen that the geosynthetic reinforcement reduces the nonuniform settlements and horizontal movements due to road widening. Thus the reinforcement reduces the potential of pavement cracking and increases the stability of the embankment on soft ground in road widening.

Key words: reinforcement; centrifuge model test; finite element model; embankment; road widening

1 Introduction

With the increase of traffic flow in China, road widening is often conducted by highway agencies to increase the number of highway lanes or to form the intersection with other roads. During road widening, the likely nonuniform settlements and associated shear force could cause longitudinal pavement cracking along the joint between the original and new pavements [1]. The possible causes of nonuniform settlements and pavement cracking include: (1) different soil compressibilities and consolidation rates between the original and new embankments; (2) uneven stress distribution in the original road caused by widening; and (3) different structural capacities between the original and new pavements. Several investigators studied the deformation behavior of the embankment during road widening through numerical analysis, experimental and field investigations [2-5]. The proposed three possible failure mechanisms in road widening include: (1) shear cracking caused by embankment slippage; (2) bottom-up cracking caused by vehicle load; and (3) top-down cracking caused by nonuniform deformation.

Many construction and foundation improvement methods, such as excavated terrace on existing slope, staged construction, preloading, light weight embankment, cement deep mixing pile, and separating walls, have been used to reduce the settlements and increase the stability of embankment on soft ground [6]. Out of these treatment methods, the geosynthetic reinforcement (geogrid or geotextile) is usually incorporated at the subgrade-ground interface to reinforce the embankment on soft subgrade layers. The suggested mechanism of geogrid reinforced embankment is to provide a stable force at the soil-geogrid interface as a result of the interlock and friction action between the layer particles and grid, and to provide membrane reinforcement. Thus, the reinforcement has the ability to better distribute the applied load over a larger area and compensate for the lack of tensile strength within surrounding soils. Many successful cases have been achieved in the strengthening of soft soil foundation with geosynthetic reinforcement to facilitate the construction process, extend the service life, reduce the necessary fill thickness, diminish the deformation, and improve the bearing capacity and long-term performance of embankment on soft ground [7-9]. The geogrid reinforcement was found to be capable of reducing the surface settlement and lateral deformation of the embankment. Thus, small differential vertical displacement was found across the section of geogrid- reinforced embankment [10-11].

Centrifuge model testing, due to its ability to reproduce the same stress levels in a small-scale model as those present in a full-scale prototype, is a useful tool in geotechnical problems. The advantage and principle of small scale modeling of prototype soil structures is to make use of the increased self-weight in a centrifuge. Centrifuge model tests have been used to evaluate the stability of embankment slope and retaining walls, the performance of embankment with wick drains, etc. [12-13]. In this work, the centrifuge model test was conducted to compare the responses of reinforced and unreinforced embankments in road widening. In  addition, a two-dimensional (2D) finite element (FE) model was developed to simulate the widening process in the centrifuge model test.

2 Centrifuge model test

The principle of centrifuge model test is dependent upon the requirement of similarity between the model and the prototype to keep the same stress level in the centrifuge model and prototype. If a model of the prototype structure was built with dimensions reduced by a factor 1/N but with the same density, then an acceleration field of N times of the acceleration of gravity would generate stresses by self-weight in the model, which was the same as that in the prototype structure.

2.1 Test configuration

The centrifuge machine used in this work was a balanced beam centrifuge with 5.5 m in radius housed at Nanjing Hydraulic Research Institute in China. The centrifuge was capable of carrying the mass of 2 000 kg payload to the acceleration of 200 g and it was instrumented with video-photography and data acquisition system. The internal dimensions of the container were 685 mm (length)×200 mm (width)× 400 mm (depth).

The scaling ratio used in the centrifuge tests was   1?62.5. The original embankment in the test was 64 mm high founded on a clay foundation with a thickness of 154 mm. This conformed to a prototype condition of 4 m high embankment and 9.6 m thick clay foundation. The width of original embankment at prototype was 26 m and the proposed widening width was 12.5 m at each side. The existing and widening embankments were constructed with the similar slopes (1?1.5).

As for the widening embankment with reinforcement, two layers of geogrid were incorporated in the compacted fill material. The first layer was directly placed on the surface of foundation and the second in the middle of new embankment. Based on the dimension analysis, the elastic modulus and tensile strength of geosynthetic reinforcement need to be l/62.5 of that of the prototype [14].

The vertical deformation at the top of embankment was measured by four laser sensors. These sensors were manufactured by WENGLOR Company in German, with the measuring range of 0-50 mm and bias of 20 μm. Two pore pressure transducers (PPT), specified to measure the pore water pressure of the foundation under original and new embankments respectively, were located 50 mm underneath the clay foundation.

The displacement of the geotextile embedded in the centrifuge model was measured using the high-resolution digital camera and image processing technology [15]. The same method was attempted in this study but failed because the camera could not work when the acceleration of centrifuge exceeded 30 g. In addition, the deformation of geogrid was less than that of geotextile under the same load, which would increase the difficulty of image processing. Thus, the stain gauges were embedded in the reinforcement (geogrid) to measure the strain of reinforcement during the test in this study [16].

The schematic representation of the centrifuge model and instrumentation is shown in Fig.1. Due to the inherent symmetry about the centerline, only one half of the structure was modeled in both centrifuge test and numerical modeling.

2.2 Test procedure

The soft clay used in the foundation was one-

Fig.1 Schematic dimensions of centrifuge model and instrumentation (Unit: mm)

dimensionally consolidated step by step with a maximum vertical pressure of 140 kPa. The undrained shear tests were carried out at different depths and the average strength was 25 kPa with the degree of saturation being 95%. The wet density of the foundation was 1.80 g/cm³.

The original embankment was constructed on soft clay foundation by making the degree of compaction of 95%. After compaction the dry density was 1.70 g/cm³ and wet density was 1.99 g/cm³. The acceleration was increased to 62.5 g in seven stages to simulate the layered embankment construction (5 min interval between successive stages, corresponding to 15 d at prototype). After achieving the stable pore pressure, the centrifuge machine was stopped. This conformed to the consolidation period of the original embankment and foundation.

The widening embankment was constructed by pouring sand from a hopper at 1 m high. The dry density of new embankment was 1.70 g/cm³ and the relative density was 0.62. After that the acceleration was increased to 62.5 g step by step and stayed at 62.5 g for about 6.5 min to simulate the consolidation period under widened new embankment (21 d at prototype). The process was done separately under both reinforced and unreinforced conditions. A polyester woven geogrid with rectangular opening dimensions of 8 mm×8 mm, having tensile strength of 1.0 kN/m and initial tensile elastic modulus of 7.0 kN/m, was used as the geosynthetic reinforcement. Thus, the equivalent strength at prototype is equal to 62.5 kN/m, and the equivalent tensile elastic modulus is equal to 448 kN/m at prototype. The width of geogrid rib is 0.5 mm. The measured tensile stress—strain curve of the geogrid reinforcement is shown in Fig.2.

In addition, another centrifuge test was conducted to study the behavior of the widened embankment at high stress level by increasing the acceleration continuously up to 200 g.

Fig.2 Tensile stress—strain relationship of geogrid reinforce- ment used in centrifuge test (Two directions)

2.3 Analysis of test results

2.3.1 Comparison of measured settlements

The measured settlements at the top of embankment under unreinforced and reinforced conditions after widening are compared in Fig.3. It is found that the settlements near the joint (S₂) are higher than those near the center of original embankment (S₁). This is probably due to different consolidation rates in the foundation under the original embankment caused by widening. It is also found that the reinforcement slightly reduces the nonuniform settlements at the top of original embankment (between S₁ and S₂) from 0.4% to 0.3%. This is possibly due to the fact that the geogrid reinforcement transfers the load to foundation more uniformly. The maximum change of transverse gradient between points S₂ and S₃ is reduced from 1.3% to 1.0% due to the effect of reinforcement.

Fig.3 Comparisons of measured settlements along surface for widened embankments under unreinforced and reinforced conditions (at 62.5 g)

The points S₃ and S₄ have much bigger settlements than S₁ and S₂ due to the higher consolidation rates in  the foundation under the new embankment. The reinforcement slightly reduces the total settlements of the new embankment (S₃ and S₄). However, it cannot substantially prevent the development of consolidation settlements of the new embankment. This is consistent with previous research that the deformation of reinforced soil is not sensitive to reinforcement characteristics and layout, but dependent mainly on the properties of the backfill soil [17].

2.3.2 Comparison of measured pore water pressure

Figs.4(a) and (b) present the curves of the development of pore water pressures during widening for

Fig.4 Development of pore pressures in foundation below widened embankment under different conditions: (a) Un- reinforced condition; (b) Reinforced condition

reinforced and unreinforced embankments, respectively. The pore water pressures at point P₂ are higher than that at point P₁ during the acceleration process. This indicates that the foundation under the original embankment has better stability than the foundation under the new embankment during widening.

The pore water pressure at points P₁ and P₂ are respectively reduced to 52 and 60 kPa due to the effect of reinforcement (Fig.4(b)), compared with 55 and 64 kPa in the unreinforced embankments (Fig.4(a)). The values of a/g at the second y axis are the ratios of the acceleration of centrifuge to the acceleration of gravity. The smaller pore water pressure indicates the smaller excess pore pressure at the same location. By using Eq.(1), it is found that the coefficient of pore pressure decreases from 0.30 to 0.27 at P₁ and from 0.42 to 0.37 at P₂ due to the effect of reinforcement. The reduction of the coefficient of pore pressure indicates that the reinforcement reduces the pore water pressure in the foundation.

                                  (1)

where   is the coefficient of pore pressure, u is the excessive pore pressure equal to measured pore pressure substracted by static pore pressure (31 kPa here), and ?σ₁ is the increment of major stress (78 kPa here).

2.3.3 Failure of original embankment by widening

The development histories at different locations are plotted in Fig.5 when the acceleration is increased to  200 g continuously in 5 min (15 d at prototype). The high acceleration is used to observe the behavior of the widened embankment at high stress level. It is found that the settlements at the top of embankment are highly dependent on the locations. For example, the points S₂ and S₃ near the joint between the original and new embankments exhibit much greater settlements than the point S₁ near the center of original embankment.

Fig.5 Development of settlements along surface for widened embankments with cracking

The maximum nonuniform settlement between points S₁ and S₂ is 2.5 mm (15.6 cm at prototype), which can change the transverse gradient on the original pavement surface as high as 2.5%. As shown in Fig.6, a longitudinal cracking is found on the surface of original embankment at 108 mm (6.25 m at prototype) away from the joint. This surface cracking propagates 35 mm (2.2 m at prototype) deep along the height of embankment.  The location of the cracking is in the region between

Fig.6 Surface cracking of widening embankment (at 200 g)

the points S₁ and S₂ in the original embankment. This suggests that road widening could causes the longitudinal top-down cracking at some distances away from the joint between the original and new pavement.

2.3.4 Tensile strain of reinforcement

Figs.7(a) and (b) present the measured tensile strains of the geogrid reinforcement on the surface of foundation and in the middle of embankment, respectively. The tensile strains of the reinforcement on the foundation surface are larger than those of the reinforcement in the middle of the embankment. This indicates that the geogrid on the foundation surface carries more load than that in the middle of embankment. This is consistent with current limit equilibrium design method for reinforced soil slope, which is based on the assumption of a triangular distribution of maximum reinforcement tensions increasing with depth from the crest of the slope [18].

Another interesting finding is that the locations of maximal tensile strains of two layers of geogrid are different; one is near the slope of original embankment and the other is near the slope of new embankment. The locations of the maximum tensile strains indicate possible slippage plane of new embankment (Fig.8). This slippage plane is far away from the toe of the original embankment.

3 Numerical modeling

A numerical model for full-scale embankment based

on plane strain finite element method (FEM) was developed to calculate the responses of embankment and foundation in road widening. The GEO SLOPE software was used in the numerical analysis. The GEO SLOPE contains seven modules including SLOPE/W, SEEP/W, SIGMA/W, QUAKE/W, TEMP/W and CTRAN/WA [19]. The SIGMA/W module for stress and deformation analysis was mainly used in this work.

3.1 Geometry parameters and loading process

The embankment is supposed to be infinite in the longitudinal direction and thus can be considered as plain strain condition. The length and depth of the old embankment in the numerical model were the same as those in the prototype of the centrifuge test, and three widening widths (4.0, 8.5 and 12.5 m) were used in the numerical model. Due to the symmetry in loading and geometry, only half of the embankment and foundation was simulated. This required to impose a boundary on the plane of symmetry in the transverse direction. Another fixed boundary was imposed at the bottom of foundation. Only the self-weight of new embankment was considered as the load input in the numerical model and the vehicle load were neglected. Consistent with the loading sequence in the centrifuge test, the total loading process was divided into five steps: (1) consolidation of the foundation; (2) construction of the original embank- ment; (3) consolidation of the original embankment; (4) construction of the new embankment; and (5) consolida-

Fig.7 Measured strain of reinforcement on foundation surface (a) and in middle of embankment (b)

Fig.8 Locations of maximum tensile strain along reinforcements in widened embankment

tion of the new embankment. The stress and strain field at the end of each consolidation step was used as the initial state for the following steps. The increment steps were used to simulate the layered construction of the embankment.

3.2 Material parameters

The soil was simulated with eight-node quadratic isoparametric element. Due to the complexity of the problem itself, a simplified constitutive model was used in this analysis within reasonable accuracy. Considering the fact that stress redistribution is a key mechanism and the properties of foundation soil and embankment fill are stress dependent, a nonlinear hyperbolic elastic model subject to the Biot consolidation theory was adopted [20-22]. The soil tangential modulus (E_t) for a given stress condition, is given as follows:

       (2)

where  R_f is the failure ratio defining the shape of the stress—strain curve, k is the dimensionless parameter representing elastic modulus, n is the modulus exponent governing the stress dependence of k on σ₃ (range of values: 0-1), φ is the internal friction angle, C is the cohesion intercept, p_a is the atmospheric pressure used for normalization of stress input, σ₁ is the first principal stress, and σ₃ is the third principal stress.

The foundation and embankment soil parameters used in the calculation were determined from the consolidated undrained triaxial tests [23], as shown in Table 1. The Poisson ratios were assumed as constant of 0.3 for clay foundation and 0.35 for embankment fill, respectively.

The reinforcement was modeled using linear elastic bar element that only has resistance to tensile deformation. The stiffness of the reinforcement was the same as that in the prototype of centrifuge test (around  1 GPa). The interaction between soil and reinforcement was simulated using the nodal compatibility slip element. These slip elements had a normal and tangent stiffness between the connected nodes. The normal stiffness was assumed as 1 GPa and tangential stiffness as 10 MPa. The relatively lower tangential stiffness simulated the possible tangential slip between reinforcement and surrounding soil [24].

3.3 Analysis of computed results

3.3.1 Response of embankment due to widening

The schematic vertical and horizontal displacement vectors after widening predicted from numerical analysis are shown in Fig.9. The maximum settlement is found in the region near the joint between the original and new embankments, while the center of the original embankment shows the minimum settlement. The shoulder of the original embankment and the foundation under the widened embankment exhibit the maximum outward horizontal movement away from the center. This indicates that the possible slippage surface of the unreinforced embankment due to widening can be along the slope of original embankment. However, the slippage plane can move away from the toe of old embankment if the reinforcement is placed in the embankment (Fig.8). The lower part of the original embankment and its underlying foundation show the horizontal movement toward the road center.

3.3.2 Comparison between non-reinforcement and reinforcement

The calculated settlements after consolidation at the top of reinforced and unreinforced embankments due to widening are plotted in Fig.10. It shows that the transverse gradient of the original pavement increases by 0.5%-1.3% due to the nonuniform settlements at the center and shoulder of the original embankment. However,

Table 1 Soil parameters of foundation and embankment

Fig.9 Schematic embankment deformation after widening (8.5 m) predicted from numerical analysis for vertical displacement vector (a) and horizontal displacement vector (b)

the reinforcement reduces the nonuniform settlements, which is consistent with the finding from the centrifuge model test. In addition，the shoulder of the original embankment shows the largest horizontal displacement after widening and the reinforcement reduces the horizontal displacement (Fig.11).

Fig.10 Calculated settlements along surface of embankment

Fig.11 Calculated horizontal displacement along surface of embankment (Positive means away from centerline, vice versa)

4 Conclusions

(1) An experimental investigation (centrifuge model test) and a numerical simulation (finite element  modeling) are conducted to compare the responses of reinforced and unreinforced embankments due to road widening. The road widening causes nonuniform settlements between the center and the shoulder of the original embankment. This is believed as the possible reason for the longitudinal top-down pavement cracking at the original pavement when the vehicle loading is not considered. The largest horizontal displacement is found at the shoulder of original embankment.

(2) The differences in settlements for the reinforced and unreinforced embankments are not great, but can still be clearly observed. The geosynthetic reinforcement slightly reduces the nonuniform settlements of the original pavements. In addition, the reinforcement reduces the coefficient of pore water pressure and horizontal displacement, thus increasing the embankment stability. The tensile strain of geosynthetic reinforcement laid on the foundation surface is larger than that in the middle of the new embankment. Further research is needed by using geogrids with different moduli and strengths in the centrifuge test and utilizing more advanced material and interface constitutive models in the simulation.

Acknowledgements

The authors would like to acknowledge XU Guang-ming of the Nanjing Hydraulic Research Institute and GE Zhe-sheng of the Southeast University of China for their help in the centrifuge model testing.

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(Edited by YANG You-ping)