NUMERICAL ANALYSIS OF THE EFFECT OF SURCHARGE ON THE MECHANICAL BEHAVIOR OF GEOCELL REINFORCED RETAINING WALL

Geocell reinforced retaining structure has been widely used in civil engineering for the protection of slopes due to its advantages. In this paper, the effects of surcharge on the horizontal displacement of the wall back, the size of the sliding wedge and the factor of safety of geocell reinforced retaining wall are numerically analyzed by employing the geotechnical finite element method software Plaxis. The research results show that, when the distance of surcharge from the wall face is small, the maximum and the minimum deformation of the wall back takes place near the top of the wall and the wall bottom respectively. After the distance of surcharge from the wall face exceeds about 13% of the wall height, the surcharge has little effect on the horizontal deformation of the wall back, the size of the sliding wedge and the safety factor of geocell reinforced retaining wall. The horizontal deformation of the wall back gradually increases with the increase of the length of the surcharge until it reaches a certain value. The effect of the length of the surcharge on the failure surface is not significant. Besides, the factor of safety of the wall gradually decreases with the increase of length of the surcharge. However, with the increase of the distance of the surcharge from the wall face, the influence of the length of the surcharge on the safety factor gradually becomes small. The study results can supplement theoretical basis for the design of geocell reinforced retaining walls in engineering practices.


INTRODUCTION
Geosynthetics are widely used as reinforcing members in the construction of earth structures due to its superior properties compared with other materials, such as those of Zigler and and Pokorný (2005) [1], Liu (2016) [2].In recent years, the use of geosynthetic materials for reinforced slopes and retaining walls has increased significantly throughout the world because of the increasing infrastructural development demands.A lot of research efforts have been made to study geosynthetic-reinforced soil structure.Leshchinsky (1989) conducted a limit equilibrium analysis for the internal stability of geosynthe-reinforced vertical walls and studied the influences of two possible extreme inclinations of the reinforcement's tensile resistance [3].Wong and Broms (1994) conducted a series of model tests to study the failure modes of a geotextile-reinforced soil wall [4].Porbaha and Goodings (1996) studied the effect of the foundation soil, the slope inclination angle and the geotextile strengths on the reinforced wall behavior by centrifuge model tests of twenty-four models of geotextile-reinforced cohesive-backfill retaining walls [5].Rowe and Skinner (2001) performed a numerical examination of the behavior of an 8 m high geosynthetic reinforced soil wall constructed on a layered foundation stratum [6].Koerner and Soong (2001) presented the evolution and a cost survey of geosynthetic reinforced segmental retaining walls in general [7].They also compared three design methods in detail.Yoo (2004) explored the possible causes of distress and unexpected large lateral wall movements of a 6-year-old geosynthetic-reinforced segmental retaining wall and recommended several remedial measures [8].Hatami and Bathurst (2005) developed a numerical model to simulate full-scale, geosynthetic-reinforced soil walls under working stress conditions [9].Bathurst et al. (2006) investigated the influence of facing type and stiffness on the reinforcement loads by the measurements of two instrumented full-scale walls with different facing stiffness [10].Benjamim et al. (2007) measured the internal distribution of reinforcement strains, the overall vertical and horizontal movements within the reinforced soil mass, as well as face displacements by field monitoring a geotextile-reinforced soil-retaining prototype wall [11].Won and Kim (2007) measured local deformation of geosynthetics, such as geogrids, and nonwoven and woven geotextiles, to analyze the stability of geosynthetic-reinforced soil (GRS) structures [12].Sabermahani et al. (2009) studied the seismic deformation modes of reinforced-soil walls by conducting a series of 1-g shaking table tests on 1 m high reinforced-soil wall models [13].Bathurst et al. (2009) studied the influence of reinforcement stiffness and compaction method on wall displacement by field monitoring four geosynthetic-reinforced soil walls [14].Leshchinsky (2009)  In this paper, by employing the geotechnical finite element method software Plaxis, the numerical models of geocell reinforced retaining walls with surcharge acting on are formulated and the mechanical behavior of the wall is studied by numerical simulation.On the basis of analysis of the numerical simulation results, the effects of the distance of the surcharge from the wall face and the length of the surcharge on the horizontal displacement, the sliding surface and the safety factor of the wall are investigated.The research results provide theoretical basis and references for the design of the wall.

Model and parameters of calculation
By employing the geotechnical finite element method software Plaxis, the mechanical behavior of a geocell reinforced retaining wall with surcharge acting on is numerically simulated in order to study the effect of the surcharge on the horizontal deformation, the failure surface and the safety factor on the wall.In this study, the geocell reinforced soil is treated as a composite material with addition cohesive strength and siffness resulted from the confinment effect.Because of its convenience and simplication, such 2-dimensional equalient model has been employed and its effectiveness has been validated by Mhaiskar and Mandal (1996) [27], Bathurst and Knight (1998) [28], Latha (2000) 2013) [35].In the computation, the 15-node triangular element is employed in this analysis to model soil, the geocell reinforced soil and the foundation.An elasticplastic model employing the Mohr-Coulomb criterion is adopted for the backfill, the geocell reinforced soil and the foundation.In addition, the interface element is set between each geocell structure layer, between the wall back and backfill, and also between the foundation and the soil to model the interaction between the structure and the soil.Phi-c reduction in Plaxis is employed to calculate failure surfaces and safety factors of the wall.The details of constitutive model of the materials, the interface element, the phi-c reduction method and the definition of safety factor in Plaxis can be referred to Brinkgreve and Broere (2000) [36], Song et al. (2013b) [24].
With references to calculation parameters adopted by Wang (2004) [37], Xie and Yang (2009) [19], based on the analysis of the mechanical property tests of geocell by Yang (2005) [38], the mechanical parameters of the wall body, the foundation and the backfill in this study are selected and listed in Table 1.In order to be conservative, the magnitudes of the strength and modus of the geocell wall body are a little smaller than the ones previously adopted.The calculation model illustrated in Figure 2 is composed of the geocell structure layers, the foundation and the backfill.a and b in Figure 2 represent respectively the distance of the surcharge from the face and the length of the surcharge.In the computation, the height of the geocell reinforced retaining wall is 10m, the width of the wall is 4m and the slope ratio is 1:0.25.In addition, the height of each geocell layer is 40cm.The geocell reinforced retaining wall and the foundations are built by stage construction in nine steps.The foundation is constructed in the first step and the embankment and geocell reinforced retaining wall are filled by 2m/d in the following eight steps.As is shown in Figure 2, ten representative points are selected along the wall back in order to study the horizontal deformation of the wall in different conditions.If the wall toe is selected as coordinate origin, the coordinates of the ten points from the wall top to the wall bottom are respectively A(6.5, 10.0), B(6.3, 9.0), C(6.0, 8.0), D(5.7, 7.0), E(5.5, 6.0), F(5.2, 5.0), G(5.0, 4.0), H(4.7, 3.0), I(4.4,1.5), J(4, 0).After the construction is finished, surcharge is exerted on the backfill surface and the horizontal deformation is predicted by a plastic calculation.After that, the failure surface and the factor of safety are calculated by the strength reduction method built in Plaxis.

EFFECT OF DISTANCE OF SURCHARGE FROM THE WALL FACE
The initial stress field is produced by K 0 procedure in Plaxis.The deformation caused by the initial stress has no actual physical meanings and is therefore removed in the first step of the calculation, which can eliminate the effect of the deformation induced by the initial stress on the successive stress and displacement field.In the successive analysis, p and H represent the magnitude of the surcharge and the wall height respectively.In the computation, b=5m, i.e. b/H=0.5, and only the value of a is changed.In some cases, for example, when a/H=0.1～0.4,p=150kPa, the soil body collapses and the calculation cannot be completed.The horizontal deformation of the wall back with different a/H values is shown in Figure 3.The case of the wall without surcharge acting on is superimposed in the figure for comparison.It can be observed from Figure 3 that when the surcharge is near the wall face, the maximum deformation of wall back takes place near the top of the wall for the cases of p=100kPa and the difference between the horizontal deformation of the top of the wall and that at about H/3 above the wall heel is relatively small for the cases of p=50kPa.For the case of p=100kPa, with the increase of the distance of the surcharge from the wall face, the location where the maximum deformation of wall back occurs gradually descends and the shape of the curve representing the deformation of the wall back changes.For all the cases, with the increase of the distance of the surcharge from the wall face, the horizontal displacement gradually decreases and the shape of the curve becomes the one with the largest horizontal deformation at location about H/3 above the wall heel, from which the horizontal deformation gradually decreases toward the wall top and wall heel respectively, which is the same case with the wall without surcharge revealed by the previous studies of Song et al. (2011).This indicates that with the increase of the distance of the surcharge from the wall face, the effect of the surcharge on the horizontal displacement gradually becomes less significant.Particularly, for the cases of p=150kPa and 200kPa, the turning points from which the horizontal deformation sharply decreases are a/H=0.7 and a/H=0.9respectively.Besides, after a/H value becomes larger than 0.4 and 0.7 respectively for the cases of p=50kPa and 100kPa, the horizontal deformation decreases slowly.
The failure surfaces of the retaining wall and the backfill with different a/H values are shown in Figure 4, from which it can be seen that when the value of a/H is small, the location where the sliding surface intersects with the wall back is relatively high and the distance between the top of the sliding surface and the wall is relatively small, indicating that the size of the sliding wedge is small.However, with the increase of a/H, the location where the sliding surface intersects with the wall back gradually descends and the distance between the top of the sliding surface and the wall gradually increases, leading to the enlargement of the size of the sliding wedge.Nevertheless, it is very interesting to note that after a/H increases to a certain value, the size of the sliding wedge does not increase any more.On the contrary, it begins to decrease and maintain almost a constant value with the continuing increase of a/H.The turning points for the case of p=50kPa, 100kPa, 150kPa and 200kPa are a/H=0.7,0.9, 1.1 and 1.3 respectively.After a/H value becomes larger than that of the turning point, the surcharge has little influence on the failure surface of the geocell reinforced retaining wall and the failure surface becomes the same one with that of the wall without surcharge acting on.The variation of the safety factor with a/H values is illustrated in Figure 5.It can be known that the safety factor of the wall without surcharge acting on is 1.423 by computation.It can be observed from Figure 5 that the safety factor increases with a/H value.However, after a/H increases to a certain value, about 0.5H, 0.9H, 1.1H and 1.3H for the cases of p=50kPa, 100kPa, 150kPa and 200kPa respectively, the safety factor maintains a constant value which is about the same one with that of the wall without surcharge acting on, showing that the effect of surcharge on the safety factor becomes small after a/H value increases to the one larger than that of the turning point.

Effect of length of surcharge
The effect of the length of the surcharge on the horizontal deformation, the sliding surface and the safety factor are also computed and analyzed by employing the geotechnical finite element method software Plaxis and p=100kPa in the computation.The deformation of the wall back with b/H=0.5, 1, 1.5, and 2 for different a/H values are shown in Figure 6, from which it can be seen that the horizontal deformation of the wall back is relatively small with small b/H values and it gradually increases with the increase of b/H.However, after the b/H value increases to be larger than a certain value, about 1.0 for the cases of a/H=0.2,0.5 and 0.8, the horizontal deformation changes very little.For the case of a/H=0.2, with the increase of the length of the surcharge, the location where the maximum deformation of wall back occurs gradually rises to the middle part of the wall.The maximum deformation of the middle part of the wall is much larger than the other part of the wall, resulting in an acute angle in the middle part of the deflection curve.The sliding surfaces of the wall and the backfill with b/H=0.5, 1, 1.5 and 2 for different a/H values are provided in Figure 7, from which it can be observed that the sliding surfaces with different b/H values are almost the same one, indicating that the effect of the length of the surcharge on the sliding surface is not obvious.When a/H is small, the sliding surface is almost the same one with the wall without surcharge acting on.With the increase of the value of a/H, the size of the sliding wedge gradually increases.However, when a/H increases to be larger than 1.1, the size of the sliding wedge reduces to be the one with the wall without surcharge acting on, which has been discussed previously concerning the influences of the distance of the surcharge from the wall face.8 that the safety factor of the wall is large with small b/H values.However, it gradually decreases with the increase of the value of b/H.Nevertheless, with the increase of a/H, the influence of the length of the surcharge on the safety factor gradually becomes small.For example, when a/H=1.1, the length of the surcharge has no effects on the safety factor of the wall, which does not vary with the value of b/H and remains the same value with that of the wall without surcharge acting on.

CONCLUSION
In this paper, the effect of the distance of the surcharge from the wall face and the length of the surcharge on the horizontal deformation, the failure surface and the factor of safety is studied by employing the geotechnical finite element method software Plaxis.The following conclusions can be primarily drawn on the basis of the analysis of the numerical simulation results.
(1) When the distance of the surcharge from the wall face is small, the horizontal deformation of the wall back is large.When the surcharge moves away from the wall face, the horizontal displacement gradually decreases and the shape of the curve representing the horizontal deformation of the wall back becomes the same one of the wall without surcharge acting on.
(2) When the distance of the surcharge from the wall face is small, the size of the sliding wedge is small.However, with the increase of the distance of the surcharge from the wall face, the size of the sliding wedge gradually increases.Nevertheless, after a/H increases to a certain value, the size of the sliding wedge does not increase any more.On the contrary, it begins to decrease with the continuing increase of a/H and maintain almost a constant value almost the same with that of the wall without surcharge acting on.
(3) The factor of safety increases with the distance of the surcharge from the wall face.However, after a/H increases to a certain value, the safety factor maintains a constant value which is about the same one with that of the wall without surcharge acting on, showing that the effect of the surcharge on the safety factor becomes small in this case.
(4) The horizontal deformation of the wall back is relatively small when the length of the surcharge is small and it gradually increases with the increase of b/H.However, after the b/H value increases to be larger than a certain value, the horizontal deformation changes very little.
(5) The effect of the length of the surcharge on the sliding surface is not significant.Besides, the safety factor of the wall gradually decreases with the increase of the length of the surcharge.However, with the increase of a/H, the influence of the length of the surcharge on the safety factor gradually becomes small and after a/H becomes larger than a certain value, the length of the surcharge will have no effect on the safety factor.

Figure 2 -
Figure 2 -Sketch of the calculation model (Unit: m)

Figure 3 -
Figure 3 -Effect of distance of surcharge from wall face on the horizontal deformation (Unit: m)

Figure 4 -
Figure 4 -Effect of distance of surcharge from wall face on the sliding surface (Unit: m)

Figure 6 -
Figure 6 -Effect of length of surcharge on the horizontal deformation (Unit: m)

Figure 7 -
Figure 7 -Effect of length of surcharge on the sliding surface

Figure 8 -
Figure 8 -Variation of Safety factors of the wall with b/H values

Table 1 -
Calculation Parameters of Model