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Backanalyses of geosynthetic reinforced embankments on soft soils
Geotextiles and Geomembranes 16 (1998) 273—292
Backanalyses of geosynthetic reinforced embankments on soft soils Ennio M. Palmeira*, Jose H.F. Pereira, Antonio R.L. da Silva Department of Civil Engineering, University of Brası& lia, FT 70910-900 Brası& lia, DF, Brazil
Abstract Geosynthetic reinforcement can be effectively used to increase the factor of safety of embankments on soft soils, particularly for shallow soft foundations layers. Several design approaches can be found in the literature dealing with the design of reinforced embankments on weak subgrades. Unfortunately, only a few well-documented case histories of reinforced embankments which led to failure have been reported. This paper presents backanalyses of some reinforced embankments that can be found in the literature using stability analysis methods commonly employed in routine works. Predicted values of safety factors at failure heights were close to one, and in spite of the limited amount of data available the results obtained suggest that these rather simple methods are useful tools for predicting factors of safety of reinforced embankments when the required input data are available and accurate. Nevertheless, even in these cases the backanalyses of the reinforced embankments suggest the use of factors of safety greater than 1.2 in routine works. ( 1998 Elsevier Science Ltd. Keywords: Geosynthetic; Embankments; Soft soils; Foundations
1. Introduction Geosynthetics have been commonly used for the reinforcement of embankments on soft soils and the advantages and limitations of the reinforcement presence have been discussed elsewhere (e.g., Jewell, 1987; Rowe, 1997). Limit equilibrium method and solutions based on the theory of plasticity have been used for the analysis of this type of work. These methods assume that the tensile force mobilised in the reinforcement increases the factor of safety against global instability in a way which depends on the
*Corresponding author. Tel.: 55 61 273 7313; fax: 55 61 273 4644; e-mail: [email protected]. unb.br 0266—1144/98/$ — see front matter ( 1998 Elsevier Science Ltd. All rights reserved. PII: S 02 6 6— 1 14 4 ( 98 ) 0 00 1 4— 4
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method’s approach (Figs. 1(a) and (b). Some works in the literature dealing with the subject (Leshchinsky, 1987; Low et al., 1990; Kaniraj, 1994) present straightforward methods for the design of geosynthetic reinforced embankments for particular, but usual, cases. Most of the limit equilibrium methods available assume circular slip surfaces or the combination of circular and log spiral or plane surfaces. The force in the reinforcement can be assumed acting horizontally or inclined to the horizontal direction to some extent up to the limit of tangency to the slip surface. Low et al. (1990) and Kaniraj (1996) show that predicted tangential forces may be up to 50% smaller than predicted horizontal forces. The angle between the tangent to the failure surface, at the interception with the reinforcement direction, and the horizontal direction depends on the position and characteristics of the slip surface. So, if the reinforcement force is assumed inclined to the horizontal by a constant fraction of the tangential angle this procedure will lead to different reinforcement force inclinations depending on the position, dimensions and shape of the failure surface. Results presented by Sabhahit et al. (1994) suggest little influence of the reinforcement force inclination on the safety factor, although it is not clear if these authors investigated a fixed failure surface and varied the reinforcement force inclination or considered several different failure surfaces with constant reinforcement force inclination in their analyses. Indeed, the formation of a shear zone close to the embankment collapse will cause some deviation of the reinforcement force from its original direction. Large-scale direct shear tests on reinforced dense sand shows that deviation to be negligible at peak stress values (Palmeira, 1987; Palmeira and Milligan, 1989). Although in reinforced embankments on soft soil this deviation will certainly be larger than in stiff systems, significant values may only occur at large strains, when the operational conditions of the embankment may already be compromised. However, when a deformed reinforcement inside a shear zone is considered a more complex approach must be considered regarding equilibrium conditions. At present, an accurate way to predict the reinforcement force inclination based on field or laboratory test investigations is not available. In situations where cracks or light damages of the embankments can be neglected, probably a more consistent approach for the consideration of the inclination of the reinforcement force in limit equilibrium analysis would be first to find the critical slip surface assuming horizontal reinforcement forces and, then, for that critical surface, to investigate the influence of the reinforcement force inclination within reasonable limits. In this paper a rigorous and traditional approach for limit equilibrium analyses was assumed, where all the materials were considered perfectly rigid and failing simultaneously at their maximum strength. Therefore, the reinforcement force was assumed horizontal and failing at its maximum tensile strength. The data presented later in this work will show that this assumption yielded to predicted values that compared well with observed results. Analytical solutions, based or inspired on the theory of plasticity, are also available (Jewell, 1987, 1996) for the design of reinforced embankments where a different approach is used to consider the beneficial effect of the reinforcement. In this case it is
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assumed that the presence of the reinforcement induces favourable shear stresses on the foundation soil surface that increase the bearing capacity of the soft soil (Fig. 1(b)). With regard to the evaluation of the soft soil stability these solutions neglect the strength parameters of the fill material and the problem is treated in a similar way to the evaluation of bearing capacity of shallow foundations under undrained conditions. However, fill strength parameters are required for reinforcement force calculations (Jewell, 1996). The aim of this work is to carry out backanalyses of some trial reinforced embankments found in the literature in order to evaluate the accuracy of the different approaches described above.
2. Methods of analysis employed Two slip circle methods and an analytical solution were used to predict the safety factor of the test embankments studied. The first slip circle method employed was the traditional modified Bishop’s method. The contribution of the reinforcement can be taken into account by including the effect of its tangential and normal components at the slice base (inside the fill) on the general equilibrium of the slice (hereafter referred as MBF approach) or by adding the moment of the reinforcement force with respect to the circle center to the sum of resisting moments against sliding (MBM approach). Both approaches were considered in this study being the latter most commonly used in works such as the ones presented by Low et al. (1990) and Kaniraj (1994). The second slip circle method used was the one presented by the United States Army Corp of Engineers (USACE, 1970), hereafter referred as USCE method, where the factor of safety is obtained by trial and error conditioned to the closure of the force polygons of all slices. In the present study the interslice forces in this case were considered horizontal. Methods like the ones presented by Leshchinsky (1987), Low et al. (1990) and Kaniraj (1994) are not readily applicable to the cases investigated because the boundary conditions or material properties in the trial embankments are significantly different from the hypotheses assumed in those methods. For these reasons these methods were not employed in the present study, although some of them are based on or are very similar to the modified Bishop’s method used in this work. In all of the cases analysed the force mobilised in the geosynthetic was assumed horizontal (Fig. 1(a)) and equal to its tensile strength, as commented above. Computer programs developed at the University of Brasilia to obtain safety factors of reinforced soil structures by the methods described above were employed in this study. These programs allow different boundary conditions and any variation of undrained strength with depth, which is particularlly interesting for the present study. All the values of parameters related to the reinforcement and soils used in the calculations were obtained in the original works of the case histories studied, unless when stated otherwise. Analytical expressions for the factor of safety of reinforced and unreinforced embankments on soft soils (Jewell, 1996) were also employed to the test embankments
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Fig. 1. Methods of analysis used.
studied. The presence of a crust or a shallow channel at the surface of the soft layer limits the application of these expressions and some approximations were required in some cases. Jewell (1996) presents the following analytical solutions to obtain safety factors and reinforcement forces for embankments on soft soils (Fig. 1(b). For a foundation soil with uniform strength and limited depth:
C C
D
S 8D#2nH F" 6 , 0 cH 2D#k H !
(1)
D
nH S , F " 6 4#(1#a) 3 cH D
C
(2)
D
anD k # ! . ¹ "cH2 .!9 4D#(1#a)nH 2
(3)
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For a foundation soil with strength increasing with depth:
C
S
D
2(1#a)onH S onH F or F " 60 4# #2 , 3 0 cH S S 60 60 anS k 60# ! . ¹ "cH2 .!9 F cH 2 3 Jewell (1996) suggests the use of the expressions above under the condition
C
F cH 3 *6, S 6
D
(4) (5)
(6)
where F and F are safety factors for unreinforced and reinforced embankments, 0 3 respectively; ¹ is the required reinforcement force; S , soft soil undrained strength; .!9 6 n, slope of the embankment (Fig. 1(a)); a, ratio between mobilised shear stress and undrained strength at the subgrade surface (Fig. 1(b)); H, embankment height; k , ! Rankine’s active earth pressure coefficient; D, thickness of the soft subgrade; c, fill unit weight; S , undrained strength at the surface of the subgrade; and o, the rate of 60 increase of undrained strength with depth. A full mobilization of the undrained strength at the surface of the soft soil (a"1) was assumed for the analyses presented in this work. It should be pointed out that expression (4) is valid for reinforced and unreinforced embankments. However, for the latter case a is given by the expression below and the solution is obtained by trial and error: k F cH a"! ! 0 0 . (7) 2nS 60 In all the cases analysed, the foundation soil was assumed to behave under undrained conditions with its friction angle under total stress conditions equals to zero. The fill materials were assumed to be sheared under perfectly drained conditions.
3. Case histories analysed Six case histories of embankments led to failure were investigated. Their main characteristics are summarised below. (a) Case History 1 (Volman et al., 1977) In this case history two trial embankments constructed on a 4.2 m deep soft subgrade consisting of layers of peat and clay were failed. One of the embankments was unreinforced and the other was reinforced with a layer of a woven geotextile (Stabilenka N99), as shown in Fig. 2. Table 1 summarises the main characteristics of the materials involved in this case. The reinforcement had a tensile strength of 61 kN/m, deformation at failure equal to 20% and average tensile stiffness equal to
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Fig. 2. Case history 1 (Volman et al., 1977).
258 kN/m. Fill material properties are not provided and a large variation of cohesions and friction angles obtained in terms of total stresses for the foundation soils can be observed. The authors report that the unreinforced embankment failed when it reached a height of 3.5 m, while the reinforced embankment reached a height of 4.5 m without failure. Because the determination of the undrained strength of the foundation soil in this case history is very complex, one can backanalyse the unreinforced embankment to estimate the average foundation strength in order to infer how close to failure the reinforced embankment was at its final height. Having in mind that for low embankments variations of the fill friction angle have little influence on the factor of safety and that the fill material used was sand, a friction angle of 30° can be adopted for estimate purposes. Using the modified Bishop’s method one can obtain an average undrained strength of 12 kPa for the foundation soil for a safety factor equal to unity at the observed failure height of 3.5 m. If this undrained strength is used to analyse the stability of the reinforced embankment at its final height (4.5 m) a safety factor of 1.012 is obtained. Despite the rather crude analysis, but in view of the satisfactory accuracy observed for this method for other embankments to be discussed later in the present work, this value suggests that the reinforced embankment might be close to failure at the end of construction. The assumption of a reinforced embankment failure height equal to 4.5 m is then conservative. Further information on this work can also be found in van Leeuwen and Volman (1976). (b) Case History 2 (Rowe and Soderman, 1984) Rowe and Soderman (1984, 1985) present a study of stability analysis of reinforced embankments combining limit equilibrium and finite element methods. The Authors report the construction of trial embankments on a 3.3 m thick soft subgrade with an average undrained strength of 8 kPa (Fig. 3 and Table 1). The tensile strength of the reinforcement (Stabilenka 200, 450 g/m2) is 215 kN/m and its tensile stiffness 2000 kN/m. The authors report that the unreinforced and the reinforced embankments failed with heights equal to 1.75 and 2.75 m, respectively (Rowe and Soderman, 1985). Failure of the reinforced embankment was governed by fabric pull-out from the
Rowe et al., 1995 Schaefer and Duncan, 1988
Volman et al., 1977 Rowe and Soderman, 1984 Delmas et al., 1990 Loke et al., 1994
Reference
18 18 19 19.5 19.5 19.6 16.9$ 18.2
c (kN/m3) 0 0 9 10 10 0 0 0
c° (kPa)
Fill data
30 33 35 30 30 42.3 34 34
/° ( @) 3.9! 3.3 24 11 11 10 10 10
D (m) 16 61 50 24 24 34 21 —
B (m) 12 8 43 51 51 16 48 48
S 60 (kPa) — — 32 12 12 — 11 11
S 6. (kPa)
Soft soil data
0 0 0 3.71 3.71 2.50 2.26 2.26
o (kPa/m) 61 215 225 42.9# 200 216 45.2 —-
¹ .!9 (kN/m)
6.26" 4.0/5.1% —
3.5 1.75 8.20" 4.0
H 0 (m)
4.5 2.75 8.75 4.2 6.0 8.2 6.0 4.5
H 3 (m)
Notes: Except when otherwise indicated, all the data presented were obtained from the original works; See also Figs. 1—7 for relevant data on soft foundation soils and additional information. c"specific weight, c°" cohesion, /@"friction angle, D"depth of soft soil below the embankment, B"embankment base width (not including berms, when present), S "undrained strength at the foundation surface, S "minimum foundation undrained strength (Fig. 1), o"rate of increase of undrained strength 60 6. with depth; ¹ "reinforcement tensile strength, H "unreinforced embankment failure height and H "reinforced embankment failure height. .!9 0 3 !D"4.2 m for the unreinforced embankment. "Predictions from the modified Bishop’s method. #Sum of the tensile strength of the four reinforcement layers used. $c"18.1 kN/m3 for the unreinforced embankment. %Failure heights for unreinforced embankments 6UA and 6UB, respectively.
1 2 3 4 (4RA) (4RB) 5 6 (6RA) (6RB)
Case history no.
Table 1 Summary of the characteristics of the case histories studied
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Fig. 3. Case history 2 (Rowe and Soderman, 1984).
Fig. 4. Case history 3 (Delmas et al., 1990).
soil at fabric strains between 4% and 5%, mobilising a force in the reinforcement at this stage of the order of 60 kN/m. Limit equilibrium analyses (Bishop’s method) of these embankments performed by the authors predicted embankment heights at failure equal to 1.7 m and 2.55 m for the unreinforced and the reinforced cases, respectively. These predictions compare well with the observed embankment heights at failure in both cases. (c) Case History 3 (Delmas et al., 1990) Delmas et al. (1990) present a case history of a reinforced embankment built on a 24 m deep soft subgrade. The geometrical characteristics of this embankment are presented in Fig. 4 and the main properties of the reinforcement and soils are listed in Table 1. The undrained strength of the soft foundation varied between 32 kPa and 43 kPa throughout its depth. A geotextile (Bidim Rock) with a tensile strength (wide
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strip test) of 225 kN/m, 2250 kN/m tensile stiffness and 10% strain at failure was used as reinforcement. The reinforcement layer was installed on a 1 m granular blanket on the soft foundation. The reinforced embankment failed when it reached a height of 8.75 m. Fig. 4 shows the location of the observed failure surface. (d) Case History 4 (Loke et al, 1994) In this case, two geosynthetic reinforced embankments and one unreinforced embankment with similar geometrical characteristics were led to failure on a 11 m deep soft subgrade. The soft soil presents a crust at its top (3 m deep), below which the undrained strength increases steadly with depth (Fig. 5). One of the reinforced embankments was reinforced with four layers of non-woven geotextiles and will be referred hereafter by the code 4 RA. The first layer, placed directly on the foundation soil, had a tensile strength of 18 kN/m and a mass per unit area equal to 280 g/m2 (Fig. 5(a)). Above this layer three other non-woven geotextile layers (0.3 m spacing), with tensile strength of 8.3 kN/m each and mass per unit area of 180 g/m2, were installed. The other reinforced embankment (code 4RB) was reinforced with a single
Fig. 5. Case history 4 (Loke et al., 1994).
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geotextile layer with a tensile strength of 200 kN/m installed at the fill-subgrade interface, as shown in Fig. 5(b). In all cases a trench was excavated alongside the embankment toe possibly for drainage or to facilitate failure. Additional information on the materials are presented in Table 1. The unreinforced embankment failed with a height of 4 m and embankments 4RA and 4RB failed with heights of 4.2 m and 6 m, respectively. The first run of the program used in the present work for the unreinforced embankment led to a factor of safety at failure equal to 1.41 (modified Bishop’s method), therefore with a significant deviation from the expected value of one. This difference may be attributed to inaccuracies of the method employed or quality of the input data used in the calculations. Because the same method yielded good results for other case histories investigated in the preset work, it is assumed at this stage that this difference may be associated with uncertanities on the determination of the undrained strength in the crust in the soft soil surface, due to the presence of organic matter (leaves and roots) that may significantly affect the results obtained in vane tests. Note that other reasons for this discrepancy could be presented, such as drainage of the soft ground during construction or scatter or different values of shear vane test results under that particular embankment. Nevertheless, in order to allow the comparison between predictions for reinforced and unreinforced embankments under the same conditions the result (height at failure) obtained for the unreinforced embankment was used to backanalyse the undrained strength along the crust depth assuming that the values of undrained strength obtained by vane tests below the crust were accurate. This procedure led to the distribution of undrained strength with depth given in Fig. 5, which was then used for the analysis of the reinforced embankments. (Additional information on this case history can also be found in Bergado et al. (1994)). (e) Case History 5 (Rowe et al., 1995) Rowe et al. (1995) present a detailed and comprehensive study on the failure of a trial reinforced embankment built on a 10 m deep soft foundation, as shown in Fig. 6. The undrained strength of the foundation soil obtained by field vane tests showed some scatter but varied approximately linearly with depth. The average vane
Fig. 6. Case history 5 (Rowe et al., 1995).
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test results are presented in Fig. 6 and in Table 1 and were used for the stability analysis. A sandy fill material was employed and its main properties are also summarised in Table 1. A woven geotextile (Nicolon 68300) was used as reinforcement, being installed 0.4 m above the foundation surface. The reinforcement had a mass per unit area equal to 631 g/m2, tensile strength of 216 kN/m, tensile strain at failure equal to 13% and average tensile stiffness of 1920 kN/m (secant stiffness of 1466 kN/m at 5% strain). The failure mechanism of the embankment started when it reached a height of 8.2 m. Fig. 6 also shows the failure mechanisms identified in this case history (Rowe et al., 1995). Further information on this case history can also be found in Rowe and Gnanendran (1994). (f) Case History 6 (Schaefer and Duncan, 1988) Schaefer and Duncan (1988) describe the failure of reinforced and unreinforced test embankments constructed on a 10 m deep soft silty clay deposit, as shown in Fig. 7. The soft foundation has a thin crust at its surface and the undrained strength presented in Fig. 7 was obtained by field vane tests. One of the reinforced embankments (referred hereafter by the code 6RA) had a geogrid Tensar SR2 installed at its base and failed when its height reached 6 m. The other reinforced embankment (6RB) had a geocell at its base end failed with a height equal to 4.5 m. The geocell was formed using the same grid placed in an upright position forming a mattress. Unfortunately, the geometrical characteristics of this mattress are not available to the knowledge of the authors of the present work. Two unreinforced embankments (codes 6UA and 6UB) were also failed in different occasions and presented failures heights equal to 4.0 m (6UA) and 5.1 m (6UB). The main characteristics of the materials in these embankments are summarised in Table 1. The index tensile strength of the geogrid reinforcement is 69 kN/m with a strain at failure equal to 17% (McGown, 1982). However, because the mobilised tensile strength of this reinforcement depends on the rate of strain applied during
Fig. 7. Case history 6 (Schaefer and Duncan, 1988).
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loading, this value has to be corrected to account for this dependency. The period of construction of the reinforced embankment 6RA up to failure lasted about 18 days, which yields to an average strain rate of 6.6]10~4 %/min. According to McGown (1982), for this level of strain rate the index tensile strength of this geogrid must be reduced by 35% to obtain the expected mobilised tensile strength at failure. Doing so one obtains for the expected geogrid tensile strength at failure the value 45.2 kN/m, which was the one used in the backanalysis of the geogrid reinforced test embankment. Due to the complexity of the analysis for embankment 6RB and lack of relevant data, particularly with regard to the mobilised tensile force in the geocell, the result of this embankment was analysed by the analytical solution only. Additional information on materials and construction details of the case histories described above can be found in their original works and in Silva (1996).
4. Results obtained 4.1. Slip circle analyses Table 2 summarises the predictions of safety factors at failure for reinforced embankments by methods of analysis based on slip circles. It can be observed that in spite of the simplicity of the methods the predicted values generally compare reasonably well with unity, with typical deviations smaller than 0.07 in most cases. The greatest deviations (of the order of 0.18) were observed for case histories 4 and 2 (MBF approach). This can be attributed to uncertanties related to the accuracy of the undrained strength of the subgrade and to the simplified approach to deal with it for case history 4, as described earlier in this work. The two different slip circle methods also predicted similar values of safety factor at failure. In spite of the limited amount of data, the results obtained suggest that the hypothesis of horizontal force in the reinforcement is appropriate in this type of analysis. This was also observed by Rowe and Soderman (1984). Table 2 Predicted safety factors at failure — circular slip surfaces Case history
MBF
MBM
USCE
1! 2 3 4 (4RA) 4 (4RB) 5
1.012 0.810 0.977 1.181/1.116" 1.051/1.085" 1.045
0.979 0.870 0.982 1.159 1.059 1.036
0.959 0.911 0.970 1.179 1.056 0.941
6 (6RA)
1.037
1.035
0.970
Notes: !Reinforced embankment did not fail at final height. "Without and with a tension crack at the embankment surface, respectively;
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It is important to note the accurate results of 0.97 to 1.037 (depending on the method considered) for the predicted safety factor for case history 6RA (geogrid reinforced embankment) at failure. This shows the importance of using realistic values of reinforcement tensile strengths for reinforcements whose tensile characteristics are sensitive to the strain rate applied. Similar good agreement between predicted and observed strength of reinforced sand was observed by Palmeira (1987) and Palmeira and Milligan (1989) using the same type of geogrid and the same approach to estimate reinforcement tensile strength. Analyses of stability considering a tension crack at the surface of cohesive fills soils were also conducted and yielded similar results (Table 2, case history 4) due to the low values of soil cohesion ()10 kPa). The depth of the tension crack in these cases was estimated using the traditional expression derived from Rankine’s earth pressure theory. From the results presented in Tables 1 and 2 one can observe that for the situations where the thickness of the soft soil is small compared to the width of the embankment, the stronger the reinforcement the greater the ratio between reinforced and unreinforced embankment heights at failure. The results of embankment heights at failure (Table 1) also emphasize the limited contribution from the reinforcement for lightly reinforced embankments (case history 4 — embankment 4RA) or for embankments on thicker soft soil layers (case history 3). Increases on the unreinforced embankment heights at failure up to 57% were observed for the reinforced cases (Table 1). It should be pointed out that neither Delmas et al (1996) nor Rowe et al (1995) reported the failure of unreinforced embankments. For the sake of the exercise the use of the modified Bishop’s method in these cases predicted unreinforced fill heights at failure equal to 8.20 m and 6.26 m, respectively. These predicted unreinforced embankment heights at failure are also presented in Table 1 for comparison purposes. Figs. 8—10 presents the comparison between observed and predicted circular failure surfaces. As expected in total stress analysis of this type the predicted failure surfaces
Fig. 8. Predicted and observed failure surfaces — Case history 3.
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Fig. 9. Predicted and observed failure surfaces — Case history 4.
are not as accurate as the factors of safety obtained. With the exception of case history 5 the predicted failure mechanisms in the other case histories involved a larger soil mass than the failure surfaces actually observed. Nevertheless, it is interesting to note that the methodology predicted rather well that the critical failure mechanism in case history 5 would pass behind the reinforcement edge (Fig. 10). 4.2. Analytical solution For the use of the analytical solution some approximations had to be made in some cases and are described as follows. Actually, this approach would not be strictly applicabe for case histories 2 and 4, because of the presence of a channel and an excavation close to the toe of the embankments, respectively, besides the crust at the
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Fig. 10. Predicted and observed failure surfaces — Case history 5.
Table 3 Predictions by the analytical method Case history
F 3
¹ predicted! (kN/m) .!9
¹ observed (kN/m) .!9
1 2 3 4RA 4RB 5 6RA 6RB
0.93 0.99 0.97 1.68 1.26 0.98 1.01 1.11
152 57 505 208 332 260 158 —
61 60 225 42.9 200 216" 45.2 —
Notes: !See limitations of the approach in the text; "Reinforcement did not fail.
foundation surface in case history 4. Nevertheless, the solution was also applied to these cases for the sake of the exercise. For case history 4 an average linear variation of undrained strength with depth (yielding S "24 kPa and o"0.6 kPa/m) was 60 assumed for the calculations. In case history 3 a constant mean undrained strength of 34 kPa was assumed for the soft soil and in case history 6 the presence of the thin crust at the surface was neglected. Table 3 summarizes the comparison between predictions by the analytical solution (for a"1) and the results obtained for the reinforced embankments. With the exception of case history 4 the predicted values of safety factor also compare well with unity. The large deviations observed in case history 4 are likely to have been caused by the presence of the excavation at the toe of the embankments (which is not considered by the method) and by the approximate foundation undrained strength variation with depth assumed in the calculations. It is interesting to note that despite the presence of a channel close to the embankment toe in case history 2, the predicted factor of safety
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was equal to 0.99. The results for case history 4 emphasize the need for caution when making rough approximations for the use of more simply applicable methods of analysis, which one may be tempeted to do in some preliminary safety factor estimates in routine works. The required reinforcement strength for F equal to one predicted for the 3 case histories was significantly overestimated in most of the cases analysed by the analytical solution. This may be due to the following reasons. Firstly, the presence of some cohesion in the fill material, that may have been neglected in some case histories and which was also not considered in the method as proposed, can reduce significantly the lateral active trust in the fill and consequently the required reinforcement force. Secondly, the value of the computed reinforcement force is very
Fig. 11. Observed and predicted bearing capacity factors by the analytical solution — reinforced embankments.
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Fig. 12. Observed and predicted bearing capacity factors by the analytical solution — unreinforced embankments.
sensitive to the undrained strength at the foundation surface, which itself is highly sensitive to shear testing conditions, test data fitting and approximations. Thirdly, some drainage is likely to occur at the foundation surface and the interface shear between reinforcement and soft soil would take place under drained (or partially drained) rather than undrained conditions. Therefore, the results suggest that for the estimate of required reinforcement forces the analytical solution should be used only when the factors above are accounted for appropriately and with a sound engineering judgement. Figs. 11 and 12 present comparisons between observed and predicted apparent bearing capacity factors (N and N ) by the analytical solution for reinforced and #3 #0 unreinforced embankments, respectively. The apparent bearing capacity factor was defined as the ratio between the vertical stress at the foundation surface (cH) at failure and the undrained strength at the soft foundation surface (S ). The results compare 60 resonably well, particularly for the reinforced embankments, with the restrictions commented above regarding case history 4 and also with the exception of case history 6UB. Fig. 11 also shows the theoretical curve for a"0 for the reinforced case but it is clear that the best fit for the field results is obtained for a"1. For the unreinforced embankments the value of a varied between !0.67 and !0.47. Despite the limited amount of data, these results suggest that the analytical method, when applicable, may provide quick and reliable estimates for preliminary analyses.
5. Conclusions This work presented backanalyses of trial reinforced embankments presented in the literature. Two slip circle methods and an analytical method were employed to
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estimate the safety factor of six trial embankments at their failure heights. The main conclusions are summarised below. z In spite of the limited amount of test embankment data available, the results obtained suggest that the simple slip circle methods employed to estimate the factor of safety can be useful tools for this type of analysis if the properties and parameters of the materials involved are accurately determined. In most of the cases the deviation of the predicted safety factor at failure from the reference unity value was smaller than 0.07. z The assumption of the reinforcement force acting horizontally in the slip circle methods proved to be satisfactory. z Both slip circle methods used yielded similar values of safety factors for the case histories analysed. z Despite its simplicity the analytical solution for the safety factor of reinforced embankments on soft soil presented an accuracy comparable to the slip circle methods. Under controlled and well-defined conditions this method can provide quick estimates of safety factors of reinforced embankments on soft soils for preliminary design investigations. The field results were best fitted for a"1 for reinforced embankments, while a varied between !0.67 and !0.47 for unreinforced embankments. However, the analytical solution overestimated the required tensile reinforcement force for the case histories analysed. This can be attributed to uncertanities related to the value of parameters such as soft soil undrained strength at surface, fill characteristics and the possibility of drainage at the reinforcement— subgrade interface. z The backanalysis of an embankment reinforced by a geosynthetic layer with a significant strain rate dependency also yielded satisfactory results. However, it is important to point out that for an accurate prediction of the factor of safety under these circumstances it is of utmost importance a thorough knowledge of the relation between reinforcement tensile strength and rate of strain, which was possible in the present case. z This work indicates that total stress limit equilibrium stability analysis, using a circular slip surface, provides a good measure for safety factor of reinforced embankment. However, the actual slip surface and hence, the location of maximum reinforcement force, is not predicted very well. z The limited amount of data on field trial reinforced embankments suggests that even in the case of well-known soils and reinforcement relevant parameters a minimum factor of safety greater than 1.2 would be recommended when using traditional limit equilibrium methods of analysis, such as the ones employed in the present work.
Notation B c
embankment base width (not including berms, when present); fill material cohesion;
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D F F 0 F 3 H H 0 H 3 k ! n N #0 N #3 S 6 S 60 ¹ ¹ .!9 z a / c o
291
depth of soft soil below the embankment; factor of safety; safety factor for the unreinforced embankment; safety factor for reinforced embankment; embankment height; unreinforced embankment failure height; reinforced embankment failure height; Rankine’s active earth pressure coefficient; slope of the embankment; bearing capacity factor for the unreinforced case; bearing capacity factor for the reinforced case; soft soil undrained strength undrained strength at the surface of the soft soil; tensile force in the reinforcement; reinforcement tensile strength; depth; ratio between mobilised shear stress and undrained strength at the soft foundation surface; fill material friction angle; soil unit weight; rate of increase of undrained strength with depth.
Acknowledgements The authors would like to thank CAPES—Brazilian Ministry of Education and CNPq — Brazilian Research Council for sponsoring part of the research programme that made this work possible.
References Bergado, D.T., Long, P.V., Lee, C.H., Loke, K.H., Werner, G., 1994. Performance of reinforced embankment on soft Bangkok clay with high- strength geotextile reinforcement. Geotextiles and Geomembranes 13 (6—7), 403—420. Delmas, P., Queyroi, D., Quaresma, M., Amand, D.S., Peuch, A., 1990. Failure of an experimental embankment on soft soil reinforced with geotextile: Guiche. Proceedings of the 4th Internat. Conf. on Geotextiles, Geomembranes and Related Products, The Hague, Vol. 3, pp. 1019—1025. Jewell, R.A., 1987. The mechanics of reinforced embankments on soft soils. OUEL Report No. 071/87, University of Oxford, UK. Jewell, R.A., 1996. Soil reinforcement with geotextiles. CIRIA Special Publication 123, UK, 332 p. Kaniraj, S.R., 1994. Rotational stability of unreinforced and reinforced embankments on soft soils. Geotextiles and Geomembranes 13 (11), 707—726. Kaniraj, S.R., 1996. Directional dependency of reinforcement force in reinforced embankments on soft soils. Geotextiles and Geomembranes 14 (9), 507—519. Leshchinsky, D., 1987. Short-term stability of reinforced embankments over clay foundation. Soils and Foundations 27 (3), 43—57.
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Loke, K.H., Ganeshan, V., Wener, G., Bergado, D.T., 1994. Composite behaviour of geotextile reinforced embankment on soft clay. Proceedings of the 5th Interlat Conf. on Geotextiles, Geomembranes and Related Products Vol. 1, 25—28. Low, B.K., Wong, H.S., Lim, C., Broms, B.B., 1990. Slip circle analysis of reinforced embankments on soft ground. Geotextiles and Geomembranes 9 (2), 165—181. Palmeira, E.M. 1987. The study of soil reinforcement interaction by means of large scale laboratory tests. D.Phil. Thesis, University of Oxford, UK, 238 p. Palmeira, E.M., Milligan, G.W.E., 1989. Large scale laboratory tests on reinforced sand. Soils and Foundations 29 (1), 1—18. Rowe, R.K., 1997. Reinforced embankment behaviour: Lessons from a number of case histories. Proc. Interna Symp. on Recent Developments in Soil and Pavement Mechanics, Rio de Janeiro, Brazil, Vol. 1, 147-160. Rowe, R.K., Gnanendran, C.T., 1994. Geotextile strain in a full scale reinforced test embankment. Geotextiles and Geomembranes 13 (2), 781—806. Rowe, R.K., Gnanendran, C.T., Landva, A.O., Valsangkar, A.J., 1995. Construction and performance of a full-scale geotextile reinforced test embankment. Sackville, New Brunswick. Canadian Geotechnical Journal 32, 512—534. Rowe, R.K., Soderman, K.L., 1984. Comparison of predicted and observed behaviour of two test embankments. Geotextiles and Geomembranes 1 (2), 143—160. Rowe, R.K., Soderman, K.L., 1985. Geotextile reinforcement of embankments on peat. Geotextiles and Geomembranes 2 (4), 277—298. Sabhahit, N., Basudhar, P.K., Madhav, M.R., 1994. Generalized stability analysis of reinforced embankments on soft clay. Geotextile and Geomembranes 13 (12), 765—780. Schaefer, V.R., Duncan, J.M., 1988. Finite element analysis of the St. Alban test embankments. Proc. of the Symp. on Geosynthetics for Soil Improvement, ASCE Geotechnical Special Publication No. 18, ASCE, USA, Vol.1, pp. 158—177. Silva, A.R.L., 1996. The stability of geosynthetic reinforced embankments on soft soils. MSc Thesis, University of Brasilia, Brazil, 104 p (in Portuguese). USACE, 1970. Engineering and design stability of earth and rock-fill dams. Engineer Manual EM 1110-2-1902, Dept. of the Army, USA Corps of Engineers, Washington, DC, USA. Volman, W., Krekt, L., Risseeuw, P., 1977. Armature de traction en textile, un nouveau proce´de´ pour ame´liorer la stabilite´ des grands remblais sur sols mous. Proceedings Coll. Int. Sols Textiles, Paris, Vol. 1, pp. 55—59. van Leeuwen, J.H., Volman, W.J.J.G., 1976. Etude prospective du roˆle constructif des nappes Stabilenka dans les remblais de sable. Information Publication, Industrial Fabrics of Enka Glanzstoff, 30 p.
Backanalyses of geosynthetic reinforced embankments on soft soils Ennio M. Palmeira*, Jose H.F. Pereira, Antonio R.L. da Silva Department of Civil Engineering, University of Brası& lia, FT 70910-900 Brası& lia, DF, Brazil
Abstract Geosynthetic reinforcement can be effectively used to increase the factor of safety of embankments on soft soils, particularly for shallow soft foundations layers. Several design approaches can be found in the literature dealing with the design of reinforced embankments on weak subgrades. Unfortunately, only a few well-documented case histories of reinforced embankments which led to failure have been reported. This paper presents backanalyses of some reinforced embankments that can be found in the literature using stability analysis methods commonly employed in routine works. Predicted values of safety factors at failure heights were close to one, and in spite of the limited amount of data available the results obtained suggest that these rather simple methods are useful tools for predicting factors of safety of reinforced embankments when the required input data are available and accurate. Nevertheless, even in these cases the backanalyses of the reinforced embankments suggest the use of factors of safety greater than 1.2 in routine works. ( 1998 Elsevier Science Ltd. Keywords: Geosynthetic; Embankments; Soft soils; Foundations
1. Introduction Geosynthetics have been commonly used for the reinforcement of embankments on soft soils and the advantages and limitations of the reinforcement presence have been discussed elsewhere (e.g., Jewell, 1987; Rowe, 1997). Limit equilibrium method and solutions based on the theory of plasticity have been used for the analysis of this type of work. These methods assume that the tensile force mobilised in the reinforcement increases the factor of safety against global instability in a way which depends on the
*Corresponding author. Tel.: 55 61 273 7313; fax: 55 61 273 4644; e-mail: [email protected]. unb.br 0266—1144/98/$ — see front matter ( 1998 Elsevier Science Ltd. All rights reserved. PII: S 02 6 6— 1 14 4 ( 98 ) 0 00 1 4— 4
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method’s approach (Figs. 1(a) and (b). Some works in the literature dealing with the subject (Leshchinsky, 1987; Low et al., 1990; Kaniraj, 1994) present straightforward methods for the design of geosynthetic reinforced embankments for particular, but usual, cases. Most of the limit equilibrium methods available assume circular slip surfaces or the combination of circular and log spiral or plane surfaces. The force in the reinforcement can be assumed acting horizontally or inclined to the horizontal direction to some extent up to the limit of tangency to the slip surface. Low et al. (1990) and Kaniraj (1996) show that predicted tangential forces may be up to 50% smaller than predicted horizontal forces. The angle between the tangent to the failure surface, at the interception with the reinforcement direction, and the horizontal direction depends on the position and characteristics of the slip surface. So, if the reinforcement force is assumed inclined to the horizontal by a constant fraction of the tangential angle this procedure will lead to different reinforcement force inclinations depending on the position, dimensions and shape of the failure surface. Results presented by Sabhahit et al. (1994) suggest little influence of the reinforcement force inclination on the safety factor, although it is not clear if these authors investigated a fixed failure surface and varied the reinforcement force inclination or considered several different failure surfaces with constant reinforcement force inclination in their analyses. Indeed, the formation of a shear zone close to the embankment collapse will cause some deviation of the reinforcement force from its original direction. Large-scale direct shear tests on reinforced dense sand shows that deviation to be negligible at peak stress values (Palmeira, 1987; Palmeira and Milligan, 1989). Although in reinforced embankments on soft soil this deviation will certainly be larger than in stiff systems, significant values may only occur at large strains, when the operational conditions of the embankment may already be compromised. However, when a deformed reinforcement inside a shear zone is considered a more complex approach must be considered regarding equilibrium conditions. At present, an accurate way to predict the reinforcement force inclination based on field or laboratory test investigations is not available. In situations where cracks or light damages of the embankments can be neglected, probably a more consistent approach for the consideration of the inclination of the reinforcement force in limit equilibrium analysis would be first to find the critical slip surface assuming horizontal reinforcement forces and, then, for that critical surface, to investigate the influence of the reinforcement force inclination within reasonable limits. In this paper a rigorous and traditional approach for limit equilibrium analyses was assumed, where all the materials were considered perfectly rigid and failing simultaneously at their maximum strength. Therefore, the reinforcement force was assumed horizontal and failing at its maximum tensile strength. The data presented later in this work will show that this assumption yielded to predicted values that compared well with observed results. Analytical solutions, based or inspired on the theory of plasticity, are also available (Jewell, 1987, 1996) for the design of reinforced embankments where a different approach is used to consider the beneficial effect of the reinforcement. In this case it is
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assumed that the presence of the reinforcement induces favourable shear stresses on the foundation soil surface that increase the bearing capacity of the soft soil (Fig. 1(b)). With regard to the evaluation of the soft soil stability these solutions neglect the strength parameters of the fill material and the problem is treated in a similar way to the evaluation of bearing capacity of shallow foundations under undrained conditions. However, fill strength parameters are required for reinforcement force calculations (Jewell, 1996). The aim of this work is to carry out backanalyses of some trial reinforced embankments found in the literature in order to evaluate the accuracy of the different approaches described above.
2. Methods of analysis employed Two slip circle methods and an analytical solution were used to predict the safety factor of the test embankments studied. The first slip circle method employed was the traditional modified Bishop’s method. The contribution of the reinforcement can be taken into account by including the effect of its tangential and normal components at the slice base (inside the fill) on the general equilibrium of the slice (hereafter referred as MBF approach) or by adding the moment of the reinforcement force with respect to the circle center to the sum of resisting moments against sliding (MBM approach). Both approaches were considered in this study being the latter most commonly used in works such as the ones presented by Low et al. (1990) and Kaniraj (1994). The second slip circle method used was the one presented by the United States Army Corp of Engineers (USACE, 1970), hereafter referred as USCE method, where the factor of safety is obtained by trial and error conditioned to the closure of the force polygons of all slices. In the present study the interslice forces in this case were considered horizontal. Methods like the ones presented by Leshchinsky (1987), Low et al. (1990) and Kaniraj (1994) are not readily applicable to the cases investigated because the boundary conditions or material properties in the trial embankments are significantly different from the hypotheses assumed in those methods. For these reasons these methods were not employed in the present study, although some of them are based on or are very similar to the modified Bishop’s method used in this work. In all of the cases analysed the force mobilised in the geosynthetic was assumed horizontal (Fig. 1(a)) and equal to its tensile strength, as commented above. Computer programs developed at the University of Brasilia to obtain safety factors of reinforced soil structures by the methods described above were employed in this study. These programs allow different boundary conditions and any variation of undrained strength with depth, which is particularlly interesting for the present study. All the values of parameters related to the reinforcement and soils used in the calculations were obtained in the original works of the case histories studied, unless when stated otherwise. Analytical expressions for the factor of safety of reinforced and unreinforced embankments on soft soils (Jewell, 1996) were also employed to the test embankments
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Fig. 1. Methods of analysis used.
studied. The presence of a crust or a shallow channel at the surface of the soft layer limits the application of these expressions and some approximations were required in some cases. Jewell (1996) presents the following analytical solutions to obtain safety factors and reinforcement forces for embankments on soft soils (Fig. 1(b). For a foundation soil with uniform strength and limited depth:
C C
D
S 8D#2nH F" 6 , 0 cH 2D#k H !
(1)
D
nH S , F " 6 4#(1#a) 3 cH D
C
(2)
D
anD k # ! . ¹ "cH2 .!9 4D#(1#a)nH 2
(3)
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277
For a foundation soil with strength increasing with depth:
C
S
D
2(1#a)onH S onH F or F " 60 4# #2 , 3 0 cH S S 60 60 anS k 60# ! . ¹ "cH2 .!9 F cH 2 3 Jewell (1996) suggests the use of the expressions above under the condition
C
F cH 3 *6, S 6
D
(4) (5)
(6)
where F and F are safety factors for unreinforced and reinforced embankments, 0 3 respectively; ¹ is the required reinforcement force; S , soft soil undrained strength; .!9 6 n, slope of the embankment (Fig. 1(a)); a, ratio between mobilised shear stress and undrained strength at the subgrade surface (Fig. 1(b)); H, embankment height; k , ! Rankine’s active earth pressure coefficient; D, thickness of the soft subgrade; c, fill unit weight; S , undrained strength at the surface of the subgrade; and o, the rate of 60 increase of undrained strength with depth. A full mobilization of the undrained strength at the surface of the soft soil (a"1) was assumed for the analyses presented in this work. It should be pointed out that expression (4) is valid for reinforced and unreinforced embankments. However, for the latter case a is given by the expression below and the solution is obtained by trial and error: k F cH a"! ! 0 0 . (7) 2nS 60 In all the cases analysed, the foundation soil was assumed to behave under undrained conditions with its friction angle under total stress conditions equals to zero. The fill materials were assumed to be sheared under perfectly drained conditions.
3. Case histories analysed Six case histories of embankments led to failure were investigated. Their main characteristics are summarised below. (a) Case History 1 (Volman et al., 1977) In this case history two trial embankments constructed on a 4.2 m deep soft subgrade consisting of layers of peat and clay were failed. One of the embankments was unreinforced and the other was reinforced with a layer of a woven geotextile (Stabilenka N99), as shown in Fig. 2. Table 1 summarises the main characteristics of the materials involved in this case. The reinforcement had a tensile strength of 61 kN/m, deformation at failure equal to 20% and average tensile stiffness equal to
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Fig. 2. Case history 1 (Volman et al., 1977).
258 kN/m. Fill material properties are not provided and a large variation of cohesions and friction angles obtained in terms of total stresses for the foundation soils can be observed. The authors report that the unreinforced embankment failed when it reached a height of 3.5 m, while the reinforced embankment reached a height of 4.5 m without failure. Because the determination of the undrained strength of the foundation soil in this case history is very complex, one can backanalyse the unreinforced embankment to estimate the average foundation strength in order to infer how close to failure the reinforced embankment was at its final height. Having in mind that for low embankments variations of the fill friction angle have little influence on the factor of safety and that the fill material used was sand, a friction angle of 30° can be adopted for estimate purposes. Using the modified Bishop’s method one can obtain an average undrained strength of 12 kPa for the foundation soil for a safety factor equal to unity at the observed failure height of 3.5 m. If this undrained strength is used to analyse the stability of the reinforced embankment at its final height (4.5 m) a safety factor of 1.012 is obtained. Despite the rather crude analysis, but in view of the satisfactory accuracy observed for this method for other embankments to be discussed later in the present work, this value suggests that the reinforced embankment might be close to failure at the end of construction. The assumption of a reinforced embankment failure height equal to 4.5 m is then conservative. Further information on this work can also be found in van Leeuwen and Volman (1976). (b) Case History 2 (Rowe and Soderman, 1984) Rowe and Soderman (1984, 1985) present a study of stability analysis of reinforced embankments combining limit equilibrium and finite element methods. The Authors report the construction of trial embankments on a 3.3 m thick soft subgrade with an average undrained strength of 8 kPa (Fig. 3 and Table 1). The tensile strength of the reinforcement (Stabilenka 200, 450 g/m2) is 215 kN/m and its tensile stiffness 2000 kN/m. The authors report that the unreinforced and the reinforced embankments failed with heights equal to 1.75 and 2.75 m, respectively (Rowe and Soderman, 1985). Failure of the reinforced embankment was governed by fabric pull-out from the
Rowe et al., 1995 Schaefer and Duncan, 1988
Volman et al., 1977 Rowe and Soderman, 1984 Delmas et al., 1990 Loke et al., 1994
Reference
18 18 19 19.5 19.5 19.6 16.9$ 18.2
c (kN/m3) 0 0 9 10 10 0 0 0
c° (kPa)
Fill data
30 33 35 30 30 42.3 34 34
/° ( @) 3.9! 3.3 24 11 11 10 10 10
D (m) 16 61 50 24 24 34 21 —
B (m) 12 8 43 51 51 16 48 48
S 60 (kPa) — — 32 12 12 — 11 11
S 6. (kPa)
Soft soil data
0 0 0 3.71 3.71 2.50 2.26 2.26
o (kPa/m) 61 215 225 42.9# 200 216 45.2 —-
¹ .!9 (kN/m)
6.26" 4.0/5.1% —
3.5 1.75 8.20" 4.0
H 0 (m)
4.5 2.75 8.75 4.2 6.0 8.2 6.0 4.5
H 3 (m)
Notes: Except when otherwise indicated, all the data presented were obtained from the original works; See also Figs. 1—7 for relevant data on soft foundation soils and additional information. c"specific weight, c°" cohesion, /@"friction angle, D"depth of soft soil below the embankment, B"embankment base width (not including berms, when present), S "undrained strength at the foundation surface, S "minimum foundation undrained strength (Fig. 1), o"rate of increase of undrained strength 60 6. with depth; ¹ "reinforcement tensile strength, H "unreinforced embankment failure height and H "reinforced embankment failure height. .!9 0 3 !D"4.2 m for the unreinforced embankment. "Predictions from the modified Bishop’s method. #Sum of the tensile strength of the four reinforcement layers used. $c"18.1 kN/m3 for the unreinforced embankment. %Failure heights for unreinforced embankments 6UA and 6UB, respectively.
1 2 3 4 (4RA) (4RB) 5 6 (6RA) (6RB)
Case history no.
Table 1 Summary of the characteristics of the case histories studied
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Fig. 3. Case history 2 (Rowe and Soderman, 1984).
Fig. 4. Case history 3 (Delmas et al., 1990).
soil at fabric strains between 4% and 5%, mobilising a force in the reinforcement at this stage of the order of 60 kN/m. Limit equilibrium analyses (Bishop’s method) of these embankments performed by the authors predicted embankment heights at failure equal to 1.7 m and 2.55 m for the unreinforced and the reinforced cases, respectively. These predictions compare well with the observed embankment heights at failure in both cases. (c) Case History 3 (Delmas et al., 1990) Delmas et al. (1990) present a case history of a reinforced embankment built on a 24 m deep soft subgrade. The geometrical characteristics of this embankment are presented in Fig. 4 and the main properties of the reinforcement and soils are listed in Table 1. The undrained strength of the soft foundation varied between 32 kPa and 43 kPa throughout its depth. A geotextile (Bidim Rock) with a tensile strength (wide
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281
strip test) of 225 kN/m, 2250 kN/m tensile stiffness and 10% strain at failure was used as reinforcement. The reinforcement layer was installed on a 1 m granular blanket on the soft foundation. The reinforced embankment failed when it reached a height of 8.75 m. Fig. 4 shows the location of the observed failure surface. (d) Case History 4 (Loke et al, 1994) In this case, two geosynthetic reinforced embankments and one unreinforced embankment with similar geometrical characteristics were led to failure on a 11 m deep soft subgrade. The soft soil presents a crust at its top (3 m deep), below which the undrained strength increases steadly with depth (Fig. 5). One of the reinforced embankments was reinforced with four layers of non-woven geotextiles and will be referred hereafter by the code 4 RA. The first layer, placed directly on the foundation soil, had a tensile strength of 18 kN/m and a mass per unit area equal to 280 g/m2 (Fig. 5(a)). Above this layer three other non-woven geotextile layers (0.3 m spacing), with tensile strength of 8.3 kN/m each and mass per unit area of 180 g/m2, were installed. The other reinforced embankment (code 4RB) was reinforced with a single
Fig. 5. Case history 4 (Loke et al., 1994).
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geotextile layer with a tensile strength of 200 kN/m installed at the fill-subgrade interface, as shown in Fig. 5(b). In all cases a trench was excavated alongside the embankment toe possibly for drainage or to facilitate failure. Additional information on the materials are presented in Table 1. The unreinforced embankment failed with a height of 4 m and embankments 4RA and 4RB failed with heights of 4.2 m and 6 m, respectively. The first run of the program used in the present work for the unreinforced embankment led to a factor of safety at failure equal to 1.41 (modified Bishop’s method), therefore with a significant deviation from the expected value of one. This difference may be attributed to inaccuracies of the method employed or quality of the input data used in the calculations. Because the same method yielded good results for other case histories investigated in the preset work, it is assumed at this stage that this difference may be associated with uncertanities on the determination of the undrained strength in the crust in the soft soil surface, due to the presence of organic matter (leaves and roots) that may significantly affect the results obtained in vane tests. Note that other reasons for this discrepancy could be presented, such as drainage of the soft ground during construction or scatter or different values of shear vane test results under that particular embankment. Nevertheless, in order to allow the comparison between predictions for reinforced and unreinforced embankments under the same conditions the result (height at failure) obtained for the unreinforced embankment was used to backanalyse the undrained strength along the crust depth assuming that the values of undrained strength obtained by vane tests below the crust were accurate. This procedure led to the distribution of undrained strength with depth given in Fig. 5, which was then used for the analysis of the reinforced embankments. (Additional information on this case history can also be found in Bergado et al. (1994)). (e) Case History 5 (Rowe et al., 1995) Rowe et al. (1995) present a detailed and comprehensive study on the failure of a trial reinforced embankment built on a 10 m deep soft foundation, as shown in Fig. 6. The undrained strength of the foundation soil obtained by field vane tests showed some scatter but varied approximately linearly with depth. The average vane
Fig. 6. Case history 5 (Rowe et al., 1995).
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283
test results are presented in Fig. 6 and in Table 1 and were used for the stability analysis. A sandy fill material was employed and its main properties are also summarised in Table 1. A woven geotextile (Nicolon 68300) was used as reinforcement, being installed 0.4 m above the foundation surface. The reinforcement had a mass per unit area equal to 631 g/m2, tensile strength of 216 kN/m, tensile strain at failure equal to 13% and average tensile stiffness of 1920 kN/m (secant stiffness of 1466 kN/m at 5% strain). The failure mechanism of the embankment started when it reached a height of 8.2 m. Fig. 6 also shows the failure mechanisms identified in this case history (Rowe et al., 1995). Further information on this case history can also be found in Rowe and Gnanendran (1994). (f) Case History 6 (Schaefer and Duncan, 1988) Schaefer and Duncan (1988) describe the failure of reinforced and unreinforced test embankments constructed on a 10 m deep soft silty clay deposit, as shown in Fig. 7. The soft foundation has a thin crust at its surface and the undrained strength presented in Fig. 7 was obtained by field vane tests. One of the reinforced embankments (referred hereafter by the code 6RA) had a geogrid Tensar SR2 installed at its base and failed when its height reached 6 m. The other reinforced embankment (6RB) had a geocell at its base end failed with a height equal to 4.5 m. The geocell was formed using the same grid placed in an upright position forming a mattress. Unfortunately, the geometrical characteristics of this mattress are not available to the knowledge of the authors of the present work. Two unreinforced embankments (codes 6UA and 6UB) were also failed in different occasions and presented failures heights equal to 4.0 m (6UA) and 5.1 m (6UB). The main characteristics of the materials in these embankments are summarised in Table 1. The index tensile strength of the geogrid reinforcement is 69 kN/m with a strain at failure equal to 17% (McGown, 1982). However, because the mobilised tensile strength of this reinforcement depends on the rate of strain applied during
Fig. 7. Case history 6 (Schaefer and Duncan, 1988).
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loading, this value has to be corrected to account for this dependency. The period of construction of the reinforced embankment 6RA up to failure lasted about 18 days, which yields to an average strain rate of 6.6]10~4 %/min. According to McGown (1982), for this level of strain rate the index tensile strength of this geogrid must be reduced by 35% to obtain the expected mobilised tensile strength at failure. Doing so one obtains for the expected geogrid tensile strength at failure the value 45.2 kN/m, which was the one used in the backanalysis of the geogrid reinforced test embankment. Due to the complexity of the analysis for embankment 6RB and lack of relevant data, particularly with regard to the mobilised tensile force in the geocell, the result of this embankment was analysed by the analytical solution only. Additional information on materials and construction details of the case histories described above can be found in their original works and in Silva (1996).
4. Results obtained 4.1. Slip circle analyses Table 2 summarises the predictions of safety factors at failure for reinforced embankments by methods of analysis based on slip circles. It can be observed that in spite of the simplicity of the methods the predicted values generally compare reasonably well with unity, with typical deviations smaller than 0.07 in most cases. The greatest deviations (of the order of 0.18) were observed for case histories 4 and 2 (MBF approach). This can be attributed to uncertanties related to the accuracy of the undrained strength of the subgrade and to the simplified approach to deal with it for case history 4, as described earlier in this work. The two different slip circle methods also predicted similar values of safety factor at failure. In spite of the limited amount of data, the results obtained suggest that the hypothesis of horizontal force in the reinforcement is appropriate in this type of analysis. This was also observed by Rowe and Soderman (1984). Table 2 Predicted safety factors at failure — circular slip surfaces Case history
MBF
MBM
USCE
1! 2 3 4 (4RA) 4 (4RB) 5
1.012 0.810 0.977 1.181/1.116" 1.051/1.085" 1.045
0.979 0.870 0.982 1.159 1.059 1.036
0.959 0.911 0.970 1.179 1.056 0.941
6 (6RA)
1.037
1.035
0.970
Notes: !Reinforced embankment did not fail at final height. "Without and with a tension crack at the embankment surface, respectively;
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It is important to note the accurate results of 0.97 to 1.037 (depending on the method considered) for the predicted safety factor for case history 6RA (geogrid reinforced embankment) at failure. This shows the importance of using realistic values of reinforcement tensile strengths for reinforcements whose tensile characteristics are sensitive to the strain rate applied. Similar good agreement between predicted and observed strength of reinforced sand was observed by Palmeira (1987) and Palmeira and Milligan (1989) using the same type of geogrid and the same approach to estimate reinforcement tensile strength. Analyses of stability considering a tension crack at the surface of cohesive fills soils were also conducted and yielded similar results (Table 2, case history 4) due to the low values of soil cohesion ()10 kPa). The depth of the tension crack in these cases was estimated using the traditional expression derived from Rankine’s earth pressure theory. From the results presented in Tables 1 and 2 one can observe that for the situations where the thickness of the soft soil is small compared to the width of the embankment, the stronger the reinforcement the greater the ratio between reinforced and unreinforced embankment heights at failure. The results of embankment heights at failure (Table 1) also emphasize the limited contribution from the reinforcement for lightly reinforced embankments (case history 4 — embankment 4RA) or for embankments on thicker soft soil layers (case history 3). Increases on the unreinforced embankment heights at failure up to 57% were observed for the reinforced cases (Table 1). It should be pointed out that neither Delmas et al (1996) nor Rowe et al (1995) reported the failure of unreinforced embankments. For the sake of the exercise the use of the modified Bishop’s method in these cases predicted unreinforced fill heights at failure equal to 8.20 m and 6.26 m, respectively. These predicted unreinforced embankment heights at failure are also presented in Table 1 for comparison purposes. Figs. 8—10 presents the comparison between observed and predicted circular failure surfaces. As expected in total stress analysis of this type the predicted failure surfaces
Fig. 8. Predicted and observed failure surfaces — Case history 3.
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Fig. 9. Predicted and observed failure surfaces — Case history 4.
are not as accurate as the factors of safety obtained. With the exception of case history 5 the predicted failure mechanisms in the other case histories involved a larger soil mass than the failure surfaces actually observed. Nevertheless, it is interesting to note that the methodology predicted rather well that the critical failure mechanism in case history 5 would pass behind the reinforcement edge (Fig. 10). 4.2. Analytical solution For the use of the analytical solution some approximations had to be made in some cases and are described as follows. Actually, this approach would not be strictly applicabe for case histories 2 and 4, because of the presence of a channel and an excavation close to the toe of the embankments, respectively, besides the crust at the
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Fig. 10. Predicted and observed failure surfaces — Case history 5.
Table 3 Predictions by the analytical method Case history
F 3
¹ predicted! (kN/m) .!9
¹ observed (kN/m) .!9
1 2 3 4RA 4RB 5 6RA 6RB
0.93 0.99 0.97 1.68 1.26 0.98 1.01 1.11
152 57 505 208 332 260 158 —
61 60 225 42.9 200 216" 45.2 —
Notes: !See limitations of the approach in the text; "Reinforcement did not fail.
foundation surface in case history 4. Nevertheless, the solution was also applied to these cases for the sake of the exercise. For case history 4 an average linear variation of undrained strength with depth (yielding S "24 kPa and o"0.6 kPa/m) was 60 assumed for the calculations. In case history 3 a constant mean undrained strength of 34 kPa was assumed for the soft soil and in case history 6 the presence of the thin crust at the surface was neglected. Table 3 summarizes the comparison between predictions by the analytical solution (for a"1) and the results obtained for the reinforced embankments. With the exception of case history 4 the predicted values of safety factor also compare well with unity. The large deviations observed in case history 4 are likely to have been caused by the presence of the excavation at the toe of the embankments (which is not considered by the method) and by the approximate foundation undrained strength variation with depth assumed in the calculations. It is interesting to note that despite the presence of a channel close to the embankment toe in case history 2, the predicted factor of safety
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was equal to 0.99. The results for case history 4 emphasize the need for caution when making rough approximations for the use of more simply applicable methods of analysis, which one may be tempeted to do in some preliminary safety factor estimates in routine works. The required reinforcement strength for F equal to one predicted for the 3 case histories was significantly overestimated in most of the cases analysed by the analytical solution. This may be due to the following reasons. Firstly, the presence of some cohesion in the fill material, that may have been neglected in some case histories and which was also not considered in the method as proposed, can reduce significantly the lateral active trust in the fill and consequently the required reinforcement force. Secondly, the value of the computed reinforcement force is very
Fig. 11. Observed and predicted bearing capacity factors by the analytical solution — reinforced embankments.
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Fig. 12. Observed and predicted bearing capacity factors by the analytical solution — unreinforced embankments.
sensitive to the undrained strength at the foundation surface, which itself is highly sensitive to shear testing conditions, test data fitting and approximations. Thirdly, some drainage is likely to occur at the foundation surface and the interface shear between reinforcement and soft soil would take place under drained (or partially drained) rather than undrained conditions. Therefore, the results suggest that for the estimate of required reinforcement forces the analytical solution should be used only when the factors above are accounted for appropriately and with a sound engineering judgement. Figs. 11 and 12 present comparisons between observed and predicted apparent bearing capacity factors (N and N ) by the analytical solution for reinforced and #3 #0 unreinforced embankments, respectively. The apparent bearing capacity factor was defined as the ratio between the vertical stress at the foundation surface (cH) at failure and the undrained strength at the soft foundation surface (S ). The results compare 60 resonably well, particularly for the reinforced embankments, with the restrictions commented above regarding case history 4 and also with the exception of case history 6UB. Fig. 11 also shows the theoretical curve for a"0 for the reinforced case but it is clear that the best fit for the field results is obtained for a"1. For the unreinforced embankments the value of a varied between !0.67 and !0.47. Despite the limited amount of data, these results suggest that the analytical method, when applicable, may provide quick and reliable estimates for preliminary analyses.
5. Conclusions This work presented backanalyses of trial reinforced embankments presented in the literature. Two slip circle methods and an analytical method were employed to
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estimate the safety factor of six trial embankments at their failure heights. The main conclusions are summarised below. z In spite of the limited amount of test embankment data available, the results obtained suggest that the simple slip circle methods employed to estimate the factor of safety can be useful tools for this type of analysis if the properties and parameters of the materials involved are accurately determined. In most of the cases the deviation of the predicted safety factor at failure from the reference unity value was smaller than 0.07. z The assumption of the reinforcement force acting horizontally in the slip circle methods proved to be satisfactory. z Both slip circle methods used yielded similar values of safety factors for the case histories analysed. z Despite its simplicity the analytical solution for the safety factor of reinforced embankments on soft soil presented an accuracy comparable to the slip circle methods. Under controlled and well-defined conditions this method can provide quick estimates of safety factors of reinforced embankments on soft soils for preliminary design investigations. The field results were best fitted for a"1 for reinforced embankments, while a varied between !0.67 and !0.47 for unreinforced embankments. However, the analytical solution overestimated the required tensile reinforcement force for the case histories analysed. This can be attributed to uncertanities related to the value of parameters such as soft soil undrained strength at surface, fill characteristics and the possibility of drainage at the reinforcement— subgrade interface. z The backanalysis of an embankment reinforced by a geosynthetic layer with a significant strain rate dependency also yielded satisfactory results. However, it is important to point out that for an accurate prediction of the factor of safety under these circumstances it is of utmost importance a thorough knowledge of the relation between reinforcement tensile strength and rate of strain, which was possible in the present case. z This work indicates that total stress limit equilibrium stability analysis, using a circular slip surface, provides a good measure for safety factor of reinforced embankment. However, the actual slip surface and hence, the location of maximum reinforcement force, is not predicted very well. z The limited amount of data on field trial reinforced embankments suggests that even in the case of well-known soils and reinforcement relevant parameters a minimum factor of safety greater than 1.2 would be recommended when using traditional limit equilibrium methods of analysis, such as the ones employed in the present work.
Notation B c
embankment base width (not including berms, when present); fill material cohesion;
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D F F 0 F 3 H H 0 H 3 k ! n N #0 N #3 S 6 S 60 ¹ ¹ .!9 z a / c o
291
depth of soft soil below the embankment; factor of safety; safety factor for the unreinforced embankment; safety factor for reinforced embankment; embankment height; unreinforced embankment failure height; reinforced embankment failure height; Rankine’s active earth pressure coefficient; slope of the embankment; bearing capacity factor for the unreinforced case; bearing capacity factor for the reinforced case; soft soil undrained strength undrained strength at the surface of the soft soil; tensile force in the reinforcement; reinforcement tensile strength; depth; ratio between mobilised shear stress and undrained strength at the soft foundation surface; fill material friction angle; soil unit weight; rate of increase of undrained strength with depth.
Acknowledgements The authors would like to thank CAPES—Brazilian Ministry of Education and CNPq — Brazilian Research Council for sponsoring part of the research programme that made this work possible.
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