Investigating Time Dependent Behaviour of Reinforced and

Investigating Time Dependent Behaviour of Reinforced and Unreinforced Embankment Built on Soft Soil Capped with Crust Using Slope Stability Software

Abrahams Mwasha Faculty of Engineering, University of West Indies, St Augustine Campus, Trinidad and Tobago W. I.

ABSTRACT Soil crusting is not only important in crop production due to its influence in infiltration of soil and seeding emergence but has colossal engineering properties enhancing stability of an engineering structure erected on the soft soil. However the stability of any engineering structure erected on these soft soils capped with crust could be faced with unexpected failure if improperly designed for short-term and long-term service life. In order to achieve the objectives of this paper a comprehensive analyses on the stability and the amount of required tensile force to achieve a specific FOS was conducted by varying effective crust strength/thickness, foundation and embankment parameters. A method of slices is used in computer program GEO5 which can accommodate variable soil condition as well as pore water pressure parameters. Time-dependent behaviour of an embankment constructed on soft soil capped with crust of varying thickness and strength. is discussed.

KEYWORDS:

Crust strength and thickness, soft soil, consolidation, Time Factor,

Basal reinforcements

INTRODUCTION One of the major post–depositional processes, which affect the soft clays, is the formation of desiccation crust on the upper horizons of normally consolidated clay. Usually desiccation from evaporation, plant transpiration and other physico-chemical produces a stiff crust at the top of

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otherwise very soft clay. The most interactions affecting crust strength are between soilaggregates size, rainfall duration-aggregates and soil–rainfall duration in that order. Ekwue [1] described the relationship between increase in crust strength with increasing rainfall duration and decrease in aggregate sizes. The thickness of the drying crust normally varies between 1-3 m [2], the same thickness was reported by [3] for soft clays in Canada. The crust may improve the stability of an embankment constructed on the soft soil but if the weight of an embankment breaks the crust the embankment could fail[4]. On erecting an embankment on the soft soil, major items such as pore water pressures, slope geometry, soil properties for both embankment and foundation soil are to be determined. The applicability of Limit equilibrium Methods (LEM) in the slope stability has been confirmed by [5] . On using LEM it is important to ensure that the resisting forces Fp are sufficiently greater than the forces tending to cause a slope to fail FA. The factor of safety (FOS) is defined based on the force of equilibrium of the circular slip block as shown on equation 1[6]

SCOPE The scope of this paper is to conduct a parametric study on a typical embankment erected on homogeneous and heterogeneous soft soils capped with crust of various thickness and strength. An analysis is conducted using slope stability software GEO5 [7]. No verification of the results with field trial embankment or case studies were conducted. In this paper two major tasks will be conducted in order to explain the effects of crust depth and strength on the stability of an embankment erected on homogenous and heterogeneous soft soil. Firstly a parametric study will be conducted. A computer program GEO5 will be used to analyse these parameters with varying time factor (Tv), and secondly a time strength envelops for different slopes will be created for preliminary design of an embankment constructed on the sot soil

ANALYTICAL MODEL To investigate the geotechnical aspects of an embankment erected of soft soil capped with crust of different strength and thickness, a typical configuration of an embankment over soft ground was defined and typical values were assigned to the relevant parameters from the review of typical cases of embankments built on soft clays. The major influencing parameters are considered to be: ϕ ′ (Effective angle of internal friction for both the fill and the foundation soil), β (slope inclination), γ (bulk unit weight), He embankment fill height, Hf (the depth of the soft soil layer), cv (Coefficient of consolidation) and FOS (Factor of Safety required) [8] The idealized situation that will be analyzed is as shown in Figure 1 where He is embankment height, Dcr crust depth and Dcl soft soil depth. The ground water level (GWL) is at the ground surface. In order to analyze this situation numerically it was necessary to assign physical quantities to the situation and the relevant parameters. Parameters used were selected from physical values for the situation considered. The embankment was 3m high and composed of free-draining material. The soft clay of the foundation soil was taken as fully saturated and ground water was at ground level.

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Figure 1: Typical Embankment erected on soft soil capped with crust

Parameters Crust The thickness of the drying crust normally varies between 1-3 m. Typical crust thickness in some parts of Canada is approximately 2m [9] The parameters for crust are given in Tables 1.

Table 1: Data for the crust on soft clay deposits CRUST Properties

Minimum

Maximum

Source

γ (kN/m3) ϕ o′ c′ (kN/m2)

15 18° 1.9

25 23° 5

[10]

γ (kN/m3) ϕ o′ c′ (kN/m2)

18 13° 1

26 21° 5

[11]

The selected parameters (bulk unit weight; effective crust strength effective angle of internal friction and the depth of crust) for the foundation soil are shown in Table 2.

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Table 2: Selected soft clay parameters

Full parametric study For full parametric study the parameters for embankment, foundation soil and crust are shown in Table 3.

Table 3: Typical values of the relevant parameters for full parametric study

Embankment

Crust

Soft soil

Typical steepest slope (V: H)

Slope range chosen for analysis V: H

1:1 to 1:5 Typical shear strength parameters c′ = 0(kN/m2) , ϕ o′ = 35 o to 41 o Range of bulk unit weight 18 to 20(kN/m3) Typical range of thickness (m) 0 to 3m Typical shear strength parameters c′= 1.5 to 5 (kN/m2) , ϕ o′= 13 o to 21 o Range of bulk unit weight 15 to 22(kN/m3) Typical shear strength parameters c′ = 0 , ϕ o′= 14 o to 26 o Range of bulk unit weight 15 to 20(kN/m3)

1:2 to1:5 Selected shear strength parameters c′(kN/m2) = 0 , ϕ o′ = 35 o and 41 o Selected bulk unit weight 18(kN/m3) Thickness range for analysis m 0 – 3m Selected shear strength parameters c′ = 1.0 to 5′ (kN/m2) , ϕ o′= 14 o to 26 o Selected unit weight 15 to 22(kN/m3) Selected shear strength parameters c′ = 0 , ϕ o′= 14 o to 26 o Selected bulk unit weight 15 to 22(kN/m3)

Representing water pore pressure at the slice base In this paper a typical example is taken of which an embankment is rapidly constructed on the soft soil. The excess pore pressure generated by the sudden application of load dissipates by drainage or consolidation over period of time and the variation with time can be estimated using Terzaghi’s differential equation 2 [12]. During the process of consolidation a time dependent behaviour of an embankment erected on the soft soil capped with crust was analysed. Isolines were used represent total pore pressure values[13]. The total pore water pressure values incorporate both hydrostatic and excess pore pressure as shown in equation 2

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m =α

zγw + u(z ,t)= zγw +  2 u o (sin m * z / D )exp( − m 2T v ) ……………………………….2 m m =0

The process of estimating the values of pore pressure isolines was conducted by selecting

the depth ratio z/D varying from 0.00 to 1.00 as shown in Figure 2 The number of isolines for each Time Factor was 13 the same number of Time Factor was used, ranging from Tv=0.01 to Tv=2.00. The total amount of isolines investigated for each slope was 169.

Figure 2: Representing isolines in the foundation capped with crust

Analytical method The overall analytical procedure adopted in this paper is by assuming a circular failure surface which is found to be the most critical in slopes containing homogeneous soft soil. The shearing strength of the soil is the primary stabilizing agent for slopes and the factor of Safety against instability is often more or less the ratio of the shear strength to the applied shear stress. This situation is analyzed on the basis of equilibrium of disturbing and resisting moments/forces. Analytical model is shown in Figure 3 where Hcl- depth of natural clay , He - embankment height, W - weight of soil mass, X – assumed distance from lever arm Y to the centre of gravity of the slipping mass W , R – Radius of critical slip surface, TR – Required geotextiles tensile strength for the given factor of safety, Y = Lever arm of reinforcement, GWL- ground water level, and O – Centre of chosen slip surface The inclusion of the geotextiles reinforcement has been simulated as a single restoring force acting at the point of intersection of the free-body boundary and the reinforcement plane equation 1 [13],[14], [15], [16]. The stability of slope was investigated by observing the change in Factor

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of Safety (FOS) with time using slope stability soft ware GEO 5. GEO 5 has been validated by [17].

Figure 3: Analytical model showing parameters to be analyzed

RESULTS AND DISCUSSION Using GEO 5 more than 2600 analyses were performed by varying foundation and embankment parameters conducted earlier in this paper. The variation of crust strength and thickness was performed for slopes V:H 1:2; V:H =1:3; V:H = 1:4 and V:H = 1:5. The crust strength chosen are 0.00, 1.00; 2.50 and 5.00kN/m. The thicknesses are 0; 1.20 and 2.40 meters. 13 different Time Factors were chosen from Tv= 0.00 (undrained state) to Tv=2.00 (the end of consolidation.). In order to investigate the effects increasing crust strength and depth slope stability, the values of FOS without crust were rigorously analysed both at undrained state and at fully drained state. The results were compared with varying increase in crust strength and thickness. It was found that for slope V:H = 1:2 at Tv = 0.00 there was 42% increase in Factor of safety for crust thickness of 1.20 meters. On increasing crust thickness to 2.4 meters, FOS was increased to 78%. For slope V:H 1:3 at Tv =0.00 there was 57% increase in Factor of safety for crust thickness of 1.20 meters. On increasing crust thickness to 2.4 meters, FOS was increased to 74%. At the end of consolidation for slope V:H= 1:2 The FOS increased by 26% and 48% for thickness of 1.2 and 2.4 meters respectfully. For slope V:H = 1:3 at Tv = 2.00 the increase in FOS was 17% and 31% for crust thickness of 1.20 and 2.40 meters respectfully. For slope V:H = 1:4 these was increase in FOS as crust thickness increases. At Tv = 0.00 FOS increased by 31% and 61% for crust thickness of 1.2 and 2.4 meters respectfully. For slope V:H = 1:5 at Tv= 0.00 FOS increased

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by 10% and 27% for crust thickness of 1.2m and 2.40 meters respectfully. Crust strength and thickness have influence on the stability both on short and on long term. Effects of crust thickness and strength on FOS for different slopes is shown in Figure 4. These few examples have clearly shown that crust play a major role to maintain the stability of an embankment erected on soft soil capped with crust.

4 (a) increasing shear strength due to consolidation and crust strength for slope 1:2 crust depth 1.2 m 1.8 1.6

Factor of safety

1.4 1.2 1 0.8 0.6 0.4 0.2 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 c'=0.00kN/m

Time Factor (Tv) c'=1.00kN/m c'=2.50kN/m

c'=5.00kN/m

4 (b) Effects of crust strength/depth and consolidation on slope stability V:H 1:2 and crust depth 2.4m 1.8 1.6

Factor of Safety (FOS)

1.4 1.2 1 0.8 0.6 0.4 0.2 0 0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

1

1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9

2

Time Factors (Tv)

c'=0.00kN/m

c'=1.00kN/m

c'=2.50kN/m

c'=5.00kN/m

Figures 4a, 4b: Time dependent behaviour of slopes having different crust strength and thickness Effect of crust thickness/strength on the long term and short term stability of slopes (Fig. 4 continues in the next page).

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4(c) Effects of crust strength/depth and consolidation on the stability of slope V:H 1:3 crust depth 1.2m 1.8 1.6

Factor of Safety (FOS)

1.4 1.2 1 0.8 0.6 0.4 0.2 0 0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

1

1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9

2

Time Factor (Tv)

c'=0.00kN/m

c'=1.00kN/m

c'=2.50kN/m

c'=5.00kN/m

4(d) Effect of crust strength/depth and consolidation on stability of slope 1:3 Crust depth 2.4 m 1.8 1.6

Factor of Safety (FOS)

1.4 1.2 1 0.8 0.6 0.4 0.2 0 0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

1

1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9

2

Time Factor (Tv)

c'=0.00kN/m

c'=1.00kN/m

c'=2.50kN/m

c'=5.00kN/m

Figures 4c, 4d: Time dependent behaviour of slopes having different crust strength and thickness Effect of crust thickness/strength on the long term and short term stability of slopes.

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Effect of crust thickness/strength on amount of reinforcement required to achieve a specific FOS The effect on combining consolidation process and effect of crust strength and thickness on reinforcement required to maintain a specific FOS could be explained as shown in Equation 3.

FGLOBAL =

F (S ,Cr ,T ) + F (T R)

(3)

The Global Factor of Safety ((FGLOBAL)) is compose of shear strength from crust (Cr)embankment and foundation shear strength (S) and the effect of consolidation (T) additional strength from reinforcement are represented as F (T ) R

Figure 5: Schematic diagram showing the effects of consolidation and crust at different part of an embankment erected on the soft soil capped with crust On considering the effects of crust on stability of embankment erected on the soft soil can reduce the amount of tensile force as well as the duration of which the reinforcement is required parameters from parametric study were used. A typical embankment (slope V:H= 1:2 to V:H= 1:5) resting on the soft soil was investigated by varying the effective crust cohesion (c'= 0, 1, 2.5 and 5kN/m2) for three different thicknesses 1.2m and 2.4m at various Time Factors (Tv= 0.00 0.05; 0.10; 0.20; 0.30; 0.40; 0.50; 1.00 and 2.00). In order to understand the effects of effective crust cohesion and its thickness on the tensile forces required to achieve global FOS of unity at the given Time Factor It was inevitable to vary both crust thickness and effective crust cohesion from zero to 5kN/m2. Initially the crust thickness was considered to cover 2.4m and 1.2m. The results of these analyses are shown in Figures 5, 6.and 7. It was found that if the crust cohesion was zero, both the tensile force required to achieve global FOS of unity was highest for all slopes and the duration of which reinforcement was required was much longer then in all other cases when the crust was considered. It was found that for the steepest slope V:H =1:2, on increasing

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the crust cohesion from zero to 1kN/m2, both the tensile force which was required to achieve global FOS of unity sharply decreased from the end of construction (Tv=0.00) and the duration of which the reinforcement was required got diminished by almost 50%. If the crust effective cohesion was increased from 1 kN/m2 to 2.5 kN/m2 the tensile force required was reduced even more sharply at the beginning of consolidation and the duration of which the reinforcement was reduced by more than 80%. It was also found that when the crust cohesion was zero, the reinforcements was required for 5.6 years, but on increasing foundation crust cohesion to 2.5kN/m2 the duration of which reinforcement was required was reduced to 1 year. If the crust cohesion was increased to 5 kN/m2 no reinforcement was required at the end of construction (Tv=0.00). REQUIRED REINFORCEMENT WITH TIME Phi(e)=41 DEGREES

(V:H = 1:3); c' = 1( kN/m)

REQUIRED REINFORCEMENT (kN/m)

300 250 200 150 100 50 0 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9

2

TIME FACTOR (Tv) FOS=1

FOS=1.2

FOS=1.5

FOS=2

Figure 6: Estimation of required reinforcement (crust strength 1kN/m2; depth 1.2m) As shown in Figure 6 Slope V:H = 1:3 was investigated with varying crust parameters and consolidation. It was found that there was no need for reinforcement at Tv=0.2 At Tv=0.5 there was no need of reinforcement to maintain FOS 1.2 as compared to Tv=0.6 without crust. The effects of increasing crust strength and depth was investigated using crust depth 2.4m and crust strength 5kN/m;2. Figure 6 shows that there was no need of reinforcement to maintain FOS=1. The amount of reinforcement required to maintain FOS=1.2 at Tv=0.00 was reduced by 14% as compared with results from figure 9 but there was no need of reinforcement at Tv = 0.05. The amount reinforcement required to maintain FOS =2.00 at Tv=2.00 was reduced by only 10%.

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Required reinforcement (kN/m)

Estimation of required reinforcement c'=5kN/m and depth 2.4m

300 250 200 150 100 50 0 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9

2

Time Factor

FOS=1

FOS=1.2

FOS=1.5

FOS=2

Figure 7: Estimation of required reinforcement ( crust strength 5kN/m;2 depth 2.4m)

Empirical relationship GEO5 was used to investigate the effects of varying crust parameters as well as degree of consolidation. The combined crust strength and thickness (C’x DCR) were varied from 0.00 to 6.00kN/m for Time Factor ranging from Tv = 0 to Tv = 0.6 for slope V1:2H. The results are shown in Table 5.

Table 5: Typical chart showing the effects of crust strength-depth and consolidation on the amount of required reinforcement to achieve FOS = 1 Thickness D(m) 0.00 0.50 0.50 1.00 1.00

Strength C′ kN/m2 0.00 1.50 3.00 3.00 6.00

Tv=0.00 90.00 87.00 84.00 78.00 66.00

Required reinforcement (kN/m) on varying DX C’ and Tv Tv=0.1 Tv=0.2 Tv=0.3 Tv=0.4 Tv=0.5 52.05 36.33 24.27 14.10 5.15 48.10 31.99 19.63 9.20 0.026 44.25 27.65 14.99 4.31 36.26 18.97 5.70 20.46 1.60

Tv=0.6

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VARIATION OF CRUST-STRENGTH-THICKNESS ON REINFORCEMENT REQUIRED

TENSILE STRENGTH (kN/m2)

100 90 80 70 60 50 40 30 20 10 0 0

1

2

3

4

5

6

CRUST STRENGTH-THICKNESS (C'XDCR )kN/m PREDICTED TENSILE STRENGTH

GEO5 RESULTS

Figure 8: Comparing predicted and GEO5 results An empirical equation 4 shows that there is approximate linear relation between amount of reinforced required to achieve a specific FOS to crust strength and thickness. An inconsistence on predicted amount of require reinforcement shows how complicated the relationship could be and therefore further investigation is required Figure 8.

T

Rt

(

'

= T RO − 4 x C x DCR

)

(4)

Where: TRt :

Tensile strength at given time (t)

TR0 :

Tensile strength at the end of construction (t = 0)

C:

Crust strength (kN/m2)

DCR:

Crust thickness (in meters)

CONCLUSION AND RECOMMENDATIONS 1. This paper has demonstrated that crust strength can sustain an engineering structure such as an embankment. 2. It was found that the amount of reinforcement required to achieve a specific FOS could be reduced depending on strength and thickness of crust.

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3. This paper demonstrated that both effective strength and thickness are the major parameters affecting the short-term and long-term stability of an embankment erected on the soft soil capped with crust. 4. Though crust could enhance the stability of an embankment on the soft soil, care should be taken during construction period as well, not to overload to avoid cracking of crust and failure of an embankment. 5. Limited Life Geotextiles could be used to stabilize embankment erected on soft soil capped with crust, since the duration of which reinforcement is required diminishes In future further research is required to establish the effect of crust strength on varying foundation depth and larger embankment heights. This research will enable to create charts and graphs for preliminary design of an embankment on the soft clay capped with crust having different strength and thickness.

REFERENCES [1] EKWUE E. I (1991) Effects of peat content, Rainfall Duration and Aggregates size on soil crust strength [2] CHRISTOULAS S. (1987) Embankment on the soft ground. Bulletin of the public works research center, Athens [3] KRYNINE, P. D. and JUDD, W. A. (1957) Principal of engineering geology and geotechnics McGraw-Hill Book Company New-York [4] R. K. ROWE and A. L. LI (2005) Geosynthetic-reinforced embankments over soft foundations Geosynthetics International pp50-85 [5] D. T. BERGADOD, G. A. LORENZO and P. V. LONG (2002) Limit equilibrium method backanalysis of geotextile reinforced embankments on the soft bagkok clay- a case study. Geosynthetic international Vol 9 No 3 pp 217-245 [6] DUNCAN M. J. and WRIGHT G. S. (2005) Soil strength and Slope Stability. John Wiley & Sons. INC [7] GEO 4/5 www.gts.com/online-store.htm cited 2004, 2004-2008 [8] SARSBY R.W. (2000) Environmental Geotechnics. Thomas Telford Ltd. ISBN: 0727727524 [9] GRAMMATIKOULOU, l; ZDRAVKOVIC and POTTS D. M (2007)The effects of the yield and plastic potential deviatoric surface on the failure height of an embankment Geotechnique 57, No. 10. pp 795-806 [10] PERRY, J. (1989) A survey of slope condition on motorways earthwork in England and Wales. Research report 199. Transport and Road Research Laboratory Crowthorne [11] SNIP-2.02.01-83 -Russian standards (1983) [12] TERZAGHI, K. (1966) Theoretical Soil mechanics, Wiley, New York. [13] MWASHA, A. (2005). Limited Life Geotextiles for Reinforcing an Embankment on Soft Ground. Ph.D. Thesis, University of Wolverhampton

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[14] ROWE, R.K. and SODERMAN, K.L., (1984) Comparison of predicted and observed behaviour of two test embankments. International Journal of Geotextiles and Geomembranes, Vol. 1, No. 2, pp. 143-160 [15] HIND C. RUSSEL D. and JEWEL R. (1996) Stability of single stage constructed reinforced embankment on the soft soil. Proc. Inst. Civ. Enginrs pp 391-205 [16 KOERNER, R.M. (1994). Designing with Geosynthetics, Third Edition. Prentice Hall, 783 pp [17] MWASHA ABRAHAMS (2008) Investigating the effects of basal reinforcement on the critical slip circle parameters of an embankment on soft ground: A parametric study. Electronic Journal of geotechnical Engineering Volume 13, Bundle J

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