Indian Geotechnical Conference (December 18-20, 2003) s6

Collapse Height of Reinforced Embankments over Non-Homogeneous Soil with Oblique Pull IGC 2009, Guntur, INDIA

COLLAPSE HEIGHT OF REINFORCED EMBANKMENTS OVER NON- HOMOGENEOUS SOIL WITH OBLIQUE PULL

V.K. Chakravarthi Research Scholar, Dept. of Civil Engineering, JNTUCE, Kakinada, A.P. & Associate Professor, Dept. of Civil Engineering, GMRIT, Rajam. E-mail: [email protected] K. Ramu Associate Professor, Dept. of Civil Engineering JNTUCE, Kakinada,. A.P. M.R. Madhav Professor Emeritus, Dept. of Civil Engineering JNTU, Hyderabad. A.P.

ABSTRACT: Stability of embankments on soft soils can be enhanced by providing basal reinforcement with geosynthetics, as suggested by many authors in the past. At failure, due to weight of sliding mass geosynthetic reinforcement will be subjected to pull. Many authors analyzed the problem by considering only horizontal/axial pull of reinforcement with full mobilization of frictional stresses. The geosynthetics reinforcement selected should withstand higher order tensile stresses to avoid rupture. Many authors in the past concluded that the tensile forces developed in reinforcement are function of fill properties, fill geometry and fill-reinforcement interface properties and strain in reinforcement. The strain in reinforcement can be influenced due to several parameters like failure condition of embankment either in collapse or in working condition and stiffness of soil etc. This paper presents stability analysis of basal reinforced embankments constructed on soils whose strength increases with depth. A new approach is suggested in the form of oblique pull force in reinforcement for computing stability. Collapse height is computed for critical factor of safety. From the results, it is observed that stability increases with depth wise strength increase and conventional design with axial pull under estimates the stability of the embankment. Hence the collapse height will be different considering oblique pull over conventional axial pull in reinforcement.

1. INTRODUCTION Geometry of embankment and thickness of soft soil influences collapse height (Rowe et al. 1999, 2005). The collapse height 1.1 Basal Reinforced Embankments on Soft Soils of reinforced embankment is the height corresponds to full If embankments are constructed on soft foundation soils, mobilization of shear stresses in soil or due to strains/forces because of the low strength of foundation soil the stability developed in reinforcement. A rough estimate for collapse will be a concern.. Reinforced Soil concept (Vidal, 1969b) height Hc is F* H (Rowe et al., 1985a) where F is the FS using geosynthetics proved as the best technique, which corresponding to a given height of embankment H. The can be used to enhance the strength and deformation strength of top soil, rate of increase of strength with depth behavior of soil in difficult situations. In basal reinforced and presence of crust at top will influences collapse height embankments a layer of geosynthetics material provided (Rowe 1984, Abrahams, 2006). The collapse height Hc = F* horizontally at the interface of the embankment soil and H, where F is the factor of safety. The stability of reinforced foundation soil extending for the full width and length of embankment depends on several factors namely, drainage the embankment. The basal reinforcement can serve to conditions, rate of construction of embankment, strain in resist some or all of the earth pressure within the reinforcement, tensile strength of reinforcement, type of soil embankment and to resist the lateral deformations of the etc (Rowe et al. 1984, 1985a, 2002, 2005). foundation, thereby increasing bearing capacity and stability, Jewell (1988). 2. KINEMATICS OF REINFORCEMENT-BACKFILL RESPONSE-OBLIQUE PULL 1.2 Collapse Height of Geosynthetic-Reinforced Kinematics of the deformation (Figures 1 and 2) dictates Embankment on Non Homogeneous Soils typical failure of reinforced soil structures. At failure of soil Limit equilibrium methods and programs developed through mass the reinforcement is subjected to pull. However, in FEM have been used to asses short term stability (undrained) actual case at failure reinforcement is subjected oblique pull. stability of reinforced embankments constructed on soft (Figure 3 and 4). Under the action of oblique force or foundation soils (Rowe 1984, Rowe et al. 1985a, 2002). displacement, the soil beneath the reinforcement mobilizes

35 Collapse Height of Reinforced Embankments over Non-Homogeneous Soil with Oblique Pull additional normal stresses as the reinforcement deforms transversely. Considerable literature Madhav et al. (2003, 2005), Gourc et al. (1986), exists on analysis of geosynthetic reinforced granular beds demonstrating oblique deformation of reinforcement.

Fig. 4: Deformation of Reinforced Earth Wall-Shape of Reinforcement at the Intersection of Failure Surface (Viswanadham et al. 2007)

3. PROBLEM CONSIDERED AND ANALYSIS An embankment fill of height He is constructed on nonhomogeneous soil of thickness (H) 5 m and whose strength is a function of z, the thickness of soil with its value Fig.1. Kinematics of Reinforcement and Soil Interaction increasing with depth. Collapse height is computed from different He/ H ranging from 0.3 to 1.0 maintaining H as constant and by varying He. A graph is plotted between He/ Center of slip surface H and Factor of safety. He/H giving Factor of safety 1.0 is selected from graph. Collapse height is computed as Hc = H* {He/ H for FS=1}. Cross-section of embankment is shown in Geosynthetic Figure 5. Details of geometry and properties considered are Reinforcement shown in Table 1 to Table 4. Geosynthetic Reinforcement 27m C= 0 kPa Φ = 300 Slip 2htl:1vtl γ = 18.0 kN/cu.m Surface He Fig. 2: Horizontal Pullout Force Basal reinforcement

Cu(0) = 10 kPa Φ = 00 H= 5m γ =16 kN/cu.m

Fig. 5: Cross-section of Embankment Considered

Table 1: Geometry Ranges for Study Parameter Range Top width 27m Bottom width Varies from 33m to 57m to suit He/H

Φe Side slope 1vtl :2htl Fig. 3: Postulated Shape of Reinforcement Adjacent to the Failure Surface (Gourc et al. 1986) He/ H 0.3 to 1.0

Table 2: Embankments Fill Properties for Study Parameter Range Ce 0 kpa Φe 30 degrees

36 Collapse Height of Reinforced Embankments over Non-Homogeneous Soil with Oblique Pull

Unit weight 18 kN/cu.m 3.3 Stability of Basal Reinforced Embankment with Transverse Pull Induced Table 3: Foundation Soil Properties for Study At failure due to weight of sliding mass, the failure surface Parameter Range intersects the reinforcement at an oblique angle, as demonstrated Thickness H 5m in Figure 5. This inclined force in reinforcement causes Cu(0) 10 Kpa transverse displacement of reinforcement and axial pull out. Variation of Cu Cu(z)= Cu(0)[ 1+ αz/H), The governing equations for analysis considered are the α= 0.5, 1, 2 equations developed by Madhav et al. (2003, 2005) for linear Φ 0 and nonlinear sub grade response as shown in Figure 7A, B Unit weight 16 kN/cu.m and Figure 8. For various free end displacement ratio’s ranging from 0 to 0.1 of reinforcement at failure tension force in reinforcement is computed from their expressions Table 4: Reinforcement Details given for Normalized Normal component of force and Parameter Range Normal force (equations 1 to 3). These Normal forces will Location 0.3 m above ground in to fill develop additional axial forces in the reinforcement. Due to Length Φe entire width the contribution of additional axial (equation 3) and Tensile capacity 50 kN transverse force additional resisting moments will be Transfer efficiency 100% developed about slip circle center. The horizontal and normal component of maximum tension 3.1 Stability of Embankment-Unreinforced develop at the end, B, are estimated. The horizontal component of maximum tension (i.e. the pullout force) is Factor of safety is computed using GEOSLOPE. The non-dimensionalized as shown in equation 2 and 3. The program output is validated with available results before normal force develops additional axial force T addi. Axial in computing for the problem considered. Critical FS and slip the reinforcement which is given by equation [4] as shown circle are obtained with search option in GEOSLOPE w.r.t. below. grid of centers. P w 1 W 1 n  P    o  1  W  (1) 3.2 Stability of Basal Reinforced Embankment with DL L n 2  i Axial Pull Induced  i2  Basal reinforcement in the form of geosynthetics is provided horizontally between foundation soil and embankment fill. (Fig. 5) for the full width of embankment at the base. The Unit Weight y properties of reinforcement are detailed in Table 4. Considering axial pull computations are carried out using GEOSLOPE and critical slip circle is identified. Typical figure for axial pull is shown in Figure 6.

Fig. 7A: Definition Sketch of Transverse Pull

Fig. 7B: Definition Sketch of Transverse Pull

Fig. 6: Typical Slip Surface and Axial Pull in Reinforcement

37 Collapse Height of Reinforced Embankments over Non-Homogeneous Soil with Oblique Pull

Fig. 9: Computation of Collapse Height Fig. 8: Equilibrium of Element

 Tn1 cos n1  Tmax cos n1   Tn1 cos n1 (2) 2DL tan r

The normalized normal component of maximum tension is obtained as, T sin T  sin  n1 n1  2T  sin  tan  (3) max n1 DL n1 n1 r T (addi axial) = 2 P Tan Phir. (4) Where, Phir is the mobilized contact friction angle at the interface of reinforcement, P is the transverse force at the Fig. 10: Comparison of Collapse Height with Different Forces in Reinforcement end of reinforcement.

For the same critical circle obtained in axial case knowing 5. CONCLUSIONS length of reinforcement Le, moment center the transverse force developed due to oblique pull is computed by From the results obtained the following conclusions are considering a rotation of 0.001 rad, 0.002 rad and 0.003 rad made: at the point of intersection of reinforcement with slip surface. 1. The factors of safety is a function of non For each rotation transverse displacements, transverse force homogenity of soil i.e. rate of change of Cu rate with and additional axial force and their moments about slip depth. Collapse height increases with strength of top soil center are computed. These additional moments together and its rate of increase with depth. with resisting moments of axial case increases resisting 2. As free end displacement ratio (w/L) increases i.e. moments thus factor of safety and collapse height. for maximum free end displacement, factor of safety and collapse height increased with combination of moments from transverse force and additional axial force. 4. RESULTS 3. This clearly explains and for considerations of Results of analysis of embankment considered are shown in transverse pull in addition to axial pull in stability Figures 9 and 10 as given below. Figure 9 describes the analyses, wherein the designs will be more economical. Factor of safety variation with He/H ratio. Figure 10 details graphically collapse height for unreinforced, reinforced with REFERENCES axial and additional axial force respectively. It is evident as alpha increases ground is becoming stiffer thus collapse Abrahams M. (2006). “Investigating Time Dependent increased. It is observed effect of increase in collapse height Behavior of Reinforced and Unreinforced Embankment is very less for smaller values of alpha. Collapse height has on Soft Soil Capped with Crust Using Slope Stability Software”, EJGE, Vol. 14 Bund. E pp. 1–14. been increased for oblique pull effect.

Gourc, J.P., Ratel, A. and Delmas, P. (1986). “Design of Fabric Retaining Walls: The Displacement Method”,

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