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

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1 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. 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 1.1 Basal Reinforced Embankments on Soft Soils If embankments are constructed on soft foundation soils, because of the low strength of foundation soil the stability will be a concern.. Reinforced Soil concept (Vidal, 1969b) using geosynthetics proved as the best technique, which can be used to enhance the strength and deformation behavior of soil in difficult situations. In basal reinforced embankments a layer of geosynthetics material provided horizontally at the interface of the embankment soil and foundation soil extending for the full width and length of the embankment. The basal reinforcement can serve to resist some or all of the earth pressure within the embankment and to resist the lateral deformations of the foundation, thereby increasing bearing capacity and stability, Jewell (1988). 1.2 Collapse Height of Geosynthetic-Reinforced Embankment on Non Homogeneous Soils Limit equilibrium methods and programs developed through FEM have been used to asses short term stability (undrained) stability of reinforced embankments constructed on soft foundation soils (Rowe 1984, Rowe et al. 1985a, 2002). Geometry of embankment and thickness of soft soil influences collapse height (Rowe et al. 1999, 2005). The collapse height of reinforced embankment is the height corresponds to full mobilization of shear stresses in soil or due to strains/forces developed in reinforcement. A rough estimate for collapse height Hc is F* H (Rowe et al., 1985a) where F is the FS corresponding to a given height of embankment H. The strength of top soil, rate of increase of strength with depth and presence of crust at top will influences collapse height (Rowe 1984, Abrahams, 2006). The collapse height Hc = F* H, where F is the factor of safety. The stability of reinforced embankment depends on several factors namely, drainage conditions, rate of construction of embankment, strain in reinforcement, tensile strength of reinforcement, type of soil etc (Rowe et al. 1984, 1985a, 2002, 2005). 2. KINEMATICS OF REINFORCEMENT-BACKFILL RESPONSE-OBLIQUE PULL Kinematics of the deformation (Figures 1 and 2) dictates typical failure of reinforced soil structures. At failure of soil 803

2 mass the reinforcement is subjected to pull. However, in actual case at failure reinforcement is subjected oblique pull. (Figure 3 and 4). Under the action of oblique force or displacement, the soil beneath the reinforcement mobilizes 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) Fig.1. Kinematics of Reinforcement and Soil Interaction Center of slip surface 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 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/ 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 Figure 5. Details of geometry and properties considered are shown in Table 1 to Table 4. Geosynthetic Reinforcement Geosynthetic Reinforcement 2htl:1vtl He 27m C= 0 kpa Φ = 30 0 γ = 18.0 kn/cu.m Basal reinforcement Slip Surface Fig. 2: Horizontal Pullout Force H= 5m Cu(0) = 10 kpa Φ = 0 0 γ =16 kn/cu.m Fig. 5: Cross-section of Embankment Considered Table 1: Geometry s for Study Top width 27m Bottom width Varies from 33m to 57m to suit He/H Side slope 1vtl :2htl He/ H 0.3 to 1.0 Fig. 3: Postulated Shape of Reinforcement Adjacent to the Failure Surface (Gourc et al. 1986) Table 2: Embankments Fill Properties for Study Ce 0 kpa Φe 30 degrees Unit weight 18 kn/cu.m 804

3 Table 3: Foundation Soil Properties for Study Thickness H 5m Cu(0) 10 Kpa Variation of Cu Cu(z)= Cu(0)[ 1+ αz/h), α= 0.5, 1, 2 Φ 0 Unit weight 16 kn/cu.m Table 4: Reinforcement Details Location 0.3 m above ground in to fill Length Φe entire width Tensile capacity 50 kn Transfer efficiency 100% 3.1 Stability of Embankment-Unreinforced Factor of safety is computed using GEOSLOPE. The program output is validated with available results before computing for the problem considered. Critical FS and slip circle are obtained with search option in GEOSLOPE w.r.t. grid of centers. 3.2 Stability of Basal Reinforced Embankment with Axial Pull Induced 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 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 Stability of Basal Reinforced Embankment with Transverse Pull Induced At failure due to weight of sliding mass, the failure surface intersects the reinforcement at an oblique angle, as demonstrated in Figure 5. This inclined force in reinforcement causes transverse displacement of reinforcement and axial pull out. The governing equations for analysis considered are the equations developed by Madhav et al. (2003, 2005) for linear and nonlinear sub grade response as shown in Figure 7A, B 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 given for Normalized Normal component of force and Normal force (equations 1 to 3). These Normal forces will develop additional axial forces in the reinforcement. Due to the contribution of additional axial (equation 3) and transverse force additional resisting moments will be developed about slip circle center. The horizontal and normal component of maximum tension develop at the end, B, are estimated. The horizontal component of maximum tension (i.e. the pullout force) is non-dimensionalized as shown in equation 2 and 3. The normal force develops additional axial force T addi. Axial in the reinforcement which is given by equation [4] as shown below. P n P wo 1 W1 + 1 = = μ + Wi γdl L n 2 i= 2 Unit Weight y (1) Fig. 7A: Definition Sketch of Transverse Pull Fig. 6: Typical Slip Surface and Axial Pull in Reinforcement Fig. 7B: Definition Sketch of Transverse Pull 805

4 Fig. 8: Equilibrium of Element Fig. 9: Computation of Collapse Height T max T cosθ cos θ + (2) n+ 1 n+ 1 n+ 1 = = Tn+ 1 cosθ n 1 2γDL tan φr The normalized normal component of maximum tension is obtained as, Tn + 1 sin θn+ 1 Tmax sin θn+ 1 = = 2Tn + 1 sin θn+ 1 tan φr (3) γdl 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 end of reinforcement. For the same critical circle obtained in axial case knowing length of reinforcement Le, moment center the transverse force developed due to oblique pull is computed by considering a rotation of rad, rad and rad at the point of intersection of reinforcement with slip surface. For each rotation transverse displacements, transverse force and additional axial force and their moments about slip center are computed. These additional moments together with resisting moments of axial case increases resisting moments thus factor of safety and collapse height. 4. RESULTS Results of analysis of embankment considered are shown in Figures 9 and 10 as given below. Figure 9 describes the Factor of safety variation with He/H ratio. Figure 10 details graphically collapse height for unreinforced, reinforced with axial and additional axial force respectively. It is evident as alpha increases ground is becoming stiffer thus collapse increased. It is observed effect of increase in collapse height is very less for smaller values of alpha. Collapse height has been increased for oblique pull effect. Fig. 10: Comparison of Collapse Height with Different Forces in Reinforcement 5. CONCLUSIONS From the results obtained the following conclusions are made: 1. The factors of safety is a function of non homogenity of soil i.e. rate of change of Cu rate with depth. Collapse height increases with strength of top soil and its rate of increase with depth. 2. As free end displacement ratio (w/l) increases i.e. for maximum free end displacement, factor of safety and collapse height increased with combination of moments from transverse force and additional axial force. 3. This clearly explains and for considerations of transverse pull in addition to axial pull in stability analyses, wherein the designs will be more economical. REFERENCES Abrahams M. (2006). Investigating Time Dependent Behavior of Reinforced and Unreinforced Embankment on Soft Soil Capped with Crust Using Slope Stability Software, EJGE, Vol. 14 Bund. E pp

5 Gourc, J.P., Ratel, A. and Delmas, P. (1986). Design of Fabric Retaining Walls: The Displacement Method, Proc. 3 rd Int. Conf. on Geotextiles, Geomembranes and other Products, Vienna, Vol. II, pp Jewell, R.A. (1988). The Mechanics of Reinforced Embankments on Soft Soils, Geotextiles and Geomembranes, 7, Madhav, M.R. and Umashankar, B. (2003). Analysis of Inextensible Sheet Reinforcement Subjected to Transverse Displacement/Force: Linear Subgrade Response, Geotextiles and Geomembranes, Vol. 21, pp Madhav, M.R. and Umashankar, B. (2005). Analysis of Inextensible Sheet Reinforcement Subjected to Transverse Displacement/pull, Journal of South East Asian geotechnical Society, pp Rowe, R.K. (1984). Reinforced Embankments: Analysis and Design, Journal of Geotechnical Engineering, ASCE, 110, No. GT2, Rowe, R.K. and Soderman, K.L. (1985a). An Approximate Method for Estimating the Stability of Geotextile Reinforced Embankments, Canadian Geotechnical Journal, 22, No. 3, Rowe, R.K. and Li, A.L. (1999). Reinforced Embankments Over Soft Foundations Under Undrained and Partially Drained Conditions, Geotextiles and Geomembranes, 17, No. 3, Rowe, R.K. and Li, A.L. (2002). Behaviour of Reinforced Embankments on Soft Rate Sensitive Soils, Geotechnique, 52, No. 1, Rowe, R.K. and Li, L.L. (2005). Geosynthetic-reinforced Embankments Over Soft Foundations, Geosynthetics International, Special Issue on the Giroud Lectures, 12, No. 1, Vidal, H. (1969b). The Principle of Reinforced Earth, Highway Research Record 282, Highway Research Board, National Research Council, Washington D.C, Viswanadham, B.V.S. and Mahajan, R.R. (2007). Centrifuge Model Tests on Geotextile-Reinforced Slopes, Geosynthetics International, 14, No. 6,