Seismic Displacement of Retaining Wall with Reinforced Backfill Saran, S.K. Viladkar, M.N. 1 Scientist Professor e-mail: [email protected]e-mail: [email protected]Geotechnical Engineering Division, Central Building Research Institute, Roorkee 1 Department of Civil Engineering, IIT Roorkee, Roorkee ABSTRACT In this paper firstly the salient features of the procedure of obtaining the displacement of a retaining wall having reinforced backfill under seismic condition have been presented. Both the translational and rotational modes of vibration of reinforced wall have been considered. The mass of retaining wall is lumped at its centre of gravity. The analysis indicated that the displacement depends on (i) frequency of excitation, (ii) acceleration, (iii) yield displacement and (iv) amount of reinforcement. Variation of its displacement with respect to these four parameters have been studied and presented herein. It was found that the displacement becomes very large when excitation frequency becomes closer to either of the two natural frequencies. Increase in excitation acceleration increases the displacement. The displacement of the wall decreases with increase in the amount of yield displacement and amount of reinforcement at all frequencies. Indian Geotechnical Conference – 2010, GEOtrendz December 16–18, 2010 IGS Mumbai Chapter & IIT Bombay 1. INTRODUCTION Rigid retaining walls are susceptible to failure if their displacements under static and dynamic conditions are not properly predicted. Therefore, in the design of retaining walls, a displacement criterion becomes important. The effect of displacement on the behaviour of retaining wall with reinforced backfill under static condition was thoroughly investigated by the authors and complete details are given Saran (1998). The design of retaining walls based on allowable displacement under dynamic conditions has gained importance in recent years. There are very few methods available in the published literature for computing displacements of retaining walls during earthquake namely Richard-Elms Model (1979) based on Newmark’s approach (1965), Solution inpure translation (Nandakumaran, 1973), Solution in pure rotation (Prakash et al. 1981), Nadim- Whitman Model (1983) using finite element technique and Reddy’s Model (1985) which incorporate both modes of movement i.e. translation and rotation. However, no work is available in literature to predict the displacement of rigid retaining walls with reinforced backfill and subjected to seismic condition. In this paper an attempt is made to present a simplified approach for this problem. 2. MATHEMATICAL MODEL AND ANALYSIS Fig. 1(a) shows a section of a rigid retaining wall of height H having reinforced backfill. The backfill properties are given in terms of density (γ), angle of internal friction (φ) and soil modulus (η h ). The reinforcement in the backfill is provided at vertical spacing of ΔH. f* represents the apparent coefficient of friction between the soil and reinforcement. Fig. 1: Proposed Mathematical Model of Wall for Displacement Analysis Under Seismic Conditions The backfill soil has been replaced by closely spaced independent elastic springs by sliding elements (Fig. 1(a)). Spring constants are computed using the concept of soil modulus which depends on the type of soil. It varies linearly with depth in sands and normally consolidated clays. If n h is presents the soil modulus, spring constants at various point of subdivision would be as under (Fig. 1):
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Seismic Displacement of Retaining Wall with …igs/ldh/conf/2010/articles/052.pdfSeismic Displacement of Retaining Wall with Reinforced Backfill 215 Integrating the above equations
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Seismic Displacement of Retaining Wall with Reinforced Backfill