SEISMIC EARTH PRESSURES AND DISPLACEMENT ANALYSIS OF RIGID RETAINING WALLS HAVING REINFORCED SAND BACKFILL

Abstract

Reinforced earth is comparatively a new construction material which is formed by the association of frictional soil and tension resistant elements in the form of sheets, strips, nets or mats of metal, synthetic fabrics or fibre reinforced plastics and arranged in the soil mass in such a way as to reduce or suppress the tensile strain which might develop under the action of gravity and boundary forces. It is well known that most of the granular soils are strong in compression and shear but weak in tension. The engineering performance of such soils can be substantially improved by introducing reinforcing elements in the direction of tensile strains in the same way as in reinforced concrete. The technique of reinforcing the soil, though widely accepted all over the world, will take some more time in this country to be accepted by the civil engineers as an economical alternative construction technique for earth retaining structures and for improving the poor ground. This may be partly because of high cost of reinforcing materials and partly due to lack of understanding of various design methodologies. Situations can be encountered in practice where reinforced earth walls may not provide ideal solution. This can be true in case of locations with limited space behind the walls or narrow hill roads on unstable slopes where it may not be possible to adopt design length of reinforcement. In such cases, a rigid (iii) wall with reinforced earth backfill appears more appropriate. Backfill is reinforced with unattached horizontal strips/mats laid normal to the wall. This causes appreciable reduction in the lateral thrust. The wall can therefore be designed for reduced sliding and overturning forces. No special technology or soil is involved in the construction of such walls. All the earlier investigations, both analytical and experimental till mid seventies, were directed towards the conventional reinforced earth. Very scanty literature is available on wall with reinforced backfill. Broms (1977a) was the first to report on the internal and external stability analysis of wall retaining backfill reinforced with unattached continuous fabric reinforcement. According to him, sufficient anchor zone, which is capable of transferring a force more than the allowable tension in fabric, is needed just behind the wall elements for enabling the reinforcement thus provided to behave as an attached reinforcement. Talwar (1981) analysed the behaviour of rigid wall retaining reinforced backfill with no surcharge loading. The analysis considers unattached reinforcement in the form of strips embedded in cohesionless soil. Non-dimensional design charts have been provided to obtain total pressure and height of the point of application of pressure, both for varying and constant value of apparent coefficient of soilstrip friction. Garg (1988) analysed the behaviour of rigid wall retaining reinforced backfill with uniformly distributed surcharge loading and presented an analytical approach for normal placement and effective placement of reinforcement in the backfill soil. Khan (1991) extended the work of Talwar (1981) and Garg (1988) and analysed the behaviour of rigid wall retaining reinforced backfill with surcharge in the form of a line load. (iv) These studies highlight the effectiveness of unattached reinforcement in reducing the lateral earth pressure on rigid wall. However, the effect of seismic/earthquake loading on rigid wall retaining reinforced backfill was not considered in these studies. In practice, the retaining wall must be strong enough to resist earthquake loading if located in seismic zone. Thus, there is a need to develop an analysis for the design of rigid walls which retain reinforced backfill that is subjected to external loading and an earthquake loading simultaneously. Further, no work has been reported in the literature regarding displacement analysis of rigid walls retaining reinforced backfill under static and seismic conditions. It is with this background that the proposed investigation has been taken up for study. The present investigation is aimed to study the following aspects pertaining to the design methodology for the retaining wall having reinforced earth as backfill under both static and seismic conditions: (1) Seismic Earth Pressures Behind Rigid Retaining Walls Having Reinforced Sand Backfill An attempt has been made to develop a pseudo-static analysis for determining seismic earth pressure behind vertical retaining walls having reinforced earth as backfill. Both horizontal and vertical seismic coefficients (ah and «v) are considered in the analysis. Reinforcement characteristics have been represented by two non-dimensional parameters, namely Dp =-p^-and-£jT where f* is the coefficient of apparent friction between reinforcing material and soil; w, the width of reinforcement strip; H, the height of wall; Sx, the horizontal spacing between the strips; Sz, vertical spacing between reinforcing layers; and L, the length of (v) reinforcing strips perpendicular to the wall. For geogrid and mat type f* H reinforcements, both w and Sx will be unity and therefore D will reduce to -W—. In z the analysis, soil properties are represented by <j>, the angle of internal friction. The results of analysis have been presented in the form of non-dimensional charts so that the earth pressure can be conveniently obtained for known wall and backfill properties (H, <f>, Dp) and the values of seismic coefficients (ah and av). (2) Displacement Analysis of Rigid Retaining Walls Having Reinforced Sand Backfill Under Static Condition The displacement analysis of rigid retaining walls having unreinforced backfill have been studied by few investigators [Dubrova (1963); Reddy et al. (1985). Bakeer et al. (1989) and Garg (1995)]. So far nobody had given analysis to predict displacement of rigid retaining walls having reinforced backfill. In this investigation a displacement analysis under static condition has been carried out by modelling the backfill as closely spaced independent elastic springs fixed to the back of rigid wall at different locations and the other ends of the springs fixed to an immovable support. The spring constants are evaluated treating the retaining wall as a beam simply supported at spring locations and subjected to soil reaction which depends on the type of soil and the direction of wall movement. The reinforcing elements are proposed to have frictional stiffness which is considered as a function of length of reinforcement and the overburden pressure. The analysis is based on a concept of limiting displacement (= mZj/100) in springs, indicating that a spring can not generate a force more than its stiffness multiplied by the limiting amplitude. Z- is the depth of the spring location from top of wall (vi) and 'm' is the limiting strain. Computations of earth pressures have been done corresponding to pre-assigned values of in and displacement of wall. (3) Displacement Analysis of Rigid Retaining Walls Having Reinforced Backfill Under Seismic Condition Various simple mathematical models [Newmark (1965), Nandakumaran (1973), Richard and Elms (1979), Zarrabi (1979), Prakash et al. (1981), Nadim and Whitman (1983), Saran et al. (1985)] are available for obtaining displacement of rigid retaining walls having unreinforced backfill under seismic condition. So far, no analysis is available to predict the displacement of rigid retaining walls having reinforced backfill and subjected to seismic condition. In this investigation, a simplified approach has been proposed for the estimation of displacements of rigid retaining walls having reinforced backfill for combined rotation and translation mode. The mass of wall is lumped at its centre of gravity. The backfill is treated as an elasto-plastic material when the wall moves away from the backfill and as elastic when it moves towards the backfill. Besides displacement, the method of analysis allows detennination of natural frequency of the system. (4) Experimental Investigations into Interfacial Characteristics The following tests were conducted in laboratory: i) Tensile strength of reinforcing materials (Tensar SS20 geogrid). ii) Pull-out tests on reinforcing materials with length and overburden pressure as variable parameters to evaluate the frictional stiffness and the apparent coefficient of friction. (vii) For determination of frictional stiffness and the apparent coefficient of friction between soil and the reinforcement which are required in the displacement analysis, pull-out tests have been conducted in a specially designed tank. The effect of length of reinforcing strip and normal pressure has been studied. The pull-out load versus displacement characteristics were obtained as also the normal stress versus pull-out shear stress for finding the apparent coefficient of friction. For the determination of tensile strength of reinforcement, stretch tests were conducted on samples of Tensar SS-20 geogrid in longitudinal and transverse directions. Stretch load versus displacement characteristics have been obtained. 5. Conclusions Based upon the studies undertaken, the following significant conclusions have been drawn : (i) The earth pressure on a rigid wall under seismic condition can be appreciably reduced by reinforcing the backfill by unattached horizontal strips/mats placed normal to the back of wall. The method of placement of reinforcement is simple and economical and materials of low strength can be employed. The resultant pressure is a function of the length of strips and the non-dimensional parameter DP and the former reduces as the values of the later two increases. For practical values of DP, the resultant pressure is reduced to one-half by reinforcing the backfill with strips of length equal to 0.8 times height of wall, H. (viii) For the same value of <p, -p- ratio and D,,, the piessuie intensity increases as the seismic coefficient increases. For economical design of rigid wall with reinforced earth backfill, L/H = 0.6 to 0.8 and DP = 1 may be adopted. (ii) The proposed methodology of displacement analysis under static condition is simple and applicable for studying the effect of wall movement on earth pressure and for determination of pressure distribution in active condition. It was noted that for a ptcassigncd value of limiting strain, in, earth pressure decreases with the increase in wall displacement before it attains a constant value. Further, it was observed that earth pressure increases with increase in seismic coefficient. Computations of earth pressure have been repeated for various values of m and then plots between the constant value of earth pressure and m were prepared. From these plots, the value of m has been obtained corresponding to the active earth pressure computed using classical theories. This has enabled to get an estimation of displacement of wall ( = ml 1/100) for active condition. It was found that the displacement of wall was a function of: height of wall, non-dimensional factor DP, angle of internal friction <p and seismic coefficients ah and av. (iii) The methodology proposed for displacement analysis under seismic condition considers translational and rotational motions simultaneously. The (ix displacement of wall is greatly influenced by the operating frequency. If the operating frequency approaches close to one of the natural frequencies of wall, the displacement becomes very large. The displacement of wall decreases as the backfill soil changes from loose sand to dense sand. Also, the displacement of wall increases with increase in the magnitude of seismic load. The findings of the present study are useful in understanding the behaviour of rigid retaining wall with reinforced earth backfill in earthquake prone areas. It is expected that this study will lead to more economical and safe design of walls retaining the reinforced backfill.