THREE DIMENSIONAL ANALYSIS OF •ROCKFILL DAMS UNDER GRAVITY LOADING

Abstract

The objective of this study is to carry out three dimensional sequential non-linear analysis of rockfill dams with central core for gravity loading. The dams have been considered to be located in valleys of different shapes to bring out the effects of valley width, valley slope and material properties on the stresses and deformations in them. Parameters of the valley under which a plane strain analysis of the maximum transverse section would be adequate to predict the response of the dam , have been brought out. The canyon and section of a proposed 260 m high dam has been used in this study. The canyon has a valley width factor (top valley width to height ratio) of 2.25. Other valley shapes have been considered with valley width factors of 1.12, 4.5 and 9.0. The same transverse section has been used for all the three dimensional analyses and plane strain analysis to facilitate comparison of the results of 3-D and plane strain analyses. The materials of the various zones (shell, transition and core) of the dam have been taken to exhibit non-linear behaviour. The hyperbolic model (16) has been adopted to model the stress strain behaviour of the materials. The weight of the dam is applied in six sequential stages to simulate the construction sequence. The dam is discretised into 98 number of 20-noded brick elements and consists of 724 nodes, each having 3 degrees of freedom, thus a total of 2172 degrees of freedom. For plane strain analysis of the maximum transverse section of the dam, 8-noded isoparametric elements have been used. The foundations and the abutments for all the analyses have been (iv) taken as rigid. A digital computer program has been developed to carry out the three dimensional sequential non-linear analysis of rockfill dams. The program uses residual force approach (56) to equilibrate the loads applied. The ratio of the norm of residual loads to that of the applied loads has been used as the criteria to stop further iterations. Another program to plot the results of all the 3-D analyses and plane strain analysis jointly or individually on a calcomp plotter has also been developed. Study has also been made to assess separately the contribution of valley base width and valley wall slope in comparison to the effect of valley width factor. Three base widths of valley (20, 40 and 80 m) at a valley wall slope of 0.5H:1V , two base widths (40 and 80 m) at 1H:1V valley wall slope and 80 m base width at 2H:1V valley wall slope, have been taken. The effect of core stiffness on the dam behaviour has also been studied with four values of core stiffness, keeping all other material properties unchanged, for one valley with valley width factor of 2.25 . The effect of material properties on the performance of the dam due to change in valley width factor has also been studied at two different valley shapes with valley width factors of 2.25 and 4.50 respectively, each with two values of core stiffness. The studies show that for dams situated in valleys with valley width factor 3 greater than or equal to 4.5, a plane strain analysis of the maximum transverse section is adequate (v) to accurately predict the stresses in the dam section. For displacements, however, the limiting valley width factor beyond which a 3-D analysis will not be required is 9. For narrow valleys significant differences in magnitudes of stresses and displacements are observed, with 3-D stresses and displacements being substantially lower than those given by plane strain analysis, and therefore a three dimensional analysis is a must for such valleys. The effect of increase in valley base width on the stresses and displacements in the dam is more than that of the effect of valley wall slope. For the valley shapes studied, flattening of valley wall beyond 1H:1V at a constant valley base width does not significantly affect the stresses in the dam and the displacements are not affected beyond 2H:1V slope. The effect of valley wall slope goes on decreasing as the valley base width increases. The studies indicate that the change in core stiffness has practically no effect on the stresses in the pervious zones of the dam while the stresses in the core increase as the core stiffness increases. With increase in core stiffness, the displacements in the dam decrease, the reduction increasing from the dam faces upto the core centre line. With the change in material properties the performance of the dam with respect to valley shape is not affected.