DYNAMIC PROPERTIES OF REINFORCED SAND

Abstract

The dynamic stiffness properties of soils must be determined for the purpose of analyzing machine foundations and substructures subjected to earthquakes. The significant advances in mathematical techniques for analyzing dynamic soil-structure interaction problems necessitate a realistic determination of pertinent stiffness properties. This determination can be quite involved because of the dependence of these properties on a large number of parameters. During the past three decades, reinforced earth has been extensively used to improve the static strength characteristics of soils. The study of dynamic response of foundations on reinforced sand beds and the dynamic properties, however, has not received the needed quantum of attention. The present research work has been carried out to study the dynamic response of foundations on reinforced sand beds experimentally and to interpret the dynamic stiffness properties of reinforced sand on the basis of experimental data and analytical analysis. It is anticipated that the study would help in better understanding of the dynamic behaviour of foundations on reinforced sand beds and lead to realistic and safe design. In India, the cyclic plate load and block vibration tests are generally used for the determination of dynamic stiffness properties of soils. A large number of reinforcement parameters are likely to influence the dynamic behaviour of soil; the present study, however, has been undertaken to investigate the following aspects : (1) The effect of size & number of reinforcement layers, density of sand and size of footing on the coefficient of elastic uniform compression, Cu of the sand by performing cyclic plate load tests in the laboratory. (2) To perform vertical and horizontal forced vibration tests on reinforced sand beds in the laboratory to study the effect of size and number of reinforcement layers on the dynamic response, coefficient of elastic uniform compression Cu, the coefficient of elastic uniform shear CT and the damping ratio. (3) Analysis and interpretation of experimental data for developing non-dimensional plots and correlations. (4) To develop an analytical approach for determining the coefficient of elastic uniform compression Cu and coefficient of elastic uniform shear CT of reinforced sand, treating it macro-homogeneous. The experimental investigation includes the determination of physical and mechanical properties of sand and geogrid reinforcement. The cyclic plate load tests have been performed on unreinforced and reinforced sand beds at relative densities of 50% and 70%. The sizes of the plates used in the tests are 0.15m square and 0.3m square and thickness 20 mm each. The sand beds are prepared in rigid steel tanks of sizes 0.9mx0.9mxl.0m and 1.5mxl.5rnxl.0m for conducting tests on the two plates respectively. The sand beds are reinforced with 2 to 8 layers of geogrid Netlon CE-121, having size one to five times the width of the plate. A total of 38 cyclic plate load tests were conducted for different combinations of the above mentioned parameters affecting the behaviour. Considering the cyclic plate load tests as the static tests, the data has been analyzed to determine the coefficient of elastic uniform compression Cu and damping capacity ratio. The static strength characteristics like, the bearing capacity ratio and settlement ratio are also determined. The pressure versus elastic rebound plots are bilinear; the two straight lines meet at a pressure value close to the ultimate bearing capacity of the sand bed. The slope of the first line gives Cu, and that of the other showing post-failure behaviour has been represented by symbol C'u. The confining pressure and area corrections have been applied to determine the standard values of Cu and C„ for unreinforced and reinforced sand beds. A comparison of the damping capacities of the reinforced and the unreinforced sand beds has been made by measuring the areas of the hysteresis loops of the first ten cycles of loading and unloading (till the failure of the unreinforced sand bed ii occurred) from the pressure-settlement plots. The second part of the experimental investigation consists of performing vertical and horizontal block vibration tests (total number 200) on unreinforced and reinforced sand beds. A rigid steel tank of size 1.5mxl.5mxl.0m was used to prepare the sand beds reinforced with 2 to 6 geogrid layers of different sizes. An M-20 concrete block of size 0.8mx0.4mx0.4m was cast for performing the block vibration tests. The frequency and amplitude observations were recorded at four force levels using the equipment specified in IS:5249-1977 and the soil data logger NE-4201. The vertical and horizontal vibration test data have been analyzed to determine the coefficient of elastic uniform compression Cu and the coefficient of elastic uniform shear CT respectively. The corrections for confining pressure and area of foundation are applied to obtain the standard values of Cu and CT. The ratio of dynamic force F to weight of block W, and the strain levels associated with different tests have been determined. The values of Cu and CT are interpreted at various F/W ratios and strain levels. In vertical vibration tests, the damping ratio £ has been determined by the bandwidth method. The damping ratios £, and £2 corresponding to the first and second modes of vibration in the horizontal vibration tests have also been determined by the bandwidth method and their values are found to differ, while the values of CT obtained in both the modes of vibration are almost the same. Non-dimensional plots and correlations have been obtained for the coefficient of elastic uniform compression Q, damping capacity ratio, bearing capacity ratio and the settlement ratio using the cyclic plate load test data. Non-dimensional plots and correlations have also been developed for the coefficient of elastic uniform compression Cu, the coefficient of elastic uniform shear CT, damping ratios £ and £i and the amplitude reduction factors with reference to the number and sizes of geogrid layers from the vertical and horizontal vibration test data. An equivalent parameter analysis has been developed to determine the coefficient of elastic uniform compression and coefficient of elastic uniform shear of reinforced sand from the coefficient of elastic uniform compression and coefficient of elastic iii uniform shear respectively of the unreinforced sand and the elastic modulus of the geogrid reinforcements. The composite material is assumed to be homogeneous and elastic with negligible mobilization of interface friction between the soil and geogrid at low strain levels. The analytically predicted values of coefficient of elastic uniform compression and coefficient of elastic uniform shear are compared with the experimental values and a reasonable agreement is obtained. Based upon the experimental and analytical studies, the following conclusions are drawn : (1) In cyclic plate load tests, the values of coefficient of elastic uniform compression of reinforced sand decrease, with the maximum decrease being 45%. This decrease is more with the increase in number and decrease in size of geogrid layers. However, the pressure range for validity of Cu value of reinforced sand bed is higher than that for the unreinforced sand bed. The damping capacity is increased, the improvement being more with increase in number and size of reinforcement layers. The ultimate bearing capacity values are increased upto about four times and the total settlements are reduced to less than half as compared to those of unreinforced sand, depending upon the size and number of geogrid layers. (2) In vertical vibration tests, the maximum amplitudes are reduced maximum by 43% for reinforced sand beds. The decrease in amplitudes is generally more with the increase in size and number of geogrid layers. The resonant frequency is reduced by a maximum of 14%, the decrease being dependent upon the size and number of geogrid reinforcements. The damping ratio, £ increases depending upon the size and number of reinforcements. The coefficient of elastic uniform compression Cu decreases by a maximum of about 26% depending upon the size and number of the reinforcement layers. The Cu-values of reinforced sand beds are less than the Cu-values of unreinforced sand bed for strain levels less than 3%; whereas for strain levels higher than this, Cu values for reinforced sand beds are more. This shows that for strain levels less than 3%, the mobilization of interface IV friction between sand and geogrid is not significant to contribute to the coefficient of elastic uniform compression of reinforced sand. (3) In horizontal vibration tests on reinforced sand beds, the maximum amplitudes corresponding to both the modes of vibration are reduced upto about 50% depending upon the size and number of geogrid layers. The resonant frequencies corresponding to the first and second modes of vibration decrease by a maximum of 28% and 20%, the decrease being more with the increase in size and number of reinforcement layers. The damping ratios €>l and £2> f°r tne two modes of vibration increase depending upon the configuration of the reinforcement and are found to be different. The coefficient of elastic uniform shear is reduced by a maximum of 48%, the decrease being dependent upon the size and number of reinforcement layers. A comparison of the values of coefficient of elastic uniform compression, (Cul00)10 with the corresponding values of coefficient of elastic uniform shear, (CT100)10 shows that (Cul00)10/(CT100)10 ratio is 2.8 to 2.95 for unreinforced sand bed whereas it is 3.2 to 3.9 for the reinforced sand beds. Thus, the decrease in CT is more than the decrease in Cu for the similar geogrid reinforced sand beds. The results of this study are especially useful in the design of foundations of machines, where the natural frequency of the soil-foundation system may lie close to the operating frequency of machine otherwise and the maximum amplitude exceeds permissible limits. The maximum amplitudes can be brought under control and the disturbance during the starting and stopping of the machine can be reduced. Another important conclusion drawn on the basis of test results is that though the static strength characteristics of the sand are considerably improved upon reinforcing with geogrid layers, but the coefficient of elastic uniform compression is marginally reduced at low strain levels till the mobilization of interface friction effectively contributes to the modulus of reinforced sand.