ELASTIC ANALYSIS OF PILE GROUPS SUBJECTED TO VERTICAL AND LATERAL LOADS

Abstract

This dissertation reports on an analytical and experimental study of pile groups subjected to vertical and lateral loads. The study v/as carried out with the following objectives in view - 1. To develop a rational method of analysis of pile groups subjected to vertical and lateral loads based on elastic theory; 2. To check the method of analysis by a series of tests on instrumented and noninstrumented model piles; 3. To check the findings of model tests with the tests in field; and 4. To examine the different methods of determining the elastic parameters of soil. The scope of study is restricted to two dimensional problem in granular soil for groups comprising of vertical piles which are connected by rigid pile caps. The cap is kept free from the ground. Using the concept of stiffness matrix, an analysis of pile groups subjected to vertical and lateral loads is developed. The pile constants, which are the forces and moments exerted by the piles on pile cap for unit displacement or rotation, are found by the elastic theory using Mindlin's solution for a point force inside a semi-infinite space. The effect of lengths to diameter, xxvi the modulus of elasticity of pile and soil, the spacing and configuration of piles in ground are analytically determined by the same theory. Since the above analysis based on the assumption that the soil acts as an elastic material, the reliability of the analysis depends on the correct assessment of the elastic parameters the modulus of elasticity and the poisson's ratio of soil. Based upon the study of many investigations in past, the effects of different factors on the elastic parameters are reviewed. A very large number of model tests on instrumented and noninstrumented piles were conducted to check the proposed elastic analysis. In case of noninstrumented piles, the effect of lengths to diameter ratio (L/d), the stiffness of piles (EpIp)» the spacing to diameter ratio of piles (S/d) and the relative density of soil (Rd) on the behaviour of piles are experimentally examined. The tests on instrumented piles were conducted to determine the distribution of strains, moments, shears, deflections, rotations and soil pressures along the depths of piles. In these tests also, the effects of S/d and Rd were examined. All the model tests were conducted on alluminium alloy hollow tubes which were jacked down in dry sand. The following tests were performed: XXV11 1. Tests on single noninstrumented piles of different E I 's with L/d ratios of 10, 20, 30, 40 and 50. The testsp p were conducted in loose and dense soil (Rd = 50 per cent and 80 per cent respectively). The horizontal load was applied at and above ground levels. The piles were subjected to pure moments also. 2. Tests on noninstrumented 9 pile groups of 3 different El's with L/d ratios of 50 and S/d of 2, 4, 6 and 8. P P The tests were conducted in loose and dense soils. The groups were subjected to the following loading conditions: (a) horizontal loads at ground level, (b) horizontal loads and moments, (c) moments only, (d) horizontal and vertical loads and (e) horizontal and vertical loads and moments. 3. Tests on single instrumented piles of a particular EI with L/d ratio of 50. The tests were conducted both in loose and dense soils. The piles were subjected to the following loading conditions: (a) vertical loads, (b) lateral loads at ground level, (c) lateral loads and moments, (d) vertical and lateral loads and (e) moments only. 4. Tests on instrumented piles of a particular EpI with L/d ratios of 50 and S/d of 2, 4, 6 and 8. The tests were conducted in loose and dense soils. The groups v/ere subjected to (a) horizontal loads at ground level, (b) horizontal loads and moments, (c) moments only, (d) horizontal and vertical loads and (e) horizontal and vertical loads and moments. To verify the findings of model tests, a few field tests on instrumented and noninstrumented piles were conducted. All the field tests were conducted on hollow steel piles which were driven by a hammer of 65 kg. in silty sand. To avoid the possibility of damage to strain gauges during driving of instrumented piles, XXV111 a special technique of instrumentation of these piles was followed. The pipes were splitted longitudinally and the gauges were fixed inside the pipes. They were then welded taking the necessary precautions to avoid any overheating of pipes. The following tests were conducted: 1, The tests on single instrumented piles - the tests were carried out on piles of 4 different EpI 's. Pies of a particular EL with L/d ratios of 10, 2(F, 30, 40- and 60 were also tested under lateral loads. Two piles were tested under vertical loads. 2, A group of 4-noninstrumented piles were tested under vertical and horizontal loads and moments. The S/d ratio of piles wa3 kept at 4 and L/d was greater than 50. 3. A single instrumented pile with L/d ratio of 50 was tested under vertical and lateral loads. 4. A 9-pile group comprising of instrumented piles, with L/d ratio of 50 and S/d of 4, was tested under vertical and lateral loads and moment. Since the reliability of the elastic theory depends on the correct assessment of elastic parameters, a study was conducted to determine the modulus of elasticity (Eg) and poisson ratio ( ju ) of soil for model and field tests. All the tests such as the vibration tests, plate load tests, standard penetration tests, static penetration tests or triaxial tests give different values of the parameters. Moreover, the modulus is a function of state of stress of soil. XXIX Hence a unique value cannot be assigned to it. However, an average value corresponding to one third to half the ultimate load in case of plate load tests or confining pressure equal to average overburden pressure of the whole depths of pile, in case of triaxial tests give a reasonable estimate of the modulus. A cyclic plate load test has been found to give a unique value of Es, Using the average value of the modulus of elasticity and poisson's ratio, the behaviours of single piles and pile groups under different test loading conditions are predicted by the elastic theory and compared with the observed behaviours of the piles in model and field tests. It is found that the predicted and observed behaviour of piles compare reasonably only at the low ranges of leads. There is considerable difference at higher loads. This is mainly due to the nonlinear behaviour of soil. The value of E reduces considerably when the soil is subjected to very high stresses. The study shows that the elastic theory can give reliable results provided the non-linear behaviour of soil is taken into account in the analysis. It is also found that the normal axial loads acting at ground level do not signiLcantly change the lateral load deflection characteristics of piles. The S/d ratios of piles in a group significantly alter the behaviour of piles. XXX * However, at spacings more than 6d, the interference is not very significant. A comparative study has also been made between the existing pile constant relations which are based on subgrade theory and the elastic theory. It is found that the pile constants compare well in case of single pile. However, the pile constants for piles in groups, the subgrade theories do not give any mathematical account relation to take into the interference of piles and the elastic theory is better suited in such cases. Finally, a few suggestions are put forward for further research on this topic. The main suggestions are (a) to modify the analysis to take into account the nonlinear behaviour of soil; (b) to study the behaviour of piles and pile groups in clay soils to examine the validity of the elastic theory; (c) to examine the behaviour of groups comprising of batter and vertical piles in the light of elastic theory. The pile constants in this case will have to be suitably modified to take into account the batter of piles; and (d) to study the behaviour of pile groups and elastic parameters of soil under cyclic loads. In the appendix of the thesis, a few computer programmes are included which are mainly used to analyse the pile groups using the elastic theory based on Hrennikoff's procedure and the Mindlin's equation.