Finite Element analysis of Laterally Loaded Piles on Sloping Ground

Transcription

1 Indian Geotechnical Journal, 41(3), 2011, Technical Note Finite Element analysis of Laterally Loaded Piles on Sloping Ground K. Muthukkumaran 1 and N. Almas Begum 2 Key words Lateral load, finite element model, cohesionless soil, pilesoil interaction, embedment length Abstract: Pile foundations are slender structural elements used to transfer loads from structures into deep hard strata below the ground level. It should withstand various types of loads including axial and lateral loads. The load transfer mechanism for laterally loaded pile is more complex when it is located on the sloping ground. It is time consuming and expensive to carry out field test over the piles in larger lengths. Model test can be carried out as an alternative to field test, even though scaling effects influence the results of study involves great significance. Computer simulations of Finite Element Modelling will allow for in depth studies to analyze the pile soil interaction of laterally loaded piles in sloping ground. This paper presents results of a finite element analysis for the lateral response of pile located at the crest of slopes: Horizontal (H), 1V:2H (S1), 1V:1.5H (S2) with relative densities: 30%, 45%, and 70%. Equivalent sheet-pile wall is represented as a pile, and plane strain analysis is performed. A soil stratum is represented by 15 noded triangular elements of elastic-plastic Mohr Coulomb model. FEA and Model test results are compared and analyzed. Conclusions are drawn regarding application of the analytical method to study the effect of slope on laterally loaded pile. Introduction The ultimate resistance of a vertical pile to a lateral load and the deflection of the pile as the load build up to its ultimate value are complex phenomena involving the interaction between a structural element and the soil, which deforms partly elastically and partly plastically (elasto plastic analysis). In the case of long pile, failure takes place at the point of maximum bending moment, and for the purpose of analysis a plastic hinge capable of transmitting shear is assumed to develop at the point of fracture. The analytical approaches developed for single pile and pile group under lateral load are the subgrade reaction approach, the elastic approach and the finite element approach. The main disadvantage of the subgrade reaction approach is that the continuum nature of soil is ignored, whereas the elastic approach assumes the soil to be an ideal elastic continuum. This approach does not take into account the soil yielding and it is therefore only suitable for prediction of load-deflection response of laterally loaded piles at small strain levels. Due to the limitation of the above mentioned methods two dimensional nonlinear finite element analysis has been considered to predict the actual load-deflection behaviour of pile under lateral load. Many transmission towers, high rise buildings and bridges are constructed near steep slopes and are supported by piles. These structures may be subjected to large lateral loads such as violent winds and earthquakes. Under lateral loads, the behaviour of pile placed in the sloping ground is different from piles placed in the horizontal ground, resulting in a reduction of pile carrying capacity. The reduction depends mainly on reduction of soil mass around the pile and the fixity condition of the pile. And also, the initial horizontal confining pressure acting on the piles on the slope side is smaller than in horizontal ground. Hence, the study of laterally loaded pile on sloping surface is also necessary. The design of pile located on sloping surface subjected to lateral loading from horizontal soil movements may be based on semi-empirical or theoretical analysis. The literature on the adequacy of the finite element method (FEM) modeling of the laterally loaded pile located on sloping surface is limited. The available data are generally limited in extent and complicated by variations in geometry or soil conditions. Hence, there are many uncertainties in the estimation of bending moments and lateral deflections induced in piles under these conditions. If the bending moments and deflections induced in piles can be accurately estimated, then more cost-effective construction procedures may be confidently implemented to take advantage of sizes and configurations of an alternative pile. In this paper, a finite element approach is described for analysis of piles subjected to lateral load which is located on sloping surface. The approach is based on a plane strain representation of the problem. Results are compared with model test results. 1 Assistant Professor, Department of Civil Engineering, National Institute of Technology, Tiruchirapalli, , kmk@nitt.edu 2 Ph.D. scholar, Department of Civil Engineering, National Institute of Technology, Tiruchirapalli,620015, n_almas@rediffmail.com

2 156 Finite Element Analysis of Laterally Loaded Piles on Sloping Ground K. Muthukkumaran and N. Almas Begum Geotechnical Data Laboratory tests were carried out to find the properties of the soil sample used in model test. Direct shear test, triaxial test and relative density tests were performed to obtain the soil design parameters, which are presented in Table 1. Numerical Modeling Numerical models involving FEM can offer several approximations to predict true solutions. The accuracy of these approximations depends on the modeler s ability to portray what is happening in the field. Often the problem being modeled is complex and has to be simplified to obtain a solution. Two of the major factors which have a vast impact on both the real and model piles are; (1) the constitutive properties of the sand and (2) the soil structure interaction at the interface over the structural surface. The important literature reported on a single pile and pile groups under lateral loads are Matlock and Reese (1960) provided generalised solution for elastic and rigid pile under lateral load. Poulos (1971) and Banerjee and Davies (1978) reported the elastic solution for laterally loaded pile. Pise (1983) presented theoretical results for fixed head piles while Pise (1984) presented theoretical results for free head piles. Budhu and Davies (1988) reported elasto-plastic analysis of laterally loaded pile based on boundary-element method. Alizadeh and Lalvani (2000) provided useful results of full-scale, field lateral load tests on four instrumented single piles installed in sand. Finite element method has become popular as a soil response prediction tool. Chae et al. (2004) presented the finite element analyses of short rigid piles and a prototype pier foundation located near the crest of a slope and compared the measurements of model tests and field tests. Johnson et al. (2006) conducted numerical modeling for both square and circular piles, to explore the effect of pile shape, sand properties, pile length and loading conditions on the capacity of a pile. Karthigeyan et al. (2006) used 3-dimensional finite element program GEOFEM3D, developed by authors to analyse the pile soil interaction. The validity of this model was verified by back predicting the pile load test data for two different cases (short rigid pile and long flexible pile). Martin and Chen (2005), evaluated the response of piles caused by an embankment slope, induced by a weak soil layer or a liquefied layer beneath the embankment using FLAC3D program. Sensitivity studies varying soil and pile parameters were also presented. Plane strain representation Several forms of finite element analysis with various approximations have been proposed to assess the response of piles influenced by lateral soil movements. The finite element approaches are threedimensional finite element analysis, plain strain analysis and axisymmetric finite element analysis. In this present study, plain strain finite element approach is adopted. Randolph (1981) performed a site-specific plane-strain analysis, where the piles were replaced by an equivalent sheet-pile wall. The sheet pile wall was modeled with stiffer elements within the finite element mesh. Naylor (1982) extended this type of approach by connecting the sheet-pile wall to the soil with link elements, thus allowing relative displacement of the soil and the wall, and more closely approximating the true three dimensional behaviour around the piles. However, limiting soil pressure between the soil and wall was not allowed for, since the soft stratum, embankment and link elements were represented by linear elastic models. They concluded that link elements were not required in cases where the piles were quite flexible or the soft layer was deep. A similar approach was adopted by Rowe and Poulos (1979) for the analysis of stabilizing piles installed at the crest of a slope, although an elastic plastic soil model was used and limiting soil pressure on the piles were specified to allow plastic flow of the soil past the piles. Table 1 Soil Properties Nature of soil Loose Sand Medium Sand Dense Young s modulus(es) [N/mm 2 ] Unit Weight () [KN/m 3 ] Poisson s ratio () Angle of internal friction () [] Dilation angle (ψ) [] Sand

3 157 Indian Geotechnical Journal, 41(3), 2011 Description of approach For this study, the model tests are analyzed using a plane strain finite element approach, with the piles represented as equivalent sheet-pile wall. Plane strain analysis is the most straightforward of the finite element approaches described above, and allows good representation of the pile group configuration and geometry, without being unduly complicated. The equivalent sheet-pile walls are modeled with beamcolumn elements connected to the finite element mesh, and the soil strata are represented by 15 noded triangular elements of elastic plastic Mohr Coulomb model. Soil structure interaction is modeled by means of a bilinear Mohr Coulomb model. The finite element program PLAXIS is used for this study. In the model study, the same dimensions of the model test conducted in the laboratory are adopted. The soil strata are modeled with 15 noded triangular elements and the equivalent sheet-pile walls are defined by 5 noded beam-column elements with nodes separate from those defining from the soil. The soil nodes and pile nodes are connected by bilinear Mohr Coulomb interface elements. This allowed an approximate representation of the development of lateral resistance with relative soil-pile movement and ultimately the full limiting soil pressure acting on the piles. Then the self-weight load is applied to the mesh for generating the initial stress condition. The typical finite element discretization of the sloping ground is shown in Figure 1. under geostatic conditions. Hydrostatic state of stress with Ko = 1.0 was considered as a initial state of stress, where Ko represents the coefficient of lateral earth pressure at rest. The pile-soil interface was modeled with contact elements using interface condition. The soil stratum is idealized by 15 nodes triangular elements with elastic plastic Mohr Coulomb model and the structural elements are idealized by beam element. Soil properties The analyses are conducted with sand represented by Mohr Coulomb model. The Mohr Coulomb model is used for the proposed (linear elastic plastic) model, with plastic flow governed by an associated flow rule. Values of angle of internal friction and dilatancy angle for loose, medium and dense sand are obtained from laboratory tests. The required density of the sand in the test tank was achieved by a sand raining device. This arrangement contains a hopper connected to a 750 mm long pipe and an inverted cone at the bottom, with a holding capacity of about 78N of sand. The sand poured through a 31mm internal diameter pipe and was dispersed by 60 o due to the inverted cone placed at the bottom. By varying the height of free fall of dispersed sand particles, the density of the sand was varied. The height of free fall from the bottom of the pipe was maintained constant using an adjustable length pointer fixed at bottom. This arrangement was calibrated by number of trials to get height of fall required for relative density corresponding to 30%, 45%, and 70% and it was found to be 50 mm, 205 mm, and 710 mm respectively. The angle of internal friction and dilatancy angle (Table-1) were obtained for the corresponding relative density, which are given as the soil input parameters. A small cohesion intercept of 1N/mm 2 was chosen in order to make the problem stable numerically. The soil shear strength parameters used in the FE analyses are under undrained loading condition. Young s modulus (Es) of soil profile is estimated by using the triaxial test stress strain relation. Poisson s ratio values are appropriately selected based on the relative density of the sand. The values of soil properties are presented in Table 1. Fig. 1 Discretization of finite element mesh (fine mesh) It is assumed that sloping ground has an effect on the load-displacement behavior of the pile-soil system. The problem shown in figure was modeled using a two-dimensional (2-D), plane strain FE model of a sloping ground. In this model, symmetry boundary conditions were applied on the top and bottom boundaries of the mesh as shown in figure. The left and right boundaries of the mesh were initially constrained in the x-direction to establish initial states of stress Structural properties The pile is represented by three noded plate elements. The plate elements are used to simulate the behavior of pile based on Mindlin s beam theory. This theory allows for beam deflection due to shearing as well as bending. Bending (flexural rigidity) stiffness EI and axial stiffness EA are input as the average of the soil and pile properties over an equivalent 1-m thickness of the mesh. As the soil stiffness is much lower than the structural stiffness, the equivalent wall properties are

4 158 Finite Element Analysis of Laterally Loaded Piles on Sloping Ground K. Muthukkumaran and N. Almas Begum effectively independent of the soil properties and do not vary with depth. The structural member s properties are presented in Table 2. Table 2 Pile properties used in finite element analysis Normal Stiffness EA 3.842E06 N Flexural Rigidity EI 2.878E08 Nmm 2 Equivalent Thickness d mm Poisson s Ratio 0.3 Analysis Sequence The analyses are carried out in total stresses by generating initial stresses using the drained parameters of soils and connection with soil element presented in Table 1 and the structural parameters presented in Table 2. The single model tests were conducted considering three different slopes [zero slope, 1V:2H, 1V:1.5H] and three different relative density [30%, 45%, 70%] having the embedment length of 775mm. Load Deflection Behaviour Lateral load behaviour of the pile was studied by using lateral load deflection curves which shows the lateral load applied and the lateral deflection at the soil surface. The lateral load was applied at a distance of 75mm above the ground surface and lateral deflections were measured at the soil surface. Figure 2 shows the deformed shape of the pile and relative shear strain shading of the soil movement towards slope. It is observed that the soil movement is much greater in top layers due to initial horizontal confining pressure acting on the piles on the slope side is smaller than that in the horizontal ground. Hence lateral resistances of piles near slopes will be small, compared to the piles on horizontal ground. This reduction is due to reduction in passive resistance mobilized in front of the pile. The deflection of piles on sloping ground will be more than that on the horizontal ground. From the deformed shape of the mesh, it can be observed that the failure zone is like a circular slip failure. Figure 3 shows the comparison of experimental results of Almas et al. (2008) with results from present FE analysis. The present FE analysis results have reasonable agreement with the experimental result. It is found that the lateral resistance of the pile decreases as the slope of surface increases. Fig. 2 Deformed shape of pile and shear strain shading of soil Fig. 3 Experimental and FEA lateral load displacement curves for 30% Dr

5 159 Indian Geotechnical Journal, 41(3), 2011 Figure 4 shows the lateral load-deflection curves of different relative density (30%, 45% and 70%) for different slopes of H, S1 and S2. The load carrying capacity of the pile embedded in S2 slope is lower than that of the pile embedded in the horizontal and S1 sloping ground. Fig. 4 Lateral load displacement curves for various slopes and Dr slope (horizontal ground) has more ultimate load capacity than pile located in slope S1. It is also observed that the ultimate lateral load capacity of pile located in S1 slope having 30% and 45% relative density is exactly equal to the pile located in S2 slope having relative density of 45% and 70% respectively. From this observation it is concluded that even in steeper slope the lateral carrying capacity can be increased by increasing the relative density of the soil. Figure 6 shows the relationship between the load ratio and displacement at the loading point. It is found that the value of load ratio is affected markedly in the small displacement range by increasing the relative density for the two slopes. However the load ratio is constant value as the displacement increases. The value of load ratio is approximately 0.73 when the pile is located in a higher density sand (Dr = 70%) for the slope S1 and for the pile located in slope S2 the value of load ratio is approximately 0.63 for the same relative density. To obtain a load ratio = 1 (equivalent to the horizontal ground condition), it may be necessary to increase the relative density of the soil greater than 70% and the embedment length of the pile can also be increased. Generally, determining the ultimate load from lateral pile load tests depends on the tolerance of the structure supported by the piles. Where no such criterion is available, the criterion usually accepted for estimating the ultimate lateral load is corresponding to 20% of pile diameter lateral movement or displacement normal to the pile axes (Narasimha Rao et al. 1998). The ultimate lateral load capacities of the piles were established based on this criterion and are presented in Figure 5. Fig. 6 Normalized loading curves Fig. 5 Lateral load capacity versus relative density for different slope surfaces The figure clearly shows that pile located in zero The distribution of the bending moment along the pile shaft at different load increments has the same pattern for all cases and also the moments in the pile increase with applied load as expected. Figure 7 shows the bending moment variation along the depth for the three ground surfaces and three relative density of sand for an applied lateral load of 60N. The value of the moment increases regularly as the slope of the surface increases and also the location of the maximum bending moment slightly deeper with increase in the steepness of the slope, which shows that the load is transferred further down the pile with increasing load. The maximum bending moment occurs (also called depth of fixity) at about 12%, 14% and 16% of the embedded depth of the pile for the horizontal ground, S1 and S2 slope respectively.

6 160 Finite Element Analysis of Laterally Loaded Piles on Sloping Ground K. Muthukkumaran and N. Almas Begum Pile located in zero slope had a larger ultimate load than pile located in slope S1, which in turn had a larger ultimate load than pile located in slope S2. The lateral behaviour of pile located in S1 slope having 30% and 45% relative density is almost equal to the pile located in S2 slope having relative density of 45% and 70% respectively. It is found that the value of load ratio is affected markedly in the small displacement range by increasing the relative density for the two slopes. Fig. 7 Bending moment variation along the depth for different slopes and Dr The effect of relative density on maximum bending moment is shown in Figure 8 for different ground surfaces. The increase in relative density of the soil decreases the maximum bending moment due to decrease the relative stiffness of the pile soil system (T), which leads to act the pile as more flexible in nature. The decrease in relative stiffness of the pile soil system has lead to decreases the depth of maximum bending moment occurrence (depth of fixity). The load ratio is constant value as the displacement increases. The value of load ratio is approximately 0.73 when the pile is located in a higher density sand (Dr = 70%) for the S1 slope and for the pile located in S2 slope the value of load ratio is approximately 0.63 for the above said relative density. The value of bending moment increases regularly as the slope of the surface increases. The location of the maximum bending moment becomes slightly deeper with increase in the slope. The maximum moment occurs at about 12% of the embedded depth of the pile for the horizontal ground surface, 14% of the embedded depth of the pile for S1 slope and 16% of the embedded depth of the pile for S2 slope. The increase in relative density of the soil decreases the maximum bending moment due to increase in the relative stiffness of the pile and the soil. The range of percentage decrease in maximum bending moment when the relative density of the soil changes from 30% to 45% is by 2.5% to 3.0% and for the relative density 45% to 70% is by 3% to 3.5% for all the three slopes. References Almas Begum, N., Seethalakshmi, P. and Muthukkumaran, K. (2008): Lateral load capacity of single pile located at slope crest, Indian Geotechnical Journal, 38(3), pp Fig. 8 Effect of relative density on maximum bending moment for various slopes Conclusions The behavior of single pile subject to lateral load located on sloping ground has been investigated through a series of 2D finite element analysis. Based on the results from this analysis the following conclusions can be drawn Banerjee, P.K. and Davies, T.G. (1978): The Behaviour of Axially and Laterally Loaded Single Piles Embedded in Nonhomogeneous Soils, Geotechnique, 28(3), pp Budhu, M. and Davis, T.G. (1988): Analysis of Laterally Loaded Piles in Soft Clays, J. of Geotechnical Engineering, ASCE, 114(1), pp Chae, K.S., Ugai, K. and Wakai, A. (2004): Lateral Resistance of Short Single Piles and Pile Groups Located Near slopes, Int. J. of Geomechanics, 4(1), pp

7 161 Indian Geotechnical Journal, 41(3), 2011 Karthigeyan, S., Ramakrishna, V.V.G.S.T. and Rajagopal, K. (2006): Influence of Vertical Load on the Lateral Response of Piles in Sand, Computers and Geotechnics, 133(5), pp Martin, G.R. and Chen, C.Y. (2005): Response of Piles due to Lateral Slope Movement, Computers and Structures, 83(8-9), pp Matlock, H. and Reese, L.C. (1960): Generalized Solution for the Laterally Loaded Piles, J. of Soil Mechanics and Foundation Div., ASCE, 86(5), pp Mokwa, R.L. and Duncan, J.M. (2001): Experimental Evaluation of Lateral-Load Resistance of Pile Caps, J. of Geotech and Geoenv Engg, 127(2), pp Narasimha Rao, S., Ramakrishna, V.G.S.T. and Babu Rao, M. (1998): Influence of rigidity on laterally loaded pile groups in marine clay, J of Geotech and Geoenv Engg, 124(6), pp Naylor, D.J. (1982): Finite element study of embankment loading on piles, Report for the Department of Transport, Department of Civil Engineering, University College of Swansea. Peck, R.B., Hansen, W.E. and Thornburn, T.H. (1974): Foundation Engineering, 2 nd ed., John Wiley and Sons, New York. Pise, P.J. (1983): Lateral Response of Free-Head Pile, J. of Geotechnical Engineering, ASCE, 109(8), pp Pise, P.J. (1984): Lateral Response of Free-Head Pile, J. of Geotechnical Engineering, 110(12), pp Poulos, H.G. (1971): Behaviour of Laterally Loaded Piles I- Single Piles, J. of Soil Mechanics and Foundation Division, ASCE, 97(5), pp Randolph, M.F. (1981): Pilot study of lateral loading of piles due to movement caused by embankment loading, Report for the Department of Transport, Cambridge University. Rowe, R.K. and Poulos, H.G. (1979): A method for predicting the effect of piles on slope behaviour, Proc. Third Int. Conf. on Numerical Methods in Geomechanics, Aachen, 3, pp