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Finite Element Analysis of Axisymmetric
Assistant Professor, Civil Engineering Group Birla Institute of Technology and Science, Pilani, Rajasthan, India e-mail: dilip_maharaj@yahoo.com , dkm@bits-pilani.ac.in
Desika P. Lakshmi Student, Civil Engineering Group
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ABSTRACT
In this paper an axisymmetric shell raft foundation has been analysed by nonlinear finite element method. The shell raft and soil has been discretized into four noded isoparametric finite elements. The soil has been modeled as Drucker-Prager elastoplastic medium. The effect of soil modulus, pile and pile stiffness on the load settlement behaviour of shell raft has been studied. The load settlement curves of shell raft, shell raft with pile and the regular raft have been compared. The effect of increase in soil modulus has been found to improve the load carrying capacity of the shell raft foundation. The addition of even a single pile below a shell raft increases its load carrying capacity. The effect of increase in pile modulus has been found to increase the load carrying capacity and reduce the settlement of the shell raft. The improvement in load carrying capacity due to increase in stiffness is only up to limiting value of pile stiffness. The load carrying capacity of a shell raft foundation has been found more than that of the regular raft foundation
Keywords: Analysis, Nonlinear, Settlement, Shell Raft, Raft, Pile
introduction
The shell foundation has been found to be an economical foundation in areas having high material-to-labor cost ratio. Such shell foundations have been provided in United States of America, Maxico and several European Countries. The conical shell raft foundation which is a combined foundation is suitable for water tanks and tower like structures. In this paper a conical shell raft foundation (Figure 1) has been analysed by nonlinear finite element method. The soil has been modeled as Drucker-Prager elastoplastic medium. Load settlement curves have been provided based on the nonlinear finite element analysis. The effect of increase in soil modulus, addition of pile below shell raft and increase in stiffness of pile on load settlement curves have also been analysed.
Figure 1. Axisymmetric Shell raft foundation
FINITE ELEMENT FORMULATION
The element stiffness matrix, element load vector, the assembly of element stiffness matrix and load vector, the constitutive model considered, derivation of elastoplastic matrix and the iterative method considered for solving the nonlinear finite element equation and the validation of the axisymmetric finite element model considered is same as reported by the author, Maharaj (2004)
FINITE ELEMENT ANALYSES
The shell raft has been analysed as an axisymmetric problem. Figure 2 shows the finite element discretization for the shell raft, pile and soil system. The raft, shell, pile and soil has been discretized into four noded isoparametric finite elements. The nonlinear finite element equation has been solved by Newton Raphson Iterative Procedure. The soil has been modeled as Drucker-Prager elastoplastic medium. A soil zone equal to 20 meter width and 20 meter depth has been considered from the center of the axisymmetric shell raft foundation. The lower boundary of the discretized domain has been allowed to have no degree of freedom while the edge boundaries have been allowed to have only vertical degree of freedom.
Figure 2. Finite element discretization for axisymmetric shell raft
Parameters used
Parameters and Material Properties used are:
Thickness of raft = 0.20 m
The thickness of shell = 0.20 m
The depth of shell foundation = 1.20 m
The taper of shell = 450
The length of pile = 10 m
The diameter of pile = 0.4 m
Modulus of raft material = 2x107 kN/m2
Modulus of pile material = 2 x 107, 2x 108, 2 x 109 kN/m2
Poisson’s ratio for raft and pile material = 0.30
Modulus of soil = 32000, 76000 kN/m2 (Type 1, Type 2)
Poisson’s ratio of soil = 0.45 (For both Type 1 and Type 2)
Cohesion of soil = 29.10, 63.4 kN/m2 (Type 1, Type 2)
RESULTS AND DISCUSSIONS
Figure 3 shows the UDL vs settlement curve for an axisymmetric shell raft foundation in a soil of modulus 32000 kN/m2. Here UDL is the uniformly distributed load on the foundation which is defined as the loading intensity on the foundatoion. The effect of increase in loading intensity is to increase the settlement of the foundation. This increase in settlement is linear in the initial portion while found to be nonlinear with further increase of the load. The rate of increase of settlement is more than that of the load.
Figure 4 shows the effect of soil modulus on the load settlement curve of the shell raft foundation. The effect of increase in soil modulus is to improve the load carrying capacity of the foundation significantly. This increase is found to be significant at higher loading intensity. The figure shows that the load carrying capacity of the shell raft is more in soil with higher modulus than in soil with lower modulus.
Figure 5 shows the effect of addition of pile on the load carrying capacity of shell raft foundation. The effect of addition of pile below the shell raft can be seen to reduce the settlement and increase the load carrying capacity of the shell raft. The load settlement curve of shell raft with pile is above the load settlement curve of that of the shell raft. This clearly shows that for the range of settlement, the load carrying capacity of shell raft with pile is always more than that of the shell raft without pile.
Figure 3. Load-settlement curve for Shell-Raft foundation (Es = 32 Mpa)
Figure 4. Effect of soil modulus on load-settlement curves of Shell-Raft foundation
Figure 5. Load-settlement curves for Shell-Raft with and without pile
Figure 6 shows the effect of increase in stiffness of pile on the load settlement behaviour of shell raft. Mat1, mat2 and mat3 represents the pile with modulus 2 x 107, 2x 108, 2 x 10 9 kN/m2 respectively. The effect of increase in stiffness of pile is to increase the load carrying capacity of the shell raft significantly. In other words the settlement of shell raft reduces significantly with increase in stiffness of the pile. This increase is only up to a limiting stiffness of pile. With further increase in the stiffness of pile beyond this limiting stiffness, there is no improvement in the load carrying capacity of pile.
Figure 7 shows the comparison of the load settlement curves between the shell raft and a regular raft having the same diameter. The diameter of the regular raft has been considered equal to the base diameter of the shell raft It can be seen that load carrying capacity of the shell raft is more than that of the regular raft. Thus a shell raft can be considered as a better option than that of the regular raft while selecting a foundation from these two types.
Figure 6. Effect of pile stiffness on load-settlement curve of Shell-Raft foundation
conclusions
The effect of increase in soil modulus is to improve the load carrying capacity of the shell raft foundation. The addition of even a single pile below a shell raft increases its load carrying capacity. The effect of increase in pile modulus below is to increase the load carrying capacity and reduce the settlement significantly. This improvement in load carrying capacity of shell raft by increasing the stiffness of pile is only up to limiting stiffness of pile. The bearing capacity of a shell raft foundation is found more than that of the regular raft foundation
Figure 7. Comparison of load-settlement curves for Shell-Raft and Raft
Acknowledgement
The Authors acknowledge Professor L. K .Maheshwari (Director) Birla Institute of Technology and Science for providing all facilities. The authors also acknowledge Professor A. K. Sarkar (Dean Instruction Division, Dean Faculty Division-I and Unit Chief of Community Welfare Division). The first author acknowledges staffs of all groups specially his Civil Engineering Group. The first author cannot remain without acknowledging his wife and his loving sons Ashish and Manish for their full support in this paper.
references
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