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Finite Element Analysis of Strip Type Shell Foundation and its Interaction
Assistant Professor, Civil Engineering Group Students, Civil Engineering Group |
ABSTRACT
In this research paper the load settlement behaviour and interaction between strip shell footings have been analysed by Nonlinear Finite Element Method considering soil as elastoplastic material. The elastoplastic behaviour of soil has been modeled by Drucker-Prager Yield Criterion. The shell and soil continuum have been discretized into four noded isoparametric elements. The load settlement curves for a single strip footing and that of an individual footing in a group of two strip footings have been presented for different soil modulus. The effect of increase in soil modulus has been found to increase the load carrying capacity of the shell foundation. This increase is seen even at smaller load. The load carrying capacity of an individual shell foundation is maximum than a unit of shell foundation interacting with each other. The interaction is found maximum when the footings are at closer spacing and this interaction is found to reduce with increase in spacing. Hence it is suggested that while designing a strip shell footings, the spacing between the two must be kept at a distance such that each of the shells behaves as an individual footing. In other words the distance between the two shells should be kept such that the interaction effect is almost zero.
Keywords: Analysis, Strip type shell , Foundation, Interaction, Settlement, Unit shell
INTRODUCTION
The main aim of providing a shell foundation is to reduce the cost of foundation. Such shell footings require smaller quantities of construction material. This saving of construction material is at high labor cost. In areas having high material-to-labor cost ratio, shell foundation is considered economical foundation. Such shell foundations have been provided in United States of America, Maxico and several European Countries Figure 1. and Figure 2. show a single strip shell footing and a group of two strip shell footings interacting with each other. In this paper a strip type shell foundation and a group of two strip shell foundations have been analysed by nonlinear finite element method. The soil has been modeled as Drucker-Prager elastoplastic medium. Load settlement curves for single strip foundation and interacting strip foundation have been provided based on the nonlinear finite element analysis. Also the effect of soil modulus on the load settlement behaviour of single strip foundation and the interacting foundation has been presented.
LITERATURE REVIEW
The literatures reported on shell foundations are Nicholls and Izadi (1968), Kurian and Varghese (1969), Iyer and Rao (1970), Kurian and Mohan (1981), Agarwal and Gupta (1983), Melerski (1988), Hanna and Abdel-Rahman (1990), Kurian (2004). Nicholls and Izadi (1968), Iyer and Rao (1970), Agarwal and Gupta (1983), Hanna and Abdel-Rahman (1990) reported the bearing capacity of shell foundation. Kurian and Varghese(1969), Kurian and Mohan (1981)reported the contact pressure distribution. Harrop-Williams and Grivas(1985), Chandrashekhra and Antony (1996) reported the interaction between the footings. Melerski (1988) presented an approximate elastic solution to the statical problem of a thin concrete shell foundation. Kurian (2004) discussed the scope and advantages of using shells in the substructures.
Figure 1. A Strip shell footing
Figure 2. Two strip shell footings considered in the analyses to see the interaction effects
The literatures reported are mostly on the investigation of shell foundation on sand. Very few literatures are reported on interaction between shell foundations. The present paper aims to see the interaction between the shell foundation for a range of clayey soil by nonlinear finite element method. The effect of interaction of the shells on its load carrying capacity has also been investigated by nonlinear finite element method.
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, the iterative method considered for solving the nonlinear finite element equation and the validation of the two-dimensional finite element model considered is same as reported by Author, Maharaj (2003-Ppr-338)
FINITE ELEMENT ANALYSIS
Figure 3 shows the finite element discretization considered for a strip type of shell foundation. The foundation and soil has been discretized as four noded isoparametric finite elements. The soil has been modeled as an elastoplastic medium by Drucker-Prager Yield Criterion. The nonlinear finite element equation has been solved by Newton-Raphson iterative procedure. A domain of soil equal to 10 meter has been considered from the center of shell foundation on either direction for a single shell foundation as well as for a group of two shell foundation. The depth of soil considered from top of the foundation is equal to 20 meter. The bottom boundary has been provided no translation while the edge boundaries consist only vertical translation. The load has been applied as concentrated loads at the center of the foundation in the top portion.
Figure 3. Finite element discretization for strip type shell foundation
Varying Parameters and Material Properties
The thickness of the top of the shell footing = 0.20 m
The thickness of the side walls of the shell footing = 0.20 m
The width of the bottom portion of shell at 0.20 meter depth = 0.40 m
The depth of the foundation from top = 1.2 meter
The taper angle of shell = 450
Modulus of concrete = 2 x107 kN/m2 (kPa)
Poisson’s ratio of concrete = 0.30
The modulus of soil = 32, 76 MN/m2 (MPa)
Poisson’s ratio of soil = 0.45
Cohesion of soil = 29.10, 63.4 kN/m2 (kPa)
RESULTS AND DISCUSSIONS
The load settlement curve for a single shell unit out of the two footings interacting with each other has been plotted because the two footings are symmetrical in all respects and hence all the results for each of the footings interacting with each other will remain the same and has also been found the same.
Figure 4 shows the load settlement curve for a single unit of strip foundation. The initial portion of the curve is found to be linear and becomes nonlinear with increase in load. The load carrying capacity of the foundation increases with increase in the settlement. The foundation also reaches to its ultimate load carrying capacity but at higher settlement.
Figure 4. Load-settlement curve for single strip shell footing (Es=32 Mpa)
Figure 5 shows the effect of soil modulus on the load settlement behaviour of shell foundation. The effect of increase in soil modulus is to improve the load carrying capacity of foundation significantly. This increase starts even from the lower load and increases with increase in load . The increase in load carrying capacity is very much significant at higher load though it has been found significant even at lower load. Type1 and Type 2 soil are with modulus 3200 kN/m2and 7600 kN/m2.
Figure 5. Effect of soil modulus on the load settlement curves (a single shell footing)
Figure 6 shows the interaction between the two strip type shell footings. Initially the two curves overlap each other. With increase in loading the load carrying capacity of the shell foundation interacting with each other decreases at any settlement. This shows that the pressure bulb formed by the two foundations overlap each other and there is more interaction and hence excessive settlement in the foundation.
Figure 6. Effect of interaction of shell footings on load-settlement curve (Es=32Mpa)
Figure 7 shows the load settlement curve for a single strip footing and the two footings interacting with each other which are at 0.10 meter and 1.0 meter distance from each other in a soil of modulus 32000 kN/m2. It can be seen that when the spacing between the footing has increased the interaction between the footings has reduced. Maximum interaction is when the footings are at closer spacing. The load carrying capacity of a single unit is larger than each unit of two footings interacting with each other at 1.0 meter while the load carrying capacity is least for the footings which are at 0.10 meter.
Figure 7. Effect of interaction of shell footings on load-settlement curve (Es=32Mpa)
Figure 8 shows the load settlement curve for a single strip footing and the two footings interacting with each other which are at 0.10 meter and 1.0 meter distance from each other in a soil of modulus 76000 kN/m2. It can be observed that the effect of decrease in spacing is to increase the interaction between the footings. While maximum interaction is when the footings are at closer spacing. The load carrying capacity of a single unit is larger than each unit of two footings interacting with each other at 1.0 meter while the load carrying capacity is least for the footings which are at 0.10 meter.
Figure 8. Effect of interaction on load-settlement curves of strip shell footings (Es=76 Mpa)
CONCLUSIONS
The finite element method predicts the nonlinear load settlement curve of the shell foundation as expected in the field. The effect of increase in soil modulus has been found to increase the load carrying capacity of the strip type shell foundation. This increase has been found even at smaller load. The load carrying capacity of a single shell foundation is maximum than a unit of shell foundation interacting with each other. The interaction is found maximum when the footings are at closer spacing while this interaction is found to reduce with increase in spacing. Hence it is suggested that while designing a strip shell foundation, the spacing between the two foundations must be kept at a distance such that each of the shells behaves as a single unit. In other words the distance between the two shells be kept such that the interaction effect is almost zero.
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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