Optimum Design of Reinforced Concrete Raft Foundations Using Finite Element Analysis
Chapter One
Aim and Objectives
The aim of this research is to use finite element analysis in the optimum design of reinforced concrete raft foundations. The detailed objectives are to:
- Design a simple reinforced concrete raft foundation structure using the conventional method of design. The design will then be subjected to deformation using finite element analysis in order to obtain the stress pattern and
- Identify the need to provide additional compression reinforcement to the design at different percentages of the reinforcement ratio based on the cross sectional area of the raft slab and hence determine its effectiveness in providing resistance against differential
- Appreciate the need to use finite element analysis in the design of reinforced concrete raft
CHAPTER TWO
LITERATURE REVIEW
Site Investigation
All successful designs require greater geotechnical input including well planned site investigations, field and laboratory testing, together with consideration of the method of construction (GEO, 2006). A broad understanding of the ground conditions, site constraints, geological profile, site history and the properties of the various strata are necessary for the success of a foundation project.
Sites with a history of industrial developments involving substances which may contaminate the ground (e.g. dye factories, oil terminals) will require detailed chemical testing to evaluate the type, extent and degree of possible contamination (GEO, 2006 ; Ijimdiya, 2010a,b). An understanding of the geology of the site is a fundamental requirement in planning and interpreting the subsequent ground investigation (GEO, 2006). A useful summary of the nature and occurrence of rocks and soils should be obtained (GEO, 2006). Information on the groundwater regime is necessary for the design and selection of foundation type and method of construction (GEO, 2006).
It is always a recommended practice to retrieve good quality soil samples and continuous rock cores from boreholes for both geological logging and laboratory testing (GEO, 2006). For a rational design, it is necessary to have data on the strength and compressibility of the soil and rock at the appropriate stress levels within the zone of influence of the proposed foundations (GEO, 2006). The variation of elastic modulus of soil and presence of rock media plays a significant role and affects the moments and deformations of raft foundation (Venkatesh et al., 2009).
An appropriate geological model of a site is an essential requirement for safe foundation design (GEO, 2006). There are inherent uncertainties in any geological models given that only a relatively small proportion of the ground can be investigated, sampled and tested (GEO, 2006). It is therefore important that all available information is considered in characterising the ground profile and compiling a representative geological model for the site (GEO, 2006).
- Bearing Capacity of Foundations
In 1921, Prandtl published the result of his study in the penetration of hard bodies, such as metal punches, into a softer material. Terzaghi (1943) developed an analytical bearing capacity equation, based on superposition. In the past decades, the concept of bearing pressure in foundation design was introduced to investigate the excessive settlements occurring in buildings (Terzaghi and Peck 1967).
More recently, conventional finite element analyses (Griffiths, 1982; Burd and Frydman, 1997) have been used to predict the upper- and lower-bounds of bearing capacity of soils. These techniques have reduced the subjectivity and empiricism associated with the bearing capacity factors (Jason, 2006).
Corrections to the bearing capacity equations are also required for water table location (Small, 2001) and the friction angle of the soil obtained using the triaxial test (Meyerhof, 1963). Because of the different bearing capacity factors and correction factors, Bowles (1997) suggested a use for the more common solutions. However, he also indicated that more than one solution should be predicted to allow verification. Bowles (1997) discussed several procedures that yield estimates of the bearing capacity of a soil directly from in situ test results.
- Total and Differential Settlements
Bowles (1997) considered settlement estimates of a foundation as a best guess of the footing deformation after a load has been applied. Holtz (1991) observed that the design of a shallow foundation is typically governed by a limiting settlement criterion while Bowles (1997) noted that most structural distress is caused by excessive settlements and not the shear failures associated with bearing capacity. Settlement occurs in three stages: immediate or distortion; consolidation; and secondary compression settlement (Holtz, 1991).
Small (2001) suggested that it is generally acceptable to assume elastic behavior, as the working loads are typically lower than those governing the bearing capacity of the foundation. This is because settlement is typically estimated after the foundation has been designed for bearing capacity (Holtz, 1991). However, Small (2001) warned that the adopted elastic modulus must be appropriate for the stress range in the soil.
Bowles (1997) suggested that the term elastic modulus is not strictly correct as soil is not an elastic medium, even though, the elastic modulus is the most common term used for this parameter. Additional methods have been used to estimate the immediate settlement under the corner of a footing (Harr, 1966; Perloff, 1975; Mayne and Poulos, 1999).
Bowles (1997) suggested that differential settlements are the major cause of structural distress and therefore should be controlled by the designer. However, Day (1999) commented that the total settlement of a foundation can have serious effects on the use of the structure being supported. Therefore, it is recommended that both total and differential settlement be considered alike. Numerical methods like Finite Element Analysis (FEA) are excellent means for estimating the predicted settlement of a raft but there are several simplified methods that do not require such numerical procedures. In these methods, it is important that the actual stiffness of the raft is considered (Small, 2001). He also warned that analyses representing the raft as a Winkler foundation do not represent the true behavior of the soil and the analyses using elastic continuum is not site specific.
- Soil Horizontal Variability
Soil properties are known to vary from one location to another and this may have a significant effect on the overall design of a raft foundation. Even when soils are considered reasonably homogenous, soil properties exhibit considerable variability (Vanmarcke, 1977a). This variability is due to the complex and varied physical phenomena experienced during their formation (Jaksa, 1995). Variability between soil properties is called spatial variability and has recently been modeled as a random variable (Spry et al., 1988). Soil variability has been categorised by Jason (2006) into the following:
- Property randomness,
- Statistical parameters of soil properties,
- Modeling spatial
CHAPTER THREE
RESEARCH METHODOLOGY
Introduction
The methodology in this chapter involves the design of a simple reinforced concrete raft foundation using the conventional method of design. Other models are designed and tested using FEA which have additional compression reinforcement at various percentages of the reinforcement ratio based on the cross sectional area. This is to determine the effect of the compression reinforcement in providing resistance against differential settlement. The design is carried out according to Eurocode 2 (EN 1992-1-1:2004), which specified the depth of foundation, area and amount of reinforcement, and all the necessary checks used in the design calculations.
The finite element analysis (FEA) is carried out with the aid of a computer program. The program that is used is SIMULIA ABAQUS 6.10. ABAQUS is a finite element analysis software that is used in a wide range of industries like automotive, aerospace etc., and is also extensively used in academic and research institutions due to its capability to address non-linear problems (Manjunath, 2009). The ABAQUS program can be used to model reinforced concrete structures,analyse and generate test results using a state of the art 3D modeling and finite element technology. The type of analysis carried out in this research is non-linear involving reinforced concrete.
During the modeling in ABAQUS, the analysis parts for the soil, slab, and reinforcement are created and assigned material and section properties. The embedded element option is used to detail the reinforcements in the slab. The elastic foundation option is used to model the soil surface to make it act as springs to ground which includes the stiffness effects of a support (such as the soil under a building) without modeling the details of the support. The parts are then assembled together, the loads and boundary conditions imposed and the job executed to obtain the results.
CHAPTER FOUR
RESULTS
Design of Raft Foundation According to Eurocode 2
CHAPTER FIVE
DISCUSSION
Stress Patterns in the Raft Foundation
The Von Mises stress pattern obtained after the analysis for the raft foundation models can be seen in the deformed diagram of the models shown in Fig. 4.19 –
4.26. The Von Mises stress refers to the theory called Maxwell-Huber-Hencky- Von Mises criterion for ductile failure. The analysis shows that there are no Von Mises stresses within all the raft foundation models. The contour blue indicates zero Von Mises stresses and hence it is an indication that the foundation is stable after the deformation caused by the applied loads.
Settlement of the Raft Foundation
Bowles (1997) considered settlement estimates of a foundation as a best guess of the footing deformation after a load has been applied. He noted that most structural distress is caused by excessive settlements and not the shear failures associated with bearing capacity. Eurocode 2 (2008) specifies that where differential settlements are taken into account a partial safety factor for settlement effects should be applied. Also Eurocode 7 (2004) specifies that differential movements of foundations leading to deformation in the supported structure shall be limited to ensure that they do not lead to a limit state in the supported structure.
The immediate settlement of the raft foundation models takes place in the direction in which the load is applied. The spatial displacement of the models can be seen in Fig. 4.27 – 4.34. It can be seen that the maximum immediate settlement in the first raft foundation model occurred at the points where the loads are applied while the minimum immediate settlement occurred at the center where there is an upward heave. The result indicates that the tensile reinforcement provided is insufficient to provide adequate resistance against deformation and differential settlement.The addition of compression reinforcement increases then resistance until uniform settlement is obtained at a value 0.9%, a percentage of the cross sectional area of the raft slab.
CHAPTER SIX
SUMMARY, CONCLUSIONS AND RECOMMENDATION
Summary
In the course of this research, the following were carried out:
- A simple raft foundation is designed using the conventional method of design according to Eurocode
- The design is subjected to finite element analysis in order to obtain the stress and settlement
- The settlement pattern indicates there is differential settlement within the raft foundation and hence additional compression reinforcement is provided to this initial design from 0.1% to 0.9% of the cross sectional area of the raft
- The raft foundation design with the additional reinforcements is then subjected to finite element analysis until uniform settlement is obtained at 0.9%.
Conclusions
This work has successfully achieved its objectives through the literature review and the studies conducted. On the basis of the study carried out, the following conclusions may be drawn:
- The variation of the amount of reinforcement in compression and tension in a raft foundation plays a significant role and affects the moments and deformations of the
- Compression reinforcement is effective in providing resistance against differential settlement in a reinforced concrete raft
- Settlement estimate of a foundation is the best guess of the footing deformation after a load has been applied as proved from the nodal representations of elements in the finite element analysis
- The overall settlement of the raft foundation was reduced by about 20% due to the increase in the stiffness of the foundation as proved from the displacement of nodes and elements in the finite element analysis results.
- The finite element analysis is a good method for the design and analysis of raft foundations.
Recommendation
This work suggests that a suitable percentage of the concrete cross sectional area of raft slab foundations should be used as compression reinforcement in order to prevent differential settlements. The percentage should be derived using finite element analysis (FEA) by testing the conventional design of the raft foundations. This value is obtained as 0.9% of the concrete cross section when using Eurocode 2 and may be generally applied for the design of reinforced concrete raft foundations.
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