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1 The Eighth Asia-Pacific Conference on Wind Engineering, December 10 14, 2013, Chennai, India Design methodologies of wind-sensitive tower foundations under conditions of partial contact Bharathi Priya, C 1, Balamonica, K 3, Gopalakrishnan, N 1 Sathish Kumar, K 1, Muthumani, K 1, Venkatumesh, S 2 & Mahadev, C V K 2 1 Scientist, CSIR-Structural Engineering research Centre, Chennai, India ABSTRACT 2 Wind Electric Initiatives, L&T Construction, Chennai, India 3 M.Tech Student, AcSIR, India Corresponding author: ng@serc.res.in Tall towers are amongst the critical classes of structures which are designed to resist a variety of dynamic and static loads, due to cyclonic winds, machinery and seismic loads. The foundations used for supporting them are generally of solid circular rafts or of annular type and are of reinforced concrete. These foundations resting on rocks or granular soil are sometimes designed to be in partial contact with only a portion of raft under compressive pressures. The paper presents the various design philosophies followed with reference to tall towers under extreme lateral load conditions. This paper describes a methodology of computing the base pressure distribution of a raft under partial contact conditions and subjected to extreme lateral loads. The results of finite element analysis using compression only springs are described. A formulation is also made such that using simple design aids and charts, non-dimensionalised contact pressures and effective contact area can be computed. Keywords: Tall tower foundations, Partial contact, Codes of practice Introduction The growing need for sustainable power generation has led to an increased number of power plants, both of fossil-fuel type and of non-conventional type. The foundation types of tall towers in power plant structures are mainly arrived at based on geotechnical considerations and other engineering conditions. The safety and economic conditions also play a vital role in the design of foundations. Such foundations must be effectively designed which can deal with large overturning moments and dynamic loading such as extreme wind and cyclones. This paper focusses on the various design philosophies followed in the design of tall towers under extreme lateral loading condition. Literature Studies Reinforced concrete spread footing is commonly used type of foundation for towers and chimneys. The type of foundation is dependent on site conditions with good soil bearing capacity. However, if the soil is weak or the site has uncommon conditions such as constraint of space, or if the terrain is sloping or involves off shore construction, other types of foundation are used. These include pile foundations, drilled shafts, caissons, etc. Svensson (2010) discussed various wind turbine foundation types that can be used on different soil conditions using case studies. Göransson and Nordenmark (2011) studied fatigue effects for a foundation slab for a wind power plant, comparing methods for fatigue assessment according to Eurocode 2 and fib Model Code 2010 as well as performing parametric studies of the fatigue design of a foundation slab and identified parameters that have significant impact on fatigue of a foundation slab for a wind power plant. Proc. of the 8th Asia-Pacific Conference on Wind Engineering Nagesh R. Iyer, Prem Krishna, S. Selvi Rajan and P. Harikrishna (eds) Copyright c 2013 APCWE-VIII. All rights reserved. Published by Research Publishing, Singapore. ISBN: doi: / p4 1316

2 Details of the study This paper covers the foundation design of a typical tower situated in a hypothetical Indian site such that the extreme loading conditions are typical of a tower of m height. Structural connections between the tower and the foundation are not covered in this paper and only foundation design aspects with reference to limiting the allowable bearing pressures are dealt with. The foundation of the tower is of reinforced concrete, circular in plan having base mat and pedestal. The base mat is a tapered slab projecting from the pedestal all around. The pedestal is supporting foundation mounting part. The bottom of tower is fixed to the foundation mounting part. The founding level below ground is assumed to be 3m. Table-1 gives the assumed material and site description. The wind speed in the site is assumed from the wind speed map of India given by Lakshmanan et.al. (2009). The design loads considered for arriving the foundation dimensions and also for analysis are based on a tower of m height situated in a critical Indian site. Table 1 Typical design details of the foundation Grade of concrete M 30 Reinforcing steel strength Fe 500 Modulus of Elasticity of concrete 5000fck = N/mm 2 Poisson's ratio 0.3 Density of concrete 25 kn/m 3 Net SBC of soil 250 kn/m 2 Density of soil kn/m 3 Gross SBC (Allowable) kn/m 2 The maximum vertical load applied to the foundation would be relatively small, compared to the maximum horizontal load and applied overturning moment on the foundation. The foundation must be designed to resist these loads adequately. The design, as such follows the loading given for extreme loads without adopting any load factor. Hence a working stress design principle is followed as usually carried out for machine foundations with no additional load factors. The loads considered for the analysis are typical of a tower of m height which includes self-weight of tower and equipment, operating loads etc. In addition to these loading, the self-weight of foundation and soil weight above the foundation is considered for the design for all the load cases. For the tower, the coordinate system followed is given in Fig 1 and typical loading adopted is presented in Table 2. The design also presumes a weathered rock soil with a net bearing capacity of 250 kn/m 2 at a depth of 3.0 m from the normal ground level. The founding depth of the tower is assumed to be 3.0 m from the normal ground level so as to utilize this bearing capacity. 1317

3 Table 2 Loads adopted for analysis Fx = -850 kn (Horizontal) Fy= 230 kn (Vertical) Fz = kn Mx= kn.m My = 100 kn.m Mz = kn.m The diameter of the circular raft is arrived at based on a trial and error process such that the maximum allowable pressure is not exceeded at the extreme point of the foundation. A partial loss of contact is assumed for the extreme load condition with neutral axis near the mid-point of the circle. However the maximum compressive pressure due to the partial contact is found to be less than the allowable bearing pressure. Figure 1. Coordinate system followed for the analysis Details of the analysis Analysis of the tower foundation is carried out using STAAD Pro V8i. Foundation is modelled using shell Elements. All elements are having four nodes with six degrees of freedom at each node. The elastic mat is analyzed as a flexible plate supported on springs considering the modulus of sub-grade reaction. Based on the allowable settlement of 40mm under a specified bearing capacity, the subgrade modulus is found to be 6250 kn/m 2 /m. 1318

4 Since no tension can be developed between bottom of foundation and soil, the springs considered are taken as compression only springs. The thickness of the elements are assigned by trial and error, for the pedestal and base mat by calculating average thickness along the base mat. The thickness of the base mat varies radially outward in a decreasing manner. The foundation is modelled for load application. The load transfer from the tower to the foundation is simulated close to realistic transfer using rigid links. From the analysis, the maximum bearing pressure distribution (Figure 2) is found out and the same is used for further design of the foundation. Figure 2. 3D view of the staad pro model with Maximum bearing pressure distribution Details of the analytical formulations A mechanics based formulation is developed using cylindrical coordinate system. Expressions for non-dimensionalised base pressure and over-turning moments are developed as functions of either theta (angle subtended by the partial contact area) or the neutral axis depth. Nondimensionalised moments and axial forces in addition to their ratios (which gives the eccentricity of the axial load in the presence of the lateral load) are plotted. Since the eccentricity of the axial load with reference to the centroid of the total foundation area is known, theta and partial contact distances can be evaluated. The physical moment or axial load expression (as against the non-dimensionalised values) are used to evaluate the actual bearing pressure at an extreme point normal to the neutral axis plane. 1319

5 Figure 3 Bearing pressure distribution on a circular foundation Figure 3 shows the earth pressure ( ) distribution on a circular foundation when it is subjected to an uplift from oneside. The shaded portion represents the part that is in contact with the soil. The load on the foundation and moment can be derived as follows Load (1) (2) (3) 1320

6 (4) (5) (6) Moment (7) (8) (9) (10) (11) (12) Equation 6 and 12 gives the axial force and moment for a specified base pressure ( ) and angle (). To find and : Generally for a practical problem like cooling tower or chimney the axial force and the moment coming on to the foundation is a known quantity. From the load and the moment the eccentricity of the axial load can be evaluated and can be normalized with respect to radius. From the plot (Figure 4) corresponding to the normalized eccentricity can be found which can be used to calculate the. For evaluated, and can be interpreted from the Figure 5 and 6. From these, the earth pressure can be easily calculated. 1321

7 Cos() Normalized Eccentricity Figure 4 Eccentricity Vs Cos() Pu/( 0 *a 2 ) Angle (Radians) Figure 5 Angle Vs 1322

8 M u /*a Angle (Radians) Figure 6 Angle Vs For the analysis carried out, the total axial load acting on the tower is found to be kn including the self-weight of the tower, self-weight of the foundation and soil weight. The total overturning moment is kn-m. From these, the eccentricity is calculated. Using the eccentricity, angle is found with plot 4. From the above values, using plots given in Fig 5 and Fig 6, the bearing pressure is arrived as 383 kn/m 2 which is close to the bearing pressure found in finite element analysis. These results are also verified to be less than the maximum allowable bearing pressures. Conclusions This paper describes the process of foundation design of a tall tower foundation. A typical finite element analysis of the tower foundation under conditions of partial contact is described. The results from the finite element investigations are bench-marked with analytical formulations. The procedure adopted for solid circular rafts can be followed with minor modifications in the case of annular raft foundations in the future. Acknowledgement This paper is being published with the kind permission of Director, SERC, Chennai. The authors would like to thank M/s. L&T Construction - Wind Electric Initiatives for their active support. The authors also thank the scientists and laboratory staff of ASTaR laboratory for their valuable inputs. 1323

9 References Bureau of Indian Standard. IS 875 (Part 3):1987, Indian standard code of practice for design loads (other than earthquake) for buildings and structures, New Delhi, Lakshmanan, N., Gomathinayagam, S., Harikrishna, P. Abraham, A, Chitra Ganapathi, S. (2009), Basic wind speed map of India with long-term hourly wind data Current Science, 96(7), Henrik Svensson (2010), Design of Foundations for Wind Turbines, Master s Dissertation, Lund University.Sweden. Göransson, F and Nordenmark, A. (2011), Fatigue Assessment of Concrete Foundations for Wind Power Plants, Master of Science Thesis in the Master s Programme Structural Engineering and Building Performance Design, Chalmers University Of Technology, Sweden. Joseph.E.Bowles, (1996), Foundation Analysis and Design, Fifth Edition, McGraw-Hill, New York, U.S.A 1324