Wind Energy The Efficiency Analysis of Some Modern Foundation Solutions for Wind Turbines

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1 Wind Energy The Efficiency Analysis of Some Modern Foundation Solutions for Wind Turbines ALEXANDRA CIOPEC, CIPRIAN COSTESCU, IOAN PETRU BOLDUREAN Department of Land Communication Ways, Foundations and Cadastral Survey Politehnica University Timisoara Ioan Curea Street, no. 1A ROMANIA Abstract: In the present situation, the European directives and also the technological development conducted to the increase of the electrical power production coming from renewable sources of energy. Today, in Romania the energy produced by wind turbines represents approximately 20 % from the produced and consumed electrical energy. To obtain such a production capacity it is necessary a permanent development of the equipments that produce these quantities of energy. So, the wind turbines reached now days to a production capacity of 2.5 MW MW. These equipments of high capacity conducted to the need of construction of some sustaining towers of m m height, the rotating shaft having a diameter of approximately m. To sustain such equipments that are subjected to very large horizontal forces, the foundations of such structures must be designed and calculated carefully. It is necessary also to adopt some foundation solutions that should be efficient from technical and economical point of view. In these conditions, the dimensions of the foundation block, the number of piles, the dimensions of piles and the piles distribution under the foundation base are variables in the design of the foundation system. The paper analyzes the distribution of the load transmitted by the sustaining tower of the generator to the foundation ground through piles and also through the direct contact between the foundation base and the foundation ground. Key-Words: wind, energy, foundation solution, wind turbine, sustaining tower, piles, horizontal load 1 Introduction The wind turbines do not produce any air pollution and if they are placed properly, they produce a minimum impact upon the environment. The electrical power produced by the use of wind turbines represents a renewable source of energy. The growth of electrical power production using wind energy is carried out intensively in Romania, in the last years the electrical power produced by wind turbines generators exceeding 100 MW. This production of electric energy is obtained by installing new wind turbines with increasingly higher installed capacity [2]. Now days are produced wind turbines with installed capacity of 2.5 MW MW. They need sustaining towers with a height of approximately m. The equipment producing the electric energy by wind is composed by an electric generator and a switchgear, that are mounted at the top of the sustaining tower in a casing called nacelle and to the electric generator is attached a three-blade propeller. The three-blade propeller has a diameter of approximately m. The propeller blades are made of glass-reinforced epoxy similar to fibreglass. The turbines use moving air to produce power by transferring the wind s momentum to the rotor blades and localizing that energy in a single rotating shaft. The larger turbines rotate at about 15 revolutions per minute [1]. Fig. 1 Dimensions of a wind turbine The electrical energy will be generated only if the wind speed reaches a value of approximately 16 km/hour. If the wind speed is greater, the turbines will function at their rated capacity, but in ISBN:

2 the cases when this speed exceeds 90 km/hour the turbines are shutting down automatically. 2 Foundation Systems for Wind Turbines The foundation systems for wind turbines that are subjected to very large horizontal loads must be designed and calculated carefully. It is necessary to choose a foundation solution that is efficient from technical and economical point of view. Due to the eccentric loads with great eccentricity to which are subjected these structures, the design of the foundations for these structures requires to fulfill some stability and bearing capacity conditions. The first one consists in the verification of the rotational stiffness in the conditions of static loads and also of dynamic loads. Then it must be verified the pressure distribution on the foundation base because the foundation base remains only partially in contact with the foundation ground, the effect being that the bearing capacity of the foundation will be decreased. The variation of the bending moments and shear stresses generated inside the foundation block must be very carefully verified, so that the reinforcement disposal and the reinforcement quantity could vary significantly for each foundation, depending on the wind turbine characteristics and the soil conditions at the site. The design of the foundation system is based first on the determination of the site conditions. The geotechnical engineers will conduct a subsurface exploration program, then the obtained results are analysed and further on, it is designed a foundation system that is most suitable for the investigated site. The classical foundation system for this kind of structures consists in a shallow circular mat foundation with a great weight that contributes to the equilibrium of the entire system. But, this foundation system requires a great consumption of reinforced concrete, becoming an uneconomical solution. The diameter of this foundation system is m m and the height of the mat foundation is 2.00 m m, depending on the generator type and on the subsoil conditions at the site. In these conditions, an advantageous variant for wind turbine foundations is that to perform a pile foundation solution [3]. The paper analyzes the influence of the presence of a certain number of piles placed below the foundation base, having different length. The presence of the piles will increase the bearing capacity of the foundation and will reduce significantly the rotation of the foundation, respectively the rotation of the sustaining tower. 3 Bearing Capacity of the Shallow Circular Foundation The verification of the pressure transmitted to the ground through the base of a foundation loaded eccentrically, in case of Ultimate Limit State (ULS), is performed considering instead the pressure with a linear variation on the foundation base surface a pressure uniformly distributed on a reduced surface of the foundation base (Meyerhof, 1953) [8]. The general condition for the verification of the bearing capacity becomes in these conditions: (1) where: V d design eccentrically vertical load at the level of foundation base; R d design bearing capacity of the foundation. In the case when the load eccentricity, e, is greater than R/4, the vertical load is acting outside the central core, fact that will have as consequence the partial loading of the foundation base with the contact pressure (Fig. 2). Fig. 2 Reduced area of the circular foundation base The active zone below the base of a circular foundation becomes a surface (A ACBD ) formed by two circle segments. The centre of this surface is placed at the distance e, from the centre of the circle. This surface bordered by the two circle arches (ACB and ADB) is equated with a rectangular surface that will be considered to be loaded with a constant pressure of Meyerhof type. This reaction ISBN:

3 pressure is considered uniformly distributed, corresponding to the ULS of the foundation ground. The rectangular reduced area A of the foundation base is considered to be equal with the area of ACBD surface formed by two circle segments. Knowing that A ACBD area is equal with: (2) respectively, that the ratio between the sides of the rectangle, representing the reduced surface of the foundation base, is equal with the ratio between and segments: (3) results that the reduced area can be obtained using the relationship (4). (4) Analyzing the relationship (4) can be observed that the reduced area of the foundation base can be calculated only function of the foundation radius and function of the eccentricity of the applied load on it. In the case of a Vestas wind turbine of 2.5 MW and for a foundation with the diameter of 16.0 m results the following values for the geometrical characteristics and for the pressures distribution on the contact surface between the foundation base and the foundation ground (Fig. 3) [7]: HANSEN'S METHOD Actions Vertical Design Force [kn] V Design Bending Moment [knm] M Design Horizontal Force [kn] H Eccentricity [m] e=m / V 5.67 Base Inclination [ o ] η Dimensions Radius R 8.00 Effective Area [m 2 ] A' Soil Stress Case A1&M1 V / A' Soil Characteristics Design Angle of Friction [ o ] Φ' Design Shear Stress [kn/m 2 ] c u Effective Density of Soil (above) [kn/m 3 ] γ' Effective Density of Soil (below) [kn/m 3 ] γ Foundation Depth D f 2.70 Base Inclination [ o ] η 0.00 Stabilizing Soil Pressure [kn/m 2 ] γ' * D f Bearing Factors N q N γ π - for cohesive soils-undrained N c Depth Factors Force Inclination Factors d γ,b d c,b d q,b i q,b i γ,b Since H L = 0,00 i γ,l i c,b Shape Factors s γ,b s q,b s c,b Base Inclination Factors Base Inclination [rad] η b c,b b q,b b γ,b ULTIMATE BEARING CAPACITY [kn/m 2 ] q ult ALLOWABLE BEARING CAPACITY [kn/m 2 ] q ult / ALLOWABLE VERICAL LOAD [kn] V all VERTICAL LOAD [kn] V Must be > 1 V all / V 4.10 SLIDING RESISTANCE MAXIMUM SLIDING RESISTANCE [kn] R sliding MAXIMUM HORIZONTAL FORCE [kn] H Must be > 1 R sliding / H SOIL STRESS BASED ON ELASTIC DISTRIBUTION Foundation diameter D e Foundation base area A Section modulus W Central core D/ Load eccentricity e 5.67 Maximum effective pressure [kn/m 2 ] p ef Minimum effective pressure [kn/m 2 ] p ef Fig. 3 Calculus of the circular foundation base It results that the bearing capacity conditions are fulfilled for the vertical load (V all /V) and also for the horizontal load (R sliding /H). In the case when is considered a linear distribution of the pressure on the foundation base, the maximum compression pressure is equal with p ef1 = kn/m 2, respectively the minimum pressure is equal with p ef2 = kn/m 2. This linear distributed pressure, in the case when there is no possibility of transmitting the tension stresses between the foundation base and the ground, will be transformed, theoretically, into a rectangular surface loaded with a uniform compression pressure. The centre of this rectangular surface corresponds to the point defined by the eccentricity of the applied load. This rectangular surface will have, for the analyzed example, the area equal with m 2, smaller than the area of the foundation base, which is equal with m 2. The bearing capacity verification was performed for this reduced area of the foundation base. ISBN:

4 The next verification necessary to be performed consists in the calculus of the amount of the rotation of the foundation base. Following the calculus of the norm NP [5] it results that the rotation of the foundation exceeds the minimum allowed condition, representing a maximum vertical displacement of the foundation of 3 mm/m. Due to this situation, it is necessary to provide some piles under the foundation base which will reduce significantly the foundation rotation. 4 Foundation System on Piles The pile foundation which has been analyzed has the same diameter of 16.0 m, but below the foundation base is placed a number of 14 piles [6]. The Finite Elements Method consists of three main stages. In the first stage is achieved the analyzed domain s decomposition in parts of simple geometric forms, followed in the next stage by the analysis of the geometric parts created in the first stage and, in the last stage, is the recomposition of the domain while meeting certain mathematical requirements. In terms of fields of application, the method can be extended to various fields that describe a phenomenon using differential equations [4]. The foundation design was performed using a Finite Element Method (F.E.M.) computer code. The calculus was realized considering that the piles have different bearing capacities function of their length. The piles were modelled as single supports with variable stiffness. It was also considered the distributed contact pressure between the foundation base and the supporting soil. the bending moments and horizontal forces transmitted to the foundation by the wind turbine shaft. The calculus was conducted in seven steps, modifying the stiffness of the single supports and maintaining constant the subgrade reaction coefficient of the supporting soil. In the first step the stiffness of the single supports was considered to be approximately zero (K z = 1 kn/mm). In the next calculus steps, the stiffness of the modelled piles was increased with an increment of 500 kn/mm (K z = 500 kn/mm, K z = 1000 kn/mm, K z = 1500 kn/mm, K z = 2000 kn/mm and K z = 2510 kn/mm). In the Fig. 5 is represented the foundation displacements in the case without any rigid supports corresponding to the piles, the entire load supported by the foundation being transmitted to the soil only by the contact pressure between the foundation base and the supporting soil. Fig. 5 Foundation base vertical displacements in the case when the entire load is transmitted by contact pressures to the supporting soil It results that the maximum vertical downward displacement was equal with mm and the minimum upward displacement was mm. Increasing the stiffness of the single supports, modelling the piles, the rotation of the foundation decreased significantly and the foundation will be deformed due to the increase of the bending moments generated by the presence of the rigid supports modelling the piles (Fig. 6). Fig. 4 FEM model of the foundation base on piles The piles were considered as compression piles and also as tension piles, due to the great values of Fig. 6 Foundation base vertical displacements in the case when the entire load is transmitted by the rigid single supports modelling the piles ISBN:

5 The results of the performed calculus are presented in Table 1. There are presented the single supports stiffness and the reactions generated due to the increased stiffness of the piles. Also, are presented the values of the maximum and the minimum vertical displacements and of the foundation due to the base rotation. Table 1 Kza [N/mm 3 ] Kz [kn/mm] Fz [kn] emax [mm] emin [mm] θ [ ] It should be mentioned that the maximum tension force, respectively the necessary pullout resistance of the piles needs to have a value of minimum 990 kn. Increasing the stiffness of the single supports to the values mentioned previously consequently increased also the vertical reactions in the considered piles. The values of these reactions are also presented in the Table 1, respectively in the Fig. 7. Fz [kn] Variation of the Pile Load - Fz Kz [kn/mm] Fig. 7 Variation of the pile load versus stiffness of the single supports It can be observed that from the value of the reaction F z = 2500 kn corresponding to a stiffness K z = 1000 kn/mm, the increase of the reaction, respectively the load transmitted to the most loaded pile does not increase significantly. Function of the load F z transmitted to the piles, the piles can be designed by establishing their length and diameter function of the conditions given by the foundation ground from the site. In Fig. 8 is represented the variation of the maximum and minimum displacements of the foundation base, function of the stiffness of the single supports. emax, emin [mm] Foundation Maximum and Minimum Vertical Displacements Kz [kn/mm] Fig. 8 Variation of the vertical minimum and maximum displacements versus stiffness of the single supports Calculating the rotation of the foundation for each calculus step can be observed that the obtained values for the first two steps exceeds the allowable value of 3 mm/m (3 ). Analyzing the values of the rotation obtained by calculus, presented in Table 1, results that the bearing capacity of the piles placed below the foundation base should have a minimum value of 2600 kn, respectively a pullout resistance having a value of 990 kn. Using the previously presented values of compression and tension forces, function of the foundation ground conditions, can be established the length, respectively the diameter of the piles necessary to overtake these loads. Analyzing the bending moment variation of the foundation slab relative to the increasing stiffness of the single supports, results also a significant increase of the bending moments generated inside the reinforced concrete foundation. The Fig. 9 presents the bending moment (M xx ) distribution for the foundation slab. Fig. 9 Bending moment distribution in the foundation slab The Table 2 presents the minimum, respectively the maximum bending moment values generated in ISBN:

6 the foundation slab, function of the stiffness (K z ) of the single supports modelling the piles. Table 2 K z [kn/mm] M xx min [knm/m] M xx max [knm/m] Analyzing the values from Table 2 it results that the minimum bending moment is increasing with 28.8 %, respectively the maximum bending moment is increasing with 22.5 %. These percentages result by comparing the values obtained in the case when the entire load is supported by the supporting soil, as a contact pressure, with the values obtained when the load is transferred to the soil by piles. 5 Conclusions Designing a foundation for a wind turbine represents a complex problem due to the large loads transmitted to the foundation system by the shaft, especially due to the important horizontal loads which generate huge bending moments. The bending moments produce the rotation of the foundation which can exceed the limit condition of 3 mm/m. The limit condition is necessary to be fulfilled for the proper functioning of the wind turbine. To prevent the rotation of the foundation it must be found an adequate foundation solution which will fulfill the requirements regarding the limited value of the foundation rotation. The solution proposed in this paper consists in a pile foundation system. The analyzed case supposed the presence of 14 piles distributed circularly on the circumference of the foundation. To limit the rotation of the foundation base to 3 mm/m, it is necessary to realize a number of 14 piles around the circumference of the foundation which should have a minimum bearing capacity of 2600 kn for compression forces, respectively a pullout resistance of 990 kn. Regarding the foundation slab, the presence of the piles as rigid supports will produce an increase of the bending moments. They will increase with approximately 25 % compared to the values of the bending moments obtained in the case when the entire load is supported by the supporting soil as a contact pressure. References: [1] Bogdan I., Boldurean I.P., Ciopec Alexandra. Foundation Solution with Reduced Material Consumptions for Wind Turbines, Proceeding of the International Workshop Global and Regional Environmental Protection, Politehnica Publishing House, vol. 1, 2010, pp [2] Ciopec Alexandra, Costescu C. Efficient Foundation Solution for Ecological Systems of Electrical Power Production by Wind Energy, 12 th International Multidisciplinary Scientific GeoConference SGEM 2012, Bulgaria, vol. II, 2012, pp [3] Ciopec Alexandra, Roman L., Roman O. Study of Some Foundation Solutions for Wind Turbines, 13 th International Multidisciplinary Scientific GeoConference SGEM 2013, Bulgaria, vol. II, 2013, pp [4] Costescu C., Belc F., Marc P. Numerical Modeling Applied on the Behavior of Road Pavements, 12 th International Multidisciplinary Scientific GeoConference SGEM 2012, Bulgaria, vol. II, 2012, pp [5] Normative Regarding the Design of the Shallow Foundations, Indicative NP [6] Romanian Standard: Performance of Special Geotechnical Works. Drilled Piles, SR EN 1536, [7] Smith I. Smith s Elements of Soil Mechanics, Blackwell Publishing, [8] Stanciu A., Lungu Irina. Foundations, Tehnica Publishing House, 2006, pp ISBN: