Stress-strain state of the "combined tower-reinforced concrete foundation-foundation soil" system for high-rise structures

The aim of the work was to evaluate the effectiveness of the "combined tower-reinforced concrete foundation-foundation soil" system for high-rise structures on the example of a wind power plant (wind turbine) with a capacity of 1.5-2.0 MW using computer modeling in the PC "Ansys". Thus, under the combined tower the article refers to a high-rise building, consisting of two parts: the lower composite, the upper – in the form of a thin-walled core-shell closed profile. In both cases, the shell is a pipe with a weak taper. As an analogue, the VEU considered in foreign literature is adopted: the radius of the rotor is R=41 m, the height to the axis of the wind wheel is zhub =80 m, the shell is made of high-strength C355 steel and unlike the analog in this work the cavity of the tower lower part to a height of 20 m was filled with B60 class concrete. The modeling took into account the spatial work of the elements of the structural system and the physical nonlinearity of the materials from which they are made. At the same time, the Mises strength theory was used for steel, the Williams – Varnake theory - for concrete, and the Drukker – Prager theory - for the foundation soil. Comparison of the calculation results with the analogue showed that the destructive load of the tower increased by 37% due to filling the lower part of it with concrete, which indicates the effectiveness of the proposed solution. In this case, the destruction of the tower with a concrete core and without it occurred from the loss of steel shell local stability at the level of the tower junction with the foundation (with a compressed zone).


Introduction
This article discusses the joint static operation of the elements of the "combined towerreinforced concrete foundation-foundation soil" construction system using an example of a wind power installation.At the same time, the combined tower in the article is a high-rise structure consisting of two parts: the lower one is pipe-concrete, the upper one is in the form of a thin-walled rod-shell of a closed profile.In both cases, a pipe with a weak taper acts as a shell.An analysis of the literature showed that a holistic methodology for calculating such a system is currently missing.And when developing it, the following factors should be taken into account most fully: -physical nonlinearity of material properties; -geometric non-linearity of system elements (blades, etc.); -cyclic fatigue of materials -steel and concrete; -dynamic effects; -resonant phenomena; -friction between concrete and steel shell, as well as between concrete and soil.To analytically describe the influence of all these factors completely is not yet possible, which is reflected in existing standards on the wind turbines' design [1,2] and educationmethodical resources [3].However, a powerful tool can be used for this -computer simulation in PC "Ansys".In the article [4], this tool was already used by us to study the joint work of the system "steel support of power lines -foundation -foundation soil".Moreover, in contrast to it, the following features are taken into account in the system considered here: -the wind load on the surfaces of the rotating blades sweeping, the important characteristic of which is not pressure, but the speed of the wind flow; -the concrete presence at the bottom part of the tower; -friction forces between the steel shell and the concrete core.
The last two circumstances turn the lower part of the tower barrel into the so-called pipe-concrete structure, which, due to a number of advantages [5,6], significantly increases the operational properties of wind turbines, including strength, reliability and durability.The use of pipe concrete as a part of a combined wind turbine tower, apparently, is proposed here for the first time.
Along with the advantages, pipe concrete also has disadvantages, which nevertheless are easily eliminated with minimal additional costs.The most significant drawback is the difficulty in ensuring the joint operation of the concrete core and the outer steel shell at operational loads.Due to the difference in the lateral deformation coefficients of concrete and steel (νb≈0, 18÷0,25, νs≈0,3), under these conditions, the concrete core and steel cage work inefficiently.To eliminate this drawback of pipe concrete, the following solutions can be applied (both separately and in combination): weld special steel anchors on the inner surface of the pipe-shell; use expanding non-shrink cement for the manufacture of concrete mix; to make a pipe-concrete structure of circular section: with an external and internal shell of a steel pipe with filling the space between them with concrete.The instalation has the following characteristics: rotor radius -R = 41 m, swept area -S = 5345 m 2 , height to the axis of the wind wheel -zhub = 80 m, height to the gondola bottom -76.7 m (tower height), mass of each blade -5.78 t (total 3 pcs.),rotor mass -32.34 t, gondola mass -52.5 t; the wind turbine tower is made in the form of a thin-walled rod-shell of a closed profile, has a weak taper and consists of three parts of equal height, connected by flanges, the wall thickness of each part is different: lower -t1 = 30 mm, middle -t2 = 25 mm and upper -t3 = 15 mm, the tower has a cross-sectional diameter along the outer perimeter at the bottom -D1 = 4.3 m, at the top -D2 = 2.6 m.The tower shell is made of high-strength steel C355.In contrast to the analogue [7.8] in this work, the cavity of the lower part of the tower to a height of 20 m is filled with concrete of class B60.To avoid squeezing concrete up during deformation, a steel plate 50 mm thick and 3.0 m in diameter was made above its surface, which is rigidly connected to the walls of the tower shell.
The foundation under the tower is adopted as massive because of B25 class monolithic concrete, reinforced with steel reinforcement.In plan there is a foundation of a circular cross section.
Base soils at the supports' installation site can be different, we will take the worst case scenario that SP 22.13330.2011"Foundations of buildings and structures" allows: the type of soil is clay, non-slip, non-swellable; porosity coefficient 0.95; strain modulus E = 8 MPa; liquidity rate IL = 0.

Results and discussion
The loads acting on the wind turbine design are adopted taking into account the safety factors for the load γf = 1,0 and the responsibility of the structure γn= 1,0.In Table 2 GOST R 54418.1-2012prescribed 8 design cases for the wind turbines' calculation.The most characteristic is the first -"Power Generation" -calculation using the normal turbulence model.To reduce the amount of computation, we consider only this design case ( -dead weight of the tip: P1 = 5.78 × 3 + 32.34 + 52.5 = 102.2t (applied at the top); -dead weight of the steel tower shell: P2 = 135 t (evenly distributed in height and automatically taken into account in the program when setting the density of the material and gravity); -dead weight of concrete filling the bottom of the tower: P3 = 491 t (evenly distributed in height and taken into account in the program automatically); -the speed of the incident air flow at the height of the axis of the wind wheel (for wind turbines with a horizontal axis of rotation) -20 hub V  m / s; -average wind speed -Vave = 7.5 m / s; -maximum average wind speed (determined with a measurement interval of 10 minutes and not exceeding its value for 50 years) -Vref = 37.5 m / s; -launching wind speed -Vin = 3 m / s; -restart wind speed -Vout = 20 m / s; -extreme speed of a wind gust (determined with a measurement interval of 3 seconds and not exceeding its value for 50 years) -Ve50 = 52.5 m / s; -horizontal traction force caused by a wind flow running onto the blades:  The most complete dependence of the drag coefficient for the cylinder (1) and sphere (2) on the Reynolds number [11] Simplified dependency (Re) x C for cylinder [12] . For the coefficient x C in Fig. 3 shows a more complete dependence [10] and simplified [11].The latter is suitable for engineering calculations and is further taken as a basis.Moreover, to simplify the margin of the bearing capacity we will accept 0.7 x C const  .
-the torque resulting from a change of the wind direction (applied at the top of the tower), , 0 146 is the external radius of the cross section averaged over the height of the tower (the adopted coordinate system and force diagram are shown in Fig. 4 according to [3]); -the gyroscopic moment on the gondola (applied at the top of the tower), where ωR is the current angular velocity of rotor rotation (wind wheel) relative to the x axis, ωR = 16.1 rpm = 1.686 rad / s; ωn is the angular velocity of rotation of the nacelle relative to the z axis, ωn = 1 rpm = 0.105 rad / s; θR is the polar moment of rotor inertia relative to its rotation axis.For a three-bladed rotor it is determined by the expression:   The structure under consideration includes elements formed from materials with qualitatively and quantitatively different physical and mechanical properties.The mathematical expressions describing the diagrams in Fig. 2, a-b are given in the article [12].As a law of steel deformation, a bilinear diagram of kinematic hardening was adopted (see Fig. 5, b).The law assumes that in the "σ-ε" diagram the sum of different signs' stresses during loading and unloading is always equal to twice the yield strength σy, that is, the Bausinger effect is taken into account.The model is recommended for elastoplastic problems with small deformations of a material that follows Mises flow condition.
Thus, the physical law of deformation of a thin-walled shell was described by four parameters: elastic modulus E = 206·10 3 MPa, tangential modulus E'=75·10 3  To determine the foundation dimensions, the tower was previously calculated as a rigidly fixed cantilever rack, that is, without taking into account the foundation and foundation soil:  As a result, loads were obtained on the edge of the foundation, according to which the required foundation dimensions were calculated by using the SP 22.13330.2011"Foundations of buildings and structures" formulas: 18 × 18 m, height 1.8 m.
The results of determining the equivalent stresses in the tower are shown in Fig. 6.

Fig. 3 .
Fig. 3.The dependence of the drag coefficient on the Reynolds number -the wind load distribution profile of the tower corresponding to this model (Fig. 2, b)       2

Fig. 4 .
Fig. 4.The coordinate system at the tower top and the scheme of existing efforts[3]

Fig. 5 Fig. 5 .
Fig.5shows the material deformation diagrams used to create the model.

Fig. 6 . 1 E3S
Fig. 6.The results of the tower computer simulation