Structural design of a water intake tower located inside a reservoir

Transcription

1 Structural design of a water intake tower located inside a reservoir Abstract João Pedro Rodrigues Fernandes Jardim joao.jardim@tecnico.ulisboa.pt Instituto Superior Técnico, Lisboa, Portugal October 2016 The work that follows is the design of a reinforced concrete water intake tower located inside a reservoir, following the rules of European standards and other works. Taking as initial data the geometric definition of an existing water intake tower, designed in the 1950 decade, the reinforced concrete design of the structure was made in the perspective of modern codes, to guarantee safety. The materials used and cover of reinforcement were discussed taking into account durability issues. The actions on the structure were analysed taking into special attention the seismic hydrodynamic added masses. The structure was modelled in a finite element analysis program in order to evaluate the stresses resulting from the defined actions. Having the design stresses, it is possible to accurately perform the safety checks and reinforcement calculations for the relevant ultimate and serviceability limit states. Finally, some aspects relevant for the correct detailing of rebar are mentioned and some conclusions are taken about this type of structure and its behaviour. Keywords: Intake tower, hydrodynamic added masses, structural design, reinforced concrete 1 Introduction A water intake tower is a hydraulic structure with the purpose of collecting water for a variety of uses, such as providing water to populations and agricultural fields, utilization in industrial facilities and power generation. Therefore, its concept should be based on hydraulic principles that guarantee the necessary flow of water upstream. Nonetheless, its structural safety must be guaranteed, and is the main aspect of this work. The present work will consider the analysis and design of a reinforced concrete tower structure, with an initial geometry that was previously defined, and hypothetically situated inside a reservoir in West Algarve city, near Lagos, a region of high seismic effects in the Portuguese context. 2 Geometrical definition The structure, represented in figure 1, has 61,8 meters of height above foundation, which is admitted to be supported in a concrete foundation with sufficient weight to ensure stability. The ground foundation is considered as good quality foundation, a competent rock. As it s possible to see, the structure is composed of 10 columns, 4 of those only supporting the beam of the rolling bridge, whereas the other six go from the base to the top. These 6 columns change their cross-section along their height, having a considerable dimension near the base, which allows them to resist significant loads. The main tower composed of columns P1-A, P1-D and P2 has four plans of diagonal bracings, very effective for resistance against horizontal actions. These bracings need to be stopped at 13,5m above footing level so there is space for the grates that move along a guideline in the columns to stay. This structural discontinuity is analysed in detail. Figure 1 - Three dimensional geometric model of the structure 1

2 Although the grates are most of the time on the mentioned place, the most compromising place that they can be for the safety of the structure is at its top, so when designing the structure, this position was the one considered, especially for seismic action Columns P1-A, P1-D and P2 are also supported on base walls, with a high resistant capability and stiffness. These walls provide a significant resistance to the tower for lateral loading, and inside them is the beginning of the hydraulic circuit of the intake tower. Columns P2, P1-B and P1-C are also connected by beams, with a similar purpose to the diagonal bracing, but those aren t as effective. Joining both columns P1-B and P1-C is another plan of diagonal bracings, similar to the other four. On the beams from the backside of the tower are ladders that give access to the lower levels of the structure. This structure has two slabs, one of which has no particular purpose and the other is a support platform for works on the tower. It is usually acted by live loading, basically from normal operation of the structure. 3 Materials and durability Nowadays, when projecting a structure, besides the usual concerns with safety and functionality, there is also the issue of durability. The structure needs to guarantee those for a determined period of time or the project won t be economic and sustainable. Therefore, there are norms such as NP EN [1] that determine some parameters that should be met so the required durability is provided. Usually the design is made taking into account a 50 year minimum lifespan for the structure, but in certain cases such as hard to repair structures or important projects, the minimum lifespan should be widened for 100 years. This tower is part of both of those exceptions, and therefore was projected to have a 100 year lifespan. The choice of materials on the design of a reinforced concrete structure, more specifically the choice of the concrete class, and the choice of the cover for the reinforcement are the main aspects that need to be controlled so the durability requirements are met. As mentioned before, NP EN [1] determines some measures to be taken, based on the structures exposition to degrading agents. First, it s determined the structure s class of exposition. As this structure is far from the ocean and placed on an environment that s cyclic wet and dry, its reinforcement corrosion shall only happen due to carbonation. Therefore its class of exposition is, as defined by NP EN [1] XC4. This norm imposes a minimum resistance class for the concrete to be used according to its class of exposition. The type of concrete used was C30/37 and was solely determined by this, because for the stresses generated for the static and dynamic actions, a lower class of resistance was enough. As for the reinforcement, there is no such thing as a minimum class of resistance because the steel is not as important as concrete when it comes to durability issues. The steel chosen was A500 NR. The materials used and their characteristics are specified on tables 2 and 3. Table 1-C30/37 concrete properties Class f ck [MPa] f cd [MPa] f ctk 0.05 [MPa] f ctm [MPa] f ctk 0.95 [MPa] E c,28 [GPa] C30/ Table 2- Reinforcement steel A500 NR properties Class f yk [MPa] f yd [MPa] E s [GPa] ε yd [x10-3 ] A500 NR ,175 The covers used follow as well the premises of NP EN [1]. They are dependent from the structural class and exposition class 4 Actions The project actions that were taken into account were the imposed load, the dead load, the permanent load, the wind action, the seismic action on full and empty reservoir and the temperature action. 2

3 4.1 Imposed load The platform slab has a function of supporting any works that may happen on the tower. Because of this, this slab is often loaded by heavy materials such as machinery, or other deposited materials. The document Critérios de Projecto Civil de Usinas Hidroelétricas from Eletrobras [2] gives insight about intake towers and the actions that should be considered on their design. This document suggests the use of a distributed imposed load of 15kN/m 2 on the platform slab, and this was the only imposed load considered. 4.2 Permanent load There are many loads beside the dead load that are permanently acting on the structure and with values well defined. They are the ladders, grates, floodgate, crane and some other materials that are permanently loading the structure. They take the values presented on table 3. Table 3- Values of the permanent load 4.3 Wind load Action Value Ladders 2kN Grates 100kN Floodgate 200kN Crane 200kN Materials 1kN/m 2 Usually on tall, slender structures the wind action can be problematic, because the global forces and moments generated tend to be high. This tower is one of those cases, and therefore the correct definition of the wind load is very important. The wind load was defined following the procedures recommended by NP EN [3]. According to this norm, the structure is located on zone A of Portugal, as it is farther away than 5km from the coast and at a height below 600m. Its terrain category is I, because it is inside a reservoir which is similar to a lake. This norm also classifies the structure pieces according to their cross-sections. The types present in this work are elements with rectangular cross section, elements with sharp edged cross section, lattice structures and walls. Having this classification made, the wind forces were obtained taking into account what s written on NP EN [3]. 4.4 Seismic action The seismic action in Portugal is very important on the structural design, seeing as its frequency is relatively high and can lead to large scale disasters. Furthermore, this structure is located in the most unfavourable place of Portugal s mainland for seismic effects. Therefore, the dynamic characterization of the tower should be careful and the definition of the seismic action correct. To do so, the procedures of NP EN [4] were followed in the definition of this action. As the seismic shake accelerates masses, two different cases should be defined for the structure: one where the reservoir is full and another on in which the reservoir is empty. When the reservoir is empty, the seismic effects on the structure are the typical ones, just like when designing a normal building. However, when the reservoir is full, due to the fact of water mass acceleration because of the seismic shake, there are hydrodynamic effects on the structure that need to be counted for. There are some ways to take these into account, but in this work the method used was first talked about by Goyal and Chopra [5], it s based on the concept of hydrodynamic added masses and will be explained short after Seismic action definition NP EN [4] defines the seismic action using the concept of response spectrum which provides the maximum value of ground acceleration as a function of the structure vibration period. These 3

4 response spectrums depend on the zone of the structure and the type of foundation grounds. This tower is located on zones 1.1 and 2.1 and the foundation ground is type A. Having this defined, the norm s Nacional Annex [6] indicates the values needed to define the elastic response spectrum of the horizontal and vertical acceleration. They are also affected by an importance factor that tries to evaluate the risk for the populations associated with a possible collapse of the structure collapse. This structure was evaluated as class of importance 2, and therefore the importance factor is equal to 1,0 for seismic actions type 1 and type 2. However, these elastic response spectrums are too conservative to be used on the actual design, because when the seismic shake happens the structure loses stiffness and as such, it s easier for the seismic displacements to happen and fewer forces are generated. Because of this, if the structure has enough ductility its response spectrum can be divided by the behaviour factor q, to obtain the design response spectrum, as described by equation (1). 4 S d = S e q Dynamic characterization of the structure The behaviour factor to be used on the design of a certain structure depends mostly on the distribution of forces on the structure when there s a seismic shake and also on the materials own ductility. The forces distribution depends on its dynamic characterization, particularly its torsional effects. Therefore, to make a proper assessment of the behaviour factor to be used, the dynamic characteristics of the structure should be studied. Studies were made to determine which values of the behaviour factor should be used for certain common structure types. However, a reinforced concrete latticed water intake tower is not that common and there aren t many studies about it. Seeing as the forces distribute on the structure because of the lattice structure, the many columns and the base walls, admittedly its behaviour was compared as that of a one-bay frame and so the behaviour factor used for the seismic motion in the biggest plan dimension was of 3,6. As for the other dimension, seeing as there isn t a one-bay frame, the factor used was half of the other dimension, 1,8. For the vertical motion the behaviour factor used was 1, Hydrodynamic added masses To take into account the hydrodynamic effects of the seismic acceleration, water masses were discretized into the structure to simulate the hydrodynamic effects that are similar to a determined mass of water having the seismic acceleration. The method was devised by Goyal and Chopra [5] Temperature The effects of temperature on the vast majority of structures aren t usually concerning for their safety, because of the loss of stiffness on the ultimate limit states. These effects may pose problems for the serviceability limit states as the loss of stiffness isn t as significant. However, the thermal action is slow and as a cause of that NP EN [7] allows the designer to consider the modulus of elasticity of concrete as half of the real one to ease the stresses due to temperature, as the variation isn t instantaneous. As this structure is most of the time submerged, the change of temperature considered for the load combinations was that of inside the water. However the temperature of the water below water level doesn t change as described by NP EN [7], because the variations mentioned in this norm are air temperature. Therefore, studies made by University of Évora for Alqueva reservoir [8] were consulted and comparisons were drawn for this reservoir about the temperature below water level. Figure 2 illustrates the temperature variation at various levels below water level. It s possible to see that below a certain level the temperature is constant and with a value of 15ºC. Well, in Lagos and according to NP EN [7] this would mean a 0ºC variation of Figure 2 - Temperature changes below water lever at Alqueva reservoir [8] (1)

5 temperature and no stresses generated due to the thermal load, so, to simulate the higher variation on the upper levels, on the part of the structure that s always above water level was applied an uniform variation of temperature of 10ºC and bellow an uniform variation of 5ºC. This approach is very simplified and supposedly conservative Load combinations The load combinations for the ultimate limit states ULS and service limit states SLS, are defined by NP EN [9], and are summarized on table 4: Table 4 Load combinations for the ultimate and serviceability limit states Load Seismic empty Seismic full combinations reservoir reservoir Wind Vertical load ULS G+A Ed + ψ 2,i Q i G+A Ed + ψ 2,i Q i 1,35G+1,5Q 1 + γ Q,i ψ 0,i Q i 1,35G+1,5Q 1 + γ Q,i ψ 0,i Q i SLS G+νA Ed + ψ 2,i Q i G+νA Ed + ψ 2,i Q i - G+ ψ 2,i Q i The values for ν are 0,4 or 0,45 if it is seismic action type or type 2 accordingly. As for γ Q,i, if the action is unfavourable on the structure its value is 1,5 and if it s favourable is 0. 5 Finite element modelling To make a proper analysis on the behaviour of the structure for the project actions due to its complexity, the tower has to be modelled on a finite elements program [10]. The model was composed of beam elements and shell elements, and its geometry was defined by the axis of the elements. Whenever any simplification was needed it was always with the intention of reducing lever arms, increasing the resultant stresses. The step by step modelling is as described: 5.1 Materials The materials used were C30/37 concrete, with some modifications to its properties according to the project situation. Whenever a temperature load was acting on the structure, the concrete modulus of elasticity was reduced by 50%, by indication of NP EN [7]. 5.2 Columns The columns were defined as beam elements respecting the geometrical cross-section characteristics. As their cross-section changes along height, so do their axis. However, the axes were continued from bottom to top to simplify the model. The material used was C30/37 concrete. 5.3 Slabs The slabs were defined as shell thin elements, so as to generate all slab and membrane stresses, and ignoring the shear deformability of these elements. They were modelled by the axes of the beams, and meshed into properly refined meshes, so the results given were as accurate as possible. 5.4 Beams The definition of the beams was very similar as that of the pillar and therefore won t be as detailed. 5.5 Bracing truss The modelling of the bracing truss is very similar to that of the beams and columns. It should be mentioned however that some of its parts were ignored, due to being hard to model and having a big influence on the structure behaviour. 5

6 5.6 Base walls The base walls were modelled as shell thin elements similarly to the slabs, due to its laminar aspect. This is the way their characteristics are best represented, however they could also have been modelled considering beam elements. Due to its cross-section being hard to represent, a simplification was made, considering for each wall the thickness of the zone where it was the less thick. 5.7 Support conditions As the structure is founded on a massive footing on good quality rocks, its support conditions are well described by fully fixed conditions. Therefore, these were used to describe the support conditions of the structure. 5.8 Actions The dead load of the structure is automatically considered on the model. The wind and imposed loads and the permanent load on the slab were modelled as uniformly distributed loads. The other permanent loads due to the crane, flood gates, grates and ladders were modelled as point loads on the most compromising place. The thermal action was taken into account applying a temperature change on the elements. To model the seismic action, response spectrums for both horizontal and vertical shakes were defined. The modal combination used was the complete quadratic combination, and the directional combination was a linear add of the seismic motion in one of the three directions plus 30% of the others, as suggested by NP EN [4]. The modes considered were the ones whose effective modal masses added to 90% of the total mass, to avoid disproportioned work using all the modes. To model the hydrodynamic added masses, masses were added to the discretized points of the structure. The first three modes of vibration in an empty and full reservoir are represented on figure 3 Figure 3 - First three vibration modes of the structure from top to bottom. Left ones are empty reservoir, right ones full 6

7 The period of vibration from the modes increases when adding the water masses, which was expected because for the same stiffness of the structure there s an increase in mass, meaning the period of vibration for each mode will be higher. The overall aspect of the three dimensional model with the added masses is as shown in figure 4. 6 Safety checks for the ultimate limit states and service behaviour When design any kind of structure, certain criteria must be met. The structure must function properly during its lifespan and safety must always be verified, even on exceptional situations. Therefore, proper reinforcement should be calculated and some other verifications must be made to ensure the quality of the project. Since this is an academic work, not every section of every element was verified, but only a select few. 6.1 Ultimate limit states verification Rolling bridge beam Three limit states are needed to verify the rolling bridge beam safety and they are bending, shear and the corbel where the beam is supported safety, where this last one is a zone of discontinuity. Figure 4 - Finite element model with hydrodynamic added masses Bending The conditioning stresses for the bending design of the rolling bridge beam are the ones shown on table 5. To take into account the dynamic effect of the crane moving on top of the bridge, its action was aggravated by a dynamic factor, as described in Swiss norm SIA 261/1:2003 [11] and its value was 1,20. Table 5 Bending moments and reinforcement for the rolling bridge beam Section A B C D E M sd [knm] ,4 or 199, ,4-713,16 Reinforcement[cm 2 14,73(3φ25)- ] 9,42(3φ20) 6,28(2φ20)+ 12,56(4φ20) 19,64(4φ25) 19,64(4φ25) M Rd [knm] or Shear To ensure a proper design for shear and a ductile failure mode, the shear stresses on the beam were obtained using capacity design, meaning the stresses were the result of the equilibrium of resistant moment and not acting moments. The acting stresses resulting of this and the reinforcement needed is displayed on table 6. Table 6 Shear stresses and reinforcement for the rolling bridge beam Span A-B B-C C-D D-E V sd [kn] 100,6 222, The reinforcement used for all spans was two stirrups of diameter 8mm spaced 20 cm of each other. The compressive resistance of the shear strut is 926kN, so there won t happen any problems of the concrete crushing Platform slab To verify safety on the platform slab, bending and shear limit states must be verified. This slab is supported by many beams, so despite it being heavily loaded, it isn t expected high stresses. 7

8 Bending The stresses and reinforcement needed on both bending directions of the slab are shown on table 7 Table 7 Bending moments and reinforcement for the slab Shear m 11 [knm/m] m 22 [knm/m] Reinforcement[cm 2 ] ,93(φ10//20) Usually slab aren t reinforced for shear, because due mostly to the arc effect, slabs have great resistance to this solicitation. This is shown on table 8, where we can compare the acting and resistant shear stresses. Table 8 Shear stresses and resistance for the slab v 11 [kn/m] v 22 [kn/m] v tot [kn/m] v Rd,c,min [kn/m] Bracing truss Due to its geometry, this lattice structure is mostly acted by axial force. Therefore, its most compromising design situation is when huge tension forces act upon it. The values that determine its reinforcement are the ones represented on table 9: Table 9 Stresses and reinforcement on the bracing truss 8 N sd [kn] M sd [knm] V sd [kn] Reinforcement[cm 2 ] 913,6-4,9 0,7 21(4φ25+2φ16) Columns The columns need to be verified for bending acting together with axial forces as well as shear. Also, because they are subjected to huge compressive axial forces, to ensure ductility they need to be reinforced for confinement of the cross-section Bending with axial force An analysis was run to determine the most compromising situation for the columns cross-section. On the zone where the lattice structure ends, there s a significant concentration of stresses that lead to the most unfavourable condition to the design. The worst situation and the reinforcement needed are represented on table 10. Table 10 Axial force, bending moments and reinforcement for the column Shear N sd [kn] M sd,y [knm] M sd,x [knm] Reinforcement[cm 2 ] ,33(63φ25) Although this may be discussible and is a bit conservative, the acting shear stresses, similarly to the beams were obtained by capacity design. The stresses obtained and the respective reinforcement are as shown on table X Table 11 Shear stresses and reinforcement on the columns V sd,y [kn] V sd,x [knm] Reinforcement[cm 2 ] Reinforcement[cm 2 ] ,6 26,3 To guarantee adequate confinement, as indicated by NP EN [4] the mechanical volumetric ratio of the required confinement reinforcement should be bigger than a certain value, described by equation (2).

9 αω wd 30μ φ ν d ε sy,d b c b o 0,035 (2) Base walls Since the base walls have great stiffness, they are acted by considerable forces. The values of the stresses are the ones shown on table 12, and the reinforcement needed was calculated using a section design program [12]. Table 12 Stresses on the wall N 11 [kn/m] m 11 [knm/m] Service limit states verification To ensure the proper functioning of the tower some verifications had to be made regarding service limit states. Cracking had to be controlled, and the long term displacements on the structure as well as the relative displacements between grid guides had also to be limited Cracking control Cracking control can be made mostly by limiting the tension on the reinforcement bars. According to NP EN [1] crack width should be limited to 0,3mm for class of exposition XC4 like the one on this structure. The proceedings for calculating cracks width were also the ones present on NP EN [1] Slab Slabs have a big capacity for redistributing stresses and because of this aren t usually prone to problem regarding cracking. However, since the loading on this slab is very heavy and is almost always acting on the structure, the resultant stresses for the quasi-permanent combination are relatively high. These stresses are shown on table 13 and the resulting crack width. Table 13 Stresses for the quasi-permanent combination on the slab m 11 [knm/m] m 22 [knm/m] N 11 [knm/m] N 22 [knm/m] w k [mm] ,19 To get this acceptable crack width, another reinforcement of φ8//20 was needed, to reduce the tension on the steel Verification of the relative displacements on the equipment guides The guides can support very big displacements due to its mechanical looseness. However, if they sustain a difference of 20mm on their displacements it s clear that the grid or floodgate would fall. Therefore, these displacements should be limited to this value. The phenomenon described is easier to understand with the help of figure 4. When calculating the displacements for the seismic action, these should be multiplied by the behaviour factor, to take into account the nonelastic effects of cracking and reinforcement yielding. The values of the relevant displacements to evaluate security are the ones on table 14. Seeing as none exceeds 20mm, all the conditions are met. Figure 4 Displacements on the equipment guide sections 9

10 Table 14 Displacements on the equipment guide sections Load combination Δ1[m] Δ2[m] Δ2 Δ1[m] Seismic empty reservoir 0,135 0,135 0 Seismic full reservoir 0,1894 0,189-0, Relevant detailing aspects When design a reinforced concrete structure, special attention should be paid to the detailing of the sections. If this is not done carefully, the reinforcement loses its purpose and the resistance to tension conferred by it is gone. Some relevant aspects are for example the anchorage length, the lapping of reinforcement bars, the existence of a minimum space between bars to ensure proper concreting and vibration, the use of the established value of cover and the guarantee that the minimum mandrel diameter for bending bars is used. Another problem altogether, but also related to the detailing of the structure are the deviation forces acting for outside the structure. These should by all means possible be avoided and to do so the detailing should be careful. 8 Conclusions and future works The structure elements were conditioned by the wind load. The effect the hydrodynamic added masses have an interesting effect on the design. On most cases, the stresses due to the situation with a full reservoir were higher than with an empty one without water masses oscillating. This shows how important the seismic effect is for the design of submerged slender structures. It would be interesting if more studies were made on the dynamic behaviour of reinforced concrete towers, and also it would be beneficial if a more precise method to account for hydrodynamic added masses for towers with different geometries was devised. 9 References [1] NP EN :2010, Eurocódigo 2 Projecto de estruturas de betão, Parte 1-1: Regras gerais e regras para edifícios; [2] Eletrobrás (2003), Critérios de Projeto Civil de Usinas Hidroelétricas [3] NP EN :2009, Eurocódigo 1 Acções em estruturas, Parte 1-1: Acções gerais pesos volúmicos, pesos próprios, sobrecargas em edifícios [4] NP EN :2010, Eurocódigo 8 Projecto de estruturas para resistência aos sismos, Parte 1: Regras gerais, acções sísmicas e regras para edifícios; [5] U.S Army Corps of Engineers, Structural Design and Evaluation of Outlet Works, 2003 [6] Anexo Nacional da NP EN :2010, Eurocódigo 8 Projecto de estruturas para resistência aos sismos, Parte 1: Regras gerais, acções sísmicas e regras para edifícios; [7] NP EN :2009, Eurocódigo 1 Acções em estruturas, Parte 1-5: Acções gerais Acções térmicas [8] University of Évora, Evolução da temperatura da água a várias profundidades (Alqueva-Montante), consulted in May 2016 [9] NP EN 1990:2009, Eurocódigo Bases para o projecto de estruturas [10] Manual of Software SAP2000 Ultimate V Csi Berkeley [11] SIA 261/1:2003, Actions sur les structures porteuses Spécifications complementaires [12] ALASHKI, Ilia, Gala Reinforcement Version 4.1e,