Staggered Structural-Heat Flow Analysis of Young Hardening Concrete

Transcription

1 Temperature [ C] Crack index [-] Staggered Structural-Heat Flow Analysis of Young Hardening Concrete

2 Outline 1 Description 1.1 Material Properties 1.2 Modeling Approach 2 Finite Element Model 2.1 Units 2.2 Geometry Definition 2.3 Properties Soil Concrete Convection - Base Convection - Wall 2.4 Boundary Conditions Thermal boundary conditions Static boundary conditions 2.5 Loads Static load 2.6 Meshing 3 Phased Transient Analysis 3.1 Analysis Commands Phase 1 - Base casting Phase 2 - Wall casting 3.2 Results Degrees of reaction Temperature Crack formation Young s modulus Tensile strength Appendix A Additional information Staggered Structural-Heat Flow Analysis of Young Hardening Concrete 2/57

3 1 Description In this tutorial we show a thermal and structural analysis of the early-age concrete in a purification wall 1 by means of a staggered flow-stress phased analysis. The structure, shown in [Fig. 1], is 28.5 m long and consists of a base slab (0.8 m thick and 5.3 m wide), on which a water purification wall (0.7 m thick and 2.3 m high) was casted 36 days later. The structure is directly founded on the underlaying soil. The formwork of the base slab and the wall are removed when the concrete is 7 days old (the detailed timeline of the of construction phases is shown in [Fig. 2]). mid section soil purification wall base day 1 day 7 PHASE 1 Base casting base formwork removed day 36 day 43 PHASE 2 Wall casting wall formwork removed day 72 Figure 1: Purification wall (dimensions are in meters) Figure 2: Timeline of the construction phases Since in this example we neglect the effects at the boundary, we will model only the mid section of the problem (dashed line in [Fig. 1]). To completely analyze the structure we will perform a staggered analysis for each of the two construction phases: i) the casting of the slab and ii) the casting of the wall. 1 Hendriks and Rots, Finite elements in civil engineering applications Proceedings of the Third DIANA World Conference, 2002 Staggered Structural-Heat Flow Analysis of Young Hardening Concrete 3/57

4 1.1 Material Properties The base slab and the purification wall, made of concrete, are modelled according to the specification in the Japanese Standards for Civil Engineering. The soil is considered elastic and isotropic. The corresponding material properties of the concrete and the soil are listed in [Table 1]. Concrete Characteristic strength at 91 days 2.9e+07 N/m 2 Modulus of elasticity at 91 days 2.7e+10 N/m 2 Young s modulus Poisson s ratio 2.7e N/m 2 Thermal expansion coefficient 1e-05 1/ C Mass density 2300 kg/m 3 Conductivity 3.11e+05 N/day C Capacity 2.657e+06 J/m 3 C Convection coefficient (with formwork) 7.0+e05 N/m day C Convection coefficient (without formwork) 1.5e+06 N/m day C Soil Young s modulus Poisson s ratio 6.3e N/m 2 Mass density 1720 kg/m 3 Thermal expansion coefficient 7e-06 1/ C Conductivity 1.91e+05 N/day C Capacity 3.20e+06 J/m 3 C Table 1: Material properties Staggered Structural-Heat Flow Analysis of Young Hardening Concrete 4/57

5 1.2 Modeling Approach The following aspects were considered: 2D Plain Strain is used for the modeling of this problem; only half of the model is considered due to symmetry; a phased analysis is performed to take into to account of the building steps required for this structure: i) casting of the base slab and ii) casting of the wall; the lateral and bottom boundaries of the model are constrained in the normal direction [Fig. 3]; interface boundary elements (denoted by the colored lines in [Fig. 3]) are used to model convection. Due to the different construction phases (i.e., different puring and casting of the concrete during time) two interfaces will be modelled: i) a boundary interface around the base slab (blue) and ii) a boundary interface around the wall (green). will automatically deactivate the temporary boundary around the slab during the second analysis phase since it will be covered by the wall; the external temperature (T ext ) is assumed equal to 20 C around the concrete wall and 15 C around the soil. Both temperatures are assumed constant through the analysis; the temperature around the right and bottom edges of the soil is set to 15 C; the initial temperature (T init ) of the concrete is set equal to 20 C while that of the soil to 15 C; a transient staggered thermal-structural analysis is performed in order to investigate the hydration (i.e., the degree of reaction) and temperature variation in time and the formation of cracks in the concrete; the model is discretized using quadratic elements. To ensure strain compatibility a, will automatically solve the heat flow problem using linear elements and the structural one with quadratic elements. Consequently, the thermal strain and total strain fields are linearly interpolated across the elements. a The differential equations governing the heat flow problem are one order lower than those defining the structural problem. Thus, if the same approximation was employed in the staggered analysis, the strain field from the heat flow problem would be one order higher than that from the structural one. Y Z wall boundary 20 C base boundary (temporary) base boundary (permanent) T init = 20 C X T ext = 20 C T init = 15 C 15 C 20 C = convection = fixed temperature 15 C 15 C Figure 3: Model of the purification wall implemented in (the details of the geometry are shown in [Fig. 1]) Staggered Structural-Heat Flow Analysis of Young Hardening Concrete 5/57

6 2 Finite Element Model For the modeling session we start a new project in which structural and heat flow analyses can be performed [Fig. 4] and plain strain conditions are imposed. The dimensions of the domain are set equal to 100 m. Quadratic finite elements will be used in the analysis. We will dominantly use quadrilater elements in the mesh. Main menu File New project [Fig. 4] Figure 4: New project dialog Staggered Structural-Heat Flow Analysis of Young Hardening Concrete 6/57

7 2.1 Units We choose meter for the Length unit, day for Time unit and Celsius for the Temperature unit. Geometry browser Reference system Units [Fig. 5] Property Panel [Fig. 6] Figure 5: Geometry browser Figure 6: Property Panel - Units Staggered Structural-Heat Flow Analysis of Young Hardening Concrete 7/57

8 2.2 Geometry Definition To model the geometry of the problem we create three polygon sheets representing the Soil, the Base and the Wall [Fig. 3]. The node coordinates required to define these sheets are in [Table 2] (we model only half of the problem due to symmetry). Although the sheets defining the geometry of the Soil and the Base are rectangular, their shapes will be created using 5 nodes. These are needed to have extra edges that required to apply the thermal boundary conditions. Main Menu Geometry Create Add polygon sheet (X3) [Fig. 7] [Fig. 8] [Fig. 9] Shape x y z name [m] [m] [m] Soil Base Figure 7: Geometry - Add polygon sheet Soil Wall Table 2: Node coordinates of the polygon sheets Figure 8: Geometry - Add polygon sheet Base Figure 9: Geometry - Add polygon sheet Wall Staggered Structural-Heat Flow Analysis of Young Hardening Concrete 8/57

9 Viewer Viewpoints Top View Viewer Fit all [Fig. 10] Figure 10: Top view Staggered Structural-Heat Flow Analysis of Young Hardening Concrete 9/57

10 2.3 Properties Soil We assign the material properties to the Soil. The soil is modeled as linear elastic isotropic (see the properties in [Table 1]). Main Menu Geometry Analysis Property assignments [Fig. 11] Property assignments Add new material [Fig. 12] [Fig. 13] Figure 11: Property assignments to the Soil Figure 12: Add new material - Soil Figure 13: Material properties - Soil Staggered Structural-Heat Flow Analysis of Young Hardening Concrete 10/57

11 2.3.2 Concrete We assign the material properties to the Base and the Wall. The mechanical properties of the concrete are defined according to the JSCE standards (see [Table 1]). In this step, we must specify Material model as JSCE and include the Young hardening concrete and heat flow aspects [Fig. 15] [Fig. 16]. Main Menu Geometry Analysis Property assignments [Fig. 14] Property assignments Add new material [Fig. 15]-[Fig. 18] Figure 14: Property assignments to the wall Figure 15: Add new material - Concrete Figure 16: Material properties - Concrete Staggered Structural-Heat Flow Analysis of Young Hardening Concrete 11/57

12 The thermal properties of the concrete are defined according to [Table 1]. Moreover, the adiabatic heat development curve is provided as shown in [Table 3] and [Fig. 18] to take into account of the heat released during the hydration of the young hardening concrete (differently from 2, we use only one adiabatic curve for the modeling of the heat generation in the base slab and the purification wall). Property assignments - Edit material Heat flow Adiabatic heat development Edit table [Fig. 17] [Table 3] [Fig. 18] Figure 17: Material properties - Concrete Age Temperature [day] [ C] Table 3: Adiabatic heat development data Figure 18: Adiabatic heat development curve 2 Hendriks and Rots, Finite elements in civil engineering applications Proceedings of the Third DIANA World Conference, 2002 Staggered Structural-Heat Flow Analysis of Young Hardening Concrete 12/57

13 2.3.3 Convection - Base We model the convection phenomena along the edges of the Base. Therefore, we assign the properties to edges of the slab that will be exposed to the external environment. Convection is modelled using boundary interface elements. Main Menu Geometry Analysis Connection property assignments [Fig. 19]-[Fig. 22] Figure 19: Connection property assignment Figure 20: Top view - edge selection Figure 21: Add new material - Interface base Figure 22: Edit interface properties Staggered Structural-Heat Flow Analysis of Young Hardening Concrete 13/57

14 Since we perform a transient analysis we need to specify the variation of the concrete conduction coefficient in time [Fig. 23]. The sudden changes for the conduction coefficients correspond to the removal of the concrete formwork occurring 7 days after the beginning of the casting. Connection property assignment - Edit material [Fig. 22] Time conduction ocefficient Edit table [Table 4] [Fig. 23] Age Heat transfer coefficient [day] [N/m day C] 0 7.0e e e e+05 Table 4: Time-dependent conduction coefficients for the Base concrete Figure 23: Time vs conduction coefficient curve for the Base concrete Staggered Structural-Heat Flow Analysis of Young Hardening Concrete 14/57

15 2.3.4 Convection - Wall We model the convection phenomena along the edges of the Wall exposed to air. Geometry browser Geometry Shapes Select Wall Right click ( ) Show Main Menu Geometry Analysis Connection property assignments [Fig. 24]-[Fig. 27] Figure 24: Connection property assignment Figure 25: Top view - edge selection Figure 26: Add new material - Interface wall Figure 27: Edit interface properties Staggered Structural-Heat Flow Analysis of Young Hardening Concrete 15/57

16 We specify the variation of the concrete conduction coefficient in time also for the interface around the Wall [Fig. 28]. The sudden changes for the conduction coefficients correspond to the removal of the concrete cast formwork that happens at day 43 (7 days after the beginning of its casting). Connection property assignment - Edit material [Fig. 27] Time conduction ocefficient Edit table [Table 5] [Fig. 28] Age Conduction coefficient [day] [N/m day C] 0 7.0e e e e+5 Table 5: Time-dependent conduction coefficients for the Wall concrete Figure 28: Time vs conduction coefficient curve for the Wall concrete Staggered Structural-Heat Flow Analysis of Young Hardening Concrete 16/57

17 2.4 Boundary Conditions Thermal boundary conditions To set a constant temperature equal to 15 C around the edges of the Soil, it is first required to attach a fixed temperature condition along these edges (this will keep temperature constant during the analysis). Main menu Geometry Analysis Attach fixed temperatures [Fig. 29] [Fig. 30] Figure 29: Attach thermal boundary condition to the Soil Figure 30: Edge selection (thick red lines) Staggered Structural-Heat Flow Analysis of Young Hardening Concrete 17/57

18 We can now impose to the boundary of the Soil shape a temperature equal to 15 C. Main menu Geometry Analysis Attach boundary conditions [Fig. 31] [Fig. 32] Figure 31: Attach thermal boundary condition to the Soil Figure 32: Edge selection (thick red lines) Staggered Structural-Heat Flow Analysis of Young Hardening Concrete 18/57

19 We assign the time curve to the fixed temperature around the Soil (in this example, the temperature will be considered constant during the analysis). Geometry browser Boundary conditions Right click ( ) Prescribed soil boundaries temperature Edit time dependency [Fig. 33] [Fig. 34] [Fig. 35] Figure 33: Geometry browser Figure 34: Edit time dependent factors Figure 35: Geometry browser Staggered Structural-Heat Flow Analysis of Young Hardening Concrete 19/57

20 We set the external temperature equal to 20 C along the edges of the Base and Wall shapes (i.e., along the Slab boundary and the Wall boundary). Main menu Geometry Analysis Attach boundary conditions [Fig. 36] Figure 36: Attach thermal boundary condition Staggered Structural-Heat Flow Analysis of Young Hardening Concrete 20/57

21 We assign the time curve to the external temperature around the Base and Wall. Geometry browser Boundary conditions Right click ( ) External temperature Edit time dependency [Fig. 37] [Fig. 38] [Fig. 39] Figure 37: Geometry browser Figure 38: Edit time dependent factors Figure 39: Geometry browser Staggered Structural-Heat Flow Analysis of Young Hardening Concrete 21/57

22 By default assumes a zero temperature field for the shapes of the model at the start of a transient heat flow analysis. However, in this example the environmental temperature is 20 C and that around the soil 15 C. Therefore, we assume that these are also the initial temperatures of the concrete structure (Base and Wall) and the soil (Soil). We will assume that the initial temperature of the edge between the Base and the Wall is 20 C. To ensure this we will need to assign an initial field also to the bottom edge of the Base (see Figure 42). Main menu Geometry Analysis Attach initial field [Fig. 40] [Fig. 41] [Fig. 43] Figure 40: Attach initial temperature to the Base and Wall Figure 41: Attach initial temperature to the Soil Figure 42: Attach initial temperature to Base edge Figure 43: Geometry browser Staggered Structural-Heat Flow Analysis of Young Hardening Concrete 22/57

23 2.4.2 Static boundary conditions We constrain the horizontal displacement (X-direction) of the left and right edges of the model [Fig. 45]. Main menu Geometry Analysis Attach support [Fig. 44] [Fig. 45] Figure 44: Attach support - horizontal displacement Figure 45: Constrained lateral edge Staggered Structural-Heat Flow Analysis of Young Hardening Concrete 23/57

24 We constrain the vertical displacement (Y -direction) of the bottom edge of the Soil [Fig. 47]. Main menu Geometry Analysis Attach support [Fig. 46] [Fig. 47] Figure 46: Attach support - vertical displacement Figure 47: Constrained bottom edge Staggered Structural-Heat Flow Analysis of Young Hardening Concrete 24/57

25 2.5 Loads Static load We include the effect of the dead weight in the analysis. Main menu Geometry Analysis Global load [Fig. 48] Figure 48: Attach global load - Dead weight Staggered Structural-Heat Flow Analysis of Young Hardening Concrete 25/57

26 2.6 Meshing We use a mesh where the elements in the Soil, Base and Wall have a characteristic size of 0.4, 0.16 and 0.06 m, respectively. Main Menu Geometry Analysis Set mesh properties (X3) [Fig. 49] [Fig. 50] [Fig. 51] Figure 49: Mesh seeding - Soil Figure 50: Mesh seeding - Base Figure 51: Mesh seeding - Wall Staggered Structural-Heat Flow Analysis of Young Hardening Concrete 26/57

27 Now, we can generate the finite element mesh. Main Menu Geometry Analysis Generate mesh [Fig. 52] Figure 52: Finite element mesh Staggered Structural-Heat Flow Analysis of Young Hardening Concrete 27/57

28 3 Phased Transient Analysis 3.1 Analysis Commands The problem is investigated through a phased analysis. Since we first analyze the casting of the base and later that of wall, the phased analysis has the following two steps ([Table 6]): i) casting of the base slab ( Base casting ) (here, the Wall is not considered in the analysis) and ii) casting of the wall ( Wall casting ). In both phases we perform a staggered analysis to account for the thermal and mechanical response of the model. Phase Name Description Analysis type Transient heat transfer 1 Base casting Soil + Slab & Structural nonlinear Transient heat transfer 2 Wall casting Soil + Slab + Wall & Structural nonlinear Table 6: Sequence of the phased analysis To set up a phase we follow these steps: 1. create a new Phase (rename accordingly) 2. open the Edit properties dialog box to: select the Element sets to be active during the phase select the element material properties (if required) select the Support sets and Tying sets to be active during the phase (if required) 3. add the required analysis commands (in this tutorial we perform Transient heat transfer and Structural nonlinear analyses). For the Structural nonlinear analysis: add a Start steps block if new elements are included in the model add a Time steps block such that the Structural nonlinear analysis will take into account of the material evolution in the Transient heat transfer analysis set up the details for the calculations (e.g., solver, convergence criteria, superposition,...) Staggered Structural-Heat Flow Analysis of Young Hardening Concrete 28/57

29 3.1.1 Phase 1 - Base casting We start by creating the first phase to analyze the thermal and structural response of Base and Soil during the casting of the Base. This is performed by means of a staggered analysis coupling Transient heat transfer and Structural nonlinear analyses. In this first phase, the Wall and the corresponding interfaces, used to model the convection transfer, are not considered. During phase property assignement (see [Fig. 56]), check the Covered and not connected boundaries. This allows for automatic deactivation of the portion of the boundary interface around the slab that will be covered by the Wall in the next phase (i.e., during Phase 2 the interface elements corresponding to this portion of boundary will not be considered during the calculations). Main Menu Analysis New Analysis Analysis browser Right click ( ) Analysis1 Rename PhasedAnalysis [Fig. 53] Analysis browser Right click ( ) PhasedAnalysis Add command Phased [Fig. 54] Analysis browser PhasedAnalysis Right click ( ) Phased Rename Base casting [Fig. 55] Analysis browser PhasedAnalysis Right click ( ) Base casting Edit properties [Fig. 56] Figure 53: Analysis window Figure 54: Command menu Figure 55: Analysis tree Figure 56: Edit properties phase of Base casting Staggered Structural-Heat Flow Analysis of Young Hardening Concrete 29/57

30 We add a Transient heat transfer analysis command to the Base casting phase. This is to analyze the hydration processes and heat transfer in the model. We need to specify the initial conditions for the heat transfer analysis [Fig. 58]. We use the Initial temperature field previously defined. Furthermore, by performing a nonlinear analysis, we can take into account the hydration process in the young concrete of the Base slab, setting the initial degree of reaction equal to 0.01 (this very small value is required to start the hydration). To take into account of the maturity dependent properties of the concrete during time, we need to calculate the concrete equivalent age during the analysis (select Calculate equivalent age for the initial condition properties dialog box as shown in [Fig. 58]) Analysis browser PhasedAnalysis Right click ( ) PhasedAnalysis Add command Transient heat transfer [Fig. 57] Analysis browser PhasedAnalysis Base casting Right click ( ) Initial conditions Edit properties [Fig. 58] Figure 57: Analysis window Figure 58: Initial conditions Staggered Structural-Heat Flow Analysis of Young Hardening Concrete 30/57

31 We define the time steps to perform the transient heat transfer analysis. Here, we assume the following time steps: 0.1(20) 0.5(10) 1(3) 5(4) 6 where the notation n (m) means that a time step equal to n days is repeated m times consecutively. Analysis browser PhasedAnalysis Base casting Right click ( ) Execute analysis Edit properties [Fig. 59] Figure 59: Properties execute analysis Staggered Structural-Heat Flow Analysis of Young Hardening Concrete 31/57

32 We now add a Structural nonlinear analysis command to investigate the mechanical response. We remove the existing new execute block command and add a Start steps block to account for the initialization of the stresses of the Base and Soil dead weight in the Soil. Analysis browser PhasedAnalysis Right click ( ) Base casting Add command Structural nonlinear [Fig. 60] Analysis browser PhasedAnalysis Right click ( ) Structural nonlinear Right click ( ) new execute block remove Analysis browser PhasedAnalysis Right click ( ) Structural nonlinear Add Execute steps - start steps [Fig. 61] Analysis browser PhasedAnalysis Structural nonlinear Right click ( ) new execute block 2 Rename Add Base [Fig. 62] Analysis browser PhasedAnalysis Structural nonlinear Add Base Right click ( ) Start steps Edit properties [Fig. 63] Figure 60: Add Structural nonlinear Figure 61: Add Execute steps - Start step Figure 62: Rename new execute block 2 Figure 63: Start step properties Staggered Structural-Heat Flow Analysis of Young Hardening Concrete 32/57

33 We add a Time steps block to calculate the mechanical problem during the first 36 days after the casting of the base slab. More specifically, this is to monitor i) the stress interactions between Base and Soil due to the dead weight and ii) the mechanical response of the Base induced by the thermal effects from the hydration process in the concrete. The time steps used for this execution blocks are the same employed for the transient heat transfer analysis (i.e., 0.1(20) 0.5(10) 1(3) 5(4) 6). Analysis browser PhasedAnalysis Right click ( ) Structural nonlinear Add Execute steps - time steps [Fig. 64] Analysis browser PhasedAnalysis Structural nonlinear Right click ( ) new execute block Rename 1st 36 days [Fig. 65] Analysis browser PhasedAnalysis Structural nonlinear 1st 36 days Right click ( ) Time steps Edit properties [Fig. 66] Figure 64: Add a new execute block Execute steps - Time step Figure 65: Rename new execute block as 1st 36 days Figure 66: Time steps for the nonlinear structural analysis Staggered Structural-Heat Flow Analysis of Young Hardening Concrete 33/57

34 We select the desired output results (displacements and stresses and crack index). Analysis browser PhasedAnalsysis Base casting Structural nonlinear Right click ( ) Output Edit properties [Fig. 67] Properties - OUTPUT Modify Results Selection [Fig. 68] [Table 7] [Fig. 69] Figure 68: Results selection Displacement field Stress field Crack index DISPLA TOTAL TRANSL GLOBAL STRESS TOTAL CAUCHY GLOBAL STRESS TOTAL CAUCHY CRKIND Figure 67: Output properties Table 7: Required output data Figure 69: Output properties Staggered Structural-Heat Flow Analysis of Young Hardening Concrete 34/57

35 3.1.2 Phase 2 - Wall casting We add a second phase to the analysis that accounts for the installation of the concrete wall. Compared to the previous phase, the model will consider the element sets for the Wall and its boundary interfaces (i.e., Wall boundary and Wall boundary). At the same time, the element set Temporary slab boundary, where the Wall and the Base are in contact, is not considered. Analysis browser Right click ( ) PhasedAnalysis Add command Phased [Fig. 70] [Fig. 71] Analysis browser PhasedAnalysis Right click ( ) Phased Rename Wall casting [Fig. 72] Analysis browser PhasedAnalysis Right click ( ) Wall casting Edit properties [Fig. 73] Figure 70: Analysis window Figure 71: Command menu Figure 72: Analysis tree Figure 73: Edit properties phase of Wall casting Staggered Structural-Heat Flow Analysis of Young Hardening Concrete 35/57

36 The command list for the Transient heat transfer and Structural nonlinear analyses for this second phase (Wall casting) are created by copying those from the previous one (Base casting). Analysis browser PhasedAnalysis Base casting Right click ( ) Transient heat transfer Duplicate [Fig. 74] Analysis browser PhasedAnalysis Base casting Right click ( ) Structural nonlinear Duplicate [Fig. 74] Analysis browser PhasedAnalysis Wall casting Right click ( ) Copy of Transient heat transfer Rename Transient heat transfer 1 [Fig. 75] Analysis browser PhasedAnalysis Wall casting Right click ( ) Copy of Structural nonlinear Rename Structural nonlinear 1 [Fig. 75] Figure 74: Duplicated commands Figure 75: Renamed commands Staggered Structural-Heat Flow Analysis of Young Hardening Concrete 36/57

37 We need to rename also the Start step and Time steps execution blocks in analysis Structural nonlinear 1. Analysis browser PhasedAnalysis Wall casting Structural nonlinear 1 Right click ( ) Add Base Rename Add Wall [Fig. 76] [Fig. 77] Analysis browser PhasedAnalysis Wall casting Structural nonlinear 1 Right click ( ) 1st 36 days Rename 2nd 36 days [Fig. 76] [Fig. 77] Figure 76: Duplicated execute blocks Figure 77: Renamed execute blocks Staggered Structural-Heat Flow Analysis of Young Hardening Concrete 37/57

38 In this phase we use the same time steps employed in the previous one. Nonetheless, some changes are required both in Transient heat transfer 1 and Structural nonlinear 1. Namely, we need to change the start time of the Transient heat transfer 1 analysis and the Add Wall execution block in Structural nonlinear 1 to 36 days (see [Fig. 78] and [Fig. 80]). Moreover, in Add Wall execution block, we specify that we will use the same load set from the previous phase (see [Fig. 79]). Then, we can run the analysis. Analysis browser PhasedAnalysis Wall casting Transient heat transfer 1 Initial conditions Right click ( ) Edit properties Start time 36 [Fig. 78] Analysis browser PhasedAnalysis Wall casting Structural nonlinear 1 Add Wall Right click ( ) Start steps Edit properties [Fig. 79] Property panel Start time 36 [Fig. 80] Main menu PhasedAnalysis Run analysis Figure 78: Initial condition properties Figure 79: Start steps properties Figure 80: Edit start time Staggered Structural-Heat Flow Analysis of Young Hardening Concrete 38/57

39 3.2 Results We will investigate the development of degree of reaction, temperature and crack formation in the concrete base and wall during time. Since in this tutorial we are not interested in the thermal and mechanical response of the soil, we will display only the mesh of the Base and the Wall. Mesh browser Element sets Right click ( ) Base Show only [Fig. 81] Mesh browser Element sets Right click ( ) Wall Show [Fig. 82] [Fig. 83] Figure 81: Show only Base Figure 82: Show Wall Figure 83: Base and Wall mesh Staggered Structural-Heat Flow Analysis of Young Hardening Concrete 39/57

40 3.2.1 Degrees of reaction Contour plot.. We investigate the degree of reaction (DGR) in the concrete. We will specify the color scale limits based on the minimum and maximum value that DGR can take: 0 and 1 correspond to no reacted and fully reacted concrete, respectively. Results browser Analysis output Element results Degrees of reaction DGR [Fig. 84] Property panel Result view settings Contour plot settings Color scale limits Specified values [Fig. 85] Property panel Result view settings Contour plot settings Specified values Minimum value 0 [Fig. 86] Property panel Result view settings Contour plot settings Specified values Maximum value 1 [Fig. 86] Figure 84: Results browser Figure 85: Property panel - Specified values for color scale limits Figure 86: Property panel - Minimum and maximum value for color scale limits Staggered Structural-Heat Flow Analysis of Young Hardening Concrete 40/57

41 We show the changes in DGR after 0.1, 1, 2, 4, 6 and 36 days from the beginning of the base slab casting. After 6 days ([Fig. 92]), almost all the concrete in the Slab has reacted. Results browser Case Base casting, Time-step 1, Time [Fig. 87] Repeat for the other time steps ([Fig. 88] [Fig. 92]) Figure 87: Degree of reaction DGR (0.1 day) Figure 88: Degree of reaction DGR (1 day) Figure 89: Degree of reaction DGR (2 days) Figure 90: Degree of reaction DGR (4 days) Figure 91: Degree of reaction DGR (6 days) Figure 92: Degree of reaction DGR (36 days) Staggered Structural-Heat Flow Analysis of Young Hardening Concrete 41/57

42 Similarly, we display the degree of reaction in the Wall that is installed 36 days after the casting of the Base. As for the Base, after 6 days of casting (i.e., at 42 days in the analysis, [Fig. 97]) almost all the concrete in the Wall has reacted. Results browser Case Wall casting, Time-step 1, Time [Fig. 93] Repeat for the other time steps ([Fig. 94] [Fig. 98]) Figure 93: Degree of reaction DGR (36.1 day) Figure 94: Degree of reaction DGR (37 day) Figure 95: Degree of reaction DGR (38 days) Figure 96: Degree of reaction DGR (40 days) Figure 97: Degree of reaction DGR (42 days) Figure 98: Degree of reaction DGR (72 days) Staggered Structural-Heat Flow Analysis of Young Hardening Concrete 42/57

43 3.2.2 Temperature Contour plot.. We investigate the temperature field (PTE) in the concrete. We will specify the color scale limits based on the minimum and maximum value that PTE takes during the simulation: 20 and 40 C, respectively. Results browser Analysis output Nodal results Temperature PTE [Fig. 99] Property panel Result view settings Contour plot settings Color scale limits Specified values [Fig. 100] Property panel Result view settings Contour plot settings Specified values Minimum value 20 [Fig. 101] Property panel Result view settings Contour plot settings Specified values Maximum value 40 [Fig. 101] Figure 99: Results browser Figure 100: Property panel - Specified values for color scale limits Figure 101: Property panel - Minimum and maximum value for color scale limits Staggered Structural-Heat Flow Analysis of Young Hardening Concrete 43/57

44 We show the changes in PTE after 0.1, 1, 2, 4, 6 and 36 days from the beginning of the base slab casting. The maximum temperature in the Base is reached after 2 days from the casting [Fig. 104]. Results browser Case Base casting, Time-step 1, Time [Fig. 102] Repeat for the other time steps ([Fig. 103] - [Fig. 107]) Figure 102: Temperature PTE (0.1 day) Figure 103: Temperature PTE (1 day) Figure 104: Temperature PTE (2 days) Figure 105: Temperature PTE (4 days) Figure 106: Temperature PTE (6 days) Figure 107: Temperature PTE (36 days) Staggered Structural-Heat Flow Analysis of Young Hardening Concrete 44/57

45 Similarly, we display the temperature in the Wall. The maximum temperature in the Wall is reached after 1-2 days from the casting (i.e., 37 and 38 days in the analysis) [Fig. 109] [Fig. 110]. Results browser Case Wall casting, Time-step 1, Time [Fig. 108] Repeat for the other time steps ([Fig. 109] - [Fig. 113]) Figure 108: Temperature PTE (36.1 day) Figure 109: Temperature PTE (37 day) Figure 110: Temperature PTE (38 days) Figure 111: Temperature PTE (40 days) Figure 112: Temperature PTE (42 days) Figure 113: Temperature PTE (72 days) Staggered Structural-Heat Flow Analysis of Young Hardening Concrete 45/57

46 Diagram Temperature Vs Time.. For a better understanding of the temperature development, we will make a graph of the temperature at some nodes along the symmetry axis with respect to time. We choose 3 nodes along the symmetry axis of the Base (y = 3.1 m, y = 3.4 m and y = 3.7 m) and 3 nodes along the symmetry axis of the Wall (y = 3.83 m, y = 4.98 m and y = 6.07 m) shown in [Fig. 114]. Result browser Analysis output Nodal results Temperature PTE Show table [Fig. 115] Chart view Results selection x axis data case value [Fig. 116] Chart view Results selection y axis data Temperatures - PTE [Fig. 116] 6.7 Y Figure 114: Select nodes Figure 115: Show table of PTE Figure 116: Chart view Staggered Structural-Heat Flow Analysis of Young Hardening Concrete 46/57

47 The nodes can be selected either manually or through python command. In this tutorial, due to its simplicity, we use the second option. Once the python command is provided to through command console, the nodes will be selected. Command console select( NODE, findnearestnodes( [ (0,3.1,0), (0,3.4,0), (0,3.7,0), (0,3.83,0), (0,4.98,0), (0,6.07,0) ] ) ) [Fig. 117] Figure 117: Chart view Due to the casting of the Wall, the temperature in the slab shows a second maximum at about 37 days. Staggered Structural-Heat Flow Analysis of Young Hardening Concrete 47/57

48 Probe curve.. To investigate the variation of the temperature along an arbitrary line intersecting the model and at a specific time, in it is possible to plot the corresponding graph along a probe curve. We will plot the temperature profile along the probe curve that starts at (0, 3.4, 0) m and ends at (2.65, 3.4, 0) m (see [Fig. 122]). Results browser Analysis output Nodal results Temperatures PTE [Fig. 99] Property panel Result view settings Probing curve setting Add Curve [Fig. 118] Property panel Result view settings Probing curve setting probe-curve Number of intervals between points 20 [Fig. 119] Property panel Result view settings Probing curve setting probe-curve add Point coordinates [Fig. 120] Property panel Result view settings Probing curve setting probe-curve Point coordinates [Fig. 121] Figure 118: Add curve Figure 119: Rename curve and interval number Figure 120: Add coordinates for probe-curve Figure 121: Probe-curve point coordinates Staggered Structural-Heat Flow Analysis of Young Hardening Concrete 48/57

49 It is possible to visualize the diagram along the probe curve in [Fig. 123] on a Cartesian plane as shown in at different time steps [Fig. 124] [Fig. 125]. Results browser Analysis output Nodal results Temperatures Right click ( ) PTE Show contour probe [Fig. 123] Results browser Case Base casting, Time-step 20, Time [Fig. 124] Results browser Case Wall casting, Time-step 20, Time [Fig. 125] Figure 124: Temperature PTE along probe-curve at 2 days probe curve Figure 122: Probe curve Figure 123: Show contour probe Figure 125: Temperature PTE along probe-curve at 38 days Staggered Structural-Heat Flow Analysis of Young Hardening Concrete 49/57

50 3.2.3 Crack formation Contour plot.. We investigate the formation of cracks in the concrete through the crack index ICR defined as ICR = f t σ I, (1) where f t is the tensile strength of concrete and σ I is the maximal principal stress, thus cracks occurs when ICR is lower than 1. As general guidelines: 0.7 ICR < 1.2 high risk of harmful cracks in the concrete; 1.2 ICR < 1.5 few cracks might form; ICR 1.5 probability of crack formation is very low. To better visualize if the concrete is cracked, we will display the contour plot of ICR only if its value is smaller than 1.5. This is achieved by setting the color scale between 0 and 1.5 and hiding data outside the color scale limits. Moreover, we will set the lower bound color to red ( high risk ) and the upper bound color to blue ( small risk ) [Fig. 127]. Results browser Analysis output Element results Crack indices ICR [Fig. 126] Property panel Contour plot settings Color scale limits Specified values [Fig. 127] Property panel Contour plot settings Specified values Minimum value 0 [Fig. 127] Property panel Contour plot settings Specified values Maximum value 1.5 [Fig. 127] Property panel Contour plot settings Specified values Values outside specified bounds Hide data outside limits [Fig. 127] Property panel Contour plot settings Bounding colors Upper bound color Blue [Fig. 127] Property panel Contour plot settings Bounding colors Lower bound color Red [Fig. 127] Figure 126: Results browser Figure 127: Color scale limits Staggered Structural-Heat Flow Analysis of Young Hardening Concrete 50/57

51 Here, we show the results for some time steps. We do not consider the contour plot of ICR at the start steps: since the strength f t of the concrete is null at time 0, from eq. (1) we obtain ICR equal to 0 for any σ I. The results show that the value of ICR in the core of the base slab is about between 36 and 72 days from casting [Fig. 129] [Fig. 131]. Therefore, there is a high risk of harmful cracks in the concrete. No harmful cracks form in the concrete wall. Results browser Case Base casting, Time-step 20, Time [Fig. 128] Results browser Case Base casting, Time-step 38, Time [Fig. 129] Results browser Case Wall casting, Time-step 21, Time [Fig. 130] Results browser Case Wall casting, Time-step 39, Time [Fig. 131] Figure 128: Crack index ICR (2 days) Figure 129: Crack index ICR (36 days) Figure 130: Crack index ICR (38 days) Figure 131: Crack index ICR (72 days) Staggered Structural-Heat Flow Analysis of Young Hardening Concrete 51/57

52 3.2.4 Young s modulus Contour plot.. We investigate the development of the Young s modulus during time. We will specify the color scale limits based on the minimum and maximum value that the Young s modulus of the concrete takes during the simulation: 1.5 and 27 GPa, respectively. Results browser Analysis output Element results Elastic parameters YOUNG [Fig. 132] Property panel Contour plot settings Color scale limits Specified values [Fig. 133] Property panel Contour plot settings Specified values Minimum value 1.5e+09 [Fig. 133] Property panel Contour plot settings Specified values Maximum value 2.7e+10 [Fig. 133] Property panel Contour plot settings Specified values Values outside specified bounds Color by minimum/maximum value colors [Fig. 133] Figure 132: Results browser Figure 133: Color scale limits Staggered Structural-Heat Flow Analysis of Young Hardening Concrete 52/57

53 We display the variation of the Young s modulus during time in the Base and in the Wall. As expected, the Young s modulus of the concrete increases during time reaching the maximum value of 27 GPa (see [Fig. 134] [Fig. 139]). Results browser Case Base casting, Time-step 2, Time 2 hour 24 min, Dead weight [Fig. 134] Repeat for the other time steps ([Fig. 137] - [Fig. 139]) Figure 134: Young s modulus YOUNG (2.5 hours) Figure 135: Young s modulus YOUNG (4 day) Figure 136: Young s modulus YOUNG (36 days) Figure 137: Young s modulus YOUNG (37 days) Figure 138: Young s modulus YOUNG (40 days) Figure 139: Young s modulus YOUNG (72 days) Staggered Structural-Heat Flow Analysis of Young Hardening Concrete 53/57

54 3.2.5 Tensile strength Contour plot.. We investigate the development of the tensile strength during time. We will specify the color scale limits based on the minimum and maximum value that the tensile strength of the concrete takes during the simulation: 0.3 and 2.5 MPa, respectively. Results browser Analysis output Element results Total strain parameters TENSTR [Fig. 140] Property panel Contour plot settings Color scale limits Specified values [Fig. 141] Property panel Contour plot settings Specified values Minimum value 3.0e+05 [Fig. 141] Property panel Contour plot settings Specified values Maximum value 2.5e+06 [Fig. 141] Figure 140: Results browser Figure 141: Color scale limits Staggered Structural-Heat Flow Analysis of Young Hardening Concrete 54/57

55 As in the rpevious section, we display the variation of the tensile strength during time in the Base and in the Wall. The tensile strength of the concrete increases during time reaching the maximum value of 2.5 MPa (see [Fig. 142] [Fig. 147]). Results browser Case Base casting, Time-step 2, Time 2 hour 24 min, Dead weight [Fig. 142] Repeat for the other time steps ([Fig. 145] - [Fig. 147]) Figure 142: Tensile strength TENSTR (2.5 hours) Figure 143: Tensile strength TENSTR (4 day) Figure 144: Tensile strength TENSTR (36 days) Figure 145: Tensile strength TENSTR (37 days) Figure 146: Tensile strength TENSTR (40 days) Figure 147: Tensile strength TENSTR (72 days) Staggered Structural-Heat Flow Analysis of Young Hardening Concrete 55/57

56 Appendix A Additional information Folder: Tutorials/PurificationWall Number of elements 550 Keywords: analys: flow flowst heat nonlin phase physic stagge transi. constr: initia suppor temper. elemen: b2ht cq16e ct12e flow potent pstrai q4ht t3ht. load: elemen node temper time weight. materi: adiaba concre conduc elasti hydrat isotro jsce maturi power viscoe. option: direct newton regula units. post: binary ndiana. pre: dianai. result: cauchy crkind displa equage flux inttmp reacti stress temper total. References: [1] M. A. N. Hendriks and J. G. Rots. Finite elements in civil engineering applications Proceedings of the Third DIANA World Conference. A. A. Balkema Publishers, Tokyo, Japan, 9 11 October 2002, Staggered Structural-Heat Flow Analysis of Young Hardening Concrete 56/57

57 DIANA FEA BV Delftechpark 2628 XJ Delft 19a The Netherlands T +31 (0) F +31 (0) DIANA FEA BV Vlamoven 6826 TN Arnhem 34 Netherlands T The +31 (0) F +31 (0)