Concrete Inclusion in an Elastic Medium

Note

To view this project in FLAC3D, use the menu command Help ► Examples…. Choose “Thermal/ConcreteInclusion” and select “ConcreteInclusion.prj” to load. The project’s main data files are shown at the end of this example.

This example consists of a concrete inclusion inside an elastic and thermal isotropic material. The model has a size of 10 m × 1 m × 10 m and is fixed in the \(y\)-direction (Figure 1). Roller boundary conditions are applied at the model boundaries. The material properties are listed in Table 1 (elastic frame) and Table 2 (concrete inclusion). The model was run for a thermal time of two days.

Figure 2 to Figure 6 show the evolution of various parameters during the hydration process: gridpoint temperatures at five points (Figure 2); hydration grade (Figure 3); tensile and compressive strength (Figure 4); elastic parameters (Figure 5); and the generated hydration heat (Figure 6).

Figure 1: FLAC3D model for the concrete inclusion test.

Table 1: Material Properties for the Elastic Frame

Bulk modulus (\(K\))	1000 MPa
Shear modulus (\(G\))	700 MPa
Specific heat (\(C_p\))	0.2 J/kg/K
Thermal conductivity (\(k\))	20.0 W/m/K
Linear thermal expansion coefficient (\(\alpha_t\))	10-4 K-1

Table 2: Material Properties for the Concrete Inclusion

Maximum amount of generated heat (\(Q^{max}_{Ce}\))	105 J/kg
Cement concentration (\(C\))	330 kg/m3
Material parameter (\(b\))	-1.114
Material parameter (\(t_1\))	7.2 \(\cdot\) 104 [s]
Universal gas constant (\(R\))	8.314 J/mol
Activation energy (\(E_{A,1}\))	33.5 J/mol
Slope of energy change (\(dE_{A,T}\))	1.47 J/mol/K
Specific heat (\(C_{P,1}\))	0.2 J/kg/K
Thermal conductivity (\(\lambda_1\))	2.0 W/m/K
Linear thermal expansion coefficient (\(\alpha_t\))	10-5 K-1
Specific parameter for cement (\(\alpha_0\))	0.20
Young’s modulus after complete hydration (\(E_{cte}\))	1000 MPa
Material parameter (\(c\))	0.4
Material parameter (\(a\))	0.6
Minimum value for (\(\alpha - \alpha_0\))	10-4

Figure 2: Evolution of gridpoint temperatures for the concrete inclusion test as a function of the concrete age.

Figure 3: Evolution of the hydration grade for the center zone of the concrete inclusion as a function of the concrete age.

Figure 4: Evolution of the tensile and compressive strength for the center zone of the concrete inclusion as a function of the concrete age.

Figure 5: Evolution of the elastic parameters for the center zone of the concrete inclusion as a function of the concrete age.

Figure 6: Evolution of the hydration heat for the center zone of the concrete inclusion as a function of the concrete age.

Data File

;--------------------------------------------------------------
;  Concrete inclusion in an elastic, thermal isotropic medium
;--------------------------------------------------------------
model new
model large-strain off
model title "Concrete inclusion in an elastic, thermal isotropic medium"
fish automatic-create off
model configure thermal
;
zone create brick size 11 1 11
zone face skin
zone group 'concrete' range position (4,0,4) (7,1,7)
zone cmodel assign hydration-drucker-prager range group 'concrete'
zone thermal cmodel assign hydration range group 'concrete'
zone cmodel assign elastic range group 'concrete' not
zone thermal cmodel assign isotropic range group 'concrete' not
;
zone property densit=2000 
zone property bulk=1e9 shear=0.7e9 range group 'concrete' not
zone thermal property conductivity=20.0 expansion=1e-4 specific-heat=0.2
; Mechanical hydration
zone property bulk-reference=0.98e9  shear-reference=0.50e9 ...
              range group 'concrete'
zone property constant-c=0.4 constant-a=0.6 range group 'concrete'
zone property hydration-minimum=0.20 tension-reference=2.0e6 ...
              range group 'concrete'
zone property hydration-difference-minimum=1e-4 range group 'concrete'
; Thermal hydration
zone thermal property conductivity=2.0 expansion=1e-5 specific-heat=0.2 ...
             range group 'concrete'
zone thermal property density-cement=330 constant-jonasson-b=-1.114 ...
             constant-jonasson-t1=7.2e4 range group 'concrete'
zone thermal property constant-gas=8.314 temperature-reference=293 ...
             hydration-grade-maximum=1.0 hydration-temperature-maximum=1e4 ...
             range group 'concrete'
zone thermal property constant-energy-1=33.5 constant-energy-dt=1.47 ...
             constant-energy-halftime=273 constant-heat-1=0.2 ...
             range group 'concrete'
zone thermal property hydration-binding-maximum=1e5 ...
             constant-conductivity-1=2.0 range group 'concrete'
;
zone gridpoint initialize temperature 300
zone face apply temperature 300 ...
                range group 'Top' or 'Bottom' or 'West' or 'East' 
;
zone face apply velocity-x 0 range group 'West' or 'East'
zone face apply velocity-y 0 range group 'North' or 'South'
zone face apply velocity-z 0 range group 'Top' or 'Bottom'
;
zone history temperature position (1,0,5)
zone history temperature position (2,0,5)
zone history temperature position (3,0,5)
zone history temperature position (4,0,5)
zone history temperature position (5,0,5)
[global hzp = zone.near.all(6.5,0.5,6.5)]
fish define h_alpha
    global h_alpha   = zone.therm.prop(hzp,'hydration-grade')
    global h_q       = zone.therm.prop(hzp,'hydration-rate')
    global h_te      = zone.therm.prop(hzp,'age-concrete-effective')
    global h_tension = zone.prop(hzp,'tension')
    global h_comp    = zone.prop(hzp,'compression')
    global h_young   = zone.prop(hzp,'young')
    global h_bulk    = zone.prop(hzp,'bulk')
    global h_shear   = zone.prop(hzp,'shear')
    global h_time    = thermal.time.total    
end
fish history h_alpha
fish history h_q
fish history h_te
fish history h_tension
fish history h_comp
fish history h_young
fish history h_bulk
fish history h_shear
fish history h_time
;
zone geometry-update 1
history interval 100
model solve time-total [2*24*3600]
model save 'concreteInclusion'