3. Validation of the data processing methodology

Several works have been developed to evaluate the validity and accuracy of the results obtained by applying this processing method to QOC tests. In the paper [30, 32], a series of numerical simulations of quasi-oedometric tests was conducted considering different behaviors of concrete. The Abaqus/Explicit FE code was selected to benefit from a user subroutine 'Vumat' in which the Krieg, Swenson and Taylor model is implemented [38, 39]. In this model, the hydrostatic behavior is described by a compaction law represented as a piece-wise linear function defined by several points (ε<sup>v</sup> i , pi) (Table 1). On the other hand, the model includes a limitation of the equivalent stress σeq (von Mises criterion) according to the following elliptic equation that depends on the hydrostatic pressure (P)

$$(\sigma\_{eq})\_{limit} = \sqrt{a\_0 + a\_1 P + a\_2 P^2} \tag{15}$$

The parameters used in KST model in (Forquin et al. [32]) are gathered in Table 3. Next, the processing methodology described in Figure 6 was applied to the numerical data in the same way as experimental data would be processed. Figure 8 presents the results for seven numerical simulations of a quasi-oedometric compression test. The left side of Figure 8 corresponds to the deviatoric behavior and the right-hand column to the hydrostatic behavior. The data processing described in Figure 6 was applied to the numerical calculations in which a friction was introduced at both plug/sample and cell/sample interfaces with a friction coefficient set to 0.1 or 0.2. Based on these numerical simulations, two methods were proposed to estimate the level of friction encountered during the QOC experiments: the first method relies on the ratio of two hoop strains measured at different locations on the outer surface of the cell. In the second method, the ratio of axial strain to hoop strain in the symmetry plane of the cell is considered. Finally it was concluded that a friction coefficient lower than 0.1 should be expected in the experiments conducted in [32]. In addition, an elastic deformation of the Chrysor® resin was simulated in two simulations with the parameters provided in Table 3. Finally, it was concluded that the maximum error made due to the lack of consideration of friction at plug/sample or cell/sample interfaces or Chrysor® resin in the play between the ring and the sample should not exceed about 4% regarding the deviatoric behaviour and about 12% regarding the hydrostatic behavior, whether the friction at the vessel/specimen interface remained below 0.1.

Another validation strategy was developed in [31] by conducting QOC experiments with cylindrical samples made of aluminum alloy (2017 T4), a reference material which elastoplastic behavior was well-characterized with a uniaxial tensile test. The deviatoric behavior and hydrostatic behavior obtained by data processing of one QOC test are compared with the expected responses in Figure 9. Again, the error made on the estimation of each deviatoric and hydrostatic response can be

estimated. One the one hand, whereas the deviatoric strength is slightly

Quasi-oedometric compression tests applied to an aluminum alloy sample. (a) Deviatoric behavior and

made up to a certain level of pressure when applying the data processing

4. Experimental results obtained with different types of concrete

QOC experiments have been conducted and applied to different kinds of concretes, mortars, particle-reinforced mortars, microconcrete and high-strength concrete with the sample dimensions mentioned in Table 1. Their composition, the

methodology to QOC experimental data.

Figure 8.

Figure 9.

79

(b) hydrostatic behavior [31].

4.1 Composition of concretes tested under QOC tests

underestimated in the range of weak strain it is well predicted above 5% of equivalent strain. On the other hand, the hydrostatic response shows that a gap seems to be eliminated between the compression plate and the specimen at the beginning of the test. Furthermore, the linear bulk modulus of the aluminum alloy is well captured. Finally, both validation techniques provide an estimation of error that can be

Processing of data from a numerical simulation of a quasi-oedometric compression test conducted with M2S small particle-reinforced mortar (cf. Table 4). (fp/s: Friction at plug/sample interface, fv/s: Friction at cell/sample interface, with Chrysor: A gap of thickness 0.3 mm is filled with a solid which behavior corresponds to a polymeric resin) [32].

Investigation of the Quasi-Static and Dynamic Confined Strength of Concretes by Means…

DOI: http://dx.doi.org/10.5772/intechopen.89660


#### Table 3.

Parameters used for concrete and Chrysor® resin in the calculation.

Investigation of the Quasi-Static and Dynamic Confined Strength of Concretes by Means… DOI: http://dx.doi.org/10.5772/intechopen.89660

#### Figure 8.

3. Validation of the data processing methodology

by several points (ε<sup>v</sup>

Compressive Strength of Concrete

i

Concrete (Krieg, Swenson and Taylor model)

Table 3.

78

Compaction curve (3 points) ε<sup>v</sup>

Parameters used for concrete and Chrysor® resin in the calculation.

Several works have been developed to evaluate the validity and accuracy of the results obtained by applying this processing method to QOC tests. In the paper [30, 32], a series of numerical simulations of quasi-oedometric tests was conducted considering different behaviors of concrete. The Abaqus/Explicit FE code was selected to benefit from a user subroutine 'Vumat' in which the Krieg, Swenson and Taylor model is implemented [38, 39]. In this model, the hydrostatic behavior is described by a compaction law represented as a piece-wise linear function defined

limitation of the equivalent stress σeq (von Mises criterion) according to the follow-

The parameters used in KST model in (Forquin et al. [32]) are gathered in Table 3. Next, the processing methodology described in Figure 6 was applied to the numerical data in the same way as experimental data would be processed. Figure 8 presents the results for seven numerical simulations of a quasi-oedometric compression test. The left side of Figure 8 corresponds to the deviatoric behavior and the right-hand column to the hydrostatic behavior. The data processing described in Figure 6 was applied to the numerical calculations in which a friction was introduced at both plug/sample and cell/sample interfaces with a friction coefficient set to 0.1 or 0.2. Based on these numerical simulations, two methods were proposed to estimate the level of friction encountered during the QOC experiments: the first method relies on the ratio of two hoop strains measured at different locations on the outer surface of the cell. In the second method, the ratio of axial strain to hoop strain in the symmetry plane of the cell is considered. Finally it was concluded that a friction coefficient lower than 0.1 should be expected in the experiments conducted in [32]. In addition, an elastic deformation of the Chrysor® resin was simulated in two simulations with the parameters provided in Table 3. Finally, it was concluded that the maximum error made due to the lack of consideration of friction at plug/sample or cell/sample interfaces or Chrysor® resin in the play between the ring and the sample should not exceed about 4% regarding the deviatoric behaviour and about 12% regarding the hydrostatic behavior, whether the friction at the vessel/specimen interface remained below 0.1. Another validation strategy was developed in [31] by conducting QOC experiments with cylindrical samples made of aluminum alloy (2017 T4), a reference material which elastoplastic behavior was well-characterized with a uniaxial tensile test. The deviatoric behavior and hydrostatic behavior obtained by data processing of one QOC test are compared with the expected responses in Figure 9. Again, the error made on the estimation of each deviatoric and hydrostatic response can be

q

Elastic parameters E, ν 46 GPa, 0.2

εv

εv

Chrysor® resin [31] Elastic parameters E, ν 2.2 GPa, 0.28

Coefficient of elliptical equation a0, a1, a2 625 MPa<sup>2</sup>

(i), P(i) (i = 1)

(i), P(i) (i = 2)

(i), P(i) (i = 3)

ing elliptic equation that depends on the hydrostatic pressure (P)

limit ¼

σeq � �

, pi) (Table 1). On the other hand, the model includes a

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi <sup>a</sup><sup>0</sup> <sup>þ</sup> <sup>a</sup>1<sup>P</sup> <sup>þ</sup> <sup>a</sup>2P<sup>2</sup>

(15)

�0.0003, 7.67 MPa �0.042, 200 MPa �0.15, 580 MPa

, 270 MPa, 0.505

Processing of data from a numerical simulation of a quasi-oedometric compression test conducted with M2S small particle-reinforced mortar (cf. Table 4). (fp/s: Friction at plug/sample interface, fv/s: Friction at cell/sample interface, with Chrysor: A gap of thickness 0.3 mm is filled with a solid which behavior corresponds to a polymeric resin) [32].

#### Figure 9.

Quasi-oedometric compression tests applied to an aluminum alloy sample. (a) Deviatoric behavior and (b) hydrostatic behavior [31].

estimated. One the one hand, whereas the deviatoric strength is slightly underestimated in the range of weak strain it is well predicted above 5% of equivalent strain. On the other hand, the hydrostatic response shows that a gap seems to be eliminated between the compression plate and the specimen at the beginning of the test. Furthermore, the linear bulk modulus of the aluminum alloy is well captured. Finally, both validation techniques provide an estimation of error that can be made up to a certain level of pressure when applying the data processing methodology to QOC experimental data.
