Issue 50

K. Kaklis et alii, Frattura ed Integrità Strutturale, 50 (2019) 395-406; DOI: 10.3221/IGF-ESIS.50.33

with a lateral pressure of 1.15 MPa were not used in Fig.9a and in the subsequent derivation of the damage index relationship because of two reasons: (a) these tests exhibited a strain-softening behavior, while specimens under higher triaxial compression pressures exhibited a strain-hardening behavior and (b) the behavior of the specimen tested under a lateral pressure of 1.15 MPa exhibited a failure mode (Fig.7c) similar to that of uniaxial test (Fig.7a) and dissimilar to that of high pressure triaxial tests (Fig.8).

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

d = 0.42 - 0.91 ε -1.32

c = 0.123 σ 3

+ 0.5866

R 2 =0.99

d = 0.29 - 0.62 ε -1.10

+ 0.5557

b = 0.0498 σ 3

R 2 =0.42

d = 0.31 - 0.73 ε -0.83

a b c

Damage index, d

α = 0.0284 σ 3

+ 0.2253

Coefficients a,b,c

R 2 =0.65

2.09 MPa

3.96 MPa

6.06 MPa

0

1

2

3

4

5

6

7

8

0

2

4

6

8

10

12

14

Confining pressure, σ 3

(MPa)

Total axial strain, ε (x10 -3 )

(a) (b) Figure 9 : (a) Fitting results of damage index d for triaxial compression cyclic tests with confining pressures of 2.09 MPa, 3.96 MPa and 6.06 MPa. (b) Fitting results for coefficients , and . In this work, a similar model with those proposed for concrete [24, 25, 26, 27, 28, 29] was adopted in order to predict the damage evolution relationship for the pozzolanic lime mortar, which is described in Eq.(9): ൌ െ ∙ ି௖ (9) where a , b are coefficients of the damage evolution relationship; c is an optimum order related to the speed of damage propagation, which controls the curvature of the damage evolution curve. The fitting curves on the calculated damage index for each confining pressure are plotted in Fig.9a, while the fitting results for coefficients a , b and c are listed in Table 2.

σ 3

a

b

c

2.09 3.96 6.06

0.31 0.29 0.42

0.73 0.62 0.91

0.83 1.10

1.32 Table 2 : Fitting results for coefficients a , b and c .

As illustrated in Fig.9b, the coefficients a, b and c are functions of the confining pressure. From a regression analysis, these coefficients are determined in Eqs.(10-12). The corresponding fitting lines and least square correlation coefficients are shown in Fig.9b. ൌ 0.0284 ∙ ଷ ൅ 0.2253 (10) ൌ 0.0498 ∙ ଷ ൅ 0.5557 (11) ൌ 0.123 ∙ ଷ ൅ 0.5866 (12) The evolution of d as a function of the confining pressure (Eq.(13)) is calculated by substituting Eqs.(10-12) in Eq.(9): ൌ 0.0284 ∙ ଷ ൅ 0.2253 െ ሺ0.0498 ∙ ଷ ൅ 0.5557ሻ ∙ ିሺ଴.ଵଶଷ∙ఙ య ା଴.ହ଼଺଺ሻ (13) The verification of this damage model expressed in Eq.(13) is shown in Fig.10, where the predicted elastic moduli E d for each loop of the triaxial compression cyclic tests with confining pressure of 2.09 MPa (Fig.10a) and 6.06 MPa (Fig. 10b) are compared with the corresponding experimental values. The values of the predicted elastic moduli are in good agreement with the elastic moduli that were determined experimentally. The different behavior between uniaxial and triaxial compression tests with respect to plastic strain versus total strain and plastic strain versus deviator stress can be

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