PSI - Issue 64

Rebecca Grazzini et al. / Procedia Structural Integrity 64 (2024) 1532–1539 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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Fig. 2. (a) load versus secant stiffness diagram of Sst-C-D-02, the original diagram in light blue, and in orange the moving average based on blocks of length 30 mm; (b) reference CML for the dry specimens and related characterizing points.

The diagram enables to evaluate the initial phase, ending in P 1 , and during which the secant stiffness is on the substantially constant branch; hence, the slip at the internal and external interfaces are connected to the ascending branches of the CML, ( ) ≤ 1 . On the secant stiffness diagram, it is subsequently observed a second phase during which the secant stiffness is substantially decreasing with a linear trend ending in P 2 . In this second phase, where partial deterioration of the interfacial behavior has clearly occurred, it is assumed that the internal interface still experiences a linear ascending trend, while the external has entered a linear softening trend, although not at the end of it, i.e. 1 ≤ ( ) ≤ 1 . When the secant stiffness shows a non-linear trend, the interfaces have undergone a more serious damage, i.e., both interfaces entered in the softening phase, here assumed linear, 1 ≤ ( ) ≤ 0 ; Finally, a friction trend is encountered in the pre-peak phase, ( ) > . The asymmetry in the interface behavior depends on the different boundary conditions to which the mortar layers are. The external interface is not able to activate a frictional restraining action, since the mortar layer shows free-from-restraints boundaries. The points of the internal and external CMLs are defined based on the previously mentioned phases, on the load vs secant stiffness and load vs slip diagrams providing: 1 = 1 2 2 2 1 ; 1 = 1 1 1 ; 2 = 2 1 ( 1 + 1 ) − 2 2 2 ( 1 − 1 ) ; 0 = 1 1 − 2 1 1 − 2 = 3 2 − 2 ( 1 0 + 1 ) 2 ( − 1 ) (1) The CMLs are defined as ( ): = {0 ≤ ≤ 1 ; 1 } ∧ { 1 ≤ ≤ 0 ; 2 + } (2) ( ): = {0 ≤ ≤ 1 ; 1 } ∧ { 1 ≤ ≤ ; 2 + } ∧ { ≥ ; } (3) where, k 1 is the tangent stiffness of the ascending branches, k 2e and k 2i are the tangent stiffness of the external and internal softening branches, respectively, while q e and q i are the intercept values of the softening branches, with similar meaning of the lower cases. Then, the differential problem of equilibrium showing the following general form: ′′( ) − 2 ( ( )) = 0 (4) can be specified in phase 1, i.e., up to P 1 and 1 ƒ• : ′′( ) −2 1 ( ) =0 ; ′(0)=0 ; ( )= 1 (5)