Showing papers by "Luís F. Ramos published in 2007"

Progressive damage analysis based on vibration signatures : an application to a masonry arch

Abstract: The paper aims at exploring damage assessment in masonry structures at an early stage by vibration measurements. One arch replicate of historical constructions was built as reference, undamaged, state. Afterwards, progressive damage was induced and sequential modal identification analysis was performed at each damage stage, aiming to find adequate correspondence between dynamic behaviour and internal crack growth. 72 ARCH’07 – 5th International Conference on Arch Bridges vention and respect of the original construction. The assumption that damage can be linked to a decrease of stiffness seems to be reasonable to this type of structures. Many methods are presented in literature, see Doebling et al. (1996), for damage identification based on vibration signatures but there are only a few papers on the application to masonry structures. An important task before damage can be identified from vibration characteristics is the study and subsequent elimination of the environmental effects (Peeters, 2000). 2.1 Proposed Methodology Experience with other studies related to masonry structures indicates that, in several cases, simpler models (or methods) give better quality and more comprehensive results than more elaborated ones (Ramos, 2002). In this sense, it is desirable to use different techniques/tools to study the masonry structures in a holistic way. Ideally, the analyzer should have a group of methods/results to make a decision about the structure or to assist in the decision on additional studies. This is the basis for the methodology of damage identification presented next. A group of damage methods has been selected from the literature. In one hand, it is intended to study the applicability of existing methods to the masonry structures, and, in another hand, it is aimed to have a wide view of the problem (different results are provided by different methods), assisting in the conclusions related to damage identification. If significant damage is present in the structure, the results provided from different methods would converge in a unique conclusion, giving more confidence to the analyzer. The selected methods were applied to an arch model, where progressive and controlled damage scenarios were imposed. From the point of view of the applicability of dynamic based identification methods to masonry structures, the methodology would be successful if the detection (Level 1), the localization (Level 2) and the assessment (Level 3) will be attained with these methods. The selected methods together with the required modal information are presented in Table 1 (see Doebling et al., 1996, for the complete description of each method). Table 1 : Selected damage identification methods Modal Information Method Expected Identification Level Comparison Scenario ω φ φ′′ φ φ′′ COMAC Level 2 • ○ ○ ○ ○ Parameter Method (PM) Level 2 • • ○ ○ ○ ○ Mode Shape Curvature Method (MSCM) Level 2 • ○ ○ Damage Index Method (DIM) Level 2 • ○ ○ Change Flexibility Method (CFM) Level 2 and 3 • • • ○ FE Model Updating (FEMU) Level 2 and 3 ○ ○ ○ ○ ○ ○ – Optional modal quantities; • – Compulsory modal quantities All methods have one common aspect; they all use spatial modal information of the structure, through the mass scaled or non-scaled mode shapes φ and φ, respectively (or/and through the mass scaled or non-scaled curvatures mode shapes φ′′ and φ′′, respectively). The global and local approach should be considered as complementary tasks. For the case of historical constructions these two approaches seem to be suitable, since they are non-destructive procedures to evaluate health conditions. L.F. Ramos, P.B. Lourenço, G. De Roeck, and A. Campos-Costa 73 3 ARCH MODEL DESCRIPTION AND PRELIMINARY STUDIES One replicate of ancient masonry arches was built with clay bricks with 100 × 50 × 25 mm, manually produced in the Minho region, at the northern area of Portugal. The clay brick, with low compression strength, and the Mapei mortar, with poor mechanical properties, used for the joints tries to be representative of the materials used in the historical constructions. Figure 1 shows some images of the replicate construction. The arch has a semicircular shape with a radius of 0.77 m, a span of 1.50 m, a width of 0.45 m, and a thickness of 0.05 m, and rests in two concrete abutments fixed to the ground floor with bolts. (a) (b) (c) Figure 1 : Arch model: (a) construction initiation: (b) construction ending; and (c) arch completed 3.1 Numerical Crack Prediction A FE model was use to predict the possible location of damage. The numerical model was built with 8 node plane stress elements in DIANA (2006). To simulate the nonlinear behavior of masonry structures the constitutive models for cracking (a combination of tension cut-off, tension softening and shear retention) was used. Nonlinearities were considered only in tensile behavior to make the analysis simpler. It should be stressed that the results are analyzed in a qualitatively way and they were useful only to predict the possible location of cracks. For that reason a sensitivity analysis was performed by changing the tensile strength of the masonry material. Figure 2 summarizes the results of four analyses. Although the static response varies, according to the tensile strength (see Figure 2b), all the analyses shows four cracks (hinges) at ultimate load of the arch (three hinges are needed to produce a static determinate structure and four hinges are needed to form a mechanism). The numerical crack sequence is (see Figure 2a): first crack (c1) in the intrados under the load application point; second crack (c2) in the intrados at the right support; third crack (c3) in the extrados and, apparently, approximately in the symmetrical position of the first crack; and the last crack (c4) in the extrados near the left support. (a) Arch Static Response 0.0 0.5 1.0 1.5 2.0 2.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 Vertical Displacement [mm] V er tic al L oa d [k N ] ft = 0.05 MPa ft = 0.10 MPa ft = 0.20 MPa ft = 0.40 MPa (b) Figure 2 : Numerical crack prediction: (a) crack location; and (b) different static response for four values of the tensile strength ft. c1 c2

Vibration signatures to identify damage in historical constructions

Abstract: The paper aims at exploring damage assessment in masonry structures at an early stage by vibration measurements. One arch replicate of historical constructions was built as reference, undamaged, state. Afterwards, progressive damage was induced and sequential modal identification analysis was performed at each damage stage, aiming to find adequate correspondence between dynamic behaviour and internal crack growth.