PSI - Issue 64

Maysam Jalilkhani et al. / Procedia Structural Integrity 64 (2024) 161–167 Author name / Structural Integrity Procedia 00 (2019) 000–000

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different parameter sets, with simplicity ranging from 2 parameters to complexity encompassing 13 parameters. Although methods with fewer parameters may seem efficient, they often sacrifice accuracy. Conversely, complex methods may offer greater accuracy but are time-consuming, particularly in urban settings with numerous buildings. Moreover, although these methods may demonstrate consistency, they prioritize different parameters. Thus, in cases lacking clear method preference, averaging damage calculations from each method may seem logical but prove less efficient. Recent attempts to evaluate building damage resulting from mining activities primarily rely on digitalization of specific areas (Diao et al, 2018; Hejmanowski et al, 2019). Diao et al. (2018) used radar (InSAR) time series analysis to assess structural damage caused by mine subsidence in China. They developed a model to correlate construction deformation/damage levels with ground deformation from mining subsidence, enabling the assessment of mining-induced damage to village constructions. Their classification, based on horizontal deformation and curvature, for masonry structures is shown in Table 3. Table 3. Cross-reference between surface construction damage grades and ground deformation, as outlined by Diao et al. (2018) Damage Grade Description of damaged constructions Horizontal deformation (mm/m) I Cracks in walls of masonry buildings < 4 mm in width and total width of multiple cracks < 10 mm ≤ 2.0 II Cracks in walls of masonry buildings < 15 mm in width and total width of multiple cracks < 30 mm ≤ 4.0 III Cracks in walls of masonry buildings < 30 mm in width and total width of multiple cracks < 50 mm ≤ 6.0 IV Cracks in walls of masonry buildings ¬ ≥ 30 mm in width and total width of multiple cracks ≥ 50 mm > 6.0 3. Analytical methods Various analytical methods, such as those proposed by Boone (1996), Boscardin and Cording (1989), and Burland (1995), use Timoshenko beam theory to evaluate the structural response and behavior of buildings. These methods typically involve modeling the building as a simply supported deep, isotropic, elastic, and weightless beam, subjected to either a mid-span point load or a uniformly distributed load along its length. By analyzing stress and strain distributions in structural members, these methods facilitate the evaluation of building damage. The first analytical method was proposed by Burland and Wroth (1975) and then extended by other researchers. For example, Boscardin and Cording (1989) and Burland (1995) used a beam model with a rectangular cross-section to assess damage in masonry buildings. Boone (2001) further modified the method by employing simple frame models to estimate structural damage in steel and concrete structures. However, these simplified building models limit the ability to consider building typology effects accurately and may lead to inaccurate estimations of structural damages. In analytical methods, the beam undergoes a deflection ( ∆ ) to simulate ground subsidence-induced deformation (see Figure 1).

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Fig. 1. The use of a deep beam model in analytical methods for structural damage assessment (after Saeidi et al, 2012) Strain values vary along the beam's length based on its deformation mode. Tensile strains resulting from pure bending ( ε br ) and pure shear ( ε sr ) deflections are subsequently determined using Timoshenko beam theory: