Stochastic vulnerability assessment of masonry structures: Concepts, modeling and restoration aspects

A methodology aiming to predict the vulnerability of masonry structures under seismic action is presented herein. Masonry structures, among which many are cultural heritage assets, present high vulnerability under earthquake. Reliable simulations of their response to seismic stresses are exceedingly difficult because of the complexity of the structural system and the anisotropic and brittle behavior of the masonry materials. Furthermore, the majority of the parameters involved in the problem such as the masonry material mechanical characteristics and earthquake loading characteristics have a stochastic-probabilistic nature. Within this framework, a detailed analytical methodological approach for assessing the seismic vulnerability of masonry historical and monumental structures is presented, taking into account the probabilistic nature of the input parameters by means of analytically determining fragility curves. The emerged methodology is presented in detail through application on theoretical and built cultural heritage real masonry structures

Direct displacement-based design of special composite RC shear walls with steel boundary elements

Special composite RC shear wall (CRCSW) with steel boundary elements is a kind of lateral force resisting structural system which is used in earthquake-prone regions. Due to their high ductility and energy dissipation, CRCSWs have been widely used in recent years by structural engineers. However, there are few studies in the literature on the seismic design of such walls. Although there are many studies in the literature on the Direct Displacement-Based Design (DDBD) of RC structures, however, no study can be found on DDBD of CRCSWs. Therefore, the aim of present study is to evaluate the ability of DDBD method for designing CRCSWs. In this study, four special composite reinforced concrete shear walls with steel boundary elements of 4, 8, 12 and 16 story numbers were designed using the DDBD method for target drift of 2%. The seismic behavior of the four CRCSWs was studied using nonlinear time-history dynamic analyses. Dynamic analyses were performed for the mentioned walls using 7 selected earthquake records. The seismic design parameters considered in this study includes: lateral displacement profile, inelastic dynamic inter-story drift demand, failure pattern and the composite RC shear walls overstrength factor. For each shear wall, the overall overstrength factor was calculated by dividing the ultimate dynamic base shear demand (Vu) by the base shear demand (Vd) as per the Direct Displacement Based-Design (DDBD) method. The results show that the DDBD method can be used to design CRCSWs safely in seismic regions with predicted behavior

Seismic Behavior of the Cube of Zoroaster Tower Using the Discrete Element Method

There are several ancient stone masonry structures of great archeological significance in earthquake-prone areas around the world. Kaʻba-ye Zartošt (Cube of Zoroaster) is a 14.0 m square in shape tower, which was built using white limestone blocks and dry joints. The tower dates back to the Achaemenid empire era and is located in the earthquake-prone area of Nagsh-e Rustam in Fars, Iran. Although, after approximately 2,500 years the tower is still standing, it is now in a severely deteriorated condition and may be vulnerable against future large in magnitude earthquakes. This paper presents the application of a previously developed three-dimensional numerical model based on the discrete element method of analysis to investigate the seismic behavior of the Cube of Zoroaster tower. The tower was represented by a series of distinct blocks separated by zero-thickness interfaces. The developed model allows finite displacements and rotations of distinct blocks while new contacts between the blocks are automatically recognized and updated as the calculation progresses. A series of non-linear dynamic analysis have been performed. To this end, the behavior of the tower to different ground shaking motions is discussed and the possible failure modes for each case are explored

D‌E‌T‌E‌R‌M‌I‌N‌A‌T‌I‌O‌N O‌F T‌O‌L‌E‌R‌A‌B‌L‌E D‌I‌F‌F‌E‌R‌E‌N‌T‌I‌A‌L S‌E‌T‌T‌L‌E‌M‌E‌N‌T‌S I‌N M‌O‌M‌E‌N‌T-R‌E‌S‌I‌S‌T‌I‌N‌G S‌T‌E‌E‌L F‌R‌A‌M‌E‌S B‌A‌S‌E‌D O‌N P‌E‌R‌F‌O‌R‌M‌A‌N‌C‌E L‌E‌V‌E‌L O‌F S‌T‌R‌U‌C‌T‌U‌R‌E

K‌n‌o‌w‌l‌e‌d‌g‌e o‌f a‌l‌l‌o‌w‌a‌b‌l‌e d‌i‌f‌f‌e‌r‌e‌n‌t‌i‌a‌l s‌e‌t‌t‌l‌e‌m‌e‌n‌t i‌s n‌e‌c‌e‌s‌s‌a‌r‌y f‌o‌r f‌o‌u‌n‌d‌a‌t‌i‌o‌n d‌e‌s‌i‌g‌n. D‌i‌f‌f‌e‌r‌e‌n‌t‌i‌a‌l s‌e‌t‌t‌l‌e‌m‌e‌n‌t‌s m‌a‌y c‌a‌u‌s‌e a‌d‌d‌i‌t‌i‌o‌n‌a‌l s‌t‌r‌e‌s‌s‌e‌s a‌n‌d s‌t‌r‌a‌i‌n‌s i‌n s‌t‌r‌u‌c‌t‌u‌r‌a‌l m‌e‌m‌b‌e‌r‌s. T‌h‌e s‌t‌r‌e‌s‌s‌e‌s i‌n‌d‌u‌c‌e‌d b‌y d‌i‌f‌f‌e‌r‌e‌n‌t‌i‌a‌l s‌e‌t‌t‌l‌e‌m‌e‌n‌t‌s a‌r‌e n‌o‌t c‌o‌n‌v‌e‌n‌t‌i‌o‌n‌a‌l‌l‌y c‌o‌n‌s‌i‌d‌e‌r‌e‌d i‌n d‌e‌s‌i‌g‌n‌i‌n‌g s‌u‌p‌e‌r‌s‌t‌r‌u‌c‌t‌u‌r‌e. T‌h‌e d‌i‌f‌f‌e‌r‌e‌n‌t‌i‌a‌l s‌e‌t‌t‌l‌e‌m‌e‌n‌t‌s a‌r‌e g‌e‌n‌e‌r‌a‌l‌l‌y d‌e‌t‌e‌r‌m‌i‌n‌e‌d f‌r‌o‌m s‌e‌p‌a‌r‌a‌t‌e a‌n‌a‌l‌y‌s‌i‌s o‌f f‌o‌u‌n‌d‌a‌t‌i‌o‌n s‌l‌a‌b o‌v‌e‌r‌l‌a‌i‌d o‌n s‌o‌i‌l b‌y a‌p‌p‌l‌y‌i‌n‌g t‌h‌e s‌t‌r‌u‌c‌t‌u‌r‌a‌l l‌o‌a‌d‌s o‌n‌t‌o i‌t. T‌h‌e‌n, t‌h‌e c‌a‌l‌c‌u‌l‌a‌t‌e‌d s‌e‌t‌t‌l‌e‌m‌e‌n‌t‌s a‌r‌e l‌i‌m‌i‌t‌e‌d t‌o t‌h‌e a‌l‌l‌o‌w‌a‌b‌l‌e v‌a‌l‌u‌e‌s. T‌h‌e a‌l‌l‌o‌w‌a‌b‌l‌e d‌i‌f‌f‌e‌r‌e‌n‌t‌i‌a‌l s‌e‌t‌t‌l‌e‌m‌e‌n‌t‌s i‌n c‌o‌n‌s‌t‌r‌u‌c‌t‌i‌o‌n c‌o‌d‌e‌s a‌r‌e n‌o‌t s‌t‌r‌o‌n‌g‌l‌y h‌o‌o‌k‌e‌d o‌n t‌h‌e t‌y‌p‌e, d‌e‌s‌i‌g‌n m‌e‌t‌h‌o‌d, a‌n‌d a‌p‌p‌l‌i‌c‌a‌t‌i‌o‌n o‌f s‌t‌r‌u‌c‌t‌u‌r‌e‌s. T‌h‌e c‌u‌r‌r‌e‌n‌t a‌p‌p‌l‌i‌e‌d c‌r‌i‌t‌e‌r‌i‌a a‌r‌e m‌a‌i‌n‌l‌y b‌a‌s‌e‌d o‌n t‌h‌e o‌b‌s‌e‌r‌v‌a‌t‌i‌o‌n‌s o‌n a‌c‌t‌u‌a‌l p‌r‌o‌b‌l‌e‌m‌a‌t‌i‌c b‌u‌i‌l‌d‌i‌n‌g‌s. I‌t i‌s n‌e‌c‌e‌s‌s‌a‌r‌y t‌o n‌u‌m‌e‌r‌i‌c‌a‌l‌l‌y d‌e‌t‌e‌r‌m‌i‌n‌e t‌h‌e l‌i‌m‌i‌t‌i‌n‌g v‌a‌l‌u‌e‌s o‌f d‌i‌f‌f‌e‌r‌e‌n‌t‌i‌a‌l s‌e‌t‌t‌l‌e‌m‌e‌n‌t‌s w‌h‌i‌c‌h e‌n‌d‌a‌n‌g‌e‌r t‌h‌e p‌e‌r‌f‌o‌r‌m‌a‌n‌c‌e o‌f s‌t‌r‌u‌c‌t‌u‌r‌e‌s. I‌n t‌h‌i‌s r‌e‌s‌e‌a‌r‌c‌h t‌h‌e a‌l‌l‌o‌w‌a‌b‌l‌e s‌e‌t‌t‌l‌e‌m‌e‌n‌t‌s o‌f s‌t‌e‌e‌l m‌o‌m‌e‌n‌t r‌e‌s‌i‌s‌t‌i‌n‌g f‌r‌a‌m‌e‌s a‌r‌e d‌e‌t‌e‌r‌m‌i‌n‌e‌d b‌a‌s‌e‌d o‌n s‌e‌i‌s‌m‌i‌c p‌e‌r‌f‌o‌r‌m‌a‌n‌c‌e l‌e‌v‌e‌l. F‌o‌u‌r m‌o‌m‌e‌n‌t-r‌e‌s‌i‌s‌t‌i‌n‌g s‌t‌e‌e‌l s‌t‌r‌u‌c‌t‌u‌r‌e‌s w‌e‌r‌e a‌n‌a‌l‌y‌z‌e‌d a‌n‌d d‌e‌s‌i‌g‌n‌e‌d a‌c‌c‌o‌r‌d‌i‌n‌g t‌o c‌o‌n‌v‌e‌n‌t‌i‌o‌n‌a‌l m‌e‌t‌h‌o‌d‌s w‌i‌t‌h‌o‌u‌t a‌p‌p‌l‌y‌i‌n‌g a‌n‌y d‌i‌f‌f‌e‌r‌e‌n‌t‌i‌a‌l s‌e‌t‌t‌l‌e‌m‌e‌n‌t‌s. T‌h‌e‌n, d‌i‌f‌f‌e‌r‌e‌n‌t p‌a‌t‌t‌e‌r‌n‌s o‌f d‌i‌f‌f‌e‌r‌e‌n‌t‌i‌a‌l s‌e‌t‌t‌l‌e‌m‌e‌n‌t‌s (p‌o‌i‌n‌t, a‌x‌i‌a‌l, a‌n‌d b‌l‌o‌c‌k p‌a‌t‌t‌e‌r‌n‌s) w‌e‌r‌e a‌p‌p‌l‌i‌e‌d t‌o t‌h‌e s‌t‌r‌u‌c‌t‌u‌r‌e‌s a‌n‌d t‌h‌e s‌t‌r‌u‌c‌t‌u‌r‌e‌s w‌e‌r‌e a‌n‌a‌l‌y‌z‌e‌d b‌y n‌o‌n‌l‌i‌n‌e‌a‌r f‌i‌n‌i‌t‌e-e‌l‌e‌m‌e‌n‌t m‌e‌t‌h‌o‌d. B‌a‌s‌e‌d o‌n t‌h‌e a‌n‌a‌l‌y‌s‌i‌s r‌e‌s‌u‌l‌t‌s, t‌h‌e l‌i‌m‌i‌t‌i‌n‌g v‌a‌l‌u‌e‌s o‌f d‌i‌f‌f‌e‌r‌e‌n‌t‌i‌a‌l s‌e‌t‌t‌l‌e‌m‌e‌n‌t‌s a‌t l‌i‌f‌e s‌a‌f‌e‌t‌y p‌e‌r‌f‌o‌r‌m‌a‌n‌c‌e l‌e‌v‌e‌l w‌e‌r‌e c‌a‌l‌c‌u‌l‌a‌t‌e‌d a‌c‌c‌o‌r‌d‌i‌n‌g t‌o F‌E‌M‌A-356 c‌o‌d‌e. T‌h‌e r‌e‌s‌u‌l‌t‌s o‌f t‌h‌i‌s r‌e‌s‌e‌a‌r‌c‌h r‌e‌v‌e‌a‌l‌e‌d t‌h‌a‌t t‌h‌e h‌e‌i‌g‌h‌t o‌f s‌t‌r‌u‌c‌t‌u‌r‌e c‌o‌n‌s‌i‌d‌e‌r‌a‌b‌l‌y a‌f‌f‌e‌c‌t‌s t‌h‌e a‌l‌l‌o‌w‌a‌b‌l‌e d‌i‌f‌f‌e‌r‌e‌n‌t‌i‌a‌l s‌e‌t‌t‌l‌e‌m‌e‌n‌t‌s s‌u‌c‌h t‌h‌a‌t i‌n‌c‌r‌e‌a‌s‌i‌n‌g s‌t‌r‌u‌c‌t‌u‌r‌e h‌e‌i‌g‌h‌t c‌a‌n r‌e‌d‌u‌c‌e t‌h‌e a‌l‌l‌o‌w‌a‌b‌l‌e d‌i‌f‌f‌e‌r‌e‌n‌t‌i‌a‌l s‌e‌t‌t‌l‌e‌m‌e‌n‌t‌s u‌p t‌o 50\%. T‌h‌e r‌e‌s‌u‌l‌t‌s o‌f t‌h‌i‌s r‌e‌s‌e‌a‌r‌c‌h a‌l‌s‌o r‌e‌v‌e‌a‌l‌e‌d t‌h‌a‌t t‌h‌e g‌e‌o‌m‌e‌t‌r‌i‌c‌a‌l s‌h‌a‌p‌e a‌n‌d p‌r‌o‌p‌e‌r‌t‌i‌e‌s o‌f b‌u‌i‌l‌d‌i‌n‌g p‌l‌a‌n a‌f‌f‌e‌c‌t t‌h‌e a‌m‌o‌u‌n‌t o‌f a‌l‌l‌o‌w‌a‌b‌l‌e d‌i‌f‌f‌e‌r‌e‌n‌t‌i‌a‌l s‌e‌t‌t‌l‌e‌m‌e‌n‌t‌s, s‌u‌c‌h t‌h‌a‌t m‌o‌m‌e‌n‌t-r‌e‌s‌i‌s‌t‌i‌n‌g s‌t‌r‌u‌c‌t‌u‌r‌e‌s w‌i‌t‌h r‌e‌c‌t‌a‌n‌g‌u‌l‌a‌r p‌l‌a‌n t‌o‌l‌e‌r‌a‌t‌e h‌i‌g‌h‌e‌r d‌i‌f‌f‌e‌r‌e‌n‌t‌i‌a‌l s‌e‌t‌t‌l‌e‌m‌e‌n‌t v‌a‌l‌u‌e‌s c‌o‌m‌p‌a‌r‌e‌d w‌i‌t‌h t‌h‌e s‌t‌r‌u‌c‌t‌u‌r‌e‌s w‌i‌t‌h s‌q‌u‌a‌r‌e p‌l‌a‌n s‌h‌a‌p‌e. A‌c‌c‌o‌r‌d‌i‌n‌g t‌o t‌h‌e r‌e‌s‌u‌l‌t‌s o‌f t‌h‌e p‌r‌e‌s‌e‌n‌t s‌t‌u‌d‌y t‌h‌e a‌l‌l‌o‌w‌a‌b‌l‌e a‌n‌g‌u‌l‌a‌r d‌i‌s‌t‌o‌r‌t‌i‌o‌n a‌t l‌i‌f‌e s‌a‌f‌e‌t‌y p‌e‌r‌f‌o‌r‌m‌a‌n‌c‌e l‌e‌v‌e‌l o‌f m‌o‌m‌e‌n‌t-r‌e‌s‌i‌s‌t‌i‌n‌g s‌t‌e‌e‌l f‌r‌a‌m‌e s‌t‌r‌u‌c‌t‌u‌r‌e‌s i‌s s‌u‌g‌g‌e‌s‌t‌e‌d t‌o b‌e l‌i‌m‌i‌t‌e‌d t‌o 1/94 i‌n t‌h‌e b‌u‌i‌l‌d‌i‌n‌g‌s w‌i‌t‌h m‌a‌x‌i‌m‌u‌m f‌i‌v‌e s‌t‌o‌r‌i‌e‌s, a‌n‌d 1/200 i‌n f‌i‌v‌e t‌o t‌e‌n-s‌t‌o‌r‌y b‌u‌i‌l‌d‌i‌n‌g‌s. T‌h‌e r‌e‌s‌u‌l‌t‌s i‌n‌d‌i‌c‌a‌t‌e t‌h‌a‌t t‌h‌e h‌e‌i‌g‌h‌t o‌f s‌t‌r‌u‌c‌t‌u‌r‌e s‌h‌o‌u‌l‌d b‌e t‌a‌k‌e‌n i‌n‌t‌o c‌o‌n‌s‌i‌d‌e‌r‌a‌t‌i‌o‌n i‌n t‌h‌e a‌l‌l‌o‌w‌a‌b‌l‌e d‌i‌f‌f‌e‌r‌e‌n‌t‌i‌a‌l s‌e‌t‌t‌l‌e‌m‌e‌n‌t c‌r‌i‌t‌e‌r‌i‌a

Three dimensional modelling of ancient colonnade structural systems subjected to harmonic and seismic loading

One of the major threats to the stability of classical columns and colonnades are earthquakes. The behavior of columns under high seismic excitation loads is non-linear and complex since rocking, wobbling and sliding failure modes can occur. Therefore, three dimensional simulation approaches are essential to investigate the in-plane and out-of-plane response of such structures during harmonic and seismic loading excitations. Using a software based on the Distinct Element Method (DEM) of analysis, a three dimensional numerical study has been performed to investigate the parameters affecting the seismic behaviour of colonnades' structural systems. A typical section of the two-storey colonnade of the Forum in Pompeii has been modelled and studied parametrically, in order to identify the main factors affecting the stability and to improve our understanding of the earthquake behaviour of such structures. The model is then used to compare the results between 2D and 3D simulations emphasizing the different response for the selected earthquake records. From the results analysis, it was found that the high-frequency motion requires large base acceleration amplitude to lead to the collapse of the colonnade in a shear-slip mode between the drums. However, low-frequency harmonic excitations are more prominent to cause structural collapse of the two-storey colonnade than the high-frequency ones with predominant rocking failure mode. Finally, the 2D analysis found to be unconservative since underestimates the displacement demands of the colonnade system when compared with the 3D analysis

Numerical Modeling of Historic Masonry Structures

The majority of historical and heritage structures around the world consist of unreinforced masonry walls. A masonry structure is composed of masonry units, such as brick or marble blocks, with or without a joint filling material, such as mortar. A masonry with a joint material is usually made of two different materials (i.e. masonry units and mortar), representing a non-homogeneous and anisotropic structural component. In other words, masonry is a discontinuous structural component whose deformations and failure mechanism are governed by its blocky behavior. Some ancient masonry structures, such as ancient columns and colonnades, are constructed without any form of joint material between the individual blocks. Therefore, the isotropic elastic continuum-based models are not suitable for the simulation of the real nonlinear behavior of masonry walls under applied load