Predicting Uniaxial Cyclic Compressive Behavior of Brick Masonry: New Analytical Model

Abstract

A constitutive model for simulating the compressive response of unreinforced brick masonry subjected to cyclic loading is presented and discussed. The developed formulations are consistent with the smeared rotating crack approach and may be easily implemented in finite element codes for nonlinear analysis. The analysis approach includes different features such as nonlinear curves for capturing the shape of the unloading/reloading branches, both in case of full unloading from the envelope curve and partial unloading/reloading. A unified model for predicting the residual plastic strain as a function of the strain recovered during unloading is also proposed. Particular attention is paid to the stiffness degradation occurring during reloading and to the prediction of the stress and strain values at which the reloading branch intersects the envelope. The calibration of most of the proposed formulations is based on experimental results reported in the literature, as well as from two uniaxial cyclic compression tests carried out within the present work. Finally, the model effectiveness is tested with some verification examples.

Experimental and Analytical Study of Masonry Subjected to Uniaxial Cyclic Compression

“…Nevertheless, the analytical models proposed by Crisafulli [ 26 ] and Facconi et al [ 28 ] reasonably predict the experimental envelop curves, especially the model suggested by Facconi et al [ 28 ] accurately predicted all the experimental envelop curves. The reason for this quite accurate prediction is due their assimilation of two set envelop curve formulations (pre-peak and post-peak), whereas the other three models outlined single formulation.…”

“…The formulation used to define the unloading and reloading curve was mainly taken from Crisafulli [ 26 ]. The idea of reloading curve and stiffness for the model was taken from concrete models [ 28 , 30 ]. Also, an empirical formulation similar to that given in Subramaniam and Sinha [ 25 ] was used to predict the plastic strain as the function of unloading strain.…”

“…Subsequently, the experimental cyclic compression stress–strain curves obtained for the four masonry unit-to-mortar combinations in this research (CB1-NHL, CB1-CM, CB2-NHL, and CB2-CM) and two cyclic stress–strain literature curves were considered. The two cyclic stress–strain literature curves were taken from the experimental studies of Naraine and Sinha [ 18 ] and Facconi et al [ 28 ]. The characteristics of the cyclic compression stress–strain curves comprised of envelop curve, plastic strain, and unloading/reloading curves.…”

“…The reason for this quite accurate prediction is due their assimilation of two set envelop curve formulations (pre-peak and post-peak), whereas the other three models outlined single formulation. Especially envelop curve model proposed by Facconi et al [ 28 ] was taken from Hoshikuma et al [ 50 ] and recently Thamboo and Dhanasekar [ 40 ] have shown that this envelop model predict the behaviour of relatively low strength masonry as well. Thus it can be stated that this model is capable of predicting the envelop curves of different masonry assemblies verified in this research.…”

“…A study by Sima et al [ 27 ] outlined a comprehensive analytical model and calibrated it against the experimental data from Naraine and Sinha [ 18 ]. Recently, Facconi et al [ 28 ] improved the Crisafulli [ 26 ] model constants with the smeared rotating crack approach. Most of those cyclic analytical models were derived from related cyclic analytical models of concrete [ 29 , 30 , 31 , 32 , 33 , 34 ].…”