B UILDING
6.2. N UMERICAL S TUDY OF URM WALLS
One of the primary objectives of the present study was to numerically evaluate the lateral load behavior of the structural components (walls) of the URM building as well as the building as a whole. This was achieved by carrying out the nonlinear pushover analyses of the walls and the building using two numerical approaches - Strand7 (Strand 7.2 User’s
Manual 2013)(Strand 7.2 User’s Manual, 2013)(2013) and Abaqus (2010). The failure mechanism and the lateral capacity of all the models were tuned to reflect the experimentally observed behavior. The analyses were carried out by discretizing the walls into 1040 eight-noded solid elements and 1703 nodes in Model 1, 872 eight-noded solid elements and 1493 nodes in Model 2, and 944 eight-noded solid element and 1598 nodes in Model 3 as shown in Figure 6.1. The FE model of URM building consisted of 10160 eight-noded solid elements (Figure 6.2). All the nodes located at the base of the models were fully restrained to simulate the fixed base conditions for simplicity. The vertical dead load was applied over the slab and an incremental lateral load was applied at the slab level up to failure as done during the experimental study.
(a) (b) (c)
Figure 6.1. FE models of wall specimens tested in the present study: (a) Wall 1, (b) Wall 2, and (c) Wall 3.
(a) (b)
Figure 6.2. Finite element models of URM Building: (a) View 1, and (b) View 2.
The material characteristics used in the analysis were taken from Table 4.1.
However, the numerical simulation carried out using Strand7 required a minor calibration to fix the value of φ (angle of internal friction), which was varied between 30o to 45o as
3m
3m
3m 3m
suggested in the past studies (NTC 2008). Finally, the Mohr-Coulomb failure criterion was considered for masonry with a friction angle of 35oand cohesion value of 0.145 MPa in order to calibrate the results with the experimental study. The maximum strength in tension and compression were calculated using the Mohr-Coulomb yield criterion under plane stress condition. As already discussed, the non-linear analyses in Abaqus was carried out considering the Concrete Damage Plasticity model for which the non-linear parameters were taken as: dilatation angle = 10o, eccentricity = 0.1, the ratio of initial equibiaxial and uniaxial compressive yield stress (fbo/fco) = 1.16, parameter Kc = 0.667 and viscosity parameter = 0.0001, based on established literature (Lubliner et al., 1989; Page 1981).
Material non-linearity was defined exclusively for masonry elements, whereas reinforced concrete lintels and slabs were assumed to behave elastically. Such assumption was made considering the fact that concrete possesses strength that was much larger than that of masonry, and therefore, no damage was observed in these elements during the tests. Tensile damage property was used for masonry elements for the non-linear analysis. During the tensile bond test, the material exhibited sudden brittle failure, leaving no scope of capturing the post peak softening behavior, which was required for simulating the tensile behavior of masonry in Abaqus. Hence, the experimentally obtained stress-strain curve (Figure 4.5b) in the post-peak region was modified according to the curve suggested in the Abaqus reference Manual (Abaqus,2010), which defines the damage criteria required to perform the analysis (Figure 3.1a).
6.2.1. Numerical Results 6.2.1.1. Wall 1
Pushover analysis was carried out using the aforementioned finite element programs along the in-plane direction, in accordance with the experimental study. In order to rationally use the results of the numerical study, calibration of the numerical model was carried out with the experimental results, and the same calibrated properties were used throughout the numerical study. After calibration, the force-displacement response predicted by Abaqus matched quite well with the experimental response (Figure 6.3a). As already discussed, Strand7 ignores the shear failure and material softening behavior. Therefore, though the drop in lateral capacity was not observed in the numerical simulation carried out using Strand7, the predicted lateral strength was quite close to that of the experimentally obtained values. The damage patch (DAMAGET or dt defined as the tensile damage variable), which was one of the outcomes of the numerical simulation in Abaqus, gives interesting
information on the modes of failure of different elements and the active failure mechanisms. It can be observed from Figure 6.3b-c that the experimentally observed damage pattern (i.e., failure at the bottom of the wall) can be simulated in the numerical analysis using Abaqus. Strand7 can also indirectly provide an approximate damage pattern given by total strain values in masonry. As shown in Figure 6.3d, the maximum strain values occur at both the ends of the wall near the base. This observation also matches well with the experimentally observed damage pattern.
(a) (b)
(c) (d)
Figure 6.3. Comparison of experimental and numerical results for Wall 1: (a) load displacement curves, (b) damage observed experimentally, (c) damage pattern in Abaqus, and (d) damage pattern in Strand7.
6.2.1.2. Wall 2
Numerical analysis of Wall 2 was carried out by following the similar calibration techniques adopted earlier, and the analysis results show similar trends as shown by Wall 1. The lateral load behavior obtained from numerical simulations was found to match well with the experimental results (Figure 6.4). It can be noted from the results of numerical simulation that the tensile damage variable in Abaqus and the total masonry strain in Strand7 show a concentration of inelastic deformation near the top of door opening and at the bottom of the wall at the end of the simulation (failure point) as shown in Figure 6.4c-
0 5 10 15 20 25 30 35
0 2.5 5 7.5 10
Lateral Load (kN)
Displacement (mm) Experimental Abaqus Strand7
d. Such a behavior matches well with the experimental response of the wall that exhibited a mixed failure combining flexure and sliding shear cracking (Figure 6.4b).
(a) (b)
(c) (d)
Figure 6.4. Comparison of experimental and numerical results for Wall 2: (a) load displacement curves, (b) damage observed experimentally, (c) damage pattern in Abaqus, and (d) damage pattern in Strand7.
6.2.1.3. Wall 3
Results of the numerical analyses conducted on the wall consisting of a central window opening show that the lateral force-deformation curve predicted by Abaqus closely matches with that of the experimental study (Figure 6.5a). As discussed already, Strand7 was also able to satisfactorily predict the lateral strength of Wall 3, though the complete non-linear response could not be predicted. However, the numerically simulated damage pattern of Wall 3, using both Strand7 and Abaqus, was significantly different when compared with the experimental results. The numerical analysis results correctly predicts the stress concentration near the corners of the opening (Figure 6.56.5c-d). Whereas, the experimental results showed flexural sliding failure at the base of the structure as shown in Figure 6.5b. This may be due to presence of a weaker course of masonry at the base of the test specimen. It was clear from the results that the tensile stress concentration occurs at the critical zones near the corners of the openings, which needs special attention.
0 5 10 15 20 25
0 2 4 6 8
Lateral Load (kN)
Displacement (mm) Experimental Abaqus Strand7
After comparing the pushover curves obtained numerically for the three wall models, it was observed that the introduction of a door opening has a considerable negative influence on the lateral load carrying capacity of the URM wall. Model 1 having no openings, was associated with the highest collapse load, and Model 2 with a door opening, exhibited the least load carrying capacity. Model 3 with a central window opening fared better than Model 2 because of smaller opening size and its ideal location as discussed in the experimental results.
(a) (b)
(c) (d)
Figure 6.5. Comparison of experimental and numerical results for Wall 3: (a) load displacement curves, (b) damage observed experimentally, (c) damage pattern in Abaqus, and (d) damage pattern in Strand7.