Experimental Observations: Out-of-Plane Failure in Brick Masonry
The experimental campaign, conducted at LNEC (Lisbon), investigated the out-of-plane seismic response of a full-scale unreinforced brick masonry building. The specimen featured a central window opening and two perpendicular return walls, representative of traditional masonry construction, as shown in figure 1. No horizontal diaphragms were provided, intentionally preventing box-type behavior and allowing out-of-plane mechanisms to develop freely.
Figure 1. Experimental campaign: (top) wallettes for compression tests and (bottom) real scale specimens for shaking table tests.
To accurately capture the structural response during seismic excitation, the specimen was instrumented with accelerometers and linear variable displacement transducers (LVDTs) distributed across the main wall and return walls. The location of these sensors is shown in Figure 2, which defines the measurement basis for the displacement and acceleration responses discussed later.
Figure 2. Instrumentation layout for the brick masonry specimen, showing the location of accelerometers and LVDTs used to measure dynamic response during the shake table tests.
The brick masonry specimen was subjected to a sequence of eight seismic excitations of increasing intensity. During the first six ground motions, no significant structural damage was observed, and the response remained largely elastic. Cracking initiated only during the final two motions, culminating in sudden out-of-plane collapse during the strongest excitation. This progression highlights the absence of gradual damage accumulation and underscores the brittle, instability-driven nature of the observed response.
As loading intensity increased, the structure exhibited a clear and repeatable failure sequence:
- Diagonal cracking initiating at window corners.
- Progressive cracking at wall intersections and return walls.
- Sudden out-of-plane collapse of the upper wall portion (tympanum) at a peak ground acceleration of 1.27 g, as shown in Figure 3.
Figure 3. Observed out-of-plane failure mechanism of the brick masonry specimen, including diagonal cracking at window corners and collapse of the tympanum.
The collapse occurred abruptly, with limited deformation capacity prior to failure. This behavior highlights the inherently brittle nature of brick masonry under out-of-plane seismic demand and establishes a demanding benchmark for numerical modeling.
From Experiment to Numerical Strategy in DIANA
To investigate this behavior numerically, the study implemented two modeling approaches in DIANA:
- Macro-modeling: masonry is treated as a homogeneous continuum using DIANA’s Total Strain Crack Model.
- Simplified micro-modeling: brick units are represented as continuum elements and mortar joints are modeled explicitly using DIANA interface elements.
Material properties were derived directly from experimental wallette tests and mechanical characterization, ensuring consistency between the physical specimens and their numerical representations.
Macro-Modeling of the Brick Structure in DIANA
Model setup and discretization
The macro-model employed 20-node solid elements to discretize the masonry walls. Several modeling decisions were systematically evaluated:
- Fixed crack models with 20% and 5% shear retention.
- A rotating crack model.
- Mesh sensitivity using one, two, and four elements through the wall thickness.
This reflects a typical DIANA workflow for a large-scale masonry assessment, where constitutive assumptions and discretization choices strongly influence predicted response.
Pushover Analysis: Strength and Stiffness Trends
Nonlinear static pushover analyses were performed in both pushing and pulling directions.
As shown in Figure 4, DIANA’s rotating crack model produced a realistic post-peak softening response, while fixed crack models exhibited artificial hardening after peak load. Figure 4 (below) shows a roughly 33% reduction in capacity when loading direction was reversed, reflecting asymmetric stiffness.
While pushover analysis proved effective for assessing stiffness, strength, and crack initiation, it did not reproduce the experimentally observed out-of-plane collapse.
Nonlinear Time-History Analysis: Limits of Continuum Modeling
The nonlinear dynamic analyses were performed using the Hilber–Hughes–Taylor (HHT) time integration scheme, also referred to as the α-method. To account for energy dissipation during cyclic loading, Rayleigh viscous damping was included in the simulations. In this study, the numerical parameters were defined using a value of α = −0.1 and a damping ratio ζ = 5%, consistent with the experimental conditions and the assumptions adopted in the original testing program.
The applied seismic input is shown in Figure 6.
As shown in Figure 7, the macro-model captures:
- In-plane cracking at window corners.
- Global deformation trends.
However, full tympanum collapse is not reproduced, indicating that homogenized continuum modeling is insufficient for simulating sudden out-of-plane instability in this configuration. The experimental collapse was governed by geometric instability and three-dimensional detachment, mechanisms that remain difficult to trigger numerically without explicit contact or imperfection modeling.
Simplified Micro-Modeling of the Brick Structure in DIANA
Model setup
The simplified micro-model explicitly represents:
- Brick units as 3D continuum elements
- Mortar joints as DIANA interface elements governed by a combined cracking–shearing–crushing law
This allows DIANA to localize damage at joints and openings.
Material properties for masonry units and timber lintels are summarized in Table 2, while interface behavior parameters are reported in Table 3.
Static and Dynamic Results
Pushover analysis of the micro-model demonstrated improved representation of localized damage mechanisms, as shown in Figure 9.
Figure 9. Pushover response of the brick micro-model, showing localized cracking at window corners and wall intersections.
Dynamic analyses (Figure 10) further enhanced crack localization relative to the macro-model.
Despite these improvements, predicted maximum displacements remained significantly lower than experimental measurements, and collapse was still not reproduced. This underscores the challenge of capturing displacement-driven instability in brittle masonry systems, even with enhanced modeling detail.
Comparative Performance: Macro vs. Micro Modeling
A direct comparison of macro- and micro-model predictions for return wall displacement provides further insight.
Figure 11. Comparison of return wall displacements predicted by macro and micro models for the brick masonry structure.
The results illustrate how modeling assumptions influence displacement demand and damage distribution, clarifying the limits of each approach when applied to collapse-prone masonry typologies.
Engineering Implications for Brick Masonry Modeling in DIANA
For brick masonry structures dominated by sudden out-of-plane collapse:
- Pushover analysis is useful for understanding stiffness and crack initiation, but not collapse.
- Nonlinear time-history analysis is essential to expose instability mechanisms.
- Rotating crack models should be preferred for brittle behavior.
- Micro-modeling improves damage localization but may remain conservative in displacement prediction.
DIANA enables engineers to explore these behaviors explicitly, clarifying when simplified modeling assumptions reach their limits.
Conclusions
For the brick masonry specimen investigated, DIANA reliably captures global response trends and crack initiation observed in full-scale shake table tests. However, sudden out-of-plane collapse remains difficult to reproduce numerically, even with enhanced micro-modeling strategies.
These findings provide practical guidance for engineers assessing seismic vulnerability in unreinforced brick masonry buildings, particularly in heritage contexts where brittle collapse mechanisms govern risk. By supporting both macro- and micro-modeling approaches within a validated nonlinear framework, DIANA equips practitioners with the tools needed to make informed, defensible engineering decisions grounded in experimental evidence.
While this study focuses on brick masonry, the same experimental campaign also examined a structurally distinct stone masonry specimen, whose out-of-plane seismic response reveals both parallels and critical contrasts explored in Part 2.