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Out-of-Plane Seismic Response of Stone Masonry Buildings

Progressive cracking mechanisms and DIANA-based numerical interpretation from full-scale shake table tests.

Stone masonry defines some of the most architecturally and culturally significant structures worldwide, from historic churches and civic buildings to vernacular residential construction. Unlike brick masonry, stone masonry is inherently heterogeneous, composed of irregular units, variable joint thicknesses, and nonuniform material properties. 

Under out-of-plane seismic loading, this heterogeneity promotes gradual stiffness degradation, crack localization along joints, and torsional amplification driven by geometric and material asymmetry. Capturing such behavior numerically requires nonlinear modeling approaches capable of representing joint-governed mechanisms and spatially localized damage. 

This article presents DIANA-based numerical simulations of full-scale shake table tests on a stone masonry structure. Focusing exclusively on the stone specimen tested within the same experimental campaign as the brick structure discussed in Part 1, the study links observed failure mechanisms to the capabilities and limitations of DIANA’s macro- and simplified micro-modeling strategies under pushover and nonlinear dynamic analyses.
 

Experimental Observations: Out-of-Plane Response of Stone Masonry 

The experimental campaign, conducted at LNEC (Lisbon), included a full-scale unreinforced stone masonry building with a central door opening and two perpendicular return walls, as shown in Figure 1. As with the brick specimen, no horizontal diaphragms were provided, intentionally preventing box behavior and allowing out-of-plane mechanisms to develop freely. 

© Candeias et al. (2016) 
Figure 1. Experimental campaign: (top) wallettes used for mechanical characterization and (bottom) real-scale specimens prepared for shake table tests. 

To capture the dynamic response, the structure was instrumented with accelerometers and linear variable displacement transducers (LVDTs) distributed along the main wall and return walls. The instrumentation layout, shown in Figure 2, provided the displacement and acceleration data used to validate numerical simulations. 


© Candeias et al. (2016) 
Figure 2. Instrumentation layout for the stone masonry specimen, showing the location of accelerometers and LVDTs. 

The stone specimen was subjected to a sequence of seismic excitations of increasing intensity. Unlike the brick structure, damage initiated earlier and evolved progressively. Cracking developed gradually as excitation intensity increased, without a single abrupt collapse event. 

The observed failure sequence included: 

  • Cracking concentrated along mortar joints.
  • Diagonal cracking initiating near the door opening.
  • Vertical cracking in the upper wall portion (tympanum).
  • Severe damage and large deformations at a peak ground acceleration of 1.07 g, without complete collapse.

These damage patterns, shown in Figure 3, highlight a deformation-driven response dominated by joint behavior rather than sudden geometric instability.

© Candeias et al. (2016)
Figure 3. Observed out-of-plane cracking and damage patterns in the stone masonry specimen following shake table testing. 

From Experiment to Numerical Strategy in DIANA 

To investigate the observed behavior numerically, the study implemented two modeling approaches in DIANA: 

  • Macro-modeling, representing stone masonry as an equivalent homogeneous continuum using DIANA’s Total Strain Crack Model.
  • Simplified micro-modeling, explicitly representing stone units and mortar joints using DIANA interface elements.

Material properties were derived directly from wallette testing and mechanical characterization, ensuring consistency between experimental observations and numerical input parameters. 

Macro-Modeling of the Stone Structure in DIANA 

Model setup and discretization 

The macro-model employed 20-node solid elements to discretize the masonry walls. As with the brick specimen, the following modeling parameters were 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 modeling strategy reflects a typical DIANA workflow for assessing global response in irregular masonry structures. 

Pushover Analysis: Progressive Damage and Capacity Trends 

Nonlinear static pushover analyses were performed to evaluate stiffness degradation and damage progression. 


Figure 4. Pushover curves of the stone masonry model due to incremental pushing loading 

As shown in Figure 4, the stone macro-model exhibited stable load-displacement behavior with limited sensitivity to mesh refinement. Unlike the brick specimen, post-peak response was less abrupt, reflecting the more progressive nature of stone masonry damage. 

Rotating crack models again provided the most realistic softening behavior, while fixed crack formulations tended to overestimate residual capacity. 

Figure 5. Pushover response of the stone macro-model in DIANA due to incremental load pulling, highlighting stiffness degradation and post-peak behavior.

In contrast to the brick case, pushover analysis for the stone specimen provided meaningful insight into both strength and damage evolution. 

Nonlinear Time-History Analysis: Agreement with Experimental Behavior 

Nonlinear dynamic analyses were performed using the Hilber–Hughes–Taylor (HHT) time integration scheme with Rayleigh damping (α = −0.1, ζ = 5%). The applied seismic input is shown in Figure 6. 

Figure 6. Applied ground motion record for the stone masonry shake table test.

As shown in Figure 7, DIANA’s macro-model captured: 

  • Crack localization near the door opening.
  • Damage concentration at the gable-return wall intersections.
  • Overall deformation patterns consistent with experimental observations.

Unlike the brick specimen, the macro-model reproduced the dominant out-of-plane response mechanisms with good fidelity, demonstrating that continuum modeling is better suited to stone masonry behavior in this configuration. 

 

Figure 7.  Hysteretic response of the stone continuum model: (a) fixed model with 20% of shear retention, (b) fixed model with 5% of shear retention, (c) rotating crack model, and (d) envelope.

Simplified Micro-Modeling of the Stone Structure in DIANA 

Model setup

The simplified micro-model explicitly represents: 

  • Stone units as 3D continuum elements. 
  • Mortar joints as DIANA interface elements governed by a combined cracking-shearing-crushing law. 

This approach is particularly relevant for stone masonry, where joint behavior dominates structural response. 

 


Figure 8. Simplified micro-model of the stone masonry structure in DIANA.
Static and Dynamic Results 

Pushover analysis of the micro-model showed realistic crack initiation and propagation along mortar joints, with conservative displacement capacity. 

Figure 9. Pushover analysis results of stone masonry simplified micro model.

Pushover analyses, shown in Figure 9, further improved crack localization and reproduced the experimentally observed damage patterns, including vertical cracking in the tympanum. However, predicted peak displacements remained significantly lower than experimental measurements (16 mm numerically versus 219 mm experimentally).

Torsional Effects and Asymmetric Response 

One of the most significant findings for the stone specimen is the role of torsional response driven by asymmetric stiffness. DIANA clearly captured this effect. 

As shown in Figure 10, the return wall containing the door opening experienced substantially larger displacements than the opposite return wall — up to an order of magnitude difference — closely matching experimental measurements. 

 

Figure 10.  Displacements at the top of the return walls of the stone model: (a) macro-modeling with fixed crack model and 5% of shear retention and (b) micro-modeling 

Engineering Implications for Stone Masonry Modeling in DIANA 

For stone masonry structures dominated by progressive cracking and joint-controlled behavior: 

  • Pushover analysis provides valuable insight into stiffness degradation and damage progression.
  • Nonlinear time-history analysis confirms crack localization and torsional amplification.
  • Macro-modeling in DIANA captures global response effectively.
  • Micro-modeling enhances understanding of joint behavior and crack distribution.
  • Rotating crack models remain preferable for realistic softening behavior.

DIANA enables engineers to evaluate these mechanisms systematically, supporting informed decisions when assessing irregular stone masonry structures under seismic loading. 

Conclusions 

For the stone masonry specimen investigated, DIANA’s macro- and micro-modeling approaches reproduced experimentally observed damage patterns and deformation mechanisms with good agreement. Progressive cracking, joint-governed response, and torsional effects were captured reliably, even though displacement capacity remained conservative in dynamic simulations. 

These results demonstrate that DIANA provides a robust and transparent framework for assessing out-of-plane seismic vulnerability in stone masonry buildings, particularly where damage evolves gradually rather than through sudden collapse. By enabling both continuum and interface-based modeling strategies, DIANA supports defensible, experiment-backed engineering assessments of complex masonry systems. 

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