The study, conducted by Mehmet Sari of Aksaray University, focused on a slope above Belisirma where a rock mass composed of hard ignimbrite, soft ignimbrite, and soft tuff serves as a persistent source of falling blocks. The upper section of the source rock consists of hard ignimbrite cut by persistent joints, while the lower portion is softer ignimbrite with nonpersistent joints, and the base is joint-free tuff. Stereographic analysis of the rock mass revealed three major joint sets: two sub-vertical orthogonal sets created by thermal cracks during cooling of the ignimbrite, and a near-horizontal bedding plane formed by different outflow facies of the ignimbrite deposition. Because joint spacing largely controls the size of blocks that can detach, this geological architecture determines whether the slope releases small debris or massive boulders.

To quantify what the slope could actually produce, Sari used the RocSlope3 program to reconstruct the fractured rock mass in three dimensions. Synthetic traverses defined on the upper slope generated a probabilistic joint network in which joint planes were represented as circular discs with known spacing and radius. The program then discretized the rock mass into individual blocks, identifying 354 discrete blocks with volumes ranging from a mere 0.01 cubic meters to a substantial 18.16 cubic meters. This in-situ block size distribution, a cumulative frequency curve capturing the natural variability of joint spacing and orientation, became the statistical backbone for the subsequent trajectory simulations, ensuring that the modeled rocks reflected what the cliff face could genuinely deliver.

With the block inventory established, the study turned to the central question: how do different impact models change the predicted behavior of falling rocks? The research compared two fundamentally different approaches available in the RocFall3 software. The lumped-mass model treats every rock as a dimensionless point mass, an infinitesimal particle with no physical volume, shape, or true rotation. Energy loss during impacts is governed entirely by a preset coefficient of restitution, and rotation is reduced to a kind of pseudo-rotation derived from an equivalent radius. The rigid-body model, by contrast, uses non-smooth multi-contact dynamics that explicitly account for the rock’s exact three-dimensional geometry, volume, and mass distribution. Impacts are computed at the actual instantaneous contact points on the rock’s surface rather than at its center of mass, allowing the software to capture the eccentric, chaotic behavior of real boulders.

The contrast between the two models was stark. In the lumped-mass simulations, most particles stopped close to the slope toe, and not a single one reached the edge of the model where the endangered houses stand. The rigid-body model told a very different story: most blocks crossed the road, and some reached the downslope houses, successfully reproducing the rockfall paths observed in previous events. The blocks accumulated in three distinct zones along the slope, with rounded, more angular blocks traveling furthest and sharp-edged, less angular blocks coming to rest closer to the toe. Larger blocks consistently traveled farther than smaller ones, carrying greater kinetic energy throughout their descent while also possessing the mass to propel themselves onward after each impact.

Shape emerged as a surprisingly powerful variable. Spherical blocks traveled the longest distances, as expected, but were excluded from the main simulations because freshly detached blocks rarely remain perfectly round. Among the fifteen custom shapes tested across seven size groups spanning 5 to 46,000 kilograms, blocks with extruded octagonal geometry exhibited unexpected lateral spread compared with all other shapes. This finding echoes large-scale experiments by the WSL Institute for Snow and Avalanche Research and ETH Zurich, in which wheel-shaped concrete blocks diverged laterally and occupied far larger impact areas than cube-shaped blocks, which followed the steepest descent path in narrow corridors. Lateral dispersion matters enormously because it controls the width of hazard zones and determines how long a protective barrier must be.

The physics behind these differences is rooted in rotational dynamics. When an irregular rock strikes the slope, the contact point is usually offset from its center of mass, producing an impulse torque that converts translational kinetic energy into rotational energy and back again. Flat edges can trigger sudden sliding or dampening, while sharp vertices cause chaotic, high-velocity angular deviations. Size also determines the moment of inertia, the resistance of a body to changes in its rotation. Larger, more elongated blocks have higher moments of inertia, meaning that once they begin to roll or spin, they store substantial rotational energy that stabilizes their trajectory and drives longer runout distances and higher bounce paths. None of these effects can be represented in a model where the rock has no shape at all.

Armed with the rigid-body results, the study proceeded to design an actual protection system. The optimal fence location was chosen at the end of the first accumulation zone, where block energies and bounce heights are relatively low, minimizing the size of the structure needed. Barrier length was calculated from the geometry of lateral spread using a similarity ratio between the distances from the fence to the source and to the houses, yielding a design length of 20 meters that was doubled for safety. Simulations of a 1400-throw scenario then tested barriers of increasing energy capacity. Without a barrier, 595 of the 1400 blocks, or 42.5 percent, passed the proposed fence location. A 100-kilojoule barrier captured only small blocks, letting 19.6 percent through, while 500-kilojoule and 1000-kilojoule barriers still allowed a handful of large blocks to reach the model edge where the houses stand.

The decisive insight came when specific block geometries were excluded from the analysis. Large, rounded, wheel-like blocks proved to be the highest-risk shapes for bypassing barriers, driven either by excessive energy or by eccentric motion arising from their shape. When these round and large blocks were systematically removed from the simulations, both 1000-kilojoule and 2000-kilojoule barriers achieved complete capture. A sensitivity analysis across 175 to 1400 throws confirmed that barrier performance was independent of sample size. The final recommendation was clear: a 2000-kilojoule fence barrier achieves a 99 percent catching ratio under the full range of realistic block shapes and sizes, while a 1000-kilojoule barrier suffices only if large, rounded blocks are excluded from the hazard scenario.

The implications reach well beyond one Turkish village. The study acknowledges limitations, including input parameters derived from back analysis of only two observed rockfall events, and the simplification of barriers as flat, rigid, undeformable bodies when real fences are flexible structures that deform under repeated impacts. Even so, the message for engineers and heritage managers is unambiguous: nominal barrier energy ratings alone may be insufficient, and design protocols must account for block geometry and rotation beyond standard vertical drop tests. For historic sites like Belisirma, where tourism, cultural heritage, and human lives converge beneath unstable cliffs, the difference between a point mass and a real boulder is not a technical footnote. It is the difference between a barrier that looks adequate on paper and one that actually stops the rock.

Subject of Research: Three-dimensional rockfall trajectory modeling and protection barrier design for a slope above the historic Belisirma village in Cappadocia, Türkiye

Article Title: Application of 3D rockfall impact models for a slope in the historical Belisirma village (Cappadocia) considering block shape and size effects on the design of protection barriers

Article References: Sari, M. (2026). Application of 3D rockfall impact models for a slope in the historical Belisirma village (Cappadocia) considering block shape and size effects on the design of protection barriers. Discover Geoscience, 4(1), Article 324. https://doi.org/10.1007/s44288-026-00699-9

Image Credits: AI Generated

DOI: 10.1007/s44288-026-00699-9

Keywords: rockfall, 3D modeling, rigid-body dynamics, lumped-mass model, Cappadocia, Belisirma village, Ihlara Valley, protection barriers, block shape, block size, hazard assessment, geotechnical engineering

Dry-joint stone construction, in which precisely shaped blocks are stacked without mortar, is found across the globe, from Inca Peru to ancient Greek fortifications and medieval retaining walls. The technique produces remarkably durable structures, but it also leaves them with a fundamental weakness: with nothing gluing the stones together, the walls depend entirely on gravity and friction for their stability. When an earthquake shakes a wall perpendicular to its face, a loading direction engineers call out-of-plane, the blocks can slide, rock and ultimately overturn in a cascade of falling stones. Understanding the threshold at which that overturning begins is one of the central problems in the seismic assessment of historic masonry.

The research team, led by Leonel Lipa of the Pontificia Universidad Católica del Perú and Universidad San Ignacio de Loyola, together with Nicola Tarque of the Universidad Politécnica de Madrid and Luca Pelà of the Universitat Politècnica de Catalunya, chose one of the most iconic examples of the technique as their template. The Coricancha temple, whose polished stone walls later formed the foundations of the convent of Santo Domingo, is celebrated for its trapezoidal openings, gently inclined wall faces and joints so tight that a knife blade cannot slip between the blocks. Reproducing those characteristics at reduced scale was the first challenge of the project.

Rather than carving scarce and protected andesite, the researchers cast concrete blocks whose geometry and arrangement mirrored a section of the Coricancha’s dry-jointed stonework. Three walls were built at 1:2 scale, each following the block layout, aspect ratios and construction details of the original heritage fabric as closely as the material substitution allowed. The concrete mix was characterised through a battery of standardised tests covering compressive strength, density and aggregate properties, so that the mechanical inputs to the numerical models rested on measured values rather than assumptions. Building the replicas block by block also meant that every joint in the test walls corresponded to a joint in the real structure, preserving the discontinuous nature that governs how these assemblies move.

The test rig was a tilting table, a device that slowly rotates a platform on which the wall stands until gravity’s effective direction tilts away from vertical. This pseudo-static approach is a well-established way to probe out-of-plane stability: as the table inclines, the wall experiences an increasing horizontal component of its own weight, mimicking the lateral forces an earthquake would impose. The researchers tilted each of the three walls until collapse, recording the angle at which the structure first showed visible movement, the sequence of block displacements that led to failure, and the final angle at which overturning became irreversible. These pre-collapse drifts, collapse mechanisms and collapse angles form the experimental benchmark against which any numerical model must be judged.

What the tests revealed was a consistent pattern of behaviour. The walls did not crumble randomly; instead they developed well-defined failure mechanisms in which portions of the masonry separated along joint lines and rotated as coherent groups of blocks. This is the hallmark of dry-joint masonry: because the blocks carry almost no tensile strength across their joints, deformation concentrates in the interfaces, and the wall behaves less like a continuous solid and more like an assembly of rigid bodies pushing against one another. Capturing that behaviour numerically is difficult for conventional finite element codes, which are built around continuous materials and can struggle with the opening, closing, sliding and impacting of many separate contact surfaces.

The team’s answer was a hybrid approach that embeds rigid-body mechanics within a finite element framework. In this formulation, each stone is idealised as a rigid block, an idealisation justified by the fact that the stresses within individual stones remain far below the material’s strength, so the blocks themselves barely deform. All of the action happens at the joints, where the model accounts for contact, friction and the small local deformations that occur where two stone faces meet. The numerical simulations were set up with the geometry of the scaled walls and the measured material and interface properties, then subjected to the same progressive tilting as the physical specimens.

The agreement between experiment and simulation was the study’s decisive result. The numerical models accurately predicted the collapse angles at which the walls overturned, reproduced the experimentally observed failure patterns, and matched the average drift measured at various inclination angles throughout the loading history. In other words, the models did not merely get the final failure threshold right; they tracked the wall’s response along the way, capturing how the structure leaned, cracked open along its joints and redistributed its weight as the tilt increased. That level of fidelity matters, because a model that only matches the collapse angle could do so for the wrong reasons, while one that reproduces the full deformation path gives engineers genuine confidence in its predictions.

For heritage custodians, the implications are immediate. Structures like the Coricancha cannot be instrumented, loaded or dismantled to assess their safety, so any evaluation must rely on numerical analysis. A validated modelling strategy means engineers can now build a digital twin of a real Inca wall, using its surveyed geometry and representative material properties, and estimate with quantified confidence how close it sits to overturning under the seismic demands of a region as earthquake-prone as the Peruvian Andes. The approach also opens the door to testing hypothetical interventions digitally, allowing conservators to compare strengthening options before committing to any physical alteration of protected fabric.

The work also fits into a broader research effort by the same groups, who have previously applied rigid-body dynamics to the colossal terraced walls of Sacsayhuamán above Cusco and developed a taxonomy of pre-Hispanic stone wall types in southern Peru. By anchoring the new models to physical experiments on faithful scaled replicas, the team has closed the loop between field observation, laboratory evidence and computational prediction. The dataset from the study has been released in the Zenodo repository so that other researchers can scrutinise and extend the results. As seismic risk grows across the mountainous regions where dry-stone heritage concentrates, the image of three concrete replicas of an Inca temple wall toppling on cue in a Lima laboratory may prove to be a turning point: the moment the ancient builders’ empirical mastery of friction and gravity finally became something modern engineering could simulate, verify and defend.

Subject of Research: Out-of-plane seismic behaviour and rigid-body numerical modelling of historical dry-joint stone walls based on scaled Coricancha temple replicas

Article Title: Experimental and numerical analysis of out-of-plane behaviour of historical dry-joint stone walls: insights from a scaled laboratory wall model of the Coricancha temple, Peru

Article References: Lipa, L., Tarque, N., Goicolea, J. M., Santa-Cruz, S., Quispe, L., Pillaca, E., & Pelà, L. (2026). Experimental and numerical analysis of out-of-plane behaviour of historical dry-joint stone walls: insights from a scaled laboratory wall model of the Coricancha temple, Peru. Bulletin of Earthquake Engineering. https://doi.org/10.1007/s10518-026-02710-7

Image Credits: AI Generated

DOI: 10.1007/s10518-026-02710-7

Keywords: dry-joint masonry, out-of-plane behaviour, Coricancha temple, Inca architecture, rigid body dynamics, finite element method, tilting table test, collapse mechanism, heritage structures, seismic assessment, scaled wall model, earthquake engineering