Perspective Framework Links Progressive Breakwater Failure to Evolving Inter-Block Contact Networks

A newly published perspective framework in coastal engineering demonstrates that progressive damage and catastrophic collapse in rubble-mound breakwaters can be interpreted through the internal reorganisation of inter-block contact networks rather than through external wave-loading statistics alone. Published in Discover Civil Engineering by researcher Tayfun Er, the conceptual work addresses a fundamental limitation in traditional marine structure design: established empirical equations evaluate armour-layer stability using time-averaged scalar damage metrics, yet they do not resolve how individual concrete units or rocks transmit forces through internal contact chains. By treating the protective armour layer as a dense granular assembly whose load-bearing capacity relies directly on the redundancy and persistence of load-bearing inter-block contacts, the author develops a testable theoretical formulation mapping structural response across four distinct behavioural regimes. Rather than proposing an uncalibrated replacement for standard engineering manuals, the perspective paper introduces operational contact-network descriptors that bridge visible profile erosion with the hidden mechanical pathways through which repeated wave impacts degrade coastal defences over time.

For decades, coastal-engineering practice has relied on empirical stability equations to size natural rock armour and precast concrete units against storm attack. The dominant analytical tools remain the classical Hudson formula, which calculates a stability number based on wave height, submerged unit density, and an empirically tabulated stability coefficient denoted KD, and the subsequent Van der Meer formulations. Van der Meer’s equations advanced the discipline by incorporating the cumulative number of waves N, a surf-similarity parameter known as the Iribarren number, a notional permeability factor P, and an allowable damage parameter S derived from profile changes. Reference reviews catalogue more than twenty hydraulic stability equations and eleven damage-progression models developed over a century of research. However, because each formulation captures time-averaged responses calibrated against specific hydraulic flume datasets, they remain strictly scalar in their structural representation. A single damage parameter S simply records displaced material volumes; it cannot distinguish whether an armour layer retains redundant, force-bearing contact pathways or has deteriorated into an internally fragile state on the verge of sudden structural collapse.

To resolve this analytical blind spot, the framework draws upon dynamic stability principles from granular physics and critical-transition theory to conceptualise how wave energy redistributes inside the breakwater slope. In dense granular media, external loads are not transmitted uniformly across all constituent particles; instead, compressive forces concentrate along sparse, highly stressed contact pathways known as force chains, leaving surrounding elements relatively unloaded. When severe storm waves strike a rubble-mound breakwater, hydraulic uplift and drag perturb individual armour blocks, shifting forces onto neighbouring contacts. The author emphasises that scalar stability numbers and cumulative damage values return identical scores whether total structural resistance is carried by a few highly stressed chains or safely distributed across many redundant connections. Under repeated cyclic loading, the sudden displacement or rotation of just a few key armour units can eliminate primary load-transfer paths, forcing immediate and disproportionate stress transfers onto adjacent blocks. If these neighbouring units lack sufficient geometric redundancy, the local disturbance triggers widespread rearrangement throughout the entire granular matrix.

To translate these granular principles into measurable engineering variables for future laboratory flumes, field monitoring campaigns, and numerical simulations, the study defines specific operational descriptors. Foremost is the normalised contact-network connectivity, designated CN, which quantifies the redundancy of load-bearing contacts across a tracked assembly of armour units. In any given measurement window k, the formulation identifies an active contact set Ck by requiring inter-block clearance to fall below a geometric gap tolerance gtol while the normal contact force Fn meets or exceeds a defined minimum load threshold Fmin. This load-bearing set is then normalised against the total unit count Na and a reference coordination degree zref characteristic of the armour class. To complement contact redundancy, the paper introduces the persistent-contact fraction PCF, calculated as the ratio between intersecting and union sets of contacts across consecutive measurement windows, thereby tracking contact durability. Simultaneously, kinematic movement is captured through an armour-motion amplitude descriptor Am, which operationalises observable rocking motions, displacement rates, or extracted unit tallies under wave action.

Using these operational descriptors, the paper maps armour layer stability under cumulative cyclic wave loading across four qualitatively distinct behavioural regimes. In the first regime, termed stable interlocking, wave energy remains well below critical instability thresholds; load-bearing contacts maintain high redundancy, small wave perturbations are dissipated through micro-rocking and frictional contact sliding, and the conventional damage parameter S accumulates negligibly. As wave intensity approaches and intermittently surpasses local equilibrium thresholds, the armour transitions into the second regime, cyclic reorganisation. Here, individual concrete blocks rock and translate by modest increments under successive wave groups, causing contact network edge weights, clustering, and persistence to shift. Depending on packing characteristics, this phase can either induce stable shakedown through self-tightening compaction or trigger progressive ratcheting degradation. If degradation dominates, the structure enters the third regime of local connectivity loss, where key load-bearing paths lose redundancy, individual blocks become partially extracted, and load redistribution accelerates subsequent damage increments. Beyond this threshold lies the fourth regime, cascading failure, where neighbouring contact paths can no longer absorb redistributed loads, resulting in rapid multi-unit displacement that strips the armour and exposes the core.

To organise these dynamic transitions without claiming a prematurely calibrated predictive model, the author formulates a minimal discrete-time two-variable sketch coupling connectivity CN and motion amplitude Am across successive wave groups. The dynamical formulation incorporates an effective amplification or recovery factor r, an incident wave-group energy proxy Ek, an irregularity term, motion-induced contact erosion governed by coefficient eta, and a recovery mechanism rho representing gravity-driven re-interlocking. This analytical sketch identifies three conceptual operating states: a stable shakedown point ES where recovery offsets motion-induced contact losses and motion decays; a degradation-dominated region ED where motion amplitudes grow while contact connectivity falls; and a loss-of-redundancy transition ET where connectivity drops below a critical threshold Ccrit or the percolating load-bearing cluster fraction Pi approaches critical percolation. From this framework arise two distinct, sequential instability analogies: a cyclic-amplification analogy, where motion gradually grows within an interconnected structure accompanied by lengthening post-wave recovery times tau_r; and a subsequent abrupt damage-transition analogy, representing the rapid collapse of structural equilibrium once network connectivity drops below the threshold required to span the system.

A notable working hypothesis advanced in the perspective is that maximizing geometric interlocking does not necessarily guarantee superior long-term cyclic stability across every class of armour unit. In classical coastal design, units such as Accropode, CORE-LOC, and Xbloc are explicitly engineered for strong mutual engagement, relying on high placement density and tight interlocking to resist hydraulic extraction. The author stresses that these established single-layer design rules remain fully valid within their calibrated operational envelopes. However, the contact-network perspective posits a potentially non-monotonic relationship between contact density and structural resilience under prolonged storm histories. At very low connectivity, blocks are poorly restrained, allowing modest wave forces to cause immediate dislodgement. Conversely, at exceptionally high placement densities and rigid contact coordination, kinematic freedom becomes severely constrained, forcing imposed cyclic loads onto fewer, stiffer, and highly concentrated contact pathways. Under severe wave action, these rigid networks may experience brittle stress concentrations that trigger sudden failure. An intermediate connectivity state might instead provide an optimal mechanical balance, allowing small, reversible rocking motions to dissipate incoming wave energy frictionally without causing irreversible network unraveling.

To illustrate how multi-stage structural degradation unfolds in prototype marine environments, the paper examines the documented failure of the Sines breakwater in Portugal between 1978 and 1979. The massive west breakwater, protected by unreinforced concrete Dolos units, suffered catastrophic damage during severe Atlantic storms, an event widely scrutinised in coastal-engineering history. The author applies a mechanism-separated chronology to demonstrate the interpretive utility of the contact-network approach while strictly delineating its theoretical boundaries. First, severe storm loading initiated progressive rocking and localised unit displacement. Second, repeated cyclic impacts generated intense internal stress concentrations that caused material breakage in the slender unreinforced Dolos units. Third, the mechanical fracture and physical extraction of these units abruptly severed vital load-transfer paths, destroying the redundancy of the surrounding contact network. Fourth, because neighbouring units could not sustain the redistributed stresses, damage spread rapidly into a cascading collapse that stripped the armour layer and exposed the vulnerable underlayer and core. While unit breakage itself represents a material strength problem outside contact-network kinematics, the subsequent rapid systemic collapse aligns directly with the cascading-failure regime.

Although the perspective paper presents a theoretical framework rather than new laboratory data, it establishes close alignment with modern three-dimensional numerical simulations and physical instrumentation workflows. The author demonstrates that the data required to calculate the proposed connectivity metrics already exist within published combined finite-discrete element method (FEMDEM) studies. Specifically, earlier FEMDEM research by Latham and colleagues on CORE-LOC armour packs with packing densities between 0.59 and 0.63 documented that tighter packing produced a steady rise in unit coordination numbers alongside a steep concentration of maximum contact forces. In the framework’s terminology, these coordination outputs serve as direct literature proxies for normalised connectivity CN. Similarly, subsequent FEMDEM placement evaluations by Anastasaki and co-workers utilised a safe displacement percentage under vibration loading, capturing the same class of kinematic observables envisioned for motion descriptor Am. Furthermore, emerging physical monitoring tools—including embedded internal motion sensors measuring unit rocking, high-resolution photogrammetry, and terrestrial laser scanning using scan-to-BIM point clouds—now provide the empirical precision needed to resolve inter-block contacts in experimental flumes and prototype breakwaters.

To move from theoretical hypothesis to empirical validation, the author outlines a rigorous experimental testing protocol for wave flumes and numerical simulation platforms. Under this protocol, an initially scanned breakwater armour configuration is subjected to successive storm blocks, recording the post-loading decay of motion and contact reorganisation after each wave sequence. By tracking contact connectivity CN, persistence PCF, motion amplitude Am, and the characteristic motion recovery time tau_r, researchers can directly distinguish between shakedown-dominated stabilization and degradation-dominated breakdown. A degrading system is expected to exhibit rising motion amplitude, falling contact persistence, and a lengthening recovery time tau_r before entering local connectivity loss. The author concludes with an explicit statement of scope: the formulation is an interpretive, hypothesis-generating framework rather than a calibrated design equation. It applies specifically to cyclic wave action rather than impulsive tsunami inundation, and its operational tolerances must be independently calibrated across natural rock, placed blocks, and interlocking units. By establishing an objective vocabulary for internal load-transfer dynamics, the perspective provides coastal engineers with a rigorous foundation for investigating progressive breakwater stability.

Subject of Research: Contact-network mechanics and progressive failure regimes in rubble-mound breakwaters

Article Title: Interlocking, rearrangement and progressive failure in rubble‑mound breakwaters

Article References: Er, T. (2026). Interlocking, rearrangement and progressive failure in rubble‑mound breakwaters. Discover Civil Engineering, 3(1), Article 232. https://doi.org/10.1007/s44290-026-00609-5

Image Credits: AI Generated

DOI: 10.1007/s44290-026-00609-5

Keywords: rubble-mound breakwaters, coastal engineering, armour layer stability, contact-network connectivity, progressive failure, cyclic reorganisation, cascading failure, Hudson formula, Van der Meer formulae, Iribarren number, FEMDEM simulations, discrete element method, Sines breakwater, granular mechanics, shakedown operating state, inter-block interlocking, armour-motion amplitude