Gravity caisson breakwaters built on soft seabeds replace the upper mud with sand, leaving a thin soft clay layer intercalated beneath the rubble mound that must withstand decades of wave cyclic loading. A 2016 dynamic finite-element study of this system derived an empirical degradation law for the undrained shear strength of the intercalated soft layer as a function of cycle number and cyclic stress level, calibrated entirely on Tianjin harbor soft clay, and left unresolved issues that the subsequent research program documented: experimental coverage, sensitivity to implementation assumptions (capped pore-pressure ratio and strength, sinusoidal standing-wave loading, neglected frequency effects), transferability of the fitted parameter relations to other soft clays, and the unexplored post-yield and large-deformation (flow-type) failure evolution of the softened layer. Subsequent literature shows that the same group and others refined the constitutive form (damage-based and bounding-surface post-cyclic degradation models) and mapped failure modes versus sand-replacement ratio, centrifuge physical-model data now exists for bucket-foundation breakwaters in clay, wave-flume model tests have measured pore-pressure response in clay seabeds beneath vertical caissons, and element-level cyclic testing of soft clays has broadened considerably — but no work yet delivers an experimentally validated, transferable degradation-and-failure framework for the caisson-on-soft-foundation system under realistic wave loading. The problem remains open.

Background

A caisson breakwater is a massive gravity retaining structure (typically a reinforced-concrete box floated into place and sunk onto a prepared base) that protects harbors by reflecting wave energy; it usually rests on a rubble mound of quarried stone over the seabed. On soft coastlines such as Tianjin's, the upper mud is dredged and replaced with sand, but a weaker soft clay layer often remains sandwiched ('intercalated') between the sand replacement and deeper firm strata; the fraction of the initial soft-layer thickness that is replaced by sand (the sand-replacement ratio) is a central design variable. Under the wave loading transmitted through the caisson, this layer is sheared essentially undrained — that is, fast enough that pore water cannot escape. In saturated clay, cyclic undrained shearing generates excess pore pressure (pressure in the pore water above the static value), which reduces the effective stress and hence the undrained shear strength sus_{u}, the clay's capacity to resist shear without drainage; the pore-pressure ratio is this excess pressure normalized by the applied stress. The cyclic stress ratio (CSR), the ratio of cyclic shear stress to effective confining stress, and any initial static shear bias govern how fast this softening, called cyclic degradation, accumulates with the number of loading cycles NN. Cyclic degradation of clay strength under wave loading has been studied experimentally since the 1980s: Andersen and Lauritzsen (1988) derived cyclic bearing-capacity design procedures from stress-controlled laboratory tests on clay, Hyodo, Yamamoto and Sugiyama (1994) showed how an initial static shear stress changes the cyclic failure behavior of normally consolidated clay, and Yasuhara (1994) formulated the widely used concept of post-cyclic undrained strength — the idea that the strength lost through wave-induced pore pressure can be predicted by treating the pore-pressure build-up as equivalent to an unloading (overconsolidating) of the clay. Wang, Yan and Wang (2016) combined Yasuhara-type reasoning with a pore-pressure development model in a dynamic finite-element analysis (implemented in the commercial FEM package ABAQUS with the Mohr–Coulomb yield criterion, a standard plasticity condition for frictional-cohesive soils) to derive a 'dynamic degradation law' — the undrained shear strength of the intercalated soft layer expressed as a function of cycle number and cyclic stress level σ∗\sigma^{*} (the CSR defined above; σ∗=σd/p′\sigma^{*}=\sigma_{\mathrm{d}}/p', the cyclic stress amplitude divided by the effective confining pressure), with empirical coefficients that depend on the stress levels, including the initial static shear stress level σ0∗\sigma_{0}^{*} (the initial static shear stress divided by the effective confining pressure) — calibrated on dynamic triaxial tests (laboratory tests applying cyclic deviator stress to a cylindrical clay specimen) of Tianjin harbor soft clay. They demonstrated that this dynamic method predicts more realistic strength losses beneath the breakwater than the static or quasi-static (monotonic, equivalent-load) design analyses then in use. The method's evidentiary base, however, was one site's clay, one set of soil conditions, and a sinusoidal standing-wave loading history, with additional numerical conveniences imposed for convergence (prescribed caps on the pore-pressure ratio and a floor on the undrained strength, and the assumption that soil yields and fails quickly once the cyclic stress ratio reaches a threshold value) whose influence was unquantified; elements exceeding the threshold were simply marked as yielded, with no modeling of what the softened clay does afterward. The unresolved question is therefore whether a degradation-and-failure analysis of this kind can be made predictive and general — validated across soft clays and stress states, robust to realistic wave loading, and able to trace the foundation through post-yield softening into its actual large-deformation failure mechanisms — rather than remaining a site-specific empirical description.

Problem Statement

Establish and validate a generalizable cyclic degradation-and-failure framework for gravity caisson breakwaters resting on soft clay foundations under wave cyclic loading, replacing the Tianjin-specific empirical treatment of Wang, Yan and Wang (2016) with one that is predictive across sites. Concretely, the unresolved question documented by the source research program comprises four scientifically linked open directions: (1) experimental generalization — determine whether the functional form of the degradation law relating undrained shear strength to cycle number, cyclic stress level σ∗\sigma^{*} and initial static shear stress level σ0∗\sigma_{0}^{*} holds across a range of soft clays, confining pressures, cyclic stress ratios and initial static shear states; (2) loading realism and implementation sensitivity — quantify how predictions change when the idealizations of the source implementation are removed, namely the sinusoidal standing-wave loading (a stationary wave field created by the reflection of incident waves at the structure, versus irregular wave spectra and differing wave frequencies), and the convergence-driven implementation assumptions — that the soil yields and fails quickly once the cyclic stress ratio reaches a threshold value, and the prescribed lower limit on the undrained strength ratio and upper limits on the accumulated pore-pressure ratio; (3) transferability — determine what measurable soil properties control the calibrated empirical coefficients of the fitted parameter relations, so that the relations can be transferred beyond the tested Tianjin material; and (4) post-yield failure representation — model the constitutive evolution of the softened clay after elements exceed the yield threshold and resolve the large-deformation and flow-type failure mechanisms of the intercalated soft layer (the outward squeezing and unbounded displacement of the fully softened clay) under repeated wave loading, connecting the degradation law to the observable failure modes (sliding, bearing-capacity failure, combined) of the caisson–rubble mound–foundation system. The four directions are the linked parts of the degradation-and-failure analysis that is to be generalized and validated beyond the site-specific empirical treatment. Directions (1) and (3) are complementary rather than independent: (1) tests whether the functional form of the law generalizes, and (3) identifies which measurable soil properties control the calibrated coefficients.

References

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