Compound flood characterisation and structural reliability

Abstract

The Mekong delta in Vietnam is subjected to compound flood forcing from the interaction of riverine, tidal, storm surge, and wave drivers, whose joint statistical behaviour is poorly characterised. In the absence of advanced probabilistic tools, hydraulic structures in such environments are typically designed using univariate extreme value analysis, which combines independent return values for each driver and may misrepresent the joint probability of compound loading. This research quantifies the difference in design loads on a conceptual caisson barrier in the Hàm Luông estuary, Vietnam, when comparing a traditional deterministic approach with a multivariate probabilistic framework, addressing the research question: to what extent do design loads on the barrier differ between these two approaches, considering the dominant stability failure mode of overturning. Two parallel modelling tracks are followed.

In the deterministic track, Generalised Pareto Distributions were fitted to Peak-over-Threshold exceedances of five environmental drivers (H_s, T_p, U₁₀, h_surge, h_river) to establish univariate design values for a 100-year return period in the deterministic baseline. In the probabilistic track, the joint occurrence of environmental drivers is instead captured using a vine-copula: a multivariate model that decomposes the dependence structure between many variables into a network of simpler bivariate building blocks (pair-copulas), allowing realistic joint scenarios to be simulated. A seven-dimensional regular vine-copula (environmental drivers, θ_wind, and θ_wave) was fitted to n = 77 overlapping, concomitant observations of extreme surge events, using Dißmann's algorithm to model the multivariate dependence structure between the input boundary conditions. From this vine-copula, N = 10,000 synthetic weather events were generated, of which a representative subset of M = 200 cases, selected through the Maximum Dissimilarity Algorithm (MDA), was propagated through a SFINCS hydrodynamic model. Downscaling through MDA was necessary as direct Monte Carlo propagation of all N samples through SFINCS is computationally infeasible. The subset size M = 200 was adopted following a convergence study which balanced surrogate accuracy against computational cost.

Within the probabilistic track, two methodologically distinct surrogate models were then trained on the resulting SFINCS input--output pairs to upscale the M = 200 simulated cases back to the full population of synthetic loadcases. The first is a vine-copula surrogate fitted to the joint 11-dimensional distribution of inputs and outputs, which, like the boundary vine-copula, models the barrier responses probabilistically and can therefore generate responses beyond those observed during training. The second surrogate is a Gaussian Process regression with a Radial Basis Function (RBF) kernel, a deterministic regression model that interpolates directly between the input boundary conditions and the observed barrier responses, without representing their joint probability. Both surrogates were evaluated at a newly drawn, larger Monte Carlo sample of N = 100,000 synthetic events to enable the structural reliability assessment.

Comparing the 11-dimensional surrogate vine-copula against the original seven-dimensional boundary vine-copula showed that several of the input dependencies weaken once the barrier responses are incorporated into the joint model, most notably between θ_wave, and θ_wind (Kendall's τ reduced from 0.65 to 0.43). This indicates that the dependence structure of the environmental drivers changes once local hydrodynamic responses are jointly modelled. The fitted vine-copula reveals that coastal drivers (storm surge, wave height, wind speed) are strongly co-dependent under NE monsoon forcing, whilst river stage is seasonally decoupled from these drivers, reducing but not eliminating compound flood risk. The vine-copula surrogate yields a probabilistic 100-year overturning moment of M_ext,100  = 2,024 kNm/m, exceeding the deterministic estimate of M_ext,det = 1,971 kNm/m by roughly 2.7%. Redesigning the caisson with the same design limits yields a required base width of B = 13.3 m, 0.8 m wider than the deterministic baseline of B = 12.5 m. This indicates an annual probability of exceeding the deterministic design margin of P_f^annual =  3.02%. The RBF surrogate did not induce failure at the deterministic design margin, and yielded a redesigned width that is 2.2 m narrower than the deterministic baseline. No samples exceeding the deterministic design margin does not mean that the structure will never fail, but rather indicates that the current set of forcing conditions does not induce failure of the structure. This happens because, beyond the support of the M = 200 training cases, the RBF prediction is governed by the decay of its Gaussian kernel: the small fitted shape parameter (c = 0.10) for all barrier responses causes the predicted responses to collapse towards zero over a short distance, preventing the surrogate from generating responses more extreme than observed in training. As the two surrogates represent methodologically distinct quantities, they are better interpreted as approximate bounds on the failure probability than as independent estimates of the same quantity.

A decomposition of the dominant-side force into its hydrostatic and wave-induced components for the vine-copula loadcases exceeding M_ext,det, shown in Figure 1, reveals a bimodal pattern: alongside cases consistent with the deterministic wave contribution, a second cluster exhibits a noticeably higher wave contribution to the total overturning moment. This is traced to a bimodal distribution of H_s at the barrier location combined with a reduced upstream hydrostatic force across nearly all exceeding cases, which lowers the restoring moment. This indicates that the increased joint load is physically driven by a shift towards more wave-dominated loading conditions.

In practical terms, the deterministic caisson design, which is designed with a design margin below the ultimate limit state, fails on rotational stability under the multivariate load distribution with a probability of 3.02%, indicating that under compound loading, the intended 100-year return level (corresponding to a failure probability of 1%) at the design margin can not be guaranteed. The results suggest that employing a multivariate probabilistic framework to quantify design loads provides a more robust basis for structural design, and that the assumption of univariate return values may underestimate the joint return load in a compound environment. This finding should be interpreted in the context of absent partial safety factors in the deterministic baseline: in code-compliant design, partial safety factors implicitly account for the joint probability of load combinations and model uncertainty, meaning that replacing the univariate assumption with a multivariate load quantification removes part of the conservatism those factors provide.