Seepage criteria based optimal design of water retaining structures with reliability quantification utilizing surrogate model linked simulation-optimization approach
The safety of hydraulic water retaining structures (HWRS) is an important issue as many instances of HWRS failure have been reported. Failure of HWRS may lead to catastrophic events, especially those associated with seepage failures. Therefore, seepage safety factors recommended for HWRS design are generally very conservative. These safety factors have been developed based on approximation calculations, unreliable assumptions, and ideal experimental conditions, which are rarely replicated in real field situations. However, with the development of the numerical methods, and high speed processors, more accurate seepage analysis has become possible, even for complex flow domains, different scenarios of boundary conditions, and varied hydraulic conductivity. On the other hand, because construction of HWRS requires a significant amount of construction material and engineering effort, the construction cost efficiency of HWRS is an issue that must be considered in design of HWRS.
This study aims to determine the minimum cost design of HWRS constructed on permeable soils, incorporating numerical solutions of a seepage system related to HWRS, utilizing linked a simulation–optimization (S-O) model. Due to the complexity and inefficacy of directly linking a simulation model to the optimization model, the numerical simulation model was replaced by trained surrogate models. These surrogate models can be trained based on numerically simulated data sets. Therefore, trained surrogate models expeditiously and accurately provide predicted responses relating to seepage characteristics pertaining to HWRS. The optimization model based on the linked S-O technique incorporated different safety factors and hydraulic structure design requirements as constraints. The majority of these constraints and objective function(s) were affected by the responses of predicted seepage characteristics based on the developed surrogate models.
To improve the safety of HWRS design, the effect of non-homogenous and anisotropic hydraulic conductivity were incorporated in the S-O model. Obtained solution results demonstrated that considering stratification of the flow domain due to different hydraulic conductivity values or anisotropic ratios can significantly change the optimum design of HWRS. Low hydraulic conductivity and anisotropic ratios resulted in more critical seepage characteristics. Consequently, the minimum construction cost increased due to an increase of dimensions of involved seepage protection design variables.
Furthermore, uncertainty in estimating hydraulic conductivity is incorporated in the S-O model. The reliability based optimal design (RBOD) framework based on the multi-realization optimization technique was implemented using the S-O model. The uncertainty in seepage quantities due to uncertainty of hydraulic conductivity was represented using many stochastic ensemble surrogate models. Each ensemble model included many surrogate models trained in utilizing input– output data sets simulated with different scenarios of hydraulic conductivity drawn from diverse random fields based on different log-normal distributions. Obtained results of this approach demonstrated substantial consequences of considering uncertainty in hydraulic conductivity. Also, the deterministic safety factors, especially for those pertaining to the exit gradient, were insufficient to provide prescribed safety in the long term.
Although surrogate models are utilized in S-O approaches, each run of the S-O model takes a long time as developed S-O models are applied to complex and large scale problems. Hence, efficiency of the S-O model was a key factor to successfully implement the methodology. Three main techniques were utilized to increase the efficiency of the S-O technique: using parallel computing, utilizing nested function technique, and using a vectorised formulation system. These strategies substantially boosted efficiency of implementing the S-O model.
The S-O models were implemented for many hypothetical scenarios for different purposes. In general, results demonstrated that optimum design of the seepage protection system relating to HWRS design must include two end cut-offs with an apron between them. The dimensions of these components were augmented with an increase of upstream water head, and reduction of anisotropic ratios or hydraulic conductivity value. The main role of the downstream cut-off was to decrease the actual exit gradient value. This impact is more pronounced if the inclination angle of the cut-off is toward the downstream side (>90 degrees). The role of the upstream cut-off was to decrease uplift pressure values on the HWRS base. Consequently, this partially contributed to decreasing the exit gradient value. The effect of the upstream cut-off in reducing the uplift pressure was more when the inclination angle was toward the upstream side (<90 degrees). Moreover, the apron (floor) width helped to increase the stability of HWRS. This variable provided the required weight to improve HWRS resistance to external hydraulic forces and to uplift pressure. Incorporating the weight of water (hydrostatic pressure) at the upstream side in counterbalancing momentum and hydraulic forces showed improvement in the safety of the HWRS. Also, all conditions and safety factors pertaining to HWRS design were satisfied. The exit gradient safety factor was the most important critical factor affecting optimum design as obtained optimum solutions satisfied the minimum permissible values of the exit gradient safety factor, i.e., at the minimum permissible value. Also, the eccentric load condition played a crucial role in resulting optimum solutions.
Finally, applying the S-O model to obtain reliable and safe design of HWRS at minimum cost was successfully implemented for performance evaluation purposes. This technique may be extended to incorporate more complex scenarios in HWRS design where the impact of dynamic and seismic load could be incorporated. The effect of unsteady state seepage system could be another interesting direction for future studies. Further, incorporating more sources of the uncertainty associated with design parameters could achieve a more accurate estimation of actual safety for the HWRS design
