Optimization of retaining wall and excavation enclosure structures according to the criteria of strength, stiffness, water impermeability and cost taking into account the uncertainty of engineering geological data

Abstract

Optimization of retaining wall and excavation support structures according to the criteria of strength, stiffness, watertightness, and cost is accomplished by accounting for the spatial variability of soil mass properties caused by the discreteness of sampling, testing errors, and heterogeneity of deposits formed under different facies conditions. Traditional deterministic models lead either to an excessive safety margin and increased project costs or to an underestimation of risks associated with the scatter of soil pressure, horizontal displacements, and seepage inflow, since normative reliability coefficients do not reflect the actual statistical structure of data from specific sites. Stochastic modeling employing random fields generated by the Karhunen–Loève decomposition method and parameters identified by the maximum likelihood method from the results of cone penetration testing, pressuremeter tests, laboratory experiments, and pumping tests makes it possible to transform uncertainty in the angle of internal friction, cohesion, deformation modulus, and permeability coefficient into quantitative reliability assessments through Monte Carlo simulation series of five hundred to one thousand realizations per variant integrated with finite element analysis. The multi-objective genetic algorithm NSGA-II generates a Pareto front in the space of competing responses that include maximum bending moment, horizontal displacement of the wall top, filtration discharge, and total cost of drilling, concreting, anchoring, and dewatering for excavations ranging in depth from 8.5 to 18.2 meters under conditions of dense urban development with varying geomorphological zones. Coefficients of variation for the parameters reach 0.08-0.17 for the friction angle, 0.25-0.48 for cohesion, 0.20-0.39 for the deformation modulus, and 0.45-1.12 for the permeability coefficient, with the greatest variability in filtration characteristics attributable to lens-shaped sandy inclusions within moraine loams that cause a sharp increase in inflow when permeable interlayers intersect the active zone. Sensitivity analysis with respect to uncertainty levels demonstrates an 88,1% increase in optimal cost when moving from a reduced to an elevated coefficient of variation, accompanied by changes in wall thickness from 0,7 to 1,0 m, embedment depth from 3,2 to 5,9 m, and number of anchor rows from two to three, while maintaining reliability indices of approximately 3.0 for both strength and deformations. The Pareto front reveals a nonlinear relationship between cost and reliability index with an inflection point in the range 3.0-3.5, where an increase in reliability from 3,07 to 4,48 requires an 86,5% rise in costs, while filtration discharge decreases exponentially with greater embedment depth, achieving virtually complete watertightness when aquitard horizons are intersected. The economic benefit of reducing uncertainty through detailed site investigations consistently amounts to 42,8-46,8% of the enclosure cost across four sites, justifying investment in additional boreholes and tests, since narrowing confidence intervals permits less conservative decisions without loss of robustness. Correlations confirm the dominant influence of wall thickness on cost, embedment depth on strength and watertightness, and the switching of governing criteria depending on excavation depth, together with a stepwise increase in the number of anchors and a power-law dependence of cost on depth with an exponent of 1,7-2,1. The robust solutions obtained minimize the loss function relative to deterministic approaches, supplying a set of non-dominated alternatives for incorporating technological, urban-planning, and economic factors under conditions of objectively existing yet quantitatively evaluated uncertainty in engineering-geological data, thereby promoting informed selection of structural parameters and reconsideration of site investigation practice.