Constructability-Aware Earthwork Optimization for Large-Scale Site Grading Using a Mixed-Integer Second-Order Cone Programming Framework

Determining the design elevations of multiple development parcels on rugged terrain is a key cost driver in large-scale site preparation. In practice, however, elevations are still selected largely by manual iteration in commercial software—a process that terminates when a design is acceptable rather than optimal, examines only a few alternatives at days to weeks per cycle, and verifies constructability only after the elevations are fixed. This paper proposes a constructability-aware optimization framework that determines optimal parcel elevations by combining linear programming for cut, fill, and inter-parcel haul volumes with a second-order cone program (SOCP) for slope earthwork, whose volume grows quadratically with elevation differences. Constructability requirements—slope feasibility, retaining wall fallback, and road longitudinal grades—are embedded as constraints rather than checked after the fact. The discrete interface modes are assigned by a deterministic feasibility screening step before the solve, so that each optimization is a convex second-order cone program whose global optimality certificate applies under the assigned modes. The comparative experiments apply the slope term as a cost penalty on every interface (penalty variant); a strict variant that enforces the screened slope footprint constraints raises the material cost by 44.2% and is incompatible with zero off-site exchange on this site. The convex formulation guarantees a global optimum and solves in under one second of solver time (210 model variables) using CVXPY and Gurobi within a Rhino/Grasshopper pipeline. Applied to a 13-parcel semiconductor industrial complex in South Korea with up to 100 m of relief, the computed cut volume of 51.19 million m³ agreed with two independent external estimates to within 0.4%. Ablation experiments showed that prohibiting inter-parcel haul multiplies material cost by 3.4, while slope-aware optimization prices in a further 7.4% that slope-blind designs defer to construction. Against a prescribed fixed surface baseline with identically optimized haulage, the optimized elevations reduce the total material cost by 32.8%. An ε-constraint Pareto analysis quantified the trade-off between cost and maximum elevation difference, supporting transparent, reproducible decision-making in site-grading design.