Probabilistic Foundation Design in Volcanic Boulder-Rich Lateritic Soils: A Random Field Monte Carlo Framework Applied to Nyabihu District, Rwanda

Conventional deterministic foundation design fails fundamentally in two-phase composite geomaterials such as volcanic boulder–laterite profiles, where bearing capacity is controlled by the spatial arrangement of discrete phases. This paper presents a random field Monte Carlo framework for bearing capacity and differential settlement assessment, validated through a G+1 reinforced concrete building case study in Nyabihu District, Rwanda. Field DCP testing (n = 48) revealed bearing capacities of 12.6–100.9 kPa (COV = 83.2%) within a 77% volcanic boulder matrix. Deterministic design yielded a natural-ground allowable bearing capacity of only 9.98 kPa (FS = 3), presenting an order-of-magnitude shortfall against real column service loads of 172.5–455.1 kPa. Spatially correlated log-normal random field Monte Carlo simulations under the actual 1.9 m × 1.9 m column pad footprints revealed pre-improvement failure probabilities of 99.5–100% and a 57.6% differential settlement exceedance probability (>25 mm). Excavation to 3.0 m depth and replacement with compacted SW-SM murram (CBR = 26%, MDD = 1.697 Mg/m3) increased the footing-scale ultimate bearing capacity to 1534.8 kPa under general shear (allowable 511.6 kPa). This ground improvement reduced the column failure probability and differential settlement exceedance to <0.1%. Under conservative local shear, the failure probability remains <1% for three of four footings but reaches 59.8% under the heaviest column, emphasizing the critical role of field compaction quality control. Construction to suspended slab level has proceeded with zero observed distress, validating the probabilistic design.