Reliability-Based Design of Foundations on Soft Clay with Deep Soil Mixing: Quantifying the Economic Value of Soil Improvement under Parameter Uncertainty

Abstract

Conventional foundation design on soft clay relies on deterministic factors of safety that do not explicitly account for the substantial spatial variability of soil parameters typically encountered in practice. This paper presents a reliability-based design (RBD) framework integrating Monte Carlo simulation, deep soil mixing (DSM) ground improvement, and life-cycle cost analysis to quantify the true economic value of soil improvement under realistic parameter uncertainty. A 2.0 m × 2.0 m square footing supporting a 700 kN column load on soft Holocene clay (Su = 25 kPa) is investigated. Four design alternatives are compared: (i) conventional shallow footing with FOS = 3.0; (ii) shallow footing with stone column treatment (As = 0.20); (iii) shallow footing with deep soil mixing (As = 0.30); and (iv) RBD-calibrated DSM design directly targeting reliability index β = 3.0. Soil parameters are treated as lognormally distributed random variables with coefficients of variation reflecting Indian field conditions: Su (COV = 30%), φ' (COV = 12%), and elastic modulus E (COV = 35%). Monte Carlo simulation with 10,000 realizations quantifies failure probability for each alternative. Results demonstrate that the conventional FOS = 3.0 design corresponds to an actual reliability index β = 2.41 well below the target value of 3.0 exposing a critical and largely-overlooked safety deficit. DSM treatment with As = 0.30 raises the achieved reliability to β = 3.74 at a 32% cost increase, while RBD-calibrated DSM achieves the target β = 3.0 at FOS = 1.85, producing a 21% cost saving relative to the conventional design. The bearing capacity increase ratio (BCIR) achieved by DSM is 2.99, with settlement reduction ratio (SRR) of 2.36. The framework provides a quantitative basis for adopting probabilistic design methods and economically rational soil improvement decisions in Indian geotechnical practice.