A Practical Method to Account for Strength Variability of Deep-Mixed Ground

The strength of deep-mixed ground has relatively high variability with coefficients of variation ranging from about 0.3 to 0.8. This variability can be taken into account in stability analyses by performing reliability calculations. Alternatively, if design is based on deterministic calculations, the specified strength of deep-mixed ground can be adjusted to obtain a design value that accounts for the higher variability of the strength of deep-mixed ground compared to the typical variability of the strength of soil deposits. The magnitude of the adjustment depends on five factors: (1) the probability that the actual untreated soil strength exceeds the assumed design strength of the untreated soil, p_s, (2) the coefficient of variation of the soil strength, V_s, (3) the probability that the actual deep-mixed ground strength exceeds the specified deep-mixed ground strength, P_dm, (4) the coefficient of variation of the deep-mixed ground strength, V_dm, and (5) the design value of the factor of safety, F_d. Statistical calculations provide values of the variability factor, f_v, that can be applied to produce a design strength of the deep-mixed ground such that the probability that the shear strength of the deep-mixed ground will exceed the shear stress in the deep-mixed ground along a potential failure surface is the same as the probability that the actual shear strength of the untreated soil will exceed the shear stress in the untreated soil along the same potential failure surface in limit equilibrium analyses. The methodology and results of such statistical calculations are presented in this paper.