Reliability Design of Footings in Cohesionless Soils using Soft Computing Metamodelings

1. Introduction

In the design of footings on cohesionless soils under axial compression loading, the overall load-settlement behaviour is important for estimating the settlement at a given load and also for determining the failure load/bearing capacity. The ultimate bearing capacity (q_ult) which is defined as the maximum load per unit area that can be imposed on a soil at a given depth is dependent on a number of parameters including the physical properties of the soil (unit weight and strength parameters), foundation geometry, foundation depth, and soil failure mode. Although bearing capacity has been studied extensively, there has been only limited full-scale field verification of the theory, especially for footings (e.g., Muhs 1965, Perkins and Madson 1996).

Generally for a footing on cohesionless soil, the predicted bearing capacity is given by the following equation:

• = Footing area,

• = Footing width,

• = Footing depth,

• = Effective soil unit weight,

• and = Bearing capacity factors,

• and = Intermediate relevant modifiers (refer to Vesić (1975) for details).

The predictive model given in Eq. (1), primarily based on work by Vesić (1975) and Hansen (1970) with minor improvements by Kulhawy et al. (1983), has evolved over many years and is the result of research by many authors. However, one limitation of using Eq. (1) or similar white-box/empirical models is the reliance on the use of many assumed intermediate parameters. Furthermore, these intermediate parameters are functions of other introduced parameters. For example, in Eq. (1) is defined as:

• = Effective friction angle,

• = Footing length,

• = Reduced rigidity index, and

• is a function of rigidity index , volumetric strain Δ, and shear modulus of soil G.