Reliability Design of Footings in Cohesionless Soils using Soft Computing Metamodelings

Reliability Design of Footings in Cohesionless Soils using Soft Computing Metamodelings

Anthony T. C. Goh (Nanyang Technological University, Singapore) and Wengang Zhang (Nanyang Technological University, Singapore)
DOI: 10.4018/978-1-4666-9479-8.ch016


An extensive database of full-scale field load tests was used to build predictive models to determine the bearing capacity of footings under axial compression in cohesionless soils. Based on this database, soft computing techniques, i.e., the multivariate adaptive regression splines (MARS) and artificial neural networks (ANN) are adopted for comparison for surrogate model building on bearing capacity. The performances of the two computing techniques are compared. A reliability-based design of footings was then presented. It allows one to obtain the probability that the ultimate limit state was exceeded for a given soil variability.
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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 (qult) 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 978-1-4666-9479-8.ch016.m01 is given by the following equation:

(1) in which:

  • 978-1-4666-9479-8.ch016.m03 = Footing area,

  • 978-1-4666-9479-8.ch016.m04 = Footing width,

  • 978-1-4666-9479-8.ch016.m05 = Footing depth,

  • 978-1-4666-9479-8.ch016.m06 = Effective soil unit weight,

  • 978-1-4666-9479-8.ch016.m07 and 978-1-4666-9479-8.ch016.m08 = Bearing capacity factors,

  • and 978-1-4666-9479-8.ch016.m09 = 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,978-1-4666-9479-8.ch016.m10 in Eq. (1) is defined as:

(2) in which:

  • 978-1-4666-9479-8.ch016.m12 = Effective friction angle,

  • 978-1-4666-9479-8.ch016.m13 = Footing length,

  • 978-1-4666-9479-8.ch016.m14 = Reduced rigidity index, and

  • 978-1-4666-9479-8.ch016.m15 is a function of rigidity index 978-1-4666-9479-8.ch016.m16, volumetric strain Δ, and shear modulus of soil G.

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